White, Case, Pratt Principles of Engineering Economic Analysis, 6th Edition solution manual by TBtutors

Type:

Solution Manual

Resource:

Principles of Engineering Economic Analysis

Edition:

6th Edition

Author(s):

John A. White Kenneth E. Case David B. Pratt

A 1 PROBLEM 1.1 2 3 4 5 6 7 8 9

WYLIE IS OFFERED THIS AMOUNT NOW=

$5,000.00

WYLIE IS WILLING TO TAKE THIS AMOUNT IN A YEAR=

$5,700.00

THE INCREASE REQ'D BY WYLIE OVER ONE YEAR=

$700.00 =$5,700.00-$5,000.00

THEREFORE WYLIE'S TVOM =

14.00% =$700.00/$5,000.00

A 1 PROBLEM 1.2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a 16 17 b 18 19 20

RT LOANS=

$20,000.00

RT'S TVOM=

8.00%

RT INTEREST REQ'D=

$1,600.00

CYNTHIA BORROWS=

$20,000.00

CYNTHIA'S TVOM= CYNTHIA'S EARNINGS=

12.00% $2,400.00

YES, THEY SHOULD BE ABLE TO NEGOTIATE THE LOAN RT REQUIRES $1,600 OR MORE IN INTEREST CYNTHIA IS WILLING TO PAY $2400 OR LESS IN INTEREST THE ACCEPTABLE RANGE IS FROM $1,600 TO $2,400

A 1 PROBLEM 1.3 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

a b

RT LOANS= $20,000.00 RT'S TVOM= 12.00% RT INTEREST REQ'D= $2,400.00 MINIMUM INTEREST REQUIRED BY RT CYNTHIA BORROWS= $20,000.00 CYNTHIA'S TVOM= 8.00% CYNTHIA'S EARNINGS= $1,600.00 WILLING TO PAY= $2,000.00 MAXIMUM INTEREST CYNTHIA WILLING TO PAY NO, THEY SHOULD NOT BE ABLE TO NEGOTIATE THE LOAN UNLESS ONE OR BOTH CHANGE THEIR MIND RT REQUIRES $2,400 OR MORE IN INTEREST CYNTHIA CAN EARN $1,600 ON HER MONEY; HOWEVER, CYNTHIA IS WILLING TO PAY $2,000 IN INTEREST CYNTHIA'S MONEY MUST BE INVESTED AND SHE NEEDS TO BORROW MONEY NOW, EVEN IF SHE HAS TO PAY $2,000 IN INTEREST. THERE IS STILL NO ACCEPTABLE RANGE. RT REQUIRES $2,400 OR MORE IN INTEREST; CYNTHIA WILL PAY $2,000 OR LESS. THEY ARE $400 OFF

A B 1 PROBLEM 1.4 2 3 LOAN AMOUNT= 4 5 YOUR TVOM= 6 7 FRIEND'S TVOM= 8

9 10 11 12

$3,000.00 15.00% OR

$450.00 INTEREST

20.00% OR

$600.00 INTEREST

YOU ARE WILLING TO MAKE THE LOAN TO YOUR FRIEND FOR $450.00 INTEREST OR MORE. YOUR FRIEND IS WILLING TO ACCEPT THE LOAN FOR $600 INTEREST OR LESS. SO, ANY INTEREST NEGOTIATION WITH YOU AS THE LENDER THAT IS ACCEPTABLE TO BOTH PARTIES IS BETWEEN $450 AND $600. YOUR FRIEND IS WILLING TO MAKE THE LOAN TO YOU FOR $600 INTEREST OR MORE. YOU ARE WILLING TO ACCEPT THE LOAN FOR $450 INTEREST OR LESS. SO, THE ACCEPTABILITY GAP BETWEEN YOU AND YOUR FRIEND IS $150.

1 2 3 4 5 6 7 8

A PROBLEM 1.5

STAGE 1 2 3 4

INVESTMENT STATION ANTENNA AMPLIFIER LIGHTNING PROTECTION CONTROL CONSOLE

9 5 10 11

12 13 14

COSTS IN REVS IN NET CUM CUM CUM TODAY'S $ TODAY'S $ REV-COST COSTS REVS REV-COST $180,000 $270,000 $90,000 $180,000 $270,000 $90,000 $30,000 $50,000 $20,000 $210,000 $320,000 $110,000 $40,000 $30,000 -$10,000 $250,000 $350,000 $100,000 $30,000

$60,000

$30,000 $280,000 $410,000

$130,000

$15,000

$5,000

-$10,000 $295,000 $415,000

$120,000

PURCHASE THE FIRST FOUR STAGES. NOTE THAT THIS GIVES THE HIGHEST ACCUMULATED TOTAL NET REVENUE-COST. IN TODAY'S $. NOTE THAT THE AMPLIFIER DOES NOT PAY OUT, BUT IT IS NECESSARY FOR THE LIGHTNING PROTECTION THAT PAYS OUT NICELY

2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 6. MONEY SHOULD CONTINUE TO BE INVESTED AS LONG AS EACH ADDITIONAL INCREMENT OF INVESTMENT YIELDS A RETURN THAT IS GREATER THAN THE INVESTOR'S TVOM

1. IDENTIFY THE INVESTMENT ALTERNATIVES 5. COMPARE THE ALTERNATIVES 7. SELECT THE PREFERRED ALTERNATIVE

15 16

18 19 20 21

A B C D E 1 PROBLEM 1.6 2 3 ORIGINAL WSI BID= $5,500.00 4 5 BARB & FRED EXPENSES= $1,900.00 6 $1,100.00 MATERIALS - NO RETURN 7 $400.00 TRENCHER AT $80 FOR 5 DAYS 8 $400.00 JACKHAMMER AT $80 FOR 5 DAYS 9 10 REVISED WSI BID= $4,500.00 11 $5,500.00 ORIGINAL 12 -$500.00 MATERIALS 13 -$500.00 TRENCHING 14 15 a $1,900.00 BARBARA AND FRED HAVE ALREADY SPENT 16 17 b $6,400.00 TOTAL SPENT AFTER WSI 18 19 c $6,000.00 SS CHARGE GO WITH WSI, NOT SS. COMPARING SS AT $6,000 AND WSI AT $6,400 TAKES INTO ACCOUNT SUNK COSTS 20 21 SUNK COSTS SHOULD NOT BE CONSIDERED. 22 23 $4,500 FUTURE SPENDING WITH WSI 24 25 $6,000 FUTURE SPENDING WITH SS 26 27 GO WITH WSI, NOT SS. 28 29 d 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 10. PAST COSTS ARE IRRELEVANT IN ENGINEERING ECONOMIC ANALYSES, UNLESS THEY IMPACT FUTURE COSTS 30 31 32 e 1. IDENTIFY THE INVESTMENT ALTERNATIVES 33 4. ESTIMATE THE CASH FLOWS 34 5. COMPARE THE ALTERNATIVES 35 7. SELECT THE PREFERRED ALTERNATIVE

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

A B 1 PROBLEM 1.7 2 3 a EXAMPLES OF NON-MONETARY FACTORS INCLUDE: 4 QUALITY 5 SAFETY 6 ENVIRONMENTAL IMPACT 7 COMMUNITY ATTITUDES 8 LABOR-MANAGEMENT RELATIONSHIPS 9 SYSTEM RELIABILITY 10 SYSTEM AVAILABILITY 11 SYSTEM MAINTAINABILITY 12 SYSTEM OPERABILITY 13 SYSTEM FLEXIBILITY 14 IMPACT ON PERSONNEL LEVELS 15 TRAINING REQUIREMENTS 16 COMPARISON WITH COMPETITORS 17 IMPACT ON DIFFERENT UNITS WITHIN THE ORGANIZATION 18 BRINGING ABOUT CHANGE 19 EGO 20 CUSTOMER PREFERENCES 21 DEPENDING UPON WHAT TYPES OF ALTERNATIVES ARE BEING CONSIDERED, THIS LIST 22 COULD BE ALMOST LIMITLESS. 23 24 b NONE 25 26 c 5. COMPARE THE ALTERNATIVES 27 6. PERFORM SUPPLEMENTARY ANALYSES 28 7. SELECT THE PREFERRED ALTERNATIVE

A B C D E F G H 1 PROBLEM 1.8 2 3 ACCEPT PROPOSAL: 1 4 REJECT PROPOSAL: 0 5 6 a ALT PROP PROP PROP PROP WHY NOT FEASIBLE 7 A B C D 8 9 1 0 0 0 0 10 2 0 0 0 1 11 3 0 0 1 0 12 4 0 0 1 1 13 5 0 1 0 0 B CONTINGENT ON C OR D 14 6 0 1 0 1 15 7 0 1 1 0 16 8 0 1 1 1 17 9 1 0 0 0 A CONTINGENT ON D 18 10 1 0 0 1 19 11 1 0 1 0 NOT BOTH A AND C A CONTINGENT ON D 20 12 1 0 1 1 NOT BOTH A AND C 21 13 1 1 0 0 B CONTINGENT ON C OR D A CONTINGENT ON D 22 14 1 1 0 1 23 15 1 1 1 0 NOT BOTH A AND C A CONTINGENT ON D 24 16 1 1 1 1 NOT BOTH A AND C 25 26 b NONE 27 28 c 1. IDENTIFY THE INVESTMENT ALTERNATIVES

A B C D E F G H 1 PROBLEM 1.9 2 3 ACCEPT PROPOSAL: 1 REJECT PROPOSAL: 0 4 5 a ALT PROP PROP PROP PROP PROP WHY NOT FEASIBLE 6 V W X Y Z 7 1 0 0 0 0 0 AT LEAST 2 AND NO MORE THAN 4 2 0 0 0 0 1 AT LEAST 2 AND NO MORE THAN 4; Z 8 CONTINGENT ON X OR Y 9 3 0 0 0 1 0 AT LEAST 2 AND NO MORE THAN 4 10 4 0 0 0 1 1 11 5 0 0 1 0 0 AT LEAST 2 AND NO MORE THAN 4 12 6 0 0 1 0 1 13 7 0 0 1 1 0 X AND Y MUTUALLY EXCLUSIVE 14 8 0 0 1 1 1 X AND Y MUTUALLY EXCLUSIVE 15 9 0 1 0 0 0 AT LEAST 2 AND NO MORE THAN 4 16 10 0 1 0 0 1 Z CONTINGENT ON X OR Y 17 11 0 1 0 1 0 18 12 0 1 0 1 1 19 13 0 1 1 0 0 20 14 0 1 1 0 1 21 15 0 1 1 1 0 X AND Y MUTUALLY EXCLUSIVE 22 16 0 1 1 1 1 X AND Y MUTUALLY EXCLUSIVE 23 17 1 0 0 0 0 AT LEAST 2 AND NO MORE THAN 4 24 18 1 0 0 0 1 Z CONTINGENT ON X OR Y 25 19 1 0 0 1 0 NOT V IF W, X, Y 26 20 1 0 0 1 1 NOT V IF W, X, Y 27 21 1 0 1 0 0 NOT V IF W, X, Y 28 22 1 0 1 0 1 NOT V IF W, X, Y X AND Y MUTUALLY EXCLUSIVE; NOT V 23 1 0 1 1 0 IF W, X, Y 29 X AND Y MUTUALLY EXCLUSIVE; NOT V 24 1 0 1 1 1 IF W, X, Y 30 31 25 1 1 0 0 0 NOT V IF W, X, Y 32 26 1 1 0 0 1 Z CONTINGENT ON X OR Y 33 27 1 1 0 1 0 NOT V IF W, X, Y 34 28 1 1 0 1 1 NOT V IF W, X, Y 35 29 1 1 1 0 0 NOT V IF W, X, Y 36 30 1 1 1 0 1 NOT V IF W, X, Y X AND Y MUTUALLY EXCLUSIVE; NOT V 31 1 1 1 1 0 IF W, X, Y 37 32 1 1 1 1 1 AT LEAST 2 AND NO MORE THAN 4; X AND Y MUTUALLY EXCLUSIVE; NOT V IF 38 W, X, Y 39 40 b NONE 41 42 c 1. IDENTIFY THE INVESTMENT ALTERNATIVES

A B C D E F 1 PROBLEM 1.10 2 3 ACCEPT PROPOSAL: 1 REJECT PROPOSAL: 0 4 5 ALTERNATIVE PROPOSAL PROPOSAL PROPOSAL WHY NOT FEASIBLE 6 P Q R 7 8 1 0 0 0 EXACTLY 1 OR 2 CHOSEN 9 2 0 0 1 R CONTINGENT ON P 10 3 0 1 0 11 4 0 1 1 R CONTINGENT ON P 12 5 1 0 0 13 6 1 0 1 14 7 1 1 0 P AND Q MUTUALLY EXCLUSIVE EXACTLY 1 OR 2 CHOSEN; P AND 8 1 1 1 Q MUTUALLY EXCLUSIVE 15

A B C D E F G H 1 PROBLEM 1.11 2 3 NOTE TO INSTRUCTOR 4 THIS IS AN INTERESTING PROBLEM, ESPECIALLY WHEN DISCUSSED WITH 5 ITS COMPANION PROBLEM 1.12 6 7 WHAT YOU SHOULD KNOW ABOUT THIS PROBLEM IS: 8 9 THERE IS NO SINGLE CORRECT ANSWER 10 THE EXPECTED VALUE (PROBABILITY-WEIGHTED RETURNS LESS 11 PROBABILITY-WEIGHTED FAILURES) IS THE SAME FOR EACH: $10.00. 12 13 ECONOMICALLY SPEAKING, THE THREE ARE EQUIVALENT 14 ONE WHO SELECTS ALTERNATIVE A IS RISK AVERSE (OR QUITE 15 CONSERVATIVE) - MANY WILL GAMBLE $100 ON B OR C 16 THE STUDENTS SHOULD NOT BE EXPECTED TO DO A PROBABILISTIC 17 ANALYSIS - THEY WILL SEE HOW TO DO THAT IN CHAPTER 13 18 THE STUDENTS SHOULD BE EXPECTED TO DO A "GUT" ANALYSIS - HOW 19 WOULD THEY ACTUALLY DECIDE HERE? 20 21 RETURNED RETURNED 22 YOU CHANCE OF TO YOU IF CHANCE OF TO YOU IF EXPECTED 23 ALTERNATIVE INVEST SUCCESS SUCCESS FAILURE FAILURE VALUE 24 A $100.00 95% $110.79 5% $95.00 $10.00 25 B $100.00 60% $150.00 40% $50.00 $10.00 26 C $100.00 20% $510.00 80% $10.00 $10.00 27 28 a I WOULD SELECT ALTERNATIVE A IF PLAYING THIS ONLY ONCE. 29 30 b I STILL DON'T LIKE LOSING $50 OR $90. 31 32 c MAY WISH TO MAKE A CASE FOR 2, 3, 4, 5. NUMBER 9 IS FOR SURE. 33 34 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT 35 MAXIMIZES ECONOMIC WORTH 4. TWO INVESTMENT ALTERNATIVES ARE EQUIVALENT IF THEY HAVE THE 36 SAME ECONOMIC WORTH 37 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 38 9. RISKS AND RETURNS TEND TO BE POSITIVELY CORRELATED 39 d MAY WANT TO MAKE A CASE FOR 6, WITH THE EV ANALYSIS - ALTHOUGH 40 THAT SHOULD NOT BE EXPECTED 41 42 1. IDENTIFY THE INVESTMENT ALTERNATIVES 43 4. ESTIMATE THE CASH FLOWS 44 5. COMPARE THE ALTERNATIVES 45 6. PERFORM SUPPLEMENTARY ANALYSES 46 7. SELECT THE PREFERRED ALTERNATIVE

A B C D 1 PROBLEM 1.12 2 3 NOTE TO INSTRUCTOR 4

THERE IS NO SINGLE CORRECT ANSWER THE EXPECTED VALUE (PROBABILITY-WEIGHTED RETURNS LESS PROBABILITY-WEIGHTED FAILURES) IS THE SAME FOR EACH: $10,000. ECONOMICALLY SPEAKING, THE THREE ARE EQUIVALENT ONE WHO SELECTS ALTERNATIVE C IS A RISK SEEKER (OR QUITE RISK PRONE) - NOT MANY WILL GAMBLE ON B OR C

15 16

THE STUDENTS SHOULD NOT BE EXPECTED TO DO A PROBABILISTIC ANALYSIS - THEY WILL SEE THAT IN CHAPTER 13

17 18

THE STUDENTS SHOULD BE EXPECTED TO DO A "GUT" ANALYSIS HOW WOULD THEY ACTUALLY DECIDE HERE? RETURNED RETURNED YOU CHANCE OF TO YOU IF CHANCE OF TO YOU IF EXPECTED ALT INVEST SUCCESS SUCCESS FAILURE FAILURE VALUE A $100,000.00 95% $110,789.47 5% $95,000.00 $10,000.00 B $100,000.00 60% $150,000.00 40% $50,000.00 $10,000.00 C $100,000.00 20% $510,000.01 80% $10,000.00 $10,000.00 a

I WOULD SELECT A

IT HAS A 95% CHANCE OF POCKETING A QUICK PROFIT OF $10,789.47 WITH ONLY $5,000 DOWNSIDE

MAY WISH TO MAKE A CASE FOR 2, 3, 4, 5. NUMBER 9 IS FOR SURE. 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 4. TWO INVESTMENT ALTERNATIVES ARE EQUIVALENT IF THEY HAVE THE SAME ECONOMIC WORTH 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 9. RISKS AND RETURNS TEND TO BE POSITIVELY CORRELATED

35 36 37 38 39 40 41 42 43 44 45 46

WHAT YOU SHOULD KNOW ABOUT THIS PROBLEM IS:

11 12 13 14

30 31 32 33 34

THIS IS AN INTERESTING PROBLEM, ESPECIALLY WHEN DISCUSSED WITH ITS COMPANION PROBLEM 1.11.

5 6 7 8 9 10

19 20 21 22 23 24 25 26 27 28 29

MAY WANT TO MAKE A CASE FOR 6, WITH THE EV ANALYSIS ALTHOUGH THAT SHOULD NOT BE EXPECTED 1. IDENTIFY THE INVESTMENT ALTERNATIVES 4. ESTIMATE THE CASH FLOWS 5. COMPARE THE ALTERNATIVES 6. PERFORM SUPPLEMENTARY ANALYSES 7. SELECT THE PREFERRED ALTERNATIVE

A B 1 PROBLEM 1.13 2 AUTOFOUNDRY SHOULD DO NOTHING AT ALL! THEIR ANALYSIS IS INCORRECT, a EVEN IF ALL DATA WERE RIGHT. 3 4 THE MAJOR FLAW IS THAT THE TIME HORIZON IN ONE CASE IS 5 YEARS AND 9 IN THE OTHER. 5 6 7 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 8 b 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 9 4. TWO INVESTMENT ALTERNATIVES ARE EQUIVALENT IF THEY HAVE THE SAME ECONOMIC WORTH 10 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 11 8. COMPARE INVESTMENT ALTERNATIVES OVER A COMMON PERIOD OF TIME (STRONG) 12 13 1. IDENTIFY THE INVESTMENT ALTERNATIVES 14 c 2. DEFINE THE PLANNING HORIZON (STRONG) 15 4. ESTIMATE THE CASH FLOWS 16 5. COMPARE THE ALTERNATIVES 17 7. SELECT THE PREFERRED ALTERNATIVE 18

A B 1 PROBLEM 1.14 2 USE A 10 YEAR PLANNING HORIZON. THE REASON IS THAT EACH PROJECT IS A ONEa SHOT ALTERNATIVE AND IN ORDER TO CONSIDER EACH, THE PLANNING HORIZON MUST MATCH THAT OF THE LONGEST-LIVED PROJECT OR ALTERNATIVE. 3 4 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 5 b 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 6 8. COMPARE INVESTMENT ALTERNATIVES OVER A COMMON PERIOD OF TIME 7 8 1. IDENTIFY THE INVESTMENT ALTERNATIVES 9 c 2. DEFINE THE PLANNING HORIZON 10 5. COMPARE THE ALTERNATIVES 11 7. SELECT THE PREFERRED ALTERNATIVE 12

A B 1 PROBLEM 1.15 2 VIRTUALLY ANY PLANNING HORIZON COULD BE SELECTED. MOST LIKELY IT WOULD a BE SOME NUMBER OF YEARS FROM THE SHORTEST-LIVED ALTERNATIVE (4 YEARS) TO THE LONGEST-LIVED (10 YEARS), ALTHOUGH THIS IS NOT NECESSARILY SO. THE DECISION MAKER MUST FIRST ASK "OVER WHAT PERIOD OF TIME DO I WANT TO MAKE THE BEST DECISION?" FOR ANY SELECTED PLANNING HORIZON, SAY 6 YEARS FOR EXAMPLE, THE 4 YEAR ALTERNATIVE REQUIRES SPECIFICATION OF WHAT WILL HAPPEN IN YEARS 5 AND 6 (SUCH AS REPAVING) AND THEN WILL REQUIRE ESTIMATION OF A RESIDUAL OR SALVAGE VALUE AT THE END OF YEAR 6. IN THE CASE OF THE RV HOOK UPS, A RESIDUAL OR SALVAGE VALUE WOULD NEED TO BE ESTIMATED AT THE END OF 6 YEARS TO PROPERLY REFLECT THE REMAINING VALUE IN THAT ALTERNATIVE AFTER THE 6 YEAR PLANNING HORIZON. SIMILAR THINKING IS REQUIRED FOR ANY OTHER PLANNING HORIZON SELECTED. 3 4 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 5 b. 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 6 8. COMPARE INVESTMENT ALTERNATIVES OVER A COMMON PERIOD OF TIME 7 8 1. IDENTIFY THE INVESTMENT ALTERNATIVES 9 c. 2. DEFINE THE PLANNING HORIZON 10 5. COMPARE THE ALTERNATIVES 11 7. SELECT THE PREFERRED ALTERNATIVE 12

A B C D E F G H I J K L M 1 PROBLEM 1.16 2 3 a BC CI SW WC 4 FACTOR WT RT SC RT SC RT SC RT SC 5 P 20 9.2 184 10 200 6.7 134 8.2 164 6 Q 30 10 300 7 210 8 240 6 180 7 D 25 9 225 7 175 10 250 7 175 8 R 15 6 90 5 75 7 105 10 150 9 E 10 8 80 9 90 6 60 10 100 10 11 TOTALS 879 750 789 769 12 b QUALITY (Q), DELIVERY (D), AND RELIABILITY (R) ARE ALL BETTER FOR BC THAN FOR CI. THEY OVERCAME THE $85,000 - $79,000 = $6,000 PRICE DIFFERENCE OF CI OVER BC. THEREFORE, THEY MUST 13 BE WORTH AT LEAST $6,000. 14 15 c 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 16 17 d 1. IDENTIFY THE INVESTMENT ALTERNATIVES 18 5. COMPARE THE ALTERNATIVES 19 7. SELECT THE PREFERRED ALTERNATIVE

A B C D E F G H I J K L M 1 PROBLEM 1.17 NOTE! THIS PROBLEM IS SIMILAR TO EXAMPLE 1.8 2 3 a A B C D 4 FACTOR WT RT SC RT SC RT SC RT SC 5 PW 35 6.3 220.5 10 350 7.5 262.5 8.8 308 6 PP 40 9.1 364 7.7 308 10 400 5.8 232 7 RL 25 7.5 187.5 9 225 9 225 10 250 8 9 TOTALS 772 883 887.5 790 10 11 RECOMMEND ALTERNATIVE C BY A SMALL MARGIN OVER B 12 b PAYBACK PERIOD WAS THE DIFFERENCE MAKER IN SELECTING C OVER B, EVEN THOUGH B HAD A HIGHER PRESENT WORTH ($300,000) THAN C ($225,000) FOR A DIFFERENCE OF $75,000. PAYBACK PERIOD FROM 3 TO 1 13 YEARS MUST BE WORTH AT LEAST $75,000 TO THE COMPANY. 14 15 c 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 16 17 d 1. IDENTIFY THE INVESTMENT ALTERNATIVES 18 5. COMPARE THE ALTERNATIVES 19 7. SELECT THE PREFERRED ALTERNATIVE

A B C D E F G 1 PROBLEM 1.18 2 3 COST/GAL G1= $7.50 4 COST/GAL G2= $13.50 5 % BLUE G1= 11.00% 6 % BLUE G2= 22.00% 7 8 DESIRED % BLUE 18.00% 9 X= PROPORTION OF G1 USED IN FINAL MIXTURE 10 1-X= PROPORTION OF G2 USED IN FINAL MIXTURE 11 12 13 a SOLVING FOR X 14 % BLUE FORMULA= 18.00% =11%*X+22%*(1-X) 15 REARRANGING TERMS= 11%*X=4% 16 X= 36.36% =(22.00%-18.00%)/(22.00%-11.00%) 17 1-X= 63.64% =1-36.36% 18 USE 36.36% OF G1 AND 63.64% OF G2 IN THE FINAL PAINT MIXTURE 19 20 b COST EQUATION 21 COST= $11.32 =7.5*36.36%+13.5*(1-36.36%)

A 1 PROBLEM 1.19 2 3 4 5 6 7 8 9 10 11 12 a 13 14 15 16 17 18 b 19 20 21 22 23 24 25 c

ORDER SIZE= OLD MATERIAL COST/UNIT= OLD LABOR COST/UNIT= NEW MATERIAL COST/UNIT= NEW LABOR COST/UNIT= ADDITIONAL TOOLING COST=

500,000 UNITS $0.75 $0.25 $0.52 $0.16 $90,000.00

TOTAL COST = MATERIAL COST + LABOR COST + NON-FACTORY COST CONTINUE OLD METHOD MATERIAL COST= LABOR COST= NON-FACTORY COST= TOTAL COST=

$187,500.00 =(500000/2)*0.75 $62,500.00 =(500000/2)*0.25 $125,000.00 =2*62500 $375,000.00 =187500+62500+125000

SWITCH TO NEW METHOD NEW TOOLING COST= MATERIAL COST= NEW LABOR COST/UNIT= NON-FACTORY COST= TOTAL COST=

$90,000.00 =90000 $130,000.00 =(500000/2)*0.52 $40,000.00 =(500000/2)*0.16 $80,000.00 =2*40000 $340,000.00 =90000+130000+40000+80000

SWITCH TO THE NEW METHOD - LESS COSTLY

A 1 PROBLEM 1.20 2 3 4 5 6 7 8 9 10 11 12 a 13 14 15 16 17 18 19 b 20

COST/GAL A= COST/GAL B= % CRANBERRY A= % CRANBERRY B=

$1.00 $2.50 12.50% 20.00%

DESIRED % CRANBERRY X= 1-X=

15.50% PROPORTION OF CRANBERRY A USED IN FINAL MIXTURE PROPORTION OF CRANBERRY B USED IN FINAL MIXTURE

SOLVING FOR X % CRANBERRY FORMULA 15.50% =12.5%*X+20%*(1-X) REARRANGING TERMS= 7.5%*X=4.5% X= 60.00% =(20.00%-15.50%)/(20.00%-12.50%) 1-X= 40.00% =1-60% USE 60.0% OF A AND 40.0% OF B IN THE FINAL CRANBERRY MIXTURE COST EQUATION COST/GAL=

$1.60 =1*60%+2.5*(1-60%)

A 1 PROBLEM 1.21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

COST OF RAW MAT'L A PER LB= COST OF RAW MAT'L B PER LB= COST OF RAW MAT'L C PER LB=

$5.18 $1.61 $2.82 ALTERNATIVE 1 ALTERNATIVE 2 ALTERNATIVE 3

COST OF RAW MAT'L A PER UNIT= LBS/UNIT= COST A/UNIT CALCULATIONS ARE= COST A/UNIT=

0.050 =$5.18*0.05 $0.2590

0.070 =$5.18*0.07 $0.3626

0.075 =$5.18*0.075 $0.3885

COST OF RAW MAT'L B PER UNIT= LBS/UNIT= COST B/UNIT CALCULATIONS ARE= COST B/UNIT=

0.190 =$1.61*0.190 $0.3059

0.180 =$1.61*0.180 $0.2898

0.260 =$1.61*0.260 $0.4186

COST OF RAW MAT'L C PER UNIT= LBS/UNIT= COST C/UNIT CALCULATIONS ARE= COST C/UNIT=

0.140 =$2.82*0.140 $0.3948

0.120 =$2.82*0.120 $0.3384

0.170 =$2.82*0.170 $0.4794

TOTAL RAW MAT'L COST/UNIT

$0.9597

$0.9908

$1.2865

OTHER COSTS/UNIT

$0.2400

$0.3600

$0.3400

TOTAL COSTS/UNIT=

$1.1997

$1.3508

$1.6265

PRICE/UNIT=

$1.4300

$1.5800

$1.8800

PROFIT/UNIT

$0.2303

$0.2292

$0.2535

SALES VOLUME=

1,000,000

1,250,000

800,000

TOTAL PROFIT=

$230,300

$286,500

$202,800

SELECT ALTERNATIVE 2 TO MAXIMIZE PROFIT

A 1 PROBLEM 1.22 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 a 18 19 b

LABOR COST PER ACCEPTABLE UNIT

$1.40

COST OF MATERIAL PER UNIT

$5.50

PRODUCTION RATE REJECTION RATE ACCEPTABLE UNITS

100 3.00% 97

125 150 8.00% 20.00% 115 120

LABOR COST AT $1.40/ACCEPTABLE UNIT COST OF MATERIAL AT $5.50 PER UNIT

$135.80 $161.00 $168.00 $550.00 $687.50 $825.00

TOTAL DAILY COSTS COST PER ACCEPTABLE UNIT

$685.80 $848.50 $993.00 $7.07 $7.38 $8.28

WORKERS PREFER 150 UNIT PRODUCTION RATE TO MAX DAILY PAY AT $168.00 PRODUCTION RATE FOR LOWEST UNIT COST PER ACCEPTABLE UNIT IS 100 UNITS

ORDER SIZE COMPARING M1 TO M2: 300+9X=750+3X 6X=450 X=75 COMPARING M1 TO M3 300+9X=500+5X 4X=200 X=50 COMPARING M2 TO M3 750+3X=500+5X 2X=250 X=125

M1 PREFERRED TO M2 AT 75 OR LESS M2 PREFERRED TO M1 AT 75 OR MORE

M1 PREFERRED TO M3 AT 50 OR LESS M3 PREFERRED TO M1 AT 50 OR MORE

M3 PREFERRED TO M2 AT 125 OR LESS M2 PREFERRED TO M3 AT 125 OR MORE

USE M1 FOR X OF 0 TO 50 USE M3 FOR X OF 50 TO 125 USE M2 FOR X OF 125 OR MORE GRAPHICAL REPRESENTATION OF BREAKEVEN POINTS THIS GRAPH WAS DEVELOPED FROM THE TABLE OF COSTS AFTER PART c $2,500.00 $2,000.00 $1,500.00

TOOL M1 TOOL M2

$1,000.00

TOOL M3

$500.00 $0.00

FOR X=75 USE M3 FOR $875

=500+5*75

FOR X=160 USE M2 FOR $1230 IF NOT AVAILABLE, USE M3 FOR $1300

=750+3*160 =500+5*160 PENALTY IS $70 EXTRA OVER M2

IF NEITHER AVAILABLE, USE M1 FOR $1740 =300+9*160 PENALTY IS $510 EXTRA OVER M2 PENALTY IS $440 EXTRA OVER M3

SEE COMPLETE TABLE OF COSTS BELOW

1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193

A 1 PROBLEM 1.23 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 b 47 48 c 49 50 51 52 53 54 55 56 57

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

FIXED COST= VARIABLE COST/UNIT=

ORDER SIZE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

C D E MACHINE MACHINE MACHINE TOOL M1 TOOL M2 TOOL M3 $300.00 $750.00 $500.00 $9.00 $3.00 $5.00 MACHINE MACHINE MACHINE TOOL M1 TOOL M2 TOOL M3 $309.00 $753.00 $505.00 $318.00 $756.00 $510.00 $327.00 $759.00 $515.00 $336.00 $762.00 $520.00 $345.00 $765.00 $525.00 $354.00 $768.00 $530.00 $363.00 $771.00 $535.00 $372.00 $774.00 $540.00 $381.00 $777.00 $545.00 $390.00 $780.00 $550.00 $399.00 $783.00 $555.00 $408.00 $786.00 $560.00 $417.00 $789.00 $565.00 $426.00 $792.00 $570.00 $435.00 $795.00 $575.00 $444.00 $798.00 $580.00 $453.00 $801.00 $585.00 $462.00 $804.00 $590.00 $471.00 $807.00 $595.00 $480.00 $810.00 $600.00 $489.00 $813.00 $605.00 $498.00 $816.00 $610.00 $507.00 $819.00 $615.00 $516.00 $822.00 $620.00 $525.00 $825.00 $625.00 $534.00 $828.00 $630.00 $543.00 $831.00 $635.00 $552.00 $834.00 $640.00 $561.00 $837.00 $645.00 $570.00 $840.00 $650.00 $579.00 $843.00 $655.00 $588.00 $846.00 $660.00 $597.00 $849.00 $665.00 $606.00 $852.00 $670.00 $615.00 $855.00 $675.00 $624.00 $858.00 $680.00 $633.00 $861.00 $685.00 $642.00 $864.00 $690.00 $651.00 $867.00 $695.00 $660.00 $870.00 $700.00 $669.00 $873.00 $705.00 $678.00 $876.00 $710.00 $687.00 $879.00 $715.00 $696.00 $882.00 $720.00 $705.00 $885.00 $725.00 $714.00 $888.00 $730.00 $723.00 $891.00 $735.00 $732.00 $894.00 $740.00 $741.00 $897.00 $745.00 $750.00 $900.00 $750.00

A 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171

B 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

C D E $759.00 $903.00 $755.00 $768.00 $906.00 $760.00 $777.00 $909.00 $765.00 $786.00 $912.00 $770.00 $795.00 $915.00 $775.00 $804.00 $918.00 $780.00 $813.00 $921.00 $785.00 $822.00 $924.00 $790.00 $831.00 $927.00 $795.00 $840.00 $930.00 $800.00 $849.00 $933.00 $805.00 $858.00 $936.00 $810.00 $867.00 $939.00 $815.00 $876.00 $942.00 $820.00 $885.00 $945.00 $825.00 $894.00 $948.00 $830.00 $903.00 $951.00 $835.00 $912.00 $954.00 $840.00 $921.00 $957.00 $845.00 $930.00 $960.00 $850.00 $939.00 $963.00 $855.00 $948.00 $966.00 $860.00 $957.00 $969.00 $865.00 $966.00 $972.00 $870.00 $975.00 $975.00 $875.00 $984.00 $978.00 $880.00 $993.00 $981.00 $885.00 $1,002.00 $984.00 $890.00 $1,011.00 $987.00 $895.00 $1,020.00 $990.00 $900.00 $1,029.00 $993.00 $905.00 $1,038.00 $996.00 $910.00 $1,047.00 $999.00 $915.00 $1,056.00 $1,002.00 $920.00 $1,065.00 $1,005.00 $925.00 $1,074.00 $1,008.00 $930.00 $1,083.00 $1,011.00 $935.00 $1,092.00 $1,014.00 $940.00 $1,101.00 $1,017.00 $945.00 $1,110.00 $1,020.00 $950.00 $1,119.00 $1,023.00 $955.00 $1,128.00 $1,026.00 $960.00 $1,137.00 $1,029.00 $965.00 $1,146.00 $1,032.00 $970.00 $1,155.00 $1,035.00 $975.00 $1,164.00 $1,038.00 $980.00 $1,173.00 $1,041.00 $985.00 $1,182.00 $1,044.00 $990.00 $1,191.00 $1,047.00 $995.00 $1,200.00 $1,050.00 $1,000.00 $1,209.00 $1,053.00 $1,005.00 $1,218.00 $1,056.00 $1,010.00 $1,227.00 $1,059.00 $1,015.00 $1,236.00 $1,062.00 $1,020.00 $1,245.00 $1,065.00 $1,025.00 $1,254.00 $1,068.00 $1,030.00 $1,263.00 $1,071.00 $1,035.00

A 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228

B 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164

C D E $1,272.00 $1,074.00 $1,040.00 $1,281.00 $1,077.00 $1,045.00 $1,290.00 $1,080.00 $1,050.00 $1,299.00 $1,083.00 $1,055.00 $1,308.00 $1,086.00 $1,060.00 $1,317.00 $1,089.00 $1,065.00 $1,326.00 $1,092.00 $1,070.00 $1,335.00 $1,095.00 $1,075.00 $1,344.00 $1,098.00 $1,080.00 $1,353.00 $1,101.00 $1,085.00 $1,362.00 $1,104.00 $1,090.00 $1,371.00 $1,107.00 $1,095.00 $1,380.00 $1,110.00 $1,100.00 $1,389.00 $1,113.00 $1,105.00 $1,398.00 $1,116.00 $1,110.00 $1,407.00 $1,119.00 $1,115.00 $1,416.00 $1,122.00 $1,120.00 $1,425.00 $1,125.00 $1,125.00 $1,434.00 $1,128.00 $1,130.00 $1,443.00 $1,131.00 $1,135.00 $1,452.00 $1,134.00 $1,140.00 $1,461.00 $1,137.00 $1,145.00 $1,470.00 $1,140.00 $1,150.00 $1,479.00 $1,143.00 $1,155.00 $1,488.00 $1,146.00 $1,160.00 $1,497.00 $1,149.00 $1,165.00 $1,506.00 $1,152.00 $1,170.00 $1,515.00 $1,155.00 $1,175.00 $1,524.00 $1,158.00 $1,180.00 $1,533.00 $1,161.00 $1,185.00 $1,542.00 $1,164.00 $1,190.00 $1,551.00 $1,167.00 $1,195.00 $1,560.00 $1,170.00 $1,200.00 $1,569.00 $1,173.00 $1,205.00 $1,578.00 $1,176.00 $1,210.00 $1,587.00 $1,179.00 $1,215.00 $1,596.00 $1,182.00 $1,220.00 $1,605.00 $1,185.00 $1,225.00 $1,614.00 $1,188.00 $1,230.00 $1,623.00 $1,191.00 $1,235.00 $1,632.00 $1,194.00 $1,240.00 $1,641.00 $1,197.00 $1,245.00 $1,650.00 $1,200.00 $1,250.00 $1,659.00 $1,203.00 $1,255.00 $1,668.00 $1,206.00 $1,260.00 $1,677.00 $1,209.00 $1,265.00 $1,686.00 $1,212.00 $1,270.00 $1,695.00 $1,215.00 $1,275.00 $1,704.00 $1,218.00 $1,280.00 $1,713.00 $1,221.00 $1,285.00 $1,722.00 $1,224.00 $1,290.00 $1,731.00 $1,227.00 $1,295.00 $1,740.00 $1,230.00 $1,300.00 $1,749.00 $1,233.00 $1,305.00 $1,758.00 $1,236.00 $1,310.00 $1,767.00 $1,239.00 $1,315.00 $1,776.00 $1,242.00 $1,320.00

A 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264

B 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

C D E $1,785.00 $1,245.00 $1,325.00 $1,794.00 $1,248.00 $1,330.00 $1,803.00 $1,251.00 $1,335.00 $1,812.00 $1,254.00 $1,340.00 $1,821.00 $1,257.00 $1,345.00 $1,830.00 $1,260.00 $1,350.00 $1,839.00 $1,263.00 $1,355.00 $1,848.00 $1,266.00 $1,360.00 $1,857.00 $1,269.00 $1,365.00 $1,866.00 $1,272.00 $1,370.00 $1,875.00 $1,275.00 $1,375.00 $1,884.00 $1,278.00 $1,380.00 $1,893.00 $1,281.00 $1,385.00 $1,902.00 $1,284.00 $1,390.00 $1,911.00 $1,287.00 $1,395.00 $1,920.00 $1,290.00 $1,400.00 $1,929.00 $1,293.00 $1,405.00 $1,938.00 $1,296.00 $1,410.00 $1,947.00 $1,299.00 $1,415.00 $1,956.00 $1,302.00 $1,420.00 $1,965.00 $1,305.00 $1,425.00 $1,974.00 $1,308.00 $1,430.00 $1,983.00 $1,311.00 $1,435.00 $1,992.00 $1,314.00 $1,440.00 $2,001.00 $1,317.00 $1,445.00 $2,010.00 $1,320.00 $1,450.00 $2,019.00 $1,323.00 $1,455.00 $2,028.00 $1,326.00 $1,460.00 $2,037.00 $1,329.00 $1,465.00 $2,046.00 $1,332.00 $1,470.00 $2,055.00 $1,335.00 $1,475.00 $2,064.00 $1,338.00 $1,480.00 $2,073.00 $1,341.00 $1,485.00 $2,082.00 $1,344.00 $1,490.00 $2,091.00 $1,347.00 $1,495.00 $2,100.00 $1,350.00 $1,500.00

A B C D E F G 1 PROBLEM 1.24 2 3 a AVERAGE TOTAL COST 4 SQUARE FEET FLOORS TOTAL COST COST PER FLOOR DECREASE 5 6 400,000 1 $112,800,000.00 $112,800,000.00 N/A 7 400,000 2 $73,600,000.00 $36,800,000.00 $39,200,000.00 8 400,000 3 $61,066,666.67 $20,355,555.56 $12,533,333.33 9 400,000 4 $55,200,000.00 $13,800,000.00 $5,866,666.67 10 400,000 5 $52,000,000.00 $10,400,000.00 $3,200,000.00 11 400,000 6 $50,133,333.33 $8,355,555.56 $1,866,666.67 12 400,000 7 $49,028,571.43 $7,004,081.63 $1,104,761.90 13 400,000 8 $48,400,000.00 $6,050,000.00 $628,571.43 14 400,000 9 $48,088,888.89 $5,343,209.88 $311,111.11 15 400,000 10 $48,000,000.00 $4,800,000.00 $88,888.89 *** 16 400,000 11 $48,072,727.27 $4,370,247.93 -$72,727.27 17 400,000 12 $48,266,666.67 $4,022,222.22 -$193,939.39 18 19 b *** OPTIMUM IS 10 FLOORS 20 21 c TC= (200+80X+2(X^2))(400,000/X)NOTE THAT A=400,000/X 22 23 dTC/dX= (80+4X)(400,000/X)+(200+80X+2(X^2))(-400,000/X^2)=0 24 25 800,000-80,000,000/X^2=0 26 27 X^2=80,000,000/800,000=100 28 29 X=10 30 31 THIS AGREES WITH THE 10 FLOORS SPECIFIED IN THE TABLE.

1 26 51 76 101 126 151 176 201 226 251 276 301 326 351 376 401 426 451 476 501 526 551 576 601

A B C D E F G 1 PROBLEM 1.25 2 3 a ENGINE LATHE EQN TC=$7Q 4 TURRET LATHE EQN TC=$120N+5.25Q 5 6 N=1 FOR Q=1 TO 300 7 N=2 FOR Q=301 TO 600, ETC. 8 9 SETTING THE TWO TC EQUATIONS EQUAL FOR N=1, 10 $7Q=$120+$5.25Q 11 1.75Q=120 12 13 Q=120/1.75= 68.57 UNITS USE ENGINE LATHE IF Q=68 OR LESS 14 USE TURRET LATHE IF Q=69 TO 300 15 16 SETTING THE TWO EQUATIONS EQUAL FOR N=2, 17 $7Q=$240+$5.25Q 18 1.75Q=240 19 20 Q=240/1.75= 137.14 UNITS SINCE THIS IS BELOW 301, 21 USE TURRET LATHE IF Q=301 TO 600 22 23 GRAPHICAL REPRESENTATION OF BREAKEVEN POINT 24 THIS GRAPH WAS DEVELOPED FROM THE TABLE OF COSTS AFTER PART c 25 26 27 $4,500.00 28 29 30 $4,000.00 31 32 $3,500.00 33 34 $3,000.00 35 36 $2,500.00 37 ENGINE L 38 39 $2,000.00 TURRET L 40 41 $1,500.00 42 43 $1,000.00 44 45 $500.00 46 47 48 $0.00 49 50 51 52 53 b Q= 68 UNITS 54 N= 1 SETUP 55 TC(ENGINE LATHE)= $476.00 =7*68 56 TC(TURRET LATHE)= $477.00 =120*1+5.25*68 57 USE ENGINE LATHE FOR Q=68

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

Q= N= ENGINE LATHE TC= TURRET LATHE TC= SAVINGS WITH TURRET LATHE=

400 UNITS 2 SETUPS $2,800.00 =7*400 $2,340.00 =120*2+5.25*400 $460.00 =2800-2340

BRUTE FORCE TABLE OF COSTS FOR Q FROM 0 TO 600 Q N ENGINE L TURRET L 0 1 $0.00 $120.00 1 1 $7.00 $125.25 2 1 $14.00 $130.50 3 1 $21.00 $135.75 4 1 $28.00 $141.00 5 1 $35.00 $146.25 6 1 $42.00 $151.50 7 1 $49.00 $156.75 8 1 $56.00 $162.00 9 1 $63.00 $167.25 10 1 $70.00 $172.50 11 1 $77.00 $177.75 12 1 $84.00 $183.00 13 1 $91.00 $188.25 14 1 $98.00 $193.50 15 1 $105.00 $198.75 16 1 $112.00 $204.00 17 1 $119.00 $209.25 18 1 $126.00 $214.50 19 1 $133.00 $219.75 20 1 $140.00 $225.00 21 1 $147.00 $230.25 22 1 $154.00 $235.50 23 1 $161.00 $240.75 24 1 $168.00 $246.00 25 1 $175.00 $251.25 26 1 $182.00 $256.50 27 1 $189.00 $261.75 28 1 $196.00 $267.00 29 1 $203.00 $272.25 30 1 $210.00 $277.50 31 1 $217.00 $282.75 32 1 $224.00 $288.00 33 1 $231.00 $293.25 34 1 $238.00 $298.50 35 1 $245.00 $303.75 36 1 $252.00 $309.00 37 1 $259.00 $314.25 38 1 $266.00 $319.50 39 1 $273.00 $324.75 40 1 $280.00 $330.00 41 1 $287.00 $335.25 42 1 $294.00 $340.50 43 1 $301.00 $345.75 44 1 $308.00 $351.00 45 1 $315.00 $356.25 46 1 $322.00 $361.50

C 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E $329.00 $336.00 $343.00 $350.00 $357.00 $364.00 $371.00 $378.00 $385.00 $392.00 $399.00 $406.00 $413.00 $420.00 $427.00 $434.00 $441.00 $448.00 $455.00 $462.00 $469.00 $476.00 $483.00 $490.00 $497.00 $504.00 $511.00 $518.00 $525.00 $532.00 $539.00 $546.00 $553.00 $560.00 $567.00 $574.00 $581.00 $588.00 $595.00 $602.00 $609.00 $616.00 $623.00 $630.00 $637.00 $644.00 $651.00 $658.00 $665.00 $672.00 $679.00 $686.00 $693.00 $700.00 $707.00 $714.00 $721.00

F $366.75 $372.00 $377.25 $382.50 $387.75 $393.00 $398.25 $403.50 $408.75 $414.00 $419.25 $424.50 $429.75 $435.00 $440.25 $445.50 $450.75 $456.00 $461.25 $466.50 $471.75 $477.00 $482.25 $487.50 $492.75 $498.00 $503.25 $508.50 $513.75 $519.00 $524.25 $529.50 $534.75 $540.00 $545.25 $550.50 $555.75 $561.00 $566.25 $571.50 $576.75 $582.00 $587.25 $592.50 $597.75 $603.00 $608.25 $613.50 $618.75 $624.00 $629.25 $634.50 $639.75 $645.00 $650.25 $655.50 $660.75

C 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E $728.00 $735.00 $742.00 $749.00 $756.00 $763.00 $770.00 $777.00 $784.00 $791.00 $798.00 $805.00 $812.00 $819.00 $826.00 $833.00 $840.00 $847.00 $854.00 $861.00 $868.00 $875.00 $882.00 $889.00 $896.00 $903.00 $910.00 $917.00 $924.00 $931.00 $938.00 $945.00 $952.00 $959.00 $966.00 $973.00 $980.00 $987.00 $994.00 $1,001.00 $1,008.00 $1,015.00 $1,022.00 $1,029.00 $1,036.00 $1,043.00 $1,050.00 $1,057.00 $1,064.00 $1,071.00 $1,078.00 $1,085.00 $1,092.00 $1,099.00 $1,106.00 $1,113.00 $1,120.00

F $666.00 $671.25 $676.50 $681.75 $687.00 $692.25 $697.50 $702.75 $708.00 $713.25 $718.50 $723.75 $729.00 $734.25 $739.50 $744.75 $750.00 $755.25 $760.50 $765.75 $771.00 $776.25 $781.50 $786.75 $792.00 $797.25 $802.50 $807.75 $813.00 $818.25 $823.50 $828.75 $834.00 $839.25 $844.50 $849.75 $855.00 $860.25 $865.50 $870.75 $876.00 $881.25 $886.50 $891.75 $897.00 $902.25 $907.50 $912.75 $918.00 $923.25 $928.50 $933.75 $939.00 $944.25 $949.50 $954.75 $960.00

A 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285

C 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E F $1,127.00 $965.25 $1,134.00 $970.50 $1,141.00 $975.75 $1,148.00 $981.00 $1,155.00 $986.25 $1,162.00 $991.50 $1,169.00 $996.75 $1,176.00 $1,002.00 $1,183.00 $1,007.25 $1,190.00 $1,012.50 $1,197.00 $1,017.75 $1,204.00 $1,023.00 $1,211.00 $1,028.25 $1,218.00 $1,033.50 $1,225.00 $1,038.75 $1,232.00 $1,044.00 $1,239.00 $1,049.25 $1,246.00 $1,054.50 $1,253.00 $1,059.75 $1,260.00 $1,065.00 $1,267.00 $1,070.25 $1,274.00 $1,075.50 $1,281.00 $1,080.75 $1,288.00 $1,086.00 $1,295.00 $1,091.25 $1,302.00 $1,096.50 $1,309.00 $1,101.75 $1,316.00 $1,107.00 $1,323.00 $1,112.25 $1,330.00 $1,117.50 $1,337.00 $1,122.75 $1,344.00 $1,128.00 $1,351.00 $1,133.25 $1,358.00 $1,138.50 $1,365.00 $1,143.75 $1,372.00 $1,149.00 $1,379.00 $1,154.25 $1,386.00 $1,159.50 $1,393.00 $1,164.75 $1,400.00 $1,170.00 $1,407.00 $1,175.25 $1,414.00 $1,180.50 $1,421.00 $1,185.75 $1,428.00 $1,191.00 $1,435.00 $1,196.25 $1,442.00 $1,201.50 $1,449.00 $1,206.75 $1,456.00 $1,212.00 $1,463.00 $1,217.25 $1,470.00 $1,222.50 $1,477.00 $1,227.75 $1,484.00 $1,233.00 $1,491.00 $1,238.25 $1,498.00 $1,243.50 $1,505.00 $1,248.75 $1,512.00 $1,254.00 $1,519.00 $1,259.25

A 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342

C 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E F $1,526.00 $1,264.50 $1,533.00 $1,269.75 $1,540.00 $1,275.00 $1,547.00 $1,280.25 $1,554.00 $1,285.50 $1,561.00 $1,290.75 $1,568.00 $1,296.00 $1,575.00 $1,301.25 $1,582.00 $1,306.50 $1,589.00 $1,311.75 $1,596.00 $1,317.00 $1,603.00 $1,322.25 $1,610.00 $1,327.50 $1,617.00 $1,332.75 $1,624.00 $1,338.00 $1,631.00 $1,343.25 $1,638.00 $1,348.50 $1,645.00 $1,353.75 $1,652.00 $1,359.00 $1,659.00 $1,364.25 $1,666.00 $1,369.50 $1,673.00 $1,374.75 $1,680.00 $1,380.00 $1,687.00 $1,385.25 $1,694.00 $1,390.50 $1,701.00 $1,395.75 $1,708.00 $1,401.00 $1,715.00 $1,406.25 $1,722.00 $1,411.50 $1,729.00 $1,416.75 $1,736.00 $1,422.00 $1,743.00 $1,427.25 $1,750.00 $1,432.50 $1,757.00 $1,437.75 $1,764.00 $1,443.00 $1,771.00 $1,448.25 $1,778.00 $1,453.50 $1,785.00 $1,458.75 $1,792.00 $1,464.00 $1,799.00 $1,469.25 $1,806.00 $1,474.50 $1,813.00 $1,479.75 $1,820.00 $1,485.00 $1,827.00 $1,490.25 $1,834.00 $1,495.50 $1,841.00 $1,500.75 $1,848.00 $1,506.00 $1,855.00 $1,511.25 $1,862.00 $1,516.50 $1,869.00 $1,521.75 $1,876.00 $1,527.00 $1,883.00 $1,532.25 $1,890.00 $1,537.50 $1,897.00 $1,542.75 $1,904.00 $1,548.00 $1,911.00 $1,553.25 $1,918.00 $1,558.50

A 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399

C 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $1,925.00 $1,563.75 $1,932.00 $1,569.00 $1,939.00 $1,574.25 $1,946.00 $1,579.50 $1,953.00 $1,584.75 $1,960.00 $1,590.00 $1,967.00 $1,595.25 $1,974.00 $1,600.50 $1,981.00 $1,605.75 $1,988.00 $1,611.00 $1,995.00 $1,616.25 $2,002.00 $1,621.50 $2,009.00 $1,626.75 $2,016.00 $1,632.00 $2,023.00 $1,637.25 $2,030.00 $1,642.50 $2,037.00 $1,647.75 $2,044.00 $1,653.00 $2,051.00 $1,658.25 $2,058.00 $1,663.50 $2,065.00 $1,668.75 $2,072.00 $1,674.00 $2,079.00 $1,679.25 $2,086.00 $1,684.50 $2,093.00 $1,689.75 $2,100.00 $1,695.00 $2,107.00 $1,820.25 $2,114.00 $1,825.50 $2,121.00 $1,830.75 $2,128.00 $1,836.00 $2,135.00 $1,841.25 $2,142.00 $1,846.50 $2,149.00 $1,851.75 $2,156.00 $1,857.00 $2,163.00 $1,862.25 $2,170.00 $1,867.50 $2,177.00 $1,872.75 $2,184.00 $1,878.00 $2,191.00 $1,883.25 $2,198.00 $1,888.50 $2,205.00 $1,893.75 $2,212.00 $1,899.00 $2,219.00 $1,904.25 $2,226.00 $1,909.50 $2,233.00 $1,914.75 $2,240.00 $1,920.00 $2,247.00 $1,925.25 $2,254.00 $1,930.50 $2,261.00 $1,935.75 $2,268.00 $1,941.00 $2,275.00 $1,946.25 $2,282.00 $1,951.50 $2,289.00 $1,956.75 $2,296.00 $1,962.00 $2,303.00 $1,967.25 $2,310.00 $1,972.50 $2,317.00 $1,977.75

A 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456

C 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $2,324.00 $1,983.00 $2,331.00 $1,988.25 $2,338.00 $1,993.50 $2,345.00 $1,998.75 $2,352.00 $2,004.00 $2,359.00 $2,009.25 $2,366.00 $2,014.50 $2,373.00 $2,019.75 $2,380.00 $2,025.00 $2,387.00 $2,030.25 $2,394.00 $2,035.50 $2,401.00 $2,040.75 $2,408.00 $2,046.00 $2,415.00 $2,051.25 $2,422.00 $2,056.50 $2,429.00 $2,061.75 $2,436.00 $2,067.00 $2,443.00 $2,072.25 $2,450.00 $2,077.50 $2,457.00 $2,082.75 $2,464.00 $2,088.00 $2,471.00 $2,093.25 $2,478.00 $2,098.50 $2,485.00 $2,103.75 $2,492.00 $2,109.00 $2,499.00 $2,114.25 $2,506.00 $2,119.50 $2,513.00 $2,124.75 $2,520.00 $2,130.00 $2,527.00 $2,135.25 $2,534.00 $2,140.50 $2,541.00 $2,145.75 $2,548.00 $2,151.00 $2,555.00 $2,156.25 $2,562.00 $2,161.50 $2,569.00 $2,166.75 $2,576.00 $2,172.00 $2,583.00 $2,177.25 $2,590.00 $2,182.50 $2,597.00 $2,187.75 $2,604.00 $2,193.00 $2,611.00 $2,198.25 $2,618.00 $2,203.50 $2,625.00 $2,208.75 $2,632.00 $2,214.00 $2,639.00 $2,219.25 $2,646.00 $2,224.50 $2,653.00 $2,229.75 $2,660.00 $2,235.00 $2,667.00 $2,240.25 $2,674.00 $2,245.50 $2,681.00 $2,250.75 $2,688.00 $2,256.00 $2,695.00 $2,261.25 $2,702.00 $2,266.50 $2,709.00 $2,271.75 $2,716.00 $2,277.00

A 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513

C 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $2,723.00 $2,282.25 $2,730.00 $2,287.50 $2,737.00 $2,292.75 $2,744.00 $2,298.00 $2,751.00 $2,303.25 $2,758.00 $2,308.50 $2,765.00 $2,313.75 $2,772.00 $2,319.00 $2,779.00 $2,324.25 $2,786.00 $2,329.50 $2,793.00 $2,334.75 $2,800.00 $2,340.00 $2,807.00 $2,345.25 $2,814.00 $2,350.50 $2,821.00 $2,355.75 $2,828.00 $2,361.00 $2,835.00 $2,366.25 $2,842.00 $2,371.50 $2,849.00 $2,376.75 $2,856.00 $2,382.00 $2,863.00 $2,387.25 $2,870.00 $2,392.50 $2,877.00 $2,397.75 $2,884.00 $2,403.00 $2,891.00 $2,408.25 $2,898.00 $2,413.50 $2,905.00 $2,418.75 $2,912.00 $2,424.00 $2,919.00 $2,429.25 $2,926.00 $2,434.50 $2,933.00 $2,439.75 $2,940.00 $2,445.00 $2,947.00 $2,450.25 $2,954.00 $2,455.50 $2,961.00 $2,460.75 $2,968.00 $2,466.00 $2,975.00 $2,471.25 $2,982.00 $2,476.50 $2,989.00 $2,481.75 $2,996.00 $2,487.00 $3,003.00 $2,492.25 $3,010.00 $2,497.50 $3,017.00 $2,502.75 $3,024.00 $2,508.00 $3,031.00 $2,513.25 $3,038.00 $2,518.50 $3,045.00 $2,523.75 $3,052.00 $2,529.00 $3,059.00 $2,534.25 $3,066.00 $2,539.50 $3,073.00 $2,544.75 $3,080.00 $2,550.00 $3,087.00 $2,555.25 $3,094.00 $2,560.50 $3,101.00 $2,565.75 $3,108.00 $2,571.00 $3,115.00 $2,576.25

A 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570

C 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $3,122.00 $2,581.50 $3,129.00 $2,586.75 $3,136.00 $2,592.00 $3,143.00 $2,597.25 $3,150.00 $2,602.50 $3,157.00 $2,607.75 $3,164.00 $2,613.00 $3,171.00 $2,618.25 $3,178.00 $2,623.50 $3,185.00 $2,628.75 $3,192.00 $2,634.00 $3,199.00 $2,639.25 $3,206.00 $2,644.50 $3,213.00 $2,649.75 $3,220.00 $2,655.00 $3,227.00 $2,660.25 $3,234.00 $2,665.50 $3,241.00 $2,670.75 $3,248.00 $2,676.00 $3,255.00 $2,681.25 $3,262.00 $2,686.50 $3,269.00 $2,691.75 $3,276.00 $2,697.00 $3,283.00 $2,702.25 $3,290.00 $2,707.50 $3,297.00 $2,712.75 $3,304.00 $2,718.00 $3,311.00 $2,723.25 $3,318.00 $2,728.50 $3,325.00 $2,733.75 $3,332.00 $2,739.00 $3,339.00 $2,744.25 $3,346.00 $2,749.50 $3,353.00 $2,754.75 $3,360.00 $2,760.00 $3,367.00 $2,765.25 $3,374.00 $2,770.50 $3,381.00 $2,775.75 $3,388.00 $2,781.00 $3,395.00 $2,786.25 $3,402.00 $2,791.50 $3,409.00 $2,796.75 $3,416.00 $2,802.00 $3,423.00 $2,807.25 $3,430.00 $2,812.50 $3,437.00 $2,817.75 $3,444.00 $2,823.00 $3,451.00 $2,828.25 $3,458.00 $2,833.50 $3,465.00 $2,838.75 $3,472.00 $2,844.00 $3,479.00 $2,849.25 $3,486.00 $2,854.50 $3,493.00 $2,859.75 $3,500.00 $2,865.00 $3,507.00 $2,870.25 $3,514.00 $2,875.50

A 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627

C 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $3,521.00 $2,880.75 $3,528.00 $2,886.00 $3,535.00 $2,891.25 $3,542.00 $2,896.50 $3,549.00 $2,901.75 $3,556.00 $2,907.00 $3,563.00 $2,912.25 $3,570.00 $2,917.50 $3,577.00 $2,922.75 $3,584.00 $2,928.00 $3,591.00 $2,933.25 $3,598.00 $2,938.50 $3,605.00 $2,943.75 $3,612.00 $2,949.00 $3,619.00 $2,954.25 $3,626.00 $2,959.50 $3,633.00 $2,964.75 $3,640.00 $2,970.00 $3,647.00 $2,975.25 $3,654.00 $2,980.50 $3,661.00 $2,985.75 $3,668.00 $2,991.00 $3,675.00 $2,996.25 $3,682.00 $3,001.50 $3,689.00 $3,006.75 $3,696.00 $3,012.00 $3,703.00 $3,017.25 $3,710.00 $3,022.50 $3,717.00 $3,027.75 $3,724.00 $3,033.00 $3,731.00 $3,038.25 $3,738.00 $3,043.50 $3,745.00 $3,048.75 $3,752.00 $3,054.00 $3,759.00 $3,059.25 $3,766.00 $3,064.50 $3,773.00 $3,069.75 $3,780.00 $3,075.00 $3,787.00 $3,080.25 $3,794.00 $3,085.50 $3,801.00 $3,090.75 $3,808.00 $3,096.00 $3,815.00 $3,101.25 $3,822.00 $3,106.50 $3,829.00 $3,111.75 $3,836.00 $3,117.00 $3,843.00 $3,122.25 $3,850.00 $3,127.50 $3,857.00 $3,132.75 $3,864.00 $3,138.00 $3,871.00 $3,143.25 $3,878.00 $3,148.50 $3,885.00 $3,153.75 $3,892.00 $3,159.00 $3,899.00 $3,164.25 $3,906.00 $3,169.50 $3,913.00 $3,174.75

A 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668

C 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $3,920.00 $3,180.00 $3,927.00 $3,185.25 $3,934.00 $3,190.50 $3,941.00 $3,195.75 $3,948.00 $3,201.00 $3,955.00 $3,206.25 $3,962.00 $3,211.50 $3,969.00 $3,216.75 $3,976.00 $3,222.00 $3,983.00 $3,227.25 $3,990.00 $3,232.50 $3,997.00 $3,237.75 $4,004.00 $3,243.00 $4,011.00 $3,248.25 $4,018.00 $3,253.50 $4,025.00 $3,258.75 $4,032.00 $3,264.00 $4,039.00 $3,269.25 $4,046.00 $3,274.50 $4,053.00 $3,279.75 $4,060.00 $3,285.00 $4,067.00 $3,290.25 $4,074.00 $3,295.50 $4,081.00 $3,300.75 $4,088.00 $3,306.00 $4,095.00 $3,311.25 $4,102.00 $3,316.50 $4,109.00 $3,321.75 $4,116.00 $3,327.00 $4,123.00 $3,332.25 $4,130.00 $3,337.50 $4,137.00 $3,342.75 $4,144.00 $3,348.00 $4,151.00 $3,353.25 $4,158.00 $3,358.50 $4,165.00 $3,363.75 $4,172.00 $3,369.00 $4,179.00 $3,374.25 $4,186.00 $3,379.50 $4,193.00 $3,384.75 $4,200.00 $3,390.00

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38ENGINE L 39 TURRET L 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

H 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

A B 1 PROBLEM 1.26 2 3 PRODUCTION CAPACITY = 4 PERCENT OF CAPACITY NOW= 5 IF PERCENT OF CAPACITY= 6 SELLING PRICE/PALLET= 7 VARIABLE COST/PALLET= 8 FIXED COST= 9 10 a ANNUAL PROFIT= 11 12 13 b LET X= 14 ANNUAL PROFIT= 15 X=BREAKEVEN SALES VOLUME 16 17 c ANNUAL PROFIT AT 90% CAP= 18 19 d LET Y= 20 % REDUCTION IN FIXED COSTS= 21 ANNUAL PROFIT= 22 Y=BREAKEVEN SALES VOLUME=

300,000 70.00% 90.00% $18.25 $15.75 $550,000.00 -$25,000.00 (OR LOSS OF $25,000.00) =300000*70%*(18.25-15.75)-550000 BREAKEVEN SALES VOLUME $0.00 =X*(18.75-15.25)-550000 220,000 =550000/(18.25-15.75) $125,000.00 =300000*90%*(18.25-15.75)-550000 BREAKEVEN SALES VOLUME 40% $0.00 =Y*(18.25-15.75)-550000*(1-40%) 132,000 =550000*(1-40%)/(18.25-15.75)

A B C D E F G H 1 PROBLEM 1.27 2 3 SEQUENCE 1 W1 W2 W3 W4 W5 4 SCRAP RATE 3.00% 5.00% 5.00% 4.00% 4.00% 5 6 SEQUENCE 2 WA WB WC 7 SCRAP RATE 5.00% 3.00% 3.00% 8 9 LOT SIZE= 1,000 10 RAW MAT'L COST= $30.00 11 SEQUENCING COST A= $180.00 PER UNIT 12 SEQUENCING COST B= $210.00 PER UNIT 13 14 PERCENT GOOD FROM SEQ 1= 80.6792% =(1-0.03)*(1-0.05)*(1-0.05)*(1-0.04)*(1-0.04) 15 PERCENT GOOD FROM SEQ 2= 89.3855% =(1-0.05)*(1-0.03)*(1-0.03) 16 17 18 SEQUENCE A TC= $210,000.00 =1000*(30+180) 19 SEQUENCE A TC/GOOD UNIT= $260.29 =210000/(1000*80.6792%) 20 21 SEQUENCE B TC= $240,000.00 =1000*(30+210) 22 SEQUENCE B TC/GOOD UNIT= $268.50 =240000/(1000*89.3855%) 23 24 25 SEQUENCE A HAS A LOWER TC/GOOD UNIT 26 27 SIDE NOTE! THESE SCRAP RATES ARE TERRIBLE. 28 THIS COMPANY WILL NOT BE COMPETITIVE

A 1 PROBLEM 1.28 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 b 16

FC/MONTH MPG MAINT COST PER MI

CAR A $550 25 $0.20

CAR B $400 19 $0.25

CAR C $800 33 $0.15

MILES/MONTH=

4,000

COST OF FUEL/GAL=

$3.25

COST/MONTH= CALC FOR CAR A= AVG COST/MILE= CALC FOR CAR C=

$1,870.00 $2,084.21 $1,793.94 =550+(4000/25)*3.25+4000*0.2 $0.47

$0.52

$0.45 =1793.94/4000

A 1 PROBLEM 1.29 2 3 4 5 6 7 8 9 10 11 12 a 13 14 15 16 17 18 19 20 21 22 23 b

TAYLOR'S TOOL LIFE EXPONENT = TOOL CHANGE TIME, MINUTES = COST $/CUTTING EDGE = COST OF LABOR AND OH $/MIN = CONSTANT =

n tc cc co K

TUNGSTEN COATED CARBIDE CARBIDE CERAMIC INSERT INSERT INSERT 0.22 0.27 0.38 2 2 2 $0.40 $1.80 $3.00 $1.00 $1.00 $1.00 150 250 550

MIN UNIT COST TOTAL TOOL LIFE = Tc= 8.509 10.274 8.158 CALCULATION 1 =(2+0.4/1)*((1/0.22)-1) CALCULATION 2 =(2+1.8/1)*((1/0.27)-1) CALCULATION 3 =(2+3/1)*((1/0.38)-1)

CUTTING SPEED = CALCULATION 1 CALCULATION 2 CALCULATION 3

V= 93.652 133.281 247.721 =150/(8.509^0.22) =250/(10.274^0.27) =550/(8.158^0.38)

BASED ON V, THE CERAMIC INSERT IS PREFERRED AT 247.721 FEET/MINUTE

A B C D 1 PROBLEM 1.30 2 3 4 MACHINE A MACHINE B 5 TOTAL SETUP TIME IN HOURS = 4 6 6 CALCULATION =8*0.75 7 MACHINING TIME PER UNIT = 0.50 0.55 8 HOURLY WAGE RATES = $20.00 $18.00 9 HOURLY OVERHEAD RATES = $30.00 $27.00 10 11 a ORDER SIZE = 100 12 COST OF ORDER SIZE = $2,700.00 $2,745.00 13 CALCULATIONS =4*(20+30)+100*0.5*(20+30) =6*(18+27)+100*0.55*(18+27) 14 15 b ORDER SIZE = 500 16 COST OF ORDER SIZE = $12,700.00 $12,645.00 17 CALCULATIONS =4*(20+30)+500*0.50*(20+30) =6*(18+27)+500*0.55*(18+27) 18 19 c LET X= BREAKEVEN ORDER QUANTITY 20 21 EQUATE THE COSTS OF MACHINES A AND B 22 4*(20+30)+X*0.5*(20+30)=6*(18+27)+X*0.55*(18+27) 23 24 SOLVE FOR X 25 X*(0.5*(20+30)-0.55*(18+27))=6*(18+27)-4*(20+30) 26 0.25*X= 70 27 X= 280

NOTES - CHAPTER 2 SOLUTIONS FOLLOWING ARE SOME THOUGHTS ABOUT THE PROBLEMS AND SOLUTIONS IN THIS CHAPTER THAT MAY BE OF HELP TO FACULTY AND STUDENTS. 1

THIS IS, PERHAPS, THE MOST CRITICAL CHAPTER IN THE BOOK IN THAT IT DEALS WITH THE "TIME VALUE OF MONEY (TVM)," A FUNDAMENTAL CONCEPT USED THROUGHOUT THE REST OF THE BOOK.

THERE ARE 180 BASE PROBLEMS, MANY WITH MULTIPLE PARTS, AND MULTIPLE SOLUTIONS FOR MANY OF THOSE PARTS ARE PRESENTED IN THIS SOLUTION MANUAL

THERE ARE FIVE DIFFERENT METHODS THAT ARE SEEN MULTIPLE TIMES IN THESE SOLUTIONS. THEY INCLUDE USE OF (1) SIMPLE AND COMPOUND INTEREST FORMULAS, (2) INTEREST TABLES SUCH AS THOSE IN APPENDICES A AND B, AS WELL AS "ELECTRONIC" INTEREST TABLES (SEE ITEM 5 BELOW), (3) USE OF MYRIAD EXCEL FUNCTIONS, (4) SEARCH PROCEDURES USING EXCEL'S "SOLVER" AND "GOAL SEEK" TOOLS, AND (5) BRUTE FORCE TABULAR APPROACHES

THE COMPOUND INTEREST FORMULAS ARE OFTEN THE MOST ONEROUS TO USE, GIVEN THAT THEY REPRESENT THE FUNDAMENTAL MATHEMATICS OF TVOM.

THE INTEREST TABLES REPRESENT THE MOST COMMON APPROACH USED HERETOFORE IN "ENGINEERING ECONOMY" COURSES; THEY USUALLY VASTLY SIMPLIFY THE MATHEMATICS INVOLVED BY INCORPORATING ONE OR MORE COMPOUND INTEREST FORMULAS INTO A SINGLE TABULATED "FACTOR" AVAILABLE IN APPENDICES A AND B. SINCE THE INTEREST TABLES ARE FOR ONLY A FINITE (ALTHOUGH VERY LARGE) SET OF INTEREST RATES (i AND j) AND TIME HORIZONS (n), THEY MAY NOT BE AVAILABLE FOR A SPECIFIC SET OF i, j, OR n NEEDED. "ELECTRONIC" INTEREST TABLES ARE AVAILABLE, AND HAVE BEEN USED WHEN UNAVAILABLE TABULATED VALUES OF i, j, AND/OR n HAVE BEEN NEEDED. PLEASE SEE NOTES 13 AND 14 BELOW FOR MORE DETAIL ON THE USE OF "ELECTRONIC" INTEREST TABLES.

PROBLEMS 25, 63, 92, 123, AND 146 ASK FOR THE DEVELOPMENT OF CERTAIN INTEREST FACTORS SUCH AS ARE PRESENTED IN THE INTEREST TABLES. THESE SERVE TO CONVINCE THE STUDENT THAT THERE IS NO "MAGIC" INVOLVED IN THE INTEREST TABLES. IN ADDITION, THE FORMULAS USED IN DEVELOPING THE INTEREST FACTORS HAVE BEEN VERY USEFUL TO THE AUTHORS IN "COPY AND PASTE" OPERATIONS IN THE DEVELOPMENT OF THE CHAPTER 2 SOLUTIONS.

THE EXCEL FUNCTIONS HAVE NOT TRADITIONALLY BEEN WIDELY USED IN TEACHING "ENGINEERING ECONOMY." THEY HAVE, HOWEVER, BEEN USED IN THE WORLD OF FINANCE. THE EXCEL FUNCTIONS ARE WELL DESIGNED, AND PROVIDE A VERY PRECISE TOOL FOR USE IN SOLVING A WIDE ARRAY OF PROBLEMS INVOLVING TVM. BEWARE! FOR THE NOVICE, THESE EXCEL FUNCTIONS MAY APPEAR CONFUSING, COMPLEX, AND NOT WORTH THE TIME TO LEARN. THEY ARE, HOWEVER, QUITE STRAIGHTFORWARD AND CONSISTENT, ONCE ONE GETS PAST THE INITIAL TRIALS OF LEARNING SOMETHING NEW. THEY ARE LIKELY TO BE YOUR FAVORITE METHOD OF PROBLEM SOLUTION IF YOU USE THEM TO SOLVE OR CHECK YOUR SOLUTIONS IN THIS CHAPTER.

SOMETIMES, YOU WILL NEED TO SOLVE FOR A MONETARY VALUE, AN INTEREST RATE, A TIME INTERVAL, A GRADIENT, OR WHATEVER, NEEDED TO MATCH OTHER PARAMETERS OF A PROBLEM (E.G., WHAT INTEREST RATE MAKES AN INVESTMENT OF $100 WORTH $150 IN THREE YEARS). WHILE IT IS OFTEN POSSIBLE AND CONVENIENT TO USE ANALYTICAL APPROACHES (E.G., ALGEBRA), SOMETIMES THESE SOLUTIONS ARE DIFFICULT AND CUMBERSOME (ANALYTICALLY INTRACTABLE OR NEARLY SO). SEARCH PROCEDURES CAN BE VERY HANDY IN THESE CASES. EXCEL PROVIDES "SOLVER" AND "GOAL SEEK," BOTH OF WHICH RECEIVE SOME USE IN THE SOLUTIONS FOR CHAPTER 2. THE AUTHORS HAVE FOUND SOLVER TO BE QUITE ROBUST AND ACCURATE FOR THE PROBLEMS OF CHAPTER 2. GOAL SEEK, ALTHOUGH CLOSE, IS NOT QUITE AS CONSISTENT. BOTH ARE EASY TO USE.

THE "BRUTE FORCE" TABULAR APPROACH CAN BE VERY USEFUL WHEN A PROBLEM IS VERY COMPLEX AND DIFFICULT TO KEEP IN MIND WHILE ATTEMPTING TO USE AN INTEREST TABLE APPROACH OR AN EXCEL FUNCTION APPROACH. IN THESE INSTANCES, IT IS OFTEN USEFUL TO SIMPLY LIST THE ENTIRE SET OF CASH FLOWS, PERIOD BY PERIOD. THEN, OFTEN AN NPV FUNCTION OR AN FV-PLUS-NPV FUNCTION OR A PMT-PLUS-NPV FUNCTION CAN BE EASILY USED ON THE TABLE. THE BRUTE FORCE TABULAR APPROACH ALSO HAS THE ADVANTAGE THAT THE ENTIRE PATTERN OF CASH FLOWS CAN BE SEEN AND UNDERSTOOD. BE CAREFUL! ACTUALLY, MOST PROBLEMS CAN BE SOLVED USING THE BRUTE FORCE APPROACH - IN FACT, IT IS QUITE COMMONLY USED IN INDUSTRY! FOR NOW, WHILE LEARNING THIS MATERIAL, USE THE BRUTE FORCE APPROACH ONLY AS A LAST RESORT OR AS A PROBLEM CHECK AS HAS BEEN DONE IN THESE SOLUTIONS. TO USE THE BRUTE FORCE APPROACH ALONE IN CHAPTER 2 IS TO NOT LEARN THE OTHER APPROACHES.

IN THIS CHAPTER, WITH MULTIPLE APPROACHES USED IN SOLVING MANY PROBLEMS, THERE ARE OFTEN SLIGHTLY DIFFERENT SOLUTIONS ACHIEVED. THESE ARE NOT WRONG! USUALLY, IF NOT ALWAYS, THE INTEREST FORMULA APPROACH AND THE EXCEL FUNCTION APPROACH WILL BE PRECISELY THE SAME BECAUSE THERE IS VIRTUALLY NO ROUND OFF ERROR WITHIN THE COMPUTER. THE INTEREST TABLE APPROACH WILL BE SLIGHTLY DIFFERENT, DUE TO THE PRESENTATION OF INTEREST FACTORS TO FIVE PLACES AFTER THE DECIMAL IN MOST CASES. MANY TABLES USE ONLY FOUR PLACES. EVEN WITH FIVE PLACES, THERE WILL BE SOME MINOR DISCREPANCIES WHEN COMPARED TO THE EVEN MORE PRECISE APPROACHES. NOTE THAT SUCH DIFFERENCES ARE ALMOST ALWAYS INCONSEQUENTIAL BECAUSE THE ESTIMATES REQUIRED IN ECONOMIC EVALUATIONS ARE USUALLY ONLY APPROXIMATIONS ANYWAY.

EVEN THOUGH MANY PROBLEMS HAVE MULTIPLE PARTS, IT IS NOT INTENDED THAT ALL PARTS OF A PROBLEM NECESSARILY BE ASSIGNED AND WORKED. IN MANY CASES, THE LEARNING THAT TAKES PLACE CAN BE ACHIEVED BY WORKING ONLY ONE OR TWO PARTS. SEE, FOR EXAMPLE, PROBLEM 79.

WHILE MULTIPLE APPROACHES ARE OFTEN USED HEREIN TO SOLVE A PROBLEM, KEEP IN MIND THAT THERE ARE AN INFINITE (LITERALLY) NUMBER OF WAYS A TVM PROBLEM CAN BE SET UP AND SOLVED. TRANSLATION - THE SOLUTIONS PRESENTED HEREIN ARE QUITE DIRECT IN THEIR APPROACH, BUT NOT THE ONLY APPROACH.

WHEN A SOLUTION MAKES USE OF BOTH INTEREST TABLES AND EXCEL FUNCTIONS, THE ANSWERS WILL OFTEN BE SOMEWHAT DIFFERENT DUE TO ROUNDOFF ERROR IN THE BOOK TABLES. IN GENERAL, THE EXCEL FUNCTIONS CARRY MANY PLACES WITHIN THE COMPUTER, THEREBY MAKING THEM "EXACT" (REMEMBER, SINCE MOST THINGS IN ENGINEERING ECONOMIC ANALYSIS ARE ESTIMATED, IT IS SOMEWHAT LUDICROUS TO REFER TO MANY SOLUTIONS AS "EXACT"). SOMEWHERE IN BETWEEN THE PRECISION OF EXCEL FUNCTIONS AND THE BOOK'S TABLES ARE "ELECTRONIC" INTEREST TABLES. A SEPARATE WORKSHEET WITH ELECTRONIC INTEREST TABLES IS AVAILABLE ON THE BOOK WEB SITE. USING THAT WORKSHEET, THE USER MAY SELECT THE NUMBER OF PLACES FOLLOWING THE DECIMAL TO USE. HERE IS THE PROTOCOL FOLLOWED IN THE SOLUTIONS TO CHAPTER 2:

IF THE VALUES OF i, j, AND n NEEDED ARE AVAILABLE IN THE BOOK'S TABLES, THEY ARE USED HEREIN TO EMULATE THE PROCEDURE USED BY SOMEONE USING THEM, THIS IS THE TRADITIONAL APPROACH TO ENGINEERING ECONOMIC ANALYSIS. NOTE THAT MOST FACTORS ARE PRESENTED TO 5 PLACES AFTER THE DECIMAL.

IF THE VALUES OF i, j, AND n NEEDED ARE NOT AVAILABLE IN THE BOOK'S TABLES, THE ELECTRONIC TABLES ARE USED. IN THIS CASE, THE NUMBER OF PLACES AFTER THE DECIMAL MUST BE DECIDED UPON FOR BOTH THE INPUT VALUES OF i AND/OR j AND ALSO FOR THE FACTOR VALUE ITSELF. HEREIN, 9 PLACES FOLLOWING THE DECIMAL ARE USED IN ALL CASES. THE REASON FOR 9 PLACES IS THAT THIS NUMBER IS SIMILAR TO THE NUMBER OF PLACES AVAILABLE ON MANY SCIENTIFIC AND FINANCIAL CALCULATORS.

NOTE THAT THE INTEREST TABLE APPROACH SOLUTION IS SLIGHTLY DIFFERENT ($0.01) FROM THE OTHER TWO APPROACHES. WHILE THIS IS INCONSEQUENTIAL, THE DISCREPANCY MAY BE MUCH LARGER, IN ABSOLUTE TERMS, DEPENDING UPON THE MONETARY FIGURES INVOLVED, THE NUMBER OF FACTORS INVOLVED, THE SPECIFIC INTEREST RATES INVOLVED, AND SO ON. d

AS A SECOND EXAMPLE, LET'S DETERMINE THE MONTHLY PAYMENT THAT IS EQUIVALENT TO A PRESENT VALUE OF $10,000 IF INTEREST IS 7% NOMINAL, COMPOUNDED MONTHLY OVER A PERIOD OF 24 MONTHS. P= $10,000.00 n= 24 MONTHS r= 7% NOMINAL COMPOUNDED MONTHLY i= 0.583333333% PER MONTH INTEREST TABLE APPROACH: A= =$10,000*(A|P 7%/12,24) OOPS! THERE IS NO BOOK INTEREST TABLE FOR 7%/12 = 0.583333333% ELECTRONIC INTEREST TABLE APPROACH: A= =$10,000*(A|P 7%/12,24) =$10,000*(A|P 0.583333333%,24) =10000*0.044772579 $447.73 EXCEL PMT FUNCTION APPROACH: A= =PMT(7%/12,24,-10000) $447.73 NOTE THAT THE INTEREST TABLE APPROACH WAS NOT USED. IT MIGHT BE SUGGESTED THAT LINEAR INTERPOLATION BE USED BETWEEN TWO TABULATED INTEREST RATES; HOWEVER, THE INTEREST FACTORS ARE NOT LINEAR, AND INTERPOLATION OFTEN INVITES UNNECESSARY ERRORS. THE TWO APPROACHES USED DID ACHIEVE THE SAME ANSWER. THIS WILL OFTEN, BUT NOT ALWAYS, BE THE CASE DUE TO THE FACT THAT THE EXCEL FUNCTIONS ARE CARRYING MORE PLACES AFTER THE DECIMAL IN THE COMPUTER THAN THE 9 PLACES USED HERE WITH THE ELECTRONIC INTEREST TABLE APPROACH.

THE ELECTRONIC INTEREST TABLE SETUP USED HERE IS MODIFIED TO THE USER'S OWN TASTE, SPECIFICALLY TO PERMIT THE USE OF 9 PLACES AFTER THE DECIMAL FOR i, j, AND THE FACTOR VALUES. PLEASE SEE THE FOLLOWING.

A B 1 PROBLEM 2.1 2 3 DCF STANDS FOR "DISCOUNTED CASH FLOW." 4 5 THE MOVEMENT OF MONEY FORWARD OR BACKWARD IN TIME 6 AN EXPLICIT METHOD FOR CONSIDERING THE TIME VALUE OF MONEY

A B 1 PROBLEM 2.2 2 FOUR DCF RULES: 3 4 1. MONEY HAS A TIME VALUE 5 2. MONEY CANNOT BE ADDED OR SUBTRACTED UNLESS IT OCCURS AT THE SAME POINT(S) IN TIME 6 3. TO MOVE MONEY FORWARD ONE TIME UNIT, MULTIPLY TIMES ONE PLUS THE DISCOUNT OR INTEREST RATE 7 4. TO MOVE MONEY BACKWARD ONE TIME UNIT, DIVIDE BY ONE PLUS THE DISCOUNT OR INTEREST RATE 8

A 1 PROBLEM 2.3 2

3 4 5 6 7 8 9 10

THE OFFER IS NOT FAIR AND EQUITABLE BECAUSE THE BUYER IS VIOLATING THE DCF RULES. SPECIFICALLY, THE BUYER IS ADDING AND SUBTRACTING MONEY AT DIFFERENT POINTS IN TIME. THE WORTH OF THE DEAL RIGHT NOW IS $200 + $100/(1+0.05) = $295.24 THE WORTH OF THE DEAL 1 YEAR FROM NOW IS $200*(1+0.05) + $100 = $310.00 OR $295.24*(1+0.05) = $310.00 THE WORTH OF THE BUYER'S OFFER RIGHT NOW IS $300/(1+0.05) = $285.71 THE WORTH OF THE BUYER'S OFFER 1 YEAR FROM NOW IS $300.00

A B 1 PROBLEM 2.4 2 3 a FAIR AMOUNT NOW = $500 + $500/(1+0.06) = $971.70 4 5 b FAIR AMOUNT 1 YEAR FROM NOW = $500*(1+0.06) + $500 = $1030.00 6 OR $971.70*(1+0.06) = $1030.00

A B C D E 1 PROBLEM 2.5 2 3 CFD FROM BANK'S PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 (+) $X $X $X 8 9 10 0 1 2 3 11 12 13 (-) 14 15 $2,000

A B C D E F G H I J K L M N O 1 PROBLEM 2.6 2 3 CFD FROM YOUR PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 $10,000 8 9 10 11 12 13 $4,000 14 15 (+) 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 19 20 (-) 21 $2,880 $2,880 $2,880 $2,880 $2,880 22 $2,880 $2,880 $2,880 $2,880 $2,880

P 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

A B C D E F G 1 PROBLEM 2.7 2 3 FROM KAELYN'S GRANDFATHER'S PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 8 (+) 9 $2,000 10 11 0 1 2 3 4 5 12 13 (-) 14 15 16 17 18 19 20 21 22 23 24 25 26 $30,000

$X+6000 $X+4500 $X+3000 $X+1500 $X

A B C D E F G 1 PROBLEM 2.8 2 3 CFD FROM DAVID'S PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 $150,000 8 9 10 11 12 13 14 15 16 17 18 19 20 (+) 21 22 23 0 1 2 3 4 5 24 25 (-) $20,000 $20,000 26 27 28 29

$X $X+8000 $X+16,000 $X+24,000

L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 $X+24,000 29

A B C D E 1 PROBLEM 2.9 2 3 CFD OF MERCRUISER CNC MACHINE 4 5 NOT NECESSARILY TO SCALE 6 7 (+) $7,000 $7,000 $7,000 8 9 10 0 1 2 3 11 $1,000 $1,000 $1,000 12 (-) 13 14 15 16 17 18 19 20 21 22 23 $50,000

$7,000

4 $1,000

6 $1,000

7 $1,000

8 $1,000

9 $1,000

10 $1,000

$1000+5000 SINCE PLANNING HORIZON IS 10 YEARS, WOULD NOT SHOW UPGRADE AT YEAR 10

A B C D E F G H I J K L M 1 PROBLEM 2.10 2 3 4 CFD OF APARTMENT RENT 5 6 NOT NECESSARILY TO SCALE 7 8 (+) 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 12 13 (-) 14 15 16 17 18 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 19 20 21 $550+450

$450

12 $150

O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

A B C D E F G H I J 1 PROBLEM 2.11 2 3 USA DENIM (TWO MACHINES) 4 5 NOT NECESSARILY TO SCALE 6 7 0 1 2 3 4 5 6 7 8 8 9 (-) 10 11 12 13 $12,000 14 $14,000 15 $16,000 16 $18,000 17 $20,000 18 $22,000 19 20 21 22 $30,000 23 24 25 26 $38,000 27 28 29 30 31 32 33 34 35 36 $30,000+24,000

K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

A B C D E 1 PROBLEM 2.12 2 3 LASER CUTTING MACHINE CFD 4 5 NOT NECESSARILY TO SCALE 6 7 $14,000 $14,000 $14,000 8 9 10 11 12 (+) 13 14 15 0 1 2 3 16 $2,000 17 (-) 18 19 20 21 22 23 24 25 26 27 $23,000

$14,000

$3,000

$4,000 $5,000

A B C D E F G H I J K L M 1 PROBLEM 2.13 2 3 CFD OF SYNTHETIC RUBBER BLENDING MACHINE 4 5 NOT NECESSARILY TO SCALE 6 $24,000-4000+8000-1600 7 $24,000-4000 $24,000-4000 $24,000-4000 8 $18,000-1600 $24,000-4000 $24,000-4000 $24,000-4000 9 $12,000-1200 10 $10,000-800 11 (+) 12 13 14 0 1 2 3 4 5 6 7 8 9 10 15 16 (-) 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 $62,000+8000

A 1 PROBLEM 2.14 2 3 4 5 6 7 a 8 9 b 10 11 12 13 14

i= n= F=

5.00% 12 $8,000

$5,000 USING SIMPLE INTEREST FORMULA THIS IS =8000/(1+0.05*12) P= $4,454.70 USING COMPOUND INTEREST FORMULA THIS IS =8000/(1+0.05)^12 P= $4,454.72 USING THE INTEREST TABLES THIS IS =$8,000*(P|F 5%,12) P= $4,454.70 USING EXCEL'S PV FUNCTION THIS IS =PV(5%,12,,-8000)

A B C D E F 1 PROBLEM 2.15 2 3 ACCT 4 5 1 i= 5.50% SIMPLE INTEREST 6 n= 5 7 P= $10,000.00 8 9 F= $12,750.00 USING SIMPLE INTEREST FORMULA THIS IS 10 =10000*(1+0.055*5) 11 12 2 i= 5.00% COMPOUNDED ANNUALLY 13 n= 5 14 P= $10,000.00 15 16 F= $12,762.82 USING COMPOUND INTEREST FORMULAS THIS IS 17 =10000*(1+0.05)^5 18 F= $12,762.80 USING THE INTEREST TABLES THIS IS 19 $10,000*(F|P 5%,5) 20 F= $12,762.82 USING EXCEL'S FV FUNCTION THIS IS 21 =FV(5%,5,,-10000) 22 23 3 i= 6.50% SIMPLE INTEREST 24 n= 5 25 P= $10,000.00 26 27 F= $13,250.00 USING SIMPLE INTEREST FORMULA THIS IS 28 =10000*(1+0.065*5) 29 30 4 i= 6.00% COMPOUNDED ANNUALLY 31 n= 5 32 P= $10,000.00 33 34 F= $13,382.26 USING COMPOUND INTEREST FORMULAS THIS IS 35 =10000*(1+0.06)^5 36 F= $13,382.30 USING THE INTEREST TABLES THIS IS 37 = $10,000*(F|P 6%,5) 38 F= $13,382.26 USING EXCEL'S FV FUNCTION THIS IS 39 =FV(6%,5,,-10000) 40 41 ACCOUNT 1 2 3 4 42 AMOUNT $12,750.00 $12,762.82 $13,250.00 $13,382.26 43 44 ACCOUNT 4 IS PREFERRED SINCE IT GIVES THE HIGHEST FUTURE VALUE

A 1 PROBLEM 2.16 2 3 a 4 5 6 7 8 9 10 11 12 13 b 14 15 16 17 18 19 20 21 22 23 24 25

i= n= P=

8.00% SIMPLE INTEREST 3 $1,000.00

$1,240.00 USING SIMPLE INTEREST FORMULA THIS IS =1000*(1+0.08*3)

TOTAL INTEREST

$240.00 THIS IS THE FUTURE VALUE OF $1,240 MINUS THE PRESENT VALUE OF $1,000

i= n= P=

8.00% COMPOUNDED ANNUALLY 3 $1,000.00

$1,259.71 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.08)^3 $1,259.71 USING INTEREST TABLES THIS IS = $1,000*(F|P 8%,3) $1,259.71 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,3,,-1000)

F= F=

TOTAL INTEREST

$259.71 THIS IS THE FUTURE VALUE OF $1,259.71 MINUS THE PRESENT VALUE OF $1,000.

A 1 PROBLEM 2.17 2 3 a 4 5 6 7 8 9 10 b 11 12 13 14 15 16 17 18 19

i= 12.00% SIMPLE INTEREST n= 5 P= $3,000.00 F= $4,800.00 USING SIMPLE INTEREST FORMULA THIS IS =3000*(1+.012*5) i= 12.00% COMPOUNDED ANNUALLY n= 5 P= $3,000.00 F= $5,287.03 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(1+0.12)^5 F= $5,287.02 USING INTEREST TABLES THIS IS =$3,000*(F|P 12%,5) F= $5,287.03 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,5,,-3000)

A 1 PROBLEM 2.18 2 3 a 4 5 6 7 8 9 10 b 11 12 c 13 14 15 16 17 18 19 20 21 22 23 d 24

i= n= P=

5.00% 3 $1,000.00

$1,150.00 USING SIMPLE INTEREST FORMULA THIS IS =1000*(1+0.05*3)

TOTAL INTEREST

$150.00

i= n= P=

5.00% 3 $1,000.00

$1,157.63 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.05)^3 $1,157.63 USING INTEREST TABLES THIS IS =$1,000*(F|P 5%,3) $1,157.63 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,3,,-1000)

F= F=

TOTAL INTEREST

$157.63 THIS IS THE FUTURE VALUE OF $1,157.63 MINUS THE PRESENT VALUE OF $1,000.

A B C D E F G 1 PROBLEM 2.19 2 3 UNCLE ESWAR 4 i= 8.00% COMPOUNDED ANNUALLY 5 n= 5 6 P= $5,000.00 7 8 F= $7,346.64 USING COMPOUND INTEREST FORMULAS THIS IS 9 =5000*(1+0.08)^5 10 F= $7,346.65 USING INTEREST TABLES THIS IS 11 =$5,000*(F|P 8%,5) 12 F= $7,346.64 USING EXCEL'S FV FUNCTION THIS IS 13 =FV(8%,5,,-5000) 14 15 UNCLE SHANKAR 16 i= 9.00% SIMPLE INTEREST 17 n= 5 18 P= $5,000.00 19 20 F= $7,250.00 USING SIMPLE INTEREST FORMULA THIS IS 21 =5000*(1+0.09*5) 22 23 GO WITH UNCLE SHANKAR'S LOAN

A 1 PROBLEM 2.20 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25

i= 8.00% n= 10 F= $8,000.00 P= $3,705.55 USING COMPOUND INTEREST FORMULAS THIS IS =8000/(1+0.08)^10 P= $3,705.52 USING INTEREST TABLES THIS IS =$8,000*(P|F 8%,10) P= $3,705.55 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,10,,-8000) i=

11.59% USING SIMPLE INTEREST FORMULA THIS IS =(8000-3705.52)/(3705.52*10) OR, CAN USE SOLVER TO FIND VALUE OF i

i= 11.59% <--SOLVER CHANGED CELL n= 10 F= $8,000.00 P= $3,705.55 <--SOLVER TARGET CELL USING SIMPLE INTEREST FORMULA THIS IS =8000/(1+i*10)

A 1 PROBLEM 2.21 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25

i= 6.00% n= 4 P= $12,000.00 F= $15,149.72 USING COMPOUND INTEREST FORMULAS THIS IS =12000*(1+0.06)^4 F= $15,149.76 USING INTEREST TABLES THIS IS =$12,000*(F|P 6%,4) F= $15,149.72 USING EXCEL'S FV FUNCTION THIS IS =FV(6%,4,,-12000) i=

6.56% USING SIMPLE INTEREST FORMULA THIS IS =(15149.72-12000)/(12000*4) OR, CAN USE SOLVER TO FIND VALUE OF i

i= 6.56% <--SOLVER CHANGED CELL n= 4 P= $12,000.00 F= $15,149.72 <--SOLVER TARGET CELL USING SIMPLE INTEREST FORMULA THIS IS =12000*(1+i*4)

A 1 PROBLEM 2.22 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

i= n= P=

7.00% 5 $11,000.00

$15,428.07 USING COMPOUND INTEREST FORMULAS THIS IS =11000*(1+0.07)^5 $15,428.08 USING INTEREST TABLES THIS IS =$11,000*(F|P 7%,5) $15,428.07 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,5,,-11000)

F= F=

PRINCIPAL $11,000.00 FINAL AMT $15,428.07 INTEREST $4,428.07 =15428.07-11000.00

A B C D E F G H 1 PROBLEM 2.23 2 3 i= 8.00% 4 n= 4 5 P= $2,500.00 6 7 AT THE END OF 4 YEARS AT 8% SIMPLE INTEREST THE MAN HAS: 8 F= $3,300.00 USING SIMPLE INTEREST FORMULA THIS IS 9 =2500*(1+0.08*4) 10 11 NOW, REINVESTING THE $3,300.00 FOR 9 YEARS RESULTS IN 12 i= 6.00% 13 n= 9 14 P= $3,300.00 15 16 AT THE END OF 9 MORE YEARS AT 6% COMPOUND INTEREST THE MAN HAS: 17 F= $5,575.28 USING COMPOUND INTEREST FORMULAS THIS IS 18 =3300*(1+0.06)^9 19 F= $5,575.28 USING INTEREST TABLES THIS IS 20 =$3,300*(F|P 6%,9) 21 F= $5,575.28 USING EXCEL'S FV FUNCTION THIS IS 22 =FV(6%,9,,-3300)

A B C D E F G H 1 PROBLEM 2.24 2 3 ACCOUNT 4 1 i= 7.00% 5 n= 4 6 P= $10,000.00 7 8 F= $13,107.96 USING COMPOUND INTEREST FORMULAS THIS IS 9 =10000*(1+0.07)^4 10 F= $13,108.00 USING INTEREST 10,000*(F|P TABLES 7%,4) THIS IS 11 =$10,000*(F|P 7%,4) 12 F= $13,107.96 USING EXCEL'S FV FUNCTION THIS IS 13 =FV(7%,4,,-10000) 14 15 2 i= 7.50% 16 n= 4 17 P= $10,000.00 18 19 F= $13,000.00 USING SIMPLE INTEREST FORMULA THIS IS 20 =10000*(1+0.075*4) 21 22 3 i= 7.50% 23 n= 4 24 P= $10,000.00 25 26 F= $13,354.69 USING COMPOUND INTEREST FORMULAS THIS IS 27 $13,354.69 28 F= $13,354.70 USING INTEREST TABLES (USER TAB) THIS IS 29 =$10,000*(F|P 7.5%,4) 30 F= $13,354.69 USING EXCEL'S FV FUNCTION THIS IS 31 =FV(7.5%,4,,-10000) 32 33 4 i= 8.25% 34 n= 4 35 P= $10,000.00 36 37 F= $13,300.00 USING SIMPLE INTEREST FORMULA THIS IS 38 =10000*(1+0.0825*4) 39 40 ACCOUNT 1 2 3 4 41 AMOUNT OWED $13,107.96 $13,000.00 $13,354.69 $13,300.00 42 PREFER LOAN 2

A B C D E F G H 1 PROBLEM 2.25 2 3 F|P 4 5 i= 8.00% 6 n= 3 7 (F|P i%,n) = 1.25971 USING COMPOUND INTEREST FORMULAS THIS IS 8 =(1+0.08)^3 9 10 P|F 11 12 i= 10.00% 13 n= 20 14 (P|F i%,n) = 0.14864 USING COMPOUND INTEREST FORMULAS THIS IS 15 =1/(1+0.1)^20 16 17 CHECKS OK WITH APPENDIX A

A 1 PROBLEM 2.26 2 3 4 5 6 7 8 9 10 11 12

i= n= P=

8.00% 5 $25,000.00

$36,733.20 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.08)^5 $36,733.25 USING INTEREST TABLES THIS IS =$25,000*(F|P 8%,5) $36,733.20 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,5,,-25000)

F= F=

A 1 PROBLEM 2.27 2 3 4 5 6 7 8 9 10 11 12

i= 4.00% n= 10 F= $100,000.00 P= P= P=

$67,556.42 USING COMPOUND INTEREST FORMULAS THIS IS =100000/(1+0.04)^10 $67,556.00 USING INTEREST TABLES THIS IS =$100,000*(P|F 4%,10) $67,556.42 USING EXCEL'S PV FUNCTION THIS IS =PV(4%,10,,-100000)

A 1 PROBLEM 2.28 2 3 4 5 6 7 8 9 10 11 12

i= 7.00% n= 10 P= $25,000.00 F= $49,178.78 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.07)^10 F= $49,178.75 USING INTEREST TABLES THIS IS =$25,000*(F|P 7%,10) F= $49,178.78 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,10,,-25000)

A 1 PROBLEM 2.29 2 3 4 5 6 7 8 9 10 11 12

i= 5.00% n= 25 F= $150,000.00 P= P= P=

$44,295.42 USING COMPOUND INTEREST FORMULAS THIS IS =150000/(1+0.05)^25 $44,295.00 USING INTEREST TABLES THIS IS =$150,000*(P|F 5%,25) $44,295.42 USING EXCEL'S PV FUNCTION THIS IS =PV(5%,25,,-150000)

A 1 PROBLEM 2.30 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

P= n= F=

$0.04 49 $0.41

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 4.8641% =(0.41/0.04)^(1/49)-1

OR, CAN USE RATE FUNCTION P= $0.04 n= 49 F= $0.41 i= 4.8641% =RATE(49,,-0.04,0.41)

OR, CAN USE SOLVER P= $0.04 n= 49 i= 4.8641% <--SOLVER CHANGED CELL F=

$0.41 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$0.04*(1+i)^49

$0.41 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,49,,-0.04)

A B 1 PROBLEM 2.31 2 3 a i= 4 n= 5 P= 6 7 F= 8 9 F= 10 11 F= 12 13 14 b i= 15 n= 16 P= 17 18 F= 19 20 F= 21 22 F= 23 24 25 c i= 26 n= 27 P= 28 29 F= 30 31 F= 32 33 F= 34 35 36 d i= 37 n= 38 P= 39 40 F= 41 42 F= 43 44 F= 45

8.00% COMPOUNDED ANNUALLY 10 $1,000.00 $2,158.92 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.08)^10 $2,158.92 USING INTEREST TABLES THIS IS $1,000*(F|P 8%,10) $2,158.92 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,10,,-1000) 11.00% 4 $5,000.00 $7,590.35 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.11)^4 $7,590.35 USING INTEREST TABLES THIS IS $5,000*(F|P 11%,4) $7,590.35 USING EXCEL'S FV FUNCTION THIS IS =FV(11%,4,,-5000) 9.00% COMPOUNDED ANNUALLY 7 $13,000.00 $23,764.51 USING COMPOUND INTEREST FORMULAS THIS IS =13000*(1+0.09)^7 $23,764.52 USING INTEREST TABLES THIS IS $13,000*(F|P 9%,7) $23,764.51 USING EXCEL'S FV FUNCTION THIS IS =FV(9%,7,,-13000) 10.00% COMPOUNDED ANNUALLY 3 $25,000.00 $33,275.00 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.1)^3 $33,275.00 USING INTEREST TABLES THIS IS $25,000*(F|P 10%,3) $33,275.00 USING EXCEL'S FV FUNCTION THIS IS =FV(10%,3,,-25000)

A 1 PROBLEM 2.32 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 c 26 27 28 29 30 31 32 33 34 35 36 d 37 38 39 40 41 42 43 44 45

i= 5.00% n= 6 F= $10,000.00 P= P= P=

$7,462.15 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.05)^6 $7,462.20 USING INTEREST TABLES THIS IS =$10,000*(P|F 5%,6) $7,462.15 USING EXCEL'S PV FUNCTION THIS IS =PV(5%,6,,-10000)

i= n= F=

8.00% 4 $6,500.00

$4,777.69 USING COMPOUND INTEREST FORMULAS THIS IS =6500/(1+0.08)^4 $4,777.70 USING INTEREST TABLES THIS IS =$6,500*(P|F 8%,4) $4,777.69 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,4,,-6500)

P= P=

i= n= F=

6.00% 12 $3,400.00

$1,689.70 USING COMPOUND INTEREST FORMULAS THIS IS =3400/(1+0.06)^12 $1,689.70 USING INTEREST TABLES THIS IS =$3,400*(P|F 6%,12) $1,689.70 USING EXCEL'S PV FUNCTION THIS IS =PV(6%,12,,-3400)

P= P=

i= 10.00% n= 5 F= $13,500.00 P= P= P=

$8,382.44 USING COMPOUND INTEREST FORMULAS THIS IS =13500/(1+0.1)^5 $8,382.42 USING INTEREST TABLES THIS IS =$13,500*(P|F 10%,5) $8,382.44 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,5,,-13500)

A 1 PROBLEM 2.33 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 c 26 27 28 29 30 31 32 33 34 35 36 d 37 38 39 40 41 42 43 44 45 46 47 e 48 49 50 51 52 53 54 55 56

i= n= P=

14.00% COMPOUNDED ANNUALLY 7 $3,000.00

$7,506.81 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(1+0.14)^7 $7,506.81 USING ELECTRONIC INTEREST TABLES THIS IS =$3,000*(F|P 14%,7) $7,506.81 USING EXCEL'S FV FUNCTION THIS IS =FV(14%,7,,-3000)

F= F=

i= n= P= F= F= F=

i= n= P=

12.00% 17 $1,600.00 $10,985.67 USING COMPOUND INTEREST FORMULAS THIS IS =1600*(1+0.12)^17 $10,985.66 USING INTEREST TABLES THIS IS =$1,600*(F|P 12%,17) $10,985.67 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,17,,-1600) 16.00% COMPOUNDED ANNUALLY 38 $20,000.00

F= $5,629,030.30 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.16)^38 F= $5,629,030.20 USING ELECTRONIC INTEREST TABLES THIS IS =$20,000*(F|P 16%,38) F= $5,629,030.30 USING EXCEL'S FV FUNCTION THIS IS =FV(16%,38,,-20000) i= n= P= F= F= F=

i= n= P= F= F= F=

8.00% COMPOUNDED ANNUALLY 71 $3,500.00 $826,332.21 USING COMPOUND INTEREST FORMULAS THIS IS =3500*(1+0.08)^71 $826,332.22 USING ELECTRONIC INTEREST TABLES THIS IS =$3,500*(F|P 8%,71) $826,332.21 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,71,,-3500) 11.50% COMPOUNDED ANNUALLY 34 $5,000.00 $202,448.93 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.115)^34 $202,448.95 USING ELECTRONIC INTEREST TABLES THIS IS =$5,000*(F|P 11.5%,34) $202,448.93 USING EXCEL'S FV FUNCTION THIS IS =FV(11.5%,34,,-5000)

A 1 PROBLEM 2.34 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 c 26 27 28 29 30 31 32 33 34 35 36 d 37 38 39 40 41 42 43 44 45 46 47 e 48 49 50 51 52 53 54 55 56

i= 9.00% n= 5 F= $19,000.00 P= $12,348.70 USING COMPOUND INTEREST FORMULAS THIS IS =19000/(1+0.09)^5 P= $12,348.67 USING INTEREST TABLES THIS IS =$19,000*(P|F 9%,5) P= $12,348.70 USING EXCEL'S PV FUNCTION THIS IS =PV(9%,5,,-19000) i= n= F=

15.00% 12 $8,300.00

$1,551.33 USING COMPOUND INTEREST FORMULAS THIS IS =8300/(1+0.15)^12 $1,551.35 USING INTEREST TABLES THIS IS =$8,300*(P|F 15%,12) $1,551.33 USING EXCEL'S PV FUNCTION THIS IS =PV(15%,12,,-8300)

P= P=

i= n= F= P= P= P=

12.00% 53 $6,200.00 $15.27 USING COMPOUND INTEREST FORMULAS THIS IS =6200/(1+0.12)^53 $15.27 USING ELECTRONIC INTEREST TABLES THIS IS =$6,200*(P|F 12%,53) $15.27 USING EXCEL'S PV FUNCTION THIS IS =PV(12%,53,,-6200)

i= 19.20% n= 18 F= $13,000.00 P= P= P=

$550.77 USING COMPOUND INTEREST FORMULAS THIS IS =13000/(1+0.192)^18 $550.77 USING ELECTRONIC INTEREST TABLES THIS IS =$13,000*(P|F 19.2%,18) $550.77 USING EXCEL'S PV FUNCTION THIS IS =PV(19.2%,18,,-13000)

i= n= F=

8.00% 10 $5,000.00

$2,315.97 USING COMPOUND INTEREST FORMULAS THIS IS =5000/(1+0.08)^10 $2,315.95 USING INTEREST TABLES THIS IS =$5,000*(P|F 8%,10) $2,315.97 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,10,,-5000)

P= P=

A B C D E F 1 PROBLEM 2.35 2 3 a P= $10,000.00 4 n= 10 5 F= $23,674.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR i 10 i=(F/P)^(1/n)-1 11 i= 9.0002% =(23674/10000)^(1/10)-1 12 13 14 OR, CAN USE RATE FUNCTION 15 P= $10,000.00 16 n= 10 17 F= $23,674.00 18 19 i= 9.0002% =RATE(10,,-10000,23674) 20 21 22 OR, CAN USE SOLVER 23 P= $10,000.00 24 n= 10 25 26 i= 9.0002% <--SOLVER CHANGED CELL 27 28 F= $23,674.00 <--SOLVER TARGET CELL 29 USING COMPOUND INTEREST FORMULAS THIS IS 30 =$10,000*(1+i)^10 31 32 F= $23,674.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 33 USING EXCEL'S FV FUNCTION THIS IS 34 =FV(i%,10,,-10000) 35 36 b P= $2,000.00 37 n= 18 38 F= $15,380.00 39 40 USING COMPOUND INTEREST FORMULAS THIS IS 41 F=P*(1+i)^n 42 SOLVING FOR i 43 i=(F/P)^(1/n)-1 44 i= 12.0000% =(15380/2000)^(1/18)-1 45 46 47 OR, CAN USE RATE FUNCTION 48 P= $2,000.00 49 n= 18 50 F= $15,380.00 51 52 i= 12.0000% =RATE(18,,-2000,15380) 53 54 55 OR, CAN USE SOLVER 56 P= $2,000.00 57 n= 18

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

12.0000% <--SOLVER CHANGED CELL

$15,380.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$2000*(1+i)^18

$15,380.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,18,,-2000)

P= n= F=

$2,500.00 5 $4,212.00 USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 10.9966% =(4212/2500)^(1/5)-1

OR, CAN USE RATE FUNCTION P= $2,500.00 n= 5 F= $4,212.00 i=

10.9966% =RATE(5,,-2500,4212)

OR, CAN USE SOLVER P= $2,500.00 n= 5 i=

10.9966% <--SOLVER CHANGED CELL

$4,212.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$2500*(1+i)^5

$4,212.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,5,,2500)

A 1 PROBLEM 2.36 2 3 4 5 6 7 a 8 9 b 10 11 c 12

i= 11.00% n= 9 F= $15,000.00 P= P= P=

$5,863.80 USING INTEREST TABLES THIS IS =$15,000*(P|F 11%,9) $5,863.87 USING COMPOUND INTEREST FORMULAS THIS IS =15000/(1+0.11)^9 $5,863.87 USING EXCEL'S PV FUNCTION THIS IS =PV(11%,9,,-15000)

A 1 PROBLEM 2.37 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

FOR EACH OF THE 3 CHOICES, DETERMINE THE VALUE AT THE SAME POINT IN TIME. BELOW, THE POINT IN TIME WILL BE THE PRESENT (TIME 0) i=

8.00%

CHOICE 1: TAKE TODAY P= $1,000.00 ALREADY AT TIME 0 CHOICE 2: WAIT 3 YEARS AND TAKE F= $1,500.00 n= 3 P= $1,190.75 USING COMPOUND INTEREST FORMULAS THIS IS =1500/(1+0.08)^3 P= $1,190.75 USING INTEREST TABLES THIS IS =$1,500*(P|F 8%,3) P= $1,190.75 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,3,,-1500) CHOICE 3: WAIT 5 YEARS AND TAKE F= 3000 n= 5 P= $2,041.75 USING COMPOUND INTEREST FORMULAS THIS IS =3000/(1+0.08)^5 P= $2,041.74 USING INTEREST TABLES THIS IS =$3,000*(P|F 8%,5) P= $2,041.75 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,5,,-3000) THE HIGHEST PRESENT VALUE IS ACHIEVED BY TAKING THE $3,000 AFTER 5 YEARS

A B C D E F G H 1 PROBLEM 2.38 2 3 i= 10.00% 4 n= 7 5 F= $23,384.61 6 7 TO FIND HOW MUCH HE BORROWED, FIND THE PW OF THE LOAN PAYOFF 8 9 P= $12,000.00 USING COMPOUND INTEREST FORMULAS THIS IS 10 =23384.61/(1+0.1)^7 11 P= $12,000.05 USING INTEREST TABLES THIS IS 12 =$23,384.61*(P|F 10%,7) 13 P= $12,000.00 USING EXCEL'S PV FUNCTION THIS IS 14 =PV(10%,7,,-23384.61)

A B C D E F G H 1 PROBLEM 2.39 2 3 i= 11.50% 4 n= 37 5 SET THE FUTURE WORTH AT $1.00 6 F= $1.00 7 8 THE (P|F 11.5%,37) FACTOR IS 9 10 P= 0.0178168 USING COMPOUND INTEREST FORMULAS THIS IS 11 =1/(1+0.115)^37 12 P= 0.0178168 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(11.5%,37,,-1) 14 15 BOTH RESULTS ARE IDENTICAL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A PROBLEM 2.40

i= 12.00% n= 7 F= $6,000.00 TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE WITHDRAWAL a

P= $2,714.10 USING INTEREST TABLES THIS IS =$6,000*(P|F 12%,7)

P= $2,714.10 USING COMPOUND INTEREST FORMULAS THIS IS =6000/(1+0.12)^7

P= $2,714.10 USING EXCEL'S PV FUNCTION THIS IS =PV(12%,7,,-6000)

A 1 PROBLEM 2.41 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

P= n= F=

$5,000.00 10 $8,955.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 6.0009% =(8955/5000)^(1/10)-1

OR, CAN USE RATE FUNCTION P= $5,000.00 n= 10 F= $8,955.00 i=

6.0009% =RATE(10,,-5000,8955)

OR, CAN USE SOLVER P= $5,000.00 n= 10 i=

6.0009% <--SOLVER CHANGED CELL

$8,955.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$5,000*(1+i)^10

$8,955.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,10,,-5000)

A 1 PROBLEM 2.42 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

P= n= F=

$1,500.00 3 $2,500.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 18.5631% =(2500/1500)^(1/3)-1

OR, CAN USE RATE FUNCTION P= $1,500.00 n= 3 F= $2,500.00 i=

18.5631% =RATE(3,,-1500,2500)

OR, CAN USE SOLVER P= $1,500.00 n= 3 i=

18.5631% <--SOLVER CHANGED CELL

F= $2,500.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1,500*(1+i)^3 F= $2,500.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,3,,-1500)

A 1 PROBLEM 2.43 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

P= i= F=

$2,500.00 5.00% $4,430.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR n n=ln(F/P)/ln(1+i) n= 11.73 =LN(4430/2500)/LN(1+0.05) USE 12 YEARS

OR, CAN USE NPER EXCEL FUNCTION P= $2,500.00 i= 5.00% F= $4,430.00 n=

11.73 =NPER(5%,,-2500,4430) USE 12 YEARS

OR, CAN USE SOLVER P= $2,500.00 i= 5.00% n=

11.73 <--SOLVER CHANGED CELL USE 12 YEARS

F= $4,430.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$2,500*(1+0.05)^n F= $4,430.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(5%,n,,-2500)

A B C D E 1 PROBLEM 2.44 2 3 a P= $1.00 4 n= 10 5 F= $2.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR i 10 i=(F/P)^(1/n)-1 11 i= 7.1773% =(2/1)^(1/10)-1 12 13 14 OR, CAN USE RATE FUNCTION 15 P= $1.00 16 n= 10 17 F= $2.00 18 19 i= 7.1773% =RATE(10,,-1.00,2.00) 20 21 22 b P= $1.00 23 n= 10 24 F= $3.00 25 26 USING COMPOUND INTEREST FORMULAS THIS IS 27 F=P*(1+i)^n 28 SOLVING FOR i 29 i=(F/P)^(1/n)-1 30 i= 11.6123% =(3/1)^(1/10)-1 31 32 33 OR, CAN USE RATE FUNCTION 34 P= $1.00 35 n= 10 36 F= $3.00 37 38 i= 11.6123% =RATE(10,,-1.00,3.00) 39 40 41 c P= $1.00 42 n= 10 43 F= $4.00 44 45 USING COMPOUND INTEREST FORMULAS THIS IS 46 F=P*(1+i)^n 47 SOLVING FOR i 48 i=(F/P)^(1/n)-1 49 i= 14.8698% =(4/1)^(1/10)-1 50 51 52 OR, CAN USE RATE FUNCTION 53 P= $1.00 54 n= 10 55 F= $4.00 56 57 i= 14.8698% =RATE(10,,-1,4)

A B C D E F 1 PROBLEM 2.45 2 3 P= $1.00 4 i= 9.00% 5 F= $2.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR n 10 n=ln(F/P)/ln(1+i) 11 n= 8.04 =LN(2/1)/LN(1+0.09) 12 USE 9 YEARS 13 14 15 OR, CAN USE NPER EXCEL FUNCTION 16 P= $1.00 17 i= 9.00% 18 F= $2.00 19 20 n= 8.04 =NPER(5%,,-2500,4430) 21 USE 9 YEARS 22 23 24 OR, CAN USE SOLVER 25 P= $1.00 26 i= 9.00% 27 28 n= 8.04 <--SOLVER CHANGED CELL 29 USE 9 YEARS 30 31 F= $2.00 <--SOLVER TARGET CELL 32 USING COMPOUND INTEREST FORMULAS THIS IS 33 =$2,500*(1+0.05)^n 34 35 F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 36 USING EXCEL'S FV FUNCTION THIS IS 37 =FV(5%,n,,-2500)

A B C D E F 1 PROBLEM 2.46 2 3 P= $1.00 4 i= 6.00% 5 F= $3.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR n 10 n=ln(F/P)/ln(1+i) 11 n= 18.85 =LN(3/1)/LN(1+0.06) 12 USE 19 YEARS 13 14 15 OR, CAN USE NPER EXCEL FUNCTION 16 P= $1.00 17 i= 6.00% 18 F= $3.00 19 20 n= 18.85 =NPER(6%,,-1.00,3.00) 21 USE 19 YEARS 22 23 24 OR, CAN USE SOLVER 25 P= $1.00 26 i= 6.00% 27 28 n= 18.85 <--SOLVER CHANGED CELL 29 USE 19 YEARS 30 31 F= $3.00 <--SOLVER TARGET CELL 32 USING COMPOUND INTEREST FORMULAS THIS IS 33 =$1.00*(1+0.06)^n 34 35 F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 36 USING EXCEL'S FV FUNCTION THIS IS 37 =FV(6%,n,,-1.00)

A 1 PROBLEM 2.47 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

P= n= F=

$1.00 10 $3.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 i=

11.6123% =(3/1)^(1/10)-1 USE 12%

OR, CAN USE RATE FUNCTION P= $1.00 n= 10 F= $3.00 i=

11.6123% =RATE(10,,-1,3) USE 12%

OR, CAN USE SOLVER P= $1.00 n= 10 i= 11.6123% <--SOLVER CHANGED CELL USE 12% F=

$3.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+i)^10

$3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,10,,-1)

A B C D E 1 PROBLEM 2.48 2 3 a P= $1.00 4 i= 6.00% 5 F= $2.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR n 10 n=ln(F/P)/ln(1+i) 11 n= 11.90 =LN(2/1)/LN(1+0.06) 12 USE 12 YEARS 13 14 15 OR, CAN USE NPER EXCEL FUNCTION 16 P= $1.00 17 i= 6.00% 18 F= $2.00 19 20 n= 11.90 =NPER(6%,,-1.00,2.00) 21 USE 12 YEARS 22 23 24 OR, CAN USE SOLVER 25 P= $1.00 26 i= 6.00% 27 28 n= 11.90 <--SOLVER CHANGED CELL 29 USE 12 YEARS 30 31 F= $2.00 <--SOLVER TARGET CELL 32 USING COMPOUND INTEREST FORMULAS THIS IS 33 =$1.00*(1+0.06)^n 34 35 F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 36 USING EXCEL'S FV FUNCTION THIS IS 37 =FV(6%,n,,-1.00) 38 39 40 b P= $1.00 41 i= 6.00% 42 F= $3.00 43 44 USING COMPOUND INTEREST FORMULAS THIS IS 45 F=P*(1+i)^n 46 SOLVING FOR n 47 n=ln(F/P)/ln(1+i) 48 n= 18.85 =LN(3/1)/LN(1+0.06) 49 USE 19 YEARS 50 51 52 OR, CAN USE NPER EXCEL FUNCTION 53 P= $1.00 54 i= 6.00% 55 F= $3.00 56 57 n= 18.85 =NPER(6%,,-1.00,3.00)

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

C USE 19 YEARS

OR, CAN USE SOLVER P= $1.00 i= 6.00% n=

18.85 <--SOLVER CHANGED CELL USE 19 YEARS

F= $3.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(6%,n,,-1.00)

P= $1.00 i= 6.00% F= $4.00 USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR n n=ln(F/P)/ln(1+i) n= 23.79 =LN(4/1)/LN(1+0.06) USE 24 YEARS

OR, CAN USE NPER EXCEL FUNCTION P= $1.00 i= 6.00% F= $4.00 n=

23.79 =NPER(6%,,-1.00,4.00) USE 24 YEARS

OR, CAN USE SOLVER P= $1.00 i= 6.00% n=

23.79 <--SOLVER CHANGED CELL USE 24 YEARS

F= $4.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n F= $4.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(6%,n,,-1.00)

A B C D E F G H 1 PROBLEM 2.49 2 3 a i= 5.00% 4 5 APPR 1 APPR 2 APPR 3 6 14.40000 F|P 5%,14 1.97993 14.20670 7 =72/(100*0.05) F|P 5%,15 2.07893 =LOG(2)/LOG(1+0.05) 8 INTERPOLATING 14.20273 9 =14+(2-1.97993)/(2.07893-1.97993) 10 11 APPR 4 APPR 5 12 14.20670 n= 14.20670 <--SOLVER CHANGED CELL 13 =NPER(5%,,-1,2) F= $2.00 <--SOLVER TARGET CELL 14 =FV(5%,n,,-1) 15 16 APPR 6 17 n= 14.20658 <--GOAL SEEK CHANGED CELL 18 F= $2.00 <--GOAL SEEK SET CELL 19 =FV(5%,n,,-1) 20 21 22 b i= 7.00% 23 24 APPR 1 APPR 2 APPR 3 25 10.28571 F|P 7%,10 1.96715 10.24477 26 =72/(100*0.07) F|P 7%,11 2.10485 =LOG(2)/LOG(1+0.07) 27 INTERPOLATING 10.23856 28 =10+(2-1.96715)/(2.10485-1.96715) 29 30 APPR 4 APPR 5 31 10.24477 n= 10.24477 <--SOLVER CHANGED CELL 32 =NPER(7%,,-1,2) F= $2.00 <--SOLVER TARGET CELL 33 =FV(7%,n,,-1) 34 35 APPR 6 36 n= 10.24499 <--GOAL SEEK CHANGED CELL 37 F= $2.00 <--GOAL SEEK SET CELL 38 =FV(5%,n,,-1) 39 40 41 c i= 10.00% 42 43 APPR 1 APPR 2 APPR 3 44 7.20000 F|P 10%,7 1.94872 7.27254 45 =72/(100*0.10) F|P 10%,8 2.14359 =LOG(2)/LOG(1+0.10) 46 INTERPOLATING 7.26315 47 =7+(2-1.94872)/(2.14359-1.94872) 48 49 APPR 4 APPR 5 50 7.27254 n= 7.27254 <--SOLVER CHANGED CELL 51 =NPER(10%,,-1,2) F= $2.00 <--SOLVER TARGET CELL 52 =FV(10%,n,,-1) 53 54 APPR 6 55 n= 7.27432 <--GOAL SEEK CHANGED CELL 56 F= $2.00 <--GOAL SEEK SET CELL 57 =FV(5%,n,,-1)

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95

i= APPR 1 4.80000 =72/(100*0.15)

APPR 4 4.95948 =NPER(15%,,-1,2)

APPR 6 n= F=

i= APPR 1 3.60000 =72/(100*0.20)

APPR 4 3.80178 =NPER(20%,,-1,2)

APPR 6 n= F=

15.00% APPR 2 F|P 15%,4 1.74901 F|P 15%,5 2.01136 INTERPOLATING 4.95670 =4+(2-1.74901)/(2.01136-1.74901) APPR 5 n= F=

4.95948 $2.00 =FV(15%,n,,-1)

APPR 3 4.95948 =LOG(2)/LOG(1+0.15)

<--SOLVER CHANGED CELL <--SOLVER TARGET CELL

4.96242 <--GOAL SEEK CHANGED CELL $2.00 <--GOAL SEEK SET CELL =FV(5%,n,,-1)

20.00% APPR 2 F|P 20%,3 1.72800 F|P 20%,4 2.07360 INTERPOLATING 3.78704 =3+(2-1.728)/(2.0736-1.728) APPR 5 n= F=

3.80178 $2.00 =FV(20%,n,,-1)

APPR 3 3.80178 =LOG(2)/LOG(1+0.20)

<--SOLVER CHANGED CELL <--SOLVER TARGET CELL

3.80304 <--GOAL SEEK CHANGED CELL $2.00 <--GOAL SEEK SET CELL =FV(5%,n,,-1)

A B C D E F G 1 PROBLEM 2.50 2 3 P= $176,000.00 4 n= 9 5 F= $525,000.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR i 10 i=(F/P)^(1/n)-1 11 12 i= 12.9116% =(525000/176000)^(1/9)-1 13 14 15 OR, CAN USE RATE FUNCTION 16 P= $176,000.00 17 n= 9 18 F= $525,000.00 19 20 i= 12.9116% =RATE(9,,-176000,525000) 21 22 23 OR, CAN USE SOLVER 24 P= $176,000.00 25 n= 9 26 27 i= 12.9116% <--SOLVER CHANGED CELL 28 29 30 F= $525,000.00 <--SOLVER TARGET CELL 31 USING COMPOUND INTEREST FORMULAS THIS IS 32 =$176000.00*(1+i)^9 33 34 F= $525,000.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 35 USING EXCEL'S FV FUNCTION THIS IS 36 =FV(i%,9,,-176000)

A B C D E F G 1 PROBLEM 2.51 2 3 i= 8.50% 4 n= 10-4= 6 5 P= $5,000.00 6 7 FINDING FW AT END OF YEAR 10 OF DEPOSIT AT END OF YEAR 4 8 9 F= $8,157.34 USING ELECTRONIC INTEREST TABLES THIS IS 10 =$5,000*(F|P 8.5%,6) 11 12 F= $8,157.34 USING COMPOUND INTEREST FORMULAS THIS IS 13 =5000*(1+0.085)^6 14 15 F= $8,157.34 USING EXCEL'S FV FUNCTION THIS IS 16 =FV(8.5%,6,,-5000)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A PROBLEM 2.52

i= n= F=

12.00% 40 $15,000,000.00

TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE DESIRED FUTURE AMOUNT P=

$161,201.97 USING COMPOUND INTEREST FORMULAS THIS IS =6000/(1+0.12)^40

$161,250.00 USING INTEREST TABLES THIS IS =$15,000,000*(P|F 12%,40)

$161,201.97 USING EXCEL'S PV FUNCTION THIS IS =PV(12%,40,,-15000000)

A B C D 1 PROBLEM 2.53 2 3 i= 7.50% COMPOUNDED ANNUALLY 4 n= 10 5 6 EOY DEPOSIT 7 0 $5,000.00 8 1 $1,000.00 9 2 $1,000.00 10 11 FIND THE FW OF EACH DEPOSIT AT YEAR 10 12 F= $14,005.87 USING COMPOUND INTEREST FORMULAS THIS IS 13 =5000*(1+0.075)^10+1000*(1+0.075)^9+1000*(1+0.075)^8 14 15 FIND THE FW OF EACH DEPOSIT AT YEAR 10 16 F= $14,005.87 USING ELECTRONIC INTEREST TABLES THIS IS 17 =$5,000*(F|P 7.5%,10)+$1,000*(F|P 7.5%,9)+$1,000*(F|P 7.5%,8) 18 19 FIND THE FW OF EACH DEPOSIT AT YEAR 10 20 F= $14,005.87 USING EXCEL'S FV FUNCTION THIS IS 21 =FV(7.5%,10,,-5000)+FV(7.5%,9,,-1000)+FV(7.5%,8,,-1000) 22 23 SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FW 24 F= $14,005.87 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 25 =FV(7.5%,10,,-(NPV(7.5%,1000,1000)+5000))

A B C D E F G 1 PROBLEM 2.54 2 3 i= 6.00% COMPOUNDED ANNUALLY 4 n= 15 5 6 EOY DEPOSIT 7 0 $2,000.00 8 1 $0.00 9 2 $3,000.00 10 3 $0.00 11 4 $0.00 12 5 $4,000.00 13 6 $0.00 14 7 $1,000.00 15 16 17 FIND THE FW OF EACH DEPOSIT AT YEAR 15 18 F= $19,949.14 USING COMPOUND INTEREST FORMULAS THIS IS 19 =2000*(1+0.06)^15+3000*(1+0.06)^13+4000*(1+0.06)^10+1000*(1+0.06)^8 20 21 FIND THE FW OF EACH DEPOSIT AT YEAR 15 22 F= $19,949.16 USING INTEREST TABLES THIS IS 23 =$2,000*(F|P 6%,15)+$3,000*(F|P 6%,13)+$4,000*(F|P 6%,10)+$1,000*(F|P 6 24 25 FIND THE FW OF EACH DEPOSIT AT YEAR 15 26 F= $19,949.14 USING EXCEL'S FV FUNCTION THIS IS 27 =FV(6%,15,,-2000)+FV(6%,13,,-3000)+FV(6%,10,,-4000)+FV(6%,8,,-1000) 28 29 SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FW 30 F= $19,949.14 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 31 =FV(6%,15,,-(NPV(6%,0,3000,0,0,4000,0,1000)+2000))

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A B C D E F G H I J K 1 PROBLEM 2.55 2 3 i= 7.00% COMPOUNDED ANNUALLY 4 n= 11 5 6 EOY 0 1 2 3 4 5 6 7 8 7 DEP/WDL $2,000.00 $0.00 $0.00 -$1,000.00 $0.00 $3,000.00 $0.00 $0.00 $1,500.00 8 9 FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11 10 F= $8,831.27 USING COMPOUND INTEREST FORMULAS THIS IS =2000*(1+0.07)^111000*(1+0.07)^8+3000*(1+0.07)^6+1500*(1+0.07)^3 11 12 13 FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11 14 F= $8,831.26 USING INTEREST TABLES THIS IS =$2,000*(F|P 7%,11)-$1,000*(F|P 7%,8)+$3,000*(F|P 7%,6)+$1,500*(F|P 7%,3) 15 16 17 FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11 18 F= $8,831.27 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,11,,-2000)+FV(7%,8,,1000)+FV(7%,6,,3000)+FV(7%,3,,-1500) 19 20 21 SUM THE PW OF EACH DEPOSIT OR WITHDRAWAL AND THEN FIND ITS FW 22 F= $4,209.70 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 23 =FV(7%,11,,-(NPV(7%,0,0,-1000,0,3000,0,0,1500)+2000))

A 1 PROBLEM 2.56 2 3 4 5 6 7 8 9 10 a

i= n=

6.50% 7

EOY NCF

0 $0.00

$150.76 USING EXCEL'S FV FUNCTION THIS IS =FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100 $150.76 USING ELECTRONIC INTEREST TABLES THIS IS =-$500*(F|P 6.5%,6)+$200*(F|P 6.5%,5)+$400*(F|P 6.5%,4)300*(F|P 6.5%,3)+500*(F|P 6.5%,2)-200*(F|P 6.5%,1)+100

11 12

1 2 3 4 5 6 7 -$500.00 $200.00 $400.00 -$300.00 $500.00 -$200.00 $100.00

13 14 15 16 17

18 19 20 21 22 23 24

$97.02 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6.5%,-500,200,400,-300,500,-200,100)+0 $97.02 USING ELECTRONIC INTEREST TABLES THIS IS =-$500*(P|F 6.5%,1)+$200*(P|F 6.5%,2)+$400*(P|F 6.5%,3)$300*(P|F 6.5%,4)+$500*(P|F 6.5%,5)-$200*(P|F 6.5%,6)+$100*(P|F 6.5%,7)

$97.02

CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION =PV(6.5%,7,,-150.76) $97.02 USING ELECTRONIC INTEREST TABLES THIS IS =$150.76*(P|F 6.5%,7)

A B C D E F G H I J 1 PROBLEM 2.57 2 3 i= 8.00% 4 n= 6 5 6 EOY 0 1 2 3 4 5 6 7 NCF $0.00 $500.00 -$200.00 $600.00 $300.00 -$100.00 $200.00 8 9 a P= $1,046.28 USING EXCEL'S NPV FUNCTION THIS IS 10 =NPV(6.5%,-500,200,400,-300,500,-200,100)+0 11 $1,046.28 USING INTEREST TABLES THIS IS =$500*(P|F 8%,1)-$200*(P|F 8%,2)+$600*(P|F 8%,3)+$300*(P|F 8%,4)-$100*(P|F 8%,5)+$200*(P|F 8%,6) 12 13 14 b F= $1,660.31 USING EXCEL'S FV FUNCTION THIS IS =FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,15 400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100 16 $1,660.31 USING INTEREST TABLES THIS IS =$500*(F|P 8%,5)-$200*(F|P 8%,4)+$600*(F|P 8%,3)+$300*(F|P 8%,2)-$100*(F|P 8%,1)+$200 17 18 19 c P= $1,046.28 CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION 20 =PV(8%,6,,-1660.31) 21 $1,046.28 USING INTEREST TABLES THIS IS 22 =$1,660.31*(P|F 8%,6) 23 24 d FIND THE WORTH AT EOY 4 25 F4= $1,423.45 USING EXCEL'S PV AND FV FUNCTIONS THIS IS =FV(8%,3,,-500)+FV(8%,2,,200)+FV(8%,1,,26 600)+300+PV(8%,1,,100)+PV(8%,2,,-200) 27 $1,423.45 USING INTEREST TABLES THIS IS =$500*(F|P 8%,3)-200*(F|P 8%,2)+600*(F|P 8%,1)+$300-$100*(P|F 28 8%,1)+$200*(P|F 8%,2) 29 30 e CONVERT THE WORTH AT EOY 4 TO PRESENT 31 P= $1,046.28 USING EXCEL'S PV FUNCTION THIS IS 32 =PV(8%,4,,-1423.45) 33 $1,046.28 USING INTEREST TABLES THIS IS 34 =$1,423.45*(P|F 8%,4)

A B C D E F G H I J K 1 PROBLEM 2.58 2 3 i= 6.00% 4 5 a $8,000 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 15 16 17 $X $X+100 $X+400 18 19 $2X b TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF RENALDO'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. 20 THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $8,000. 21 22 X= $2,272.61 <--SOLVER CHANGED CELL 23 24 P= $8,000.00 <--SOLVER TARGET CELL 25 USING EXCEL'S PV AND NPV FUNCTIONS THIS IS 26 =PV(6%,4,,-NPV(6%,X,X+100,X+400,2*X)) 27 28 CAN ALSO SOLVE USING INTEREST TABLES. 29 30 P= $8,000 USING INTEREST TABLES THIS IS 31 =$X*(P|F 6%,5)+($X+$100)*(P|F 6%,6)+($X+$400)*(P|F 6%,7)+$2X*(P|F 6%,8) 32 =$X*(0.74726)+($X+$100)*(0.70496)+($X+$400)*(0.66506)+$2X*(0.62741) 33 =3.37210*X+$336.52 34 X= $2,272.61 =(8000-336.52)/3.3721 35 36 c EOY PAYMENT 37 5 $2,272.61 $X 38 6 $2,372.61 $X+100 39 7 $2,672.61 $X+400 40 8 $4,545.23 $2X

L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

A B C D E F G H I J 1 PROBLEM 2.59 2 i= 5.50% 3 4 5 6 $5X 7 8 a $4X 9 10 $3X 11 12 $2X 13 14 $X 15 16 17 0 1 2 3 4 5 6 7 8 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 -$20,000.00 38 39 b TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF REX'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $20,000. 40 41 42 X= $1,900.97 <--SOLVER CHANGED CELL 43 44 P= $20,000.00 <--SOLVER TARGET CELL 45 USING EXCEL'S PV AND NPV FUNCTIONS THIS IS 46 =PV(5.5%,3,,-NPV(5.5%,X,2*X,3*X,4*X,5*X)) 47 48 CAN ALSO SOLVE USING INTEREST TABLES. 49 50 P= $20,000 USING ELECTRONIC INTEREST TABLES THIS IS =$X*(P|F 5.5%,4)+$2*X*(P|F 5.5%,5)+$3*X*(P|F 51 5.5%,6)+$4*X*(P|F 5.5%,7)+$5*X*(P|F 5.5%,8) =$X*(0.807216743)+$2*X*(0.765134354)+$3*X*(0.725245833)+$4 52 *X*(0.687436809)+$5*X*(0.651598871) 53 =10.52099*X

54 55 56 57 58 59 60 61 62 63 64 65

B X=

C D $1,900.97

EOY 4 5 6 7 8

PAYMENT $1,900.97 $3,801.93 $5,702.90 $7,603.87 $9,504.83

SUM INTEREST

$28,514.50 $8,514.50

E F G =20000/10.520964541

=28,514.50-20,000.00 AMOUNT OF KEN'S CHECK

K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 REX'S PAYMENTS AS THEN, USE SOLVER 40 41 42 43 44 45 46 47 48 49 50 P|F 8) 51 *X*(0.725245833)+$4 52 53

A B C D E F G H I J K 1 PROBLEM 2.60 2 3 i= 8.00% 4 n= 8 5 6 EOY 0 1 2 3 4 5 6 7 8 7 NCF $300.00 $300.00 $600.00 -$500.00 -$300.00 $0.00 $800.00 $700.00 $600.00 8 9 a P= $1,711.50 USING EXCEL'S NPV FUNCTION THIS IS 10 =NPV(8%,300,600,-500,-300,0,800,700,600)+300 11 $1,711.50 USING INTEREST TABLES THIS IS =$300+$300*(P|F 8%,1)+$600*(P|F 8%,2)-$500*(P|F 8%,3)-$300*(P|F 12 8%,4)+$800*(P|F 8%,6)+$700*(P|F 8%,7)+$600*(P|F 8%,8) 13 14 b F= $3,167.86 USING EXCEL'S FV FUNCTION THIS IS 15 =FV(8%,C4,,-C9) 16 F= $3,167.86 USING INTEREST TABLES THIS IS 17 =$1,711.50*(F|P 8%,8) 18 19 c F2= $1,996.29 USING EXCEL'S FV FUNCTION THIS IS 20 =FV(8%,2,,-1711.5) 21 F2= $1,996.29 USING INTEREST TABLES THIS IS 22 =$1,711.50*(F|P 8%,2)

1 2 3 4 5 6 7 8 9

A PROBLEM 2.61

17 18 19 20 21 22 23 24 25 26 27 28

i= n=

5.00% 8

EOY NCF

0 $150.00

10 11 12 13 14 15 16

1 $300.00

2 3 4 5 6 7 8 $450.00 $0.00 -$500.00 $0.00 $600.00 $700.00 $800.00

$1,919.20 USING COMPOUND INTEREST FORMULAS THIS IS =150+300*(1+0.05)^-1+450*(1+0.05)^-2-500*(1+0.05)^4+600*(1+0.05)^-6+700*(1+0.05)^-7+800*(1+0.05)^-8 $1,919.21 P= USING INTEREST TABLES THIS IS =$150+$300*(P|F 5%,1)+$450*(P|F 5%,2)-$500*(P|F 5%,4)$600*(P|F 5%,6)+$700*(P|F 5%,7)+$800*(P|F 5%,8) P= $1,919.20 USING EXCEL'S NPV FUNCTION THIS IS =NPV(5%,300,450,0,-500,0,600,700,800)+150

$2,835.54 USING COMPOUND INTEREST FORMULAS THIS IS =150*(1+0.05)^8+300*(1+0.05)^7+450*(1+0.05)^6500*(1+0.05)^4+600*(1+0.05)^2+700*(1+0.05)^1+800 $2,835.55 USING INTEREST TABLES THIS IS =$1,919.20*(F|P 5%,8) $2,835.54 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,8,,-1919.20)

F6= $2,571.92 USING COMPOUND INTEREST FORMULAS THIS IS =150*(1+0.05)^6+300*(1+0.05)^5+450*(1+0.05)^4500*(1+0.05)^2+600+700*(1+0.05)^-1+800*(1+0.05)^-2 F6= $2,571.93 USING INTEREST TABLES THIS IS =$1,919.20*(F|P 5%,6) F6= $2,571.92 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,6,,-1919.20)

A 1 PROBLEM 2.62 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21

i= COST PAYMENT METHOD 1 GET CASH DISCOUNT= PW=

12.00% $30,000.00

3.00% $29,100.00 =30000*(1-0.03)

PAYMENT METHOD 2 PAY ACCORDING TO THE FOLLOWING SCHEDULE EOY 0 1 2 3 4 5 CF $5,000.00 $8,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 PW= PW=

$28,414.37 USING EXCEL'S NPV FUNCTION THIS IS =NPV(12%,8000,6000,6000,6000,6000)+5000 $28,414.40 USING INTEREST TABLES THIS IS =$5,000+$8,000*(P|F 12%,1)+$6,000*(P|F 12%,2)+$6,000*(P|F 12%,3)+$6,000*(P|F 12%,4)+$6,000*(P|F 12%,5)

USE PAYMENT METHOD 2 - LOWER PW

A 1 PROBLEM 2.63 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

P|A

FACTOR

i= 8.00% USING 8% FOR EXAMPLE CALC n= 8 USING 8 FOR EXAMPLE CALC (P|A i%,n)= 5.74664 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.08)^8-1)/(0.08*(1+0.08)^8)

A|P

FACTOR

i= 3.00% USING 3% FOR EXAMPLE CALC n= 5 USING 5 FOR EXAMPLE CALC (A|P i%,n)= 0.21835 USING COMPOUND INTEREST FORMULAS THIS IS =(0.03*(1+0.03)^5)/((1+0.03)^5-1)

F|A

FACTOR

i= 10.00% USING 10% FOR EXAMPLE CALC n= 10 USING 10 FOR EXAMPLE CALC (F|A i%,n)= 15.93742 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.1)^10-1)/0.1

A|F

FACTOR

i= 3.00% USING 3% FOR EXAMPLE CALC n= 5 USING 5 FOR EXAMPLE CALC (A|F i%,n)= 0.18835 USING COMPOUND INTEREST FORMULAS THIS IS =0.03/((1+0.03)^5-1) ALL CHECK OK WITH APPENDIX A

A 1 PROBLEM 2.64 2 3 4 5 6 7 8 9 10 11 12

i= 9.00% n= 7 P= $40,000.00 A= $7,947.62 USING COMPOUND INTEREST FORMULAS THIS IS =40000*(0.09*(1+0.09)^7)/((1+0.09)^7-1) A= $7,947.60 USING INTEREST TABLES THIS IS 40,000*(A|P 9%,7) A= $7,947.62 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.09,7,-40000)

A 1 PROBLEM 2.65 2 3 4 5 6 7 8 9 10 11 12

i= n= A=

4.00% 10 $5,000.00

F= $60,030.54 USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.04)^10-1)/0.04 F= $60,030.55 USING INTEREST TABLES THIS IS =$5,000*(F|A 4%,10) F= $60,030.54 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,10,-5000)

A 1 PROBLEM 2.66 2 3 4 5 6 7 8 9 10 11 12

i= n= A=

6.00% 8 $7,500.00

P= $46,573.45 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.06)^8-1)/(0.06*(1+0.06)^8) P= $46,573.43 USING INTEREST TABLES THIS IS =$7,500*(P|A 6%,8) P= $46,573.45 USING EXCEL'S PV FUNCTION THIS IS =PV(6%,8,-7500)

A 1 PROBLEM 2.67 2 3 4 5 6 7 8 9 10 11 12

i= 7.00% n= 35 F= $2,000,000.00 A= A= A=

$14,467.92 USING COMPOUND INTEREST FORMULAS THIS IS =2000000*0.07/((1+0.07)^35-1) $14,467.92 USING ELECTRONIC INTEREST TABLES THIS IS =$2,000,000*(A|F 7%,35) $14,467.92 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.07,35,,-2000000)

A 1 PROBLEM 2.68 2 3 4 5 6 7 8 9 10 11 12

i= 7.00% n= 5 P= $25,000.00 A= $6,097.27 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(0.07*(1+0.07)^5)/((1+0.07)^5-1) A= $6,097.25 USING INTEREST TABLES THIS IS =$25,000*(A|P 7%,5) A= $6,097.27 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.07,5,-25000)

A 1 PROBLEM 2.69 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 b 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

i= n= A=

4.00% 20 $7,500.00

F= $223,335.59 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^20-1)/0.04 F= $223,335.60 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,20) F= $223,335.59 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,20,-7500)

i= n= A=

4.00% 25 $7,500.00

F= $312,344.31 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^25-1)/0.04 F= $312,344.33 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,25) F= $312,344.31 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,25,-7500)

i= n= A=

4.00% 30 $7,500.00

F= $420,637.03 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^30-1)/0.04 F= $420,637.05 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,30) F= $420,637.03 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,30,-7500)

i= n= A=

5.00% 20 $7,500.00

F= $247,994.66 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^20-1)/0.05 F= $247,994.63 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,20) F= $247,994.66 USING EXCEL'S FV FUNCTION THIS IS =FV(0.05,20,-7500)

i= n= A=

5.00% 25 $7,500.00

A 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

B C D E F G H F= $357,953.24 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^25-1)/0.05 F= $357,953.25 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,25) F= $357,953.24 USING EXCEL'S FV FUNCTION THIS IS =FV(0.05,25,-7500)

i= n= A=

5.00% 30 $7,500.00

F= $498,291.36 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^30-1)/0.05 F= $498,291.38 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,30) F= $498,291.36 USING EXCEL'S FV FUNCTION THIS IS =FV(0.05,30,-7500) c

PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 4%= 39.85% =(312344.31-223335.59)/223335.59 PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 4%= 88.34% =(420637.03-223335.59)/223335.59 PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 5%= 44.34% =(357953.24-247994.66)/247994.66 PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 5%= 100.93% =(498291.36-247994.66)/247994.66 PERCENTAGE INCREASE FROM 4% TO 5% FOR 20 YEARS= 11.04% =(247994.66-223335.59)/223335.59 PERCENTAGE INCREASE FROM 4% TO 5% FOR 25 YEARS= 14.60% =(357953.24-312344.31)/312344.31 PERCENTAGE INCREASE FROM 4% TO 5% FOR 30 YEARS= 18.46% =(498291.36-420637.03)/420637.03

AT 4%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 39.85% AT 5%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 44.34% A 25% INCREASE IN INTEREST RATE YIELDED INCREASED ACCUMULATIONS OF 11.04%, 14.60%

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

I 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

A B C D E F G H 1 PROBLEM 2.70 2 3 a i= 7.00% 4 n= 5 5 P= $50,000.00 6 7 WITH THE FIRST PAYMENT AT THE END OF YEAR 1 8 A= $12,194.53 USING COMPOUND INTEREST FORMULAS THIS IS 9 =50000*(0.07*(1+0.07)^5)/((1+0.07)^5-1) 10 A= $12,194.50 USING INTEREST TABLES THIS IS 11 =$50,000*(A|P 7%,5) 12 A= $12,194.53 USING EXCEL'S PMT FUNCTION THIS IS 13 =PMT(0.07,5,-50000) 14 15 16 b i= 7.00% 17 n= 5 PAYMENTS 18 t= 4 WITH FIRST PAYMENT AT EOY 4 19 P= $50,000.00 20 21 WITH THE FIRST PAYMENT AT THE END OF YEAR 4 22 FIND VALUE OF $50,000 AT EOY 3, THEN FIND AMOUNT OF 5 ANNUAL PAYMENTS 23 A= $14,938.83 USING COMPOUND INTEREST FORMULAS THIS IS 24 =50000*((1+0.07)^(4-1))*(0.07*(1+0.07)^5)/((1+0.07)^5-1) 25 A= $14,938.75 USING INTEREST TABLES THIS IS 26 =$50,000*(F|P 7%,3)*(A|P 7%,5) 27 A= $14,938.83 USING EXCEL'S PMT AND FV FUNCTIONS THIS IS 28 =PMT(7%,5,-FV(7%,4-1,,-50000))

A B C D E 1 PROBLEM 2.71 2 3 a i= 5.00% 4 n= 10 5 A= $5,000.00 6 7 WITH THE FIRST WITHDRAWAL AT THE END OF YEAR 1 8 P= $38,608.67 USING COMPOUND INTEREST FORMULAS THIS IS 9 =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10) 10 P= $38,608.65 USING INTEREST TABLES THIS IS 11 =$5,000*(P|A 5%,10) 12 P= $38,608.67 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(5%,10,-5000) 14 15 16 b i= 5.00% 17 n= 10 WITHDRAWALS 18 t= 3 WITH FIRST WITHDRAWAL AT EOY 3 19 A= $5,000.00 20 21 WITH THE FIRST PAYMENT AT THE END OF YEAR 3 22 FIND VALUE OF 10 ANNUAL WITHDRAWALS AT EOY 2, THEN FIND PRESENT WORTH 23 24 P= $35,019.21 USING COMPOUND INTEREST FORMULAS THIS IS 25 =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)*(1/(1+0.05)^(3-1)) 26 P= $35,019.20 USING INTEREST TABLES THIS IS 27 $5,000*(P|F 5%,2)*(P|A 5%,10) 28 P= $35,019.21 USING EXCEL'S PV FUNCTION THIS IS 29 =PV(5%,3-1,,-PV(5%,10,-5000))

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

A B C D E F G 1 PROBLEM 2.72 2 3 LET'S CONSIDER INTEREST RATES FROM 0% TO 20% 4 A= $10,000.00 $5,000.00 5 n= 5 10 6 7 PV OF PV OF 8 INTEREST 10K FOR 5 YR 5K FOR 10 YR 9 0.00% $50,000.00 =PV(0%,5,-10000) $50,000.00 =PV(0%,10,-5000) 10 1.00% $48,534.31 $47,356.52 11 2.00% $47,134.60 $44,912.93 12 3.00% $45,797.07 =PV(3%,5,-10000) $42,651.01 =PV(3%,10,-5000) 13 4.00% $44,518.22 $40,554.48 14 5.00% $43,294.77 $38,608.67 15 6.00% $42,123.64 $36,800.44 16 7.00% $41,001.97 $35,117.91 17 8.00% $39,927.10 $33,550.41 18 9.00% $38,896.51 $32,088.29 19 10.00% $37,907.87 $30,722.84 20 11.00% $36,958.97 $29,446.16 21 12.00% $36,047.76 $28,251.12 22 13.00% $35,172.31 $27,131.22 23 14.00% $34,330.81 $26,080.58 24 15.00% $33,521.55 $25,093.84 25 16.00% $32,742.94 $24,166.14 26 17.00% $31,993.46 $23,293.02 27 18.00% $31,271.71 $22,470.43 28 19.00% $30,576.35 $21,694.67 29 20.00% $29,906.12 =PV(20%,5,-10000) $20,962.36 =PV(20%,10,-5000) 30 31 PREFER TO RECEIVE YOUR MONEY QUICKER AT $10K FOR EACH OF 5 YEARS 32 33 PREFER TO PAY YOUR MONEY OVER A LONGER PERIOD AT $5K FOR EACH OF 10 YEARS

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 OR EACH OF33 10 YEARS

1 2 3 4 5 6 7

A PROBLEM 2.73

i= n= A(3 TO 10)= DISPLACED n=

6.00% 8 $10,000.00 2

30 31 32 33 34 35 36 37 38

39 40 41 42 43 44

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER

8 9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26 27 28 29

A(1 TO 8)= A(1 TO 8)= A(1 TO 8)=

$8,899.96 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.06)^2 $8,900.00 USING INTEREST TABLES THIS IS =$10,000*(P|F 6%,2) $8,899.96 USING EXCEL'S PV FUNCTION THIS IS =PV(6%,2,,-10000)

OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8. A(1 TO 8)= A(1 TO 8)=

i= n= A(3 TO 10)= DISPLACED n=

$8,900.22 USING INTEREST TABLES THIS IS =$10,000*(P|A 6%,8)*(P|F 6%,2)*(A|P 6%,8) $8,899.96 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(6%,8,-PV(6%,2,,-PV(6%,8,-10000)))

10.00% 8 $10,000.00 2

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER A(1 TO 8)= A(1 TO 8)= A(1 TO 8)=

$8,264.46 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.10)^2 $8,264.50 USING INTEREST TABLES THIS IS =$10,000*(P|F 10%,2) $8,264.46 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,2,,-10000)

OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8. A(1 TO 8)= A(1 TO 8)=

$8,264.46 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(10%,8,-PV(10%,2,,-PV(10%,8,-10000))) $8,264.33 USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,8)*(P|F 10%,2)*(A|P 10%,8)

1 2 3 4 5 6 7

A PROBLEM 2.74

i= n= A(3 TO 10)= DISPLACED n=

6.00% 10 $10,000.00 10

30 31 32 33 34 35 36 37 38

39 40 41 42 43 44

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER

8 9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26 27 28 29

A(11 TO 20)= A(11 TO 20)= A(11 TO 20)=

$17,908.48 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.06)^2 $17,908.50 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10) $17,908.48 USING EXCEL'S FV FUNCTION THIS IS =FV(6%,10,,-10000)

OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 11-20. A(11 TO 20)= A(11 TO 20)=

i= n= A(3 TO 10)= DISPLACED n=

$17,908.74 USING INTEREST TABLES THIS IS =$10,000*(F|A 6%,10)*(A|P 6%,10) $17,908.48 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(6%,10,-FV(6%,10,,-PV(6%,10,-10000)))

10.00% 10 $10,000.00 10

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER A(11 TO 20)= A(11 TO 20)= A(11 TO 20)=

$25,937.42 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.10)^2 $25,937.40 USING INTEREST TABLES THIS IS =$10,000*(F|P 10%,10) $25,937.42 USING EXCEL'S FV FUNCTION THIS IS =FV(10%,10,,-10000)

OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AT EOY 10, AND THEN USE THAT AMOUNT AS A PW TO DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES OVER YEARS 11-20. A(11 TO 20)= A(11 TO 20)=

$25,938.15 USING INTEREST TABLES THIS IS =$10,000*(F|A 10%,10)*(A|P 10%,10) $25,937.42 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(10%,10,-FV(10%,10,,-PV(10%,10,-10000)))

A 1 PROBLEM 2.75 2 3 4 5 6 7 8 9 10 11 12

i= n= A=

5.00% 10 $1,000.00

F= $12,577.89 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^20-1)/0.04 F= $12,577.89 USING INTEREST TABLES THIS IS =$1,000*(F|A 5%,10) F= $12,577.89 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,20,-7500)

A B C D E F G H 1 PROBLEM 2.76 2 3 a i= 8.00% 4 n= 8 5 A= $1,000.00 6 7 FINDING THE PW AT EOY 0 8 P= $5,746.64 USING COMPOUND INTEREST FORMULAS THIS IS 9 =1000*((1+0.08)^8-1)/(0.08*(1+0.08)^8) 10 P= $5,746.64 USING INTEREST TABLES THIS IS 11 =$1,000*(P|A 8%,8) 12 P= $5,746.64 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(8%,8,-1000) 14 15 b i= 8.00% 16 n= 8 17 A= $1,000.00 18 19 FINDING THE FW AT EOY 8 20 F= $10,636.63 USING COMPOUND INTEREST FORMULAS THIS IS 21 =1000*((1+0.08)^8-1)/0.08 22 F= $10,636.63 USING INTEREST TABLES THIS IS 23 =$1,000*(F|A 8%,8) 24 F= $10,636.63 USING EXCEL'S FV FUNCTION THIS IS 25 =FV(0.08,8,-1000) 26 27 28 c i= 8.00% 29 n= 8 30 A= $1,000.00 31 t= 11 THREE YEARS AFTER LAST DEPOSIT 32 33 FINDING THE FW AT EOY 11 34 F= $13,399.09 USING COMPOUND INTEREST FORMULAS THIS IS 35 =1000*(((1+0.08)^8-1)/0.08)*(1+0.08)^3 36 F= $13,399.07 USING INTEREST TABLES THIS IS 37 =$1,000*(F|A 8%,8)*F|P(8%,3) 38 F= $13,399.09 USING EXCEL'S FV FUNCTION THIS IS 39 =FV(8%,11,,PV(8%,8,1000))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A PROBLEM 2.77

A= i= n(investment)= n(withdrawal)=

$60,000.00 10.00% 19 1 YEAR BEFORE FIRST WITHDRAWAL 10 NUMBER OF WITHDRAWALS

FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND THE PW AT EOY 0. P= $60,281.15 USING COMPOUND INTEREST FORMULAS THIS IS =60000*((1+0.1)^10-1)/(0.1*(1+0.1)^10)*(1+0.1)^-19 P= $60,281.92 USING INTEREST TABLES THIS IS $60,000*(P|A 10%,10)*(P|F 10%,19) P= $60,281.15 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,20,,-PV(10%,10,-60000)) b

A= i= n(investment)= n(withdrawal)=

$60,000.00 15.00% 19 1 YEAR BEFORE FIRST WITHDRAWAL 10 NUMBER OF WITHDRAWALS

FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND THE PW AT EOY 0. P= $21,158.72 USING COMPOUND INTEREST FORMULAS THIS IS =60000*((1+0.15)^10-1)/(0.15*(1+0.15)^10)*(1+0.15)^-19 P= $21,160.14 USING INTEREST TABLES THIS IS $60,000*(P|A 15%,10)*(P|F 15%,19) P= $21,158.72 USING EXCEL'S PV FUNCTION THIS IS =PV(15%,20,,-PV(15%,10,-60000))

A B C D E F G H 1 PROBLEM 2.78 2 3 i= 7.00% 4 n= 12 5 P= $200,000.00 6 7 WITH THE FIRST PAYMENT AT THE END OF YEAR 1 8 A= $25,180.40 USING COMPOUND INTEREST FORMULAS THIS IS 9 =200000*(0.07*(1+0.07)^12)/((1+0.07)^12-1) 10 A= $25,180.00 USING INTEREST TABLES THIS IS 11 =$200,000*(A|P 7%,12) 12 A= $25,180.40 USING EXCEL'S PMT FUNCTION THIS IS 13 =PMT(0.07,12,-200000)

A PROBLEM 2.79

A= i1= n1=

$4,000.00 5.00% 3

i2=

8.00%

7 8

n2=

1 2 3 4 5

9 10 11 12 13 14 15 16 17 18 19

$12,000.00 10.00% 10

i2=

5.00%

21 22

n2=

FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD. F= $221,394.73 USING COMPOUND INTEREST FORMULAS THIS IS =12000*(((1+10%)^10-1)/10%)*(1+5%)^3 F= $221,395.63 USING INTEREST TABLES THIS IS =$12,000*(F|A 10%,10)*(F|P 5%,5) F= $221,394.73 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,3,,-FV(10%,10,-12000)) A= i1= n1=

$18,000.00 9.00% 5

i2=

7.00%

35 36

n2=

37 38 39 40 41 42 43

FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD. F= $18,528.23 USING COMPOUND INTEREST FORMULAS THIS IS =4000*(((1+5%)^3-1)/5%)*(1+8%)^5 F= $18,528.25 USING INTEREST TABLES THIS IS =$4,000*(F|A 5%,3)*(F|P 8%,5) F= $18,528.23 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,5,,-FV(5%,3,-4000)) A= i1= n1=

23 24 25 26 27 28 29 30 31 32 33

FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD. F= $185,091.25 USING COMPOUND INTEREST FORMULAS THIS IS =18000*(((1+9%)^5-1)/9%)*(1+7%)^8 F= $185,091.64 USING INTEREST TABLES THIS IS =$18,000*(F|A 9%,5)*(F|P 7%,8) F= $185,091.25 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,8,,-FV(9%,5,-18000))

A B 1 PROBLEM 2.80 2 3 a A= 4 i= 5 n= 6 7 F= 8 9 F= 10 11 F= 12 13 14 b A= 15 i= 16 n(deposits=) 17 n(more years) 18 19 F= 20 21 F= 22 23 F= 24 25 26 c 27 i= 28 A(1st)= 29 n(1st)= 30 A(2nd)= 31 n(2nd) 32 A(3rd)= 33 n(3rd)= 34 35 F= 36 37 38

$2,000.00 5.00% 15 $43,157.13 USING COMPOUND INTEREST FORMULAS THIS IS =2000*((1+0.05)^15-1)/0.05 $43,157.12 USING INTEREST TABLES THIS IS =$2,000*(F|A 5%,15) $43,157.13 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,15,-2000) $3,000.00 8.00% 10 5 $63,856.54 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(((1+0.08)^10-1)/0.08)*(1+0.08)^5 $63,856.61 USING INTEREST TABLES THIS IS =$3,000*(F|A 8%,10)*(F|P 8%,5) $63,856.54 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,5,,-FV(8%,10,-3000))

8.00% $2,000.00 5 $4,000.00 5 $6,000.00 5 $95,010.53 TABLES =$2,000*(F|A 8%,5)*(F|P 8%,10)+$4,000*(F|A 8%,5)*(F|P 8%,5)+$6,000*(F|A 8%,5) $95,010.55 EXCEL =FV(8%,5,-6000)+FV(8%,5,,-FV(8%,5,4000))+FV(8%,5+5,,-FV(8%,5,-2000))

A B 1 PROBLEM 2.81 2 3 i= A 4 1= n1= 5

5.00% $1,200.00 YEARS 1-5 5 DEPOSITS YEARS 1-5

A2=

n2=

4 WITHDRAWALS YEARS 4-7

8 9 10 11 12 13

t2=

4 START TIME OF WITHDRAWALS

P= P=

-$700.00 YEARS 4-7

$3,051.18 USING INTEREST TABLES THIS IS =$1,200*(P|A 5%,5)-$700*(P|A 5%,4)*(P|F 5%,3) $3,051.18 USING EXCEL'S FV FUNCTION THIS IS =PV(5%,5,-1200)-PV(5%,3,,-PV(5%,4,-700))

A 1 PROBLEM 2.82 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

SINCE THE AMOUNT PAID IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $1.00 IS SELECTED HERE P= $1.00 i= 7.000% A= $0.20 20% OF P n=

6.367 USING EXCEL'S NPER FUNCTION THIS IS =NPER(7%,0.2,-1)

COULD ALSO USE SOLVER TO DETERMINE n

6.367 <--SOLVER CHANGED CELL

$1.00 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(7%,n,-0.2)

P= n= A=

$1.00 7 $0.20

i= 9.196% USING EXCEL'S RATE FUNCTION THIS IS =RATE(7,0.2,-1) COULD ALSO USE SOLVER TO DETERMINE i i= 9.196% <--SOLVER CHANGED CELL P=

$1.00 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(i%,7,-0.2)

A 1 PROBLEM 2.83 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

SINCE THE AMOUNT OF THE LOAN IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $6.00 IS SELECTED HERE. P= $6.00 n= 7 A= $1.00 i=

4.009% USING EXCEL'S RATE FUNCTION THIS IS =RATE(7,0.2,-1)

COULD ALSO USE SOLVER TO DETERMINE i i=

4.009% <--SOLVER CHANGED CELL

$6.00 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(i,7,-C6)

A B C D E F G H I 1 PROBLEM 2.84 2 3 i= 9.00% n = 4 25 NUMBER OF DEPOSITS 1 5 A= $4,000.00 6 t= 28 TIME OF FIRST WITHDRAWAL n = 7 30 NUMBER OF WITHDRAWALS 2 8 FIRST, DETERMINE THE AMOUNT IN THE ACCOUNT RIGHT AFTER THE LAST a DEPOSIT AT EOY 25. THEN, FIND THE FW OF THAT AMOUNT ONE YEAR 9 BEFORE THE FIRST WITHDRAWAL AT EOY 27 10 11 F27= $402,532.54 USING COMPOUND INTEREST FORMULAS THIS IS 12 =4000*(((1+0.09)^25-1)/0.09)*(1+0.09)^2 13 F27= $402,532.56 USING INTEREST TABLES THIS IS 14 =$4,000*(F|A 9%,25)*(F|P 9%,2) 15 F27= $402,532.54 USING EXCEL'S FV FUNCTION THIS IS 16 =FV(9%,28-25-1,,-FV(9%,25,-4000)) 17 b USING THE ANSWER TO PART a, FIND THE PAYMENT AMOUNT OVER THE WITHDRAWAL PERIOD 18 19 20 A= $39,181.05 USING COMPOUND INTEREST FORMULAS THIS IS 21 =402532.54*(0.09*(1+0.09)^30)/((1+0.09)^30-1) 22 A= $39,182.52 USING INTEREST TABLES THIS IS 23 =$402,532.54*(A|P 9%,30) 24 A= $39,181.05 USING EXCEL'S PMT FUNCTION THIS IS 25 =PMT(9%,30,-402532.54) 26 27 28 c FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN 29 30 A= $36,227.93 =402532.54*0.09

A 1 PROBLEM 2.85 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 b 16 17 c 18 19 d 20 21 22 23 24 25 26 27 28 29 30 31

i= n DEPOSITS= A= n WITHDRAWALS=

12.00% 30 $7,500.00 ($5,000 FROM YOU + $2,500 FROM EMPLOYER) 30

$1,809,995.13 USING COMPOUND INTEREST FORMULAS THIS IS =7500*(((1+0.12)^30-1)/0.12) $1,809,995.10 USING INTEREST TABLES THIS IS =$7,500*(F|A 12%,30) $1,809,995.13 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,30,-7500)

F= F=

SUM(YOU)=

$150,000.00 =5000*30

SUM(EMPLOYER)=

$75,000.00 =2500*30

EARNINGS=

$1,584,995.13 $1,584,995.13

USING THE ANSWER TO PART a, FIND THE YEARLY AMOUNT OVER THE WITHDRAWAL PERIOD A= A= A=

$224,699.42 USING COMPOUND INTEREST FORMULAS THIS IS =1809995.13*(0.12*(1+0.12)^30)/((1+0.12)^30-1) $224,692.80 USING INTEREST TABLES THIS IS =$1,809,995.13*(A|P 12%,30) $224,699.42 USING EXCEL'S PMT FUNCTION THIS IS =PMT(12%,30,-1809995.13)

FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN INTEREST ONLY= $217,199.42 =1809995.13*0.12

A 1 PROBLEM 2.86 2 3 4 5 6 7 8 9 10 11 12 13 14 15

i= 6.00% P= $10,000.00 DEPOSIT AT EOY 0 A= -$1,000.00 WITHDRAWALS AT EOY 3-7 n1= 10 YEARS FROM DEPOSIT TO FINAL WITHDRAWAL n2= 5 YEARS OF WITHDRAWALS (3, 4, 5, 6, 7) n3=

YEARS FROM 5TH WITHDRAWAL TO FINAL WITHDRAWAL

FIND THE FW AT EOY 10 OF THE INITIAL DEPOSIT AND THE FIVE WITHDRAWALS F= $11,194.61 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10)-$1,000*(F|A 6%,5)*(F|P 6%,3) F= $11,194.61 USING EXCEL'S FV FUNCTION THIS IS =FV(6%,10,,-10000)+FV(6%,3,,-FV(6%,5,-(-1000)))

A 1 PROBLEM 2.87 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

12.00%

P= A= n1= n2=

$15,000.00 LOAN VALUE AT EOY 0 $3,000.00 PAYMENTS AT EOY 1, 2, 3, 4 4 YEARS UNTIL FINAL A=$3,000 PAYMENT 1 ADDITIONAL YEARS UNTIL FINAL PAYMENT

FIND THE LOAN VALUE AT EOY 5 AND SUBTRACT OFF THE PAYMENT VALUES AT EOY 5. WHAT'S LEFT IS THE FINAL LOAN PAYMENT AT EOY 5. F= $10,376.58 USING COMPOUND INTEREST FORMULAS THIS IS =15000*(1+0.12)^(4+1)-(3000*(((1+0.12)^4-1)/0.12))*(1+0.12)^1 F= $10,376.55 USING INTEREST TABLES THIS IS =$15,000*(F|P 12%,5)-$3,000*(F|A 12%,4)*(F|P 12%,1) F= $10,376.58 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,4+1,,-15000)+FV(12%,1,,-FV(12%,4,3000)) F=

$10,376.58 IS THE AMOUNT OF THE YEAR 5 PAYMENT

A B C D 1 PROBLEM 2.88 2 3 i= 9.00% 4 n1= 10 YEARS OF WITHDRAWALS n = 5 5 WITHDRAWALS REMAINING AT EOY 45 2 6 AMT45= $32,801.60 AMOUNT LEFT IN ACCT AT EOY 45 7 THE FOLLOWING WILL BE NEEDED IN THE LAST STEPS OF THE PROBLEM n3= 8 15 YEARS FROM DEPOSIT 1 TO EOY 40 n4= 9 10 YEARS FROM DEPOSIT 2 TO EOY 40 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

n5=

YEARS FROM DEPOSIT 3 TO EOY 40

FIRST, DETERMINE THE AMOUNT OF THE ANNUAL WITHDRAWALS A= $8,432.96 USING INTEREST TABLES THIS IS =$32,801.60*(A|P 9%,5) A= $8,433.04 USING EXCEL'S PMT FUNCTION THIS IS =PMT(9%,5,-32801.6) NOW KNOWING THE ANNUAL WITHDRAWAL, DETERMINE THE AMOUNT IN THE ACCOUNT AT EOY 40 AMT40= $54,120.41 USING INTEREST TABLES THIS IS =$8433.04*(P|A 9%,10) AMT40= $54,120.39 USING EXCEL'S PV FUNCTION THIS IS =PV(9%,10,-8433.04) NOW, DETERMINE THE VALUE AT EOY 40 OF THE THREE "$X" DEPOSITS AT EOY 25, 30, AND 35 AND SOLVE FOR X AMT40= =7.54846 USING INTEREST TABLES THIS IS TIMES X =(F|P 9%,15)+(F|P 9%,10)+(F|P 9%,5) TIMES X =(3.64248+2.36736+1.53862) TIMES X =7.54846 TIMES X X= $7,169.73 =$54,120.41/7.54846 AMT40=

7.54847 USING EXCEL'S FV FUNCTION THIS IS TIMES X =(FV(9%,15,,-1)+(FV(9%,10,,-1)+(FV(9%,5,,-1)))) X= $7,169.72 =54120.39/7.54847 ****************************************************** THIS PROBLEM MAY BETTER BE ANSWERED USING SOLVER LET X BE ANY VALUE AT THIS POINT. SET UP ALL FOLLOWING EQUATIONS AS IF THE VALUE OF X IS RIGHT. SOLVER WILL LATER BE USED TO CORRECTLY SEARCH FOR AND SET THE VALUE OF X X=

$7,169.73 <--SOLVER CHANGED CELL

SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40 AMT40= $54,120.44 USING INTEREST TABLES THIS IS X*(F|P 9%,15)+X*(F|P 9%,10)+X*(F|P 9%,5) NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50 A= $8,433.05 =$54,120.84*(A|P 9%,10) =$54,120.84*0.15582 NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45 AMT45= $32,801.60 <--SOLVER TARGET CELL =$8,433.11*(P|A 9%,5)

$7,169.72 <--SOLVER CHANGED CELL

TIMES X

A 53 54 55 56 57 58 59 60 61 62 63

SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40 AMT40= $54,120.39 USING EXCEL'S FV FUNCTION THIS IS =(FV(9%,15,,-X)+FV(9%,10,,-X)+(FV(9%,5,,-X)) NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50 A= $8,433.04 USING EXCEL'S PMT FUNCTION THIS IS =PMT(9%,10,-54120.91) NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45 AMT45= $32,801.60 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(9%,5,-8433.12)

P= i= i= i= n1=

$20,000.00 5% 6% 7% 10

AT EOY 30 YEARS 31-40 YEARS 41-50 YEARS 51 AND BEYOND YEARS AT 5%

n2=

YEARS AT 6%

n3=

YEARS AT 7%

n4=

YEARS OF WITHDRAWALS

11 12 13 14 15 16 17 18 19 20 21 22

n5=

YEARS OF WITHDRAWALS REMAINING AT EOY 65

1 2 3 4 5 6 7

23 24 25 26 27

A PROBLEM 2.89

FIRST, SOLVE FOR THE AMOUNT AVAILABLE AT EOY 60 AMT60= $114,767.37 USING INTEREST TABLES THIS IS =$20,000*(F|P 5%,10)*(F|P 6%,10)*(F|P 7%,10) A= $16,340.58 USING INTEREST TABLES THIS IS =$114,767.37*(A|P 7%,10) AMT60= $114,767.63 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,10,,-FV(6%,10,,-FV(5%,10,,-20000))) A= $16,340.33 USING EXCEL'S PMT FUNCTION THIS IS =PMT(7%,10,-114767.63)

SOLVE FOR THE PW OF THE 5 REMAINING WITHDRAWALS AT EOY 66-70 PLUS THE WITHDRAWAL DUE AT EOY 65 WDL65= $83,340.22 USING INTEREST TABLES THIS IS =$16,340.58*(P|A 7%,5)+$16,340.58 WDL65= $83,338.90 USING EXCEL'S PV FUNCTION THIS IS =PV(7%,5,-16340.33)+16340.33

A B C D E F G H I J K 1 PROBLEM 2.90 2 3 i= 10.00% 4 n= 8 5 6 EOY 0 1 2 3 4 5 6 7 8 7 CF -$2,500.00 $3,000.00 $4,500.00 $0.00 -$5,000.00 $0.00 -$1,000.00 $7,000.00 $3,000.00 8 FIRST, FIND THE PW OF THIS CASH FLOW SERIES. THEN FIND THE EQUIVALENT 9 VALUE OF "A" 10 P= $4,958.43 USING INTEREST TABLES THIS IS =$2,500+$3,000*(P|F 10%,1)+$4,500*(P|F 10%,2)-$5,000*(P|F 10%,4)11 $1,000*(P|F 10%,6)+$7,000*(P|F 10%,7)+$3,000*(P|F 10%,8) 12 A= $929.41 USING INTEREST TABLES THIS IS 13 =$4,958.43*(A|P 10%,8) 14 P= $4,958.37 USING EXCEL'S NPV FUNCTION THIS IS 15 =NPV(10%,3000,4500,0,-5000,0,-1000,7000,3000)-2500 16 A= $929.42 USING EXCEL'S PMT FUNCTION THIS IS 17 =PMT(C3,C4,-C10)

A 1 PROBLEM 2.91 2 3 a 4 5 b 6 7 c 8 9 10 11 USING (a) 12 13 USING (b) 14

B*(F|P i%,1)*(F|A i%,n)

B*(1+i)*((1+i)^n-1)/i

B= n= i=

$1,000.00 5 10.00%

$6,715.61 USING INTEREST TABLES THIS IS =$1,000*(F|P 10%,1)*(F|P 10%,5) $6,715.61 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.1)*((1+0.1)^5-1)/0.1

A B C D E F 1 PROBLEM 2.92 2 3 P|G FACTOR 4 5 i= 8.00% USING 8% FOR EXAMPLE CALC 6 n= 3 USING 3 FOR EXAMPLE CALC 7 P|G= 2.44500 USING COMPOUND INTEREST FORMULAS THIS IS 8 =(1-(1+3*0.08)*(1+0.08)^(-3))/(0.08^2) 9 10 11 F|G FACTOR NOT TABULATED IN APPENDIX A 12 13 i= 12.00% USING 12% FOR EXAMPLE CALC 14 n= 25 USING 25 FOR EXAMPLE CALC 15 F|G= 902.78225 USING COMPOUND INTEREST FORMULAS THIS IS 16 =((1+0.12)^25-(1+25*0.12))/(0.12^2) 17 18 19 A|G FACTOR 20 21 i= 10.00% USING 10% FOR EXAMPLE CALC 22 n= 10 USING 10 FOR EXAMPLE CALC 23 A|G= 3.72546 USING COMPOUND INTEREST FORMULAS THIS IS 24 =(1/0.10)-(10/0.10)*(0.10/((1+0.10)^10-1)) 25 26 P|G AND A|G CHECK OK WITH APPENDIX A

A B C D E F G H 1 PROBLEM 2.93 2 3 i= 5.00% 4 n= 5 A1= 5 $800.00 6 G= $100.00 7 8 P= $4,287.28 USING INTEREST TABLES THIS IS 9 =$800*(P|A 5%,5)+$100*(P|G 5%,5) 10 P= $4,287.27 USING EXCEL'S NPV FUNCTION 11 =NPV(5%,800,900,1000,1100,1200) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $800.00 18 2 $900.00 19 3 $1,000.00 20 4 $1,100.00 21 5 $1,200.00 22 23 P= $4,287.27 =NPV(5%,800,900,1000,1100,1200)+0

A B C D E F G H 1 PROBLEM 2.94 2 3 i= 6.00% 4 n= 7 A1= $5,000.00 5 6 G= $1,000.00 7 8 FV= $65,199.79 USING INTEREST TABLES THIS IS 9 =($5,000*(P|A 6%,7)+$1,000*(P|G 6%,7))*F|P 6%,7 10 FV= $65,199.82 USING EXCEL'S FV AND NPV FUNCTIONS 11 =FV(6%,7,,-NPV(6%,5000,6000,7000,8000,9000,10000,11000)) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $5,000.00 18 2 $6,000.00 19 3 $7,000.00 20 4 $8,000.00 21 5 $9,000.00 22 6 $10,000.00 23 7 $11,000.00 24 25 FV= $65,199.82 =FV(6%,7,,-(NPV(6%,5000,6000,7000,8000,9000,10000,11000)+0))

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

A B C D E F G H 1 PROBLEM 2.95 2 3 i= 8.00% 4 n= 6 A1= $12,000.00 5 6 G= -$2,000.00 7 8 P= $34,428.02 USING INTEREST TABLES THIS IS 9 =$12,000*(P|A 8%,6)-$2,000*(P|G 8%,6) 10 P= $34,428.01 USING EXCEL'S NPV FUNCTION 11 =NPV(8%,12000,10000,8000,6000,4000,2000) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $12,000.00 18 2 $10,000.00 19 3 $8,000.00 20 4 $6,000.00 21 5 $4,000.00 22 6 $2,000.00 23 24 P= $34,428.01 =NPV(8%,12000,10000,8000,6000,4000,2000)+0

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

A B C D E F G H 1 PROBLEM 2.96 2 3 i= 10.00% 4 n= 4 A1= $2,000.00 5 6 G= $500.00 7 8 a P= $8,528.80 USING INTEREST TABLES THIS IS 9 =$2,000*(P|A 10%,4)+$500*(P|G 10%,4) 10 P= $8,528.79 USING EXCEL'S NPV FUNCTION 11 =NPV(10%,2000,2500,3000,3500) 12 13 b A= $2,690.58 USING INTEREST TABLES THIS IS 14 =$8,528.80*(A|P 10%,4) 15 A= $2,690.59 USING INTEREST TABLES THIS IS 16 =$2,000+$500*(A|G 10%,4) 17 A= $2,690.58 USING EXCEL'S PMT FUNCTION 18 =PMT(10%,4,-8528.79) 19 20 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 21 22 EOY CF 23 0 $0.00 24 1 $2,000.00 25 2 $2,500.00 26 3 $3,000.00 27 4 $3,500.00 28 29 P= $8,528.79 =NPV(10%,2000,2500,3000,3500)+0 30 31 A= $2,690.58 =PMT(10%,4,-8528.79)

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A B C D E F G H I 1 PROBLEM 2.97 2 3 i= 12.00% 4 n= 6 A = 5 -$2,000.00 1 6 G= $1,000.00 7 8 P= $707.35 USING INTEREST TABLES THIS IS 9 -$2,000*(P|A 12%,6)+$1,000*(P|G 12%,6) 10 P= $707.36 USING EXCEL'S NPV FUNCTION THIS IS 11 =NPV(12%,-2000,-1000,0,1000,2000,3000) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 -$2,000.00 18 2 -$1,000.00 19 3 $0.00 20 4 $1,000.00 21 5 $2,000.00 22 6 $3,000.00 23 24 P= $707.36 =NPV(12%,-2000,-1000,0,1000,2000,3000)+0

A B C D E F G 1 PROBLEM 2.98 2 3 a i= 6.00% 4 n= 8 5 INITIAL CF= -$75,000.00 A1= 6 $3,000.00 7 G= $3,000.00 8 9 P= $3,154.11 USING INTEREST TABLES THIS IS 10 =-$75,000+3,000*(P|A 6%,8)+3,000*(P|G 6%,8) 11 P= $3,154.12 USING EXCEL'S NPV FUNCTION THIS IS

=NPV(6%,3000,3000+3000,3000+2*3000,3000+3*3000,3000 +4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000

12 13 14 15 16 17 18 19 20 21 22 23 24 25

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER EOY CF 0 -$75,000.00 1 $3,000.00 2 $6,000.00 3 $9,000.00 4 $12,000.00 5 $15,000.00 6 $18,000.00 7 $21,000.00 8 $24,000.00 P=

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

$3,154.12 =NPV(6%,3000,6000,9000,12000,15000,18000,21000,24000 )-75000

i= 7.00% n= 8 INITIAL CF= -$75,000.00 A1= $3,000.00 G= $3,000.00 P= P=

-$719.28 USING INTEREST TABLES THIS IS =-$75,000+3,000*(P|A 7%,8)+3,000*(P|G 7%,8) -$719.29 USING EXCEL'S NPV FUNCTION THIS IS =NPV(7%,3000,3000+3000,3000+2*3000,3000+3*3000,3000 +4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER EOY CF 0 -$75,000.00 1 $3,000.00 2 $6,000.00 3 $9,000.00 4 $12,000.00 5 $15,000.00 6 $18,000.00 7 $21,000.00 8 $24,000.00 P=

-$719.29 =NPV(7%,3000,6000,9000,12000,15000,18000,21000,24000 )-75000

A B C D E F G 1 PROBLEM 2.99 2 3 a i= 5.00% 4 n= 35 5 INITIAL CF= $0.00 A1= 6 $7,500.00 7 G= $1,000.00 8 9 FW= $1,783,808.45 USING ELECTRONIC INTEREST TABLES THIS IS 10 $0+$7,500*(F|A 5%,35)+$1,000*(P|G 5%,35)*(F|P 5%,35) 11 12 13 b i= 6.00% 14 n= 35 15 INITIAL CF= $0.00 A1= 16 $7,500.00 17 G= $1,000.00 18 19 FW= $2,109,673.85 USING ELECTRONIC INTEREST TABLES THIS IS 20 $0+$7,500*(F|A 6%,35)+$1,000*(P|G 6%,35)*(F|P 6%,35) 21 22 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 23 24 a FOR 5% b FOR 6% 25 EOY CF EOY CF 26 0 $0.00 0 $0.00 27 1 $7,500.00 1 $7,500.00 28 2 $8,500.00 2 $8,500.00 29 3 $9,500.00 3 $9,500.00 30 4 $10,500.00 4 $10,500.00 31 5 $11,500.00 5 $11,500.00 32 6 $12,500.00 6 $12,500.00 33 7 $13,500.00 7 $13,500.00 34 8 $14,500.00 8 $14,500.00 35 9 $15,500.00 9 $15,500.00 36 10 $16,500.00 10 $16,500.00 37 11 $17,500.00 11 $17,500.00 38 12 $18,500.00 12 $18,500.00 39 13 $19,500.00 13 $19,500.00 40 14 $20,500.00 14 $20,500.00 41 15 $21,500.00 15 $21,500.00 42 16 $22,500.00 16 $22,500.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

B C D 17 $23,500.00 18 $24,500.00 19 $25,500.00 20 $26,500.00 21 $27,500.00 22 $28,500.00 23 $29,500.00 24 $30,500.00 25 $31,500.00 26 $32,500.00 27 $33,500.00 28 $34,500.00 29 $35,500.00 30 $36,500.00 31 $37,500.00 32 $38,500.00 33 $39,500.00 34 $40,500.00 35 $41,500.00 FW= $1,783,808.45 =FV(5%,35,,-NPV(5%,CF YR 1:CF YR 35)+0)

E F G 17 $23,500.00 18 $24,500.00 19 $25,500.00 20 $26,500.00 21 $27,500.00 22 $28,500.00 23 $29,500.00 24 $30,500.00 25 $31,500.00 26 $32,500.00 27 $33,500.00 28 $34,500.00 29 $35,500.00 30 $36,500.00 31 $37,500.00 32 $38,500.00 33 $39,500.00 34 $40,500.00 35 $41,500.00 FW= $2,109,673.85 =FV(6%,35,,-NPV(6%,CF YR 1:CF YR 35)+0)

A B C D E F G H 1 PROBLEM 2.100 2 3 i= 5.00% 4 n= 5 5 INITIAL CF= -$90,000.00 A1= 6 $30,000.00 7 G= -$3,000.00 8 9 PW= $15,173.64 USING INTEREST TABLES THIS IS 10 =-$90,000+$30,000*(P|A 5%,5)-$3,000*(P|G 5%,5) 11 PW= $15,173.55 USING EXCEL'S NPV FUNCTION THIS IS =NPV(5%,30000,30000-3000,30000-2*3000,300003*3000,30000-4*3000)-90000 12

A B C D E F G H 1 PROBLEM 2.101 2 3 a i= 6.00% 4 n= 7 5 INITIAL CF= $0.00 A1= 6 $7,000.00 7 G= -$1,000.00 8 9 EQ(t=5)= $31,618.32 USING INTEREST TABLES THIS IS 10 =($7,000*(P|A 6%,7)-$1,000*(P|G 6%,7))*(F|P 6%,5) 11 12 b i= 10.00% 13 n= 7 14 INITIAL CF= $0.00 A1= 15 $7,000.00 16 G= -$1,000.00 17 18 EQ(t=5)= $34,329.34 USING INTEREST TABLES THIS IS 19 =($7,000*(P|A 10%,7)-$1,000*(P|G 10%,7))*(F|P 10%,5) 20 21 22 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 23 24 a EOY CF b EOY CF 25 0 $0.00 0 $0.00 26 1 $7,000.00 1 $7,000.00 27 2 $6,000.00 2 $6,000.00 28 3 $5,000.00 3 $5,000.00 29 4 $4,000.00 4 $4,000.00 30 5 $3,000.00 5 $3,000.00 31 6 $2,000.00 6 $2,000.00 32 7 $1,000.00 7 $1,000.00 33 34 EQ(t=5)= $31,618.22 EQ(t=5)= $34,329.33 =FV(6%,5,,-NPV(6%,CF YR 1:CF YR =FV(10%,5,,-NPV(10%,CF YR 35 7)+0) 1:CF YR 7)+0)

A B C D E 1 PROBLEM 2.102 2 3 i= 12.00% 4 n= 8 5 INITIAL CF= -$50,000.00 A1= 6 $13,000.00 7 G= -$1,000.00 8 9 PW= $107.87 USING INTEREST TABLES THIS IS 10 =-$50,000+$13,000*(P|A 12%,8)-$1,000*(P|G 12%,8) 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 -$50,000.00 16 1 $13,000.00 17 2 $12,000.00 18 3 $11,000.00 19 4 $10,000.00 20 5 $9,000.00 21 6 $8,000.00 22 7 $7,000.00 23 8 $6,000.00 24 25 PW= $107.87 USING EXCEL'S NPV FUNCTION THIS IS 26 =NPV(12%,CF YR 1:CF YR 8)-50000

A B C D 1 PROBLEM 2.103 2 3 i= 10.00% 4 n= 8 5 INITIAL CF= -$50,000.00 A1= 6 $13,000.00 7 G= -$1,000.00 8 9 A= $623.52 USING INTEREST TABLES THIS IS 10 =-$50,000*(A|P 10%,8)+$13,000-$1,000*(A|G 10%,8) 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 -$50,000.00 16 1 $13,000.00 17 2 $12,000.00 18 3 $11,000.00 19 4 $10,000.00 20 5 $9,000.00 21 6 $8,000.00 22 7 $7,000.00 23 8 $6,000.00 24 25 A= $623.32 USING EXCEL'S PMT AND NPV FUNCTIONS THIS IS 26 =PMT(10%,8,-(NPV(10%,CF YR 1:CF YR 8)-50000))

E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A B C D E F G H I 1 PROBLEM 2.104 2 3 4 i= 8.00% 5 n= 8 6 INITIAL CF= -$50,000.00 A1= 7 $13,000.00 8 G= -$1,000.00 9 10 FW= $12,771.82 USING INTEREST TABLES THIS IS 11 =(-$50,000+$13,000*(P|A 8%,8)-$1,000*(P|G 8%,8))*(F|P 8%,8) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 -$50,000.00 17 1 $13,000.00 18 2 $12,000.00 19 3 $11,000.00 20 4 $10,000.00 21 5 $9,000.00 22 6 $8,000.00 23 7 $7,000.00 24 8 $6,000.00 25 26 FW= $12,771.80 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 27 =FV(8%,8,,-(NPV(8%,CF YR 1:CF YR 8)-50000))

A B C D E F G H I 1 PROBLEM 2.105 2 3 i= 6.00% 4 n= 8 5 INITIAL CF= -$50,000.00 A1= 6 $13,000.00 7 G= -$1,000.00 8 9 FIRST, DETERMINE THE PW OF THE CASH FLOW SERIES 10 PW= $10,885.69 USING INTEREST TABLES THIS IS 11 =-$50,000+$13,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 12 NOW, DETERMINE THE VALUE OF X FOR THE EQUIVALENT SERIES X, 2X, 3X, …, 8X 13 PW= $10,885.69 =X*(P|A 6%,8)+X*(P|G 6%,8) 14 $10,885.69 =X*(6.20979+19.84158) 15 $10,885.69 =26.05137*X 16 X= $417.85 17 18 THIS CAN ALSO BE WELL APPROACHED USING SOLVER AS FOLLOWS 19 FIRST, DETERMINE THE PW OF THE ORIGINAL CASH FLOW SERIES. THEN, LET X BE ANY VALUE AND SET UP A TABLE OVER 8 YEARS ASSUMING THE VALUE OF X IS CORRECT. DETERMINE THE PW OF THE CASH FLOWS IN THE TABLE USING THE CELL WHERE YOUR VALUE OF X IS STORED. THEN, USE SOLVER TO DETERMINE THE VALUE OF X THAT MAKES THE PW OF THE CASH FLOWS EQUAL TO THE PW VALUE OF THE ORIGINAL CASH FLOW 20 SERIES 21 22 X= $417.86 <--SOLVER CHANGED CELL 23 24 EOY CF EOY CF 25 0 -$50,000.00 0 0 26 1 $13,000.00 1 $417.86 27 2 $12,000.00 2 $835.71 28 3 $11,000.00 3 $1,253.57 29 4 $10,000.00 4 $1,671.43 30 5 $9,000.00 5 $2,089.28 31 6 $8,000.00 6 $2,507.14 32 7 $7,000.00 7 $2,925.00 33 8 $6,000.00 8 $3,342.85 34 35 PW= $10,885.74 PW= $10,885.74 <--SOLVER TARGET CELL 36 USING EXCEL'S NPV FUNCTION USING EXCEL'S NPV FUNCTION 37 =NPV(6%,CF YR 1:CF YR 8)-50000 =NPV(6%,CF YR 1:CF YR 8)+0

A B C D E F G H 1 PROBLEM 2.106 2 3 i= 6.00% 4 n= 8 5 INITIAL CF= -$45,000.00 A1= 6 $12,000.00 7 G= -$1,000.00 8 9 PW= $9,675.90 USING INTEREST TABLES THIS IS 10 =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 11 AMT6= $13,725.46 USING INTEREST TABLES THIS IS 12 =$9,675.90*(F|P 6%,6) 13 14 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 15 16 EOY CF 17 0 -$45,000.00 18 1 $12,000.00 19 2 $11,000.00 20 3 $10,000.00 21 4 $9,000.00 22 5 $8,000.00 23 6 $7,000.00 24 7 $6,000.00 25 8 $5,000.00 26 27 PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 28 00)-45000 29 AMT6= $13,725.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(6%,6,,(NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 30 00)-45000))

A B C D 1 PROBLEM 2.107 2 3 i= 6.00% n1= 4 8 YEARS IN ORIGINAL GRADIENT SERIES 5 INITIAL CF= -$45,000.00 A1= 6 $12,000.00 7 G= -$1,000.00 8 t= 3 YEAR BEFORE ANNUAL SERIES FROM 4 TO 7 n2= 9 4 YEARS IN UNIFORM ANNUAL SERIES 10 11 PW= $9,675.90 USING INTEREST TABLES THIS IS 12 =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 13 AMT3= $11,524.19 USING INTEREST TABLES THIS IS 14 =$9,675.90*(F|P 6%,3) 15 A(4-7)= $3,325.77 USING INTEREST TABLES THIS IS 16 =$11,524.19*(A|P 6%,4) 17 18 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 19 20 EOY CF 21 0 -$45,000.00 22 1 $12,000.00 23 2 $11,000.00 24 3 $10,000.00 25 4 $9,000.00 26 5 $8,000.00 27 6 $7,000.00 28 7 $6,000.00 29 8 $5,000.00 30 31 PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS 32 =NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000 33 AMT3= $11,524.21 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 34 =FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-4500 35 A(4-7)= $3,325.79 USING EXCEL'S PMT FUNCTION THIS IS 36 =PMT(6%,4,-11524.21)

E F 1 2 3 YEARS IN 4 ORIGINAL GRADIENT SERIES 5 6 7 YEAR BEFORE 8 ANNUAL SERIES FROM 4 TO 7 YEARS IN 9 UNIFORM ANNUAL SERIES 10 USING INTEREST 11 TABLES THIS IS =-$45,000+$12,000*(P|A 12 6%,8)-$1,000*(P|G 6%,8) USING INTEREST 13 TABLES THIS IS =$9,675.90*(F|P 14 6%,3) USING INTEREST 15 TABLES THIS IS =$11,524.19*(A|P 16 6%,4) 17 BULATED CASH 18 FLOWS TO CHECK ANSWER 19 20 21 22 23 24 25 26 27 28 29 30 USING EXCEL'S 31 NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000 32 USING EXCEL'S 33 FV AND NPV FUNCTIONS THIS IS =FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000)) 34 USING EXCEL'S 35 PMT FUNCTION THIS IS =PMT(6%,4,-11524.21) 36

A B C D E F G H 1 PROBLEM 2.108 2 3 FROM PROBLEM 2.106: 4 i= 6.00% 5 n= 8 6 INITIAL CF= -$45,000.00 A1= 7 $12,000.00 8 G= -$1,000.00 9 PW= $9,675.90 USING INTEREST TABLES THIS IS 10 =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 11 NOW, SET UP A NEW GRADIENT SERIES THAT HAS THE SAME PW AS THE 12 ORIGINAL SERIES 13 14 PW= $9,675.90 USING INTEREST TABLES THIS IS =A1*(P|A 6%,8)+G*(P|G 6%,8) 15 A8= 16 WE KNOW $10,000 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

WE KNOW PW=

$10,000-7*G $9,675.90 =-$45,000+($10,000-7*G)*(P|A 6%,8)+G*(P|G 6%,8) =-$45,000+($10,000-7*G)*6.20979+G*19.84158 =$17,097.90-23.62695*G $314.13

THEREFORE A8=

$10,000.00 GIVEN IN PROBLEM

A1=

$7,801.07 =10000-7*314.13 $314.13

THIS IS EASIER DONE USING SOLVER AS FOLLOWS FIRST, FIND THE PW OF THE ORIGINAL GRADIENT SERIES EOY 0 1 2 3 4 5 6 7 8 PW=

44 45 46 47 48 49

A1=

CF -$45,000.00 $12,000.00 $11,000.00 $10,000.00 $9,000.00 $8,000.00 $7,000.00 $6,000.00 $5,000.00 $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 00)-45000

NOW, SET THE GRADIENT AMOUNT "G" TO ANY VALUE AND GO FORWARD AS IF IT IS THE CORRECT VALUE G=

$314.13 <--SOLVER CHANGED CELL

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

NOW, SET UP ANOTHER TABLE OF CASH FLOWS USING THE FACT THAT A8=$10,000, A1=$10,000-7*G, AND A0=-$45,000. THEN, USE SOLVER TO FIND THE PW OF THE SERIES EQUAL TO THAT OF THE ORIGINAL SERIES WHILE CHANGING THE VALUE OF G A8=

$10,000.00 GIVEN IN PROBLEM

EOY 0 1 2 3 4 5 6 7 8

CF -$45,000.00 $7,801.08 $8,115.21 $8,429.34 $8,743.47 $9,057.60 $9,371.74 $9,685.87 $10,000.00

PW=

$9,675.95 <--SOLVER TARGET CELL =NPV(6%,CF YR 1:CF YR 8)-45000

A 1 PROBLEM 2.109 2 3 4 5 6 7 8 a 9 10 11 12 13 b 14 15 16

i= n= A1=

8.00% 5 $500.00 $100.00

P= $2,733.60 USING INTEREST TABLES THIS IS =$500*(P|A 8%,5)+$100*(P|G 8%,5) P= $2,733.60 USING EXCEL'S NPV FUNCTION THIS IS =NPV(C3,500,600,700,800,900) A= A=

$684.65 USING INTEREST TABLES THIS IS =$500+$100*(A|G 8%,5) $684.65 USING EXCEL'S PMT FUNCTION THIS IS =PMT(8%,5,-2733.60)

A 1 PROBLEM 2.110 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 b 16 17 18 19 20

i= n= A1= G= P= F= F=

A= A= A=

12.00% 25 $1,000.00 $200.00 $18,464.07 USING INTEREST TABLES THIS IS =$1,000*(P|A 12%,25)+$200*(P|G 12%,25) $313,890.26 USING INTEREST TABLES THIS IS =$18,464.07*(F|P 12%,25) $313,890.35 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,25,,-18464.07) $2,354.17 USING INTEREST TABLES THIS IS =$1,000+$200*(A|G 12%,25) $2,354.18 USING INTEREST TABLES THIS IS =$313,890.35*(A|F 12%,25) $2,354.17 USING EXCEL'S PMT FUNCTION THIS IS =PMT(12%,25,,-313890.35)

A 1 PROBLEM 2.111 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 b 16 17 18 19 20

i= n= A1=

10.00% 10 $7,000.00 -$300.00

$36,144.59 USING INTEREST TABLES THIS IS =$7,000*(P|A 10%,10)-$300*(P|G 10%,10) F= $93,749.66 USING INTEREST TABLES THIS IS =$36,144.59*(F|P 10%,10) F= $93,749.75 USING EXCEL'S FV FUNCTION THIS IS =FV(10%,10,,-36144.59)

A= A= A=

$2,354.17 USING INTEREST TABLES THIS IS =$7,000-$300*(A|G 10%,10) $5,882.80 USING INTEREST TABLES THIS IS =$93,749.66*(A|F 10%,10) $5,882.37 USING EXCEL'S PMT FUNCTION THIS IS =PMT(10%,10,,-93749.75)

A B C D E F G 1 PROBLEM 2.112 2 3 i= 8.00% 4 n= 6 5 P= $140,000.00 A1= 6 $11,000.00 7 X= G 8 a THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE 9 GRADIENT PAYMENT G. 10 11 PW= USING INTEREST TABLES THIS IS 12 =$11,000*(P|A 8%,6)+G*(P|G 8%,6) 13 =$11,000*4.62288+G*10.52327 14 SO $140,000.00 =$50,851.68+G*10.52327 15 G=X $8,471.54 =(140000-50851.68)/10.52327 16

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

40 41 42

THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G. G=X EOY 0 1 2 3 4 5 6 P=

LAST PAYMENT

i= n= P= G=X

CF $11,000.00 $19,471.54 $27,943.08 $36,414.62 $44,886.16 $53,357.69 $140,000.00 <--SOLVER TARGET CELL =NPV(8%,CF YR 1:CF YR 6)+0 $53,357.69 =11000+5*8471.54 8.00% 6 $140,000.00 -$7,500.00

THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE GRADIENT IS KNOWN, SOLVE FOR THE FIRST PAYMENT A1. PW= $140,000.00 USING INTEREST TABLES THIS IS $140,000.00 =A1*(P|A 8%,6)-$7,500*(P|G 8%,6)

43 44

$8,471.54 <--SOLVER CHANGED CELL

SO A1=

$140,000.00 =A1*4.62288-$7,500*10.52327 $140,000.00 =A1*4.62288-$78,924.53 $47,356.74 =(140000+78924.53)/4.62288

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "A1" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF A1 TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF A1. A1= EOY 0 1 2 3 4 5 6 P=

$47,356.75 <--SOLVER CHANGED CELL CF $47,356.75 $39,856.75 $32,356.75 $24,856.75 $17,356.75 $9,856.75 $140,000.00 <--SOLVER TARGET CELL =NPV(8%,CF YR 1:CF YR 6)+0

1 2 3 4 5 6 7 8 9

A PROBLEM 2.113

i= n= P= A= A1= X= a

10 11 12 13 14 15 16 17

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

10.00% 9 $170,000.00 $10,000.00 YEARS 1, 2, 3, 4 $11,000.00 YEAR 5 G

THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE GRADIENT PAYMENT G. PW=

USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,9)+G*(P|G 10%,6)*(P|F 10%,3) =$10,000*5.75902+G*9.68417*0.75131 SO $170,000.00 =$57590.20+G*7.27581 G=X= $15,449.80 $15,449.80 THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G. G=X= EOY 0 1 2 3 4 5 6 7 8 9 P=

$15,449.68 <--SOLVER CHANGED CELL CF $10,000.00 $10,000.00 $10,000.00 $10,000.00 $25,449.68 $40,899.37 $56,349.05 $71,798.74 $87,248.42 $170,000.00 <--SOLVER TARGET CELL =NPV(10%,CF YR 1:CF YR 9)+0

b LAST PAYMENT= $87,248.42 =10000+5*15449.68 c

TOTAL INTEREST PAID= $151,745.27 =SUM(CF YR 0:CF YR 9)-170000

A B C D E F G H 1 PROBLEM 2.114 2 3 i= 10.00% 4 n= 5 A = 5 $10,000.00 1 6 G= -$1,000.00 7 8 P= $31,046.10 USING INTEREST TABLES THIS IS 9 =$10,000*(P|A 10%,5)-$1,000*(P|G 10%,5) 10 AMT3= $41,322.36 USING INTEREST TABLES THIS IS 11 $31,046.10*(F|P 10%,3) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $10,000.00 18 2 $9,000.00 19 3 $8,000.00 20 4 $7,000.00 21 5 $6,000.00 22 23 AMT3= $41,322.31 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS =NPV(10%,7000,6000)+FV(10%,2,,-10000)+FV(10%,1,,24 9000)+8000

A 1 PROBLEM 2.115 2 3 a 4 5 6 7

n= A0=

4 -$10,000.00

A1=

$3,000.00 $1,000.00

THIS PROBLEM, IN WHICH THE VALUE OF THE INTEREST RATE IS TO BE FOUND, IS BEST APPROACHED USING SOLVER. THIS IS DUE TO THE DIFFICULTY OF TRYING TO SOLVE ANALYTICALLY FOR THE INTEREST RATE USING FORMULAS OR INTERPOLATION. BEGIN BY SETTING A CELL TO HOUSE THE INTEREST RATE. SELECT ANY INTEREST RATE FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

10 11 12 13

24.8883% <--SOLVER CHANGED CELL

NOW, DEVELOP A FORMULA FOR THE OVERALL PW AS A FUNCTION OF THE INTEREST RATE. THEN, USE SOLVER TO SET THE PW VALUE EQUAL TO 0 BY CHANGING THE INTEREST RATE i.

14 15 16 17 18 19

37 38 39 40 41 42 43 44

8 9

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

PW=

$0.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =-10000+3000*((1+i)^4-1)/(i*(1+i)^4)+1000*(1-(1+4*i)*(1+i)^(-4))/(i^2)

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE INTEREST RATE FOUND USING SOLVER BELOW IS THE SAME VALUE FOUND ABOVE. i=

24.8883% <--SOLVER CHANGED CELL

EOY CF 0 -$10,000.00 1 $3,000.00 2 $4,000.00 3 $5,000.00 4 $6,000.00 P=

$0.00 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(i%,3000,4000,5000,6000)-10000 24.8883%

BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE EQUAL ANNUAL INCOMES, "A." SELECT ANY VALUE FOR "A" IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE. A= P=

$4,226.00 <--SOLVER CHANGED CELL $0.00 <--SOLVER TARGET CELL FORMULAS =-10000+A*((1+0.2489)^4-1)/(0.2489*(1+0.2489)^4)

45 46 47 48 49 50 51 52 53 54 55 56 57 58

B C D E F G H SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE EQUAL ANNUAL INCOME "A" FOUND BELOW IS THE SAME VALUE FOUND ABOVE. A=

$4,226.00 <--SOLVER CHANGED CELL

EOY CF 0 -$10,000.00 1 $4,226.00 2 $4,226.00 3 $4,226.00 4 $4,226.00 P=

$0.00 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(24.8883%,4226,4226,4226,4226)-10000

A B C D E F G 1 PROBLEM 2.116 2 3 a P= INR 20,000,000.00 4 i= 5.00% 5 n= 10 A1= 6 INR 2,000,000.00 7 X= G 8 9 P= INR 20,000,000.00 USING INTEREST TABLES THIS IS 10 INR 20,000,000.00 =INR 2,000,000*(P|A 5%,10)+G*(P|G 5%,10) 11 INR 20,000,000.00 =INR 2,000,000*7.72173+G*31.65205 12 INR 20,000,000.00 =INR 15,443,460+G*31.65205 13 G=X= INR 143,957.18 =(20000000-15443460)/31.65205 14 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF G=X FOUND USING SOLVER BELOW IS 15 ESSENTIALLY THE SAME VALUE FOUND ABOVE. 16 17 G=X= INR 143,956.88 <--SOLVER CHANGED CELL 18 19 EOY CF 20 0 INR 0.00 21 1 INR 2,000,000.00 22 2 INR 2,143,956.88 23 3 INR 2,287,913.77 24 4 INR 2,431,870.65 25 5 INR 2,575,827.53 26 6 INR 2,719,784.41 27 7 INR 2,863,741.30 28 8 INR 3,007,698.18 29 9 INR 3,151,655.06 30 10 INR 3,295,611.94 31 32 P= INR 20,000,000.00 <--SOLVER TARGET CELL 33 USING EXCEL'S NPV FUNCTION THIS IS 34 =NPV(5%,CF YR 1:CF YR 10)+0 35 36 b AMT5= INR 12,960,976.54 USING INTEREST TABLES THIS IS =INR 20,000,000*(F|P 5%,5)-2,000,000(F|A 37 5%,5)-143,957.18(P|G 5%,5)(F|P 5%,5) 38 AMT5= INR 12,961,013.55 USING INTEREST TABLES THIS IS =INR 2,719,784.41*(P|A 5%,5)+INR 39 143,956.88*(P|G 5%,5) 40 AMT5= INR 12,961,004.03 USING EXCEL'S NPV FUNCTION THIS IS 41 =NPV(5%,CF YR 6:CF YR 10)

A B C D E F G H I J K L M N O 1 PROBLEM 2.117 2 3 i= 7.00% 4 5 EOY -1 0 1 2 3 4 5 6 7 8 9 10 6 CF $1,200 $1,000 $800 $500 $500 $500 $500 $0 -$800 -$800 $0 $1,500 7 8 9 10 11 12 TO FIND THE VALUE OF AMT5, 13 14 AMT5= $6,189.74 USING INTEREST TABLES THIS IS =(($1,200-$200*(A|G 7%,3))*(F|A 7%,3)*(P|F 7%,2)+$500*(P|A 7%,4)*(P|F 7%,2)-$800*(F|A 7%,2)*(P|F 7%,9)+$1,500*(P|F 15 7%,11))*(F|P 7%,6) 16 17 CHECK THIS USING EXCEL'S NPV AND FV FUNCTIONS 18 19 AMT5= $6,189.73 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS 20 =NPV(7%,CF YR 6:CF YR 10)+FV(7%,7,,-NPV(7%,CF YR -1:CF YR 5))

A 1 PROBLEM 2.118 2 3 4 5

i= n= A11=

8.00% 40 $2,000.00

G1=

$1,000.00

n1=

A12=

$21,000.00

G2=

-$1,000.00

10 11 12 13 14

n2=

30 31 32 33 34 35

36 37 38 39 40 41

42 43

FIRST, FIND THE PW OF THE CASH FLOW PROFILE. P=

15 16

17 18 19 20 21 22 23 24 25 26 27 28 29

$118,139.04 USING INTEREST TABLES THIS IS =$2,000*(P|A 8%,20)+$1,000*(P|G 8%,20)+($21,000*(P|A 8%,20)-$1,000*(P|G 8%,20))*(P|F 8%,20)

NOW, LET X EQUAL THE FIRST OF 40 AMOUNTS IN A GRADIENT SERIES WITH GRADIENT G=$500. SOLVE FOR THE PW OF THIS GRADIENT SERIES. G= P=

$500.00 $118,139.04 USING INTEREST TABLES THIS IS $118,139.04 =X*(P|A 8%,40)+$500*(P|G 8%,40) $118,139.04 =X*11.92461+$500*126.04220 $118,139.04 =11.92461*X+$63,021.10

X= $4,622.20 =(118139.04-63021.1)/11.92461 ********** OR, RATHER THAN PERFORM THE ABOVE CALCULATIONS, CAN USE SOLVER BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE. X= G=

$4,622.20 <--SOLVER CHANGED CELL $500.00

NOW, DEVELOP A FORMULA FOR THE PW AS A FUNCTION OF X. THEN, USE SOLVER TO SET THE PW VALUE TO ITS TARGET VALUE BY CHANGING THE VALUE OF X. P=

$118,139.04 <--SOLVER TARGET CELL USING INTEREST TABLES THIS IS =X*(P|A 8%,40)+$500*(P|G 8%,40)

********** SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF X FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE. BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

A 45 46 47

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

B X=

$4,622.18 <--SOLVER CHANGED CELL

FIRST SOLVE FOR THE PW OF THE ORIGINAL GRADIENT SERIES. THEN, ADJUST THE PW OF THE NEW GRADIENT SERIES WITH FIRST AMOUNT X AND GRADIENT G=500 TO THE PW OF THE ORIGINAL SERIES BY ADJUSTING THE VALUE OF X. NOTE THAT THE VALUE OF X BELOW IS ESSENTIALLY THE SAME AS THE VALUE FOUND ABOVE.

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 P=

ORIGINAL CF $0.00 $2,000.00 $3,000.00 $4,000.00 $5,000.00 $6,000.00 $7,000.00 $8,000.00 $9,000.00 $10,000.00 $11,000.00 $12,000.00 $13,000.00 $14,000.00 $15,000.00 $16,000.00 $17,000.00 $18,000.00 $19,000.00 $20,000.00 $21,000.00 $21,000.00 $20,000.00 $19,000.00 $18,000.00 $17,000.00 $16,000.00 $15,000.00 $14,000.00 $13,000.00 $12,000.00 $11,000.00 $10,000.00 $9,000.00 $8,000.00 $7,000.00 $6,000.00 $5,000.00 $4,000.00 $3,000.00 $2,000.00

NEW CF $0.00 $4,622.18 $5,122.18 $5,622.18 $6,122.18 $6,622.18 $7,122.18 $7,622.18 $8,122.18 $8,622.18 $9,122.18 $9,622.18 $10,122.18 $10,622.18 $11,122.18 $11,622.18 $12,122.18 $12,622.18 $13,122.18 $13,622.18 $14,122.18 $14,622.18 $15,122.18 $15,622.18 $16,122.18 $16,622.18 $17,122.18 $17,622.18 $18,122.18 $18,622.18 $19,122.18 $19,622.18 $20,122.18 $20,622.18 $21,122.18 $21,622.18 $22,122.18 $22,622.18 $23,122.18 $23,622.18 $24,122.18

$118,138.78 $118,138.78 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(8%,NEW CF YR 1: NEW CF YR 40)+CF YR 0

A B 1 PROBLEM 2.119 2 3 EOY 4 CF 5 6 i= 7 n= A1= 8 9 G= 10 11 PW= 12 13 14 PW= 15

0 $100

2 3 4 5 6 7 8 9 10 $80 $60 $40 $20 $0 -$20 -$40 -$60 -$80 -$100

18.00% 11 $ 100.00 -$20.00 $ 172.48 USING INTEREST TABLES THIS IS =($100*(P|A 18%,11)-$20*(P|G 18%,11))*(F|P18%,1) $172.48 USING EXCEL'S FV FUNCTION THIS IS =FV(18%,1,,-NPV(18%,100,80,60,40,20,0,-20,-40,-60,-80,-100))

A 1 PROBLEM 2.120 2 3 4 5 6 7 8 9 10 11 12

TOTAL EOY CF1 CF2 CF3 CF4 CF 0 $800.00 $800.00 1 $950.00 $0.00 $950.00 2 $950.00 -$450.00 $500.00 3 $950.00 -$900.00 $50.00 4 $950.00 -$1,350.00 -$400.00 5 -$600.00 -$600.00 6 -$600.00 -$600.00 7 -$600.00 -$600.00

A 1 PROBLEM 2.121 2 3 4 5 6 7 8 9 10 11 12 13 14

EOY CF1 CF2 CF3 CF 0 -$7,000.00 -$7,000.00 1 $0.00 2 $0.00 3 $0.00 4 $0.00 5 $1,850.00 $0.00 $1,850.00 6 $1,850.00 $200.00 $2,050.00 7 $1,850.00 $400.00 $2,250.00 8 $1,850.00 $600.00 $2,450.00 9 $1,850.00 $800.00 $2,650.00 10 $1,850.00 $1,000.00 $2,850.00

A B C D E F G H I 1 PROBLEM 2.123 2 P|A1 FACTOR 3 4 5 i= USING 7.00%7% FOR EXAMPLE CALC 6 j= USING 5.00%5% FOR EXAMPLE CALC 7 n= USING 10 10 FOR EXAMPLE CALC P|A = 8 CHECKS WITH GEOMETRIC 8.59763 SERIES-PRESENT WORTH TABLE 1 9 10 F|A1 FACTOR 11 12 13 i= 7.00% USING 7% FOR EXAMPLE CALC 14 j= 5.00% USING 5% FOR EXAMPLE CALC 15 n= 10 USING 10 FOR EXAMPLE CALC F|A1= 16.91284 CHECKS WITH GEOMETRIC SERIES-FUTURE WORTH TABLE 16 17 18 A|A1 FACTOR 19 20 21 i= 7.00% USING 7% FOR EXAMPLE CALC 22 j= 5.00% USING 5% FOR EXAMPLE CALC 23 n= 10 USING 10 FOR EXAMPLE CALC A|A1= 1.22411 NOT TABULATED IN APPENDIX A 24 25 26 NOW, COMPLETING THE PROBLEM: 27 A1= $1,000.00 28 29 i= 7.00% 30 j= 5.00% 31 32 A= $1,224.11 USING A|A1 FACTOR 33 34 35 36 37 38 39 40 41

=$1,000*1.22411 A=

$1,224.13 USING P|A1 FACTOR * A|P FACTOR =$1,000*(P|A1 7%,5%,10)*(A|P 7%,10) =$1,000*8.59763*0.14238

$1,224.15 USING F|A1 FACTOR * A|F FACTOR =$1,000*(F|A1 7%,5%,10)*(A|F 7%,10) =$1,000*16.91284*0.07238

A B C D E F G 1 PROBLEM 2.124 2 3 i= 5.00% 4 n= 30 A = 5 $7,500.00 1 6 j= 5.00% 7 8 F= $926,130.53 USING INTEREST TABLES THIS IS =$7,500*(F|A1 5%,5%,30) 9 10 ********** 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 16 1 $7,500.00 =$7,500*(1+0.05)^(1-1) 17 2 $7,875.00 =$7,500*(1+0.05)^(2-1) 18 3 $8,268.75 19 4 $8,682.19 20 5 $9,116.30 21 6 $9,572.11 22 7 $10,050.72 23 8 $10,553.25 24 9 $11,080.92 25 10 $11,634.96 26 11 $12,216.71 27 12 $12,827.55 28 13 $13,468.92 29 14 $14,142.37 30 15 $14,849.49 31 16 $15,591.96 32 17 $16,371.56 33 18 $17,190.14 34 19 $18,049.64 35 20 $18,952.13 36 21 $19,899.73 37 22 $20,894.72 38 23 $21,939.46 39 24 $23,036.43 40 25 $24,188.25 41 26 $25,397.66 42 27 $26,667.55 43 28 $28,000.92 44 29 $29,400.97 45 30 $30,871.02 =$7,500*(1+0.05)^(30-1) 46 47 F= $926,130.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 48 =FV(5%,30,,-NPV(5%,CF YR 1:CF YR 30)+0)

A B C D E F G 1 PROBLEM 2.125 2 3 i= 6.00% 4 n= 30 A = 5 $7,500.00 1 6 j= 6.00% 7 8 F= $1,219,137.30 USING INTEREST TABLES THIS IS =$7,500*(F|A1 6%,6%,30) 9 10 ********** 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 16 1 $7,500.00 =$7,500*(1+0.06)^(1-1) 17 2 $7,950.00 =$7,500*(1+0.06)^(2-1) 18 3 $8,427.00 19 4 $8,932.62 20 5 $9,468.58 21 6 $10,036.69 22 7 $10,638.89 23 8 $11,277.23 24 9 $11,953.86 25 10 $12,671.09 26 11 $13,431.36 27 12 $14,237.24 28 13 $15,091.47 29 14 $15,996.96 30 15 $16,956.78 31 16 $17,974.19 32 17 $19,052.64 33 18 $20,195.80 34 19 $21,407.54 35 20 $22,692.00 36 21 $24,053.52 37 22 $25,496.73 38 23 $27,026.53 39 24 $28,648.12 40 25 $30,367.01 41 26 $32,189.03 42 27 $34,120.37 43 28 $36,167.59 44 29 $38,337.65 45 30 $40,637.91 =$7,500*(1+0.06)^(30-1) 46 47 F= $1,219,137.28 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 48 =FV(6%,30,,-NPV(6%,CF YR 1:CF YR 30)+0)

A B C D E F 1 PROBLEM 2.126 2 3 i= 5.00% 4 n= 35 A = 5 $7,500.00 1 6 j= 8.00% 7 8 F= $2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS =$7,500*(F|A1 5%,8%,35) 9 10 ********** 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 AGE EOY CF 15 25 0 16 26 1 $7,500.00 =$7,500*(1+0.08)^(1-1) 17 27 2 $8,100.00 =$7,500*(1+0.08)^(2-1) 18 28 3 $8,748.00 19 29 4 $9,447.84 20 30 5 $10,203.67 21 31 6 $11,019.96 22 32 7 $11,901.56 23 33 8 $12,853.68 24 34 9 $13,881.98 25 35 10 $14,992.53 26 36 11 $16,191.94 27 37 12 $17,487.29 28 38 13 $18,886.28 29 39 14 $20,397.18 30 40 15 $22,028.95 31 41 16 $23,791.27 32 42 17 $25,694.57 33 43 18 $27,750.14 34 44 19 $29,970.15 35 45 20 $32,367.76 36 46 21 $34,957.18 37 47 22 $37,753.75 38 48 23 $40,774.05 39 49 24 $44,035.98 40 50 25 $47,558.86 41 51 26 $51,363.56 42 52 27 $55,472.65 43 53 28 $59,910.46 44 54 29 $64,703.30 45 55 30 $69,879.56 46 56 31 $75,469.93 47 57 32 $81,507.52 48 58 33 $88,028.12 49 59 34 $95,070.37 50 60 35 $102,676.00 =$7,500*(1+0.08)^(35-1) 51 F= $2,317,332.23 USING EXCEL'S FV AND NPV 52 FUNCTIONS THIS IS =FV(8%,35,,-NPV(8%,CF YR 1:CF 53 YR 35)+0)

PROBLEM 2.127 FIRST, REVIEW THE ORIGINAL PROBLEM 2.126 i= n= A1= j= F=

5.00% 35 $7,500.00 8.00% $2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS =$7,500*(F|A1 5%,8%,35)

NOW, SOLVE FOR THE FIRST INVESTMENT ON HIS 36TH BIRTHDAY TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A1 BE THE VALUE OF THE FIRST INVESTMENT AT EOY 36. F=

$2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS $2,317,332.23 =A1*(F|A1 5%,8%,25) $2,317,332.23 =A1*115.401008511

A1= $20,080.69 =2317332.23/115.401008511 ********** SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF A1 FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE. A1= AGE 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

$20,080.17 SOLVER CHANGED CELL ORIGINAL EOY CF 0 1 $7,500.00 =$7,500*(1+0.08)^(1-1) 2 $8,100.00 =$7,500*(1+0.08)^(2-1) 3 $8,748.00 4 $9,447.84 5 $10,203.67 6 $11,019.96 7 $11,901.56 8 $12,853.68 9 $13,881.98 10 $14,992.53 11 $16,191.94 12 $17,487.29 13 $18,886.28 14 $20,397.18 15 $22,028.95 16 $23,791.27 17 $25,694.57 18 $27,750.14 19 $29,970.15 20 $32,367.76 21 $34,957.18 22 $37,753.75 23 $40,774.05 24 $44,035.98 25 $47,558.86 26 $51,363.56

AGE EOY 25 0 26 1 27 2 28 3 29 4 30 5 31 6 32 7 33 8 34 9 35 10 36 11 37 12 38 13 39 14 40 15 41 16 42 17 43 18 44 19 45 20 46 21 47 22 48 23 49 24 50 25 51 26

NEW CF $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $20,080.17 $21,686.58 $23,421.51 $25,295.23 $27,318.85 $29,504.36 $31,864.71 $34,413.88 $37,167.00 $40,140.35 $43,351.58 $46,819.71 $50,565.29 $54,610.51 $58,979.35 $63,697.70

52 53 54 55 56 57 58 59 60

27 28 29 30 31 32 33 34 35 F=

$55,472.65 $59,910.46 $64,703.30 $69,879.56 $75,469.93 $81,507.52 $88,028.12 $95,070.37 $102,676.00 =$7,500*(1+0.08)^(35-1) $2,317,332.23

USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+0)

52 53 54 55 56 57 58 59 60

27 28 29 30 31 32 33 34 35

$68,793.51 $74,297.00 $80,240.76 $86,660.02 $93,592.82 $101,080.24 $109,166.66 $117,899.99 $127,331.99

$2,317,332.23

SOLVER TARGET CELL USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(8%,35,,NPV(8%,CF YR 1:CF YR 35)+0)

A B C D E F G H 1 PROBLEM 2.128 2 3 FIRST, REVIEW THE ORIGINAL PROBLEM 2.126 4 5 i= 5.00% 6 j= 8.00% 7 n= 35 A1= 8 $7,500.00 9 10 F= $2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS =$7,500*(F|A1 5%,8%,35) 11 12 NOW, SOLVE FOR THE UNIFORM ANNUAL INVESTMENT TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A BE THE 13 VALUE OF THE ANNUAL INVESTMENT. 14 15 F= $2,317,332.23 USING COMPOUND INTEREST FORMULAS THIS IS 16 =7500*(((1+0.05)^35-(1+0.08)^35))/(0.05-0.08) 17 18 A= $25,656.82 USING COMPOUND INTEREST FORMULAS THIS IS 19 =2317332.23*(0.05/((1+0.05)^35-1)) 20 21 A= $25,652.87 USING INTEREST TABLES THIS IS 22 =$2,317,332.23*(A|F 5%,35) 23 24 A= $25,656.82 USING EXCEL'S PMT FUNCTION THIS IS 25 =PMT(5%,35,,-2317332.23) 26

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF "A" FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE. A=

$25,656.82

AGE 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ORIGINAL CF

CHECK AGE EOY 25 0 $7,500.00 26 1 $8,100.00 27 2 $8,748.00 28 3 $9,447.84 29 4 $10,203.67 30 5 $11,019.96 31 6 $11,901.56 32 7 $12,853.68 33 8 $13,881.98 34 9 $14,992.53 35 10 $16,191.94 36 11 $17,487.29 37 12 $18,886.28 38 13 $20,397.18 39 14 $22,028.95 40 15 $23,791.27 41 16 $25,694.57 42 17 $27,750.14 43 18

NEW CF $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82

A 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

B 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

D $29,970.15 $32,367.76 $34,957.18 $37,753.75 $40,774.05 $44,035.98 $47,558.86 $51,363.56 $55,472.65 $59,910.46 $64,703.30 $69,879.56 $75,469.93 $81,507.52 $88,028.12 $95,070.37 $102,676.00

$2,317,332.23

USING EXCEL'S FV AND NPV =FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+CF YR 0)

E 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

F 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

G $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82

$2,317,332.23 SOLVER TARGET CELL USING EXCEL'S FV =FV(8%,35,,NPV(8%,CF YR 1:CF YR 35)+CF YR 0)

1 2 3 4 5 6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24 25 26

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

EXCEL

A B C D E F 1 PROBLEM 2.129 2 3 P= -$90,000.00 4 i= 5.00% 5 j= -10.00% 6 n= 5 A1= 7 $30,000.00 8 9 PW= $17,467.13 USING COMPOUND INTEREST FORMULAS THIS IS 10 =30000*((1-(1-0.1)^5*(1+0.05)^-5)/(0.05+0.1))-90000 11 12 PW= $17,467.20 USING INTEREST TABLES THIS IS =$30,000*(P|A1 5%,-10%,5)-$90,000 13 14 15 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. 16 17 EOY CF 18 0 -$90,000.00 19 1 $30,000.00 20 2 $27,000.00 21 3 $24,300.00 22 4 $21,870.00 23 5 $19,683.00 24 25 PW= $17,467.13 USING EXCEL'S NPV FUNCTION THIS IS 26 =NPV(5%,CF YR 1:CF YR 5)-90000

A B C D E F G H 1 PROBLEM 2.130 2 3 FIRST, FIND THE PW OF THE GIVEN CF PROFILE 4 5 i= 6.00% 6 n= 8 7 INIT INV= $45,000.00 A1= 8 $12,000.00 9 G= -$1,000.00 10 11 P= $9,675.90 USING INTEREST TABLES THIS IS 12 -$45,000+$12,000(P|A 6%,8)-$1,000(P|G 6%,8) 13 14 P= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 15 00)-45000 16 17 AT THIS POINT, WE KNOW THE PW OF THE CF PROFILE. 18 TO SOLVE FOR THE VALUE OF j, IT IS MUCH EASIER TO USE SOLVER 19 RATHER THAN TO TRY INTERPOLATION OR AN ANALYTICAL SOLUTION 20 21 i= 6.00% 22 n= 8 23 INIT INV= $45,000 A1= 24 $10,000 25

26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44 45 46 47

BEGIN BY SETTING THE VALUE OF "j" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF j TO DEVELOP THE CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO EQUAL THE PW OF THE ORIGINAL CF SERIES BY CHANGING j. j= P=

-4.04% <--SOLVER CHANGED CELL $9,675.90 <--SOLVER TARGET CELL USING INTEREST TABLES THIS IS -$45,000+$10,000*(P|A1 6%,j%,8)

SEE BELOW FOR TABULATED CASH FLOWS WITH SOLVER USED TO CONFIRM THE ABOVE ANSWER. NOTE THAT THE VALUE OF j FOUND IS EQUAL TO THAT FOUND ABOVE. j= EOY 0 1 2 3 4 5 6 7 8

-4.04% <--SOLVER CHANGED CELL CF -$45,000.00 $10,000.00 $9,596.29 $9,208.87 $8,837.10 $8,480.33 $8,137.97 $7,809.43 $7,494.15

A 48 49 50 51

B PW=

$9,675.95 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,CF YR 1:CF YR 8)-45000

A B C D E F G 1 PROBLEM 2.131 2 3 i= 5.00% 4 j= 10.00% 5 n= 18 A1= 6 $2,000.00 7 8 PW= $52,410.42 USING COMPOUND INTEREST FORMULA THIS IS =$2,000*(P|A1 5%,10%,18) 9 10 11 PW= $52,410.42 USING INTEREST TABLES THIS IS =$2,000*(P|A1 5%,10%,18) 12 13 14 FW= $126,131.92 USING EXCEL'S FV FUNCTION THIS IS 15 =FV(5%,18,,-52410.42) 16 17 SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER. 18 19 EOY CF 20 0 21 1 $2,000.00 22 2 $2,200.00 23 3 $2,420.00 24 4 $2,662.00 25 5 $2,928.20 26 6 $3,221.02 27 7 $3,543.12 28 8 $3,897.43 29 9 $4,287.18 30 10 $4,715.90 31 11 $5,187.48 32 12 $5,706.23 33 13 $6,276.86 34 14 $6,904.54 35 15 $7,595.00 36 16 $8,354.50 37 17 $9,189.95 38 18 $10,108.94 39 40 PW= $52,410.42 USING EXCEL'S NPV FUNCTION THIS IS 41 =NPV(5%,CF YR 1:CF YR 18)+0 42 43 FW= $126,131.96 USING INTEREST TABLES THIS IS 44 =$52,410*(F|P 5%,18)

A B C D E F G 1 PROBLEM 2.132 2 3 i= 12.00% 4 j= 15.00% 5 n= 6 A1= 6 $50,000.00 7 8 PW= $286,447.62 USING COMPOUND INTEREST FORMULAS THIS IS 9 =50000*((1-(1+0.15)^6*(1+0.12)^-6)/(0.12-0.15)) 10 11 PW= $286,447.62 USING ELECTRONIC INTEREST TABLES THIS IS =$50,000*(P|A1 12%,15%,6) 12 13 14 SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER. 15 16 EOY CF 17 0 18 1 $50,000.00 19 2 $57,500.00 20 3 $66,125.00 21 4 $76,043.75 22 5 $87,450.31 23 6 $100,567.86 24 25 PW= $286,447.62 USING EXCEL'S NPV FUNCTION THIS IS 26 =NPV(12%,CF YR 1:CF YR 6)+0

1 2 3 4 5 6 7 8 9 10 11 12 13 HE ANSWER. 14 15 16 17 18 19 20 21 22 23 24 25 26

A B C D E F 1 PROBLEM 2.133 2 3 i= 7.00% COMPOUNDED ANNUALLY 4 j= -40.00% COMPOUNDED ANNUALLY 5 n= 4 A1= 6 $60,000.00 7 8 PW= $115,038.00 USING INTEREST TABLES THIS IS =$60,000*(P|A1 7%,-40%,4) 9 10 11 PW= $115,037.72 USING FORMULAS THIS IS 12 =60000*((1-(1-0.4)^4*(1+0.07)^-4)/(0.07-(-0.4))) 13 14 SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER. 15 16 EOY CF 17 0 $0.00 18 1 $60,000.00 19 2 $36,000.00 20 3 $21,600.00 21 4 $12,960.00 22 23 PW= $115,037.72 USING EXCEL'S NPV FUNCTION THIS IS 24 =NPV(7%,60000,36000,21600,12960)+0

A B C D 1 PROBLEM 2.134 2 3 i= 15.00% 4 j= 6.00% 5 n= 20 A1= 6 $1,000.00 7 8 PW= $8,933.81 TABLES FROM APPENDIX A =$1,000*(P|A1 15%,6%,20) 9 10 11 PW= $8,933.81 TABLES FROM PROBLEM 2.123 =$1,000*(P|A1 15%,6%,20) 12 13 14 USING TABULATED CASH FLOWS 15 16 EOY CF 17 0 $0.00 18 1 $1,000.00 19 2 $1,060.00 20 3 $1,123.60 21 4 $1,191.02 22 5 $1,262.48 23 6 $1,338.23 24 7 $1,418.52 25 8 $1,503.63 26 9 $1,593.85 27 10 $1,689.48 28 11 $1,790.85 29 12 $1,898.30 30 13 $2,012.20 31 14 $2,132.93 32 15 $2,260.90 33 16 $2,396.56 34 17 $2,540.35 35 18 $2,692.77 36 19 $2,854.34 37 20 $3,025.60 38 39 PW= $8,933.81 USING EXCEL'S NPV FUNCTION THIS IS 40 =NPV(15%,CF YR 1:CF YR 20)+0

A 1 PROBLEM 2.135 2 3 4 5 6 7 8 9 10 11 12

i= j= n= A1=

5.00% 10.00% 5 $1,000.00

PW= $5,237.53 USING INTEREST TABLES THIS IS =$1,000*(P|A1 5%,10%,5) PW= $5,237.53 USING EXCEL'S NPV FUNCTION THIS IS =NPV(5%,1000,1000*1.1,1000*1.1^2,1000*1.1^3,1000*1.1^4)

I 1 2 3 4 5 6 7 8 9 10 11 12

A 1 PROBLEM 2.136 2 3 4 5 6 7 8 9 10 11

i= j= n= A1=

5.00% 15.00% 7 $4,000.00

F= $50,116.76 USING INTEREST TABLES THIS IS =$4,000*(F|A1 5%,15%,7) F= $50,116.78 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(5%,7,,NPV(5%,4000,4000*1.15,4000*1.15^2,4000*1.15^3,4000* 1.15^4,4000*1.15^5,4000*1.15^6))

A 1 PROBLEM 2.137 2 3 4 5 6 7 8 9 10 11 12

i= j= n= A1=

10.00% 5.00% 6 $9,000.00

PW=

$43,839.18 USING INTEREST TABLES THIS IS =$9,000*(P|A1 10%,5%,6)

PW=

$43,839.17 USING EXCEL'S NPV FUNCTION THIS IS =NPV(10%,9000,9000*1.05,9000*1.05^2,9000*1.05^3,9 000*1.05^4,9000*1.05^5)

A B C D E F G H 1 PROBLEM 2.138 2 3 i= 10.00% 4 j= 15.00% 5 n= 4 A1= $2,000.00 6 7 8 a PW= $7,783.80 USING INTEREST TABLES THIS IS =$2,000*(P|A1 10%,15%,4) 9 10 11 PW= $7,783.79 USING EXCEL'S NPV FUNCTION THIS IS 12 =NPV(10%,2000,2000*1.15,2000*1.15^2,2000*1.15^3) 13 14 b A= $2,455.56 USING INTEREST TABLES THIS IS 15 =$7,783.80*(A|P 10%,4) 16 17 A= $2,455.56 USING EXCEL'S PMT FUNCTION THIS IS 18 =PMT(10%,4,-7783.79)

A B C D E F G H 1 PROBLEM 2.139 2 3 i= 15.00% 4 j= 10.00% 5 n= 5 A1= $14,000.00 6 7 8 a PW= $55,801.76 USING INTEREST TABLES THIS IS =$14,000*(P|A1 15%,10%,5) 9 10 11 PW= $55,801.73 USING EXCEL'S NPV FUNCTION THIS IS =NPV(15%,14000,14000*1.1,14000*1.1^2,14000*1.1^3,14 12 000*1.1^4) 13 14 b A= $16,646.78 USING INTEREST TABLES THIS IS 15 =$55,801.76*(A|P 15%,5) 16 17 A= $16,646.52 USING EXCEL'S PMT FUNCTION THIS IS 18 =PMT(15%,5,-55801.73)

A 1 PROBLEM 2.140 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

NOTE THAT THE WORDING OF THIS PROBLEM IMPLIES THE 18 DEPOSITS START AT BIRTH (BEGINNING OF YEAR 1) AND CONTINUE THROUGH BEGINNING OF YEAR 18. THEN, THE AMOUNT AT THE END OF YEAR 18 IS REQUESTED. i= j= n= A1=

6.00% 15.00% 18 $1,500.00 AT BEGINNING OF YEAR 1

FW= $168,206.35 USING INTEREST TABLES THIS IS =$1,500*(F|A1 6%,15%,18)*(F|P 6%,1) FW= $168,206.35 USING INTEREST TABLES FROM PROBLEM 2.123 =$1,500*(F|A1 6%,15%,18)*(F|P 6%,1) USING TABULATED CASH FLOWS EOY CF 0 $1,500.00 1 $1,725.00 2 $1,983.75 3 $2,281.31 4 $2,623.51 5 $3,017.04 6 $3,469.59 7 $3,990.03 8 $4,588.53 9 $5,276.81 10 $6,068.34 11 $6,978.59 12 $8,025.38 13 $9,229.18 14 $10,613.56 15 $12,205.59 16 $14,036.43 17 $16,141.90 18 $0.00 FW= $168,206.36 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(6%,18+1,,-NPV(6%,CF YR 0:CF YR 18))

A B C D E F G H 1 PROBLEM 2.141 2 3 i= 15.00% 4 j= 10.00% 5 n= 5 A1= $140,000.00 6 7 8 PW= $558,017.60 USING INTEREST TABLES THIS IS =$140,000*(P|A1 15%,10%,5) 9 10 11 PW= $558,017.60 USING INTEREST TABLES FROM PROBLEM 2.123 =$140,000*(P|A1 15%,10%,5) 12 13 14 USING TABULATED CASH FLOWS 15 16 EOY CF 17 0 $0.00 18 1 $140,000.00 19 2 $154,000.00 20 3 $169,400.00 21 4 $186,340.00 22 5 $204,974.00 23 24 PW= $558,017.31 USING EXCEL'S NPV FUNCTION THIS IS 25 =NPV(15%,CF YR 1:CF YR 5)+0

1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A PROBLEM 2.142

IN THIS PROBLEM, IT IS MUCH EASIER TO USE A SPREADSHEET AND TO KEEP LABOR, MATERIAL, AND OVERHEAD SEPARATE UNTIL COMBINED. i=

11.00% LABOR -5.00% $2,000,000.00

MATERIAL 4.00% $3,000,000.00

OVERHEAD 8.00% $1,600,000.00

TOTAL

j= A1= EOY 0 1 2 3 4 5 6 7

$0.00 $2,000,000.00 $1,900,000.00 $1,805,000.00 $1,714,750.00 $1,629,012.50 $1,547,561.88 $1,470,183.78

$0.00 $3,000,000.00 $3,120,000.00 $3,244,800.00 $3,374,592.00 $3,509,575.68 $3,649,958.71 $3,795,957.06

$0.00 $1,600,000.00 $1,728,000.00 $1,866,240.00 $2,015,539.20 $2,176,782.34 $2,350,924.92 $2,538,998.92

$0.00 $6,600,000.00 $6,748,000.00 $6,916,040.00 $7,104,881.20 $7,315,370.52 $7,548,445.51 $7,805,139.75

$8,295,499.60 $15,693,016.73 $9,307,846.73 $33,296,363.05 USING EXCEL'S NPV FUNCTION, EACH COLUMN IS =NPV(11%,CF YR 1:CF YR 7)+0

$8,295,500.00 $15,693,030.00 $9,307,840.00 $33,296,370.00 USING INTEREST TABLES FROM PROBLEM 2.123 =$2,000,000.00*(P|A1 11%,-5%,7) =$3,000,000.00*(P|A1 11%,4%,7)

27 28 29 30 31 32 33 34 35 36

=$1,600,000.00*(P|A1 11%,8%,7) c

$7,065,996.66 USING EXCEL'S PMT FUNCTION THIS IS =PMT(11%,7,-33296363.05)

$7,066,155.64 USING INTEREST TABLES THIS IS =$33,296,370.00*(A|P 11%,7) NOTE! TABLES DO NOT SUPPORT THIS LEVEL OF PRECISION

A B C D E F G H 1 PROBLEM 2.143 2 3 i= 8.00% 4 j= 5.00% 5 n= 10 6 SALARY $70,000.00 7 % DEPOSITED 10.00% A1= 8 $7,000.00 9 10 FW= $123,673.76 USING INTEREST TABLES THIS IS =$7,000*(F|A1 8%,5%,10) 11 12 13 FW= $123,673.76 TABLES FROM PROBLEM 2.123 =$7,000*(F|A1 8%,5%,10) 14 15 16 USING TABULATED CASH FLOWS 17 18 EOY CF 19 0 $0.00 20 1 $7,000.00 21 2 $7,350.00 22 3 $7,717.50 23 4 $8,103.38 24 5 $8,508.54 25 6 $8,933.97 26 7 $9,380.67 27 8 $9,849.70 28 9 $10,342.19 29 10 $10,859.30 30 31 FW= $123,673.75 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 32 =FV(8%,10,,-NPV(8%,CF YR 1:CF YR 10)+0)

A B C D E F 1 PROBLEM 2.144 2 3 i= 15.00% 4 j= 10.00% 5 n= 5 6 P= $50,000.00 7 8 P= $50,000.00 USING INTEREST TABLES THIS IS =A1*(P|A1 15%,10%,5) 9 10 A1= 11 $12,544.41 =50000/3.98584 12 13 a SMALLEST PAYMENT $0.00 14 15 b LARGEST PAYMENT $18,366.27 =12544.41*(1+0.1)^4 16 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. 17 WILL USE SOLVER TO FIND VALUE OF A1. 18 BEGIN BY DEDICATING A CELL FOR A1 AND LET IT TAKE ON ANY VALUE AS IF IT WERE CORRECT. IT WILL BE CHANGED TO THE CORRECT 19 VALUE WHEN SOLVER IS USED. 20 A1= 21 $12,544.41 SOLVER CHANGED CELL 22 23 EOY CF 24 0 25 a 1 $12,544.41 26 2 $13,798.86 27 3 $15,178.74 28 4 $16,696.61 29 b 5 $18,366.28 30 31 P= $50,000.00 SOLVER TARGET CELL 32 USING EXCEL'S NPV FUNCTION THIS IS 33 =NPV(15%,CF YR 1:CF YR 5)+0

A 1 PROBLEM 2.145 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

i= 6.00% j= 4.00% n= 5 A1= $15,000.00 FW= $91,179.45 TABLES FROM APPENDIX A =$15,000*(F|A1 6%,4%,5) USING TABULATED CASH FLOWS EOY CF 0 $0.00 1 $15,000.00 2 $15,600.00 3 $16,224.00 4 $16,872.96 5 $17,547.88 FW= $91,179.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(6%,5,,-NPV(6%,CF YR 1:CF YR 5)+0)

A 1 PROBLEM 2.146 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24

25 26

TO GO FROM NOMINAL ANNUAL TO EFFECTIVE ANNUAL NOMINAL ANNUAL INTEREST RATE (E.G., 10.000%) COMPOUNDING PERIODS PER YEAR (E.G., 4 FOR QUARTERLY)

r= m=

10.000% USED r=10% FOR EXAMPLE 4 USED m=4 FOR EXAMPLE

EFFECTIVE ANNUAL INTEREST RATE

ieff= 10.381%

EFFECTIVE ANNUAL INTEREST RATE

USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/4)^4-1 ieff= 10.381% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,4)

TO GO FROM EFFECTIVE ANNUAL TO NOMINAL ANNUAL EFFECTIVE ANNUAL INTEREST RATE (E.G., 10.381%) COMPOUNDING PERIODS PER YEAR (E.G., 4 FOR QUARTERLY)

ieff= 10.381%

NOMINAL ANNUAL INTEREST RATE

4 USED m=4 FOR EXAMPLE

10.000% USED r=10% FOR EXAMPLE USING COMPOUND INTEREST FORMULAS THIS IS =4*((1+0.10381)^(1/4)-1)

A 1 PROBLEM 2.147 2 3 4 5 6 7 8 9 10 11 12 13 14

i= 0.75% PER MONTH n= 480 MONTHS F= $2,000,000.00 A=

$427.23 USING COMPOUND INTEREST FORMULAS THIS IS =2000000*(0.0075/((1+0.0075)^480-1))

$427.22 USING INTEREST TABLES THIS IS =$2,000,000*(A|F 0.75%,480)

$427.23 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.75%,480,,-2000000)

A B C D E 1 PROBLEM 2.148 2 3 P= $12,000.00 4 i= 0.75% PER MONTH 5 A= $400.00 PER MONTH 6 7 n= 34.1129207 MONTHS USE 35 MONTHS 8 USING EXCEL'S NPER FUNCTION THIS IS 9 =NPER(0.75%,-400,12000) 10 11 CAN ALSO USE SOLVER TO FIND n 12 13 n= 34.1129208 <--SOLVER CHANGED CELL USE 35 MONTHS 14 15 A= $400.00 <--SOLVER TARGET CELL 16 USING EXCEL'S PMT FUNCTION THIS IS 17 =PMT(0.75%,n,-12000) 18 19 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. 20 21 EOY CF PW 22 23 0 24 1 $400.00 $397.02 25 2 $400.00 $791.09 26 3 $400.00 $1,182.22 27 4 $400.00 $1,570.44 28 5 $400.00 $1,955.78 29 6 $400.00 $2,338.24 30 7 $400.00 $2,717.86 31 8 $400.00 $3,094.65 32 9 $400.00 $3,468.63 33 10 $400.00 $3,839.83 34 11 $400.00 $4,208.27 35 12 $400.00 $4,573.97 36 13 $400.00 $4,936.94 37 14 $400.00 $5,297.21 38 15 $400.00 $5,654.80 39 16 $400.00 $6,009.73 40 17 $400.00 $6,362.01 41 18 $400.00 $6,711.67 42 19 $400.00 $7,058.73 43 20 $400.00 $7,403.21 44 21 $400.00 $7,745.12 45 22 $400.00 $8,084.49 46 23 $400.00 $8,421.33 47 24 $400.00 $8,755.66 48 25 $400.00 $9,087.50 49 26 $400.00 $9,416.88 50 27 $400.00 $9,743.80 51 28 $400.00 $10,068.28 52 29 $400.00 $10,390.36 53 30 $400.00 $10,710.03 54 31 $400.00 $11,027.33 55 32 $400.00 $11,342.26 56 33 $400.00 $11,654.85 57 34 $400.00 $11,965.11

A 58 59 60 61 62 63

B 35 36 37 38 39 40

C $400.00 $400.00 $400.00 $400.00 $400.00 $400.00

D $12,273.06 $12,578.72 $12,882.11 $13,183.23 $13,482.12 $13,778.78

E FIRST PW OF >= $12,000

A 1 PROBLEM 2.149 2 3 a 4 5 6 7 8 9 10 11 b 12 13 14 15 16 17 18 19 c 20 21 22 23 24 25 26 27 d 28 29 30 31 32 33 34 35 e 36 37 38 39 40 41

r= m=

10.00% 2

ieff= 10.2500% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/2)^2-1 ieff= 10.2500% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,2) r= m=

10.00% 3

ieff= 10.3370% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/3)^3-1 ieff= 10.3370% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,3) r= m=

10.00% 4

ieff= 10.3813% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/4)^4-1 ieff= 10.3813% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,4) r= m=

10.00% 6

ieff= 10.4260% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/6)^6-1 ieff= 10.4260% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,6) r= m=

10.00% 12

ieff= 10.4713% USING COMPOUND INTEREST FORMULAS THIS IS 10.4713% ieff= 10.4713% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,12)

A 1 PROBLEM 2.150 2 3 a 4 5 6 7 8 9 10 11 b 12 13 14 15 16 17 18 19 c 20 21 22 23 24 25 26 27 d 28 29 30 31 32 33 34 35 e 36 37 38 39 40 41

r= m=

5.00% 2

ieff= ieff=

r= m= ieff= ieff=

5.0625% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/2)^2-1 5.0625% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,2) 5.00% 3 5.0838% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/3)^3-1 5.0838% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,3) 5.00% 4 5.0945% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/4)^4-1 5.0945% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,4) 5.00% 6 5.1053% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/6)^6-1 5.1053% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,6) 5.00% 12 5.1162% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/12)^12-1 5.1162% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,12)

A 1 PROBLEM 2.151 2 3 4 5 6 7 8 9 10 11 12 13

r= 6.00% PER YEAR m= 12 i= 0.50% PER MONTH n= 60 MONTHS P= $50,000.00 A=

$966.50 USING INTEREST TABLES THIS IS =$50,000*(A|P 0.50%,60)

$966.64 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.5%,60,-50000)

A 1 PROBLEM 2.152 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

i= n= P=

0.50% PER MONTH 30 MONTHLY PAYMENTS $500.00

$17.99 USING INTEREST TABLES THIS IS =$500*(A|P 0.50%,30)

$17.99 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.50%,30,-500)

i= n= P= DELAY=

0.50% PER MONTH 30 MONTHLY PAYMENTS $500.00 12 MONTHS

FIRST, DETERMINE THE FUTURE WORTH OF THE ORIGINAL $500 AFTER 12 MONTHS. THEN, DETERMINE THE MONTHLY PAYMENT AMT12MO= $530.84 USING INTEREST TABLES THIS IS =$500.00*(F|P 0.5%,12) A=

$19.10 USING INTEREST TABLES THIS IS =$530.84*(A|P 0.50%,30)

AMT12MO= $530.84 USING EXCEL'S FV FUNCTION THIS IS =FV(0.5%,12,,-C16) A=

$19.10 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.5%,30,-530.84)

A B C D E F G H 1 PROBLEM 2.153 2 3 r= 6.000% 4 m= 2 5 YRS= 10 6 P= $4,000.00 7 8 FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS 9 =4000*(1+0.06/2)^(2*10) 10 11 FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS 12 =FV(0.06/2,2*10,,-4000) 13 14 OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS 15 ieff= 16 6.090% USING EXCEL'S EFFECT FUNCTION THIS IS 17 =EFFECT(6%,2) 18 19 FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS 20 =4000*(1+0.0609)^10 21 22 FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS 23 =FV(6.09%,10,,-4000)

A B C D E F G H I 1 PROBLEM 2.154 2 3 r= 5.000% 4 m= 4 5 YRS= 4 6 F= $10,000.00 7 8 9 P= $8,197.50 USING INTEREST TABLES THIS IS 10 =$10,000*(P|F 1.25%,16) 11 12 P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(0.05/4,4*4,,-10000) 14 15 OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS 16 ieff= 17 5.09453% USING COMPOUND INTEREST FORMULAS THIS IS 18 =(1+0.05/4)^4-1 19 20 P= $8,197.46 USING COMPOUND INTEREST FORMULAS THIS IS 21 =10000*(1+0.0509453)^-4 22 23 P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS 24 =PV(5.09453%,4,,-10000)

A B C D E F G H 1 PROBLEM 2.155 2 3 a ANNUALLY 4 r= 7.000% 5 m= 1 6 YRS= 5 7 P= $10,000.00 8 9 F= $14,025.52 USING COMPOUND INTEREST FORMULAS THIS IS 10 =10000*(1+0.07/1)^(1*5) 11 F= $14,025.50 USING INTEREST TABLES THIS IS 12 =$10,000*(F|P 7%,5) 13 F= $14,025.52 USING EXCEL'S FV FUNCTION THIS IS 14 =FV(0.07/1,1*5,,-10000) 15 16 b QUARTERLY 17 r= 7.000% 18 m= 4 19 YRS= 5 20 P= $10,000.00 21 22 F= $14,147.78 USING COMPOUND INTEREST FORMULAS THIS IS 23 =10000*(1+0.07/4)^(4*5) 24 F= $14,147.80 USING INTEREST TABLES THIS IS 25 =$10,000*(F|P 1.75%,20) 26 F= $14,147.78 USING EXCEL'S FV FUNCTION THIS IS 27 =FV(0.07/4,4*5,,-10000) 28 29 c MONTHLY 30 r= 7.000% 31 m= 12 32 YRS= 5 33 P= $10,000.00 34 35 F= $14,176.25 USING COMPOUND INTEREST FORMULAS THIS IS 36 =10000*(1+0.07/12)^(12*5) 37 F= $14,176.25 USING ELECTRONIC INTEREST TABLES THIS IS 38 =$10,000*(F|P 7%/12,60) 39 F= $14,176.25 USING EXCEL'S FV FUNCTION THIS IS 40 =FV(0.07/12,12*5,,-10000) 41 42 d DAILY 43 r= 7.000% 44 m= 365 45 YRS= 5 46 P= $10,000.00 47 48 F= $14,190.20 USING COMPOUND INTEREST FORMULAS THIS IS 49 =10000*(1+0.07/365)^(365*5) 50 F= $14,190.20 USING ELECTRONIC INTEREST TABLES THIS IS 51 =$10,000*(F|P 7%/365,1825) 52 F= $14,190.20 USING EXCEL'S FV FUNCTION THIS IS 53 =FV(0.07/365,365*5,,-10000)

A B C D E F G H 1 PROBLEM 2.156 2 3 a ANNUALLY 4 r= 6.000% 5 m= 1 6 YRS= 8 7 F= $20,000.00 8 9 P= $12,548.25 USING COMPOUND INTEREST FORMULAS THIS IS 10 =20000*(1+0.06/1)^(-1*8) 11 P= $12,548.20 USING INTEREST TABLES THIS IS 12 =$20,000*(P|F 6%,8) 13 P= $12,548.25 USING EXCEL'S FV FUNCTION THIS IS 14 =PV(0.06/1,1*8,,-20000) 15 16 b SEMI-ANNUALLY 17 r= 6.000% 18 m= 2 19 YRS= 8 20 F= $20,000.00 21 22 P= $12,463.34 USING COMPOUND INTEREST FORMULAS THIS IS 23 =20000*(1+0.06/2)^(-2*8) 24 P= $12,463.40 USING INTEREST TABLES THIS IS 25 =$20,000*(P|F 3%,16) 26 P= $12,463.34 USING EXCEL'S FV FUNCTION THIS IS 27 =PV(0.06/2,2*8,,-20000) 28 29 c QUARTERLY 30 r= 6.000% 31 m= 4 32 YRS= 8 33 F= $20,000.00 34 35 P= $12,419.86 USING COMPOUND INTEREST FORMULAS THIS IS 36 =20000*(1+0.06/4)^(-4*8) 37 P= $12,419.80 USING INTEREST TABLES THIS IS 38 =$20,000*(P|F 1.5%,32) 39 P= $12,419.86 USING EXCEL'S FV FUNCTION THIS IS 40 =PV(0.06/4,4*8,,-20000) 41 42 d MONTHLY 43 r= 6.000% 44 m= 12 45 YRS= 8 46 F= $20,000.00 47 48 P= $12,390.48 USING COMPOUND INTEREST FORMULAS THIS IS 49 =20000*(1+0.06/12)^(-12*8) 50 P= $12,390.40 USING INTEREST TABLES THIS IS 51 =$20,000*(P|F 0.5%,96) 52 P= $12,390.48 USING EXCEL'S FV FUNCTION THIS IS 53 =PV(0.06/12,12*8,,-20000) 54 55 e WEEKLY 56 r= 6.000% 57 m= 52

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

B YRS= F=

C 8 $20,000.00

$12,379.09 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/52)^(-52*8) $12,379.00 USING INTEREST TABLES THIS IS =$20,000*(P|F 0.6/52%,416) $12,379.09 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/52,52*8,,-20000)

P= P=

DAILY r= m= YRS= F= P= P=

HOURLY r= m= YRS= F= P= P=

MINUTELY r= m= YRS= F= P= P=

SECONDLY r= m= YRS= F= P= P=

6.000% 365 8 $20,000.00 $12,376.16 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/365)^(-365*8) $12,376.16 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/365,365*8,,-20000)

6.000% 8760 8 $20,000.00 $12,375.69 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/8760)^(-8760*8) $12,375.69 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/8760,8760*8,,-20000)

6.000% 525600 8 $20,000.00 $12,375.67 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/525600)^(-525600*8) $12,375.67 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/525600,525600*8,,-20000)

6.000% 31536000 8 $20,000.00 $12,375.67 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/31536000)^(-31536000*8) $12,375.67 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/31536000,31536000*8,,-20000)

A 1 PROBLEM 2.157 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 a 29 30 31 32 33 b 34

BUILDING THE ACCOUNT r= 8.000% COMPOUNDED MONTHLY m= 12 MONTHS PER YEAR YRS= 20 A= $400.00 PER MONTH DETERMINE AMOUNT IN ACCOUNT AT END OF 20 YEARS, END OF MONTH 240 F(240)= $235,608.00 USING INTEREST TABLES THIS IS $400*(F|A 8/12%,240) F(240)= $235,608.17 USING EXCEL'S FV FUNCTION THIS IS =FV(0.08/12,12*20,-400) DETERMINE AMOUNT IN ACCOUNT AT END OF MONTH 251, ONE MONTH BEFORE 1ST WITHDRAWAL AT END OF MONTH 252 1ST WDL r= m= YRS=

252 MONTH 252 IS FIRST WITHDRAWAL 8.000% COMPOUNDED MONTHLY 12 MONTHS PER YEAR 15

F(251)=

$253,474.15 USING INTEREST TABLES THIS IS =$235608.00*(F|P 8/12%,11) $253,473.70 USING EXCEL'S FV FUNCTION THIS IS =FV(0.08/12,11,,-235608.17)

F(251)=

A= A=

$2,423.21 USING INTEREST TABLES THIS IS =$253,474.15*(A|P 8/12%,12*15) $2,422.33 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.08/12,12*15,-253473.7) $1,689.82 CALCULATING MONTHLY INTEREST ONLY =(0.08/12)*253473.7

A B C D E F G 1 PROBLEM 2.158 2 3 a BUILDING THE ACCOUNT FOR 30 YEARS 4 r= 8.000% 5 m= 12 MONTHS PER YEAR 6 YRS= 30 7 A= $300.00 PER MONTH 8 9 10 11 AMT360= $447,120.00 USING INTEREST TABLES THIS IS 12 =$300*(F|A 8/12%,360) 13 AMT360= $447,107.83 USING EXCEL'S FV FUNCTION THIS IS 14 =FV(8%/12,12*30,-300) 15 16 b LETTING THE ACCOUNT BUILD FOR 7 MORE QUARTERS 17 r= 12.000% 18 m= 4 QTRS/YEAR 19 YRS= 15 20 21 AMT7QTR= $549,899.47 USING INTEREST TABLES THIS IS 22 =$447,120*(F|P 3%,7) 23 AMT7QTR= $549,886.24 USING EXCEL'S FV FUNCTION THIS IS 24 =FV(12%/4,7,,-C13) 25 26 c WITHDRAWING FROM THE ACCOUNT 27 STARTING 2 YEARS AFTER LAST DEPOSIT 28 29 A= $19,867.87 USING INTEREST TABLES THIS IS 30 =$549,899.47*(A|P 3%,60) 31 A= $19,869.02 USING EXCEL'S PMT FUNCTION THIS IS 32 =PMT(12%/4,4*15,-549886.24)

A B C D E F G H 1 PROBLEM 2.159 2 3 MONTHLY RATE= 2.50% 4 m= 12 5 P= $2,000.00 6 YRS= 2 7 8 a NOM ANN RATE= 30.000% =2.5%*12 9 10 b EFF ANN RATE= 34.4889% USING COMPOUND INTEREST FORMULAS THIS IS 11 =(1+30%/12)^12-1 12 EFF ANN RATE= 34.4889% USING EXCEL'S EFFECT FUNCTION THIS IS 13 =EFFECT(30%,12) 14 15 c F= $3,617.45 USING ELECTRONIC INTEREST TABLES THIS IS 16 =$2,000*(F|P 2.5%,24) 17 F= $3,617.45 USING EXCEL'S FV FUNCTION THIS IS 18 =FV(2.5%,12*2,,-2000) 19 20 d F= $3,617.45 USING ELECTRONIC INTEREST TABLES THIS IS 21 =$2,000*(F|P 34.4889%,2) 22 F= $3,617.45 USING EXCEL'S FV FUNCTION THIS IS 23 =FV(34.4889%,2,,-2000) 24 25 e INTEREST= $1,617.45 =3617.45-2000.00 26 27 f A= $111.82 USING INTEREST TABLES THIS IS 28 =$2,000*(A|P 2.5%,24) 29 A= $111.83 USING EXCEL'S PMT FUNCTION THIS IS 30 =PMT(2.5%,12*2,-2000)

1 2

A PROBLEM 2.160

SINCE THIS PROBLEM SEEKS TO DETERMINE AN INTEREST RATE, IT IS BEST TO USE SOLVER TO AVOID A DIFFICULT ANALYTICAL SOLUTION OR INTERPOLATION.

3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

m= n= A= F=

12 MONTHS PER YEAR 40 MONTHS $250.00 PER MONTH $12,000.00

BEGIN BY ESTABLISHING A CELL FOR THE VALUE OF THE NOMINAL RATE r AND USE ANY VALUE, ASSUMING IT IS CORRECT. IT WILL LATER BE CHANGED BY SOLVER TO THE CORRECT VALUE. r= F=

10.932% <--SOLVER CHANGED CELL $12,000.00 <--SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(r%/12,40,-250)

NOW, KNOWING r, PROCEED WITH THE PROBLEM a

imonthly=

10.932% FOUND USING SOLVER ABOVE

ieff=

11.497% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.10932/12)^12-1 11.497% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10.932%,12)

ieff=

0.911% =10.932%/12

1 2

A PROBLEM 2.161

SINCE THIS PROBLEM SEEKS TO DETERMINE AN INTEREST RATE, IT IS BEST TO USE SOLVER TO AVOID A DIFFICULT ANALYTICAL SOLUTION OR INTERPOLATION.

3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

m= YRS= A= P=

12 5 $501.49 $20,000.00

BEGIN BY ESTABLISHING A CELL FOR THE VALUE OF THE NOMINAL RATE r AND USE ANY VALUE, ASSUMING IT IS CORRECT. IT WILL LATER BE CHANGED BY SOLVER TO THE CORRECT VALUE. r= P=

17.412% <--SOLVER CHANGED CELL $20,000.00 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(r/12,12*5,-20000)

NOW, KNOWING r, PROCEED WITH THE PROBLEM a

imonthly=

17.412% FOUND USING SOLVER ABOVE

ieff=

18.871% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.17412/12)^12-1 18.871% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(17.412%,12)

ieff=

1.451% =17.412%/12

A B 1 PROBLEM 2.162 2 3 a REFUND= 4 INT RATE= 5 INT PAID= 6 m= 7 8 CASH RCVD= 9 10 WEEKLY INT= b 11 12 c r= 13 ieff= 14 d 15 ieff= 16 17

$1,000.00 3.000% PER WEEK $30.00 =1000*0.03 52 WEEKS/YR $970.00 =1000-30 3.093% =30/970 160.825% =3.093%*52 387.382% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.03093)^52-1 387.382% USING EXCEL'S EFFECT FUNCTION 387.384%

A 1 PROBLEM 2.163 2 3 4 5 6 7 8 9 10 a 11 12 13 14 15 b 16 17 18 19 20 c 21 22 23 24 25 d 26 27 28 29 30 e 31 32 f

PLAN 1 r= m= YRS= P= A= A=

A= A=

ieff= ieff=

PLAN 2 7.000% 12 30 $600,000.00

r= m= YRS= P=

6.625% 12 15 $600,000.00

$3,990.00 USING INTEREST TABLES THIS IS =$600,000*(A|P 7/12%,360) $3,991.81 USING EXCEL'S PMT FUNCTION THIS IS =PMT(7%/12,12*30,-600000) $5,268.00 USING INTEREST TABLES THIS IS =$600,000*(A|P 6.625/12%,180) $5,267.96 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6.625%/12,12*15,-600000) 7.229% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.07/12)^12-1 7.229% USING EXCEL'S EFFECT FUNCTION =EFFECT(7%,12) 6.830% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.06625/12)^12-1 6.830% USING EXCEL'S EFFECT FUNCTION =EFFECT(6.625%,12)

INT PAID=

$837,053.39 =3991.81*12*30-600000

INT PAID=

$348,233.27 =5267.96*12*15-600000

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

A B C D E F G H I 1 PROBLEM 2.164 2 3 r= 6.00% PER YEAR 4 m= 4 CMPDGS PER YEAR 5 n= 60 MONTHS 6 k= 12 PAYMENTS PER YEAR 7 P= $50,000.00 8 9 FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH) 10 11 i= 0.49752063% PER MONTH 12 USING COMPOUND INTEREST FORMULAS THIS IS 13 =(1+0.06/4)^(4/12)-1 14 15 NOW, PROCEED WITH THE REST OF THE PROBLEM 16 17 A= $965.95 USING COMPOUND INTEREST FORMULAS THIS IS 18 =50000*(0.0049752063*(1+0.0049752063)^60)/((1+0.0049752063)^60-1) 19 A= $966.00 USING INTEREST TABLES THIS IS 20 =$50,000*(A|P 0.49752063%,60) 21 A= $965.95 USING EXCEL'S PMT FUNCTION THIS IS 22 =PMT(0.49752063%,60,-50000)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0049752063)^60-1) 18 19 20 21 22

A 1 PROBLEM 2.165 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

NOTE! IF YOU HAVE THE FIRST PRINTING, SEE PROBLEM 2.167 FOR SOLUTION FOLLOWING IS THE SOLUTION TO PROBLEM 2.165 IN LATER PRINTINGS r= m= k= A= F=

6.000% 4 QUARTERS PER YEAR 12 DEPOSITS PER YEAR $150.00 PER MONTH $20,000.00

FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH) i=

0.49752063% PER MONTH USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.06/4)^(4/12)-1

NOW, PROCEED WITH THE REST OF THE PROBLEM n=

102.5293974 MONTHS USING EXCEL'S NPER FUNCTION THIS IS =NPER(0.4975206%,150,,-20000)

OR COULD USE SOLVER AS FOLLOWS n= F=

102.5293974 <--SOLVER CHANGED CELL $20,000.00 <--SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(0.4975206,n,-150)

A B C D E F G H I 1 PROBLEM 2.166 2 3 r= 7.000% PER YEAR 4 m= 12 MONTHS PER YEAR 5 k= 4 DEPOSITS PER YEAR 6 A= $300.00 PER QUARTER 7 F= $15,000.00 8 9 FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (QUARTER) 10 11 i= 1.760% PER QUARTER 12 USING COMPOUND INTEREST FORMULAS THIS IS 13 =(1+0.07/12)^(12/4)-1 14 15 NOW, PROCEED WITH THE REST OF THE PROBLEM 16 17 n= 36.18126076 QUARTERS 18 USING EXCEL'S NPER FUNCTION THIS IS 19 =NPER(1.760%,300,,-15000) 20 21 OR COULD USE SOLVER AS FOLLOWS 22 23 n= 36.18126076 <--SOLVER CHANGED CELL 24 QUARTERS 25 26 F= $15,000.00 <--SOLVER TARGET CELL 27 USING EXCEL'S FV FUNCTION THIS IS 28 =FV(1.760%,n,-300)

A 1 PROBLEM 2.167 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

B C D E (ALSO PROBLEM 2.165 IN FIRST PRINTING) r= m= k= A= F=

7.000% 4 QUARTERS PER YEAR 12 DEPOSITS PER YEAR $100.00 PER MONTH $15,000.00

FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH) i=

0.5799633% PER MONTH USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.07/4)^(4/12)-1

NOW, PROCEED WITH THE REST OF THE PROBLEM n=

108.2348272 MONTHS USING EXCEL'S NPER FUNCTION THIS IS =NPER(0.57996326%,100,,-15000)

OR COULD USE SOLVER AS FOLLOWS n=

108.2348272 <--SOLVER CHANGED CELL

$15,000.00 <--SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(0.57996326,n,-100)

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A B C D E F G H I 1 PROBLEM 2.168 2 3 r= 6.000% PER YEAR 4 m= 12 MONTHS PER YEAR 5 k= 4 WITHDRAWALS PER QTR 6 A= $1,200.00 PER QUARTER 7 P= $20,000.00 8 9 FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (QUARTER) 10 11 i= 1.508% PER QUARTER 12 USING COMPOUND INTEREST FORMULAS THIS IS 13 =(1+0.06/12)^(12/4)-1 14 15 NOW, PROCEED WITH THE REST OF THE PROBLEM 16 17 n= 19.33837953 QUARTERS 18 USING EXCEL'S NPER FUNCTION THIS IS 19 =NPER(1.508%,1200,-20000) 20 21 OR COULD USE SOLVER AS FOLLOWS 22 23 n= 19.33837953 <--SOLVER CHANGED CELL QUARTERS 24 25 P= $20,000.00 <--SOLVER TARGET CELL 26 USING EXCEL'S PV FUNCTION THIS IS 27 =FV(1.508%,n,-1200)

A B C D E F G H 1 PROBLEM 2.169 2 3 r= 6.000% PER YEAR 4 m= 4 QUARTERS 5 k= 12 MONTHS 6 A= $400.00 PER MONTH 7 P= $20,000.00 8 9 FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH) 10 11 i= 0.4975206% PER MONTH 12 USING COMPOUND INTEREST FORMULAS THIS IS 13 =(1+0.06/4)^(4/12)-1 14 15 n= 57.6340855 USING EXCEL'S NPER FUNCTION THIS IS 16 =NPER(0.004975206,400,-20000) 17 OR 57 WHOLE MONTHS 18 19 OR, COULD USE SOLVER TO FIND n 20 21 n= 57.6340855 <--SOLVER CHANGED CELL 22 MONTHS 23 24 P= $20,000.00 <--SOLVER TARGET CELL 25 USING EXCEL'S PV FUNCTION THIS IS 26 =PV(0.004975206,n,-400)

A 1 PROBLEM 2.170 2 3 4 5 6 7 8 9 a 10 11 12 13 14 15 b 16 17 18 19 20 21 22 c 23 24 25 26 27 28 d 29 30 31 32

(P|F i%,n)=(1+i)-n

FOR n PERIODS

FROM EQ 2.9

(P|F i%,m)=(1+i)-m

FOR m PERIODS

FROM EQ 2.9

(F|P i%,m)=(1+i)m

FOR m PERIODS

FROM EQ 2.8

(P|F i%,n+m)=(1+i)-(n+m)

FOR n+m PERIODS

FROM EQ 2.9

(P|F i%,n+m)=(1+i)-(n+m)=

(1+i)-n*(1+i)-m=

(P|F i%,n+m)=(1+i)-(n+m)=

(P|F i%,n)*(P|F i%,m)

EQ 2.53 - QED

(P|F i%,n-m)=(1+i)-(n-m)

FOR n-m PERIODS

FROM EQ 2.9

(P|F i%,n-m)=(1+i)-(n-m)=

(1+i)-n*(1+i)m=

(P|F i%,n-m)=(1+i)-(n-m)=

(P|F i%,n)*(F|P i%,m)

EQ 2.54 - QED

(P|F i%,nm)=(1+i)-nm

FOR nm PERIODS

FROM EQ 2.9

(P|F i%,nm)=(1+i)-(nm)=

((1+i)-n)m=

(P|F i%,nm)=(1+i)-(nm)=

(P|F i%,n)m

EQ 2.55 - QED

(P|F i%,nm)=(1+i)-nm

FOR nm PERIODS

FROM EQ 2.9

(P|F i%,nm)=(1+i)-(nm)=

((1+i)-m)n=

(P|F i%,nm)=(1+i)-(nm)=

(P|F i%,m)n

EQ 2.56 - QED

A 1 PROBLEM 2.171 2 3 2.57 4 5 6 7 8 9 10 11 2.58 12 13 14 15 16 17 18 19 2.59 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 2.6 35 36 37 38 39 40 41 42 43 44 45 46 47

$0 1

0 P=$0 b

-n 2 (P|G i%,n)= (1-(1+n*i)*(1+i) )/(i ) -1 2 (P|G i%,1)= (1-(1+i)*(1+i) )/(i )=0

$0 1 A=$0

n (A|G i%,n)= (1/i)-(n/i)*(i/((1+i) -1)) 1 (A|G i%,1)= (1/i)-(1/i)*(i/((1+i) -1))=0

$A=$P*(1+i) $F=$P*(1+i) 0

$P b

n n (A|P i%,n)= (i*(1+i) )/((1+i) -1) 1 1 (A|P i%,1)= (i*(1+i) )/((1+i) -1)=1+i n (F|P i%,n)= (1+i) 1 (F|P i%,1)= (1+i) =1+i

1 $A

n (A|F i%,n)= i/((1+i) -1) 1 (A|F i%,1)= i/((1+i) -1)=1 n (F|A i%,n)= ((1+i) -1)/i 1 (F|A i%,1)= ((1+i) -1)/i=1

E 1 2 3 FIRST YEAR OF A GRADIENT SERIES IS $0 4 5 6 7 8 9 10 11 FIRST YEAR OF A GRADIENT SERIES IS $0 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

A 1 PROBLEM 2.172 2 3 a 4 5 6 7 8 9 10 11 b 12 13 14 15 16 17 18 19 c 20 21 22 23 24 25 26 27

r= m=

5.000% 1

ieff=

5.000% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/1)^1-1 5.000% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,1)

ieff=

r= m=

5.000% 365

ieff=

5.127% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/365)^365-1 5.127% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,365)

ieff=

r= 5.000% m= INFINITE=10000000 USING A VERY LARGE NUMBER ieff= ieff=

ieff=

5.127% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/10000000)^10000000-1 5.127% USING EXCEL'S EFFECT FUNCTION THIS IS ASSUME VERY LARGE m =EFFECT(5%,10000000) 5.127% USING EQUATION 2.A.1

A 1 PROBLEM 2.173 2 3 a 4 5 6 7 8 9 10 11 b 12 13 14 15 16 17 18 19 c 20 21 22 23 24 25 26 27

r= 10.000% m= 1 ieff= 10.000% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.10/1)^1-1 ieff= 10.000% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,1) r= 10.000% m= 365 ieff= 10.516% USING COMPOUND INTEREST FORMULAS THIS IS 10.516% ieff= 10.516% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,365) r= 10.000% m= INFINITE=10000000 USING A VERY LARGE NUMBER ieff= 10.517% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.10/10000000)^10000000-1 ieff= 10.517% USING EXCEL'S EFFECT FUNCTION THIS IS ASSUME VERY LARGE m =EFFECT(10%,10000000) ieff= 10.517% USING EQUATION 2.A.1

A B C D E F G H 1 PROBLEM 2.174 2 3 r= 10.000% COMPOUNDED CONTINUOUSLY 4 YRS= 5 5 P= $10,000.00 6 m= 10,000,000 LARGE NUMBER OF CPDG PERIODS PER YEAR 7 8 F= $16,487.21 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS 9 =C5*EXP(C3*C4) 10 F= $16,487.20 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$10,000*(F|P 10%,5)∞ 11 12 F= $16,487.21 USING EXCEL'S FV FUNCTION THIS IS 13 ASSUME VERY LARGE m 14 =FV(10%/10000000,5*10000000,,-10000)

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14

A B C D E F G H I J 1 PROBLEM 2.175 2 3 r= 15.000% COMPOUNDED CONTINUOUSLY 4 YRS= 4 5 F= $15,000.00 6 m= 10000000 LARGE NUMBER OF CPDG PERIODS PER YEAR 7 8 P= $8,232.17 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS 9 =15000*EXP(-15%*4) 10 P= $8,232.15 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$15,000*(P|F 15%,4)∞ 11 12 P= $8,232.17 USING EXCEL'S PV FUNCTION THIS IS 13 ASSUME VERY LARGE m 14 =PV(15%/10000000,4*10000000,,-15000)

A 1 PROBLEM 2.176 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r MUST MATCH THE PERIOD r= n= A=

5.000% PER 6 MONTHS 14 6 MONTH PERIODS $500.00 PER 6 MONTHS

F= $9,886.20 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS $9,886.20 F= $9,886.20 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$500*(F|A 5%,14)∞

P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS =500*(EXP(5%*14)-1)/(EXP(5%*14)*(EXP(5%)-1)) P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$500*(P|A 5%,14)∞

P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS =9886.2*EXP(-5%*14) P= $4,909.39 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$9,886.2*(P|F 5%,14)∞

1 2

A PROBLEM 2.177

NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r MUST MATCH THE PERIOD

3 4 5 6 7 8 9

r= n= A= G= a

10 11 12 13

5.000% PER 6 MONTHS 14 6 MONTH PERIODS $500.00 PER 6 MONTHS $100.00 PER 6 MONTHS $21,144.77 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$500*(F|A 5%,14)∞+$100*(P|G 5%,14)∞*(F|P 5%,14)∞ =$500*19.7724+$100*55.90849*2.01375

14 15 16 17

$10,500.19 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$500*(P|A 5%,14)∞+$100*(P|G 5%,14)∞ =$500*9.81868+$100*55.90849

P= 18 19 20 21

$10,500.28 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$21,144.77*(P|F 5%,14)∞ =$21,144.77*0.49659

c 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

$1,069.50 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$21,144.77*(A|F 5%,14)∞ =$21,144.77*0.05058

TABLE TO ILLUSTRATE AND CHECK ANSWER TO a AND b PERIOD 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

PYT $500.00 $600.00 $700.00 $800.00 $900.00 $1,000.00 $1,100.00 $1,200.00 $1,300.00 $1,400.00 $1,500.00 $1,600.00 $1,700.00 $1,800.00

FOR PERIOD 8

SUM

FW $957.77 $1,093.27 $1,213.28 $1,318.98 $1,411.48 $1,491.82 $1,560.97 $1,619.83 $1,669.23 $1,709.96 $1,742.75 $1,768.27 $1,787.16 $1,800.00

PW $475.61 $542.90 $602.50 $654.98 $700.92 $740.82 $775.16 $804.38 $828.92 $849.14 $865.42 $878.10 $887.48 $893.85

=1200*EXP(0.05*(14-8)) =1200*EXP(-0.05*8) $21,144.79 $10,500.19

A 1 PROBLEM 2.178 2

NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r AND c MUST MATCH THE PERIOD

3 4

NOTE! PAYMENTS ARE INCREASING AT A CONTINUOUSLY COMPOUNDED 20%, NOT JUST 20%.

5 6 7 8 9 10 11

r= c= n= A=

5.00% PER 6 MONTHS 20.00% PER 6 MONTHS 14 6 MONTH PERIODS $500.00 PER 6 MONTHS

$42,410.96 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS =500*(EXP(5%*14)-EXP(20%*14))/(EXP(5%)-EXP(20%))

$21,060.66 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS =500*(1-EXP((20%-5%)*14))/(EXP(5%)-EXP(20%)) $21,060.86 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$42,410.96*(P|F 5%,14)∞

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

$2,145.15 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS =$42,410.96*(A|F 5%,14)∞

TABLE TO ILLUSTRATE AND CHECK ANSWER TO a AND b PERIOD 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14 14 14

PYT $500.00 $610.70 $745.91 $911.06 $1,112.77 $1,359.14 $1,660.06 $2,027.60 $2,476.52 $3,024.82 $3,694.53 $4,512.51 $5,511.59 $6,731.87

FW $957.77 $1,112.77 $1,292.85 $1,502.08 $1,745.17 $2,027.60 $2,355.74 $2,736.97 $3,179.91 $3,694.53 $4,292.43 $4,987.09 $5,794.17 $6,731.87

PW $475.61 $552.59 $642.01 $745.91 $866.63 $1,006.88 $1,169.82 $1,359.14 $1,579.10 $1,834.65 $2,131.56 $2,476.52 $2,877.30 $3,342.95

=500*EXP(20%*(14-1)) =6731.87*EXP(5%*(14-14)) =6731.87*EXP(-5%*14) SUM

$42,410.96

$21,060.66

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14

15 16 LES THIS 17 IS 18 19 LES THIS 20 IS 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

A B C D E F G H 1 PROBLEM 2.179 2 3 r= 10.000% PER YEAR COMPOUNDED CONTINUOUSLY 4 YRS= 7 5 = $1,000.00 PER YEAR CONTINUOUS FLOW A 6 a F= $10,137.53 USING CONTINUOUS COMPOUNDING CONTINUOUS 7 FLOW INTEREST FORMULAS THIS IS 8 =1000*(EXP(10%*7)-1)/10% F= $10,137.53 USING CONTINUOUS COMPOUNDING CONTINUOUS 9 FLOW INTEREST TABLES THIS IS 10 =$1,000*(F| 10%,7) 11 b P= $5,034.15 USING CONTINUOUS COMPOUNDING CONTINUOUS 12 FLOW INTEREST FORMULAS THIS IS 13 =1000*((EXP(10%*7)-1)/(10%*EXP(10%*7))) P= $5,034.15 USING CONTINUOUS COMPOUNDING CONTINUOUS 14 FLOW INTEREST TABLES THIS IS 15 =$1,000*(P| 10%,7) P= $5,034.20 USING CONTINUOUS COMPOUNDING INTEREST 16 TABLES THIS IS =$10,137.53*(P|F 10%,7)∞ 17

A 1 PROBLEM 2.180 2 3 4 5 6 7 8 9 10 11

r= 10.000% PER YEAR YRS= 7 P= $20,000.00

A= A=

USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST FORMULAS THIS IS =20000*10%*EXP(10%*7)/(EXP(10%*7)-1) USING CONTINUOUS COMPOUNDING CONTINUOUS $3,972.80 FLOW INTEREST TABLES THIS IS =$20,000*( |P 10%,7) $3,972.87

NOTES - CHAPTER 3 SOLUTIONS FOLLOWING ARE SOME THOUGHTS ABOUT THE SOLUTIONS IN THIS CHAPTER THAT MAY BE OF HELP TO FACULTY AND STUDENTS. 1

THERE ARE FIVE DIFFERENT METHODS THAT ARE SEEN MULTIPLE TIMES IN THESE SOLUTIONS. THEY INCLUDE USE OF (1) COMPOUND INTEREST FORMULAS (USED VERY SPARINGLY), (2) INTEREST TABLES SUCH AS THOSE IN APPENDICES A AND B, AS WELL AS "ELECTRONIC" INTEREST TABLES (SEE ITEMS 2 AND 3 BELOW), (3) USE OF MYRIAD EXCEL FUNCTIONS, (4) SEARCH PROCEDURES USING EXCEL'S "SOLVER" TOOL, AND (5) BRUTE FORCE TABULAR APPROACHES

AS A FIRST EXAMPLE, LET'S DETERMINE THE MONTHLY PAYMENT THAT IS EQUIVALENT TO A PRESENT VALUE OF $10,000 IF INTEREST IS 6% NOMINAL, COMPOUNDED MONTHLY OVER A PERIOD OF 24 MONTHS. P= $10,000.00 n= 24 MONTHS r= 6% NOMINAL COMPOUNDED MONTHLY i= 0.500000000% PER MONTH INTEREST TABLE APPROACH: A= =$10,000*(A|P 6%/12,24) =$10,000*(A|P 0.5%,24) =10000*0.04432 $443.20 ELECTRONIC INTEREST TABLE APPROACH: A= =$10,000*(A|P 6%/12,24) =$10,000*(A|P 0.5%,24) =10000*0.044320610 $443.21 EXCEL PMT FUNCTION APPROACH: A= =PMT(6%/12,24,-10000) $443.21 NOTE THAT THE INTEREST TABLE APPROACH SOLUTION IS SLIGHTLY DIFFERENT ($0.01) FROM THE OTHER TWO APPROACHES. WHILE THIS IS INCONSEQUENTIAL, THE DISCREPANCY MAY BE MUCH LARGER, IN ABSOLUTE TERMS, DEPENDING UPON THE MONETARY FIGURES INVOLVED, THE NUMBER OF FACTORS INVOLVED, THE SPECIFIC INTEREST RATES INVOLVED, AND SO ON.

AS A SECOND EXAMPLE, LET'S DETERMINE THE MONTHLY PAYMENT THAT IS EQUIVALENT TO A PRESENT VALUE OF $10,000 IF INTEREST IS 7% NOMINAL, COMPOUNDED MONTHLY OVER A PERIOD OF 24 MONTHS.

P= n= r= i=

$10,000.00 24 MONTHS 7% NOMINAL COMPOUNDED MONTHLY 0.583333333% PER MONTH

INTEREST TABLE APPROACH: A= =$10,000*(A|P 7%/12,24) OOPS! THERE IS NO BOOK INTEREST TABLE FOR 7%/12 = 0.583333333% ELECTRONIC INTEREST TABLE APPROACH: A= =$10,000*(A|P 7%/12,24) =$10,000*(A|P 0.583333333%,24) =10000*0.044772579 $447.73 EXCEL PMT FUNCTION APPROACH: A= =PMT(7%/12,24,-10000) $447.73 NOTE THAT THE INTEREST TABLE APPROACH WAS NOT USED. IT MIGHT BE SUGGESTED THAT LINEAR INTERPOLATION BE USED BETWEEN TWO TABULATED INTEREST RATES; HOWEVER, THE INTEREST FACTORS ARE NOT LINEAR, AND INTERPOLATION OFTEN INVITES UNNECESSARY ERRORS. THE TWO APPROACHES USED DID ACHIEVE THE SAME ANSWER. THIS WILL OFTEN, BUT NOT ALWAYS, BE THE CASE DUE TO THE FACT THAT THE EXCEL FUNCTIONS ARE CARRYING MORE PLACES AFTER THE DECIMAL IN THE COMPUTER THAN THE 9 PLACES USED HERE WITH THE ELECTRONIC INTEREST TABLE APPROACH. e

A B C D E F G H I 1 PROBLEM 3.1 2 3 P= $18,000.00 4 i= 9.00% 5 n= 4 6 TOTAL 7 OWED 8 INTEREST TOTAL INTEREST PRINCIPAL TOTAL AFTER 9 METHOD EOY ACCRUED OWED PAYMENT PAYMENT PAYMENT PAYMENT 10 11 a 1 0 $18,000.00 12 1 $1,620.00 $19,620.00 $1,620.00 $0.00 $1,620.00 $18,000.00 13 2 $1,620.00 $19,620.00 $1,620.00 $0.00 $1,620.00 $18,000.00 14 3 $1,620.00 $19,620.00 $1,620.00 $0.00 $1,620.00 $18,000.00 15 4 $1,620.00 $19,620.00 $1,620.00 $18,000.00 $19,620.00 $0.00 16 17 b 2 0 $18,000.00 18 1 $1,620.00 $19,620.00 $1,620.00 $4,500.00 $6,120.00 $13,500.00 19 2 $1,215.00 $14,715.00 $1,215.00 $4,500.00 $5,715.00 $9,000.00 20 3 $810.00 $9,810.00 $810.00 $4,500.00 $5,310.00 $4,500.00 21 4 $405.00 $4,905.00 $405.00 $4,500.00 $4,905.00 $0.00 22 23 c 3 0 $18,000.00 24 1 $1,620.00 $19,620.00 $1,620.00 $3,936.04 $5,556.04 $14,063.96 25 2 $1,265.76 $15,329.72 $1,265.76 $4,290.28 $5,556.04 $9,773.68 26 3 $879.63 $10,653.32 $879.63 $4,676.40 $5,556.04 $5,097.28 27 4 $458.76 $5,556.04 $458.76 $5,097.28 $5,556.04 $0.00 28 29 d 4 0 $18,000.00 30 1 $1,620.00 $19,620.00 $0.00 $0.00 $0.00 $19,620.00 31 2 $1,765.80 $21,385.80 $0.00 $0.00 $0.00 $21,385.80 32 3 $1,924.72 $23,310.52 $0.00 $0.00 $0.00 $23,310.52 33 4 $2,097.95 $25,408.47 $7,408.47 $18,000.00 $25,408.47 $0.00 34 35 e DIFFERENT 0 $18,000.00 36 1 $1,620.00 $19,620.00 $1,620.00 $3,000.00 $4,620.00 $15,000.00 37 2 $1,350.00 $16,350.00 $1,350.00 $4,000.00 $5,350.00 $11,000.00 38 3 $990.00 $11,990.00 $990.00 $5,000.00 $5,990.00 $6,000.00 39 4 $540.00 $6,540.00 $540.00 $6,000.00 $6,540.00 $0.00

A B C D E F G H I 1 PROBLEM 3.2 2 3 P= $12,000.00 4 i= 8.50% 5 n= 5 6 7 FIRST PYT $1,612.56 SOLVER CHANGED CELL 8 9 LAST 10 METHOD 11 RATE INCR=j= 20.00% TOTAL 12 OWED 13 INTEREST TOTAL INTEREST PRINCIPAL TOTAL AFTER 14 METHOD EOY ACCRUED OWED PAYMENT PAYMENT PAYMENT PAYMENT 15 16 a 1 0 $12,000.00 17 1 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 18 2 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 19 3 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 20 4 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 21 5 $1,020.00 $13,020.00 $1,020.00 $12,000.00 $13,020.00 $0.00 22 23 b 2 0 $12,000.00 24 1 $1,020.00 $13,020.00 $1,020.00 $2,400.00 $3,420.00 $9,600.00 25 2 $816.00 $10,416.00 $816.00 $2,400.00 $3,216.00 $7,200.00 26 3 $612.00 $7,812.00 $612.00 $2,400.00 $3,012.00 $4,800.00 27 4 $408.00 $5,208.00 $408.00 $2,400.00 $2,808.00 $2,400.00 28 5 $204.00 $2,604.00 $204.00 $2,400.00 $2,604.00 $0.00 29 30 c 3 0 $12,000.00 31 1 $1,020.00 $13,020.00 $1,020.00 $2,025.19 $3,045.19 $9,974.81 32 2 $847.86 $10,822.67 $847.86 $2,197.33 $3,045.19 $7,777.48 33 3 $661.09 $8,438.57 $661.09 $2,384.10 $3,045.19 $5,393.38 34 4 $458.44 $5,851.81 $458.44 $2,586.75 $3,045.19 $2,806.63 35 5 $238.56 $3,045.19 $238.56 $2,806.63 $3,045.19 $0.00 36 37 d 4 0 $12,000.00 38 1 $1,020.00 $13,020.00 $0.00 $0.00 $0.00 $13,020.00 39 2 $1,106.70 $14,126.70 $0.00 $0.00 $0.00 $14,126.70 40 3 $1,200.77 $15,327.47 $0.00 $0.00 $0.00 $15,327.47 41 4 $1,302.83 $16,630.30 $0.00 $0.00 $0.00 $16,630.30 42 5 $1,413.58 $18,043.88 $6,043.88 $12,000.00 $18,043.88 $0.00 43 44 e DIFFERENT 0 $12,000.00 45 1 $1,020.00 $13,020.00 $1,020.00 $1,612.56 $2,632.56 $10,387.44 46 =FIRST PAYMENT 47 2 $882.93 $11,270.38 $882.93 $1,935.07 $2,818.00 $8,452.38 48 3 $718.45 $9,170.83 $718.45 $2,322.08 $3,040.53 $6,130.29 49 4 $521.08 $6,651.37 $521.08 $2,786.50 $3,307.57 $3,343.80 50 5 $284.22 $3,628.02 $284.22 $3,343.80 $3,628.02 $0.00 51 =2786.5*1.2 52 53 SUM $12,000.00 SOLVER TARGET CELL 54 =SUM(PR PYT YR 1:PR PYT YR 5)

A B C D E F G H I 1 PROBLEM 3.3 2 3 P= $140,000.00 4 i= 3.00% PER QTR 5 n= 8 QTRS 6 TOTAL 7 OWED 8 END OF INTEREST TOTAL INTEREST PRINCIPAL TOTAL AFTER 9 METHOD QTR ACCRUED OWED PAYMENT PAYMENT PAYMENT PAYMENT 10 11 a 1 0 $140,000.00 12 1 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 13 2 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 14 3 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 15 4 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 16 5 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 17 6 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 18 7 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 19 8 $4,200.00 $144,200.00 $4,200.00 $140,000.00 $144,200.00 $0.00 20 21 22 b 2 0 $140,000.00 23 1 $4,200.00 $144,200.00 $4,200.00 $17,500.00 $21,700.00 $122,500.00 24 2 $3,675.00 $126,175.00 $3,675.00 $17,500.00 $21,175.00 $105,000.00 25 3 $3,150.00 $108,150.00 $3,150.00 $17,500.00 $20,650.00 $87,500.00 26 4 $2,625.00 $90,125.00 $2,625.00 $17,500.00 $20,125.00 $70,000.00 27 5 $2,100.00 $72,100.00 $2,100.00 $17,500.00 $19,600.00 $52,500.00 28 6 $1,575.00 $54,075.00 $1,575.00 $17,500.00 $19,075.00 $35,000.00 29 7 $1,050.00 $36,050.00 $1,050.00 $17,500.00 $18,550.00 $17,500.00 30 8 $525.00 $18,025.00 $525.00 $17,500.00 $18,025.00 $0.00 31 32 33 c 3 0 $140,000.00 34 1 $4,200.00 $144,200.00 $4,200.00 $15,743.89 $19,943.89 $124,256.11 35 2 $3,727.68 $127,983.79 $3,727.68 $16,216.21 $19,943.89 $108,039.89 36 3 $3,241.20 $111,281.09 $3,241.20 $16,702.70 $19,943.89 $91,337.20 37 4 $2,740.12 $94,077.31 $2,740.12 $17,203.78 $19,943.89 $74,133.42 38 5 $2,224.00 $76,357.42 $2,224.00 $17,719.89 $19,943.89 $56,413.53 39 6 $1,692.41 $58,105.93 $1,692.41 $18,251.49 $19,943.89 $38,162.04 40 7 $1,144.86 $39,306.90 $1,144.86 $18,799.03 $19,943.89 $19,363.00 41 8 $580.89 $19,943.89 $580.89 $19,363.00 $19,943.89 $0.00 42 43 44 d 4 0 $140,000.00 45 1 $4,200.00 $144,200.00 $0.00 $0.00 $0.00 $144,200.00 46 2 $4,326.00 $148,526.00 $0.00 $0.00 $0.00 $148,526.00 47 3 $4,455.78 $152,981.78 $0.00 $0.00 $0.00 $152,981.78 48 4 $4,589.45 $157,571.23 $0.00 $0.00 $0.00 $157,571.23 49 5 $4,727.14 $162,298.37 $0.00 $0.00 $0.00 $162,298.37 50 6 $4,868.95 $167,167.32 $0.00 $0.00 $0.00 $167,167.32 51 7 $5,015.02 $172,182.34 $0.00 $0.00 $0.00 $172,182.34 52 8 $5,165.47 $177,347.81 $37,347.81 $140,000.00 $177,347.81 $0.00 53 54 55 56 57

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

DIFF

0 1 2 3 4 5 6 7 8

$4,200.00 $144,200.00 $3,990.00 $136,990.00 $3,570.00 $122,570.00 $2,940.00 $100,940.00 $2,100.00 $72,100.00 $1,260.00 $43,260.00 $630.00 $21,630.00 $210.00 $7,210.00

$4,200.00 $3,990.00 $3,570.00 $2,940.00 $2,100.00 $1,260.00 $630.00 $210.00

$7,000.00 $14,000.00 $21,000.00 $28,000.00 $28,000.00 $21,000.00 $14,000.00 $7,000.00

SUM

FIRST PYT

$140,000.00 $11,200.00 $133,000.00 $17,990.00 $119,000.00 $24,570.00 $98,000.00 $30,940.00 $70,000.00 $30,100.00 $42,000.00 $22,260.00 $21,000.00 $14,630.00 $7,000.00 $7,210.00 $0.00

$140,000.00 SOLVER TARGET CELL =SUM(PR PYT YR 1:PR PYT YR 8) $7,000.00

SOLVER CHANGED CELL

A B C D E F G H 1 PROBLEM 3.4 2 3 P= $5,000.00 4 i= 1.75% PER MONTH 5 n= 12 MONTHS 6 7 FIRST PYT $166.67 SOLVER CHANGED CELL 8 LAST 9 METHOD 10 11 12 END INTEREST TOTAL INTEREST PRINCIPAL TOTAL 13 METHOD OF MO ACCRUED OWED PAYMENT PAYMENT PAYMENT 14 15 a 1 0 16 1 $87.50 $5,087.50 $87.50 $0.00 $87.50 17 2 $87.50 $5,087.50 $87.50 $0.00 $87.50 18 3 $87.50 $5,087.50 $87.50 $0.00 $87.50 19 4 $87.50 $5,087.50 $87.50 $0.00 $87.50 20 5 $87.50 $5,087.50 $87.50 $0.00 $87.50 21 6 $87.50 $5,087.50 $87.50 $0.00 $87.50 22 7 $87.50 $5,087.50 $87.50 $0.00 $87.50 23 8 $87.50 $5,087.50 $87.50 $0.00 $87.50 24 9 $87.50 $5,087.50 $87.50 $0.00 $87.50 25 10 $87.50 $5,087.50 $87.50 $0.00 $87.50 26 11 $87.50 $5,087.50 $87.50 $0.00 $87.50 27 12 $87.50 $5,087.50 $87.50 $5,000.00 $5,087.50 28 29 b 2 0 30 1 $87.50 $5,087.50 $87.50 $416.67 $504.17 31 2 $80.21 $4,663.54 $80.21 $416.67 $496.88 32 3 $72.92 $4,239.58 $72.92 $416.67 $489.58 33 4 $65.63 $3,815.63 $65.63 $416.67 $482.29 34 5 $58.33 $3,391.67 $58.33 $416.67 $475.00 35 6 $51.04 $2,967.71 $51.04 $416.67 $467.71 36 7 $43.75 $2,543.75 $43.75 $416.67 $460.42 37 8 $36.46 $2,119.79 $36.46 $416.67 $453.13 38 9 $29.17 $1,695.83 $29.17 $416.67 $445.83 39 10 $21.88 $1,271.88 $21.88 $416.67 $438.54 40 11 $14.58 $847.92 $14.58 $416.67 $431.25 41 12 $7.29 $423.96 $7.29 $416.67 $423.96 42 43 c 3 0 44 1 $87.50 $5,087.50 $87.50 $378.07 $465.57 45 2 $80.88 $4,702.81 $80.88 $384.69 $465.57 46 3 $74.15 $4,311.40 $74.15 $391.42 $465.57 47 4 $67.30 $3,913.13 $67.30 $398.27 $465.57 48 5 $60.33 $3,507.89 $60.33 $405.24 $465.57 49 6 $53.24 $3,095.57 $53.24 $412.33 $465.57 50 7 $46.02 $2,676.02 $46.02 $419.54 $465.57 51 8 $38.68 $2,249.14 $38.68 $426.89 $465.57 52 9 $31.21 $1,814.78 $31.21 $434.36 $465.57 53 10 $23.61 $1,372.82 $23.61 $441.96 $465.57 54 11 $15.88 $923.13 $15.88 $449.69 $465.57 55 12 $8.01 $465.57 $8.01 $457.56 $465.57 56 57

TOTAL OWED AFTER PAYMENT $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $0.00 $5,000.00 $4,583.33 $4,166.67 $3,750.00 $3,333.33 $2,916.67 $2,500.00 $2,083.33 $1,666.67 $1,250.00 $833.33 $416.67 $0.00 $5,000.00 $4,621.93 $4,237.25 $3,845.83 $3,447.56 $3,042.33 $2,630.00 $2,210.45 $1,783.57 $1,349.21 $907.25 $457.56 $0.00

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89

A d

B 4

DIFFERENT

C 0 1 2 3 4 5 6 7 8 9 10 11 12

$87.50 $89.03 $90.59 $92.17 $93.79 $95.43 $97.10 $98.80 $100.53 $102.29 $104.08 $105.90

$5,087.50 $0.00 $5,176.53 $0.00 $5,267.12 $0.00 $5,359.30 $0.00 $5,453.08 $0.00 $5,548.51 $0.00 $5,645.61 $0.00 $5,744.41 $0.00 $5,844.94 $0.00 $5,947.22 $0.00 $6,051.30 $0.00 $6,157.20 $1,157.20

0 1

$87.50

$5,087.50

2 3 4 5 6 7 8 9

$84.58 $81.67 $78.75 $72.92 $67.08 $61.25 $52.50 $43.75

$4,917.92 $4,748.33 $4,578.75 $4,239.58 $3,900.42 $3,561.25 $3,052.50 $2,543.75

10 11 12

$35.00 $23.33 $11.67

$2,035.00 $1,356.67 $678.33

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $5,000.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $6,157.20

$87.50 $166.67 $254.17 =FIRST PAYMENT $84.58 $166.67 $251.25 $81.67 $166.67 $248.33 $78.75 $333.33 $412.08 $72.92 $333.33 $406.25 $67.08 $333.33 $400.42 $61.25 $500.00 $561.25 $52.50 $500.00 $552.50 $43.75 $500.00 $543.75 =3*FIRST PAYMENT $35.00 $666.67 $701.67 $23.33 $666.67 $690.00 $11.67 $666.67 $678.33

I $5,000.00 $5,087.50 $5,176.53 $5,267.12 $5,359.30 $5,453.08 $5,548.51 $5,645.61 $5,744.41 $5,844.94 $5,947.22 $6,051.30 $0.00 $5,000.00 $4,833.33 $4,666.67 $4,500.00 $4,166.67 $3,833.33 $3,500.00 $3,000.00 $2,500.00 $2,000.00 $1,333.33 $666.67 $0.00

SUM $5,000.00 SOLVER TGT CELL =SUM(PR PYT YR 1:PR PYT YR 12)

A B C D E F G H I J K 1 PROBLEM 3.5 2 3 P= $18,000.00 4 i= 9.00% TVOM RATE 5% 9% 5 n= 4 6 TOTAL 7 OWED 8 INTEREST TOTAL INTEREST PRINCIPAL TOTAL AFTER 9 METHOD EOY ACCRUED OWED PAYMENT PAYMENT PAYMENT PAYMENT 10 11 a 1 0 $18,000.00 12 1 $1,620.00 $19,620.00 $1,620.00 $0.00 $1,620.00 $18,000.00 13 2 $1,620.00 $19,620.00 $1,620.00 $0.00 $1,620.00 $18,000.00 14 3 $1,620.00 $19,620.00 $1,620.00 $0.00 $1,620.00 $18,000.00 PW(5%) PW(9%) 15 4 $1,620.00 $19,620.00 $1,620.00 $18,000.00 $19,620.00 $0.00 $20,553.08 $18,000.00 16 =NPV(5%,1620,1620,1620,19620) 17 18 b 2 0 $18,000.00 19 1 $1,620.00 $19,620.00 $1,620.00 $4,500.00 $6,120.00 $13,500.00 20 2 $1,215.00 $14,715.00 $1,215.00 $4,500.00 $5,715.00 $9,000.00 21 3 $810.00 $9,810.00 $810.00 $4,500.00 $5,310.00 $4,500.00 PW(5%) PW(9%) 22 4 $405.00 $4,905.00 $405.00 $4,500.00 $4,905.00 $0.00 $19,634.58 $18,000.00 23 24 c 3 0 $18,000.00 25 1 $1,620.00 $19,620.00 $1,620.00 $3,936.04 $5,556.04 $14,063.96 26 2 $1,265.76 $15,329.72 $1,265.76 $4,290.28 $5,556.04 $9,773.68 27 3 $879.63 $10,653.32 $879.63 $4,676.40 $5,556.04 $5,097.28 PW(5%) PW(9%) 28 4 $458.76 $5,556.04 $458.76 $5,097.28 $5,556.04 $0.00 $19,701.43 $18,000.00 29 30 d 4 0 $18,000.00 31 1 $1,620.00 $19,620.00 $0.00 $0.00 $0.00 $19,620.00 32 2 $1,765.80 $21,385.80 $0.00 $0.00 $0.00 $21,385.80 33 3 $1,924.72 $23,310.52 $0.00 $0.00 $0.00 $23,310.52 PW(5%) PW(9%) 34 4 $2,097.95 $25,408.47 $7,408.47 $18,000.00 $25,408.47 $0.00 $20,903.61 $18,000.00 35 36 e DIFF 0 $18,000.00 37 1 $1,620.00 $19,620.00 $1,620.00 $3,000.00 $4,620.00 $15,000.00 38 2 $1,350.00 $16,350.00 $1,350.00 $4,000.00 $5,350.00 $11,000.00 39 3 $990.00 $11,990.00 $990.00 $5,000.00 $5,990.00 $6,000.00 PW(5%) PW(9%) 40 4 $540.00 $6,540.00 $540.00 $6,000.00 $6,540.00 $0.00 $19,807.47 $18,000.00

13%

PW(13%) $15,858.38

PW(13%) $16,580.04

PW(13%) $16,526.27

PW(13%) $15,583.49

PW(13%) $16,440.81

A B C D E F G H I J K L 1 PROBLEM 3.6 2 3 P= $12,000.00 4 i= 8.50% 5 n= 5 6 7 FIRST PYT $1,612.56 SOLVER CHANGED CELL 8 9 LAST 10 METHOD TVOM RATE 4.00% 8.50% 13.00% 11 RATE 12 INCR=j= 20.00% TOTAL 13 OWED 14 INTEREST TOTAL INTEREST PRINCIPAL TOTAL AFTER 15 METHOD EOY ACCRUED OWED PAYMENT PAYMENT PAYMENT PAYMENT 16 17 a 1 0 $12,000.00 18 1 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 19 2 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 20 3 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 21 4 $1,020.00 $13,020.00 $1,020.00 $0.00 $1,020.00 $12,000.00 PW(4%) PW(8.5%) PW(13%) 22 5 $1,020.00 $13,020.00 $1,020.00 $12,000.00 $13,020.00 $0.00 $14,403.98 $12,000.00 $10,100.70 23 =NPV(4%,1020,1020,1020,1020,13020) 24 25 b 2 0 $12,000.00 26 1 $1,020.00 $13,020.00 $1,020.00 $2,400.00 $3,420.00 $9,600.00 27 2 $816.00 $10,416.00 $816.00 $2,400.00 $3,216.00 $7,200.00 28 3 $612.00 $7,812.00 $612.00 $2,400.00 $3,012.00 $4,800.00 29 4 $408.00 $5,208.00 $408.00 $2,400.00 $2,808.00 $2,400.00 PW(4%) PW(8.5%) PW(13%) 30 5 $204.00 $2,604.00 $204.00 $2,400.00 $2,604.00 $0.00 $13,480.08 $12,000.00 $10,768.16 31 32 c 3 0 $12,000.00 33 1 $1,020.00 $13,020.00 $1,020.00 $2,025.19 $3,045.19 $9,974.81 34 2 $847.86 $10,822.67 $847.86 $2,197.33 $3,045.19 $7,777.48 35 3 $661.09 $8,438.57 $661.09 $2,384.10 $3,045.19 $5,393.38 36 4 $458.44 $5,851.81 $458.44 $2,586.75 $3,045.19 $2,806.63 PW(4%) PW(8.5%) PW(13%) 37 5 $238.56 $3,045.19 $238.56 $2,806.63 $3,045.19 $0.00 $13,556.64 $12,000.00 $10,710.63 38 39 d 4 0 $12,000.00 40 1 $1,020.00 $13,020.00 $0.00 $0.00 $0.00 $13,020.00 41 2 $1,106.70 $14,126.70 $0.00 $0.00 $0.00 $14,126.70 42 3 $1,200.77 $15,327.47 $0.00 $0.00 $0.00 $15,327.47

43 44 45 46 47 48 49 50 51 52 53 54 55 56

C 4 5

D E $1,302.83 $16,630.30 $1,413.58 $18,043.88

F G H $0.00 $0.00 $0.00 $6,043.88 $12,000.00 $18,043.88

DIFFERENT

0 1

$1,020.00 $13,020.00

2 3 4 5

$882.93 $11,270.38 $718.45 $9,170.83 $521.08 $6,651.37 $284.22 $3,628.02

$1,020.00 $1,612.56 $2,632.56 =FIRST PAYMENT $882.93 $1,935.07 $2,818.00 $718.45 $2,322.08 $3,040.53 $521.08 $2,786.50 $3,307.57 $284.22 $3,343.80 $3,628.02 =2786.5*(1+0.2)

I J K $16,630.30 PW(4%) PW(8.5%) $0.00 $14,830.75 $12,000.00

L PW(13%) $9,793.50

$12,000.00 $10,387.44 $8,452.38 $6,130.29 $3,343.80 PW(4%) PW(8.5%) PW(13%) $0.00 $13,649.02 $12,000.00 $10,641.59

SUM $12,000.00 SOLVER TARGET CELL =SUM(PR PYT YR 1:PR PYT YR 5)

A B C D E F G H I J K L 1 PROBLEM 3.7 2 3 P= $140,000.00 4 i= 3.00% PER QTR 5 n= 8 QTRS 6 TVOM RATE 7% 12% 17% 7 FIRST 8 PYT m= 4 4 4 9 LAST 10 METHOD $7,000.00 SOLVER CHANGED CELL TOTAL 11 OWED 12 END OF INTEREST TOTAL INTEREST PRINCIPAL TOTAL AFTER 13 METHOD QTR ACCRUED OWED PAYMENT PAYMENT PAYMENT PAYMENT 14 15 a 1 0 $140,000.00 16 1 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 17 2 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 18 3 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 19 4 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 20 5 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 21 6 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 22 7 $4,200.00 $144,200.00 $4,200.00 $0.00 $4,200.00 $140,000.00 PW(7%) PW(12%) PW(17%) 23 8 $4,200.00 $144,200.00 $4,200.00 $140,000.00 $144,200.00 $0.00 $152,958.84 $140,000.00 $128,338.38 24 =NPV(0.07/4,TOT PYT YR 1:TOT PYT YR 8) 25 26 b 2 0 $140,000.00 27 1 $4,200.00 $144,200.00 $4,200.00 $17,500.00 $21,700.00 $122,500.00 28 2 $3,675.00 $126,175.00 $3,675.00 $17,500.00 $21,175.00 $105,000.00 29 3 $3,150.00 $108,150.00 $3,150.00 $17,500.00 $20,650.00 $87,500.00 30 4 $2,625.00 $90,125.00 $2,625.00 $17,500.00 $20,125.00 $70,000.00 31 5 $2,100.00 $72,100.00 $2,100.00 $17,500.00 $19,600.00 $52,500.00 32 6 $1,575.00 $54,075.00 $1,575.00 $17,500.00 $19,075.00 $35,000.00 33 7 $1,050.00 $36,050.00 $1,050.00 $17,500.00 $18,550.00 $17,500.00 PW(7%) PW(12%) PW(17%) 34 8 $525.00 $18,025.00 $525.00 $17,500.00 $18,025.00 $0.00 $147,436.84 $140,000.00 $133,122.41 35 36 c 3 0 $140,000.00 37 1 $4,200.00 $144,200.00 $4,200.00 $15,743.89 $19,943.89 $124,256.11 38 2 $3,727.68 $127,983.79 $3,727.68 $16,216.21 $19,943.89 $108,039.89 39 3 $3,241.20 $111,281.09 $3,241.20 $16,702.70 $19,943.89 $91,337.20 40 4 $2,740.12 $94,077.31 $2,740.12 $17,203.78 $19,943.89 $74,133.42 41 5 $2,224.00 $76,357.42 $2,224.00 $17,719.89 $19,943.89 $56,413.53 42 6 $1,692.41 $58,105.93 $1,692.41 $18,251.49 $19,943.89 $38,162.04

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

C 7 8

D $1,144.86 $580.89

H $19,943.89 $19,943.89

I J K L $19,363.00 PW(7%) PW(12%) PW(17%) $0.00 $147,685.59 $140,000.00 $132,901.77

0 1 2 3 4 5 6 7 8

$4,200.00 $144,200.00 $0.00 $0.00 $0.00 $4,326.00 $148,526.00 $0.00 $0.00 $0.00 $4,455.78 $152,981.78 $0.00 $0.00 $0.00 $4,589.45 $157,571.23 $0.00 $0.00 $0.00 $4,727.14 $162,298.37 $0.00 $0.00 $0.00 $4,868.95 $167,167.32 $0.00 $0.00 $0.00 $5,015.02 $172,182.34 $0.00 $0.00 $0.00 $5,165.47 $177,347.81 $37,347.81 $140,000.00 $177,347.81

$140,000.00 $144,200.00 $148,526.00 $152,981.78 $157,571.23 $162,298.37 $167,167.32 $172,182.34 PW(7%) PW(12%) PW(17%) $0.00 $154,365.59 $140,000.00 $127,121.01

0 1 2 3

$4,200.00 $144,200.00 $3,990.00 $136,990.00 $3,570.00 $122,570.00

$4,200.00 $3,990.00 $3,570.00

4 5 6 7 8

$2,940.00 $100,940.00 $2,100.00 $72,100.00 $1,260.00 $43,260.00 $630.00 $21,630.00 $210.00 $7,210.00

$2,940.00 $2,100.00 $1,260.00 $630.00 $210.00

DIFF

E $39,306.90 $19,943.89

F $1,144.86 $580.89

G $18,799.03 $19,363.00

$7,000.00 $14,000.00 $21,000.00 =3*7000 $28,000.00 $28,000.00 $21,000.00 $14,000.00 $7,000.00

$140,000.00 $11,200.00 $133,000.00 $17,990.00 $119,000.00 $24,570.00 $98,000.00 $30,940.00 $30,100.00 $22,260.00 $14,630.00 $7,210.00

$70,000.00 $42,000.00 $21,000.00 $7,000.00 PW(7%) PW(12%) PW(17%) $0.00 $147,464.68 $140,000.00 $133,063.16

SUM $140,000.00 SOLVER TARGET CELL =SUM(PR PYT YR 1:PR PYT YR 8)

A 1 PROBLEM 3.8 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 a 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 b 35 36 37 38 39 40 41 42

$5,000.00

1.75%

PER MONTH

MONTHS

FIRST PYT LAST METHOD

METHOD 1

$166.67 SOLVER CHANGED CELL

END OF MO

INTEREST ACCRUED

TOTAL OWED

INTEREST PRINCIPAL TOTAL PAYMENT PAYMENT PAYMENT

0 1 2 3 4 5 6 7 8 9 10 11 12

$87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50 $87.50 $5,087.50

$87.50 $87.50 $87.50 $87.50 $87.50 $87.50 $87.50 $87.50 $87.50 $87.50 $87.50 $87.50

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $5,000.00

0 1 2 3 4 5 6 7 8

$87.50 $5,087.50 $80.21 $4,663.54 $72.92 $4,239.58 $65.63 $3,815.63 $58.33 $3,391.67 $51.04 $2,967.71 $43.75 $2,543.75 $36.46 $2,119.79

$87.50 $80.21 $72.92 $65.63 $58.33 $51.04 $43.75 $36.46

$416.67 $416.67 $416.67 $416.67 $416.67 $416.67 $416.67 $416.67

TVOM RATE

21%

36%

TOTAL OWED AFTER PAYMENT

$5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 $87.50 $5,000.00 PW(6%) PW(21%) PW(36%) $5,087.50 $0.00 $5,726.18 $5,000.00 $4,377.87 =NPV(6%/12,TOT PYT YR 1:TOT PYT YR 12)

$504.17 $496.88 $489.58 $482.29 $475.00 $467.71 $460.42 $453.13

$5,000.00 $4,583.33 $4,166.67 $3,750.00 $3,333.33 $2,916.67 $2,500.00 $2,083.33 $1,666.67

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

C 9 10 11 12

D E $29.17 $1,695.83 $21.88 $1,271.88 $14.58 $847.92 $7.29 $423.96

F $29.17 $21.88 $14.58 $7.29

G $416.67 $416.67 $416.67 $416.67

H $445.83 $438.54 $431.25 $423.96

I J K L $1,250.00 $833.33 $416.67 PW(6%) PW(21%) PW(36%) $0.00 $5,396.95 $5,000.00 $4,644.79

0 1 2 3 4 5 6 7 8 9 10 11 12

$87.50 $5,087.50 $80.88 $4,702.81 $74.15 $4,311.40 $67.30 $3,913.13 $60.33 $3,507.89 $53.24 $3,095.57 $46.02 $2,676.02 $38.68 $2,249.14 $31.21 $1,814.78 $23.61 $1,372.82 $15.88 $923.13 $8.01 $465.57

$87.50 $80.88 $74.15 $67.30 $60.33 $53.24 $46.02 $38.68 $31.21 $23.61 $15.88 $8.01

$378.07 $384.69 $391.42 $398.27 $405.24 $412.33 $419.54 $426.89 $434.36 $441.96 $449.69 $457.56

$465.57 $465.57 $465.57 $465.57 $465.57 $465.57 $465.57 $465.57 $465.57 $465.57 $465.57 $465.57

$5,000.00 $4,621.93 $4,237.25 $3,845.83 $3,447.56 $3,042.33 $2,630.00 $2,210.45 $1,783.57 $1,349.21 $907.25 $457.56 PW(6%) PW(21%) PW(36%) $0.00 $5,409.41 $5,000.00 $4,634.27

0 1 2 3 4 5 6 7 8 9 10 11 12

$87.50 $5,087.50 $89.03 $5,176.53 $90.59 $5,267.12 $92.17 $5,359.30 $93.79 $5,453.08 $95.43 $5,548.51 $97.10 $5,645.61 $98.80 $5,744.41 $100.53 $5,844.94 $102.29 $5,947.22 $104.08 $6,051.30 $105.90 $6,157.20

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1,157.20

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $5,000.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $6,157.20

$5,000.00 $5,087.50 $5,176.53 $5,267.12 $5,359.30 $5,453.08 $5,548.51 $5,645.61 $5,744.41 $5,844.94 $5,947.22 $6,051.30 PW(6%) PW(21%) PW(36%) $0.00 $5,799.50 $5,000.00 $4,318.53

0 1 2 3 4 5 6 7

$87.50 $5,087.50 $84.58 $4,917.92 $81.67 $4,748.33 $78.75 $4,578.75 $72.92 $4,239.58 $67.08 $3,900.42 $61.25 $3,561.25

$87.50 $84.58 $81.67 $78.75 $72.92 $67.08 $61.25

$166.67 $166.67 $166.67 $333.33 $333.33 $333.33 $500.00 =3*166.67

$254.17 $251.25 $248.33 $412.08 $406.25 $400.42 $561.25

DIFFERENT

$5,000.00 $4,833.33 $4,666.67 $4,500.00 $4,166.67 $3,833.33 $3,500.00 $3,000.00

A 85 86 87 88 89 90 91 92

C 8 9 10 11 12

D E $52.50 $3,052.50 $43.75 $2,543.75 $35.00 $2,035.00 $23.33 $1,356.67 $11.67 $678.33

F $52.50 $43.75 $35.00 $23.33 $11.67

G $500.00 $500.00 $666.67 $666.67 $666.67

H $552.50 $543.75 $701.67 $690.00 $678.33

I J K L $2,500.00 $2,000.00 $1,333.33 $666.67 PW(6%) PW(21%) PW(36%) $0.00 $5,487.49 $5,000.00 $4,568.34

SUM $5,000.00 SOLVER TARGET CELL =SUM(PR PYT 1:PR PYT 12)

A B C D E F G H 1 PROBLEM 3.9 2 3 a(1) r= 9.00% NOMINAL 4 m= 12 CMPD MONTHLY 5 EFFECTIVE RATE= 9.3807% =EFFECT(9%,12) 6 PYT=A= $3,311.61 PER YEAR 7 n= 5 YEARS 8 9 PW= $12,754.77 USING COMPOUND INTEREST FORMULAS THIS IS 10 =3311.61*((1+9.3807%)^5-1)/(9.3807%*(1+9.3807%)^5) 11 PW= $12,754.77 USING INTEREST TABLES THIS IS 12 $3,311.61*(P|A 9.3807%,5) 13 PW= $12,754.77 USING EXCEL'S PV FUNCTION THIS IS 14 =PV(9.3807%,5,-3311.61) 15 16 a(2) r= 9.00% NOMINAL 17 m= 12 CMPD MONTHLY 18 PYT= $253.93 PER MONTH 19 n= 60 MONTHS 20 21 PW= $12,232.66 USING COMPOUND INTEREST FORMULAS THIS IS 22 =253.93*((1+0.09/12)^60-1)/((0.09/12)*(1+0.09/12)^60) 23 PW= $12,232.66 USING INTEREST TABLES THIS IS 24 $253.93*(P|A 0.09/12,60) 25 PW= $12,232.66 USING EXCEL'S PV FUNCTION THIS IS 26 =PV(0.09/12,60,-253.93) 27 28 MONTHLY PAYMENTS ARE BETTER 29 30 31 b(1) r= 25.00% NOMINAL 32 m= 12 CMPD MONTHLY 33 EFFECTIVE RATE= 28.0732% =EFFECT(9%,12) 34 PYT=A= $3,311.61 PER YEAR 35 n= 5 YEARS 36 37 PW= $8,372.96 USING COMPOUND INTEREST FORMULAS THIS IS 38 =3311.61*((1+28.0732%)^5-1)/(28.0732%*(1+28.0732%)^5) 39 PW= $8,372.94 USING INTEREST TABLES THIS IS 40 $3,311.61*(P|A 28.0732%,5) 41 PW= $8,372.96 USING EXCEL'S PV FUNCTION THIS IS 42 =PV(28.0732%,5,-3311.61) 43 44 b(2) r= 25.00% NOMINAL 45 m= 12 CMPD MONTHLY 46 PYT= $253.93 PER MONTH 47 n= 60 MONTHS 48 49 PW= $8,651.40 USING COMPOUND INTEREST FORMULAS THIS IS 50 =253.93*((1+0.25/12)^60-1)/((0.25/12)*(1+0.25/12)^60) 51 PW= $8,651.40 USING INTEREST TABLES THIS IS 52 $253.93*(P|A 0.25/12,60) 53 PW= $8,651.40 USING EXCEL'S PV FUNCTION THIS IS 54 =PV(0.25/12,60,-253.93) 55 56 YEARLY PAYMENTS ARE BETTER

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 1+28.0732%)^5) 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

1 2 3

A PROBLEM 3.10 a

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

FIRST, DETERMINE THE PW OF THE KNOWN-PAYMENT OPTION MUST DETERMINE ANNUAL EFFECTIVE INTEREST RATE TO MATCH PAYMENT PERIOD r= n= PYT= EFFECTIVE RATE= PW= PW= PW=

8.00% 5 $3,288.91 8.243%

NOMINAL CPD QTRLY YEARS GIVEN =EFFECT(8%,4)

$13,047.92 USING COMPOUND INTEREST FORMULAS THIS IS =3288.91*((1+8.243%)^5-1)/(8.243%*(1+8.243%)^5) $13,047.99 USING INTEREST TABLES THIS IS =$3,288.91*(P|A 8.243%,5) $13,047.92 USING EXCEL'S PV FUNCTION THIS IS =PV(8.243%,5,-3288.91)

NOW, DETERMINE THE AMOUNT OF THE QUARTERLY PAYMENT, X r= n= m= PW=

8.00% 24 4 $13,047.92

NOMINAL CPD QTRLY QUARTERS PERIODS/YEAR FROM ABOVE

PYT= PW=

X $13,047.92

$689.86

$/QTR =X*(P|A 2%,24) =X*18.91393 PER QTR

OR, RATHER THAN SOLVE MATHEMATICALLY FOR X, SOLVER CAN BE USED TO FIND X. NOTE THAT THE SAME ANSWER IS OBTAINED.

PW=

$13,047.92 SOLVER TARGET CELL =PV(8%/4,24,-X)

$689.86

SOLVER CHANGED CELL

FIRST, DETERMINE THE PW OF THE KNOWN-PAYMENT OPTION MUST DETERMINE ANNUAL EFFECTIVE INTEREST RATE TO MATCH PAYMENT PERIOD r= n= PYT= EFFECTIVE RATE=

22.00% 5 $3,288.91 23.882%

PW=

$9,051.43

PW= PW=

NOMINAL CPD QTRLY YEARS GIVEN =EFFECT(8%,4)

USING COMPOUND INTEREST FORMULAS THIS IS =3288.91*((1+23.882%)^5-1)/(23.882%*(1+23.882%)^5) $9,051.51 USING INTEREST TABLES THIS IS =$3,288.91*(P|A 23.882,5) $9,051.43 USING EXCEL'S PV FUNCTION THIS IS =PV(23.882%,5,-3288.91)

NOW, DETERMINE THE AMOUNT OF THE QUARTERLY PAYMENT, X

A 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

B r= n= m= PW=

C 22.00% 24 4 $9,051.43

D NOMINAL CPD QTRLY QUARTERS PERIODS/YEAR FROM ABOVE

PYT= PW=

X $9,051.43

$688.23

$/QTR =X*(P|A 5.5%,24) =X*13.1517 PER QTR

OR, RATHER THAN SOLVE MATHEMATICALLY FOR X, SOLVER CAN BE USED TO FIND X. NOTE THAT THE SAME ANSWER IS OBTAINED. PW=

$9,051.43

SOLVER TARGET CELL =PV(22%/4,24,-X)

$688.23

SOLVER CHANGED CELL

A B C D E F G H I J 1 PROBLEM 3.11 2 3 "BUYING A HOME" GIVES NINE USEFUL STEPS INCLUDING MAKING OFFERS AND SEEKING LOANS. 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 "SELLING A HOME" TALKS ABOUT WHAT TO FIX, SELLING BY OWNER, OR SEEKING A REALTOR. 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

58 59 60 61 62 63 64 65 66 67 68 69 "CONSUMER INFORMATION" WARNS ABOUT ALL KINDS OF FRAUD, LENDING 70 PROBLEMS, AND HOME INSPECTIONS. 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106

A B C D E F G H I J K L 1 PROBLEM 3.12 2 AFTER LOOKING AT SEVERAL "ADVERTISING" SITES, THIS ONE WAS THE BEST I FOUND FOR EXPLAINING AND "OPINIONIZING" ON VARIOUS "CLOSING COSTS" (SCROLL ALL THE WAY DOWN).THESE TYPES OF COSTS WERE DIVULGED WHEN I WAS LOOKING FOR A LARGE LOAN ON A NEW HOUSE AND FINALLY ASKED "ARE THERE ANY OTHER UP-FRONT CHARGES?" ONLY AT THAT TIME DID THE INCESSANT LIST OF CLOSING COSTS GET DETAILED, AND IT ADDED UP TO MANY THOUSANDS OF DOLLARS UP FRONT. COMPARED TO THE NUMBERS I HEARD FROM THE LENDER, THESE CLOSING COST ESTIMATES LOOK A BIT LOW TO ME. AN EXAMPLE WOULD BE THE TITLE SEARCH, WHICH SEEMS TO GO FOR $400 IN MY CITY. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

A 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

A 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

A 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162

A 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204

A 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234

O 1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

O 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

O 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

O 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162

O 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204

O 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234

A B C D E F G H I J K 1 PROBLEM 3.13 2 3 THE CORRECT RESULT OF $1496.93 WAS OBTAINED (SEE BELOW FOR SETUP AND THEN CALCULATION) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

A B C D E F G H 1 PROBLEM 3.14 2 3 P= $190,000.00 4 r= 6.8230% NOMINAL ANNUAL 5 n= 360 MONTHS 6 m= 12 MONTHS PER YEAR 7 8 a A= $1,241.57 USING ELECTRONIC INTEREST TABLES THIS IS 9 =$190,000*(A|P 6.8230%/12,360) 10 A= $1,241.57 USING EXCEL'S PMT FUNCTION THIS IS 11 =PMT(6.823%/12,360,-190000) 12 13 SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW 14 15 b FIND PRESENT WORTH OF FINAL 300 PAYMENTS 16 17 P(300)= $178,507.54 USING ELECTRONIC INTEREST TABLES THIS IS 18 =$1,241.57*(P|A 6.8230%/12,300) 19 P(300)= $178,507.54 USING EXCEL'S PMT FUNCTION THIS IS 20 =PV(6.823%/12,300,-1241.57) 21 22 c EFFECTIVE RATE 7.0405% =EFFECT(6.823%,12) 23 24 EFFECTIVE RATE 7.0405% =(1+RATE(360,-1241.57,190000))^12-1 25 26 d RECALL, THERE ARE NO POINTS AND NO OTHER FEES 27 28 A= $1,241.57 29 30 APR= 6.8230% =RATE(360,-1241.57,190000)*12 31 32 SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW 33 34 WEB-BASED CALCULATION 1: 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

A B 58 59 60 61 62 63 64 65 66 67 68 WEB-BASED CALCULATION 2: 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101

A B C D E F G H 1 PROBLEM 3.15 2 3 P= $600,000.00 4 r= 6.9932% NOMINAL ANNUAL 5 n= 360 MONTHS 6 m= 12 MONTHS PER YEAR 7 8 a A= $3,989.08 USING ELECTRONIC INTEREST TABLES THIS IS 9 =$600,000*(A|P 6.9932%/12,360) 10 A= $3,989.08 USING EXCEL'S PMT FUNCTION THIS IS 11 =PMT(6.9932%/12,360,-600000) 12 13 SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW 14 15 b FIND PRESENT WORTH OF FINAL 240 PAYMENTS 16 17 P(240)= $514,791.93 USING ELECTRONIC INTEREST TABLES THIS IS 18 =$3,988.08*(P|A 6.9932%/12,240) 19 P(240)= $514,791.91 USING EXCEL'S PMT FUNCTION THIS IS 20 =PV(6.9932%/12,240,-3989.08) 21 22 c EFFECTIVE RATE 7.2218% =EFFECT(6.9932%,12) 23 24 EFFECTIVE RATE 7.2218% =(1+RATE(360,-3989.08,600000))^12-1 25 26 d RECALL, THERE ARE NO POINTS AND NO CLOSING COSTS 27 28 A= $3,989.08 29 30 APR= 6.9932% =RATE(360,-3989.08,600000)*12 31 32 SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW 33 34 WEB-BASED CALCULATION 1: 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

A B 58 59 60 61 62 63 64 65 66 67 68 69 WEB-BASED CALCULATION 2: 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

1 2 3 4 5 6 7

A PROBLEM 3.16

P= r= n= m= c0=

p1=

1.6250%

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

p2=

33 34 35 36 37 38 39 40 41

A W/O POINTS= A= A=

$190,000.00 6.4495% NOMINAL ANNUAL 360 MONTHS 12 MONTHS / YEAR $0.00

$3,087.50

=190000*1.6250%

$1,194.63 USING ELECTRONIC INTEREST TABLES THIS IS =$190,000*(A|P 6.4495%/12,360) $1,194.63 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6.4495%/12,360,-190000)

SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW b

A W/ POINTS= $1,214.04 USING ELECTRONIC INTEREST TABLES THIS IS =($190,000+3,087.50)*(A|P 6.4495%/12,360) $1,214.04 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6.4495%/12,360,-(190000+3087.5)) SEE WEB-BASED CALCULATIONS 1, 2, 3, AND 4 BELOW

FIND PRESENT WORTH OF FINAL 300 PAYMENTS P(300)= $180,645.75 USING ELECTRONIC INTEREST TABLES THIS IS =$1,214.04*(P|A 6.4495%/12,300) P(300)= $180,645.74 USING EXCEL'S PMT FUNCTION THIS IS =PV(6.4495%/12,300,-1214.04)

EFFECTIVE RATE

6.80832% =(1+RATE(360,PMT(6.4495%/12,360,(190000+3087.5)),-190000))^12-1

EFFECTIVE RATE

6.80832% =(1+RATE(360,-1214.04,190000))^12-1

EFFECTIVE RATE

6.80832% =(1+6.60468%/12)^12-1

RECALL, THERE ARE POINTS BUT NO OTHER FEES FOR THE FOLLOWING APR CALCULATION, SEE EXAMPLE 3.6

APR (ADD)= 6.60468% =RATE(360,PMT(6.4495%/12,360,190000+ 3087.5),190000)*12 42 43 44 SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW 45 46 WEB-BASED CALCULATION 1: 47 48 49 50 51 52 53 54

A B 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 WEB-BASED CALCULATION 2: 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

A B 112 113 114 115 WEB-BASED CALCULATION 3: 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 WEB-BASED CALCULATION 4: 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

A 169 170 171 172 173 174 175 176 177 178 179 180 181 182

1 2 3 4 5 6 7

A PROBLEM 3.17

P= r= n= m= c0=

p1=

1.8750%

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

p2=

33 34 35 36 37 38 39 40 41

A W/O POINTS= A= A=

$600,000.00 6.5084% NOMINAL ANNUAL 360 MONTHS 12 MONTHS / YEAR $0.00

$11,250.00 =600000*1.875%

$3,795.72 USING ELECTRONIC INTEREST TABLES THIS IS =$600,000*(A|P 6.5084%/12,360) $3,795.72 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6.5084%/12,360,-600000)

SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW b

A W/ POINTS= $3,866.89 USING ELECTRONIC INTEREST TABLES THIS IS =($600,000+11,250.00)*(A|P 6.5084%/12,360) $3,866.89 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6.5084%/12,360,-(600000+11250)) SEE WEB-BASED CALCULATIONS 1, 2, 3, AND 4 BELOW

FIND PRESENT WORTH OF FINAL 240 PAYMENTS P(240)= $518,303.25 USING ELECTRONIC INTEREST TABLES THIS IS =$3,866.89*(P|A 6.5084%/12,240) P(240)= $518,303.21 USING EXCEL'S PMT FUNCTION THIS IS =PV(6.5084%/12,240,-3866.89)

EFFECTIVE RATE

6.8969% =(1+RATE(360,-PMT(6.5084%/12,360,(600000+11250)),600000))^12-1

EFFECTIVE RATE

6.8969% =(1+RATE(360,-3866.89,600000))^12-1

EFFECTIVE RATE

6.8969% =(1+6.688%/12)^12-1

RECALL, THERE ARE POINTS BUT NO OTHER FEES FOR THE FOLLOWING APR CALCULATION, SEE EXAMPLE 3.6 APR (ADD)=

6.6880% =RATE(360,PMT(6.5084%/12,360,600000+11 250),600000)*12

42 43 44 SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW 45 46 WEB-BASED CALCULATION 1: 47 48 49 50 51 52 53 54

A B 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 WEB-BASED CALCULATION 2: 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

A B 112 113 114 115 116 117 WEB-BASED CALCULATION 3: 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 WEB-BASED CALCULATION 4: 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

A 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185

1 2 3 4 5 6 7

A PROBLEM 3.18

P= r= n= m= c0=

p1=

2.7500%

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

p2=

A W/O POINTS= A= A=

$190,000.00 5.8750% NOMINAL ANNUAL 360 MONTHS 12 MONTHS / YEAR $6,570.00

$5,225.00 =190000*2.7500%

$1,123.92 USING ELECTRONIC INTEREST TABLES THIS IS =$190,000*(A|P 5.8750%/12,360) $1,123.92 USING EXCEL'S PMT FUNCTION THIS IS =PMT(5.875%/12,360,-190000)

SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW b

A W/ POINTS= $1,193.69 USING ELECTRONIC INTEREST TABLES THIS IS =($190,000+$6,570+$5,225)*(A|P 5.8750%/12,360) $1,193.69 USING EXCEL'S PMT FUNCTION THIS IS =PMT(5.875%/12,360,-(190000+6570+5225)) SEE WEB-BASED CALCULATIONS 1, 2, 3 AND 4 BELOW

FIND PRESENT WORTH OF FINAL 300 PAYMENTS P(300)= $187,486.62 USING ELECTRONIC INTEREST TABLES THIS IS =$1,193.69*(P|A 5.8750%/12,300) P(300)= $187,486.61 USING EXCEL'S PMT FUNCTION THIS IS =PV(5.875%/12,300,-1193.69)

EFFECTIVE RATE

6.6357% =(1+RATE(360,-PMT(5.875%/12,360,-

EFFECTIVE RATE

6.6357% =(1+RATE(360,-1193.69,190000))^12-1

EFFECTIVE RATE

6.6357% =(1+6.44202%/12)^12-1

RECALL, THERE ARE POINTS AND OTHER CLOSING COSTS FOR THE FOLLOWING APR CALCULATION, SEE EXAMPLE 3.6

APR (ADD)= 6.44202% =RATE(360,PMT(5.875%/12,360,190000+6570 +5225),190000)*12 42 43 44 SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW 45 46 WEB-BASED CALCULATION 1: 47 48 49 50 51 52 53 54 55

A B 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 WEB-BASED CALCULATION 2: 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 WEB-BASED CALCULATION 3: 106 107 108 109 110 111 112

A B 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 WEB-BASED CALCULATION 4: 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169

A 170 171 172 173 174

1 2 3 4 5 6 7

A PROBLEM 3.19

P= r= n= m= c0=

p1=

3.1250%

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

p2=

33 34 35 36 37 38 39 40 41

A W/O POINTS= A= A=

$600,000.00 6.0000% NOMINAL ANNUAL 360 MONTHS 12 MONTHS / YEAR $16,159.00

$18,750.00 =600000*3.125%

$3,597.30 USING ELECTRONIC INTEREST TABLES THIS IS =$600,000*(A|P 6%/12,360) $3,597.30 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6%/12,360,-600000)

SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW b

A W/ POINTS= $3,806.60 USING ELECTRONIC INTEREST TABLES THIS IS =($600,000+$16,159+$18,750)*(A|P 6%/12,360) $3,806.60 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6%/12,360,-(600000+16159+18750)) SEE WEB-BASED CALCULATIONS 1, 2, 3 AND 4 BELOW

FIND PRESENT WORTH OF FINAL 300 PAYMENTS P(240)= $531,328.18 USING ELECTRONIC INTEREST TABLES THIS IS =$3,806.60*(P|A 6%/12,240) P(240)= $531,328.20 USING EXCEL'S PMT FUNCTION THIS IS $531,328.17

EFFECTIVE RATE

6.7353% =(1+RATE(360,-PMT(6%/12,360,(600000+16159+18750)),600000))^12-1

EFFECTIVE RATE

6.7353% =(1+RATE(360,-3806.6,600000))^12-1

EFFECTIVE RATE

6.7353% =(1+6.53594%/12)^12-1

RECALL, THERE ARE POINTS AND OTHER CLOSING COSTS FOR THE FOLLOWING APR CALCULATION, SEE EXAMPLE 3.6 APR (ADD)=

6.53594% =RATE(360,PMT(6%/12,360,600000+16159+187 50),600000)*12

42 43 44 SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW 45 46 WEB-BASED CALCULATION 1: 47 48 49 50 51 52 53 54

A B 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 WEB-BASED CALCULATION 2: 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

A B 112 113 114 115 116 117 WEB-BASED CALCULATION 3: 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 WEB-BASED CALCULATION 4: 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

A 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188

1 2 3 4 5 6 7

A PROBLEM 3.20

P= r= n= m= c0=

p1=

2.6250%

$4,987.50

=190000*2.6250%

9 10 11 12 13 14 15 16 17 18 19 20

p2=

2.6250%

$169.17

=6444.50*2.6250%

21 22 23 24 25 26 27 28 29 30 31 32 33 34

35 36 37 38 39 40 41 42

A W/O POINTS= A= A=

$190,000.00 5.5000% NOMINAL ANNUAL 180 MONTHS 12 MONTHS / YEAR $6,444.50

$1,552.46 USING ELECTRONIC INTEREST TABLES THIS IS =$190,000*(A|P 5.5%/12,180) $1,552.46 USING EXCEL'S PMT FUNCTION THIS IS =PMT(5.5%/12,180,-190000)

SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW b

A W/ POINTS= $1,647.25 USING ELECTRONIC INTEREST TABLES THIS IS =($190,000+$6,444.50+$4,987.50+$169.17)*(A| P 5.5%/12,180) $1,647.25 USING EXCEL'S PMT FUNCTION THIS IS =PMT(5.5%/12,180,-(190000+6444.5+4987.5+169.17)) SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW NOTE THAT WEB-BASED CALCULATION 2 ASSUMES p2=0% - WRONG FOR PART b

FIND PRESENT WORTH OF FINAL 300 PAYMENTS P(120)= $151,783.50 USING ELECTRONIC INTEREST TABLES THIS IS =$1,647.25*(P|A 5.5%/12,120) P(120)= $151,783.50 USING EXCEL'S PMT FUNCTION THIS IS =PV(5.5%/12,120,-1647.25)

EFFECTIVE RATE

EFFECTIVE RATE EFFECTIVE RATE e

6.6173% USING EXCEL'S RATE AND PMT FUNCTIONS THIS IS =(1+RATE(180,-PMT(5.5%/12,180,(190000+6444.5+4987.5+169.17)),190000))^121 6.6173% USING EXCEL'S RATE FUNCTION THIS IS =(1+RATE(180,-1647.25,190000))^12-1 6.6173% =(1+6.42471%/12)^12-1

RECALL, THERE ARE POINTS AND OTHER CLOSING COSTS FOR THE FOLLOWING APR CALCULATION, SEE EXAMPLE 3.6

APR (ADD)= 6.42471% =RATE(180,PMT(5.5%/12,180,190000+6444.5+ 4987.5+169.17),190000)*12 43 44 45 SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW 46 47 48 WEB-BASED CALCULATION 1: 49 50 51

A B 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 WEB-BASED CALCULATION 2: 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108

A B 109 110 111 112 113 114 115 116 117 118 119 WEB-BASED CALCULATION 3: 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 WEB-BASED CALCULATION 4: 155 156 157 158 159 160 161 162 163 164 165

A 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187

1 2 3 4 5 6 7

A PROBLEM 3.21

P= r= n= m= c0=

p1=

3.0000%

$18,000.00

=600000*3%

9 10 11 12 13 14 15 16 17 18 19 20

p2=

3.0000%

$479.22

=15974*3%

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

A W/O POINTS= A= A=

$600,000.00 5.6250% NOMINAL ANNUAL 180 MONTHS 12 MONTHS / YEAR $15,974.00

$4,942.39 USING ELECTRONIC INTEREST TABLES THIS IS =$600,000*(A|P 5.6250%/12,180) $4,942.39 USING EXCEL'S PMT FUNCTION THIS IS =PMT(5.6250%/12,180,-600000)

SEE WEB-BASED CALCULATIONS 1 AND 2 BELOW b

A W/ POINTS= $5,226.19 USING ELECTRONIC INTEREST TABLES THIS IS =($600,000+$15,974+$18,000+$479.22)*(A|P 5.625%/12,180) $5,226.19 USING EXCEL'S PMT FUNCTION THIS IS =PMT(5.625%/12,180,-(600000+15974+18000+479.22)) SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW NOTE THAT WEB-BASED CALCULATION 2 ASSUMES p2=0% - WRONG FOR PART b

FIND PRESENT WORTH OF FINAL 60 PAYMENTS P(60)= $272,781.27 USING ELECTRONIC INTEREST TABLES THIS IS =$5,226.19*(P|A 5.625%/12,60) P(60)= $272,781.27 USING EXCEL'S PV FUNCTION THIS IS =PV(5.625%/12,60,-5226.19)

EFFECTIVE RATE

EFFECTIVE RATE EFFECTIVE RATE e

6.6957% USING EXCEL'S RATE AND PMT FUNCTIONS THIS IS =(1+RATE(180,-PMT(5.625%/12,180,(600000+15974+18000+479.22)),600000))^12-1 6.6957% USING EXCEL'S RATE FUNCTION THIS IS =(1+RATE(180,-5226.19,600000))^12-1 6.6957% =(1+6.49863%/12)^12-1

RECALL, THERE ARE POINTS AND OTHER CLOSING COSTS FOR THE FOLLOWING APR CALCULATION, SEE EXAMPLE 3.6 APR (ADD)=

6.49863% =RATE(180,PMT(5.625%/12,180,600000+15974 +18000+479.22),600000)*12

43 44 45 SEE WEB-BASED CALCULATIONS 3 AND 4 BELOW 46 47 48 WEB-BASED CALCULATION 1: 49 50 51 52 53

A B 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 WEB-BASED CALCULATION 2: 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

A B 111 112 113 114 115 116 117 118 119 120 121 122 WEB-BASED CALCULATION 3: 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 WEB-BASED CALCULATION 4: 161 162 163 164 165 166 167

A 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194

1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A PROBLEM 3.22

B NOTE! SEE EXAMPLE 3.7

RECALL THAT THE LENDING INSTITUTION COMPUTED APR BY DEDUCTING CLOSING COSTS FROM THE AMOUNT BORROWED. THEREFORE, THE APR(SUB) METHOD IS USED BY THE LENDING INSTITUTION. SEE EXAMPLE 3.6 FOR AN EXAMPLE OF APR(SUB) P= r= n= m= p1= p2= APR= A W/O PTS AND ADMIN COSTS=

$171,000.00 6.2500% NOMINAL ANNUAL 360 MONTHS 12 MONTHS / YEAR 2.3750% $4,061.25 0% 7.2330%

GIVEN

$1,052.88 PAYMENT WITHOUT POINTS AND FEES =PMT(6.25%/12,360,-171000)

A W/O PTS AND ADMIN COSTS=

$6.16 PAYMENT PER $1000 =1052.88/(171000/1000)

BASE= ADMIN COSTS=

$154,602.05 =PV(7.233%/12,360,-1052.88) $12,336.70 =171000-154602.05-4061.25

BASE= ADMIN COSTS=

$154,602.05 =PV(7.233%/12,360,-6.16)*171000/1000 $12,336.70 =171000-154602.05-4061.25

AS A CHECK, CALCULATE THE VALUE OF APR(SUB) TO SEE IF IT EQUALS 7.2330%

APR(SUB)=

7.23300% =RATE(360,PMT(6.25%/12,360, 171000),171000-4061.2512336.7)*12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A PROBLEM 3.23

B NOTE! SEE EXAMPLE 3.7

RECALL THAT THE LENDING INSTITUTION COMPUTED APR BY DEDUCTING P= r= n= m= p1= p2= APR= A W/O PTS AND ADMIN COSTS=

$280,000.00 6.1250% NOMINAL ANNUAL 360 MONTHS 12 MONTHS / YEAR 3.0000% $8,400.00 0% 6.5170%

GIVEN

$1,701.31 PAYMENT WITHOUT POINTS AND FEES =PMT(6.125%/12,360,-280000)

A W/O PTS AND ADMIN COSTS=

$6.08 PAYMENT PER $1000 =1701.31/(280000/1000)

BASE= ADMIN COSTS=

$268,690.14 =PV(6.517%/12,360,-1701.31) $2,909.86 =280000-268690.14-8400

BASE= ADMIN COSTS=

$268,690.14 =PV(6.517%/12,360,-6.08)*280000/1000 $2,909.86 =280000-268690.14-8400

AS A CHECK, CALCULATE THE VALUE OF APR(SUB) TO SEE IF IT EQUALS 6.5170% APR(SUB)=

6.51700% =RATE(360,PMT(6.125%/12,3

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A B C D 1 PROBLEM 3.24 2 3 PURCHASE PRICE = $550,000 4 DOWN PAYMENT = $55,000 5 REMAINDER FINANCED = $495,000 6 PERSONAL TVOM= 8.00% 7 TIME IN HOME= 72 MONTHS 8 9 10 11 30 YEAR JUMBO CONVENTIONAL LOAN 12 r= 6.875% c0= 13 $14,344.50 p1= 14 0.250% 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

p2= PAYMENTS PER YEAR= TERM OF LOAN= a(1)

b(1)

PW= PW=

p2= PAYMENTS PER YEAR= TERM OF LOAN= a(2i)

A= A=

MONTHS

$3,354.16 USING ELECTRONIC INTEREST TABLES THIS IS =[$495,000*(1.0025)+$14,344.50]*(A|P 6.875%/12,360) $3,354.16 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6.875%/12,360,-(495000*(1+0.25%)+14344.5)) -$484,135.80 USING ELECTRONIC INTEREST TABLES THIS IS =-$3354.16*(P|A 8%/12,72)-$3354.01*(P|A 6.875%/12,288)*(P|F 8%/12,72) -$484,135.81 USING EXCEL'S PV FUNCTION THIS IS =PV(8%/12,72,3354.16)+PV(8%/12,72,,-PV(6.875%/12,360-72,3354.16))

JUMBO 30-YEAR ARM REMAINING CONSTANT r= 6.000% c0= $13,558.25 p1= 0.125%

34 35 36 37 38 39 40 41

0% 12 360

MONTHS

$3,052.77 USING ELECTRONIC INTEREST TABLES THIS IS =[$495,000*(1.00125)+$13,558.25]*(A|P 6.000/12%,360) $3,052.77 USING EXCEL'S PMT FUNCTION THIS IS

42 43 44 45 46 47 48 49 50 51 52 53

b(2i)

PW= PW=

79 80 81 82

D E =PMT(6%/12,360,-(495000*(1+0.00125)+13558.25))

-$462,540.31 USING ELECTRONIC INTEREST TABLES THIS IS =-$3052.77*(P|A 8%/12,72)-$3053.03*(P|A 6.000%/12,288)*(P|F 8%/12,72) -$462,540.33 USING EXCEL'S PV FUNCTION THIS IS =PV(8%/12,72,C41)+PV(C$6/C36,C$7,,-PV(C32/C36,C37-C$7,C41))

JUMBO 30-YEAR ARM INCREASING AT MAX RATE OF 0.7500%/YEAR r= 6.000% c0= $13,558.25 p1= 0.125%

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

p2=

a(2ii)

PAYMENTS PER YEAR= TERM OF LOAN=

0% 12 360

MONTHS

YEAR

NOMINAL ANNUAL INTEREST RATE

SIZE OF MONTHLY PAYMENT

1 2 3 4 5 6 >6

6.00% 6.75% 7.50% 8.25% 9.00% 9.75% 9.75%

$3,052.77 $3,297.10 $3,543.87 $3,792.40 $4,042.04 $4,292.22 $4,292.22

b(2ii)

PW(8/12%) =PMT(6%/12,360,-(495000*(1+0.125%)+13558.25)) =PMT(6.75%/12,348,-PV(6%/12,348,-3052.77)) =PMT(7.5%/12,336,-PV(6.75%/12,336,-3297.10)) =PMT(8.25%/12,324,-PV(7.5%/12,324,-3543.87)) =PMT(9%/12,312,-PV(8.25%/12,312,-3792.40)) =PMT(9.75%/12,300,-PV(9%/12,300,-4042.04)) =PMT(9.75%/12,288,-PV(9.75%/12,288,-4292.22))

-$35,094.02 =PV(8%/12,12,3052.77) -$34,997.89 =PV(8%/12,12*(2-1),,PV(8%/1 -$34,734.44 =PV(8%/12,12*(3-1),,PV(8%/1 -$34,321.65 =PV(8%/12,12*(4-1),,PV(8%/1 -$33,777.41 =PV(8%/12,12*(5-1),,PV(8%/1 -$33,119.15 =PV(8%/12,12*(6-1),,PV(8%/1 -$295,569.81 =PV(8%/12,72,,PV(9.75%/12,2

SUM=PW= -$501,614.37

30 YEAR INTEREST-ONLY BALLOON LOAN r= 5.500% c0= $45,769.00 p1= 0.625% p2= PAYMENTS PER YEAR= TERM OF LOAN=

0% 12 360

MONTHS

83 84 85 86 87 88 89

a(3)

b(3)

PW= PW=

$2,492.70 =(495000*(1.00625)+45769)*0.055/12 -$479,239.93 USING ELECTRONIC INTEREST TABLES THIS IS =-$2,492.70*(P|A 8%/12,72)-[$495,000*(1.00625)+$45,769]*(P|F 8%/12,72) -$479,239.93 USING EXCEL'S PV FUNCTION THIS IS =PV(8%/12,72,2492.7)+PV(8%/12,72,,(495000*(1+0.625%)+45769))

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

H 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

A B C 1 PROBLEM 3.25 2 3 PURCHASE PRICE = $90,000 4 DOWN PAYMENT = $4,500 5 REMAINDER FINANCED = $85,500 6 PERSONAL TVOM= 5.30% 7 TIME IN HOME= 36 8 9 10 11 30 YEAR CONVENTIONAL LOAN 12 r= 6.750% c0= 13 $4,065.13 p1= 14 0.125% 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

p2= PAYMENTS PER YEAR= TERM OF LOAN= a(1)

b(1)

PW= PW=

p2= PAYMENTS PER YEAR= TERM OF LOAN= a(2i)

A= A=

MONTHS

$581.61 USING ELECTRONIC INTEREST TABLES THIS IS =[$85,500*(1.00125)+$4,065.13]*(A|P 6.750%/12,360) $581.61 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6.75%/12,360,-(85500*(1+0.125%)+4065.13)) -$93,214.87 USING ELECTRONIC INTEREST TABLES THIS IS =-$581.61*(P|A 5.3%/12,36)-$581.61*(P|A 6.75%/12,324)*(P|F 5.3%/12,36) -$93,214.87 USING EXCEL'S PV FUNCTION THIS IS =PV(5.3%/12,36,581.61)+PV(5.3%/12,36,,-PV(6.75%/12,360-36,581.61))

30-YEAR ARM REMAINING CONSTANT r= 5.250% c0= $5,991.00 p1= 2.375%

34 35 36 37 38 39 40 41

0% 12 360

MONTHS

$516.43 USING ELECTRONIC INTEREST TABLES THIS IS =[$85,500*(1.02375)+$5,991]*(A|P 5.25%/12,360) $516.43 USING EXCEL'S PMT FUNCTION THIS IS

42 43 44 45 46 47 48 49 50 51 52 53

b(2i)

PW= PW=

p2=

a(2ii)

-$93,394.85 USING ELECTRONIC INTEREST TABLES THIS IS =-$516.43*(P|A 5.3%/12,36)-$516.43*(P|A 5.25%/12,324)*(P|F 5.3%/12,36) -$93,394.85 USING EXCEL'S PV FUNCTION THIS IS =PV(5.3%/12,36,516.43)+PV(5.3%/12,36,,-PV(5.25%/12,360-36,516.43))

PAYMENTS PER YEAR= TERM OF LOAN=

0% 12 360

MONTHS

YEAR

NOMINAL ANNUAL INTEREST RATE

SIZE OF MONTHLY PAYMENT

1 2 3 >3

5.25% 6.25% 7.25% 7.25%

$516.43 $574.44 $633.78 $633.78

PW(5.3%/12) =PMT(5.25%/12,360,-(85500*(1+2.375%)+5991)) =PMT(6.25%/12,348,-PV(5.25%/12,348,-516.43)) =PMT(7.25%/12,336,-PV(6.25%/12,336,-574.44)) =PMT(7.25%/12,324,-PV(7.25%/12,324,-633.78))

b(2ii)

p2= PAYMENTS PER YEAR= TERM OF LOAN= a(3)

-$6,022.86 =PV(5.3%/12,12,516.43) -$6,354.32 =PV(5.3%/12,12*(2-1),,PV -$6,649.57 =PV(5.3%/12,12*(3-1),,PV -$76,796.82 =PV(5.3%/12,36,,PV(7.25%

SUM=PW= -$95,823.57

30 YEAR INTEREST-ONLY BALLOON LOAN r= 4.850% c0= $6,500.00 p1= 1.100%

76 77 78 79 80 81 82

D E =PMT(5.25%/12,360,-(85500*(1+0.02375)+5991))

30-YEAR ARM INCREASING AT MAX RATE OF 1.0%/YEAR r= 5.250% c0= $5,991.00 p1= 2.375%

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

0% 12 360

MONTHS

$375.63 =(85500*(1.011)+6500)*0.0485/12

83 84 85 86

A b(3)

B PW= PW=

C D E F -$91,782.83 USING ELECTRONIC INTEREST TABLES THIS IS =-$375.63*(P|A 5.3%/12,36)-[$85,500*(1.011)+$6,500]*(P|F 5.3%/12,36) -$91,782.83 USING EXCEL'S PV FUNCTION THIS IS =PV(5.3%/12,36,375.63)+PV(5.3%/12,36,,(85500*(1+1.1%)+6500))

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

H 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

A B C D E F 1 PROBLEM 3.26 2 3 P= $25,000.00 4 i= 12.000% PER YEAR 5 m= 12 MONTHS 6 n= 4 YEARS 7 8 a A= $658.25 USING INTEREST TABLES THIS IS 9 =$25,000*(A|P 12%/12,12*4) 10 $658.35 USING EXCEL'S PMT FUNCTION THIS IS 11 =PMT(12%/12,12*4,-25000) 12 U22= 13 b $15,004.94 USING INTEREST TABLES THIS IS 14 =$658.25*(P|A 12%/12,26) U22= 15 $15,007.13 USING EXCEL'S PV FUNCTION THIS IS 16 =PV(12%/12,26,-C10) I23= 17 $150.07 =(12%/12)*15007.13 18 U37= 19 c $6,825.49 USING INTEREST TABLES THIS IS 20 =$658.25*(P|A 12%/12,11) 21 $6,825.49 USING EXCEL'S PV FUNCTION THIS IS 22 =PV(12%/12,11,-C10) 23 PAYOFF42= 24 d $4,473.12 USING INTEREST TABLES THIS IS 25 =$658.25*(1+(P|A 12%/12,48-42) 26 $4,473.77 =PV(12%/12,6,-658.35)+658.35 27 28 AS A CHECK, SEE THE FOLLOWING TABLE. 29 30 BEGINNING LOAN INTEREST PRINCIPAL 31 MONTH BALANCE PAYMENT PAYMENT PAYMENT 32 33 1 $25,000.00 $658.35 $250.00 $408.35 34 2 $24,591.65 $658.35 $245.92 $412.43 35 3 $24,179.22 $658.35 $241.79 $416.55 36 4 $23,762.67 $658.35 $237.63 $420.72 37 5 $23,341.95 $658.35 $233.42 $424.93 38 6 $22,917.03 $658.35 $229.17 $429.18 39 7 $22,487.85 $658.35 $224.88 $433.47 40 8 $22,054.38 $658.35 $220.54 $437.80 41 9 $21,616.58 $658.35 $216.17 $442.18 42 10 $21,174.40 $658.35 $211.74 $446.60 43 11 $20,727.80 $658.35 $207.28 $451.07 44 12 $20,276.73 $658.35 $202.77 $455.58 45 13 $19,821.15 $658.35 $198.21 $460.13 46 14 $19,361.02 $658.35 $193.61 $464.74 47 15 $18,896.28 $658.35 $188.96 $469.38 48 16 $18,426.90 $658.35 $184.27 $474.08 49 17 $17,952.82 $658.35 $179.53 $478.82 50 18 $17,474.00 $658.35 $174.74 $483.61 51 19 $16,990.40 $658.35 $169.90 $488.44 52 20 $16,501.96 $658.35 $165.02 $493.33 53 21 $16,008.63 $658.35 $160.09 $498.26 54 22 $15,510.37 $658.35 $155.10 $503.24 55 23 $15,007.13 $658.35 $150.07 $508.27 56 24 $14,498.85 $658.35 $144.99 $513.36

ENDING BALANCE $24,591.65 $24,179.22 $23,762.67 $23,341.95 $22,917.03 $22,487.85 $22,054.38 $21,616.58 $21,174.40 $20,727.80 $20,276.73 $19,821.15 $19,361.02 $18,896.28 $18,426.90 $17,952.82 $17,474.00 $16,990.40 $16,501.96 $16,008.63 $15,510.37 $15,007.13 $14,498.85 $13,985.50

A 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

B 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

C $13,985.50 $13,467.01 $12,943.33 $12,414.42 $11,880.22 $11,340.67 $10,795.73 $10,245.34 $9,689.45 $9,128.00 $8,560.93 $7,988.20 $7,409.73 $6,825.49 $6,235.39 $5,639.40 $5,037.45 $4,429.48 $3,815.43 $3,195.24 $2,568.84 $1,936.19 $1,297.20 $651.83

D $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35 $658.35

E $139.85 $134.67 $129.43 $124.14 $118.80 $113.41 $107.96 $102.45 $96.89 $91.28 $85.61 $79.88 $74.10 $68.25 $62.35 $56.39 $50.37 $44.29 $38.15 $31.95 $25.69 $19.36 $12.97 $6.52

F $518.49 $523.68 $528.91 $534.20 $539.54 $544.94 $550.39 $555.89 $561.45 $567.07 $572.74 $578.46 $584.25 $590.09 $595.99 $601.95 $607.97 $614.05 $620.19 $626.39 $632.66 $638.98 $645.37 $651.83

G $13,467.01 $12,943.33 $12,414.42 $11,880.22 $11,340.67 $10,795.73 $10,245.34 $9,689.45 $9,128.00 $8,560.93 $7,988.20 $7,409.73 $6,825.49 $6,235.39 $5,639.40 $5,037.45 $4,429.48 $3,815.43 $3,195.24 $2,568.84 $1,936.19 $1,297.20 $651.83 $0.00

A 1 PROBLEM 3.27 2 3 4 5 6 7 8 9 10 11 12 13 14 a 15 16 17 18 19 20 21 22 23 24 25 26 b 27 28 29 30 31 32 33 34 35 36 37 38 39 c 40 41 42 43 44 45 46 47 QUARTER 48 49 1 50 2 51 3 52 4 53 5

P= $80,000.00 r= 8.000% m= 4 YEARS= 3 PERIODS= 6

PER YEAR QUARTERS YEARS QUARTERS

FIRST, CALCULATE PAYMENT A=

$7,564.77 PER QUARTER =PMT(8%/4,4*3,-80000)

U5 =

$48,959.31 USING INTEREST TABLES THIS IS =$80,000*(A|P 8%/4,12)*(P|A 8%/4,7) $979.18 USING INTEREST TABLES THIS IS =$7,564.77*(1-(P|F 8%/4,12-6+1)) $979.19 =(8%/4)*48959.31

I6= I6= U5 = I6= I6=

$48,959.11 USING EXCEL'S PV FUNCTION THIS IS =PV(8%/4,7,-7564.77) $979.18 USING EXCEL'S IPMT FUNCTION THIS IS =IPMT(8%/4,6,4*3,-80000) $979.18 =(8%/4)*48959.11

USING U5 AND I6 FROM PART a (INTEREST TABLES): P6= P6=

$6,585.58 USING INTEREST TABLES THIS IS =$7,564.77*(P|F 8%/4,12-6+1) $6,585.58 =7564.77-979.19

USING U5 AND I6 FROM PART a: (EXCEL FUNCTION) P6= P6= U6 = U6 =

$6,585.59 USING EXCEL'S PPMT FUNCTION THIS IS =PPMT(8%/4,6,4*3,-80000) $6,585.59 =7564.77-979.18 $42,373.52 USING INTEREST TABLES THIS IS =$7,564.77*(P|A 8%/4,6) $42,373.52 USING EXCEL'S PV FUNCTION THIS IS =PV(8%/4,6,-7564.77)

AS A CHECK, SEE THE FOLLOWING TABLE. BEGINNING LOAN BALANCE PAYMENT $80,000.00 $74,035.23 $67,951.17 $61,745.42 $55,415.57

$7,564.77 $7,564.77 $7,564.77 $7,564.77 $7,564.77

INTEREST PAYMENT $1,600.00 $1,480.70 $1,359.02 $1,234.91 $1,108.31

PRINCIPAL ENDING PAYMENT BALANCE $5,964.77 $6,084.06 $6,205.74 $6,329.86 $6,456.46

$74,035.23 $67,951.17 $61,745.42 $55,415.57 $48,959.11

54 55 56 57 58 59 60

A 6 7 8 9 10 11 12

B $48,959.11 $42,373.52 $35,656.23 $28,804.58 $21,815.91 $14,687.46 $7,416.44

C $7,564.77 $7,564.77 $7,564.77 $7,564.77 $7,564.77 $7,564.77 $7,564.77

D $979.18 $847.47 $713.12 $576.09 $436.32 $293.75 $148.33

E $6,585.59 $6,717.30 $6,851.64 $6,988.68 $7,128.45 $7,271.02 $7,416.44

F $42,373.52 $35,656.23 $28,804.58 $21,815.91 $14,687.46 $7,416.44 $0.00

A 1 PROBLEM 3.28 2 3 4 5 6 7 8 9 a 10 11 12 13 14 b 15 16 17 18 19 c 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

P= r= m= n= PERIODS

$200,000.00 6.000% 12 7 24

PER YEAR MONTHS YEARS MONTHS

A= A=

U24= U24=

$2,922.00 USING INTEREST TABLES THIS IS =$200,000*(A|P 6%/12,12*7) $2,921.71 USING EXCEL'S PMT FUNCTION THIS IS =PMT(6%/12,12*7,-200000) $151,142.09 USING INTEREST TABLES THIS IS =$2922.00*(P|A 6%/12,12*7-24) $151,127.13 USING EXCEL'S PV FUNCTION THIS IS =PV(6%/12,12*7-24,-2921.71) 8.500%

DETERMINE THE AMOUNT OF THE PAYOFF THAT WILL PERMIT THE LENDER TO EARN AT LEAST $2,921.71 PER MONTH U24 AT 8.5%= U24 AT 8.5%=

$142,407.66 USING INTEREST TABLES THIS IS =$2921.71*(P|A 8.5%/12,12*7-24) $142,407.64 USING EXCEL'S PV FUNCTION THIS IS =PV(6%/12,12*7-24,-2921.71)

AND WE KNOW THAT IF MED DIAGNOSTICS PAYS THIS MUCH OR LESS, THEY WILL BREAK EVEN OR BENEFIT U24 AT 6%=

$151,127.13 FROM PART b $8,719.49 =151127.13-142407.64

SO X WOULD BE FROM $0 TO $8,719.49

A B C D E F G 1 PROBLEM 3.29 2 3 P= $15,000.00 4 r= 9.000% PER YEAR 5 m= 1 YEAR 6 n= 4 YEARS 7 PERIODS= 2 8 9 a A= $4,630.05 USING INTEREST TABLES THIS IS 10 =$15,000*(A|P 9%,4) 11 A= $4,630.03 USING EXCEL'S PMT FUNCTION THIS IS 12 =PMT(9%,4,-15000) 13 14 b TOTAL $ $3,520.12 =4*4630.03-15000 15 INTEREST 16 U1 = 17 c $11,720.00 USING INTEREST TABLES THIS IS 18 =$4,630.05*(P|A 9%,4-2+1) I = 19 $1,054.80 =(9%)*$11,720.00 2 20 I2= 21 $1,054.80 USING EXCEL'S IPMT FUNCTION THIS IS 22 =IPMT(9%,2,4,-15000) 23 P2= 24 d $3,575.25 $3,575.25 25 P2= 26 $3,575.23 USING EXCEL'S PPMT FUNCTION THIS IS 27 =PPMT(9%,2,4,-15000) 28 29 e YEAR BEGINNING LOAN INTEREST PRINCIPAL ENDING 30 BALANCE PAYMENT PAYMENT PAYMENT BALANCE 31 32 1 $15,000.00 $4,630.03 $1,350.00 $3,280.03 $11,719.97 33 2 $11,719.97 $4,630.03 $1,054.80 $3,575.23 $8,144.74 34 3 $8,144.74 $4,630.03 $733.03 $3,897.00 $4,247.73 35 4 $4,247.73 $4,630.03 $382.30 $4,247.73 $0.00 36 37 SUM= $3,520.12 38 TOTAL INTEREST

1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

A PROBLEM 3.30

THREE DIFFERENT METHODS WILL BE USED TO SOLVE THIS PROBLEM. THE FIRST TWO ARE ILLUSTRATED IN EXAMPLES 3.15 AND 3.16. THE THIRD APPROACH IS PRESENTED IN SLIDES MADE AVAILABLE TO INSTRUCTORS BY THE AUTHORS. P= r= m= k= n=

$22,000.00 12.000% PER YEAR 12 MONTHS 4 DEFERRED YRS 3 YRS OF PYTS

METHOD 1 FIRST, DETERMINE THE AMOUNT OWED AT THE END OF 4 YEARS (48 MONTHS). AMT(48)= AMT(48)=

$35,469.06 USING INTEREST TABLES THIS IS =$22,000*(F|P 12%/12,12*4) $35,468.97 USING EXCEL'S FV FUNCTION THIS IS =FV(12%/12,12*4,,-22000)

NOW, DETERMINE THE AMOUNT OF THE MONTHLY DEFERRED PAYMENT Ad= $1,177.93 USING INTEREST TABLES THIS IS Ad=

=$35,469.06*(A|P 12%/12,12*3) $1,178.08 USING EXCEL'S PMT FUNCTION THIS IS =PMT(12%/12,12*3,-35468.97)

NOW, BUILD METHOD 1 - TABLE BELOW AND ANSWER QUESTIONS b, c, AND d BY INSPECTION b

Ipmt(60)= PPmt(60)=

$1,178.08 METHOD 1 $0.00 METHOD 1

Ipmt(64)= PPmt(64)=

$437.14 METHOD 1 $740.94 METHOD 1

Ipmt(68)= PPmt(68)=

$183.34 METHOD 1 $994.74 METHOD 1

PAYOFF(72)= $14,437.43 USING INTEREST TABLES THIS IS =$1,178.08*(P|A 12%/12,12)+$1,178.08 PAYOFF(72)= $14,437.43 USING EXCEL'S PV FUNCTION THIS IS =PV(12%/12,12,-1178.08)+1178.08 PAYOFF(72)= $14,437.43 BY INSPECTION OF METHOD 1 - TABLE

A B C 41 42 METHOD 1 - TABLE 43 44 UNPAID 45 BALANCE INTEREST 46 BEGINNING BEFORE DURING 47 OF MONTH PAYMENT MONTH 48 49 1 $22,000.00 $220.00 50 2 $22,220.00 $222.20 51 3 $22,442.20 $224.42 52 4 $22,666.62 $226.67 53 5 $22,893.29 $228.93 54 6 $23,122.22 $231.22 55 7 $23,353.44 $233.53 56 8 $23,586.98 $235.87 57 9 $23,822.85 $238.23 58 10 $24,061.08 $240.61 59 11 $24,301.69 $243.02 60 12 $24,544.70 $245.45 61 13 $24,790.15 $247.90 62 14 $25,038.05 $250.38 63 15 $25,288.43 $252.88 64 16 $25,541.32 $255.41 65 17 $25,796.73 $257.97 66 18 $26,054.70 $260.55 67 19 $26,315.24 $263.15 68 20 $26,578.40 $265.78 69 21 $26,844.18 $268.44 70 22 $27,112.62 $271.13 71 23 $27,383.75 $273.84 72 24 $27,657.59 $276.58 73 25 $27,934.16 $279.34 74 26 $28,213.50 $282.14 75 27 $28,495.64 $284.96 76 28 $28,780.60 $287.81 77 29 $29,068.40 $290.68 78 30 $29,359.09 $293.59 79 31 $29,652.68 $296.53 80 32 $29,949.20 $299.49 81 33 $30,248.69 $302.49 82 34 $30,551.18 $305.51

UNPAID INTEREST BEFORE PAYMENT $220.00 $442.20 $666.62 $893.29 $1,122.22 $1,353.44 $1,586.98 $1,822.85 $2,061.08 $2,301.69 $2,544.70 $2,790.15 $3,038.05 $3,288.43 $3,541.32 $3,796.73 $4,054.70 $4,315.24 $4,578.40 $4,844.18 $5,112.62 $5,383.75 $5,657.59 $5,934.16 $6,213.50 $6,495.64 $6,780.60 $7,068.40 $7,359.09 $7,652.68 $7,949.20 $8,248.69 $8,551.18 $8,856.69

AMOUNT OWED $22,220.00 $22,442.20 $22,666.62 $22,893.29 $23,122.22 $23,353.44 $23,586.98 $23,822.85 $24,061.08 $24,301.69 $24,544.70 $24,790.15 $25,038.05 $25,288.43 $25,541.32 $25,796.73 $26,054.70 $26,315.24 $26,578.40 $26,844.18 $27,112.62 $27,383.75 $27,657.59 $27,934.16 $28,213.50 $28,495.64 $28,780.60 $29,068.40 $29,359.09 $29,652.68 $29,949.20 $30,248.69 $30,551.18 $30,856.69

LOAN PAYMENT $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

UNPAID UNPAID INTEREST BALANCE INTEREST PRINCIPAL AFTER AFTER PAYMENT PAYMENT PAYMENT PAYMENT $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$220.00 $22,220.00 $442.20 $22,442.20 $666.62 $22,666.62 $893.29 $22,893.29 $1,122.22 $23,122.22 $1,353.44 $23,353.44 $1,586.98 $23,586.98 $1,822.85 $23,822.85 $2,061.08 $24,061.08 $2,301.69 $24,301.69 $2,544.70 $24,544.70 $2,790.15 $24,790.15 $3,038.05 $25,038.05 $3,288.43 $25,288.43 $3,541.32 $25,541.32 $3,796.73 $25,796.73 $4,054.70 $26,054.70 $4,315.24 $26,315.24 $4,578.40 $26,578.40 $4,844.18 $26,844.18 $5,112.62 $27,112.62 $5,383.75 $27,383.75 $5,657.59 $27,657.59 $5,934.16 $27,934.16 $6,213.50 $28,213.50 $6,495.64 $28,495.64 $6,780.60 $28,780.60 $7,068.40 $29,068.40 $7,359.09 $29,359.09 $7,652.68 $29,652.68 $7,949.20 $29,949.20 $8,248.69 $30,248.69 $8,551.18 $30,551.18 $8,856.69 $30,856.69

83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124

A 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76

B $30,856.69 $31,165.26 $31,476.91 $31,791.68 $32,109.60 $32,430.70 $32,755.00 $33,082.55 $33,413.38 $33,747.51 $34,084.99 $34,425.84 $34,770.09 $35,117.80 $35,468.97 $34,645.59 $33,813.96 $32,974.03 $32,125.69 $31,268.87 $30,403.48 $29,529.44 $28,646.65 $27,755.04 $26,854.52 $25,944.98 $25,026.36 $24,098.54 $23,161.45 $22,214.99 $21,259.06 $20,293.57 $19,318.43 $18,333.54 $17,338.80 $16,334.11 $15,319.37 $14,294.49 $13,259.35 $12,213.87 $11,157.93 $10,091.43

C $308.57 $311.65 $314.77 $317.92 $321.10 $324.31 $327.55 $330.83 $334.13 $337.48 $340.85 $344.26 $347.70 $351.18 $354.69 $346.46 $338.14 $329.74 $321.26 $312.69 $304.03 $295.29 $286.47 $277.55 $268.55 $259.45 $250.26 $240.99 $231.61 $222.15 $212.59 $202.94 $193.18 $183.34 $173.39 $163.34 $153.19 $142.94 $132.59 $122.14 $111.58 $100.91

D $9,165.26 $9,476.91 $9,791.68 $10,109.60 $10,430.70 $10,755.00 $11,082.55 $11,413.38 $11,747.51 $12,084.99 $12,425.84 $12,770.09 $13,117.80 $13,468.97 $13,823.66 $12,992.04 $12,152.10 $11,303.77 $10,446.95 $9,581.56 $8,707.51 $7,824.73 $6,933.12 $6,032.59 $5,123.06 $4,204.43 $3,276.62 $2,339.53 $1,393.06 $437.14 $212.59 $202.94 $193.18 $183.34 $173.39 $163.34 $153.19 $142.94 $132.59 $122.14 $111.58 $100.91

E $31,165.26 $31,476.91 $31,791.68 $32,109.60 $32,430.70 $32,755.00 $33,082.55 $33,413.38 $33,747.51 $34,084.99 $34,425.84 $34,770.09 $35,117.80 $35,468.97 $35,823.66 $34,992.04 $34,152.10 $33,303.77 $32,446.95 $31,581.56 $30,707.51 $29,824.73 $28,933.12 $28,032.59 $27,123.06 $26,204.43 $25,276.62 $24,339.53 $23,393.06 $22,437.14 $21,471.65 $20,496.51 $19,511.62 $18,516.87 $17,512.18 $16,497.45 $15,472.56 $14,437.43 $13,391.95 $12,336.01 $11,269.51 $10,192.35

F $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08

G $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $437.14 $212.59 $202.94 $193.18 $183.34 $173.39 $163.34 $153.19 $142.94 $132.59 $122.14 $111.58 $100.91

H I J $0.00 $9,165.26 $31,165.26 $0.00 $9,476.91 $31,476.91 $0.00 $9,791.68 $31,791.68 $0.00 $10,109.60 $32,109.60 $0.00 $10,430.70 $32,430.70 $0.00 $10,755.00 $32,755.00 $0.00 $11,082.55 $33,082.55 $0.00 $11,413.38 $33,413.38 $0.00 $11,747.51 $33,747.51 $0.00 $12,084.99 $34,084.99 $0.00 $12,425.84 $34,425.84 $0.00 $12,770.09 $34,770.09 $0.00 $13,117.80 $35,117.80 $0.00 $13,468.97 $35,468.97 $0.00 $12,645.59 $34,645.59 $0.00 $11,813.96 $33,813.96 $0.00 $10,974.03 $32,974.03 $0.00 $10,125.69 $32,125.69 $0.00 $9,268.87 $31,268.87 $0.00 $8,403.48 $30,403.48 $0.00 $7,529.44 $29,529.44 $0.00 $6,646.65 $28,646.65 $0.00 $5,755.04 $27,755.04 $0.00 $4,854.52 $26,854.52 $0.00 $3,944.98 $25,944.98 $0.00 $3,026.36 $25,026.36 $0.00 $2,098.54 $24,098.54 $0.00 $1,161.45 $23,161.45 $0.00 $214.99 $22,214.99 $740.94 $0.00 $21,259.06 $965.49 $0.00 $20,293.57 $975.14 $0.00 $19,318.43 $984.89 $0.00 $18,333.54 $994.74 $0.00 $17,338.80 $1,004.69 $0.00 $16,334.11 $1,014.74 $0.00 $15,319.37 $1,024.88 $0.00 $14,294.49 $1,035.13 $0.00 $13,259.35 $1,045.48 $0.00 $12,213.87 $1,055.94 $0.00 $11,157.93 $1,066.50 $0.00 $10,091.43 $1,077.16 $0.00 $9,014.27

125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166

A 77 78 79 80 81 82 83 84

B $9,014.27 $7,926.33 $6,827.52 $5,717.72 $4,596.82 $3,464.71 $2,321.28 $1,166.41

C $90.14 $79.26 $68.28 $57.18 $45.97 $34.65 $23.21 $11.66

D $90.14 $79.26 $68.28 $57.18 $45.97 $34.65 $23.21 $11.66

E $9,104.41 $8,005.60 $6,895.80 $5,774.90 $4,642.79 $3,499.36 $2,344.49 $1,178.08

F $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08

G $90.14 $79.26 $68.28 $57.18 $45.97 $34.65 $23.21 $11.66

H $1,087.93 $1,098.81 $1,109.80 $1,120.90 $1,132.11 $1,143.43 $1,154.86 $1,166.41

METHOD 2 FIRST, DETERMINE THE AMOUNT OWED AT THE END OF 4 YEARS (48 MONTHS). AMT(48)= AMT(48)=

$35,469.06 USING INTEREST TABLES THIS IS =$22,000*(F|P 12%/12,12*4) $35,468.97 USING EXCEL'S FV FUNCTION THIS IS =FV(12%/12,12*4,,-22000)

NOW, DETERMINE THE AMOUNT OF THE MONTHLY DEFERRED PAYMENT Ad= $1,177.93 USING INTEREST TABLES THIS IS Ad=

=$35,469.06*(A|P 12%/12,12*3) $1,178.08 USING EXCEL'S PMT FUNCTION THIS IS =PMT(12%/12,12*3,-35468.97)

NOW, BUILD METHOD 2 - TABLE BELOW AND ANSWER QUESTIONS b, c, AND d BY INSPECTION b

IPmt(60)= PPmt(60)=

$1,178.08 METHOD 2 $0.00 METHOD 2

IPmt(64)= PPmt(64)=

$437.14 METHOD 2 $740.94 METHOD 2

IPmt(68)= PPmt(68)=

$183.34 METHOD 2 $994.74 METHOD 2

I $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

J $7,926.33 $6,827.52 $5,717.72 $4,596.82 $3,464.71 $2,321.28 $1,166.41 $0.00

A 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208

B C METHOD 2 - TABLE BEGINNING OF MONTH 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60

END OF MONTH CASH FLOW

PW OF REMAINING PAYMENTS

$1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08 $1,178.08

$1,166.41 $2,321.28 $3,464.71 $4,596.82 $5,717.72 $6,827.52 $7,926.33 $9,014.27 $10,091.43 $11,157.93 $12,213.87 $13,259.35 $14,294.49 $15,319.37 $16,334.11 $17,338.80 $18,333.54 $19,318.43 $20,293.57 $21,259.06 $22,214.99 $23,161.45 $24,098.54 $25,026.36 $25,944.98

Δ PW OF REMAINING PRINCIPAL INTEREST PAYMENTS PAYMENT PAYMENT

$1,154.86 $1,143.43 $1,132.11 $1,120.90 $1,109.80 $1,098.81 $1,087.93 $1,077.16 $1,066.50 $1,055.94 $1,045.48 $1,035.13 $1,024.88 $1,014.74 $1,004.69 $994.74 $984.89 $975.14 $965.49 $955.93 $946.46 $937.09 $927.81 $918.63

$1,166.41 $1,154.86 $1,143.43 $1,132.11 $1,120.90 $1,109.80 $1,098.81 $1,087.93 $1,077.16 $1,066.50 $1,055.94 $1,045.48 $1,035.13 $1,024.88 $1,014.74 $1,004.69 $994.74 $984.89 $975.14 $965.49 $740.94 $0.00 $0.00 $0.00 $0.00

METHOD 3 a

FIRST, DETERMINE THE AMOUNT OWED AT THE END OF 4 YEARS (48 MONTHS). AMT(48)= AMT(48)=

$35,469.06 USING INTEREST TABLES THIS IS =$22,000*(F|P 12%/12,12*4) $35,468.97 USING EXCEL'S FV FUNCTION THIS IS =FV(12%/12,12*4,,-22000)

NOW, DETERMINE THE AMOUNT OF THE MONTHLY DEFERRED PAYMENT Ad= $1,177.93 USING INTEREST TABLES THIS IS

$11.66 $23.21 $34.65 $45.97 $57.18 $68.28 $79.26 $90.14 $100.91 $111.58 $122.14 $132.59 $142.94 $153.19 $163.34 $173.39 $183.34 $193.18 $202.94 $212.59 $437.14 $1,178.08 $1,178.08 $1,178.08 $1,178.08

A 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248

B Ad=

D E F =$35,469.06*(A|P 12%/12,12*3) $1,178.08 USING EXCEL'S PMT FUNCTION THIS IS =PMT(12%/12,12*3,-35468.97)

NOW, DETERMINE Nd, THE INTEGER PORTION OF THE NUMBER OF PAYMENTS OF SIZE Ad REQUIRED TO PAY OFF P, THE AMOUNT BORROWED Nd =

NOW, CALCULATE THE PW OF Nd AMOUNTS OF Ad PW(Nd Ad'S)= $21,259.06 USING INTEREST TABLES THIS IS =$1,178.08*(P|A 12%/12,20) PW(Nd Ad'S)= $21,259.06 USING EXCEL'S PV FUNCTION THIS IS =PV(12%/12,20,-1178.08) NOW, CALCULATE THE VALUE OF PPMT FOR THE 36-20TH PAYMENT (OR 48+36-20TH MONTH) PPmt(64)=

$740.94 =22000-21259.06

NOW, COMPLETE METHOD 3 - TABLE MONTH 1 TO 48 49 TO 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

PPmt $0.00 $0.00 $740.94 $965.49 =PPMT(12%/12,65-12*4,12*3,-35468.97) $975.14 $984.89 $994.74 =PPMT(12%/12,68-12*4,12*3,-35468.97) $1,004.69 $1,014.74 $1,024.88 $1,035.13 $1,045.48 $1,055.94 $1,066.50 $1,077.16 $1,087.93 $1,098.81 $1,109.80

Ipmt $0.00 $1,178.08 $437.14 $212.59 $202.94 $193.18 $183.34 $173.39 $163.34 $153.19 $142.94 $132.59 $122.14 $111.58 $100.91 $90.14 $79.26 $68.28

GIVEN INTEREST ONLY AS CALC ABOVE =1178.08-965.49

=1178.08-994.74

A 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272

B 80 81 82 83 84 SUM 72-84=

C $1,120.90 $1,132.11 $1,143.43 $1,154.86 $1,166.41

$14,294.49 FOR PART e

IPmt(60)= PPmt(60)=

$0.00 METHOD 3 $0.00 METHOD 3

IPmt(64)= PPmt(64)=

$437.14 METHOD 3 $740.94 METHOD 3

IPmt(68)= PPmt(68)=

$183.34 METHOD 3 $994.74 METHOD 3

G $57.18 $45.97 $34.65 $23.21 $11.66

PROBLEM 3.31 P= m= k= n= A= a

$14,000.00 12 1 3 $536.83

PRINCIPAL MONTHS YEAR WITH NO PAYMENTS MORE YEARS WITH PAYMENTS MONTHLY PAYMENTS

TO DETERMINE THE NOMINAL INTEREST RATE, SET THE EQUATION FOR THE PW OF THE CASH FLOWS EQUAL TO P AND SOLVE FOR THE NOMINAL RATE, r USE SOLVER TO FIND THE VALUE OF NOMINAL INTEREST RATE r r=

13.000%

SOLVER CHANGED CELL

$14,000.00

SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(r%/12,12*1,,-PV(r%/12,12*3,-536.83))

AS A CHECK, CAN USE INTEREST TABLES P=

ieff= ieff=

$14,000.07

USING ELECTRONIC INTEREST TABLES THIS IS $536.83*(P|A 13/12%,36)*(P|F 13/12%,12)

13.803% USING COMPOUND INTEREST FORMULAS THIS IS =(1+13%/12)^12-1 13.803% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(13%,12)

FOR PARTS c, d, AND e, THREE DIFFERENT METHODS WILL BE USED TO SOLVE THIS PROBLEM. THE FIRST TWO ARE ILLUSTRATED IN EXAMPLES 3.15 AND 3.16. THE THIRD APPROACH IS PRESENTED IN SLIDES MADE AVAILABLE TO INSTRUCTORS BY THE AUTHORS. METHOD 1 NOW, BUILD METHOD 1 - TABLE BELOW AND ANSWER QUESTIONS c, d, AND e BY INSPECTION c

IPmt(14)= PPmt(14)=

$536.83 METHOD 1 $0.00 METHOD 1

IPmt(18)= PPmt(18)=

$223.92 METHOD 1 $312.91 METHOD 1

IPmt(22)= PPmt(22)=

$135.51 METHOD 1 $401.32 METHOD 1

METHOD 1 - TABLE

BEGINNING OF MONTH

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

UNPAID BALANCE BEFORE PAYMENT UB $14,000.00 $14,151.67 $14,304.98 $14,459.95 $14,616.61 $14,774.96 $14,935.02 $15,096.82 $15,260.37 $15,425.69 $15,592.81 $15,761.73 $15,932.49 $15,568.26 $15,200.09 $14,827.93 $14,451.74 $14,071.47 $13,687.09 $13,298.53 $12,905.77 $12,508.76 $12,107.44 $11,701.78 $11,291.72 $10,877.22 $10,458.23 $10,034.70 $9,606.58 $9,173.82 $8,736.37

INTEREST DURING MONTH INT $151.67 $153.31 $154.97 $156.65 $158.35 $160.06 $161.80 $163.55 $165.32 $167.11 $168.92 $170.75 $172.60 $168.66 $164.67 $160.64 $156.56 $152.44 $148.28 $144.07 $139.81 $135.51 $131.17 $126.77 $122.33 $117.84 $113.30 $108.71 $104.07 $99.38 $94.65

UNPAID INTEREST BEFORE PAYMENT UIB $151.67 $304.98 $459.95 $616.61 $774.96 $935.02 $1,096.82 $1,260.37 $1,425.69 $1,592.81 $1,761.73 $1,932.49 $2,105.09 $1,736.92 $1,364.76 $988.57 $608.30 $223.92 $148.28 $144.07 $139.81 $135.51 $131.17 $126.77 $122.33 $117.84 $113.30 $108.71 $104.07 $99.38 $94.65

AMOUNT OWED AO $14,151.67 $14,304.98 $14,459.95 $14,616.61 $14,774.96 $14,935.02 $15,096.82 $15,260.37 $15,425.69 $15,592.81 $15,761.73 $15,932.49 $16,105.09 $15,736.92 $15,364.76 $14,988.57 $14,608.30 $14,223.92 $13,835.36 $13,442.60 $13,045.59 $12,644.27 $12,238.61 $11,828.55 $11,414.05 $10,995.06 $10,571.53 $10,143.41 $9,710.65 $9,273.20 $8,831.02

UNPAID UNPAID INTEREST BALANCE LOAN INTEREST PRINCIPAL AFTER AFTER PAYMENT PAYMENT PAYMENT PAYMENT PAYMENT PMT IPMT PPMT UIA $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $536.83 $536.83 $536.83 $536.83 $536.83 $223.92 $148.28 $144.07 $139.81 $135.51 $131.17 $126.77 $122.33 $117.84 $113.30 $108.71 $104.07 $99.38 $94.65

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $312.91 $388.55 $392.76 $397.02 $401.32 $405.66 $410.06 $414.50 $418.99 $423.53 $428.12 $432.76 $437.45 $442.18

$151.67 $14,151.67 $304.98 $14,304.98 $459.95 $14,459.95 $616.61 $14,616.61 $774.96 $14,774.96 $935.02 $14,935.02 $1,096.82 $15,096.82 $1,260.37 $15,260.37 $1,425.69 $15,425.69 $1,592.81 $15,592.81 $1,761.73 $15,761.73 $1,932.49 $15,932.49 $1,568.26 $15,568.26 $1,200.09 $15,200.09 $827.93 $14,827.93 $451.74 $14,451.74 $71.47 $14,071.47 $0.00 $13,687.09 $0.00 $13,298.53 $0.00 $12,905.77 $0.00 $12,508.76 $0.00 $12,107.44 $0.00 $11,701.78 $0.00 $11,291.72 $0.00 $10,877.22 $0.00 $10,458.23 $0.00 $10,034.70 $0.00 $9,606.58 $0.00 $9,173.82 $0.00 $8,736.37 $0.00 $8,294.19

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

$8,294.19 $7,847.21 $7,395.40 $6,938.69 $6,477.03 $6,010.37 $5,538.65 $5,061.82 $4,579.83 $4,092.61 $3,600.12 $3,102.29 $2,599.07 $2,090.40 $1,576.22 $1,056.46 $531.08

$89.86 $85.01 $80.12 $75.17 $70.17 $65.11 $60.00 $54.84 $49.62 $44.34 $39.00 $33.61 $28.16 $22.65 $17.08 $11.45 $5.75

$8,384.04 $7,932.23 $7,475.52 $7,013.86 $6,547.20 $6,075.48 $5,598.65 $5,116.66 $4,629.44 $4,136.95 $3,639.12 $3,135.90 $2,627.23 $2,113.05 $1,593.29 $1,067.91 $536.83

$536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83

$89.86 $85.01 $80.12 $75.17 $70.17 $65.11 $60.00 $54.84 $49.62 $44.34 $39.00 $33.61 $28.16 $22.65 $17.08 $11.45 $5.75

$446.97 $451.82 $456.71 $461.66 $466.66 $471.72 $476.83 $481.99 $487.21 $492.49 $497.83 $503.22 $508.67 $514.18 $519.75 $525.38 $531.08

METHOD 2 NOW, BUILD METHOD 2 - TABLE BELOW AND ANSWER QUESTIONS c, d, AND e BY INSPECTION c

IPmt(14)= PPmt(14)=

$536.83 METHOD 2 $0.00 METHOD 2

IPmt(18)= PPmt(18)=

$223.92 METHOD 2 $312.91 METHOD 2

IPmt(22)= PPmt(22)=

$135.51 METHOD 2 $401.32 METHOD 2

METHOD 2 - TABLE

BEGINNING OF MONTH 48 47 46 45 44 43

END OF MONTH CASH FLOW

PW OF REMAINING PAYMENTS

$536.83 $536.83 $536.83 $536.83 $536.83 $536.83

$531.08 $1,056.46 $1,576.22 $2,090.40 $2,599.07 $3,102.29

Δ PW OF REMAINING PRINCIPAL INTEREST PAYMENTS PAYMENT PAYMENT

$525.38 $519.75 $514.18 $508.67 $503.22

$531.08 $525.38 $519.75 $514.18 $508.67 $503.22

$5.75 $11.45 $17.08 $22.65 $28.16 $33.61

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$7,847.21 $7,395.40 $6,938.69 $6,477.03 $6,010.37 $5,538.65 $5,061.82 $4,579.83 $4,092.61 $3,600.12 $3,102.29 $2,599.07 $2,090.40 $1,576.22 $1,056.46 $531.08 $0.00

42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14

$536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83 $536.83

$3,600.12 $4,092.61 $4,579.83 $5,061.82 $5,538.65 $6,010.37 $6,477.03 $6,938.69 $7,395.40 $7,847.21 $8,294.19 $8,736.37 $9,173.82 $9,606.58 $10,034.70 $10,458.23 $10,877.22 $11,291.72 $11,701.78 $12,107.44 $12,508.76 $12,905.77 $13,298.53 $13,687.09 $14,071.47 $14,451.74 $14,827.93 $15,200.09 $15,568.26

$497.83 $492.49 $487.21 $481.99 $476.83 $471.72 $466.66 $461.66 $456.71 $451.82 $446.97 $442.18 $437.45 $432.76 $428.12 $423.53 $418.99 $414.50 $410.06 $405.66 $401.32 $397.02 $392.76 $388.55 $384.39 $380.27 $376.19 $372.16 $368.17

$39.00 $44.34 $49.62 $54.84 $60.00 $65.11 $70.17 $75.17 $80.12 $85.01 $89.86 $94.65 $99.38 $104.07 $108.71 $113.30 $117.84 $122.33 $126.77 $131.17 $135.51 $139.81 $144.07 $148.28 $223.92 $536.83 $536.83 $536.83 $536.83

METHOD 3 FIRST, DETERMINE THE AMOUNT OWED AT THE END OF 1 YEAR (12 MONTHS). AMT(12)= AMT(12)=

$15,932.45 USING INTEREST TABLES THIS IS =$14,000*(F|P 13%/12,12*1) $15,932.49 USING EXCEL'S FV FUNCTION THIS IS =FV(13%/12,12*1,,-14000)

NOW, DETERMINE THE AMOUNT OF THE MONTHLY DEFERRED PAYMENT Ad= $536.83 USING INTEREST TABLES THIS IS =$15,932.45*(A|P 13%/12,12*3) Ad= $536.83 USING EXCEL'S PMT FUNCTION THIS IS

=PMT(13%/12,12*3,-15932.49) NOTE THAT THE ABOVE STEPS ARE NOT NECESSARY IN THIS PROBLEM BECAUSE THE VALUE OF Ad WAS GIVEN IN THE PROBLEM. THIS MERELY SERVES AS A CHECK. NOW, DETERMINE Nd, THE INTEGER PORTION OF THE NUMBER OF PAYMENTS OF SIZE Ad REQUIRED TO PAY OFF P, THE AMOUNT BORROWED Nd =

NOW, CALCULATE THE PW OF Nd AMOUNTS OF Ad PW(Nd Ad'S)= PW(Nd Ad'S)=

$13,687.07 USING INTEREST TABLES THIS IS =$536.83*(P|A 13%/12,30) $13,687.09 USING EXCEL'S PV FUNCTION THIS IS =PV(13%/12,30,-536.83)

NOW, CALCULATE THE VALUE OF PPMT FOR THE 36-30TH PAYMENT (OR 12+36-30TH MONTH) PPmt(18)=

$312.91 =14000-13687.09

NOW, COMPLETE METHOD 3 - TABLE MONTH 1 TO 12 12 TO 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

PPmt $0.00 $0.00 $312.91 $388.55 =PPMT(13%/12,19-12*1,12*3,-15932.49) $392.76 $397.02 $401.32 =PPMT(13%/12,22-12*1,12*3,-15932.49) $405.66 $410.06 $414.50 $418.99 $423.53 $428.12 $432.76 $437.45 $442.18 $446.97 $451.82 $456.71

IPmt $0.00 $536.83 $223.92 $148.28 $144.07 $139.81 $135.51 $131.17 $126.77 $122.33 $117.84 $113.30 $108.71 $104.07 $99.38 $94.65 $89.86 $85.01 $80.12

GIVEN INTEREST ONLY AS CALC ABOVE =536.83-388.55

=536.83-401.32

35 36 37 38 39 40 41 42 43 44 45 46 47 48

$461.66 $466.66 $471.72 $476.83 $481.99 $487.21 $492.49 $497.83 $503.22 $508.67 $514.18 $519.75 $525.38 $531.08

IPmt(14)= PPmt(14)=

$536.83 METHOD 3 $0.00 METHOD 3

IPmt(18)= PPmt(18)=

$223.92 METHOD 3 $312.91 METHOD 3

IPmt(22)= PPmt(22)=

$135.51 METHOD 3 $401.32 METHOD 3

$75.17 $70.17 $65.11 $60.00 $54.84 $49.62 $44.34 $39.00 $33.61 $28.16 $22.65 $17.08 $11.45 $5.75

A B C D E F G H I 1 PROBLEM 3.32 2 3 P= $500,000.00 PRINCIPAL 4 r= 24.000% PER YEAR 5 m= 12 MONTHS 6 k= 3 YEAR 7 n= 3 MORE YEARS 8 9 METHOD 1 10 a FIRST, DETERMINE THE AMOUNT OWED AT THE END OF 3 YEARS (36 MONTHS). 11 12 AMT(36)= $1,019,945.00 USING INTEREST TABLES THIS IS 13 =$500,000*(F|P 24%/12,12*3) 14 AMT(36)= $1,019,943.67 USING EXCEL'S FV FUNCTION THIS IS 15 =FV(24%/12,12*3,,-500000) 16 17 NOW, DETERMINE THE AMOUNT OF THE MONTHLY DEFERRED PAYMENT Ad= 18 $40,012.44 USING INTEREST TABLES THIS IS 19 =$1,019,945*(A|P 24%/12,12*3) Ad= 20 $40,015.30 USING EXCEL'S PMT FUNCTION THIS IS 21 =PMT(24%/12,12*3,-1019943.67) 22 23 NOW, BUILD METHOD 1 - TABLE BELOW AND ANSWER QUESTIONS b, c, AND d BY INSPECTION 24 25 b TOTAL INTEREST= $940,550.79 METHOD 1 26 27 c TOTAL PRINCIPAL= $500,000.00 METHOD 1 28 29 d PAYOFF(60)= $423,145.18 USING INTEREST TABLES THIS IS 30 =$40,012.44*(P|A 24%/12,12) 31 PAYOFF(60)= $423,175.45 USING EXCEL'S PV FUNCTION THIS IS 32 =PV(24%/12,12,-40015.3) 33 PAYOFF(60)= $423,175.45 METHOD 1 BY INSPECTION OF METHOD 1 - TABLE 34 35 METHOD 1 - TABLE 36 37 UNPAID UNPAID UNPAID 38 BEGIN'G BALANCE INTEREST INTEREST INTEREST 39 OF BEFORE DURING BEFORE AMOUNT LOAN INTEREST PRINCIPAL AFTER 40 MONTH PAYMENT MONTH PAYMENT OWED PAYMENT PAYMENT PAYMENT PAYMENT 41 42 1 $500,000.00 $10,000.00 $10,000.00 $510,000.00 $0.00 $0.00 $0.00 $10,000.00

UNPAID BALANCE AFTER PAYMENT $510,000.00

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

A 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

B $510,000.00 $520,200.00 $530,604.00 $541,216.08 $552,040.40 $563,081.21 $574,342.83 $585,829.69 $597,546.28 $609,497.21 $621,687.15 $634,120.90 $646,803.32 $659,739.38 $672,934.17 $686,392.85 $700,120.71 $714,123.12 $728,405.59 $742,973.70 $757,833.17 $772,989.84 $788,449.63 $804,218.62 $820,303.00 $836,709.06 $853,443.24 $870,512.10 $887,922.35 $905,680.79 $923,794.41 $942,270.30 $961,115.70 $980,338.02 $999,944.78 $1,019,943.67 $1,000,327.25 $980,318.49 $959,909.56 $939,092.45 $917,859.00 $896,200.88

C $10,200.00 $10,404.00 $10,612.08 $10,824.32 $11,040.81 $11,261.62 $11,486.86 $11,716.59 $11,950.93 $12,189.94 $12,433.74 $12,682.42 $12,936.07 $13,194.79 $13,458.68 $13,727.86 $14,002.41 $14,282.46 $14,568.11 $14,859.47 $15,156.66 $15,459.80 $15,768.99 $16,084.37 $16,406.06 $16,734.18 $17,068.86 $17,410.24 $17,758.45 $18,113.62 $18,475.89 $18,845.41 $19,222.31 $19,606.76 $19,998.90 $20,398.87 $20,006.54 $19,606.37 $19,198.19 $18,781.85 $18,357.18 $17,924.02

D $20,200.00 $30,604.00 $41,216.08 $52,040.40 $63,081.21 $74,342.83 $85,829.69 $97,546.28 $109,497.21 $121,687.15 $134,120.90 $146,803.32 $159,739.38 $172,934.17 $186,392.85 $200,120.71 $214,123.12 $228,405.59 $242,973.70 $257,833.17 $272,989.84 $288,449.63 $304,218.62 $320,303.00 $336,709.06 $353,443.24 $370,512.10 $387,922.35 $405,680.79 $423,794.41 $442,270.30 $461,115.70 $480,338.02 $499,944.78 $519,943.67 $540,342.55 $520,333.79 $499,924.86 $479,107.75 $457,874.30 $436,216.18 $414,124.90

E $520,200.00 $530,604.00 $541,216.08 $552,040.40 $563,081.21 $574,342.83 $585,829.69 $597,546.28 $609,497.21 $621,687.15 $634,120.90 $646,803.32 $659,739.38 $672,934.17 $686,392.85 $700,120.71 $714,123.12 $728,405.59 $742,973.70 $757,833.17 $772,989.84 $788,449.63 $804,218.62 $820,303.00 $836,709.06 $853,443.24 $870,512.10 $887,922.35 $905,680.79 $923,794.41 $942,270.30 $961,115.70 $980,338.02 $999,944.78 $1,019,943.67 $1,040,342.55 $1,020,333.79 $999,924.86 $979,107.75 $957,874.30 $936,216.18 $914,124.90

F $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30

G $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30

I J $0.00 $20,200.00 $520,200.00 $0.00 $30,604.00 $530,604.00 $0.00 $41,216.08 $541,216.08 $0.00 $52,040.40 $552,040.40 $0.00 $63,081.21 $563,081.21 $0.00 $74,342.83 $574,342.83 $0.00 $85,829.69 $585,829.69 $0.00 $97,546.28 $597,546.28 $0.00 $109,497.21 $609,497.21 $0.00 $121,687.15 $621,687.15 $0.00 $134,120.90 $634,120.90 $0.00 $146,803.32 $646,803.32 $0.00 $159,739.38 $659,739.38 $0.00 $172,934.17 $672,934.17 $0.00 $186,392.85 $686,392.85 $0.00 $200,120.71 $700,120.71 $0.00 $214,123.12 $714,123.12 $0.00 $228,405.59 $728,405.59 $0.00 $242,973.70 $742,973.70 $0.00 $257,833.17 $757,833.17 $0.00 $272,989.84 $772,989.84 $0.00 $288,449.63 $788,449.63 $0.00 $304,218.62 $804,218.62 $0.00 $320,303.00 $820,303.00 $0.00 $336,709.06 $836,709.06 $0.00 $353,443.24 $853,443.24 $0.00 $370,512.10 $870,512.10 $0.00 $387,922.35 $887,922.35 $0.00 $405,680.79 $905,680.79 $0.00 $423,794.41 $923,794.41 $0.00 $442,270.30 $942,270.30 $0.00 $461,115.70 $961,115.70 $0.00 $480,338.02 $980,338.02 $0.00 $499,944.78 $999,944.78 $0.00 $519,943.67 $1,019,943.67 $0.00 $500,327.25 $1,000,327.25 $0.00 $480,318.49 $980,318.49 $0.00 $459,909.56 $959,909.56 $0.00 $439,092.45 $939,092.45 $0.00 $417,859.00 $917,859.00 $0.00 $396,200.88 $896,200.88 $0.00 $374,109.60 $874,109.60

85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

A 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72

B $874,109.60 $851,576.49 $828,592.72 $805,149.28 $781,236.96 $756,846.40 $731,968.03 $706,592.09 $680,708.63 $654,307.51 $627,378.36 $599,910.62 $571,893.54 $543,316.11 $514,167.13 $484,435.17 $454,108.58 $423,175.45 $391,623.66 $359,440.83 $326,614.35 $293,131.34 $258,978.66 $224,142.94 $188,610.50 $152,367.41 $115,399.45 $77,692.14 $39,230.69

C $17,482.19 $17,031.53 $16,571.85 $16,102.99 $15,624.74 $15,136.93 $14,639.36 $14,131.84 $13,614.17 $13,086.15 $12,547.57 $11,998.21 $11,437.87 $10,866.32 $10,283.34 $9,688.70 $9,082.17 $8,463.51 $7,832.47 $7,188.82 $6,532.29 $5,862.63 $5,179.57 $4,482.86 $3,772.21 $3,047.35 $2,307.99 $1,553.84 $784.61

D $391,591.79 $368,608.02 $345,164.58 $321,252.26 $296,861.70 $271,983.33 $246,607.39 $220,723.93 $194,322.81 $167,393.66 $139,925.92 $111,908.84 $83,331.41 $54,182.43 $24,450.47 $9,688.70 $9,082.17 $8,463.51 $7,832.47 $7,188.82 $6,532.29 $5,862.63 $5,179.57 $4,482.86 $3,772.21 $3,047.35 $2,307.99 $1,553.84 $784.61

E $891,591.79 $868,608.02 $845,164.58 $821,252.26 $796,861.70 $771,983.33 $746,607.39 $720,723.93 $694,322.81 $667,393.66 $639,925.92 $611,908.84 $583,331.41 $554,182.43 $524,450.47 $494,123.88 $463,190.75 $431,638.96 $399,456.13 $366,629.65 $333,146.64 $298,993.96 $264,158.24 $228,625.79 $192,382.70 $155,414.75 $117,707.44 $79,245.99 $40,015.30

F $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 SUM

METHOD 2 FIRST, DETERMINE THE AMOUNT OWED AT THE END OF 3 YEARS (36 MONTHS). AMT(36)= AMT(36)=

$1,019,945.00 USING INTEREST TABLES THIS IS =$500,000*(F|P 24%/12,12*3) $1,019,943.67 USING EXCEL'S FV FUNCTION THIS IS =FV(24%/12,12*3,,-500000)

NOW, DETERMINE THE AMOUNT OF THE MONTHLY DEFERRED PAYMENT

G $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $24,450.47 $9,688.70 $9,082.17 $8,463.51 $7,832.47 $7,188.82 $6,532.29 $5,862.63 $5,179.57 $4,482.86 $3,772.21 $3,047.35 $2,307.99 $1,553.84 $784.61

I $0.00 $351,576.49 $0.00 $328,592.72 $0.00 $305,149.28 $0.00 $281,236.96 $0.00 $256,846.40 $0.00 $231,968.03 $0.00 $206,592.09 $0.00 $180,708.63 $0.00 $154,307.51 $0.00 $127,378.36 $0.00 $99,910.62 $0.00 $71,893.54 $0.00 $43,316.11 $0.00 $14,167.13 $15,564.83 $0.00 $30,326.60 $0.00 $30,933.13 $0.00 $31,551.79 $0.00 $32,182.83 $0.00 $32,826.48 $0.00 $33,483.01 $0.00 $34,152.67 $0.00 $34,835.73 $0.00 $35,532.44 $0.00 $36,243.09 $0.00 $36,967.95 $0.00 $37,707.31 $0.00 $38,461.46 $0.00 $39,230.69 $0.00

$940,550.79 $500,000.00 INTEREST PRINCIPAL

J $851,576.49 $828,592.72 $805,149.28 $781,236.96 $756,846.40 $731,968.03 $706,592.09 $680,708.63 $654,307.51 $627,378.36 $599,910.62 $571,893.54 $543,316.11 $514,167.13 $484,435.17 $454,108.58 $423,175.45 $391,623.66 $359,440.83 $326,614.35 $293,131.34 $258,978.66 $224,142.94 $188,610.50 $152,367.41 $115,399.45 $77,692.14 $39,230.69 $0.00

A B C D E F G Ad= 127 $40,012.44 USING INTEREST TABLES THIS IS 128 =$1,019,945*(A|P 24%/12,12*3) Ad= 129 $40,015.30 USING EXCEL'S PMT FUNCTION THIS IS 130 =PMT(24%/12,12*3,-1019943.67) 131 132 NOW, BUILD METHOD 2 - TABLE BELOW AND ANSWER QUESTIONS b, c, AND d BY INSPECTION 133 134 b TOTAL INTEREST= $940,550.79 METHOD 2 135 136 c TOTAL PRINCIPAL= $500,000.00 METHOD 2 137 138 d PAYOFF(60)= $423,145.18 USING INTEREST TABLES THIS IS 139 =$40,012.44*(P|A 24%/12,12) 140 PAYOFF(60)= $423,175.45 USING EXCEL'S PV FUNCTION THIS IS 141 =PV(24%/12,12,-40015.3) 142 PAYOFF(60)= $423,175.45 METHOD 2 BY INSPECTION OF METHOD 2 - TABLE 143 BEGINNING OF MONTH 61 IS END OF MONTH 60 144 METHOD 2 - TABLE 145 146 END OF PW OF Δ PW OF 147 BEGINNING MONTH REMAINING REMAINING PRINCIPAL INTEREST 148 OF MONTH CASH FLOW PAYMENTS PAYMENTS PAYMENT PAYMENT 149 150 72 $40,015.30 $39,230.69 $39,230.69 $784.61 151 71 $40,015.30 $77,692.14 $38,461.46 $38,461.46 $1,553.84 152 70 $40,015.30 $115,399.45 $37,707.31 $37,707.31 $2,307.99 153 69 $40,015.30 $152,367.41 $36,967.95 $36,967.95 $3,047.35 154 68 $40,015.30 $188,610.50 $36,243.09 $36,243.09 $3,772.21 155 67 $40,015.30 $224,142.94 $35,532.44 $35,532.44 $4,482.86 156 66 $40,015.30 $258,978.66 $34,835.73 $34,835.73 $5,179.57 157 65 $40,015.30 $293,131.34 $34,152.67 $34,152.67 $5,862.63 158 64 $40,015.30 $326,614.35 $33,483.01 $33,483.01 $6,532.29 159 63 $40,015.30 $359,440.83 $32,826.48 $32,826.48 $7,188.82 160 62 $40,015.30 $391,623.66 $32,182.83 $32,182.83 $7,832.47 161 61 $40,015.30 $423,175.45 $31,551.79 $31,551.79 $8,463.51 162 60 $40,015.30 $454,108.58 $30,933.13 $30,933.13 $9,082.17 163 59 $40,015.30 $484,435.17 $30,326.60 $30,326.60 $9,688.70 164 58 $40,015.30 $514,167.13 $29,731.96 $15,564.83 $24,450.47 165 57 $40,015.30 $543,316.11 $29,148.98 $0.00 $40,015.30 166 56 $40,015.30 $571,893.54 $28,577.43 $0.00 $40,015.30 167 55 $40,015.30 $599,910.62 $28,017.09 $0.00 $40,015.30 168 54 $40,015.30 $627,378.36 $27,467.73 $0.00 $40,015.30

A 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210

B 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12

C $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

D $654,307.51 $680,708.63 $706,592.09 $731,968.03 $756,846.40 $781,236.96 $805,149.28 $828,592.72 $851,576.49 $874,109.60 $896,200.88 $917,859.00 $939,092.45 $959,909.56 $980,318.49 $1,000,327.25 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67

E $26,929.15 $26,401.13 $25,883.46 $25,375.94 $24,878.37 $24,390.56 $23,912.31 $23,443.45 $22,983.77 $22,533.11 $22,091.28 $21,658.12 $21,233.45 $20,817.11 $20,408.93 $20,008.75 $19,616.43 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

G $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

A 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251

B 11 10 9 8 7 6 5 4 3 2 1

C $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

D $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67 $1,019,943.67

E $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 SUM

F $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

G $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

########## $940,550.79

METHOD 3 a

FIRST, DETERMINE THE AMOUNT OWED AT THE END OF 3 YEARS (36 MONTHS). AMT(36)= AMT(36)=

$1,019,945.00 USING INTEREST TABLES THIS IS =$500,000*(F|P 24%/12,12*3) $1,019,943.67 USING EXCEL'S FV FUNCTION THIS IS =FV(24%/12,12*3,,-500000)

NOW, DETERMINE THE AMOUNT OF THE MONTHLY DEFERRED PAYMENT Ad= $40,012.44 USING INTEREST TABLES THIS IS =$1,019,945*(A|P 24%/12,12*3) Ad= $40,015.30 USING EXCEL'S PMT FUNCTION THIS IS =PMT(24%/12,12*3,-1019943.67) NOW, DETERMINE Nd, THE INTEGER PORTION OF THE NUMBER OF PAYMENTS OF SIZE Ad REQUIRED TO PAY OFF P, Nd =

NOW, CALCULATE THE PW OF Nd AMOUNTS OF Ad PW(Nd Ad'S)= PW(Nd Ad'S)=

$484,400.63 USING INTEREST TABLES THIS IS =$40,012.44*(P|A 24%/12,14) $484,435.17 USING EXCEL'S PV FUNCTION THIS IS =PV(24%/12,14,-40015.3)

NOW, CALCULATE THE VALUE OF PPMT FOR THE 36-14TH PAYMENT (OR 36+36-14TH MONTH)

A 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293

B PPmt(58)=

$15,564.83 =500000-484435.17

NOW, COMPLETE METHOD 3 - TABLE MONTH 1 TO 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

PPmt $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $15,564.83 $30,326.60 =PPMT(24%/12,59-12*3,12*3,-1019943.67) $30,933.13 $31,551.79 $32,182.83 =PPMT(24%/12,62-12*3,12*3,-1019943.67) $32,826.48 $33,483.01 $34,152.67 $34,835.73 $35,532.44 $36,243.09 $36,967.95 $37,707.31 $38,461.46

IPmt $0.00 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $40,015.30 $24,450.47 $9,688.70 $9,082.17 $8,463.51 $7,832.47 $7,188.82 $6,532.29 $5,862.63 $5,179.57 $4,482.86 $3,772.21 $3,047.35 $2,307.99 $1,553.84

GIVEN INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY INTEREST ONLY AS CALC ABOVE =40015.3-30326.6

=40015.3-32182.83

A 294 295 296 297 298 299 300 301 302 303 304 305 306 307

B 72

C $39,230.69

TOTALS

$500,000.00

TOTAL INTEREST=

$940,550.79 METHOD 3

TOTAL PRINCIPAL=

$500,000.00 METHOD 3

PAYOFF(60)= PAYOFF(60)= PAYOFF(60)=

$423,145.18

USING INTEREST TABLES THIS IS =$40,012.44*(P|A 24%/12,12) $423,175.45 USING EXCEL'S PV FUNCTION THIS IS =PV(24%/12,12,-40015.3) $423,175.45 METHOD 3 =SUM(PPmt YR 61:PPmt YR 72)

G $784.61 $940,550.79

A B C D E F 1 PROBLEM 3.33 2 3 FIRST DEP= $1,500.00 4 SALARY INCR= 6.00% 5 i= 5.00% 6 n= 36 YEARS 7 8 FV= $353,315.39 USING INTEREST TABLES THIS IS =$1,500*(F|A1 5%,6%,36) 9 10 11 THE FOLLOWING TABLE CAN BE USED TO CHECK THE RESULTS 12 13 AGE EOY INTEREST DEPOSIT TOTAL ACCT 14 24 0 15 25 1 $1,500.00 $1,500.00 16 26 2 $75.00 $1,590.00 $3,165.00 17 27 3 $158.25 $1,685.40 $5,008.65 18 28 4 $250.43 $1,786.52 $7,045.61 19 29 5 $352.28 $1,893.72 $9,291.60 20 30 6 $464.58 $2,007.34 $11,763.52 21 31 7 $588.18 $2,127.78 $14,479.48 22 32 8 $723.97 $2,255.45 $17,458.89 23 33 9 $872.94 $2,390.77 $20,722.61 24 34 10 $1,036.13 $2,534.22 $24,292.96 25 35 11 $1,214.65 $2,686.27 $28,193.88 26 36 12 $1,409.69 $2,847.45 $32,451.02 27 37 13 $1,622.55 $3,018.29 $37,091.87 28 38 14 $1,854.59 $3,199.39 $42,145.85 29 39 15 $2,107.29 $3,391.36 $47,644.50 30 40 16 $2,382.23 $3,594.84 $53,621.56 31 41 17 $2,681.08 $3,810.53 $60,113.17 32 42 18 $3,005.66 $4,039.16 $67,157.99 33 43 19 $3,357.90 $4,281.51 $74,797.40 34 44 20 $3,739.87 $4,538.40 $83,075.67 35 45 21 $4,153.78 $4,810.70 $92,040.15 36 46 22 $4,602.01 $5,099.35 $101,741.50 37 47 23 $5,087.08 $5,405.31 $112,233.89 38 48 24 $5,611.69 $5,729.62 $123,575.20 39 49 25 $6,178.76 $6,073.40 $135,827.37 40 50 26 $6,791.37 $6,437.81 $149,056.54 41 51 27 $7,452.83 $6,824.07 $163,333.44 42 52 28 $8,166.67 $7,233.52 $178,733.63 43 53 29 $8,936.68 $7,667.53 $195,337.85 44 54 30 $9,766.89 $8,127.58 $213,232.32 45 55 31 $10,661.62 $8,615.24 $232,509.17 46 56 32 $11,625.46 $9,132.15 $253,266.78 47 57 33 $12,663.34 $9,680.08 $275,610.20 48 58 34 $13,780.51 $10,260.88 $299,651.60 49 59 35 $14,982.58 $10,876.54 $325,510.71 50 60 36 $16,275.54 $11,529.13 $353,315.38

A 1 PROBLEM 3.34 2 3 4 5 6 7 8 9

GROSS INCOME= % GI INVESTED= FIRST INVESTMENT= SALARY INCR= i= n=

$60,000.00 10.00% $6,000.00 6.00% 7.50% 36

YEARS

FV= 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

$3,103,408.41 USING ELECTRONIC INTEREST TABLES THIS IS =$6,000*(F|A1 7.5%,6%,40)

THE FOLLOWING TABLE CAN BE USED TO CHECK THE RESULTS EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

INTEREST

DEPOSIT

TOTAL ACCT

$6,000.00 $6,000.00 $450.00 $6,360.00 $12,810.00 $960.75 $6,741.60 $20,512.35 $1,538.43 $7,146.10 $29,196.87 $2,189.77 $7,574.86 $38,961.50 $2,922.11 $8,029.35 $49,912.97 $3,743.47 $8,511.11 $62,167.55 $4,662.57 $9,021.78 $75,851.90 $5,688.89 $9,563.09 $91,103.88 $6,832.79 $10,136.87 $108,073.55 $8,105.52 $10,745.09 $126,924.15 $9,519.31 $11,389.79 $147,833.25 $11,087.49 $12,073.18 $170,993.92 $12,824.54 $12,797.57 $196,616.04 $14,746.20 $13,565.42 $224,927.66 $16,869.57 $14,379.35 $256,176.59 $19,213.24 $15,242.11 $290,631.94 $21,797.40 $16,156.64 $328,585.97 $24,643.95 $17,126.03 $370,355.96 $27,776.70 $18,153.60 $416,286.25 $31,221.47 $19,242.81 $466,750.53 $35,006.29 $20,397.38 $522,154.20 $39,161.57 $21,621.22 $582,936.99 $43,720.27 $22,918.50 $649,575.77 $48,718.18 $24,293.61 $722,587.56 $54,194.07 $25,751.22 $802,532.85 $60,189.96 $27,296.30 $890,019.11 $66,751.43 $28,934.08 $985,704.62 $73,927.85 $30,670.12 $1,090,302.59 $81,772.69 $32,510.33 $1,204,585.61 $90,343.92 $34,460.95 $1,329,390.47 $99,704.29 $36,528.60 $1,465,623.36 $109,921.75 $38,720.32 $1,614,265.44 $121,069.91 $41,043.54 $1,776,378.88 $133,228.42 $43,506.15 $1,953,113.45 $146,483.51 $46,116.52 $2,145,713.48 $160,928.51 $48,883.51 $2,355,525.50 $176,664.41 $51,816.52 $2,584,006.44 $193,800.48 $54,925.51 $2,832,732.44

A 56

B 40

C D E $212,454.93 $58,221.04 $3,103,408.41

A 1 PROBLEM 3.35 2 3 4 5 6 7 8 9 10 a 11 12 13 b 14 15 16

GROSS INCOME= % GI INVESTED= FIRST INVESTMENT= SALARY INCR= i= n= FW=

$143,793.49 =60000*(1+6%)^15 10.00% $14,379.35 =10%*143793.49 6.00% 7.50% 25 YEARS $1,731,723.13 USING ELECTRONIC INTEREST TABLES THIS IS =$14,379.35*(F|A1 7.5%,6%,25)

AT THIS POINT, THE WORTH OF THE ORIGINAL PLAN (PROBLEM 3.34) AFTER 40 YEARS MUST BE KNOWN ORIGINAL PLAN=

$3,103,408.41 USING ELECTRONIC INTEREST TABLES THIS IS =$6,000*(F|A1 7.5%,6%,40)

AN ADDITIONAL AMOUNT IS NECESSARY AT THE END OF YEAR 25 FOR THE ORIGINAL PLAN AND THE CURRENT PLAN TO PROVIDE THE SAME VALUE. THIS AMOUNT IS:

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

INCREMENTAL FW(25)=

$1,371,685.28 =3103408.41-1731723.13

NOW, DETERMINE THE INCREMENTAL "STARTING MONEY" NECESSARY TO YIELD THE INCREMENTAL FW(25). LET THIS VALUE BE X. X=

$224,927.66 USING ELECTRONIC INTEREST TABLES THIS IS =$1,371,685.28*(P|F 7.5%,25) $224,927.66 USING EXCEL'S PV FUNCTION THIS IS =PV(7.5%,25,,-1371685.28)

LESSON LEARNED: GET STARTED EARLIER RATHER THAN LATER THE FOLLOWING TABLES CAN BE USED TO CHECK THE RESULTS

a EOY 0 1 2 3 4

b INTEREST

$1,078.45 $2,302.49 $3,686.93

DEPOSIT $14,379.35 $15,242.11 $16,156.64 $17,126.03

TOTAL ACCT $14,379.35 $30,699.91 $49,159.04 $69,972.00

EOY 0 1 2 3 4

INTEREST

DEPOSIT TOTAL ACCT $224,927.66 $224,927.66 $16,869.57 $14,379.35 $256,176.59 $19,213.24 $15,242.11 $290,631.94 $21,797.40 $16,156.64 $328,585.97 $24,643.95 $17,126.03 $370,355.96

40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

A 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

B $5,247.90 $7,003.01 $8,971.45 $11,174.11 $13,633.76 $16,375.18 $19,425.34 $22,813.58 $26,571.82 $30,734.77 $35,340.13 $40,428.92 $46,045.66 $52,238.73 $59,060.66 $66,568.47 $74,824.07 $83,894.61 $93,852.97 $104,778.18 $116,755.96

C $18,153.60 $19,242.81 $20,397.38 $21,621.22 $22,918.50 $24,293.61 $25,751.22 $27,296.30 $28,934.08 $30,670.12 $32,510.33 $34,460.95 $36,528.60 $38,720.32 $41,043.54 $43,506.15 $46,116.52 $48,883.51 $51,816.52 $54,925.51 $58,221.04

D $93,373.50 $119,619.33 $148,988.16 $181,783.49 $218,335.75 $259,004.54 $304,181.11 $354,290.99 $409,796.89 $471,201.78 $539,052.24 $613,942.10 $696,516.36 $787,475.41 $887,579.60 $997,654.23 $1,118,594.81 $1,251,372.94 $1,397,042.43 $1,556,746.13 $1,731,723.13

F 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

G $27,776.70 $31,221.47 $35,006.29 $39,161.57 $43,720.27 $48,718.18 $54,194.07 $60,189.96 $66,751.43 $73,927.85 $81,772.69 $90,343.92 $99,704.29 $109,921.75 $121,069.91 $133,228.42 $146,483.51 $160,928.51 $176,664.41 $193,800.48 $212,454.93

H I $18,153.60 $416,286.25 $19,242.81 $466,750.53 $20,397.38 $522,154.20 $21,621.22 $582,936.99 $22,918.50 $649,575.77 $24,293.61 $722,587.56 $25,751.22 $802,532.85 $27,296.30 $890,019.11 $28,934.08 $985,704.62 $30,670.12 $1,090,302.59 $32,510.33 $1,204,585.61 $34,460.95 $1,329,390.47 $36,528.60 $1,465,623.36 $38,720.32 $1,614,265.44 $41,043.54 $1,776,378.88 $43,506.15 $1,953,113.45 $46,116.52 $2,145,713.48 $48,883.51 $2,355,525.50 $51,816.52 $2,584,006.44 $54,925.51 $2,832,732.44 $58,221.04 $3,103,408.41

J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

J 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64

A B C D E F 1 PROBLEM 3.36 2 3 1 STARTING YEARLY SALARY DURING YEAR 1 4 2 INCREASE IN SALARY PER YEAR IN PERCENT 5 3 PERCENTAGE OF YOUR SALARY THAT YOU WILL INVEST 6 4 GROWTH OF INVESTMENTS PER YEAR IN PERCENT 7 5 AMOUNT OF MONEY YOU WOULD LIKE TODAY IF RETIRED 8 6 RATE IN % THAT THINGS COST MORE TO BUY 9 10 CALCULATION FOR TESTING PURPOSES 11 12 FV= $619,962.84 =(60000*10%)*(F|A1 8%,10%,20) 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

YEAR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

MY AGE 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C D E F DESIRED ACCUMULATED AMOUNT SALARY INVESTMENT INVESTMENTS $2,000,000.00 $0.00 $2,070,000.00 $60,000.00 $6,000.00 $6,000.00 $2,142,450.00 $66,000.00 $6,600.00 $13,080.00 $2,217,435.75 $72,600.00 $7,260.00 $21,386.40 $2,295,046.00 $79,860.00 $7,986.00 $31,083.31 $2,375,372.61 $87,846.00 $8,784.60 $42,354.58 $2,458,510.65 $96,630.60 $9,663.06 $55,406.00 $2,544,558.53 $106,293.66 $10,629.37 $70,467.85 $2,633,618.07 $116,923.03 $11,692.30 $87,797.58 $2,725,794.71 $128,615.33 $12,861.53 $107,682.92 $2,821,197.52 $141,476.86 $14,147.69 $130,445.24 $2,919,939.43 $155,624.55 $15,562.45 $156,443.31 $3,022,137.31 $171,187.00 $17,118.70 $186,077.48 $3,127,912.12 $188,305.70 $18,830.57 $219,794.25 $3,237,389.04 $207,136.27 $20,713.63 $258,091.41 $3,350,697.66 $227,849.90 $22,784.99 $301,523.72 $3,467,972.08 $250,634.89 $25,063.49 $350,709.10 $3,589,351.10 $275,698.38 $27,569.84 $406,335.67 $3,714,978.39 $303,268.22 $30,326.82 $469,169.34 $3,845,002.63 $333,595.04 $33,359.50 $540,062.40 $3,979,577.73 $366,954.54 $36,695.45 $619,962.84 $4,118,862.95 $403,650.00 $40,365.00 $709,924.87 $4,263,023.15 $444,015.00 $44,401.50 $811,120.36 $4,412,228.96 $488,416.50 $48,841.65 $924,851.64 $4,566,656.97 $537,258.15 $53,725.81 $1,052,565.58 $4,726,489.97 $590,983.96 $59,098.40 $1,195,869.22 $4,891,917.12 $650,082.36 $65,008.24 $1,356,547.00 $5,063,134.22 $715,090.59 $71,509.06 $1,536,579.82 $5,240,343.91 $786,599.65 $78,659.97 $1,738,166.17 $5,423,755.95 $865,259.62 $86,525.96 $1,963,745.42 $5,613,587.41 $951,785.58 $95,178.56 $2,216,023.61 $5,810,062.97 $1,046,964.14 $104,696.41 $2,498,001.92 $6,013,415.17 $1,151,660.55 $115,166.05 $2,813,008.12 $6,223,884.70 $1,266,826.60 $126,682.66 $3,164,731.44 $6,441,720.67 $1,393,509.27 $139,350.93 $3,557,260.88 $6,667,180.89 $1,532,860.19 $153,286.02 $3,995,127.77 $6,900,532.22 $1,686,146.21 $168,614.62 $4,483,352.61 $7,142,050.85 $1,854,760.83 $185,476.08 $5,027,496.90 $7,392,022.63 $2,040,236.92 $204,023.69 $5,633,720.34

$60,000.00 10.00% 10.00% 8.00% $2,000,000.00 3.50%

A 57 58 59 60 61 62 63

B 39 40 41 42 43 44 45

C 61 62 63 64 65 66 67

D E F G $7,650,743.42 $2,244,260.61 $224,426.06 $6,308,844.03 $7,918,519.44 $2,468,686.67 $246,868.67 $7,060,420.22 $8,195,667.62 $2,715,555.33 $271,555.53 $7,896,809.37 $8,482,515.99 $2,987,110.87 $298,711.09 $8,827,265.21 $8,779,404.05 $3,285,821.95 $328,582.20 $9,862,028.62 $9,086,683.19 $3,614,404.15 $361,440.41 $11,012,431.33 $9,404,717.10 $3,975,844.56 $397,584.46 $12,291,010.29

A B 1 PROBLEM 3.37 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

A B 1 PROBLEM 3.38 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

A 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

A 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145

K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

K 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

K 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145

A 1 PROBLEM 3.39 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

BS DEGREE INIT SALARY= INCR %= GRAD AGE= RETIRE AGE= TVOM=

$58,000.00 6.00% 23 65 7.00%

SOLVING FOR PW OF SALARY FOR BS DEGREE PW= $1,890,189.84 USING INTEREST TABLE EXCEL FILE THIS IS $58,000*(P|A1 7%,6%,65-23) MS DEGREE INIT SALARY= INCR %= GRAD AGE= RETIRE AGE= TVOM= YEARLY COST= YEARS OF COST=

X 7.20% 25 65 7.00% $8,000.00 2

SOLVING FOR PW OF SALARY FOR MS DEGREE AT SAME POINT IN TIME AS PW OF BS DEGREE P (COSTS)= -$14,464.16 USING INTEREST TABLES THIS IS =-$8,000*(P|A 7%,2) P (SAVINGS)= X*38.77857*0.87344 USING INTEREST TABLE EXCEL FILE THIS IS =X*(P|A1 7%,7.2%,65-25)*(P|F 7%,2) SETTING P FOR BS DEGREE EQUAL TO P FOR MS DEGREE AND SOLVING FOR X X=

$56,233.00 =(1890189.84+14464.16)/(38.77857*0.87344)

************************ OR, CAN SOLVE THIS PROBLEM USING YEAR-BY-YEAR TABLES AS SHOWN BELOW TABLE 1 OF 2 - SOLVING FOR PW OF SALARY FOR BS DEGREE AGE 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

SALARY $58,000.00 =58000*(1+0.06)^(1-1) $61,480.00 =58000*(1+0.06)^(2-1) $65,168.80 =58000*(1+0.06)^(3-1) $69,078.93 $73,223.66 $77,617.08 $82,274.11 $87,210.56 $92,443.19 $97,989.78 $103,869.17 $110,101.32 $116,707.40 $123,709.84

A 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

B 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

C 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 PW=

85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

D E F $131,132.43 $139,000.38 $147,340.40 $156,180.82 $165,551.67 $175,484.77 $186,013.86 $197,174.69 $209,005.17 $221,545.48 $234,838.21 $248,928.50 $263,864.21 $279,696.06 $296,477.83 $314,266.50 $333,122.49 $353,109.84 $374,296.43 $396,754.21 $420,559.47 $445,793.03 $472,540.62 $500,893.05 $530,946.64 $562,803.43 $596,571.64 $632,365.94 =58000*(1+0.06)^(42-1) $1,890,189.83 USING EXCEL'S NPV FUNCTION =NPV(7%,58000,61480,…,632365.94)

TABLE 2 OF 2 - SOLVING FOR PW OF SALARY FOR MS DEGREE NOW SETTING UP TO SOLVE FOR PW OF SALARY FOR MS DEGREE WILL USE SOLVER TO FIND VALUE OF INITIAL SALARY X SET ANY ARBITRARY VALUE OF X AND THEN LET SOLVER CHANGE IT INIT SALARY=X= AGE 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

$56,233.08 SOLVER CHANGED CELL SALARY -$8,000.00 -$8,000.00 $56,233.08 =56233.08*(1+0.072)^(3-3) $60,281.86 =56233.08*(1+0.072)^(4-3) $64,622.16 =56233.08*(1+0.072)^(5-3) $69,274.95 $74,262.75 $79,609.67 $85,341.56 $91,486.16 $98,073.16 $105,134.43 $112,704.11 $120,818.80

A 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142

B 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

C 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 PW=

D E F G $129,517.75 $138,843.03 $148,839.73 $159,556.19 $171,044.24 $183,359.42 $196,561.30 $210,713.71 $225,885.10 $242,148.83 $259,583.55 $278,273.56 $298,309.26 $319,787.52 $342,812.23 $367,494.71 $393,954.32 $422,319.04 $452,726.01 $485,322.28 $520,265.48 $557,724.60 $597,880.77 $640,928.18 $687,075.01 $736,544.41 $789,575.61 $846,425.06 =56233.08*(1+0.072)^(42-3) $1,890,189.83 SOLVER TARGET CELL =NPV(7%,-8000,-8000,…,846425.06)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

SOLVER TARGET CELL

A B C D E F G H 1 PROBLEM 3.40 2 3 "PRICE" $7,000.00 4 TVOM= 10.00% USED FOR PART a 5 6 a OPTION 1 7 8 PAY= $6,500.00 NOW 9 10 PW= $6,500.00 11 12 OPTION 2 13 14 PAY DP= $1,000.00 NOW 15 16 i= 8.00% 17 m= 4 18 n= 2 19 20 A= $819.06 USING INTEREST TABLES THIS IS 21 =($7,000-$1,000)*(A|P 8%/4,4*2) 22 $819.06 USING EXCEL'S PMT FUNCTION THIS IS 23 =PMT(8%/4,4*2,-(7000-1000)) 24 25 PW= $6,872.77 USING INTEREST TABLES THIS IS 26 =$1,000+$819.06*(P|A 10%/4,4*2) 27 $6,872.76 USING EXCEL'S PV FUNCTION THIS IS 28 =1000+PV(10%/4,4*2,-819.06) 29 30 PREFER TO PAY CASH OF $6,500 31 b SOLVER IS EASILY USED TO FIND THE VALUE OF TVOM THAT WILL CAUSE THE PW OF OPTION 2 TO EQUAL THE PW=$6,500 OF OPTION 1. LET TVOM BE ANY VALUE FOR NOW. IT WILL BE CHANGED TO THE CORRECT VALUE WHEN SOLVER IS USED. 32 33 34 TVOM= 16.26% SOLVER CHANGED CELL 35 36 PW= $6,500.00 SOLVER TARGET CELL 37 =1000+PV(TVOM/4,4*2,-819.06) 38 39 TVOM= 16.26% 40 ieff= 41 17.27% =EFFECT(16.26%,4) ieff= 42 17.27% =(1+16.26%/4)^4-1

A 1 PROBLEM 3.41 2 3 4 5 6 7 8 9 10 11 12 13 a 14 15 16 17 18 19 20 21 22 b 23 24 25 26 27 28 29 30 31 32 33 34 c 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

SERIES A j= A1= n=

8.00% $1,000.00 5

SERIES B X=A= TVOM=

TO BE FOUND IN PART a 6.50%

SETTING THE PW OF SERIES A EQUAL TO THE PW OF SERIES B GIVES =$1,000*(P|A1 6.5%,8%,5) =$1,000*4.82896) X=A= LET TVOM=

=$X*(P|A 6.5%,5) =X*4.155679

$1,162.01 8.00%

PW SER A (8%)=

$4,629.63 USING ELECTRONIC INTEREST TABLES THIS IS =$1,000*(P|A1 8%,8%,5)

PW SER B (8%)

$4,639.59 USING INTEREST TABLES THIS IS =$1,162.01*(P|A 8%,5) $4,639.59 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,5,-1162.01)

PREFER A AT 8% LET TVOM=

5.00%

PW SER A (8%)=

$5,041.90 USING ELECTRONIC INTEREST TABLES THIS IS =$1,000*(P|A1 5%,8%,5)

PW SER B (8%)

$5,030.92 USING INTEREST TABLES THIS IS =$1,162.01*(P|A 5%,5) $5,030.92 USING EXCEL'S PV FUNCTION THIS IS =PV(5%,5,-1162.01)

PREFER B AT 5% THE FOLLOWING TABLE MAY BE USED TO CHECK THE RESULTS SERIES A END OF YEAR CASH FLOW

1 2 3 4 5 $1,000.00 $1,080.00 $1,166.40 $1,259.71 $1,360.49

PW SER A (6.5%)= $4,828.96 =NPV(6.5%,1000,1080,1166.4,1259.71,1360.49)+0 PW SER A (8%)= $4,629.63 PW SER A (5%)= $5,041.90

A 57 58 59 60 61 62 63

B SERIES B END OF YEAR CASH FLOW

C 0

1 2 3 4 5 $1,162.01 $1,162.01 $1,162.01 $1,162.01 $1,162.01

PW SER B (6.5%)= $5,810.07 $4,828.96 PW SER B (8%)= $5,810.07 $4,639.59 PW SER B (5%)= $5,810.07 $5,030.92

A B C D E F 1 PROBLEM 3.42 2 3 TVOM i= 14.00% 4 5 OPTION 1 A= $1,800.00 6 7 OPTION 2 A= $1,800.00 =Q+Q*(A|G 14%,5) 8 $1,800.00 =Q+Q*1.73987 9 $1,800.00 =2.73987*Q 10 Q= $656.97 11 12 OPTION 3 A= $1,800.00 =R*(P|A1 14%,10%,5)*(A|P 14%,5) 13 $1,800.00 =R*4.08879*0.29128 14 R= $1,511.36 15 16 THESE CAN ALSO BE EVALUATED USING SOLVER AS FOLLOWS 17 18 OPTION 1 A= $1,800.00 BY OBSERVATION 19 20 OPTION 2 Q= $656.97 SOLVER CHANGED CELL 1 21 22 OPTION 3 R= $1,511.34 SOLVER CHANGED CELL 2 23 24 END 25 OF 26 YEAR OPTION 1 OPTION 2 27 0 $0.00 $0.00 28 1 $1,800.00 $656.97 29 2 $1,800.00 $1,313.93 30 3 $1,800.00 $1,970.90 31 4 $1,800.00 $2,627.86 32 5 $1,800.00 $3,284.83 33 34 PW= $6,179.55 $6,179.55 35 SOLVER TARGET CELL 1

OPTION 3 $0.00 $1,511.34 $1,662.47 $1,828.72 $2,011.59 $2,212.75 $6,179.55 SOLVER TARGET CELL 2

A B C D E F G H 1 PROBLEM 3.43 2 3 TVOM i= 15.00% 4 5 FIRST, FIND THE PW OF SERIES B SINCE IT IS FIXED AS IS. 6 7 SERIES B PW= $4,668.91 USING INTEREST TABLES THIS IS 8 =-$2,500+$3,000*(P|A 15%,5)-$500*(P|G 15%,5) 9 10 SERIES A PW= $4,668.91 11 $4,668.91 =-$1,000+$X*(P|A 15%,5)+0.5$X*(P|G 15%,5) 12 $4,668.91 =-$1,000+$X*3.35216+0.5*$X*5.77514 13 $4,668.91 =-$1,000+6.239730X 14 X= $908.52 15 16 SERIES C PW= $4,668.91 =$Y+$Y*(P|A 15%,5)+$Y*(P|A 15%,3)*(P|F 15%,2) 17 $4,668.91 =$Y+$Y*(3.35216)+$Y*(2.28323)*(0.75614) 18 $4,668.91 =6.078602*$Y 19 Y= $768.09 20 21 22 THESE CAN ALSO BE EVALUATED USING SOLVER AS FOLLOWS 23 24 SERIES A X= $908.52 SOLVER CHANGED CELL 1 25 26 SERIES B AS IN TABLE 27 28 SERIES C Y= $768.09 SOLVER CHANGED CELL 2 29 30 END OF YEAR SERIES A SERIES B SERIES C 31 0 -$1,000.00 -$2,500.00 $768.09 =Y 32 1 $908.52 =X $3,000.00 $768.09 33 2 $1,362.77 =1.5*X $2,500.00 $768.09 34 3 $1,817.03 $2,000.00 $1,536.17 =2*Y 35 4 $2,271.29 $1,500.00 $1,536.17 36 5 $2,725.55 =3*X $1,000.00 $1,536.17 37 38 PW $4,668.89 $4,668.89 $4,668.89 39 SOLVER TARGET CELL 1 SOLVER TARGET CELL 2

A B C D E F G H 1 PROBLEM 3.44 2 3 TVOM i= 11.00% 4 5 FIRST, FIND THE PW OF SERIES B SINCE IT IS FIXED AS IS. 6 7 SERIES B PW= $6,295.15 USING INTEREST TABLES THIS IS 8 =$1,000+$1,500*(P|A 11%,4)+$500*(P|G 11%,4)-$2,500*(P|F 11 9 10 SERIES A PW= $6,295.15 11 $6,295.15 =3*$X+2.5*$X*(P|A 11%,4)-0.5*$X*(P|G 11%,4)-$1,000*(P|F 11 12 $6,295.15 =3*$X+2.5*$X*3.10245-0.5*$X*4.25020-$1,000*0.59345 13 $6,295.15 =-$593.45+8.631025X 14 X= $798.12 =(6295.15+593.45)/8.631025 15 16 SERIES C PW= $6,295.15 =2*$Y+$Y*(P|A 11%,5)+$Y*(P|A 11%,2) 17 $6,295.15 =2*$Y+$Y*(3.69590)+$Y*(1.71252) 18 $6,295.15 =7.40842*$Y 19 Y= $849.73 =6295.15/7.40842 20 21 22 THESE CAN ALSO BE EVALUATED USING SOLVER AS FOLLOWS 23 24 SERIES A X= $798.12 SOLVER CHANGED CELL 1 25 26 SERIES B AS IN TABLE 27 28 SERIES C Y= $849.73 SOLVER CHANGED CELL 2 29 30 31 END 32 OF 33 YEAR SERIES A SERIES B SERIES C 34 0 $2,394.36 =3*X $1,000.00 $1,699.46 =2*Y 35 1 $1,995.30 $1,500.00 $1,699.46 36 2 $1,596.24 $2,000.00 $1,699.46 37 3 $1,197.18 =1.5*X $2,500.00 $849.73 =Y 38 4 $798.12 =X $3,000.00 $849.73 39 5 -$1,000.00 -$2,500.00 $849.73 40 41 PW $6,295.14 $6,295.14 $6,295.14 42 SOLVER TARGET CELL 1 SOLVER TARGET CELL 2

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

A B C D E F G H I J 1 PROBLEM 3.45 2 3 TVOM i= 12.00% 4 5 SERIES 1 PW= $741.40 USING INTEREST TABLES THIS IS 6 =$150+$200*(P|A 12%,3)+$50*(P|G 12%,3) 7 8 SERIES 2 PW= $741.40 USING INTEREST TABLES THIS IS 9 $741.40 =$35X*(P|A 12%,4)*(P|F 12%,1)-$10X*(P|G 12%,4)*(P|F 12%,1) 10 $741.40 =$35X*(3.03735)*(0.89286)-$10X*(4.12731)*(0.89286) 11 $741.40 =57.946078*X 12 X= $12.79 =741.4/57.946078 13 14 THESE CAN ALSO BE EVALUATED USING SOLVER AS FOLLOWS 15 16 SERIES 2 X= $12.77 SOLVER CHANGED CELL 17 18 END 19 OF 20 YEAR SERIES 1 SERIES 2 21 0 $150.00 $0.00 22 1 $200.00 $0.00 23 2 $250.00 $446.89 =35*X 24 3 $300.00 $319.20 =25*X 25 4 $0.00 $191.52 =15*X 26 5 $0.00 $63.84 =5*X 27 28 PW $741.40 $741.40 29 SOLVER TARGET CELL

A B C D E F G H 1 PROBLEM 3.46 2 3 FACE/PAR VALUE= $10,000.00 4 BOND RATE= 7.00% PER YEAR 5 PAYMENTS/YR= 2 SEMIANNUAL 6 n= 15 YEARS 7 PURCHASE PRICE= $8,500.00 8 DESIRED RATE 15.00% PER YEAR NOMINAL 9 10 PW= -$3,224.15 USING INTEREST TABLES THIS IS 11 =-$8,500+$10,000*7%/2*(P|A 15%/2,30)+$10,000*(P|F 15%/2,30) 12 PW= -$3,224.15 USING EXCEL'S PV FUNCTION THIS IS 13 =-8500+PV(15%/2,2*15,-(7%/2)*10000)+PV(15%/2,2*15,,-10000) 14 DO NOT INVEST 15 16 OR, COULD FIND THE ACTUAL RATE OF RETURN ON THE BOND AND COMPARE IT TO 15%. THIS IS EASILY DONE USING SOLVER TO SEARCH FOR THE RATE. 17 18 19 ACTUAL R OF R=i= 8.823% SOLVER CHANGED CELL 20 21 PW= $0.00 SOLVER TARGET CELL 22 USING EXCEL'S PV FUNCTION 23 =-8500+PV(i%/2,2*15,-(7%/2)*10000)+PV(i%/2,2*15,,-10000) 24 25 DO NOT INVEST SINCE ACTUAL R OF R=i=8.82% WHICH IS LESS THAN 15% 26 27 28 OR, COULD USE EXCEL'S RATE FUNCTION TO FIND THE ACTUAL R OF R 29 30 RATE= 8.823% USING EXCEL'S RATE FUNCTION THIS IS 31 =RATE(2*15,10000*7%/2,-8500,10000)*2 32 33 DO NOT INVEST SINCE ACTUAL R OF R=i=8.82% WHICH IS LESS THAN 15%

1 2 3 4 5 6 7 8 9 10 0*(P|F 15%/2,30) 11 12 %/2,2*15,,-10000) 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A PROBLEM 3.47

FACE/PAR VALUE= BOND RATE= PAYMENTS/YR= n= DESIRED RATE=

$7,000.00 6.00% 2 5 8.00%

PER YEAR SEMIANNUAL YEARS PER YEAR NOMINAL

DETERMINE THE PW OF THE BOND'S INTEREST PLUS RETURN OF THE FACE VALUE AT THE DESIRED RATE OF RETURN PW= PW=

$6,432.21 USING INTEREST TABLES THIS IS =$7,000*6%/2*(P|A 8%/2,2*5)+$7,000*(P|F 8%/2,2*5) $6,432.24 USING EXCEL'S PV FUNCTION THIS IS =PV(8%/2,2*5,-7000*6%/2,-7000)

LUCY SHOULD PURCHASE THE BOND FOR $6,432.24 OR LESS

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

A PROBLEM 3.48

FACE/PAR VALUE= $5,000.00 BOND RATE= 12.00% PER YEAR PAYMENTS/YR= 2 SEMIANNUAL n= 7 YEARS DESIRED RATE 8.00% PER YEAR NOMINAL DETERMINE THE PW OF THE BOND'S INTEREST PLUS RETURN OF THE FACE VALUE AT THE DESIRED RATE OF RETURN. NOTE THAT ONLY 7 MORE YEARS (14 PAYMENTS) REMAIN ON THE BOND FOR THE BUYER. ALSO, NOTE THAT THE AMOUNT PAID FOR THE BOND BY THE SELLER ($7,000) IS IRRELEVANT FROM THE BUYER'S VIEWPOINT. PW= PW=

$6,056.34 USING INTEREST TABLES THIS IS =$5,000*12%/2*(P|A 8%/2,2*7)+$5,000*(P|F 8%/2,2*7) $6,056.31 USING EXCEL'S PV FUNCTION THIS IS =PV(8%/2,2*7,-5000*12%/2,-5000)

THE BUYER SHOULD BE WILLING TO PAY $6,056.31 OR LESS

A 1 PROBLEM 3.49 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18

FACE/PAR VALUE= $10,000.00 BOND RATE= 6.60% PER YEAR PAYMENTS/YR= 2 SEMIANNUAL n= 5 YEARS PURCHASE PRICE= $9,500.00 DESIRED RATE 12.00% PER YEAR NOMINAL DETERMINE THE FW OF THE BOND CASH FLOWS AT THE DESIRED RATE OF RETURN AS OF THE END OF YEAR 5 . NOTE THAT ONLY 5 YEARS (10 PAYMENTS) REMAIN ON THE BOND FOR THE CURRENT OWNER. FW=

-$12,663.41 USING INTEREST TABLES THIS IS =-$9,500*(F|P 12%/2,2*5)+$10,000*6.6%/2*(F|A 12%/2,2*5)

FW=

-$12,663.39 USING EXCEL'S PV FUNCTION THIS IS =FV(12%/2,2*5,-10000*6.6%/2,9500)

YOUR MINIMUM SELLING PRICE WILL BE $12,663.39

A B C D E F G H I 1 PROBLEM 3.50 2 3 FACE/PAR VALUE= $1,000.00 4 PAYMENTS/YR= 4 QUARTERLY 5 n= 7 YEARS 6 PURCHASE PRICE= $750.08 7 DESIRED RATE 16.00% PER YEAR NOMINAL 8 9 SET THE PW EQUAL TO $0.00 WITH THE ONLY UNKNOWN BEING THE BOND RATE r 10 11 PW= $0.00 USING INTEREST TABLES THIS IS 12 $0.00 =-$750.08+$1,000*r%/4*(P|A 16%/4,4*7)+$1,000*(P|F 16%/4,4*7) 13 $0.00 =-$750.08+$1,000*r%/4*(16.66306)+$1,000*(0.33348) 14 $0.00 =-$416.60+r%*$4,165.765 15 BOND RATE=r%= 10.00% 16 OR, CAN DETERMINE r USING SOLVER AND EXCEL'S PV FUNCTION. LET BOND RATE r% EQUAL ANY VALUE. IT WILL BE CHANGED BY SOLVER TO THE CORRECT PERCENTAGE. 17 18 19 BOND RATE= 10.00% SOLVER CHANGED CELL 20 NOMINAL ANNUAL 21 22 PW= $750.08 SOLVER TARGET CELL 23 USING EXCEL'S PV FUNCTION THIS IS 24 =PV(16%/4,4*7,-r%/4*1000,-1000)

A B C D E F G H 1 PROBLEM 3.51 2 3 FACE/PAR VALUE= $10,000.00 4 BOND RATE= 6.00% PER YEAR 5 PAYMENTS/YR= 4 QUARTERLY 6 n= 3 YEARS 7 SELLING PRICE= $9,800.00 8 EARNED RATE 12.00% PER YEAR NOMINAL 9 10 PW= $8,366.62 USING INTEREST TABLES THIS IS 11 =$10,000*6%/4*(P|A 12%/4,4*3)+$9,800*(P|F 12%/4,4*3) 12 PW= $8,366.62 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(12%/4,4*3,-10000*6%/4,-9800) 14 15 THE PURCHASE PRICE WAS $8,366.62

A 1 PROBLEM 3.52 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 b 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

$0.08*V $500+V

$0.08*V

-$8,628.12

BOND RATE= PAYMENTS/YR= n= PURCHASE PRICE= ACTUAL RATE

8.00% 1 5 $8,628.12 10.00%

PER YEAR ANNUAL YEARS PER YEAR

SOLVE FOR THE FACE/PAR VALUE BY SETTING THE PW EQUAL TO $0 WITH FACE/PAR VALUE V BEING THE ONLY UNKNOWN. SOLVE FOR V. PW=

PAR=V=

$0.00 $0.00 $0.00 $0.00 $9,000.01

USING INTEREST TABLES THIS IS =-$8,628.12+$F*8%*(P|A 10%,5)+($F+$500)*(P|F 10%,5) =-$8,628.12+$F*8%*(3.79079)+($F+$500)*(0.62092) =0.924183*F-$8,317.66 =8317.66/0.924183

OR, CAN DETERMINE V USING SOLVER AND EXCEL'S PV FUNCTION. LET FACE/PAR VALUE V EQUAL ANY VALUE. IT WILL BE CHANGED BY SOLVER TO THE CORRECT VALUE. PAR=V=

$9,000.00

SOLVER CHANGED CELL

INCR=

$500.00

SOLD FOR $500 MORE THAN FACE/PAR VALUE V

$8,628.12 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,5,-8%*V,-(V+500))

A B C D E F G H 1 PROBLEM 3.53 $0.08*V 2 $V-500 3 4 5 6 7 8 9 $0.08*V $0.08*V $0.08*V $0.08*V 10 11 0 1 2 3 4 5 12 13 14 15 16 17 18 19 20 21 -$9,855.57 22 23 b BOND RATE= 8.00% PER YEAR 24 PAYMENTS/YR= 1 ANNUAL 25 n= 5 YEARS 26 PURCHASE PRICE= $9,855.57 27 ACTUAL RATE 10.00% PER YEAR 28 SOLVE FOR THE FACE/PAR VALUE BY SETTING THE PW EQUAL TO $0 WITH FACE/PAR VALUE V BEING THE ONLY UNKNOWN. SOLVE FOR V. 29 30 31 PW= $0.00 USING INTEREST TABLES THIS IS 32 $0.00 =-$9,855.57+$F*8%*(P|A 10%,5)+($F-$500)*(P|F 10%,5) 33 $0.00 =-$9,855.57+$F*8%*(3.79079)+($F-$500)*(0.62092) 34 $0.00 =0.924183*F-$10,166.03 35 36 PAR=V= $11,000.02 =10166.03/0.924183 37 38 OR, CAN DETERMINE V USING SOLVER AND EXCEL'S PV FUNCTION. LET FACE/PAR VALUE V EQUAL ANY VALUE. IT WILL BE CHANGED BY SOLVER TO THE CORRECT VALUE. 39 40 41 PAR=V= $11,000.00 SOLVER CHANGED CELL 42 43 DECR= $500.00 SOLD FOR $500 LESS THAN FACE/PAR VALUE V 44 45 $9,855.57 SOLVER TARGET CELL 46 USING EXCEL'S PV FUNCTION THIS IS 47 =PV(10%,5,-8%*V,-(V-500))

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21

A PROBLEM 3.54

FACE/PAR VALUE= $20,000.00 BOND RATE= 6.00% PER YEAR PAYMENTS/YR= 2 SEMIANNUAL n= 5 YEARS PURCHASE PRICE= $18,000.00 DESIRED ieff= 8.16% EFFECTIVE SOLVE FOR THE NOMINAL YIELD THAT WILL SET PW=$0. THEN, CALCULATE THE EFFECTIVE RATE YIELD AND COMPARE IT TO THE DESIRED 8.16%. THE ACTUAL RATE OF RETURN MAY BE FOUND USING SOLVER AS FOLLOWS. NOMINAL YIELD=

8.4964% SOLVER CHANGED CELL PER YEAR NOMINAL

PW=

$0.00 SOLVER TARGET CELL EXCEL

THE EFFECTIVE ANNUAL RATE IS ieff=

8.6768%

BUY THE BOND SINCE IT EXCEEDS THE DESIRED RETURN

A B C D E F G H 1 PROBLEM 3.55 2 3 FACE/PAR VALUE=V $1,200.00 4 PAYMENTS/YR= 1 ANNUAL 5 n= 3 YEARS 6 PURCHASE PRICE=P $1,142.38 7 EARNED RATE=i 12.0000% PER YEAR 8 9 SOLVE FOR THE BOND INTEREST RATE THAT WILL CAUSE THE PW TO EQUAL $0. 10 11 PW= $0.00 USING INTEREST TABLES THIS IS 12 =-$1,142.38+r*$1,200*(P|A 12%,3)+$1,200*(P|F 12%,3) 13 =-$1,142.38+r*$1,200*(2.40183)+$1,200*(0.71178) 14 =$2,882.196*r-288.244 15 r= 10.00% 16 17 OR, CAN USE SOLVER TO DETERMINE THE BOND RATE r. 18 19 BOND RATE=r= 10.00% SOLVER CHANGED CELL 20 21 PW= $0.00 SOLVER TARGET CELL 22 USING EXCEL'S PV FUNCTION THIS IS 23 =-1142.38+PV(12%/1,1*3,-(r%/1)*1200,-1200)

A B 1 PROBLEM 3.56 2 3 END OF YEAR 4 INTEREST RATE=i= 5 CASH FLOW 6 7 a FW= 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

FW=

FW= i=

1 2.00% $0.00

$2,500.00

$3,692.51 USING COMPOUND INTEREST FORMULAS THIS IS $3,692.51 $3,692.51 USING INTEREST TABLES THIS IS =$2,500*(F|P 2%,1)*(F|P 2%,1)*(F|P 2%,1)*(F|P 2%,1)*(F|P 4%,1)*(F|P 4%,1)*(F|P 4%,1)*(F|P 4%,1)*(F|P 8%,1)*(F|P 8%,1) $3,692.51 USING EXCEL'S FVSCHEDULE FUNCTION THIS IS =FVSCHEDULE(2500,CELL FOR i YR 1:CELL FOR i YR 10) $3,692.51 =$2,500*(1+i)^10 3.97721% =(3692.51/2500)^0.1-1

$3,692.51 SOLVER TARGET CELL =FV(i%,10,,-2500) 3.97721% SOLVER CHANGED CELL

CHECK THIS BY CALCULATING FW FW=

2 3 4 5 6 7 8 9 10 2.00% 2.00% 2.00% 4.00% 4.00% 4.00% 4.00% 8.00% 8.00% $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

OR CAN USE SOLVER TO DETERMINE i FW=

$3,692.51 USING EXCEL'S FV FUNCTION THIS IS =FV(3.97721%,10,,-2500)

A B 1 PROBLEM 3.57 2 3 INVESTMENT= 4 5 END OF YEAR 6 INTEREST RATE 7 CASH FLOW 8 9 FW= 10 11 FW= 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

FW=

1 4.00% $0.00

2 6.00% $0.00

3 8.00% $0.00

4 10.00% $0.00

5 12.00% $0.00

$10,000.00 0 $10,000.00

$14,668.09 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+4%)*(1+6%)*(1+8%)*(1+10%)*(1+12%) $14,668.09 USING INTEREST TABLES THIS IS =$10,000*(F|P 4%,1)*(F|P 6%,1)*(F|P 8%,1)*(F|P 10%,1)*(F|P 12%,1) $14,668.09 USING EXCEL'S FVSCHEDULE FUNCTION THIS IS =FVSCHEDULE(10000,CELL FOR i YR 1:CELL FOR i YR 5)

END OF YEAR 0 INTEREST RATE CASH FLOW $10,000.00 FW=

1 12.00% $0.00

2 10.00% $0.00

3 8.00% $0.00

4 6.00% $0.00

5 4.00% $0.00

$14,668.09

END OF YEAR 0 1 2 3 4 5 INTEREST RATE 7.96294% 7.96294% 7.96294% 7.96294% 7.96294% CASH FLOW $10,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 FW=

$14,668.09

ALL ALTERNATIVES ARE EQUIVALENT

A B C D E F G H 1 PROBLEM 3.58 2 3 INVESTMENT= $2,000.00 AT BEGINNING OF EACH OF YEARS 1-5 4 5 END OF YEAR 0 1 2 3 4 5 6 INTEREST RATE 7.00% 6.00% 5.00% 4.00% 3.00% 7 CASH FLOW $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $0.00 8 9 FW= $11,387.82 USING EXCEL'S FVSCHEDULE THIS IS =FVSCHEDULE(2000,D6:H6)+FVSCHEDULE(2000, E6:H6)+FVSCHEDULE(2000,F6:H6)+FVSCHEDULE 10 (2000,G6:H6)+FVSCHEDULE(2000,H6) 11 FW= $11,387.82 USING COMPOUND INTEREST FORMULAS THIS IS =2000*(1+7%)*(1+6%)*(1+5%)*(1+4%)*(1+3%)+2000 *(1+6%)*(1+5%)*(1+4%)*(1+3%)+2000*(1+5%)*(1+4 %)*(1+3%)+2000*(1+4%)*(1+3%)+2000*(1+3%) 12 13 14 END OF YEAR 0 1 2 3 4 5 15 INTEREST RATE 3.00% 4.00% 5.00% 6.00% 7.00% 16 CASH FLOW $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $0.00 17 18 FW= $11,818.72 PROVIDES MAXIMUM FW - BEST ALTERNATIVE 19 20 21 END OF YEAR 0 1 2 3 4 5 22 INTEREST RATE 5.00% 5.00% 5.00% 5.00% 5.00% 23 CASH FLOW $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $0.00 24 25 FW= $11,603.83

A B 1 PROBLEM 3.59 2 3 END OF YEAR 4 INTEREST RATE 5 CASH FLOW 6 7 a FW= 8 9 FW= 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

1 5.00% $0.00

2 5.00% $0.00

3 5.00% $2,500.00

4 7.00% $0.00

5 7.00% $0.00

6 7.00% $5,000.00

$4,000.00 $13,735.17 $13,735.17

USING INTEREST TABLES THIS IS =$4,000*(F|P 5%,3)*(F|P 7%,3)+$2,500*(F|P 7%,3)+$5,000 USING EXCEL'S FVSCHEDULE FUNCTION THIS IS =FVSCHEDULE(4000,CELL FOR I YR 1:CELL FOR I YR 6)+FVSCHEDULE (2500,CELL FOR I YR 4: CELL FOR I YR 6)+5000

OR, CAN FIND FW USING SEQUENTIAL MOVEMENT OF TVOM AND CASH FLOWS

EOY 0 1 2 3 4 5 6

PW= PW= PW=

INTEREST RATE DURING PERIOD 5.00% 5.00% 5.00% 7.00% 7.00% 7.00%

EOY CASH SEQUENTIAL FLOW MOVEMENT $4,000.00 $4,000.00 =4000 $0.00 $4,200.00 =4000*(1+5%)+0 $0.00 $4,410.00 $2,500.00 $7,130.50 =4410*(1+5%)+2500 $0.00 $7,629.64 $0.00 $8,163.71 $5,000.00 $13,735.17

$9,685.34 USING COMPOUND INTEREST FORMULAS THIS IS =13735.17/((1+5%)*(1+5%)*(1+5%)*(1+7%)*(1+7%)*(1+7%)) $9,685.34 USING COMPOUND INTEREST FORMULAS THIS IS =5000/((1+5%)^3*(1+7%)^3)+2500/((1+5%)^3)+4000 $9,685.36 USING INTEREST TABLES THIS IS =$4,000+$2,500*(P|F 5%,3)+$5,000*(P|F 5%,3)*(P|F 7%,3)

OR, CAN FIND FW USING SEQUENTIAL MOVEMENT OF TVOM AND CASH FLOWS

EOY 6 5

INTEREST RATE DURING PERIOD 7.00% 7.00%

EOY CASH SEQUENTIAL FLOW MOVEMENT $5,000.00 $5,000.00 $0.00 $4,672.90

=5000 =5000/(1+7%)+0

A 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71

B 4 3 2 1 0

C 7.00% 5.00% 5.00% 5.00%

D $0.00 $2,500.00 $0.00 $0.00 $4,000.00

E F $4,367.19 $6,581.49 =4367.19/(1+7%)+2500 $6,268.09 $5,969.60 $9,685.34 =5969.6/(1+5%)+4000

WE ALREADY KNOW THE PW FOR THE ORIGINAL SERIES PW=

$9,685.34 =A*(P|A 5%,3)+A*(P|A 7%,3)*(P|F 5%,3) =A*(2.72325)+A*0.86384*2.62432 =A*4.99024 $1,940.86

OR, CAN DETERMINE "A" USING SOLVER A=

$1,940.86 SOLVER CHANGED CELL

FUTURE WORTH

EOY 0 1 2 3 4 5 6

INTEREST RATE DURING PERIOD 5.00% 5.00% 5.00% 7.00% 7.00% 7.00%

EOY CASH SEQUENTIAL FLOW MOVEMENT $0.00 $0.00 $1,940.86 $1,940.86 $1,940.86 $3,978.76 $1,940.86 $6,118.56 $1,940.86 $8,487.72 $1,940.86 $11,022.72 $1,940.86 $13,735.17 SOLVER TARGET CELL

A B 1 PROBLEM 3.60 2 3 END OF YEAR 4 INTEREST RATE 5 CASH FLOW 6 7 a FW=

$3,059.20

8 9

$3,059.20

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

FW=

1 10.00% $2,000.00

2 8.00% -$3,000.00

3 12.00% $4,000.00

$0.00

USING INTEREST TABLES THIS IS =$0*(F|P 10%,1)*(F|P 8%,1)*(F|P 12%,1)+$4,000*(F|P 8%,1)*(F|P 12%,1)$3,000*(F|P 12%,1)+$4,000 USING EXCEL'S FVSCHEDULE FUNCTION THIS IS =FVSCHEDULE(0,CELL FOR i YR 1:CELL FOR i YR 3)+FVSCHEDULE (2000,CELL FOR i YR 2:CELL FOR i YR 3)+FVSCHEDULE(-3000,CELL FOR i YR 3)+4000

OR, CAN FIND FW USING SEQUENTIAL MOVEMENT OF TVOM AND CASH FLOWS FW=

$3,059.20

FUTURE WORTH

EOY 0 1 2 3 b

PW= PW= PW=

INTEREST RATE DURING PERIOD 10.00% 8.00% 12.00%

EOY CASH SEQUENTIAL FLOW MOVEMENT $0.00 $0.00 $2,000.00 $2,000.00 -$3,000.00 -$840.00 $4,000.00 $3,059.20

$2,299.18 USING COMPOUND INTEREST FORMULAS THIS IS =3059.2/((1+10%)*(1+8%)*(1+12%)) $2,299.18 USING COMPOUND INTEREST FORMULAS THIS IS $2,299.18 $2,299.19 USING INTEREST TABLES THIS IS =$2,000*(P|F 10%,1)-$3,000*(P|F 10%,1)*(P|F 8%,1)+$4,000*(P|F 10,1)*(P|F 8%,1)*(P|F 12%,1)

OR, CAN FIND FW USING SEQUENTIAL MOVEMENT OF TVOM AND CASH FLOWS PW=

$2,299.18

PRESENT WORTH

EOY 3 2 1 0

INTEREST RATE DURING PERIOD 12.00% 8.00% 10.00%

EOY CASH SEQUENTIAL FLOW MOVEMENT $4,000.00 $4,000.00 =4000 -$3,000.00 $571.43 =4000/(1+12%)-3000 $2,000.00 $2,529.10 =571.43/(1+8%)+2000 $0.00 $2,299.18 =2529.1/(1+10%)+0

WE ALREADY KNOW THE PW FOR THE ORIGINAL SERIES

A 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67

B PW=

D E F =A*(P|F 10%,1)+A*(P|F 8%,1)*(P|F 10%,1)+A*(P|F $2,299.18 12%,1)*(P|F 8%,1)*(P|F 10%,1) =A*(0.90909)+A*(0.92593*0.90909)+A*(0.89286*0. 92593*0.90909) =A*2.502412 $918.79

OR, CAN DETERMINE "A" USING SOLVER A=

EOY 0 1 2 3

$918.79 INTEREST RATE DURING PERIOD 10.00% 8.00% 12.00%

SOLVER CHANGED CELL

EOY CASH SEQUENTIAL FLOW MOVEMENT $0.00 $0.00 $918.79 $918.79 $918.79 $1,911.08 $918.79 $3,059.20 SOLVER TARGET CELL

Prob FE-like FE1

a. DETERMINATION OF SALVAGE VALUES FOR TURNCATED CASH FLOWS rationale: CASH FLOWS ARE NOT REPEATED IN SHORTEST LIFE BUT LONGER LIVED ALTERNATIVES WILL BE TRUNCATED

FE2

a. 9.87% rationale: (6.6*0.20) + (9.9*0.50) + (12.0*0.30) = 9.87

FE3

c. BOTH (A) AND (B) rationale: SHORTER LIVED ALTERNATIVES WILL HAVE TO BE REPEATED AND THE LAST REPTITION MAY HAVE TO BETRUNCATED

FE4

a. 5.02% rationale: (7.3*(1-0.40)*0.7) + (6.5*0.30) = 5.02

FE5

a. 6 YEARS rationale: ALTERNATIVE C HAS THE LONGEST LIFE AT 6 YEARS

FE6

c. 120 YEARS rationale: LCM = 5*3*2*2*2 = 120

FE7

a. 0 YEARS rationale: LONGEST LIFE = 6 YEARS, LCM = 6 YEARS, DIFFERENCE = 0

FE8

b. WACC IS A LOWER BOUND FOR MARR rationale: NEVER INVEST FOR A RETURN LESS THAN IT COSTS TO ACQUIRE FUNDS

FE9

d. THE VALUE OF MARR IS USUALLY DETERMINED BY MANAGEMENT BASED ON MANY FACTORS rationale: MARR HAS BEARING ON ENGINEERING PROJECTS, IS NOT THE SAME FOR ALL COMPANIES, AND IS THE RATE USED IN DCF ANALYSIS

FE10

d. TAX DEDUCTIONS rationale: AFTER TAX COST OF LOAN = BEFORE TAX COST OF LOAN * (1 - TAX RATE)

FE11

c. PROPORTION OF FUNDS OBTAINED FROM EACH SOURCE rationale: WACC = SUMMATION OF ((COST OF SOURCE) * (PROPORTION FROM SOURCE)) ACROSS ALL SOURCES

FE12

d. THE VOLATILITY OF A STOCK RELATIVE TO THE OVERALL MARKET rationale: DEFINITION OF BETA

FE13

a. DEBT CAPITAL rationale: THE COST OF EQUITY CAPITAL IS NOT TAX DEDUCTIBLE THEREFORE IT IS NOT MULTIPLIED BY (1-T). THE COST OF DEBT CAPITAL IS TAX DEDUCTIBLE, THEREFORE IT IS MULTIPLIES BY (1-T)

PROBLEM 4.1

MANY ACCEPTABLE ANSWERS ARE POSSIBLE FOR THESE QUESTIONS DIFFICULTIES IN ESTIMATING CASH FLOWS ENSURING CONSIDERATION OF ALL CATEGORIES (E.G., FIRST COSTS, ROUTINE O&M, REPAIR, SALVAGE, REVENUES, COST SAVINGS, ETC.) DETERMINING APPROPRIATE TIMING FOR CASH FLOWS DETERMINING APPROPRIATE VALUES FOR CASH FLOWS DIFFICULTIES IN ESTIMATING MARR MULTIPLE APPROACHES EXIST FOR DETERMINING MARR ESTIMATING INFLATION ESTIMATING SOURCES OF FUNDS ESTIMATING THE COST OF VARIOUS FUNDING CHOICES ESTIMATING PROJECT RISKS ESTIMATING MANAGEMENT PREFERENCES/JUDGEMENTS DIFFICULTIES IN ESTIMATING PLANNING HORIZON MULTIPLE APPROACHES EXIST FOR DETERMINING PLANNING HORIZON ESTIMATING USEFUL LIFE OF ASSEST ESTIMATING ECONOMIC LIFE OF ASSESTS

PROBLEM 4.2 MANY ACCEPTABLE ANSWERS ARE POSSIBLE FOR THESE QUESTIONS a

PRIOR PROJECTS THAT ARE SIMILAR EQUIPMENT VENDORS SUBJECT AREA EXPERTS TRADE PUBLICATIONS ETC.

PRIOR PROJECTS THAT ARE SIMILAR COMPANY OBJECTIVES/GUIDELINES FEDERAL GUIDELINES COST OF CAPITAL

PRIOR PROJECTS THAT ARE SIMILAR EQUIPMENT GUIDELINES COMPANY NEEDS PLANNING HORIZON METHODOLOGY

PROBLEM 4.3 AN ANNUAL WORTH ANALYSIS WITH ALTERNATIVES HAVING DIFFERENT LIVES, IMPLIES THE USE OF A LEAST COMMON MULTIPLE PLANNING HORIZON

PROBLEM 4.4 a

LEAST COMMON MULTIPLE = 15 YEARS EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

SHORTEST LIFE = 3 YEARS EOY 0 1 2 3

ALT 1 ALT 2 -$50,000.00 -$80,000.00 $25,000.00 $35,000.00 $30,000.00 $45,000.00 -$15,000.00 $50,000.00 $25,000.00 $55,000.00 $30,000.00 -$20,000.00 -$15,000.00 $35,000.00 $25,000.00 $45,000.00 $30,000.00 $50,000.00 -$15,000.00 $55,000.00 $25,000.00 -$20,000.00 $30,000.00 $35,000.00 -$15,000.00 $45,000.00 $25,000.00 $50,000.00 $30,000.00 $55,000.00 $35,000.00 $60,000.00

ALT 1 ALT 2 -$50,000.00 -$80,000.00 $25,000.00 $35,000.00 $30,000.00 $45,000.00 $35,000.00 $60,000.00

FIXED LIFE = 2 YEARS EOY 0 1 2

ALT 1 ALT 2 -$50,000.00 -$80,000.00 $25,000.00 $35,000.00 $40,000.00 $65,000.00

PROBLEM 4.5 a

LEAST COMMON MULTIPLE = 24 YEARS

SHORTEST LIFE = 4 YEARS

LONGEST LIFE = 8 YEARS

PROBLEM 4.6 a

LEAST COMMON MULTIPLE = 12 YEARS EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

ALT 2 -$70.00 $30.00 $40.00 -$20.00 $30.00 $40.00 -$20.00 $30.00 $40.00 -$20.00 $30.00 $40.00 $50.00

SHORTEST LIFE = 3 YEARS EOY 0 1 2 3

ALT 1 -$100.00 $20.00 $20.00 $40.00 -$40.00 $20.00 $20.00 $40.00 -$40.00 $20.00 $20.00 $40.00 $60.00

ALT 1 -$100.00 $20.00 $20.00 $40.00

ALT 2 -$70.00 $30.00 $40.00 $50.00

LONGEST LIFE = 4 YEARS EOY 0 1 2 3 4

ALT 1 -$100.00 $20.00 $20.00 $40.00 $60.00

ALT 2 -$70.00 $30.00 $40.00 -$20.00 $80.00

PROBLEM 4.7 a

LCM PLANNING HORIZON = 12 YEARS EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

ALT 1 -$20,000.00 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 $28,000

ALT 2 -$40,000.00 $20,000.00 $20,000.00 20,000 + 10,000 = $30,000

ALT 3 -$70,000.00 $30,000.00 $30,000.00 30,000 + 20,000 = $50,00

ALT 1 -$20,000.00 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 $28,000

ALT 2 -$40,000.00 $20,000.00 $20,000.00 $20,000.00 20,000 - 40,000 = -$20,000 $20,000.00 20,000 + 20,000 = $40,000

ALT 3 -$70,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 30,000 + 2,000 = $32,000

ALT 2 -$40,000.00 $20,000.00 20,000 + 20,000 = $40,000

ALT 3 -$70,000.00 $30,000.00 30,000 + 30,000 = $60,000

ALT 2 -$40,000.00 $20,000.00 $20,000.00 $20,000.00 20,000 - 40,000 = -$20,000 20,000 + 30,000 = $50,000

ALT 3 -$70,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 30,000 + 5,000 = $35,000

STANDARD PLANNING HORIZON = 2 YEARS EOY 0 1 2

ALT 3 -$70,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 30,000 + 2,000 - 70,000 = -$38,000 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 30,000 + 2,000 = $32,000

LONGEST LIFE PLANNING HORIZON = 6 YEARS EOY 0 1 2 3 4 5 6

ALT 2 -$40,000.00 $20,000.00 $20,000.00 $20,000.00 20,000 - 40,000 = -$20,000 $20,000.00 $20,000.00 $20,000.00 20,000 - 40,000 = -$20,000 $20,000.00 $20,000.00 $20,000.00 $20,000.00

SHORTEST LIFE PLANNING HORIZON = 3 YEARS EOY 0 1 2 3

ALT 1 -$20,000.00 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 $28,000

ALT 1 -$20,000.00 28,000 - 20,000 = $8,000 28,000 - 10,000 = $18,000

STANDARD PLANNING HORIZON = 5 YEARS EOY 0 1 2 3 4 5

ALT 1 -$20,000.00 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 20,000 = $8,000 28,000 - 10,000 = $18,000

PROBLEM 4.8 a

7 YEARS

EOY 0 1 2 3 4 5 6

SV(A) $12,000.00 $9,000.00 $6,000.00 $3,000.00 $0.00

SV(B) $20,000.00 $16,000.00 $12,000.00 $8,000.00 $4,000.00 $0.00

SV(C) $30,000.00 $25,000.00 $20,000.00 $15,000.00 $10,000.00 $5,000.00 $0.00

SALVAGE VALUE A; 3RD YEAR OF 2ND REPETITION = $3,000 SALVAGE VALUE B; 2ND YEAR OF 2ND REPETITION = $12,000 SALVAGE VALUE C; 1ST YEAR OF 2ND REPETITION = $25,000

PROBLEM 4.9 a

PLANNING HORIZON = 2 YEARS EOY 0 1 2

ALT BETA -$160,000.00 $80,000.00 $90,000.00 100,000 + 20,000 = $120,000

ALT ALPHA -$100,000.00 $50,000.00 $60,000.00 70,000 + 0 - 150,000 = -$80,000 80,000 + 75,000 = $155,000

ALT BETA -$160,000.00 $80,000.00 $90,000.00 100,000 + 20,000 - 256,000 = -$136,000 110,000 + 160,000 = $270,000

PLANNING HORIZON = 5 YEARS EOY 0 1 2 3 4 5

ALT ALPHA -$100,000.00 $50,000.00 $60,000.00 70,000 + 0 = $70,000

PLANNING HORIZON = 4 YEARS EOY 0 1 2 3 4

ALT BETA -$160,000.00 $80,000.00 90,000 + 40,000 = $130,000

PLANNING HORIZON = 3 YEARS EOY 0 1 2 3

ALT ALPHA -$100,000.00 $50,000.00 60,000 + 20,000 = $80,000

ALT ALPHA -$100,000.00 $50,000.00 $60,000.00 70,000 + 0 - 150,000 = -$80,000 $80,000.00 90,000 + 30,000 = $120,000

ALT BETA -$160,000.00 $80,000.00 $90,000.00 100,000 + 20,000 - 256,000 = -$136,000 $110,000.00 120,000 + 64,000 = $184000

PLANNING HORIZON = 10 YEARS EOY 0 1 2 3 4 5 6 7 8 9 10

ALT ALPHA -$100,000.00 $50,000.00 $60,000.00 70,000 + 0 - 150,000 = -$80,000 $80,000.00 $90,000.00 100,000 + 0 - 225,000 = -$125,000 $110,000.00 $120,000.00 130,000 + 0 - 337,500 = -$207,500 140,000 + 168,750 = $308,750

ALT BETA -$160,000.00 $80,000.00 $90,000.00 100,000 + 20,000 - 256,000 = -$136,000 $110,000.00 $120,000.00 130,000 + 32,000 - 409,600 = -$247,600 $140,000.00 $150,000.00 160,000 + 51,200 - 655,360 = -$444,160 170,000 + 409,600 = $579,600

PROBLEM 4.10 a

7 YEARS

FUTURE WORTH

ANNUAL WORTH

CASH FLOWS IN $K ALTERNATIVE W EOY 0 1 2 3 4 5 6 7

CF -$100.00 $20.00 $20.00 $50.00 $80.00 $110.00 $0.00 $0.00

8.00% (F|P i%,n-t) 1.71382 1.58687 1.46933 1.36049 1.25971 1.16640 1.08000 1.00000

FW OF CF -$171.38 $31.74 $29.39 $68.02 $100.78 $128.30 $0.00 $0.00 $186.85 <- FW

ALTERNATIVE X EOY 0 1 2 3 4 5 6 7

CF -$150.00 $40.00 $45.00 $50.00 $55.00 $60.00 $65.00 $70.00

8.00% (F|P i%,n-t) 1.71382 1.58687 1.46933 1.36049 1.25971 1.16640 1.08000 1.00000

FW OF CF -$257.07 $63.47 $66.12 $68.02 $69.28 $69.98 $70.20 $70.00 $220.01 <- FW

PREFER X

PROBLEM 4.11 DEPOSIT = (ANNUAL WITHDRAWAL) * (P|A i%,n)

a b c d e f g

ANNUAL WITHDRAWAL LIFE (P|A 5%,n) DEPOSIT 10 $2,000.00 7.72173 $15,443.47 20 $2,000.00 12.46221 $24,924.42 30 $2,000.00 15.37245 $30,744.90 40 $2,000.00 17.15909 $34,318.17 50 $2,000.00 18.25593 $36,511.85 inf $2,000.00 20.00000 $40,000.00 SEARCHING FOR THE LOWEST VALUE OF LIFE SUCH THAT THE DEPOSIT ROUNDS TO $40K ROUNDED IN K$ 50 $2,000.00 18.25593 $36,511.85 $37 51 $2,000.00 18.33898 $36,677.95 $37 52 $2,000.00 18.41807 $36,836.15 $37 53 $2,000.00 18.49340 $36,986.81 $37 54 $2,000.00 18.56515 $37,130.29 $37 55 $2,000.00 18.63347 $37,266.94 $37 56 $2,000.00 18.69854 $37,397.09 $37 57 $2,000.00 18.76052 $37,521.04 $38 58 $2,000.00 18.81954 $37,639.08 $38 59 $2,000.00 18.87575 $37,751.51 $38 60 $2,000.00 18.92929 $37,858.58 $38 61 $2,000.00 18.98028 $37,960.55 $38 62 $2,000.00 19.02883 $38,057.67 $38 63 $2,000.00 19.07508 $38,150.16 $38 64 $2,000.00 19.11912 $38,238.25 $38 65 $2,000.00 19.16107 $38,322.14 $38 66 $2,000.00 19.20102 $38,402.04 $38 67 $2,000.00 19.23907 $38,478.13 $38 68 $2,000.00 19.27530 $38,550.60 $39 69 $2,000.00 19.30981 $38,619.62 $39 70 $2,000.00 19.34268 $38,685.35 $39 71 $2,000.00 19.37398 $38,747.96 $39 72 $2,000.00 19.40379 $38,807.58 $39 73 $2,000.00 19.43218 $38,864.36 $39 74 $2,000.00 19.45922 $38,918.44 $39 75 $2,000.00 19.48497 $38,969.94 $39 76 $2,000.00 19.50950 $39,018.99 $39 77 $2,000.00 19.53285 $39,065.71 $39 78 $2,000.00 19.55510 $39,110.20 $39 79 $2,000.00 19.57628 $39,152.57 $39 80 $2,000.00 19.59646 $39,192.92 $39 81 $2,000.00 19.61568 $39,231.35 $39 82 $2,000.00 19.63398 $39,267.96 $39 83 $2,000.00 19.65141 $39,302.81 $39 84 $2,000.00 19.66801 $39,336.01 $39 85 $2,000.00 19.68382 $39,367.63 $39 86 $2,000.00 19.69887 $39,397.75 $39 87 $2,000.00 19.71321 $39,426.42 $39 88 $2,000.00 19.72687 $39,453.74 $39 89 $2,000.00 19.73987 $39,479.75 $39

$2,000.00

19.75226

$39,504.52

$40

THE DEPOSIT FIRST ROUNDS TO $40K WHEN THE LIFE IS 90 YEARS

Problem 4.12 ANNUAL MAINTENANCE REQUIREMENT = $2,000 5.00% (P|A i%,n) 0.95238 1.85941 2.72325 3.54595 4.32948 5.07569 5.78637 6.46321 7.10782 7.72173 8.30641 8.86325 9.39357 9.89864 10.37966 10.83777 11.27407 11.68959 12.08532 12.46221 12.82115 13.16300 13.48857 13.79864 14.09394 14.37519 14.64303 14.89813 15.14107 15.37245 15.59281 15.80268 16.00255 16.19290 16.37419 16.54685 16.71129 16.86789 17.01704 17.15909 17.29437 17.42321 17.54591 17.66277 17.77407 17.88007

$2,000.00 DEPOSIT $1,904.76 $3,718.82 $5,446.50 $7,091.90 $8,658.95 $10,151.38 $11,572.75 $12,926.43 $14,215.64 $15,443.47 $16,612.83 $17,726.50 $18,787.15 $19,797.28 $20,759.32 $21,675.54 $22,548.13 $23,379.17 $24,170.64 $24,924.42 $25,642.31 $26,326.01 $26,977.15 $27,597.28 $28,187.89 $28,750.37 $29,286.07 $29,796.25 $30,282.15 $30,744.90 $31,185.62 $31,605.35 $32,005.10 $32,385.81 $32,748.39 $33,093.70 $33,422.57 $33,735.79 $34,034.08 $34,318.17 $34,588.74 $34,846.42 $35,091.82 $35,325.55 $35,548.14 $35,760.13

Required Deposit versus Life $2,000/year Maintenance Cost, 5% Inte $45,000.00 $40,000.00 $35,000.00 $30,000.00

Deposit ($)

LIFE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

$25,000.00 $20,000.00 $15,000.00 $10,000.00 $5,000.00 $0.00 0

100

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

17.98102 18.07716 18.16872 18.25593 18.33898 18.41807 18.49340 18.56515 18.63347 18.69854 18.76052 18.81954 18.87575 18.92929 18.98028 19.02883 19.07508 19.11912 19.16107 19.20102 19.23907 19.27530 19.30981 19.34268 19.37398 19.40379 19.43218 19.45922 19.48497 19.50950 19.53285 19.55510 19.57628 19.59646 19.61568 19.63398 19.65141 19.66801 19.68382 19.69887 19.71321 19.72687 19.73987 19.75226 19.76406 19.77529 19.78599 19.79619 19.80589 19.81513 19.82394 19.83232

$35,962.03 $36,154.32 $36,337.44 $36,511.85 $36,677.95 $36,836.15 $36,986.81 $37,130.29 $37,266.94 $37,397.09 $37,521.04 $37,639.08 $37,751.51 $37,858.58 $37,960.55 $38,057.67 $38,150.16 $38,238.25 $38,322.14 $38,402.04 $38,478.13 $38,550.60 $38,619.62 $38,685.35 $38,747.96 $38,807.58 $38,864.36 $38,918.44 $38,969.94 $39,018.99 $39,065.71 $39,110.20 $39,152.57 $39,192.92 $39,231.35 $39,267.96 $39,302.81 $39,336.01 $39,367.63 $39,397.75 $39,426.42 $39,453.74 $39,479.75 $39,504.52 $39,528.12 $39,550.59 $39,571.99 $39,592.37 $39,611.78 $39,630.27 $39,647.87 $39,664.64

99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

19.84031 19.84791 19.85515 19.86205 19.86862 19.87488 19.88083 19.88651 19.89191 19.89706 19.90196 19.90663 19.91108 19.91531 19.91934 19.92318 19.92684 19.93033 19.93364 19.93680 19.93981 19.94268 19.94541 19.94801 19.95048 19.95284 19.95509 19.95723 19.95926 19.96120 19.96305 19.96481 19.96649 19.96808 19.96960 19.97105 19.97243 19.97374 19.97499 19.97618 19.97732 19.97840 19.97943 19.98040 19.98134 19.98223 19.98307 19.98388 19.98465 19.98538 19.98607 19.98674

$39,680.61 $39,695.82 $39,710.31 $39,724.10 $39,737.24 $39,749.75 $39,761.67 $39,773.02 $39,783.83 $39,794.12 $39,803.92 $39,813.26 $39,822.15 $39,830.62 $39,838.69 $39,846.37 $39,853.68 $39,860.65 $39,867.29 $39,873.61 $39,879.63 $39,885.36 $39,890.82 $39,896.02 $39,900.97 $39,905.68 $39,910.17 $39,914.45 $39,918.53 $39,922.41 $39,926.10 $39,929.62 $39,932.97 $39,936.16 $39,939.20 $39,942.10 $39,944.86 $39,947.48 $39,949.98 $39,952.36 $39,954.63 $39,956.79 $39,958.85 $39,960.81 $39,962.68 $39,964.45 $39,966.15 $39,967.76 $39,969.29 $39,970.76 $39,972.15 $39,973.47

151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202

19.98737 19.98797 19.98854 19.98909 19.98961 19.99010 19.99057 19.99102 19.99145 19.99186 19.99225 19.99261 19.99297 19.99330 19.99362 19.99392 19.99421 19.99449 19.99475 19.99500 19.99524 19.99547 19.99568 19.99589 19.99608 19.99627 19.99645 19.99662 19.99678 19.99693 19.99708 19.99722 19.99735 19.99748 19.99760 19.99771 19.99782 19.99792 19.99802 19.99812 19.99821 19.99829 19.99837 19.99845 19.99852 19.99859 19.99866 19.99872 19.99879 19.99884 19.99890 19.99895

$39,974.74 $39,975.94 $39,977.09 $39,978.18 $39,979.22 $39,980.21 $39,981.15 $39,982.05 $39,982.90 $39,983.72 $39,984.49 $39,985.23 $39,985.93 $39,986.60 $39,987.24 $39,987.85 $39,988.43 $39,988.98 $39,989.50 $39,990.00 $39,990.48 $39,990.93 $39,991.36 $39,991.78 $39,992.17 $39,992.54 $39,992.90 $39,993.23 $39,993.56 $39,993.86 $39,994.15 $39,994.43 $39,994.70 $39,994.95 $39,995.19 $39,995.42 $39,995.64 $39,995.85 $39,996.04 $39,996.23 $39,996.41 $39,996.58 $39,996.75 $39,996.90 $39,997.05 $39,997.19 $39,997.32 $39,997.45 $39,997.57 $39,997.69 $39,997.80 $39,997.90

203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250

19.99900 19.99905 19.99909 19.99914 19.99918 19.99922 19.99925 19.99929 19.99932 19.99936 19.99939 19.99942 19.99944 19.99947 19.99950 19.99952 19.99954 19.99956 19.99958 19.99960 19.99962 19.99964 19.99966 19.99967 19.99969 19.99970 19.99972 19.99973 19.99975 19.99976 19.99977 19.99978 19.99979 19.99980 19.99981 19.99982 19.99983 19.99984 19.99984 19.99985 19.99986 19.99986 19.99987 19.99988 19.99988 19.99989 19.99989 19.99990

$39,998.00 $39,998.10 $39,998.19 $39,998.27 $39,998.36 $39,998.43 $39,998.51 $39,998.58 $39,998.65 $39,998.71 $39,998.77 $39,998.83 $39,998.89 $39,998.94 $39,998.99 $39,999.04 $39,999.08 $39,999.13 $39,999.17 $39,999.21 $39,999.25 $39,999.28 $39,999.32 $39,999.35 $39,999.38 $39,999.41 $39,999.44 $39,999.46 $39,999.49 $39,999.51 $39,999.54 $39,999.56 $39,999.58 $39,999.60 $39,999.62 $39,999.64 $39,999.66 $39,999.67 $39,999.69 $39,999.70 $39,999.72 $39,999.73 $39,999.74 $39,999.75 $39,999.77 $39,999.78 $39,999.79 $39,999.80

uired Deposit versus Life Maintenance Cost, 5% Interest Rate

100

150 Life (years)

200

250

300

PROBLEM 4.13 ANNUAL MAINTENANCE REQUIREMENT = $2,000 0.05 LIFE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

(P|A i%,n) =(((1+C$5)^$B7)-1)/(C$5*(1+C$5)^$B7) =(((1+C$5)^$B8)-1)/(C$5*(1+C$5)^$B8) =(((1+C$5)^$B9)-1)/(C$5*(1+C$5)^$B9) =(((1+C$5)^$B10)-1)/(C$5*(1+C$5)^$B10) =(((1+C$5)^$B11)-1)/(C$5*(1+C$5)^$B11) =(((1+C$5)^$B12)-1)/(C$5*(1+C$5)^$B12) =(((1+C$5)^$B13)-1)/(C$5*(1+C$5)^$B13) =(((1+C$5)^$B14)-1)/(C$5*(1+C$5)^$B14) =(((1+C$5)^$B15)-1)/(C$5*(1+C$5)^$B15) =(((1+C$5)^$B16)-1)/(C$5*(1+C$5)^$B16) =(((1+C$5)^$B17)-1)/(C$5*(1+C$5)^$B17) =(((1+C$5)^$B18)-1)/(C$5*(1+C$5)^$B18) =(((1+C$5)^$B19)-1)/(C$5*(1+C$5)^$B19) =(((1+C$5)^$B20)-1)/(C$5*(1+C$5)^$B20) =(((1+C$5)^$B21)-1)/(C$5*(1+C$5)^$B21) =(((1+C$5)^$B22)-1)/(C$5*(1+C$5)^$B22) =(((1+C$5)^$B23)-1)/(C$5*(1+C$5)^$B23) =(((1+C$5)^$B24)-1)/(C$5*(1+C$5)^$B24) =(((1+C$5)^$B25)-1)/(C$5*(1+C$5)^$B25) =(((1+C$5)^$B26)-1)/(C$5*(1+C$5)^$B26) =(((1+C$5)^$B27)-1)/(C$5*(1+C$5)^$B27) =(((1+C$5)^$B28)-1)/(C$5*(1+C$5)^$B28) =(((1+C$5)^$B29)-1)/(C$5*(1+C$5)^$B29) =(((1+C$5)^$B30)-1)/(C$5*(1+C$5)^$B30) =(((1+C$5)^$B31)-1)/(C$5*(1+C$5)^$B31) =(((1+C$5)^$B32)-1)/(C$5*(1+C$5)^$B32) =(((1+C$5)^$B33)-1)/(C$5*(1+C$5)^$B33) =(((1+C$5)^$B34)-1)/(C$5*(1+C$5)^$B34) =(((1+C$5)^$B35)-1)/(C$5*(1+C$5)^$B35) =(((1+C$5)^$B36)-1)/(C$5*(1+C$5)^$B36) =(((1+C$5)^$B37)-1)/(C$5*(1+C$5)^$B37) =(((1+C$5)^$B38)-1)/(C$5*(1+C$5)^$B38) =(((1+C$5)^$B39)-1)/(C$5*(1+C$5)^$B39) =(((1+C$5)^$B40)-1)/(C$5*(1+C$5)^$B40) =(((1+C$5)^$B41)-1)/(C$5*(1+C$5)^$B41) =(((1+C$5)^$B42)-1)/(C$5*(1+C$5)^$B42) =(((1+C$5)^$B43)-1)/(C$5*(1+C$5)^$B43) =(((1+C$5)^$B44)-1)/(C$5*(1+C$5)^$B44) =(((1+C$5)^$B45)-1)/(C$5*(1+C$5)^$B45) =(((1+C$5)^$B46)-1)/(C$5*(1+C$5)^$B46) =(((1+C$5)^$B47)-1)/(C$5*(1+C$5)^$B47) =(((1+C$5)^$B48)-1)/(C$5*(1+C$5)^$B48) =(((1+C$5)^$B49)-1)/(C$5*(1+C$5)^$B49) =(((1+C$5)^$B50)-1)/(C$5*(1+C$5)^$B50) =(((1+C$5)^$B51)-1)/(C$5*(1+C$5)^$B51) =(((1+C$5)^$B52)-1)/(C$5*(1+C$5)^$B52) =(((1+C$5)^$B53)-1)/(C$5*(1+C$5)^$B53) =(((1+C$5)^$B54)-1)/(C$5*(1+C$5)^$B54) =(((1+C$5)^$B55)-1)/(C$5*(1+C$5)^$B55)

2000 DEPOSIT =D$5*C7 =D$5*C8 =D$5*C9 =D$5*C10 =D$5*C11 =D$5*C12 =D$5*C13 =D$5*C14 =D$5*C15 =D$5*C16 =D$5*C17 =D$5*C18 =D$5*C19 =D$5*C20 =D$5*C21 =D$5*C22 =D$5*C23 =D$5*C24 =D$5*C25 =D$5*C26 =D$5*C27 =D$5*C28 =D$5*C29 =D$5*C30 =D$5*C31 =D$5*C32 =D$5*C33 =D$5*C34 =D$5*C35 =D$5*C36 =D$5*C37 =D$5*C38 =D$5*C39 =D$5*C40 =D$5*C41 =D$5*C42 =D$5*C43 =D$5*C44 =D$5*C45 =D$5*C46 =D$5*C47 =D$5*C48 =D$5*C49 =D$5*C50 =D$5*C51 =D$5*C52 =D$5*C53 =D$5*C54 =D$5*C55

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104

=(((1+C$5)^$B56)-1)/(C$5*(1+C$5)^$B56) =(((1+C$5)^$B57)-1)/(C$5*(1+C$5)^$B57) =(((1+C$5)^$B58)-1)/(C$5*(1+C$5)^$B58) =(((1+C$5)^$B59)-1)/(C$5*(1+C$5)^$B59) =(((1+C$5)^$B60)-1)/(C$5*(1+C$5)^$B60) =(((1+C$5)^$B61)-1)/(C$5*(1+C$5)^$B61) =(((1+C$5)^$B62)-1)/(C$5*(1+C$5)^$B62) =(((1+C$5)^$B63)-1)/(C$5*(1+C$5)^$B63) =(((1+C$5)^$B64)-1)/(C$5*(1+C$5)^$B64) =(((1+C$5)^$B65)-1)/(C$5*(1+C$5)^$B65) =(((1+C$5)^$B66)-1)/(C$5*(1+C$5)^$B66) =(((1+C$5)^$B67)-1)/(C$5*(1+C$5)^$B67) =(((1+C$5)^$B68)-1)/(C$5*(1+C$5)^$B68) =(((1+C$5)^$B69)-1)/(C$5*(1+C$5)^$B69) =(((1+C$5)^$B70)-1)/(C$5*(1+C$5)^$B70) =(((1+C$5)^$B71)-1)/(C$5*(1+C$5)^$B71) =(((1+C$5)^$B72)-1)/(C$5*(1+C$5)^$B72) =(((1+C$5)^$B73)-1)/(C$5*(1+C$5)^$B73) =(((1+C$5)^$B74)-1)/(C$5*(1+C$5)^$B74) =(((1+C$5)^$B75)-1)/(C$5*(1+C$5)^$B75) =(((1+C$5)^$B76)-1)/(C$5*(1+C$5)^$B76) =(((1+C$5)^$B77)-1)/(C$5*(1+C$5)^$B77) =(((1+C$5)^$B78)-1)/(C$5*(1+C$5)^$B78) =(((1+C$5)^$B79)-1)/(C$5*(1+C$5)^$B79) =(((1+C$5)^$B80)-1)/(C$5*(1+C$5)^$B80) =(((1+C$5)^$B81)-1)/(C$5*(1+C$5)^$B81) =(((1+C$5)^$B82)-1)/(C$5*(1+C$5)^$B82) =(((1+C$5)^$B83)-1)/(C$5*(1+C$5)^$B83) =(((1+C$5)^$B84)-1)/(C$5*(1+C$5)^$B84) =(((1+C$5)^$B85)-1)/(C$5*(1+C$5)^$B85) =(((1+C$5)^$B86)-1)/(C$5*(1+C$5)^$B86) =(((1+C$5)^$B87)-1)/(C$5*(1+C$5)^$B87) =(((1+C$5)^$B88)-1)/(C$5*(1+C$5)^$B88) =(((1+C$5)^$B89)-1)/(C$5*(1+C$5)^$B89) =(((1+C$5)^$B90)-1)/(C$5*(1+C$5)^$B90) =(((1+C$5)^$B91)-1)/(C$5*(1+C$5)^$B91) =(((1+C$5)^$B92)-1)/(C$5*(1+C$5)^$B92) =(((1+C$5)^$B93)-1)/(C$5*(1+C$5)^$B93) =(((1+C$5)^$B94)-1)/(C$5*(1+C$5)^$B94) =(((1+C$5)^$B95)-1)/(C$5*(1+C$5)^$B95) =(((1+C$5)^$B96)-1)/(C$5*(1+C$5)^$B96) =(((1+C$5)^$B97)-1)/(C$5*(1+C$5)^$B97) =(((1+C$5)^$B98)-1)/(C$5*(1+C$5)^$B98) =(((1+C$5)^$B99)-1)/(C$5*(1+C$5)^$B99) =(((1+C$5)^$B100)-1)/(C$5*(1+C$5)^$B100) =(((1+C$5)^$B101)-1)/(C$5*(1+C$5)^$B101) =(((1+C$5)^$B102)-1)/(C$5*(1+C$5)^$B102) =(((1+C$5)^$B103)-1)/(C$5*(1+C$5)^$B103) =(((1+C$5)^$B104)-1)/(C$5*(1+C$5)^$B104) =(((1+C$5)^$B105)-1)/(C$5*(1+C$5)^$B105) =(((1+C$5)^$B106)-1)/(C$5*(1+C$5)^$B106) =(((1+C$5)^$B107)-1)/(C$5*(1+C$5)^$B107) =(((1+C$5)^$B108)-1)/(C$5*(1+C$5)^$B108) =(((1+C$5)^$B109)-1)/(C$5*(1+C$5)^$B109) =(((1+C$5)^$B110)-1)/(C$5*(1+C$5)^$B110)

=D$5*C56 =D$5*C57 =D$5*C58 =D$5*C59 =D$5*C60 =D$5*C61 =D$5*C62 =D$5*C63 =D$5*C64 =D$5*C65 =D$5*C66 =D$5*C67 =D$5*C68 =D$5*C69 =D$5*C70 =D$5*C71 =D$5*C72 =D$5*C73 =D$5*C74 =D$5*C75 =D$5*C76 =D$5*C77 =D$5*C78 =D$5*C79 =D$5*C80 =D$5*C81 =D$5*C82 =D$5*C83 =D$5*C84 =D$5*C85 =D$5*C86 =D$5*C87 =D$5*C88 =D$5*C89 =D$5*C90 =D$5*C91 =D$5*C92 =D$5*C93 =D$5*C94 =D$5*C95 =D$5*C96 =D$5*C97 =D$5*C98 =D$5*C99 =D$5*C100 =D$5*C101 =D$5*C102 =D$5*C103 =D$5*C104 =D$5*C105 =D$5*C106 =D$5*C107 =D$5*C108 =D$5*C109 =D$5*C110

105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159

=(((1+C$5)^$B111)-1)/(C$5*(1+C$5)^$B111) =(((1+C$5)^$B112)-1)/(C$5*(1+C$5)^$B112) =(((1+C$5)^$B113)-1)/(C$5*(1+C$5)^$B113) =(((1+C$5)^$B114)-1)/(C$5*(1+C$5)^$B114) =(((1+C$5)^$B115)-1)/(C$5*(1+C$5)^$B115) =(((1+C$5)^$B116)-1)/(C$5*(1+C$5)^$B116) =(((1+C$5)^$B117)-1)/(C$5*(1+C$5)^$B117) =(((1+C$5)^$B118)-1)/(C$5*(1+C$5)^$B118) =(((1+C$5)^$B119)-1)/(C$5*(1+C$5)^$B119) =(((1+C$5)^$B120)-1)/(C$5*(1+C$5)^$B120) =(((1+C$5)^$B121)-1)/(C$5*(1+C$5)^$B121) =(((1+C$5)^$B122)-1)/(C$5*(1+C$5)^$B122) =(((1+C$5)^$B123)-1)/(C$5*(1+C$5)^$B123) =(((1+C$5)^$B124)-1)/(C$5*(1+C$5)^$B124) =(((1+C$5)^$B125)-1)/(C$5*(1+C$5)^$B125) =(((1+C$5)^$B126)-1)/(C$5*(1+C$5)^$B126) =(((1+C$5)^$B127)-1)/(C$5*(1+C$5)^$B127) =(((1+C$5)^$B128)-1)/(C$5*(1+C$5)^$B128) =(((1+C$5)^$B129)-1)/(C$5*(1+C$5)^$B129) =(((1+C$5)^$B130)-1)/(C$5*(1+C$5)^$B130) =(((1+C$5)^$B131)-1)/(C$5*(1+C$5)^$B131) =(((1+C$5)^$B132)-1)/(C$5*(1+C$5)^$B132) =(((1+C$5)^$B133)-1)/(C$5*(1+C$5)^$B133) =(((1+C$5)^$B134)-1)/(C$5*(1+C$5)^$B134) =(((1+C$5)^$B135)-1)/(C$5*(1+C$5)^$B135) =(((1+C$5)^$B136)-1)/(C$5*(1+C$5)^$B136) =(((1+C$5)^$B137)-1)/(C$5*(1+C$5)^$B137) =(((1+C$5)^$B138)-1)/(C$5*(1+C$5)^$B138) =(((1+C$5)^$B139)-1)/(C$5*(1+C$5)^$B139) =(((1+C$5)^$B140)-1)/(C$5*(1+C$5)^$B140) =(((1+C$5)^$B141)-1)/(C$5*(1+C$5)^$B141) =(((1+C$5)^$B142)-1)/(C$5*(1+C$5)^$B142) =(((1+C$5)^$B143)-1)/(C$5*(1+C$5)^$B143) =(((1+C$5)^$B144)-1)/(C$5*(1+C$5)^$B144) =(((1+C$5)^$B145)-1)/(C$5*(1+C$5)^$B145) =(((1+C$5)^$B146)-1)/(C$5*(1+C$5)^$B146) =(((1+C$5)^$B147)-1)/(C$5*(1+C$5)^$B147) =(((1+C$5)^$B148)-1)/(C$5*(1+C$5)^$B148) =(((1+C$5)^$B149)-1)/(C$5*(1+C$5)^$B149) =(((1+C$5)^$B150)-1)/(C$5*(1+C$5)^$B150) =(((1+C$5)^$B151)-1)/(C$5*(1+C$5)^$B151) =(((1+C$5)^$B152)-1)/(C$5*(1+C$5)^$B152) =(((1+C$5)^$B153)-1)/(C$5*(1+C$5)^$B153) =(((1+C$5)^$B154)-1)/(C$5*(1+C$5)^$B154) =(((1+C$5)^$B155)-1)/(C$5*(1+C$5)^$B155) =(((1+C$5)^$B156)-1)/(C$5*(1+C$5)^$B156) =(((1+C$5)^$B157)-1)/(C$5*(1+C$5)^$B157) =(((1+C$5)^$B158)-1)/(C$5*(1+C$5)^$B158) =(((1+C$5)^$B159)-1)/(C$5*(1+C$5)^$B159) =(((1+C$5)^$B160)-1)/(C$5*(1+C$5)^$B160) =(((1+C$5)^$B161)-1)/(C$5*(1+C$5)^$B161) =(((1+C$5)^$B162)-1)/(C$5*(1+C$5)^$B162) =(((1+C$5)^$B163)-1)/(C$5*(1+C$5)^$B163) =(((1+C$5)^$B164)-1)/(C$5*(1+C$5)^$B164) =(((1+C$5)^$B165)-1)/(C$5*(1+C$5)^$B165)

=D$5*C111 =D$5*C112 =D$5*C113 =D$5*C114 =D$5*C115 =D$5*C116 =D$5*C117 =D$5*C118 =D$5*C119 =D$5*C120 =D$5*C121 =D$5*C122 =D$5*C123 =D$5*C124 =D$5*C125 =D$5*C126 =D$5*C127 =D$5*C128 =D$5*C129 =D$5*C130 =D$5*C131 =D$5*C132 =D$5*C133 =D$5*C134 =D$5*C135 =D$5*C136 =D$5*C137 =D$5*C138 =D$5*C139 =D$5*C140 =D$5*C141 =D$5*C142 =D$5*C143 =D$5*C144 =D$5*C145 =D$5*C146 =D$5*C147 =D$5*C148 =D$5*C149 =D$5*C150 =D$5*C151 =D$5*C152 =D$5*C153 =D$5*C154 =D$5*C155 =D$5*C156 =D$5*C157 =D$5*C158 =D$5*C159 =D$5*C160 =D$5*C161 =D$5*C162 =D$5*C163 =D$5*C164 =D$5*C165

160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214

=(((1+C$5)^$B166)-1)/(C$5*(1+C$5)^$B166) =(((1+C$5)^$B167)-1)/(C$5*(1+C$5)^$B167) =(((1+C$5)^$B168)-1)/(C$5*(1+C$5)^$B168) =(((1+C$5)^$B169)-1)/(C$5*(1+C$5)^$B169) =(((1+C$5)^$B170)-1)/(C$5*(1+C$5)^$B170) =(((1+C$5)^$B171)-1)/(C$5*(1+C$5)^$B171) =(((1+C$5)^$B172)-1)/(C$5*(1+C$5)^$B172) =(((1+C$5)^$B173)-1)/(C$5*(1+C$5)^$B173) =(((1+C$5)^$B174)-1)/(C$5*(1+C$5)^$B174) =(((1+C$5)^$B175)-1)/(C$5*(1+C$5)^$B175) =(((1+C$5)^$B176)-1)/(C$5*(1+C$5)^$B176) =(((1+C$5)^$B177)-1)/(C$5*(1+C$5)^$B177) =(((1+C$5)^$B178)-1)/(C$5*(1+C$5)^$B178) =(((1+C$5)^$B179)-1)/(C$5*(1+C$5)^$B179) =(((1+C$5)^$B180)-1)/(C$5*(1+C$5)^$B180) =(((1+C$5)^$B181)-1)/(C$5*(1+C$5)^$B181) =(((1+C$5)^$B182)-1)/(C$5*(1+C$5)^$B182) =(((1+C$5)^$B183)-1)/(C$5*(1+C$5)^$B183) =(((1+C$5)^$B184)-1)/(C$5*(1+C$5)^$B184) =(((1+C$5)^$B185)-1)/(C$5*(1+C$5)^$B185) =(((1+C$5)^$B186)-1)/(C$5*(1+C$5)^$B186) =(((1+C$5)^$B187)-1)/(C$5*(1+C$5)^$B187) =(((1+C$5)^$B188)-1)/(C$5*(1+C$5)^$B188) =(((1+C$5)^$B189)-1)/(C$5*(1+C$5)^$B189) =(((1+C$5)^$B190)-1)/(C$5*(1+C$5)^$B190) =(((1+C$5)^$B191)-1)/(C$5*(1+C$5)^$B191) =(((1+C$5)^$B192)-1)/(C$5*(1+C$5)^$B192) =(((1+C$5)^$B193)-1)/(C$5*(1+C$5)^$B193) =(((1+C$5)^$B194)-1)/(C$5*(1+C$5)^$B194) =(((1+C$5)^$B195)-1)/(C$5*(1+C$5)^$B195) =(((1+C$5)^$B196)-1)/(C$5*(1+C$5)^$B196) =(((1+C$5)^$B197)-1)/(C$5*(1+C$5)^$B197) =(((1+C$5)^$B198)-1)/(C$5*(1+C$5)^$B198) =(((1+C$5)^$B199)-1)/(C$5*(1+C$5)^$B199) =(((1+C$5)^$B200)-1)/(C$5*(1+C$5)^$B200) =(((1+C$5)^$B201)-1)/(C$5*(1+C$5)^$B201) =(((1+C$5)^$B202)-1)/(C$5*(1+C$5)^$B202) =(((1+C$5)^$B203)-1)/(C$5*(1+C$5)^$B203) =(((1+C$5)^$B204)-1)/(C$5*(1+C$5)^$B204) =(((1+C$5)^$B205)-1)/(C$5*(1+C$5)^$B205) =(((1+C$5)^$B206)-1)/(C$5*(1+C$5)^$B206) =(((1+C$5)^$B207)-1)/(C$5*(1+C$5)^$B207) =(((1+C$5)^$B208)-1)/(C$5*(1+C$5)^$B208) =(((1+C$5)^$B209)-1)/(C$5*(1+C$5)^$B209) =(((1+C$5)^$B210)-1)/(C$5*(1+C$5)^$B210) =(((1+C$5)^$B211)-1)/(C$5*(1+C$5)^$B211) =(((1+C$5)^$B212)-1)/(C$5*(1+C$5)^$B212) =(((1+C$5)^$B213)-1)/(C$5*(1+C$5)^$B213) =(((1+C$5)^$B214)-1)/(C$5*(1+C$5)^$B214) =(((1+C$5)^$B215)-1)/(C$5*(1+C$5)^$B215) =(((1+C$5)^$B216)-1)/(C$5*(1+C$5)^$B216) =(((1+C$5)^$B217)-1)/(C$5*(1+C$5)^$B217) =(((1+C$5)^$B218)-1)/(C$5*(1+C$5)^$B218) =(((1+C$5)^$B219)-1)/(C$5*(1+C$5)^$B219) =(((1+C$5)^$B220)-1)/(C$5*(1+C$5)^$B220)

=D$5*C166 =D$5*C167 =D$5*C168 =D$5*C169 =D$5*C170 =D$5*C171 =D$5*C172 =D$5*C173 =D$5*C174 =D$5*C175 =D$5*C176 =D$5*C177 =D$5*C178 =D$5*C179 =D$5*C180 =D$5*C181 =D$5*C182 =D$5*C183 =D$5*C184 =D$5*C185 =D$5*C186 =D$5*C187 =D$5*C188 =D$5*C189 =D$5*C190 =D$5*C191 =D$5*C192 =D$5*C193 =D$5*C194 =D$5*C195 =D$5*C196 =D$5*C197 =D$5*C198 =D$5*C199 =D$5*C200 =D$5*C201 =D$5*C202 =D$5*C203 =D$5*C204 =D$5*C205 =D$5*C206 =D$5*C207 =D$5*C208 =D$5*C209 =D$5*C210 =D$5*C211 =D$5*C212 =D$5*C213 =D$5*C214 =D$5*C215 =D$5*C216 =D$5*C217 =D$5*C218 =D$5*C219 =D$5*C220

215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250

=(((1+C$5)^$B221)-1)/(C$5*(1+C$5)^$B221) =(((1+C$5)^$B222)-1)/(C$5*(1+C$5)^$B222) =(((1+C$5)^$B223)-1)/(C$5*(1+C$5)^$B223) =(((1+C$5)^$B224)-1)/(C$5*(1+C$5)^$B224) =(((1+C$5)^$B225)-1)/(C$5*(1+C$5)^$B225) =(((1+C$5)^$B226)-1)/(C$5*(1+C$5)^$B226) =(((1+C$5)^$B227)-1)/(C$5*(1+C$5)^$B227) =(((1+C$5)^$B228)-1)/(C$5*(1+C$5)^$B228) =(((1+C$5)^$B229)-1)/(C$5*(1+C$5)^$B229) =(((1+C$5)^$B230)-1)/(C$5*(1+C$5)^$B230) =(((1+C$5)^$B231)-1)/(C$5*(1+C$5)^$B231) =(((1+C$5)^$B232)-1)/(C$5*(1+C$5)^$B232) =(((1+C$5)^$B233)-1)/(C$5*(1+C$5)^$B233) =(((1+C$5)^$B234)-1)/(C$5*(1+C$5)^$B234) =(((1+C$5)^$B235)-1)/(C$5*(1+C$5)^$B235) =(((1+C$5)^$B236)-1)/(C$5*(1+C$5)^$B236) =(((1+C$5)^$B237)-1)/(C$5*(1+C$5)^$B237) =(((1+C$5)^$B238)-1)/(C$5*(1+C$5)^$B238) =(((1+C$5)^$B239)-1)/(C$5*(1+C$5)^$B239) =(((1+C$5)^$B240)-1)/(C$5*(1+C$5)^$B240) =(((1+C$5)^$B241)-1)/(C$5*(1+C$5)^$B241) =(((1+C$5)^$B242)-1)/(C$5*(1+C$5)^$B242) =(((1+C$5)^$B243)-1)/(C$5*(1+C$5)^$B243) =(((1+C$5)^$B244)-1)/(C$5*(1+C$5)^$B244) =(((1+C$5)^$B245)-1)/(C$5*(1+C$5)^$B245) =(((1+C$5)^$B246)-1)/(C$5*(1+C$5)^$B246) =(((1+C$5)^$B247)-1)/(C$5*(1+C$5)^$B247) =(((1+C$5)^$B248)-1)/(C$5*(1+C$5)^$B248) =(((1+C$5)^$B249)-1)/(C$5*(1+C$5)^$B249) =(((1+C$5)^$B250)-1)/(C$5*(1+C$5)^$B250) =(((1+C$5)^$B251)-1)/(C$5*(1+C$5)^$B251) =(((1+C$5)^$B252)-1)/(C$5*(1+C$5)^$B252) =(((1+C$5)^$B253)-1)/(C$5*(1+C$5)^$B253) =(((1+C$5)^$B254)-1)/(C$5*(1+C$5)^$B254) =(((1+C$5)^$B255)-1)/(C$5*(1+C$5)^$B255) =(((1+C$5)^$B256)-1)/(C$5*(1+C$5)^$B256)

=D$5*C221 =D$5*C222 =D$5*C223 =D$5*C224 =D$5*C225 =D$5*C226 =D$5*C227 =D$5*C228 =D$5*C229 =D$5*C230 =D$5*C231 =D$5*C232 =D$5*C233 =D$5*C234 =D$5*C235 =D$5*C236 =D$5*C237 =D$5*C238 =D$5*C239 =D$5*C240 =D$5*C241 =D$5*C242 =D$5*C243 =D$5*C244 =D$5*C245 =D$5*C246 =D$5*C247 =D$5*C248 =D$5*C249 =D$5*C250 =D$5*C251 =D$5*C252 =D$5*C253 =D$5*C254 =D$5*C255 =D$5*C256

PART A 0.04 (P|A i%,n) =(((1+E$5)^$B7)-1)/(E$5*(1+E$5)^$B7) =(((1+E$5)^$B8)-1)/(E$5*(1+E$5)^$B8) =(((1+E$5)^$B9)-1)/(E$5*(1+E$5)^$B9) =(((1+E$5)^$B10)-1)/(E$5*(1+E$5)^$B10) =(((1+E$5)^$B11)-1)/(E$5*(1+E$5)^$B11) =(((1+E$5)^$B12)-1)/(E$5*(1+E$5)^$B12) =(((1+E$5)^$B13)-1)/(E$5*(1+E$5)^$B13) =(((1+E$5)^$B14)-1)/(E$5*(1+E$5)^$B14) =(((1+E$5)^$B15)-1)/(E$5*(1+E$5)^$B15) =(((1+E$5)^$B16)-1)/(E$5*(1+E$5)^$B16) =(((1+E$5)^$B17)-1)/(E$5*(1+E$5)^$B17) =(((1+E$5)^$B18)-1)/(E$5*(1+E$5)^$B18) =(((1+E$5)^$B19)-1)/(E$5*(1+E$5)^$B19) =(((1+E$5)^$B20)-1)/(E$5*(1+E$5)^$B20) =(((1+E$5)^$B21)-1)/(E$5*(1+E$5)^$B21) =(((1+E$5)^$B22)-1)/(E$5*(1+E$5)^$B22) =(((1+E$5)^$B23)-1)/(E$5*(1+E$5)^$B23) =(((1+E$5)^$B24)-1)/(E$5*(1+E$5)^$B24) =(((1+E$5)^$B25)-1)/(E$5*(1+E$5)^$B25) =(((1+E$5)^$B26)-1)/(E$5*(1+E$5)^$B26) =(((1+E$5)^$B27)-1)/(E$5*(1+E$5)^$B27) =(((1+E$5)^$B28)-1)/(E$5*(1+E$5)^$B28) =(((1+E$5)^$B29)-1)/(E$5*(1+E$5)^$B29) =(((1+E$5)^$B30)-1)/(E$5*(1+E$5)^$B30) =(((1+E$5)^$B31)-1)/(E$5*(1+E$5)^$B31) =(((1+E$5)^$B32)-1)/(E$5*(1+E$5)^$B32) =(((1+E$5)^$B33)-1)/(E$5*(1+E$5)^$B33) =(((1+E$5)^$B34)-1)/(E$5*(1+E$5)^$B34) =(((1+E$5)^$B35)-1)/(E$5*(1+E$5)^$B35) =(((1+E$5)^$B36)-1)/(E$5*(1+E$5)^$B36) =(((1+E$5)^$B37)-1)/(E$5*(1+E$5)^$B37) =(((1+E$5)^$B38)-1)/(E$5*(1+E$5)^$B38) =(((1+E$5)^$B39)-1)/(E$5*(1+E$5)^$B39) =(((1+E$5)^$B40)-1)/(E$5*(1+E$5)^$B40) =(((1+E$5)^$B41)-1)/(E$5*(1+E$5)^$B41) =(((1+E$5)^$B42)-1)/(E$5*(1+E$5)^$B42) =(((1+E$5)^$B43)-1)/(E$5*(1+E$5)^$B43) =(((1+E$5)^$B44)-1)/(E$5*(1+E$5)^$B44) =(((1+E$5)^$B45)-1)/(E$5*(1+E$5)^$B45) =(((1+E$5)^$B46)-1)/(E$5*(1+E$5)^$B46) =(((1+E$5)^$B47)-1)/(E$5*(1+E$5)^$B47) =(((1+E$5)^$B48)-1)/(E$5*(1+E$5)^$B48) =(((1+E$5)^$B49)-1)/(E$5*(1+E$5)^$B49) =(((1+E$5)^$B50)-1)/(E$5*(1+E$5)^$B50) =(((1+E$5)^$B51)-1)/(E$5*(1+E$5)^$B51) =(((1+E$5)^$B52)-1)/(E$5*(1+E$5)^$B52) =(((1+E$5)^$B53)-1)/(E$5*(1+E$5)^$B53) =(((1+E$5)^$B54)-1)/(E$5*(1+E$5)^$B54) =(((1+E$5)^$B55)-1)/(E$5*(1+E$5)^$B55)

PART A 2000 DEPOSIT =F$5*E7 =F$5*E8 =F$5*E9 =F$5*E10 =F$5*E11 =F$5*E12 =F$5*E13 =F$5*E14 =F$5*E15 =F$5*E16 =F$5*E17 =F$5*E18 =F$5*E19 =F$5*E20 =F$5*E21 =F$5*E22 =F$5*E23 =F$5*E24 =F$5*E25 =F$5*E26 =F$5*E27 =F$5*E28 =F$5*E29 =F$5*E30 =F$5*E31 =F$5*E32 =F$5*E33 =F$5*E34 =F$5*E35 =F$5*E36 =F$5*E37 =F$5*E38 =F$5*E39 =F$5*E40 =F$5*E41 =F$5*E42 =F$5*E43 =F$5*E44 =F$5*E45 =F$5*E46 =F$5*E47 =F$5*E48 =F$5*E49 =F$5*E50 =F$5*E51 =F$5*E52 =F$5*E53 =F$5*E54 =F$5*E55

PART B 0.06 (P|A i%,n) =(((1+G$5)^$B7)-1)/(G$5*(1+G$5)^$B7) =(((1+G$5)^$B8)-1)/(G$5*(1+G$5)^$B8) =(((1+G$5)^$B9)-1)/(G$5*(1+G$5)^$B9) =(((1+G$5)^$B10)-1)/(G$5*(1+G$5)^$B10) =(((1+G$5)^$B11)-1)/(G$5*(1+G$5)^$B11) =(((1+G$5)^$B12)-1)/(G$5*(1+G$5)^$B12) =(((1+G$5)^$B13)-1)/(G$5*(1+G$5)^$B13) =(((1+G$5)^$B14)-1)/(G$5*(1+G$5)^$B14) =(((1+G$5)^$B15)-1)/(G$5*(1+G$5)^$B15) =(((1+G$5)^$B16)-1)/(G$5*(1+G$5)^$B16) =(((1+G$5)^$B17)-1)/(G$5*(1+G$5)^$B17) =(((1+G$5)^$B18)-1)/(G$5*(1+G$5)^$B18) =(((1+G$5)^$B19)-1)/(G$5*(1+G$5)^$B19) =(((1+G$5)^$B20)-1)/(G$5*(1+G$5)^$B20) =(((1+G$5)^$B21)-1)/(G$5*(1+G$5)^$B21) =(((1+G$5)^$B22)-1)/(G$5*(1+G$5)^$B22) =(((1+G$5)^$B23)-1)/(G$5*(1+G$5)^$B23) =(((1+G$5)^$B24)-1)/(G$5*(1+G$5)^$B24) =(((1+G$5)^$B25)-1)/(G$5*(1+G$5)^$B25) =(((1+G$5)^$B26)-1)/(G$5*(1+G$5)^$B26) =(((1+G$5)^$B27)-1)/(G$5*(1+G$5)^$B27) =(((1+G$5)^$B28)-1)/(G$5*(1+G$5)^$B28) =(((1+G$5)^$B29)-1)/(G$5*(1+G$5)^$B29) =(((1+G$5)^$B30)-1)/(G$5*(1+G$5)^$B30) =(((1+G$5)^$B31)-1)/(G$5*(1+G$5)^$B31) =(((1+G$5)^$B32)-1)/(G$5*(1+G$5)^$B32) =(((1+G$5)^$B33)-1)/(G$5*(1+G$5)^$B33) =(((1+G$5)^$B34)-1)/(G$5*(1+G$5)^$B34) =(((1+G$5)^$B35)-1)/(G$5*(1+G$5)^$B35) =(((1+G$5)^$B36)-1)/(G$5*(1+G$5)^$B36) =(((1+G$5)^$B37)-1)/(G$5*(1+G$5)^$B37) =(((1+G$5)^$B38)-1)/(G$5*(1+G$5)^$B38) =(((1+G$5)^$B39)-1)/(G$5*(1+G$5)^$B39) =(((1+G$5)^$B40)-1)/(G$5*(1+G$5)^$B40) =(((1+G$5)^$B41)-1)/(G$5*(1+G$5)^$B41) =(((1+G$5)^$B42)-1)/(G$5*(1+G$5)^$B42) =(((1+G$5)^$B43)-1)/(G$5*(1+G$5)^$B43) =(((1+G$5)^$B44)-1)/(G$5*(1+G$5)^$B44) =(((1+G$5)^$B45)-1)/(G$5*(1+G$5)^$B45) =(((1+G$5)^$B46)-1)/(G$5*(1+G$5)^$B46) =(((1+G$5)^$B47)-1)/(G$5*(1+G$5)^$B47) =(((1+G$5)^$B48)-1)/(G$5*(1+G$5)^$B48) =(((1+G$5)^$B49)-1)/(G$5*(1+G$5)^$B49) =(((1+G$5)^$B50)-1)/(G$5*(1+G$5)^$B50) =(((1+G$5)^$B51)-1)/(G$5*(1+G$5)^$B51) =(((1+G$5)^$B52)-1)/(G$5*(1+G$5)^$B52) =(((1+G$5)^$B53)-1)/(G$5*(1+G$5)^$B53) =(((1+G$5)^$B54)-1)/(G$5*(1+G$5)^$B54) =(((1+G$5)^$B55)-1)/(G$5*(1+G$5)^$B55)

=(((1+E$5)^$B56)-1)/(E$5*(1+E$5)^$B56) =(((1+E$5)^$B57)-1)/(E$5*(1+E$5)^$B57) =(((1+E$5)^$B58)-1)/(E$5*(1+E$5)^$B58) =(((1+E$5)^$B59)-1)/(E$5*(1+E$5)^$B59) =(((1+E$5)^$B60)-1)/(E$5*(1+E$5)^$B60) =(((1+E$5)^$B61)-1)/(E$5*(1+E$5)^$B61) =(((1+E$5)^$B62)-1)/(E$5*(1+E$5)^$B62) =(((1+E$5)^$B63)-1)/(E$5*(1+E$5)^$B63) =(((1+E$5)^$B64)-1)/(E$5*(1+E$5)^$B64) =(((1+E$5)^$B65)-1)/(E$5*(1+E$5)^$B65) =(((1+E$5)^$B66)-1)/(E$5*(1+E$5)^$B66) =(((1+E$5)^$B67)-1)/(E$5*(1+E$5)^$B67) =(((1+E$5)^$B68)-1)/(E$5*(1+E$5)^$B68) =(((1+E$5)^$B69)-1)/(E$5*(1+E$5)^$B69) =(((1+E$5)^$B70)-1)/(E$5*(1+E$5)^$B70) =(((1+E$5)^$B71)-1)/(E$5*(1+E$5)^$B71) =(((1+E$5)^$B72)-1)/(E$5*(1+E$5)^$B72) =(((1+E$5)^$B73)-1)/(E$5*(1+E$5)^$B73) =(((1+E$5)^$B74)-1)/(E$5*(1+E$5)^$B74) =(((1+E$5)^$B75)-1)/(E$5*(1+E$5)^$B75) =(((1+E$5)^$B76)-1)/(E$5*(1+E$5)^$B76) =(((1+E$5)^$B77)-1)/(E$5*(1+E$5)^$B77) =(((1+E$5)^$B78)-1)/(E$5*(1+E$5)^$B78) =(((1+E$5)^$B79)-1)/(E$5*(1+E$5)^$B79) =(((1+E$5)^$B80)-1)/(E$5*(1+E$5)^$B80) =(((1+E$5)^$B81)-1)/(E$5*(1+E$5)^$B81) =(((1+E$5)^$B82)-1)/(E$5*(1+E$5)^$B82) =(((1+E$5)^$B83)-1)/(E$5*(1+E$5)^$B83) =(((1+E$5)^$B84)-1)/(E$5*(1+E$5)^$B84) =(((1+E$5)^$B85)-1)/(E$5*(1+E$5)^$B85) =(((1+E$5)^$B86)-1)/(E$5*(1+E$5)^$B86) =(((1+E$5)^$B87)-1)/(E$5*(1+E$5)^$B87) =(((1+E$5)^$B88)-1)/(E$5*(1+E$5)^$B88) =(((1+E$5)^$B89)-1)/(E$5*(1+E$5)^$B89) =(((1+E$5)^$B90)-1)/(E$5*(1+E$5)^$B90) =(((1+E$5)^$B91)-1)/(E$5*(1+E$5)^$B91) =(((1+E$5)^$B92)-1)/(E$5*(1+E$5)^$B92) =(((1+E$5)^$B93)-1)/(E$5*(1+E$5)^$B93) =(((1+E$5)^$B94)-1)/(E$5*(1+E$5)^$B94) =(((1+E$5)^$B95)-1)/(E$5*(1+E$5)^$B95) =(((1+E$5)^$B96)-1)/(E$5*(1+E$5)^$B96) =(((1+E$5)^$B97)-1)/(E$5*(1+E$5)^$B97) =(((1+E$5)^$B98)-1)/(E$5*(1+E$5)^$B98) =(((1+E$5)^$B99)-1)/(E$5*(1+E$5)^$B99) =(((1+E$5)^$B100)-1)/(E$5*(1+E$5)^$B100) =(((1+E$5)^$B101)-1)/(E$5*(1+E$5)^$B101) =(((1+E$5)^$B102)-1)/(E$5*(1+E$5)^$B102) =(((1+E$5)^$B103)-1)/(E$5*(1+E$5)^$B103) =(((1+E$5)^$B104)-1)/(E$5*(1+E$5)^$B104) =(((1+E$5)^$B105)-1)/(E$5*(1+E$5)^$B105) =(((1+E$5)^$B106)-1)/(E$5*(1+E$5)^$B106) =(((1+E$5)^$B107)-1)/(E$5*(1+E$5)^$B107) =(((1+E$5)^$B108)-1)/(E$5*(1+E$5)^$B108) =(((1+E$5)^$B109)-1)/(E$5*(1+E$5)^$B109) =(((1+E$5)^$B110)-1)/(E$5*(1+E$5)^$B110)

=F$5*E56 =F$5*E57 =F$5*E58 =F$5*E59 =F$5*E60 =F$5*E61 =F$5*E62 =F$5*E63 =F$5*E64 =F$5*E65 =F$5*E66 =F$5*E67 =F$5*E68 =F$5*E69 =F$5*E70 =F$5*E71 =F$5*E72 =F$5*E73 =F$5*E74 =F$5*E75 =F$5*E76 =F$5*E77 =F$5*E78 =F$5*E79 =F$5*E80 =F$5*E81 =F$5*E82 =F$5*E83 =F$5*E84 =F$5*E85 =F$5*E86 =F$5*E87 =F$5*E88 =F$5*E89 =F$5*E90 =F$5*E91 =F$5*E92 =F$5*E93 =F$5*E94 =F$5*E95 =F$5*E96 =F$5*E97 =F$5*E98 =F$5*E99 =F$5*E100 =F$5*E101 =F$5*E102 =F$5*E103 =F$5*E104 =F$5*E105 =F$5*E106 =F$5*E107 =F$5*E108 =F$5*E109 =F$5*E110

=(((1+G$5)^$B56)-1)/(G$5*(1+G$5)^$B56) =(((1+G$5)^$B57)-1)/(G$5*(1+G$5)^$B57) =(((1+G$5)^$B58)-1)/(G$5*(1+G$5)^$B58) =(((1+G$5)^$B59)-1)/(G$5*(1+G$5)^$B59) =(((1+G$5)^$B60)-1)/(G$5*(1+G$5)^$B60) =(((1+G$5)^$B61)-1)/(G$5*(1+G$5)^$B61) =(((1+G$5)^$B62)-1)/(G$5*(1+G$5)^$B62) =(((1+G$5)^$B63)-1)/(G$5*(1+G$5)^$B63) =(((1+G$5)^$B64)-1)/(G$5*(1+G$5)^$B64) =(((1+G$5)^$B65)-1)/(G$5*(1+G$5)^$B65) =(((1+G$5)^$B66)-1)/(G$5*(1+G$5)^$B66) =(((1+G$5)^$B67)-1)/(G$5*(1+G$5)^$B67) =(((1+G$5)^$B68)-1)/(G$5*(1+G$5)^$B68) =(((1+G$5)^$B69)-1)/(G$5*(1+G$5)^$B69) =(((1+G$5)^$B70)-1)/(G$5*(1+G$5)^$B70) =(((1+G$5)^$B71)-1)/(G$5*(1+G$5)^$B71) =(((1+G$5)^$B72)-1)/(G$5*(1+G$5)^$B72) =(((1+G$5)^$B73)-1)/(G$5*(1+G$5)^$B73) =(((1+G$5)^$B74)-1)/(G$5*(1+G$5)^$B74) =(((1+G$5)^$B75)-1)/(G$5*(1+G$5)^$B75) =(((1+G$5)^$B76)-1)/(G$5*(1+G$5)^$B76) =(((1+G$5)^$B77)-1)/(G$5*(1+G$5)^$B77) =(((1+G$5)^$B78)-1)/(G$5*(1+G$5)^$B78) =(((1+G$5)^$B79)-1)/(G$5*(1+G$5)^$B79) =(((1+G$5)^$B80)-1)/(G$5*(1+G$5)^$B80) =(((1+G$5)^$B81)-1)/(G$5*(1+G$5)^$B81) =(((1+G$5)^$B82)-1)/(G$5*(1+G$5)^$B82) =(((1+G$5)^$B83)-1)/(G$5*(1+G$5)^$B83) =(((1+G$5)^$B84)-1)/(G$5*(1+G$5)^$B84) =(((1+G$5)^$B85)-1)/(G$5*(1+G$5)^$B85) =(((1+G$5)^$B86)-1)/(G$5*(1+G$5)^$B86) =(((1+G$5)^$B87)-1)/(G$5*(1+G$5)^$B87) =(((1+G$5)^$B88)-1)/(G$5*(1+G$5)^$B88) =(((1+G$5)^$B89)-1)/(G$5*(1+G$5)^$B89) =(((1+G$5)^$B90)-1)/(G$5*(1+G$5)^$B90) =(((1+G$5)^$B91)-1)/(G$5*(1+G$5)^$B91) =(((1+G$5)^$B92)-1)/(G$5*(1+G$5)^$B92) =(((1+G$5)^$B93)-1)/(G$5*(1+G$5)^$B93) =(((1+G$5)^$B94)-1)/(G$5*(1+G$5)^$B94) =(((1+G$5)^$B95)-1)/(G$5*(1+G$5)^$B95) =(((1+G$5)^$B96)-1)/(G$5*(1+G$5)^$B96) =(((1+G$5)^$B97)-1)/(G$5*(1+G$5)^$B97) =(((1+G$5)^$B98)-1)/(G$5*(1+G$5)^$B98) =(((1+G$5)^$B99)-1)/(G$5*(1+G$5)^$B99) =(((1+G$5)^$B100)-1)/(G$5*(1+G$5)^$B100) =(((1+G$5)^$B101)-1)/(G$5*(1+G$5)^$B101) =(((1+G$5)^$B102)-1)/(G$5*(1+G$5)^$B102) =(((1+G$5)^$B103)-1)/(G$5*(1+G$5)^$B103) =(((1+G$5)^$B104)-1)/(G$5*(1+G$5)^$B104) =(((1+G$5)^$B105)-1)/(G$5*(1+G$5)^$B105) =(((1+G$5)^$B106)-1)/(G$5*(1+G$5)^$B106) =(((1+G$5)^$B107)-1)/(G$5*(1+G$5)^$B107) =(((1+G$5)^$B108)-1)/(G$5*(1+G$5)^$B108) =(((1+G$5)^$B109)-1)/(G$5*(1+G$5)^$B109) =(((1+G$5)^$B110)-1)/(G$5*(1+G$5)^$B110)

=(((1+E$5)^$B111)-1)/(E$5*(1+E$5)^$B111) =(((1+E$5)^$B112)-1)/(E$5*(1+E$5)^$B112) =(((1+E$5)^$B113)-1)/(E$5*(1+E$5)^$B113) =(((1+E$5)^$B114)-1)/(E$5*(1+E$5)^$B114) =(((1+E$5)^$B115)-1)/(E$5*(1+E$5)^$B115) =(((1+E$5)^$B116)-1)/(E$5*(1+E$5)^$B116) =(((1+E$5)^$B117)-1)/(E$5*(1+E$5)^$B117) =(((1+E$5)^$B118)-1)/(E$5*(1+E$5)^$B118) =(((1+E$5)^$B119)-1)/(E$5*(1+E$5)^$B119) =(((1+E$5)^$B120)-1)/(E$5*(1+E$5)^$B120) =(((1+E$5)^$B121)-1)/(E$5*(1+E$5)^$B121) =(((1+E$5)^$B122)-1)/(E$5*(1+E$5)^$B122) =(((1+E$5)^$B123)-1)/(E$5*(1+E$5)^$B123) =(((1+E$5)^$B124)-1)/(E$5*(1+E$5)^$B124) =(((1+E$5)^$B125)-1)/(E$5*(1+E$5)^$B125) =(((1+E$5)^$B126)-1)/(E$5*(1+E$5)^$B126) =(((1+E$5)^$B127)-1)/(E$5*(1+E$5)^$B127) =(((1+E$5)^$B128)-1)/(E$5*(1+E$5)^$B128) =(((1+E$5)^$B129)-1)/(E$5*(1+E$5)^$B129) =(((1+E$5)^$B130)-1)/(E$5*(1+E$5)^$B130) =(((1+E$5)^$B131)-1)/(E$5*(1+E$5)^$B131) =(((1+E$5)^$B132)-1)/(E$5*(1+E$5)^$B132) =(((1+E$5)^$B133)-1)/(E$5*(1+E$5)^$B133) =(((1+E$5)^$B134)-1)/(E$5*(1+E$5)^$B134) =(((1+E$5)^$B135)-1)/(E$5*(1+E$5)^$B135) =(((1+E$5)^$B136)-1)/(E$5*(1+E$5)^$B136) =(((1+E$5)^$B137)-1)/(E$5*(1+E$5)^$B137) =(((1+E$5)^$B138)-1)/(E$5*(1+E$5)^$B138) =(((1+E$5)^$B139)-1)/(E$5*(1+E$5)^$B139) =(((1+E$5)^$B140)-1)/(E$5*(1+E$5)^$B140) =(((1+E$5)^$B141)-1)/(E$5*(1+E$5)^$B141) =(((1+E$5)^$B142)-1)/(E$5*(1+E$5)^$B142) =(((1+E$5)^$B143)-1)/(E$5*(1+E$5)^$B143) =(((1+E$5)^$B144)-1)/(E$5*(1+E$5)^$B144) =(((1+E$5)^$B145)-1)/(E$5*(1+E$5)^$B145) =(((1+E$5)^$B146)-1)/(E$5*(1+E$5)^$B146) =(((1+E$5)^$B147)-1)/(E$5*(1+E$5)^$B147) =(((1+E$5)^$B148)-1)/(E$5*(1+E$5)^$B148) =(((1+E$5)^$B149)-1)/(E$5*(1+E$5)^$B149) =(((1+E$5)^$B150)-1)/(E$5*(1+E$5)^$B150) =(((1+E$5)^$B151)-1)/(E$5*(1+E$5)^$B151) =(((1+E$5)^$B152)-1)/(E$5*(1+E$5)^$B152) =(((1+E$5)^$B153)-1)/(E$5*(1+E$5)^$B153) =(((1+E$5)^$B154)-1)/(E$5*(1+E$5)^$B154) =(((1+E$5)^$B155)-1)/(E$5*(1+E$5)^$B155) =(((1+E$5)^$B156)-1)/(E$5*(1+E$5)^$B156) =(((1+E$5)^$B157)-1)/(E$5*(1+E$5)^$B157) =(((1+E$5)^$B158)-1)/(E$5*(1+E$5)^$B158) =(((1+E$5)^$B159)-1)/(E$5*(1+E$5)^$B159) =(((1+E$5)^$B160)-1)/(E$5*(1+E$5)^$B160) =(((1+E$5)^$B161)-1)/(E$5*(1+E$5)^$B161) =(((1+E$5)^$B162)-1)/(E$5*(1+E$5)^$B162) =(((1+E$5)^$B163)-1)/(E$5*(1+E$5)^$B163) =(((1+E$5)^$B164)-1)/(E$5*(1+E$5)^$B164) =(((1+E$5)^$B165)-1)/(E$5*(1+E$5)^$B165)

=F$5*E111 =F$5*E112 =F$5*E113 =F$5*E114 =F$5*E115 =F$5*E116 =F$5*E117 =F$5*E118 =F$5*E119 =F$5*E120 =F$5*E121 =F$5*E122 =F$5*E123 =F$5*E124 =F$5*E125 =F$5*E126 =F$5*E127 =F$5*E128 =F$5*E129 =F$5*E130 =F$5*E131 =F$5*E132 =F$5*E133 =F$5*E134 =F$5*E135 =F$5*E136 =F$5*E137 =F$5*E138 =F$5*E139 =F$5*E140 =F$5*E141 =F$5*E142 =F$5*E143 =F$5*E144 =F$5*E145 =F$5*E146 =F$5*E147 =F$5*E148 =F$5*E149 =F$5*E150 =F$5*E151 =F$5*E152 =F$5*E153 =F$5*E154 =F$5*E155 =F$5*E156 =F$5*E157 =F$5*E158 =F$5*E159 =F$5*E160 =F$5*E161 =F$5*E162 =F$5*E163 =F$5*E164 =F$5*E165

=(((1+G$5)^$B111)-1)/(G$5*(1+G$5)^$B111) =(((1+G$5)^$B112)-1)/(G$5*(1+G$5)^$B112) =(((1+G$5)^$B113)-1)/(G$5*(1+G$5)^$B113) =(((1+G$5)^$B114)-1)/(G$5*(1+G$5)^$B114) =(((1+G$5)^$B115)-1)/(G$5*(1+G$5)^$B115) =(((1+G$5)^$B116)-1)/(G$5*(1+G$5)^$B116) =(((1+G$5)^$B117)-1)/(G$5*(1+G$5)^$B117) =(((1+G$5)^$B118)-1)/(G$5*(1+G$5)^$B118) =(((1+G$5)^$B119)-1)/(G$5*(1+G$5)^$B119) =(((1+G$5)^$B120)-1)/(G$5*(1+G$5)^$B120) =(((1+G$5)^$B121)-1)/(G$5*(1+G$5)^$B121) =(((1+G$5)^$B122)-1)/(G$5*(1+G$5)^$B122) =(((1+G$5)^$B123)-1)/(G$5*(1+G$5)^$B123) =(((1+G$5)^$B124)-1)/(G$5*(1+G$5)^$B124) =(((1+G$5)^$B125)-1)/(G$5*(1+G$5)^$B125) =(((1+G$5)^$B126)-1)/(G$5*(1+G$5)^$B126) =(((1+G$5)^$B127)-1)/(G$5*(1+G$5)^$B127) =(((1+G$5)^$B128)-1)/(G$5*(1+G$5)^$B128) =(((1+G$5)^$B129)-1)/(G$5*(1+G$5)^$B129) =(((1+G$5)^$B130)-1)/(G$5*(1+G$5)^$B130) =(((1+G$5)^$B131)-1)/(G$5*(1+G$5)^$B131) =(((1+G$5)^$B132)-1)/(G$5*(1+G$5)^$B132) =(((1+G$5)^$B133)-1)/(G$5*(1+G$5)^$B133) =(((1+G$5)^$B134)-1)/(G$5*(1+G$5)^$B134) =(((1+G$5)^$B135)-1)/(G$5*(1+G$5)^$B135) =(((1+G$5)^$B136)-1)/(G$5*(1+G$5)^$B136) =(((1+G$5)^$B137)-1)/(G$5*(1+G$5)^$B137) =(((1+G$5)^$B138)-1)/(G$5*(1+G$5)^$B138) =(((1+G$5)^$B139)-1)/(G$5*(1+G$5)^$B139) =(((1+G$5)^$B140)-1)/(G$5*(1+G$5)^$B140) =(((1+G$5)^$B141)-1)/(G$5*(1+G$5)^$B141) =(((1+G$5)^$B142)-1)/(G$5*(1+G$5)^$B142) =(((1+G$5)^$B143)-1)/(G$5*(1+G$5)^$B143) =(((1+G$5)^$B144)-1)/(G$5*(1+G$5)^$B144) =(((1+G$5)^$B145)-1)/(G$5*(1+G$5)^$B145) =(((1+G$5)^$B146)-1)/(G$5*(1+G$5)^$B146) =(((1+G$5)^$B147)-1)/(G$5*(1+G$5)^$B147) =(((1+G$5)^$B148)-1)/(G$5*(1+G$5)^$B148) =(((1+G$5)^$B149)-1)/(G$5*(1+G$5)^$B149) =(((1+G$5)^$B150)-1)/(G$5*(1+G$5)^$B150) =(((1+G$5)^$B151)-1)/(G$5*(1+G$5)^$B151) =(((1+G$5)^$B152)-1)/(G$5*(1+G$5)^$B152) =(((1+G$5)^$B153)-1)/(G$5*(1+G$5)^$B153) =(((1+G$5)^$B154)-1)/(G$5*(1+G$5)^$B154) =(((1+G$5)^$B155)-1)/(G$5*(1+G$5)^$B155) =(((1+G$5)^$B156)-1)/(G$5*(1+G$5)^$B156) =(((1+G$5)^$B157)-1)/(G$5*(1+G$5)^$B157) =(((1+G$5)^$B158)-1)/(G$5*(1+G$5)^$B158) =(((1+G$5)^$B159)-1)/(G$5*(1+G$5)^$B159) =(((1+G$5)^$B160)-1)/(G$5*(1+G$5)^$B160) =(((1+G$5)^$B161)-1)/(G$5*(1+G$5)^$B161) =(((1+G$5)^$B162)-1)/(G$5*(1+G$5)^$B162) =(((1+G$5)^$B163)-1)/(G$5*(1+G$5)^$B163) =(((1+G$5)^$B164)-1)/(G$5*(1+G$5)^$B164) =(((1+G$5)^$B165)-1)/(G$5*(1+G$5)^$B165)

=(((1+E$5)^$B166)-1)/(E$5*(1+E$5)^$B166) =(((1+E$5)^$B167)-1)/(E$5*(1+E$5)^$B167) =(((1+E$5)^$B168)-1)/(E$5*(1+E$5)^$B168) =(((1+E$5)^$B169)-1)/(E$5*(1+E$5)^$B169) =(((1+E$5)^$B170)-1)/(E$5*(1+E$5)^$B170) =(((1+E$5)^$B171)-1)/(E$5*(1+E$5)^$B171) =(((1+E$5)^$B172)-1)/(E$5*(1+E$5)^$B172) =(((1+E$5)^$B173)-1)/(E$5*(1+E$5)^$B173) =(((1+E$5)^$B174)-1)/(E$5*(1+E$5)^$B174) =(((1+E$5)^$B175)-1)/(E$5*(1+E$5)^$B175) =(((1+E$5)^$B176)-1)/(E$5*(1+E$5)^$B176) =(((1+E$5)^$B177)-1)/(E$5*(1+E$5)^$B177) =(((1+E$5)^$B178)-1)/(E$5*(1+E$5)^$B178) =(((1+E$5)^$B179)-1)/(E$5*(1+E$5)^$B179) =(((1+E$5)^$B180)-1)/(E$5*(1+E$5)^$B180) =(((1+E$5)^$B181)-1)/(E$5*(1+E$5)^$B181) =(((1+E$5)^$B182)-1)/(E$5*(1+E$5)^$B182) =(((1+E$5)^$B183)-1)/(E$5*(1+E$5)^$B183) =(((1+E$5)^$B184)-1)/(E$5*(1+E$5)^$B184) =(((1+E$5)^$B185)-1)/(E$5*(1+E$5)^$B185) =(((1+E$5)^$B186)-1)/(E$5*(1+E$5)^$B186) =(((1+E$5)^$B187)-1)/(E$5*(1+E$5)^$B187) =(((1+E$5)^$B188)-1)/(E$5*(1+E$5)^$B188) =(((1+E$5)^$B189)-1)/(E$5*(1+E$5)^$B189) =(((1+E$5)^$B190)-1)/(E$5*(1+E$5)^$B190) =(((1+E$5)^$B191)-1)/(E$5*(1+E$5)^$B191) =(((1+E$5)^$B192)-1)/(E$5*(1+E$5)^$B192) =(((1+E$5)^$B193)-1)/(E$5*(1+E$5)^$B193) =(((1+E$5)^$B194)-1)/(E$5*(1+E$5)^$B194) =(((1+E$5)^$B195)-1)/(E$5*(1+E$5)^$B195) =(((1+E$5)^$B196)-1)/(E$5*(1+E$5)^$B196) =(((1+E$5)^$B197)-1)/(E$5*(1+E$5)^$B197) =(((1+E$5)^$B198)-1)/(E$5*(1+E$5)^$B198) =(((1+E$5)^$B199)-1)/(E$5*(1+E$5)^$B199) =(((1+E$5)^$B200)-1)/(E$5*(1+E$5)^$B200) =(((1+E$5)^$B201)-1)/(E$5*(1+E$5)^$B201) =(((1+E$5)^$B202)-1)/(E$5*(1+E$5)^$B202) =(((1+E$5)^$B203)-1)/(E$5*(1+E$5)^$B203) =(((1+E$5)^$B204)-1)/(E$5*(1+E$5)^$B204) =(((1+E$5)^$B205)-1)/(E$5*(1+E$5)^$B205) =(((1+E$5)^$B206)-1)/(E$5*(1+E$5)^$B206) =(((1+E$5)^$B207)-1)/(E$5*(1+E$5)^$B207) =(((1+E$5)^$B208)-1)/(E$5*(1+E$5)^$B208) =(((1+E$5)^$B209)-1)/(E$5*(1+E$5)^$B209) =(((1+E$5)^$B210)-1)/(E$5*(1+E$5)^$B210) =(((1+E$5)^$B211)-1)/(E$5*(1+E$5)^$B211) =(((1+E$5)^$B212)-1)/(E$5*(1+E$5)^$B212) =(((1+E$5)^$B213)-1)/(E$5*(1+E$5)^$B213) =(((1+E$5)^$B214)-1)/(E$5*(1+E$5)^$B214) =(((1+E$5)^$B215)-1)/(E$5*(1+E$5)^$B215) =(((1+E$5)^$B216)-1)/(E$5*(1+E$5)^$B216) =(((1+E$5)^$B217)-1)/(E$5*(1+E$5)^$B217) =(((1+E$5)^$B218)-1)/(E$5*(1+E$5)^$B218) =(((1+E$5)^$B219)-1)/(E$5*(1+E$5)^$B219) =(((1+E$5)^$B220)-1)/(E$5*(1+E$5)^$B220)

=F$5*E166 =F$5*E167 =F$5*E168 =F$5*E169 =F$5*E170 =F$5*E171 =F$5*E172 =F$5*E173 =F$5*E174 =F$5*E175 =F$5*E176 =F$5*E177 =F$5*E178 =F$5*E179 =F$5*E180 =F$5*E181 =F$5*E182 =F$5*E183 =F$5*E184 =F$5*E185 =F$5*E186 =F$5*E187 =F$5*E188 =F$5*E189 =F$5*E190 =F$5*E191 =F$5*E192 =F$5*E193 =F$5*E194 =F$5*E195 =F$5*E196 =F$5*E197 =F$5*E198 =F$5*E199 =F$5*E200 =F$5*E201 =F$5*E202 =F$5*E203 =F$5*E204 =F$5*E205 =F$5*E206 =F$5*E207 =F$5*E208 =F$5*E209 =F$5*E210 =F$5*E211 =F$5*E212 =F$5*E213 =F$5*E214 =F$5*E215 =F$5*E216 =F$5*E217 =F$5*E218 =F$5*E219 =F$5*E220

=(((1+G$5)^$B166)-1)/(G$5*(1+G$5)^$B166) =(((1+G$5)^$B167)-1)/(G$5*(1+G$5)^$B167) =(((1+G$5)^$B168)-1)/(G$5*(1+G$5)^$B168) =(((1+G$5)^$B169)-1)/(G$5*(1+G$5)^$B169) =(((1+G$5)^$B170)-1)/(G$5*(1+G$5)^$B170) =(((1+G$5)^$B171)-1)/(G$5*(1+G$5)^$B171) =(((1+G$5)^$B172)-1)/(G$5*(1+G$5)^$B172) =(((1+G$5)^$B173)-1)/(G$5*(1+G$5)^$B173) =(((1+G$5)^$B174)-1)/(G$5*(1+G$5)^$B174) =(((1+G$5)^$B175)-1)/(G$5*(1+G$5)^$B175) =(((1+G$5)^$B176)-1)/(G$5*(1+G$5)^$B176) =(((1+G$5)^$B177)-1)/(G$5*(1+G$5)^$B177) =(((1+G$5)^$B178)-1)/(G$5*(1+G$5)^$B178) =(((1+G$5)^$B179)-1)/(G$5*(1+G$5)^$B179) =(((1+G$5)^$B180)-1)/(G$5*(1+G$5)^$B180) =(((1+G$5)^$B181)-1)/(G$5*(1+G$5)^$B181) =(((1+G$5)^$B182)-1)/(G$5*(1+G$5)^$B182) =(((1+G$5)^$B183)-1)/(G$5*(1+G$5)^$B183) =(((1+G$5)^$B184)-1)/(G$5*(1+G$5)^$B184) =(((1+G$5)^$B185)-1)/(G$5*(1+G$5)^$B185) =(((1+G$5)^$B186)-1)/(G$5*(1+G$5)^$B186) =(((1+G$5)^$B187)-1)/(G$5*(1+G$5)^$B187) =(((1+G$5)^$B188)-1)/(G$5*(1+G$5)^$B188) =(((1+G$5)^$B189)-1)/(G$5*(1+G$5)^$B189) =(((1+G$5)^$B190)-1)/(G$5*(1+G$5)^$B190) =(((1+G$5)^$B191)-1)/(G$5*(1+G$5)^$B191) =(((1+G$5)^$B192)-1)/(G$5*(1+G$5)^$B192) =(((1+G$5)^$B193)-1)/(G$5*(1+G$5)^$B193) =(((1+G$5)^$B194)-1)/(G$5*(1+G$5)^$B194) =(((1+G$5)^$B195)-1)/(G$5*(1+G$5)^$B195) =(((1+G$5)^$B196)-1)/(G$5*(1+G$5)^$B196) =(((1+G$5)^$B197)-1)/(G$5*(1+G$5)^$B197) =(((1+G$5)^$B198)-1)/(G$5*(1+G$5)^$B198) =(((1+G$5)^$B199)-1)/(G$5*(1+G$5)^$B199) =(((1+G$5)^$B200)-1)/(G$5*(1+G$5)^$B200) =(((1+G$5)^$B201)-1)/(G$5*(1+G$5)^$B201) =(((1+G$5)^$B202)-1)/(G$5*(1+G$5)^$B202) =(((1+G$5)^$B203)-1)/(G$5*(1+G$5)^$B203) =(((1+G$5)^$B204)-1)/(G$5*(1+G$5)^$B204) =(((1+G$5)^$B205)-1)/(G$5*(1+G$5)^$B205) =(((1+G$5)^$B206)-1)/(G$5*(1+G$5)^$B206) =(((1+G$5)^$B207)-1)/(G$5*(1+G$5)^$B207) =(((1+G$5)^$B208)-1)/(G$5*(1+G$5)^$B208) =(((1+G$5)^$B209)-1)/(G$5*(1+G$5)^$B209) =(((1+G$5)^$B210)-1)/(G$5*(1+G$5)^$B210) =(((1+G$5)^$B211)-1)/(G$5*(1+G$5)^$B211) =(((1+G$5)^$B212)-1)/(G$5*(1+G$5)^$B212) =(((1+G$5)^$B213)-1)/(G$5*(1+G$5)^$B213) =(((1+G$5)^$B214)-1)/(G$5*(1+G$5)^$B214) =(((1+G$5)^$B215)-1)/(G$5*(1+G$5)^$B215) =(((1+G$5)^$B216)-1)/(G$5*(1+G$5)^$B216) =(((1+G$5)^$B217)-1)/(G$5*(1+G$5)^$B217) =(((1+G$5)^$B218)-1)/(G$5*(1+G$5)^$B218) =(((1+G$5)^$B219)-1)/(G$5*(1+G$5)^$B219) =(((1+G$5)^$B220)-1)/(G$5*(1+G$5)^$B220)

=(((1+E$5)^$B221)-1)/(E$5*(1+E$5)^$B221) =(((1+E$5)^$B222)-1)/(E$5*(1+E$5)^$B222) =(((1+E$5)^$B223)-1)/(E$5*(1+E$5)^$B223) =(((1+E$5)^$B224)-1)/(E$5*(1+E$5)^$B224) =(((1+E$5)^$B225)-1)/(E$5*(1+E$5)^$B225) =(((1+E$5)^$B226)-1)/(E$5*(1+E$5)^$B226) =(((1+E$5)^$B227)-1)/(E$5*(1+E$5)^$B227) =(((1+E$5)^$B228)-1)/(E$5*(1+E$5)^$B228) =(((1+E$5)^$B229)-1)/(E$5*(1+E$5)^$B229) =(((1+E$5)^$B230)-1)/(E$5*(1+E$5)^$B230) =(((1+E$5)^$B231)-1)/(E$5*(1+E$5)^$B231) =(((1+E$5)^$B232)-1)/(E$5*(1+E$5)^$B232) =(((1+E$5)^$B233)-1)/(E$5*(1+E$5)^$B233) =(((1+E$5)^$B234)-1)/(E$5*(1+E$5)^$B234) =(((1+E$5)^$B235)-1)/(E$5*(1+E$5)^$B235) =(((1+E$5)^$B236)-1)/(E$5*(1+E$5)^$B236) =(((1+E$5)^$B237)-1)/(E$5*(1+E$5)^$B237) =(((1+E$5)^$B238)-1)/(E$5*(1+E$5)^$B238) =(((1+E$5)^$B239)-1)/(E$5*(1+E$5)^$B239) =(((1+E$5)^$B240)-1)/(E$5*(1+E$5)^$B240) =(((1+E$5)^$B241)-1)/(E$5*(1+E$5)^$B241) =(((1+E$5)^$B242)-1)/(E$5*(1+E$5)^$B242) =(((1+E$5)^$B243)-1)/(E$5*(1+E$5)^$B243) =(((1+E$5)^$B244)-1)/(E$5*(1+E$5)^$B244) =(((1+E$5)^$B245)-1)/(E$5*(1+E$5)^$B245) =(((1+E$5)^$B246)-1)/(E$5*(1+E$5)^$B246) =(((1+E$5)^$B247)-1)/(E$5*(1+E$5)^$B247) =(((1+E$5)^$B248)-1)/(E$5*(1+E$5)^$B248) =(((1+E$5)^$B249)-1)/(E$5*(1+E$5)^$B249) =(((1+E$5)^$B250)-1)/(E$5*(1+E$5)^$B250) =(((1+E$5)^$B251)-1)/(E$5*(1+E$5)^$B251) =(((1+E$5)^$B252)-1)/(E$5*(1+E$5)^$B252) =(((1+E$5)^$B253)-1)/(E$5*(1+E$5)^$B253) =(((1+E$5)^$B254)-1)/(E$5*(1+E$5)^$B254) =(((1+E$5)^$B255)-1)/(E$5*(1+E$5)^$B255) =(((1+E$5)^$B256)-1)/(E$5*(1+E$5)^$B256)

=F$5*E221 =F$5*E222 =F$5*E223 =F$5*E224 =F$5*E225 =F$5*E226 =F$5*E227 =F$5*E228 =F$5*E229 =F$5*E230 =F$5*E231 =F$5*E232 =F$5*E233 =F$5*E234 =F$5*E235 =F$5*E236 =F$5*E237 =F$5*E238 =F$5*E239 =F$5*E240 =F$5*E241 =F$5*E242 =F$5*E243 =F$5*E244 =F$5*E245 =F$5*E246 =F$5*E247 =F$5*E248 =F$5*E249 =F$5*E250 =F$5*E251 =F$5*E252 =F$5*E253 =F$5*E254 =F$5*E255 =F$5*E256

=(((1+G$5)^$B221)-1)/(G$5*(1+G$5)^$B221) =(((1+G$5)^$B222)-1)/(G$5*(1+G$5)^$B222) =(((1+G$5)^$B223)-1)/(G$5*(1+G$5)^$B223) =(((1+G$5)^$B224)-1)/(G$5*(1+G$5)^$B224) =(((1+G$5)^$B225)-1)/(G$5*(1+G$5)^$B225) =(((1+G$5)^$B226)-1)/(G$5*(1+G$5)^$B226) =(((1+G$5)^$B227)-1)/(G$5*(1+G$5)^$B227) =(((1+G$5)^$B228)-1)/(G$5*(1+G$5)^$B228) =(((1+G$5)^$B229)-1)/(G$5*(1+G$5)^$B229) =(((1+G$5)^$B230)-1)/(G$5*(1+G$5)^$B230) =(((1+G$5)^$B231)-1)/(G$5*(1+G$5)^$B231) =(((1+G$5)^$B232)-1)/(G$5*(1+G$5)^$B232) =(((1+G$5)^$B233)-1)/(G$5*(1+G$5)^$B233) =(((1+G$5)^$B234)-1)/(G$5*(1+G$5)^$B234) =(((1+G$5)^$B235)-1)/(G$5*(1+G$5)^$B235) =(((1+G$5)^$B236)-1)/(G$5*(1+G$5)^$B236) =(((1+G$5)^$B237)-1)/(G$5*(1+G$5)^$B237) =(((1+G$5)^$B238)-1)/(G$5*(1+G$5)^$B238) =(((1+G$5)^$B239)-1)/(G$5*(1+G$5)^$B239) =(((1+G$5)^$B240)-1)/(G$5*(1+G$5)^$B240) =(((1+G$5)^$B241)-1)/(G$5*(1+G$5)^$B241) =(((1+G$5)^$B242)-1)/(G$5*(1+G$5)^$B242) =(((1+G$5)^$B243)-1)/(G$5*(1+G$5)^$B243) =(((1+G$5)^$B244)-1)/(G$5*(1+G$5)^$B244) =(((1+G$5)^$B245)-1)/(G$5*(1+G$5)^$B245) =(((1+G$5)^$B246)-1)/(G$5*(1+G$5)^$B246) =(((1+G$5)^$B247)-1)/(G$5*(1+G$5)^$B247) =(((1+G$5)^$B248)-1)/(G$5*(1+G$5)^$B248) =(((1+G$5)^$B249)-1)/(G$5*(1+G$5)^$B249) =(((1+G$5)^$B250)-1)/(G$5*(1+G$5)^$B250) =(((1+G$5)^$B251)-1)/(G$5*(1+G$5)^$B251) =(((1+G$5)^$B252)-1)/(G$5*(1+G$5)^$B252) =(((1+G$5)^$B253)-1)/(G$5*(1+G$5)^$B253) =(((1+G$5)^$B254)-1)/(G$5*(1+G$5)^$B254) =(((1+G$5)^$B255)-1)/(G$5*(1+G$5)^$B255) =(((1+G$5)^$B256)-1)/(G$5*(1+G$5)^$B256)

PART B

PART C

2000

0.15

2000

DEPOSIT =H$5*G7 =H$5*G8 =H$5*G9 =H$5*G10 =H$5*G11 =H$5*G12 =H$5*G13 =H$5*G14 =H$5*G15 =H$5*G16 =H$5*G17 =H$5*G18 =H$5*G19 =H$5*G20 =H$5*G21 =H$5*G22 =H$5*G23 =H$5*G24 =H$5*G25 =H$5*G26 =H$5*G27 =H$5*G28 =H$5*G29 =H$5*G30 =H$5*G31 =H$5*G32 =H$5*G33 =H$5*G34 =H$5*G35 =H$5*G36 =H$5*G37 =H$5*G38 =H$5*G39 =H$5*G40 =H$5*G41 =H$5*G42 =H$5*G43 =H$5*G44 =H$5*G45 =H$5*G46 =H$5*G47 =H$5*G48 =H$5*G49 =H$5*G50 =H$5*G51 =H$5*G52 =H$5*G53 =H$5*G54 =H$5*G55

(P|A i%,n) =(((1+I$5)^$B7)-1)/(I$5*(1+I$5)^$B7) =(((1+I$5)^$B8)-1)/(I$5*(1+I$5)^$B8) =(((1+I$5)^$B9)-1)/(I$5*(1+I$5)^$B9) =(((1+I$5)^$B10)-1)/(I$5*(1+I$5)^$B10) =(((1+I$5)^$B11)-1)/(I$5*(1+I$5)^$B11) =(((1+I$5)^$B12)-1)/(I$5*(1+I$5)^$B12) =(((1+I$5)^$B13)-1)/(I$5*(1+I$5)^$B13) =(((1+I$5)^$B14)-1)/(I$5*(1+I$5)^$B14) =(((1+I$5)^$B15)-1)/(I$5*(1+I$5)^$B15) =(((1+I$5)^$B16)-1)/(I$5*(1+I$5)^$B16) =(((1+I$5)^$B17)-1)/(I$5*(1+I$5)^$B17) =(((1+I$5)^$B18)-1)/(I$5*(1+I$5)^$B18) =(((1+I$5)^$B19)-1)/(I$5*(1+I$5)^$B19) =(((1+I$5)^$B20)-1)/(I$5*(1+I$5)^$B20) =(((1+I$5)^$B21)-1)/(I$5*(1+I$5)^$B21) =(((1+I$5)^$B22)-1)/(I$5*(1+I$5)^$B22) =(((1+I$5)^$B23)-1)/(I$5*(1+I$5)^$B23) =(((1+I$5)^$B24)-1)/(I$5*(1+I$5)^$B24) =(((1+I$5)^$B25)-1)/(I$5*(1+I$5)^$B25) =(((1+I$5)^$B26)-1)/(I$5*(1+I$5)^$B26) =(((1+I$5)^$B27)-1)/(I$5*(1+I$5)^$B27) =(((1+I$5)^$B28)-1)/(I$5*(1+I$5)^$B28) =(((1+I$5)^$B29)-1)/(I$5*(1+I$5)^$B29) =(((1+I$5)^$B30)-1)/(I$5*(1+I$5)^$B30) =(((1+I$5)^$B31)-1)/(I$5*(1+I$5)^$B31) =(((1+I$5)^$B32)-1)/(I$5*(1+I$5)^$B32) =(((1+I$5)^$B33)-1)/(I$5*(1+I$5)^$B33) =(((1+I$5)^$B34)-1)/(I$5*(1+I$5)^$B34) =(((1+I$5)^$B35)-1)/(I$5*(1+I$5)^$B35) =(((1+I$5)^$B36)-1)/(I$5*(1+I$5)^$B36) =(((1+I$5)^$B37)-1)/(I$5*(1+I$5)^$B37) =(((1+I$5)^$B38)-1)/(I$5*(1+I$5)^$B38) =(((1+I$5)^$B39)-1)/(I$5*(1+I$5)^$B39) =(((1+I$5)^$B40)-1)/(I$5*(1+I$5)^$B40) =(((1+I$5)^$B41)-1)/(I$5*(1+I$5)^$B41) =(((1+I$5)^$B42)-1)/(I$5*(1+I$5)^$B42) =(((1+I$5)^$B43)-1)/(I$5*(1+I$5)^$B43) =(((1+I$5)^$B44)-1)/(I$5*(1+I$5)^$B44) =(((1+I$5)^$B45)-1)/(I$5*(1+I$5)^$B45) =(((1+I$5)^$B46)-1)/(I$5*(1+I$5)^$B46) =(((1+I$5)^$B47)-1)/(I$5*(1+I$5)^$B47) =(((1+I$5)^$B48)-1)/(I$5*(1+I$5)^$B48) =(((1+I$5)^$B49)-1)/(I$5*(1+I$5)^$B49) =(((1+I$5)^$B50)-1)/(I$5*(1+I$5)^$B50) =(((1+I$5)^$B51)-1)/(I$5*(1+I$5)^$B51) =(((1+I$5)^$B52)-1)/(I$5*(1+I$5)^$B52) =(((1+I$5)^$B53)-1)/(I$5*(1+I$5)^$B53) =(((1+I$5)^$B54)-1)/(I$5*(1+I$5)^$B54) =(((1+I$5)^$B55)-1)/(I$5*(1+I$5)^$B55)

DEPOSIT =J$5*I7 =J$5*I8 =J$5*I9 =J$5*I10 =J$5*I11 =J$5*I12 =J$5*I13 =J$5*I14 =J$5*I15 =J$5*I16 =J$5*I17 =J$5*I18 =J$5*I19 =J$5*I20 =J$5*I21 =J$5*I22 =J$5*I23 =J$5*I24 =J$5*I25 =J$5*I26 =J$5*I27 =J$5*I28 =J$5*I29 =J$5*I30 =J$5*I31 =J$5*I32 =J$5*I33 =J$5*I34 =J$5*I35 =J$5*I36 =J$5*I37 =J$5*I38 =J$5*I39 =J$5*I40 =J$5*I41 =J$5*I42 =J$5*I43 =J$5*I44 =J$5*I45 =J$5*I46 =J$5*I47 =J$5*I48 =J$5*I49 =J$5*I50 =J$5*I51 =J$5*I52 =J$5*I53 =J$5*I54 =J$5*I55

=H$5*G56 =H$5*G57 =H$5*G58 =H$5*G59 =H$5*G60 =H$5*G61 =H$5*G62 =H$5*G63 =H$5*G64 =H$5*G65 =H$5*G66 =H$5*G67 =H$5*G68 =H$5*G69 =H$5*G70 =H$5*G71 =H$5*G72 =H$5*G73 =H$5*G74 =H$5*G75 =H$5*G76 =H$5*G77 =H$5*G78 =H$5*G79 =H$5*G80 =H$5*G81 =H$5*G82 =H$5*G83 =H$5*G84 =H$5*G85 =H$5*G86 =H$5*G87 =H$5*G88 =H$5*G89 =H$5*G90 =H$5*G91 =H$5*G92 =H$5*G93 =H$5*G94 =H$5*G95 =H$5*G96 =H$5*G97 =H$5*G98 =H$5*G99 =H$5*G100 =H$5*G101 =H$5*G102 =H$5*G103 =H$5*G104 =H$5*G105 =H$5*G106 =H$5*G107 =H$5*G108 =H$5*G109 =H$5*G110

=(((1+I$5)^$B56)-1)/(I$5*(1+I$5)^$B56) =(((1+I$5)^$B57)-1)/(I$5*(1+I$5)^$B57) =(((1+I$5)^$B58)-1)/(I$5*(1+I$5)^$B58) =(((1+I$5)^$B59)-1)/(I$5*(1+I$5)^$B59) =(((1+I$5)^$B60)-1)/(I$5*(1+I$5)^$B60) =(((1+I$5)^$B61)-1)/(I$5*(1+I$5)^$B61) =(((1+I$5)^$B62)-1)/(I$5*(1+I$5)^$B62) =(((1+I$5)^$B63)-1)/(I$5*(1+I$5)^$B63) =(((1+I$5)^$B64)-1)/(I$5*(1+I$5)^$B64) =(((1+I$5)^$B65)-1)/(I$5*(1+I$5)^$B65) =(((1+I$5)^$B66)-1)/(I$5*(1+I$5)^$B66) =(((1+I$5)^$B67)-1)/(I$5*(1+I$5)^$B67) =(((1+I$5)^$B68)-1)/(I$5*(1+I$5)^$B68) =(((1+I$5)^$B69)-1)/(I$5*(1+I$5)^$B69) =(((1+I$5)^$B70)-1)/(I$5*(1+I$5)^$B70) =(((1+I$5)^$B71)-1)/(I$5*(1+I$5)^$B71) =(((1+I$5)^$B72)-1)/(I$5*(1+I$5)^$B72) =(((1+I$5)^$B73)-1)/(I$5*(1+I$5)^$B73) =(((1+I$5)^$B74)-1)/(I$5*(1+I$5)^$B74) =(((1+I$5)^$B75)-1)/(I$5*(1+I$5)^$B75) =(((1+I$5)^$B76)-1)/(I$5*(1+I$5)^$B76) =(((1+I$5)^$B77)-1)/(I$5*(1+I$5)^$B77) =(((1+I$5)^$B78)-1)/(I$5*(1+I$5)^$B78) =(((1+I$5)^$B79)-1)/(I$5*(1+I$5)^$B79) =(((1+I$5)^$B80)-1)/(I$5*(1+I$5)^$B80) =(((1+I$5)^$B81)-1)/(I$5*(1+I$5)^$B81) =(((1+I$5)^$B82)-1)/(I$5*(1+I$5)^$B82) =(((1+I$5)^$B83)-1)/(I$5*(1+I$5)^$B83) =(((1+I$5)^$B84)-1)/(I$5*(1+I$5)^$B84) =(((1+I$5)^$B85)-1)/(I$5*(1+I$5)^$B85) =(((1+I$5)^$B86)-1)/(I$5*(1+I$5)^$B86) =(((1+I$5)^$B87)-1)/(I$5*(1+I$5)^$B87) =(((1+I$5)^$B88)-1)/(I$5*(1+I$5)^$B88) =(((1+I$5)^$B89)-1)/(I$5*(1+I$5)^$B89) =(((1+I$5)^$B90)-1)/(I$5*(1+I$5)^$B90) =(((1+I$5)^$B91)-1)/(I$5*(1+I$5)^$B91) =(((1+I$5)^$B92)-1)/(I$5*(1+I$5)^$B92) =(((1+I$5)^$B93)-1)/(I$5*(1+I$5)^$B93) =(((1+I$5)^$B94)-1)/(I$5*(1+I$5)^$B94) =(((1+I$5)^$B95)-1)/(I$5*(1+I$5)^$B95) =(((1+I$5)^$B96)-1)/(I$5*(1+I$5)^$B96) =(((1+I$5)^$B97)-1)/(I$5*(1+I$5)^$B97) =(((1+I$5)^$B98)-1)/(I$5*(1+I$5)^$B98) =(((1+I$5)^$B99)-1)/(I$5*(1+I$5)^$B99) =(((1+I$5)^$B100)-1)/(I$5*(1+I$5)^$B100) =(((1+I$5)^$B101)-1)/(I$5*(1+I$5)^$B101) =(((1+I$5)^$B102)-1)/(I$5*(1+I$5)^$B102) =(((1+I$5)^$B103)-1)/(I$5*(1+I$5)^$B103) =(((1+I$5)^$B104)-1)/(I$5*(1+I$5)^$B104) =(((1+I$5)^$B105)-1)/(I$5*(1+I$5)^$B105) =(((1+I$5)^$B106)-1)/(I$5*(1+I$5)^$B106) =(((1+I$5)^$B107)-1)/(I$5*(1+I$5)^$B107) =(((1+I$5)^$B108)-1)/(I$5*(1+I$5)^$B108) =(((1+I$5)^$B109)-1)/(I$5*(1+I$5)^$B109) =(((1+I$5)^$B110)-1)/(I$5*(1+I$5)^$B110)

=J$5*I56 =J$5*I57 =J$5*I58 =J$5*I59 =J$5*I60 =J$5*I61 =J$5*I62 =J$5*I63 =J$5*I64 =J$5*I65 =J$5*I66 =J$5*I67 =J$5*I68 =J$5*I69 =J$5*I70 =J$5*I71 =J$5*I72 =J$5*I73 =J$5*I74 =J$5*I75 =J$5*I76 =J$5*I77 =J$5*I78 =J$5*I79 =J$5*I80 =J$5*I81 =J$5*I82 =J$5*I83 =J$5*I84 =J$5*I85 =J$5*I86 =J$5*I87 =J$5*I88 =J$5*I89 =J$5*I90 =J$5*I91 =J$5*I92 =J$5*I93 =J$5*I94 =J$5*I95 =J$5*I96 =J$5*I97 =J$5*I98 =J$5*I99 =J$5*I100 =J$5*I101 =J$5*I102 =J$5*I103 =J$5*I104 =J$5*I105 =J$5*I106 =J$5*I107 =J$5*I108 =J$5*I109 =J$5*I110

=H$5*G111 =H$5*G112 =H$5*G113 =H$5*G114 =H$5*G115 =H$5*G116 =H$5*G117 =H$5*G118 =H$5*G119 =H$5*G120 =H$5*G121 =H$5*G122 =H$5*G123 =H$5*G124 =H$5*G125 =H$5*G126 =H$5*G127 =H$5*G128 =H$5*G129 =H$5*G130 =H$5*G131 =H$5*G132 =H$5*G133 =H$5*G134 =H$5*G135 =H$5*G136 =H$5*G137 =H$5*G138 =H$5*G139 =H$5*G140 =H$5*G141 =H$5*G142 =H$5*G143 =H$5*G144 =H$5*G145 =H$5*G146 =H$5*G147 =H$5*G148 =H$5*G149 =H$5*G150 =H$5*G151 =H$5*G152 =H$5*G153 =H$5*G154 =H$5*G155 =H$5*G156 =H$5*G157 =H$5*G158 =H$5*G159 =H$5*G160 =H$5*G161 =H$5*G162 =H$5*G163 =H$5*G164 =H$5*G165

=(((1+I$5)^$B111)-1)/(I$5*(1+I$5)^$B111) =(((1+I$5)^$B112)-1)/(I$5*(1+I$5)^$B112) =(((1+I$5)^$B113)-1)/(I$5*(1+I$5)^$B113) =(((1+I$5)^$B114)-1)/(I$5*(1+I$5)^$B114) =(((1+I$5)^$B115)-1)/(I$5*(1+I$5)^$B115) =(((1+I$5)^$B116)-1)/(I$5*(1+I$5)^$B116) =(((1+I$5)^$B117)-1)/(I$5*(1+I$5)^$B117) =(((1+I$5)^$B118)-1)/(I$5*(1+I$5)^$B118) =(((1+I$5)^$B119)-1)/(I$5*(1+I$5)^$B119) =(((1+I$5)^$B120)-1)/(I$5*(1+I$5)^$B120) =(((1+I$5)^$B121)-1)/(I$5*(1+I$5)^$B121) =(((1+I$5)^$B122)-1)/(I$5*(1+I$5)^$B122) =(((1+I$5)^$B123)-1)/(I$5*(1+I$5)^$B123) =(((1+I$5)^$B124)-1)/(I$5*(1+I$5)^$B124) =(((1+I$5)^$B125)-1)/(I$5*(1+I$5)^$B125) =(((1+I$5)^$B126)-1)/(I$5*(1+I$5)^$B126) =(((1+I$5)^$B127)-1)/(I$5*(1+I$5)^$B127) =(((1+I$5)^$B128)-1)/(I$5*(1+I$5)^$B128) =(((1+I$5)^$B129)-1)/(I$5*(1+I$5)^$B129) =(((1+I$5)^$B130)-1)/(I$5*(1+I$5)^$B130) =(((1+I$5)^$B131)-1)/(I$5*(1+I$5)^$B131) =(((1+I$5)^$B132)-1)/(I$5*(1+I$5)^$B132) =(((1+I$5)^$B133)-1)/(I$5*(1+I$5)^$B133) =(((1+I$5)^$B134)-1)/(I$5*(1+I$5)^$B134) =(((1+I$5)^$B135)-1)/(I$5*(1+I$5)^$B135) =(((1+I$5)^$B136)-1)/(I$5*(1+I$5)^$B136) =(((1+I$5)^$B137)-1)/(I$5*(1+I$5)^$B137) =(((1+I$5)^$B138)-1)/(I$5*(1+I$5)^$B138) =(((1+I$5)^$B139)-1)/(I$5*(1+I$5)^$B139) =(((1+I$5)^$B140)-1)/(I$5*(1+I$5)^$B140) =(((1+I$5)^$B141)-1)/(I$5*(1+I$5)^$B141) =(((1+I$5)^$B142)-1)/(I$5*(1+I$5)^$B142) =(((1+I$5)^$B143)-1)/(I$5*(1+I$5)^$B143) =(((1+I$5)^$B144)-1)/(I$5*(1+I$5)^$B144) =(((1+I$5)^$B145)-1)/(I$5*(1+I$5)^$B145) =(((1+I$5)^$B146)-1)/(I$5*(1+I$5)^$B146) =(((1+I$5)^$B147)-1)/(I$5*(1+I$5)^$B147) =(((1+I$5)^$B148)-1)/(I$5*(1+I$5)^$B148) =(((1+I$5)^$B149)-1)/(I$5*(1+I$5)^$B149) =(((1+I$5)^$B150)-1)/(I$5*(1+I$5)^$B150) =(((1+I$5)^$B151)-1)/(I$5*(1+I$5)^$B151) =(((1+I$5)^$B152)-1)/(I$5*(1+I$5)^$B152) =(((1+I$5)^$B153)-1)/(I$5*(1+I$5)^$B153) =(((1+I$5)^$B154)-1)/(I$5*(1+I$5)^$B154) =(((1+I$5)^$B155)-1)/(I$5*(1+I$5)^$B155) =(((1+I$5)^$B156)-1)/(I$5*(1+I$5)^$B156) =(((1+I$5)^$B157)-1)/(I$5*(1+I$5)^$B157) =(((1+I$5)^$B158)-1)/(I$5*(1+I$5)^$B158) =(((1+I$5)^$B159)-1)/(I$5*(1+I$5)^$B159) =(((1+I$5)^$B160)-1)/(I$5*(1+I$5)^$B160) =(((1+I$5)^$B161)-1)/(I$5*(1+I$5)^$B161) =(((1+I$5)^$B162)-1)/(I$5*(1+I$5)^$B162) =(((1+I$5)^$B163)-1)/(I$5*(1+I$5)^$B163) =(((1+I$5)^$B164)-1)/(I$5*(1+I$5)^$B164) =(((1+I$5)^$B165)-1)/(I$5*(1+I$5)^$B165)

=J$5*I111 =J$5*I112 =J$5*I113 =J$5*I114 =J$5*I115 =J$5*I116 =J$5*I117 =J$5*I118 =J$5*I119 =J$5*I120 =J$5*I121 =J$5*I122 =J$5*I123 =J$5*I124 =J$5*I125 =J$5*I126 =J$5*I127 =J$5*I128 =J$5*I129 =J$5*I130 =J$5*I131 =J$5*I132 =J$5*I133 =J$5*I134 =J$5*I135 =J$5*I136 =J$5*I137 =J$5*I138 =J$5*I139 =J$5*I140 =J$5*I141 =J$5*I142 =J$5*I143 =J$5*I144 =J$5*I145 =J$5*I146 =J$5*I147 =J$5*I148 =J$5*I149 =J$5*I150 =J$5*I151 =J$5*I152 =J$5*I153 =J$5*I154 =J$5*I155 =J$5*I156 =J$5*I157 =J$5*I158 =J$5*I159 =J$5*I160 =J$5*I161 =J$5*I162 =J$5*I163 =J$5*I164 =J$5*I165

=H$5*G166 =H$5*G167 =H$5*G168 =H$5*G169 =H$5*G170 =H$5*G171 =H$5*G172 =H$5*G173 =H$5*G174 =H$5*G175 =H$5*G176 =H$5*G177 =H$5*G178 =H$5*G179 =H$5*G180 =H$5*G181 =H$5*G182 =H$5*G183 =H$5*G184 =H$5*G185 =H$5*G186 =H$5*G187 =H$5*G188 =H$5*G189 =H$5*G190 =H$5*G191 =H$5*G192 =H$5*G193 =H$5*G194 =H$5*G195 =H$5*G196 =H$5*G197 =H$5*G198 =H$5*G199 =H$5*G200 =H$5*G201 =H$5*G202 =H$5*G203 =H$5*G204 =H$5*G205 =H$5*G206 =H$5*G207 =H$5*G208 =H$5*G209 =H$5*G210 =H$5*G211 =H$5*G212 =H$5*G213 =H$5*G214 =H$5*G215 =H$5*G216 =H$5*G217 =H$5*G218 =H$5*G219 =H$5*G220

=(((1+I$5)^$B166)-1)/(I$5*(1+I$5)^$B166) =(((1+I$5)^$B167)-1)/(I$5*(1+I$5)^$B167) =(((1+I$5)^$B168)-1)/(I$5*(1+I$5)^$B168) =(((1+I$5)^$B169)-1)/(I$5*(1+I$5)^$B169) =(((1+I$5)^$B170)-1)/(I$5*(1+I$5)^$B170) =(((1+I$5)^$B171)-1)/(I$5*(1+I$5)^$B171) =(((1+I$5)^$B172)-1)/(I$5*(1+I$5)^$B172) =(((1+I$5)^$B173)-1)/(I$5*(1+I$5)^$B173) =(((1+I$5)^$B174)-1)/(I$5*(1+I$5)^$B174) =(((1+I$5)^$B175)-1)/(I$5*(1+I$5)^$B175) =(((1+I$5)^$B176)-1)/(I$5*(1+I$5)^$B176) =(((1+I$5)^$B177)-1)/(I$5*(1+I$5)^$B177) =(((1+I$5)^$B178)-1)/(I$5*(1+I$5)^$B178) =(((1+I$5)^$B179)-1)/(I$5*(1+I$5)^$B179) =(((1+I$5)^$B180)-1)/(I$5*(1+I$5)^$B180) =(((1+I$5)^$B181)-1)/(I$5*(1+I$5)^$B181) =(((1+I$5)^$B182)-1)/(I$5*(1+I$5)^$B182) =(((1+I$5)^$B183)-1)/(I$5*(1+I$5)^$B183) =(((1+I$5)^$B184)-1)/(I$5*(1+I$5)^$B184) =(((1+I$5)^$B185)-1)/(I$5*(1+I$5)^$B185) =(((1+I$5)^$B186)-1)/(I$5*(1+I$5)^$B186) =(((1+I$5)^$B187)-1)/(I$5*(1+I$5)^$B187) =(((1+I$5)^$B188)-1)/(I$5*(1+I$5)^$B188) =(((1+I$5)^$B189)-1)/(I$5*(1+I$5)^$B189) =(((1+I$5)^$B190)-1)/(I$5*(1+I$5)^$B190) =(((1+I$5)^$B191)-1)/(I$5*(1+I$5)^$B191) =(((1+I$5)^$B192)-1)/(I$5*(1+I$5)^$B192) =(((1+I$5)^$B193)-1)/(I$5*(1+I$5)^$B193) =(((1+I$5)^$B194)-1)/(I$5*(1+I$5)^$B194) =(((1+I$5)^$B195)-1)/(I$5*(1+I$5)^$B195) =(((1+I$5)^$B196)-1)/(I$5*(1+I$5)^$B196) =(((1+I$5)^$B197)-1)/(I$5*(1+I$5)^$B197) =(((1+I$5)^$B198)-1)/(I$5*(1+I$5)^$B198) =(((1+I$5)^$B199)-1)/(I$5*(1+I$5)^$B199) =(((1+I$5)^$B200)-1)/(I$5*(1+I$5)^$B200) =(((1+I$5)^$B201)-1)/(I$5*(1+I$5)^$B201) =(((1+I$5)^$B202)-1)/(I$5*(1+I$5)^$B202) =(((1+I$5)^$B203)-1)/(I$5*(1+I$5)^$B203) =(((1+I$5)^$B204)-1)/(I$5*(1+I$5)^$B204) =(((1+I$5)^$B205)-1)/(I$5*(1+I$5)^$B205) =(((1+I$5)^$B206)-1)/(I$5*(1+I$5)^$B206) =(((1+I$5)^$B207)-1)/(I$5*(1+I$5)^$B207) =(((1+I$5)^$B208)-1)/(I$5*(1+I$5)^$B208) =(((1+I$5)^$B209)-1)/(I$5*(1+I$5)^$B209) =(((1+I$5)^$B210)-1)/(I$5*(1+I$5)^$B210) =(((1+I$5)^$B211)-1)/(I$5*(1+I$5)^$B211) =(((1+I$5)^$B212)-1)/(I$5*(1+I$5)^$B212) =(((1+I$5)^$B213)-1)/(I$5*(1+I$5)^$B213) =(((1+I$5)^$B214)-1)/(I$5*(1+I$5)^$B214) =(((1+I$5)^$B215)-1)/(I$5*(1+I$5)^$B215) =(((1+I$5)^$B216)-1)/(I$5*(1+I$5)^$B216) =(((1+I$5)^$B217)-1)/(I$5*(1+I$5)^$B217) =(((1+I$5)^$B218)-1)/(I$5*(1+I$5)^$B218) =(((1+I$5)^$B219)-1)/(I$5*(1+I$5)^$B219) =(((1+I$5)^$B220)-1)/(I$5*(1+I$5)^$B220)

=J$5*I166 =J$5*I167 =J$5*I168 =J$5*I169 =J$5*I170 =J$5*I171 =J$5*I172 =J$5*I173 =J$5*I174 =J$5*I175 =J$5*I176 =J$5*I177 =J$5*I178 =J$5*I179 =J$5*I180 =J$5*I181 =J$5*I182 =J$5*I183 =J$5*I184 =J$5*I185 =J$5*I186 =J$5*I187 =J$5*I188 =J$5*I189 =J$5*I190 =J$5*I191 =J$5*I192 =J$5*I193 =J$5*I194 =J$5*I195 =J$5*I196 =J$5*I197 =J$5*I198 =J$5*I199 =J$5*I200 =J$5*I201 =J$5*I202 =J$5*I203 =J$5*I204 =J$5*I205 =J$5*I206 =J$5*I207 =J$5*I208 =J$5*I209 =J$5*I210 =J$5*I211 =J$5*I212 =J$5*I213 =J$5*I214 =J$5*I215 =J$5*I216 =J$5*I217 =J$5*I218 =J$5*I219 =J$5*I220

=H$5*G221 =H$5*G222 =H$5*G223 =H$5*G224 =H$5*G225 =H$5*G226 =H$5*G227 =H$5*G228 =H$5*G229 =H$5*G230 =H$5*G231 =H$5*G232 =H$5*G233 =H$5*G234 =H$5*G235 =H$5*G236 =H$5*G237 =H$5*G238 =H$5*G239 =H$5*G240 =H$5*G241 =H$5*G242 =H$5*G243 =H$5*G244 =H$5*G245 =H$5*G246 =H$5*G247 =H$5*G248 =H$5*G249 =H$5*G250 =H$5*G251 =H$5*G252 =H$5*G253 =H$5*G254 =H$5*G255 =H$5*G256

=(((1+I$5)^$B221)-1)/(I$5*(1+I$5)^$B221) =(((1+I$5)^$B222)-1)/(I$5*(1+I$5)^$B222) =(((1+I$5)^$B223)-1)/(I$5*(1+I$5)^$B223) =(((1+I$5)^$B224)-1)/(I$5*(1+I$5)^$B224) =(((1+I$5)^$B225)-1)/(I$5*(1+I$5)^$B225) =(((1+I$5)^$B226)-1)/(I$5*(1+I$5)^$B226) =(((1+I$5)^$B227)-1)/(I$5*(1+I$5)^$B227) =(((1+I$5)^$B228)-1)/(I$5*(1+I$5)^$B228) =(((1+I$5)^$B229)-1)/(I$5*(1+I$5)^$B229) =(((1+I$5)^$B230)-1)/(I$5*(1+I$5)^$B230) =(((1+I$5)^$B231)-1)/(I$5*(1+I$5)^$B231) =(((1+I$5)^$B232)-1)/(I$5*(1+I$5)^$B232) =(((1+I$5)^$B233)-1)/(I$5*(1+I$5)^$B233) =(((1+I$5)^$B234)-1)/(I$5*(1+I$5)^$B234) =(((1+I$5)^$B235)-1)/(I$5*(1+I$5)^$B235) =(((1+I$5)^$B236)-1)/(I$5*(1+I$5)^$B236) =(((1+I$5)^$B237)-1)/(I$5*(1+I$5)^$B237) =(((1+I$5)^$B238)-1)/(I$5*(1+I$5)^$B238) =(((1+I$5)^$B239)-1)/(I$5*(1+I$5)^$B239) =(((1+I$5)^$B240)-1)/(I$5*(1+I$5)^$B240) =(((1+I$5)^$B241)-1)/(I$5*(1+I$5)^$B241) =(((1+I$5)^$B242)-1)/(I$5*(1+I$5)^$B242) =(((1+I$5)^$B243)-1)/(I$5*(1+I$5)^$B243) =(((1+I$5)^$B244)-1)/(I$5*(1+I$5)^$B244) =(((1+I$5)^$B245)-1)/(I$5*(1+I$5)^$B245) =(((1+I$5)^$B246)-1)/(I$5*(1+I$5)^$B246) =(((1+I$5)^$B247)-1)/(I$5*(1+I$5)^$B247) =(((1+I$5)^$B248)-1)/(I$5*(1+I$5)^$B248) =(((1+I$5)^$B249)-1)/(I$5*(1+I$5)^$B249) =(((1+I$5)^$B250)-1)/(I$5*(1+I$5)^$B250) =(((1+I$5)^$B251)-1)/(I$5*(1+I$5)^$B251) =(((1+I$5)^$B252)-1)/(I$5*(1+I$5)^$B252) =(((1+I$5)^$B253)-1)/(I$5*(1+I$5)^$B253) =(((1+I$5)^$B254)-1)/(I$5*(1+I$5)^$B254) =(((1+I$5)^$B255)-1)/(I$5*(1+I$5)^$B255) =(((1+I$5)^$B256)-1)/(I$5*(1+I$5)^$B256)

=J$5*I221 =J$5*I222 =J$5*I223 =J$5*I224 =J$5*I225 =J$5*I226 =J$5*I227 =J$5*I228 =J$5*I229 =J$5*I230 =J$5*I231 =J$5*I232 =J$5*I233 =J$5*I234 =J$5*I235 =J$5*I236 =J$5*I237 =J$5*I238 =J$5*I239 =J$5*I240 =J$5*I241 =J$5*I242 =J$5*I243 =J$5*I244 =J$5*I245 =J$5*I246 =J$5*I247 =J$5*I248 =J$5*I249 =J$5*I250 =J$5*I251 =J$5*I252 =J$5*I253 =J$5*I254 =J$5*I255 =J$5*I256

Required Deposit versus Life $2,000/year Maintenance Cost, various Interest Rates $60,000.00

$50,000.00

Deposit ($)

$40,000.00

$30,000.00

$20,000.00

$10,000.00

$0.00 0

100

part d EACH CURVE ASSYMPTOTICALLY APPROACHES A LIMITING VALUE THE LIMIT DECREASES AS THE INTEREST RATE INCREASES THE LIMIT IS APPROACHED MORE QUICKLY AS THE INTEREST RATE INCREASES

ersus Life various Interest Rates

100

150 Life (years)

200

250

300

5 percent 4 percent 6 percent 15 percent

PROBLEM 4.14 WACC = (COST OF EQUITY)(% EQUITY) + (COST OF DEBT)(% DEBT)(1 - TAXRATE) SUBSTITUTING KNOWN VALUES 13% = (COST OF EQUITY)(60%) + (14%)(1 - 60%)(1 - 45%) 13% = (COST OF EQUITY)(60%) + 3.08% COST OF EQUITY = 16.53%

(1 - TAXRATE)

PROBLEM 4.15 a

BEFORE TAX EFFECTIVE INTEREST RATE = ((1 + r/m)^m) - 1 = ((1 + 0.10/12)^12) - 1 = 0.10471 = 10.471%

AFTER TAX EFFECTIVE INTEREST RATE = = (((1 + r/m)^m) - 1)*(1-T) = (((1 + 0.10/12)^12) - 1)*(1-0.40) =

(((1 + 0.10/12)^12) - 1)*(1-0.40) = 0.06283 = 6.283%

PROBLEM 4.16 a

FOR A STABLE STOCK PRICE: COST OF CAPITAL = DIVIDEND / SHAREPRICE COST OF CAPITAL = 10 / 75 COST OF CAPITAL = 13.33%

FOR A GROWING STOCK PRICE COST OF CAPITAL = (DIVIDEND / SHAREPRICE) + GROWTHRATE COST OF CAPITAL = 10 / 75 + 4% COST OF CAPITAL = 17.33%

PROBLEM 4.17 AFTER TAX COST OF LOAN ((1 + r/m)^m - 1)*(1-T) ((1 + 0.12/2)^2 - 1)*(1-0.36) = 0.07910 AFTER TAX COST OF BONDS ((1 + r/m)^m - 1)*(1-T) ((1 + 0.08/4)^4 - 1)*(1-0.36) = 0.05276 COST OF COMMON STOCK CSD/P + g 8/72 + 0.01 = 0.12111 COST OF RETAINED EARNINGS SAME AS COST OF COMMON STOCK = 0.12111 WACC SUMMATION OF (PROPORTION FROM SOURCE)*(COST OF SOURCE) FOR ALL SOURCES (3000000/11000000)*0.07910 + (4500000/11000000)*0.05276 + ((2000000+1500000)/11000000)*0.12111 =

+1500000)/11000000)*0.12111 = 0.08169 = 8.169%

PROBLEM 4.18 WACC = (LOAN RATE)(1-TAX RATE)(% FUNDING FROM LOAN) + (AFTER TAX BOND RATE)(% FUNDING FROM BONDS) + (DIVIDEND/STOCK PRICE)(% FUNDING FROM STOCK + % FUNDING FROM RE) WACC = (0.1025)(1-0.35)(3,750,000/10,000,000) + (0.07)(750,000/10,000,000) + (14/200)(5,000,000/10,000,000 + 500,000/10,000,000) WACC = 0.02498 + 0.00525 + 0.03850 WACC = 0.06873

PROBLEM 4.19 WACC = (LOAN RATE)(1-TAX RATE)(% FUNDING FROM LOAN) + (AFTER TAX BOND RATE)(% FUNDING FROM BONDS) + (DIVIDEND/STOCK PRICE)(% FUNDING FROM COMMON STOCK + % FUNDING FROM RE) + (DIVIDEND/(STOCK PRICE - SELLING COST))(% FUNDING FROM PREFERRED STOCK) WACC = (0.1025)(1-0.35)(3,750,000/10,000,000) + (0.07)(750,000/10,000,000) + (14/200)(3,000,000/10,000,000 + 500,000/10,000,000) (5/(100-6))(2,000,000/10,000,000) WACC = 0.02498 + 0.00525 + 0.02450 + 0.01064 WACC = 0.06537

FUNDING FROM RE) +

PROBLEM 4.20 SOURCE LOANS BONDS STOCK RE

BEFOR TAX RATE 0.08299 0.06136 0.10000 0.10000

WACC = 0.06930 + 0.04 WACC = 0.10930

TAX RATE 0.34 0.34

AFTER TAX RATE 0.05477 0.04050 0.10000 0.10000

PROPORTION 0.35 0.25 0.20 0.20

WEIGHTED RATE 0.01917 0.01012 0.02000 0.02000 0.06930

<- SUM

PROBLEM 4.21 a

EFFECTIVE TAX RATE

% FROM DEBT 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

COST OF DEBT CAPITAL BEFORE TAX 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00% 12.00%

36.00% COST OF COST OF DEBT CAPITAL WACC EQUITY CAPITAL AFTER TAX BEFORE TAX 10.00% 7.68% 10.00% 10.00% 7.68% 10.20% 10.00% 7.68% 10.40% 10.00% 7.68% 10.60% 10.00% 7.68% 10.80% 10.00% 7.68% 11.00% 10.00% 7.68% 11.20% 10.00% 7.68% 11.40% 10.00% 7.68% 11.60% 10.00% 7.68% 11.80% 10.00% 7.68% 12.00%

b (i),(ii)

THE LEFT (0%) END POINT FOR BOTH WACC LINES FALLS AT 10% SINCE THE CAPITAL IS SOURCED 100% FROM EQUITY AND THE COST OF EQUITY CAPITAL IS FIXED AT 10% THE TWO WACC CURVES ARE LINEAR BETWEEN THE LEFT END POINT AND THE RIGHT END POINT. THE RIGHT END POINT OF THE BEFORE TAX CURVE IS AT 12% SINCE THERE IS NO (1-T) MULTIPLIER FOR BEFORE TAX. THUS THE BEFORE TAX CURVE HAS A POSITIVE SLOPE. THE RIGHT END POINT ON THE AFTER TAX CURVE IS AT 7.68% SINCE THE (1-T) MULTIPLIER (0.64) IS APPLIED TO THE12% BEFORE TAX COST. THUS THE AFTER TAX CURVE HAS A NEGATIVE SLOPE.

(iii)

DEBT CAPITAL SHOULD BE USED DUE TO THE NEGATIVE SLOPE OF THIS LINE. THE HIGHER THE PERCENTAGE OF DEBT CAPITAL USED, THE LOWER THE OVERALL COST OF CAPITAL.

THE CAPITAL IS XED AT 10% AND THE RIGHT 2% SINCE THERE VE HAS A POSITIVE SINCE THE (1-T) E AFTER TAX

S LINE. THE HIGHER COST OF CAPITAL.

COST OF CAPITAL AS A FUNCTION OF SOURCE 13.00%

12.00% COST OF DEBT CAPITAL BEFORE TAX

11.00%

COST OF CAPTIAL

WACC AFTER TAX 10.00% 9.77% 9.54% 9.30% 9.07% 8.84% 8.61% 8.38% 8.14% 7.91% 7.68%

COST OF EQUITY CAPITAL

10.00%

9.00%

COST OF DEBT CAPITAL AFTER TAX

8.00%

WACC BEFORE TAX

7.00%

WACC AFTER TAX

6.00% 0%

20%

40%

60%

80%

PERCENT OF CAPITAL FROM DEBT

100%

120%

SOURCE

COST OF DEBT CAPITAL BEFORE TAX COST OF EQUITY CAPITAL COST OF DEBT CAPITAL AFTER TAX WACC BEFORE TAX WACC AFTER TAX

PROBLEM 4.22 WACC = (BEFORE TAX LOAN RATE)(1 - TAX RATE)(PROPORTION LOAN) + (STOCK RATE)(1 - PROPORTION LOAN) 0.10509 = (0.096)(1 - 0.34)(PROPORTION LOAN) + (11.90 / 100)(1 - PROPORTION LOAN) 0.10509 = (0.06144)(PROPORTION LOAN) + (0.1190)(1 - PROPORTION LOAN) 0.10509 = (0.06336)(PROPORTION LOAN) + (0.1190) - (0.1190)(PROPORTION LOAN) -0.01391 = -0.05564(PROPORTION LOAN) PROPORTION LOAN = 25% THEREFORE, PROPORTION STOCK = 75%

PROBLEM 4.23 SOURCE LOANS BONDS STOCK RE

BEFOR TAX RATE 0.14490 0.12551 0.10000 0.10000

WACC = 0.09455 + 0.08 WACC = 0.17455

TAX RATE 0.34 0.34

AFTER TAX RATE PROPORTION 0.09563 0.1733 0.08284 0.2733 0.10000 0.3333 0.10000 0.2200

WEIGHTED RATE 0.01658 0.02264 0.03333 0.02200 0.09455

<- SUM

PROBLEM 4.24 SOURCE BEFOR TAX RATE TAX RATE AFTER TAX RATE PROPORTION LOANS 0.14490 0.34 0.09563 0.1733 BONDS 0.12551 0.34 0.08284 0.2733 STOCK 0.13000 0.13000 0.3333 RE 0.13000 0.13000 0.2200

WACC = 0.11115 + 0.08 WACC = 0.19115

WEIGHTED RATE 0.01658 0.02264 0.04333 0.02860 0.11115

<- SUM

PROBLEM 4.25 SOURCE BEFOR TAX RATE TAX RATE AFTER TAX RATE PROPORTION LOANS 0.14490 0.34 0.09563 0.1733 BONDS 0.12551 0.34 0.08284 0.2733 STOCK 0.07531 0.07531 0.3333 RE 0.07531 0.07531 0.2200

WACC = 0.08089 + 0.08 WACC = 0.16089

WEIGHTED RATE 0.01658 0.02264 0.02510 0.01657 0.08089

<- SUM

PROBLEM 4.26 SOURCE BEFOR TAX RATE TAX RATE AFTER TAX RATE PROPORTION WEIGHTED RATE LOANS 0.15000 0.36 0.09600 0.3636 0.03491 BONDS 0.12551 0.36 0.08033 0.1818 0.01460 STOCK 0.10857 0.10857 0.1818 0.01974 RE 0.10857 0.10857 0.2727 0.02961 1.0000 WACC = 0.09886 = 9.886%

0.09886

<- SUM

PROBLEM 4.27 AFTER TAX RATE = BEFORE TAX RATE * (1 - TAX RATE) AFTER TAX RATE = 0.05 * (1 - 0.45) AFTER TAX RATE = 0.0275 = 2.75%

PROBLEM 4.28 COST OF BONDS = (EFFECTIVE BOND RATE)*(1- TAX RATE) COST OF BONDS = (0.06)*(1- 0.36) COST OF BONDS = 0.0384 = 3.84%

PROBLEM 4.29

BEFORE TAX BOND RATE IS DETERMINED USING THE RATE FUNCTION AS SHOWN IN EXAMPLE 4 BEFORE TAX BOND RATE = RATE(10,35,-450,500) BEFORE TAX RATE = AFTER TAX BOND RATE = BEFORE TAX BOND RATE * (1-T) AFTER TAX BOND RATE = 8.526% * (1-0.36) AFTER TAX RATE =

=RATE(10,35,-450,500)

=E5*(1-0.36)

PROBLEM 4.30

COWBOY CONSTRUCTION EITHER PAYS 0.98X IN 10 DAYS OR X IN 90 DAYS THE FOLLOWING EQUATION CAN BE USED TO DETERMINE THE IMPLIED DAILY INTEREST RATE X = 0.98X*(1+i)^80 (1+i) = (1/0.98)^(1/80) = 1.000253 i = 0.000253 = 0.0253% ASSUMING 365 DAYS/YEAR THE EFFECTIVE ANNUAL INTEREST IS GIVEN BY: (1.000253)^365 - 1 = 0.09673 = 9.673% SINCE THE COST OF MATERIAL IS TAX DEDUCTIBLE, THE EFFECTIVE AFTER TAX COST IS: 0.09673(1-TAX RATE) = 0.09673(1 - 0.42) = 0.0561 = 5.61%

PROBLEM 4.31 COWBOY CONSTRUCTION EITHER PAYS 0.98X IN 10 DAYS OR X IN 60 DAYS THE FOLLOWING EQUATION CAN BE USED TO DETERMINE THE IMPLIED DAILY INTEREST RATE X = 0.98X*(1+i)^50 (1+i) = (1/0.98)^(1/50) = 1.000404 i = 0.000404 = 0.0404% ASSUMING 365 DAYS/YEAR THE EFFECTIVE ANNUAL INTEREST IS GIVEN BY: (1.000404)^365 - 1 = 0.15891 = 15.891% SINCE THE COST OF MATERIAL IS TAX DEDUCTIBLE, THE EFFECTIVE AFTER TAX COST IS: 0.15891*(1-TAX RATE) = 0.15891*(1 - 0.42) = 0.09217 = 9.217%

LIED DAILY INTEREST RATE

E AFTER TAX COST IS:

PROBLEM 4.32 BASE RATE

0.09

ADJUSTMENTS: TECHNOLOGY COST SAVINGS ALLOCATED CAPITAL

0.008 0.024 -0.018

DISCOUNT RATE

=SUM(C3:C8)

PROBLEM 4.33 BASE RATE

9.00%

ADJUSTMENTS: PUBLICLY OWNED ACQUISITION FRACTION OWNED PLANT PROFILE TECHNOLOGY REVENUE GAGR SAVINGS VS. REVENUE GROWTH ALLOCATED CAPITAL LOCATION VENTURE CAPITAL

0.00% 1.00% 1.00% 0.00% 0.00% 2.40% 0.00% 2.00% 0.00%

DISCOUNT RATE

15.40%

PROBLEM 4.34 BASE RATE

9.00%

ADJUSTMENTS: PUBLICLY OWNED ACQUISITION FRACTION OWNED PLANT PROFILE TECHNOLOGY REVENUE GAGR SAVINGS VS. REVENUE GROWTH ALLOCATED CAPITAL LOCATION VENTURE CAPITAL

0.00% 0.50% 1.00% 0.00% 0.00% 2.40% 0.00% 2.00% 0.00%

DISCOUNT RATE

14.90%

PROBLEM 4.35 PROJECT MOVED TO CHILE BASE RATE

9.00%

ADJUSTMENTS: PUBLICLY OWNED ACQUISITION FRACTION OWNED PLANT PROFILE TECHNOLOGY REVENUE GAGR SAVINGS VS. REVENUE GROWTH ALLOCATED CAPITAL LOCATION VENTURE CAPITAL

0.00% 1.00% 1.00% 0.00% 0.00% 2.40% 0.00% 0.50% 0.00%

DISCOUNT RATE

13.90%

RISK RATE FOR BRAZIL INCREASED BY 0.5% BASE RATE 9.00% ADJUSTMENTS: PUBLICLY OWNED ACQUISITION FRACTION OWNED PLANT PROFILE TECHNOLOGY REVENUE GAGR SAVINGS VS. REVENUE GROWTH ALLOCATED CAPITAL LOCATION VENTURE CAPITAL

0.00% 1.00% 1.00% 0.00% 0.00% 2.40% 0.00% 2.50% 0.00%

DISCOUNT RATE

15.90%

PROBLEM 4.36 a b c d

STOCK IN QUESTION IS LESS VOLATILE THAN THE MARKET AS A WHOLE STOCK IN QUESTION IS RISK FREE STOCK IN QUESTION CARRIES THE SAME RISK AS THE MARKET AS A WHOLE STOCK IN QUESTION IS MORE VOLATILE THAN THE MARKET AS A WHOLE

PROBLEM 4.37 RESPONSES ARE BASED ON 2007 PREDICTED BETA a

LOWEST VOLATILITY IS LOWEST PREDICTED BETA COCA COLA HAS THE LOWEST 2007 PREDICTED BETA OF 0.52

HIGHEST VOLATILITY IS HIGHEST PREDICTED BETA FORD HAS THE HIGHEST 2007 PREDICTED BETA OF 1.86

THREE LOWEST VOLITILITIES ARE COCA COLA, PROCTER & GAMBLE, AND JOHNSON & JOHNSON ALL THREE COMPANIES FOCUS PRIMARIALLY ON RETAIL CONSUMABLES

TWO HIGHEST VOLITILITIES ARE FORD AND GENERAL MOTORS BOTH ARE AUTOMOTIVE MANUFACTURERS

THE LARGEST DIFFERENTIAL IS XEROX AT A DIFFERENCE OF 0.91 (1.90 - 0.99) SINCE THE HISTORICAL IS SIGNIFICANTLY HIGHER THAN THE PREDICTED, THE RARE EVENT CAN BE CHARACTERIZED AS POSITIVE SINCE THE STOCKS VOLITILITY HAS SIGNIFICANTLY REDUCED.

E, AND JOHNSON & JOHNSON

PROBLEM 4.38

FOR EACH CASE: COST OF EQUITY CAPITAL = (RISK FREE RATE) + (BETA)(MARKET RATE - RISK FREE RATE) COST OF EQUITY CAPITAL = (0.06) + (0.75)(0.11 - 0.06) COST OF EQUITY CAPITAL = 0.0975 = 9.75% COST OF EQUITY CAPITAL = (0.06) + (0.90)(0.11 - 0.06) COST OF EQUITY CAPITAL = 0.1050 = 10.50% COST OF EQUITY CAPITAL = (0.06) + (1.20)(0.11 - 0.06) COST OF EQUITY CAPITAL = 0.1200 = 12.00% COST OF EQUITY CAPITAL = (0.06) + (0.00)(0.11 - 0.06) COST OF EQUITY CAPITAL = 0.0060 = 6.00% COST OF EQUITY CAPITAL = (0.06) + (1.00)(0.11 - 0.06) COST OF EQUITY CAPITAL = 0.1100 = 11.00%

PROBLEM 4.39

a b c d e

RISK FREE RATE

EXPECTED MARKET RETURN

0.05 0.05 0.05 0.05 0.05

0.11 0.11 0.11 0.11 0.11

BETA 0.75 0.9 1.2 0 1

AFTER TAX COST OF DEBT CAPITAL

% % DEBT EQUITY CAPITAL CAPITAL

0.05 0.04 0.06 0.06 0.05

0.6 0.5 0.2 0.8 0.6

=1-F5 =1-F6 =1-F7 =1-F8 =1-F9

COST OF EQUITY CAPITAL

WACC

=B5+(D5*(C5-B5)) =B6+(D6*(C6-B6)) =B7+(D7*(C7-B7)) =B8+(D8*(C8-B8)) =B9+(D9*(C9-B9))

=(G5*H5)+(F5*E5) =(G6*H6)+(F6*E6) =(G7*H7)+(F7*E7) =(G8*H8)+(F8*E8) =(G9*H9)+(F9*E9)

PROBLEM 5.1 a

THE FOLLOWING RESPONSE IS BASED ON HOME DEPOT'S 2006 ANNUAL REPORT. ON PAGE 26 WITHIN THE SECTION TITLED "LIQUIDITY AND CAPITAL RESOURCES", REFERENCE IS MADE TO USING THE NET PRESENT VALUE OF LEASE OBLIGATIONS ON THE BALANCE SHEET UNDER LONG-TERM DEBT. IN SEVERAL OTHER PLACES THROUGHOUT THE REPORT, NET PRESENT VALUES OF LEASE OBLIGATIONS IS MENTIONED. ON PAGE 52 WITHIN THE SECTION TITLED "GOODWILL AND OTHER INTANGIBLE ASSETS", REFERENCE IS MADE TO ESTIMATING THE VALUE OF THE REPORTING UNITS BASED ON "EXPECTED PRESENT VALUE OF DISCOUNTED CASH FLOWS". ON PAGE 58 WITHIN THE SECTION TITLED "DEBT" REFERENCE IS MADE TO THE PRESENT VALUE OF REMAINING SCHEDULED PAYMENTS OF PRINCIPAL AND INTEREST.

HOME DEPOT USES THE TERM "PRESENT VALUE" RATHER THAN "PRESENT WORTH".

PROBLEM 5.2 a

THE FOLLOWING RESPONSE IS BASED ON CONOCOPHILLIPS' 2006 ANNUAL REPORT. ON PAGE 54 WITHIN THE SECTION TITLED "IMPAIRMENT OF ASSETS" REFERENCE IS MADE TO USING THE NET PRESENT VALUE OF EXPECTED FUTURE CASH FLOWS TO VALUE LONG-LIVED ASSETS IN SEVERAL OTHER PLACES THROUGHOUT THE REPORT, NET PRESENT VALUES OF EXPECTED FUTURE CASH FLOWS IS USED WHEN CURRENT MARKET VALUES ARE DIFFICULT TO ASSESS. ON PAGE 92 WITHIN THE SECTION TITLED "STOCK UNIT PROGRAM", REFERENCE IS MADE TO THE MARKET VALUE OF STOCK LESS THE NET PRESENT VALUE OF DIVIDENDS THAT WILL NOT BE RECEIVED. ON PAGE 109 WITHIN THE SECTION TITLED "STANDARDIZED MEASURE OF DISCOUNTED FUTURE NET CASH FLOWS…", REFERENCE IS MADE TO THE PRESENT VALUE OF CASH FLOWS TO BE OBTAINED FROM DEVELOPMENT AND PRODUCTION.

CONOCOPHILLIPS USES THE TERM "PRESENT VALUE" RATHER THAN "PRESENT WORTH".

PROBLEM 5.3 A SEARCH OF THE WWW USING A POPULAR SEARCH ENGINE RESULTED IN OVER 500,000 HITS. HERE ARE A FEW. BAYER BOEING BRINK'S COMPANY COMMONWEALTH OF KENTUCKY GENERAL ELECTRIC HARLEY-DAVIDSON IBM NASSAU COUNTY, NEW YORK NATO ROLLS-ROYCE TRANSCOM UNILEVER US POSTAL SERVICE WISER OIL COMPANY

PROBLEM 5.4 BEFORE TAX COST OF CAPITAL = (PROPORTION DEBT)*(BT COST OF DEBT) + (PROPORTION EQUITY)*(COST OF EQUITY) AFTER TAX COST OF CAPITAL = ((PROPORTION DEBT)*(BT COST OF DEBT)*(1-TAX RATE)) + (PROPORTION EQUITY)*(COST OF EQUITY)

a b c d e

% DEBT

BEFORE TAX COST OF DEBT

TAX RATE

0.0% 25.0% 50.0% 75.0% 100.0%

12.0% 12.0% 12.0% 12.0% 12.0%

40.0% 40.0% 40.0% 40.0% 40.0%

% EQUITY

COST OF EQUITY

BEFORE TAX COST OF CAPITAL

AFTER TAX COST OF CAPITAL

100.0% 75.0% 50.0% 25.0% 0.0%

10.0% 10.0% 10.0% 10.0% 10.0%

10.00% 10.50% 11.00% 11.50% 12.00%

10.00% 9.30% 8.60% 7.90% 7.20%

PROBLEM 5.5 THE FOLLOWING TABLE IS A REPEAT OF THE RESULTS FROM PROBLEM 5.4

% DEBT

BEFORE TAX BT COST OF DEBT

TAX RATE

% EQUITY

COST OF EQUITY

0.0% 25.0% 50.0% 75.0% 100.0%

12.0% 12.0% 12.0% 12.0% 12.0%

40.0% 40.0% 40.0% 40.0% 40.0%

100.0% 75.0% 50.0% 25.0% 0.0%

10.0% 10.0% 10.0% 10.0% 10.0%

BEFORE TAX AFTER TAX BT COST AT COST OF CAPITAL OF CAPITAL 10.00% 10.50% 11.00% 11.50% 12.00%

10.00% 9.30% 8.60% 7.90% 7.20%

MARR BEFORE TAX = MARR AFTER TAX / (1-T) EST OF MARR AT (1-T) MARR BT AFTER TAX BEFORE TAX 10.00% 60.0% 16.7% 9.30% 60.0% 15.5% 8.60% 60.0% 14.3% 7.90% 60.0% 13.2% 7.20% 60.0% 12.0%

THE ESTIMATING EQUATION BECOMES LESS ACCURATE AS THE PROPORTION OF FUNDING FROM EQUITY SOURCES INCREASES.

MARR AFTER TAX = MARR BEFORE TAX * (1-T) EST OF MARR (1-T) MARR BEFORE TAX AFTER TAX 10.00% 60.0% 6.0% 10.50% 60.0% 6.3% 11.00% 60.0% 6.6% 11.50% 60.0% 6.9% 12.00% 60.0% 7.2% AGAIN, THE ESTIMATING EQUATION BECOMES LESS ACCURATE AS THE PROPORTION OF FUNDING FROM EQUITY SOURCES INCREASES SO THE ANSWER DOES NOT CHANGE.

PROBLEM 5.6 a b c d e f g h j j k l m n o p q

PREFER PROJECT, PW>0 PREFER DO NOTHING, IRR<MARR PREFER DO NOTHING, AW<0 PREFER PROJECT, B/C>1 PREFER PROJECT, FW>0 PREFER PROJECT, ERR>MARR PREFER DO NOTHING, PW<0 PREFER PROJECT, IRR>MARR PREFER PROJECT, AW>0 PREFER DO NOTHING, B/C<1 PREFER DO NOTHING, FW<0 PREFER DO NOTHING, ERR<MARR THE ASSUMPTION BEING MADE IS THAT THE UNINVESTED FUNDS CAN BE INVESTED ELSEWHERE TO EARN AT LEAST MARR NO, IT IS NOT POSSIBLE; PW AND IRR ARE CONSISTENT MEASURES OF WORTH; WHEN CORRECTLY CALCULATED THEY WILL LEAD TO THE SAME ACCEPT/REJECT DECISION YES, IT IS POSSIBLE; AW AND B/C ARE CONSISTENT MEASURES OF WORTH AND THEY LEAD TO THE SAME ACCEPT/REJECT CONCLUSION THE PW MUST BE LESS THAN ZERO FOR PROJECT (J) THE IRR MUST BE LESS THAN MARR FOR PROJECT (J)

PROBLEM 5.7 CHOICE a b c d e f g

DEFINITION 3 5 7 6 1 4 2

PROBLEM 5.8 CHOICE a b c d e f

DEFINITION 1 2 3 1 3 1

PROBLEM 5.9 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

5.00% + CF - CF NET CF (P|F i%,n) PW OF CF -$100,000.00 -$100,000.00 1.00000 -$100,000.00 $12,000.00 -$2,000.00 $10,000.00 0.95238 $9,523.81 $12,000.00 -$2,000.00 $10,000.00 0.90703 $9,070.29 $12,000.00 -$2,000.00 $10,000.00 0.86384 $8,638.38 $12,000.00 -$2,000.00 $10,000.00 0.82270 $8,227.02 $12,000.00 -$2,000.00 $10,000.00 0.78353 $7,835.26 $12,000.00 -$2,000.00 $10,000.00 0.74622 $7,462.15 $12,000.00 -$2,000.00 $10,000.00 0.71068 $7,106.81 $12,000.00 -$2,000.00 $10,000.00 0.67684 $6,768.39 $12,000.00 -$2,000.00 $10,000.00 0.64461 $6,446.09 $12,000.00 -$2,000.00 $10,000.00 0.61391 $6,139.13 $12,000.00 -$2,000.00 $10,000.00 0.58468 $5,846.79 $12,000.00 -$2,000.00 $10,000.00 0.55684 $5,568.37 $12,000.00 -$2,000.00 $10,000.00 0.53032 $5,303.21 $12,000.00 -$2,000.00 $10,000.00 0.50507 $5,050.68 $12,000.00 -$2,000.00 $10,000.00 0.48102 $4,810.17 $3,796.58

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(0.05,NET CF FOR t=1,15) PW = $3,796.58 =E7+NPV(0.05,E8:E22) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(0.05,15,-NET CF FOR t=1,15) PW = $3,796.58 =E7+PV(0.05,15,-E8) SOLUTION USING FACTOR TABLES PW = -$100,000 + $10,000(P|A 5%,15) PW = -$100,000 + $10,000(10.37966) PW = $3,796.60 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD BUY THE GANG PUNCH

<- PW

PROBLEM 5.10 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

5.00% - CF NET CF (P|F i%,n) PW OF CF -$135,000.00 -$135,000.00 1.00000 -$135,000.00 $12,000.00 -$2,000.00 $10,000.00 0.95238 $9,523.81 $12,000.00 -$2,000.00 $10,000.00 0.90703 $9,070.29 $12,000.00 -$2,000.00 $10,000.00 0.86384 $8,638.38 $12,000.00 -$2,000.00 $10,000.00 0.82270 $8,227.02 $12,000.00 -$2,000.00 $10,000.00 0.78353 $7,835.26 $12,000.00 -$2,000.00 $10,000.00 0.74622 $7,462.15 $12,000.00 -$2,000.00 $10,000.00 0.71068 $7,106.81 $12,000.00 -$2,000.00 $10,000.00 0.67684 $6,768.39 $12,000.00 -$2,000.00 $10,000.00 0.64461 $6,446.09 $12,000.00 -$2,000.00 $10,000.00 0.61391 $6,139.13 $12,000.00 -$2,000.00 $10,000.00 0.58468 $5,846.79 $12,000.00 -$2,000.00 $10,000.00 0.55684 $5,568.37 $12,000.00 -$2,000.00 $10,000.00 0.53032 $5,303.21 $12,000.00 -$2,000.00 $10,000.00 0.50507 $5,050.68 $12,000.00 -$2,000.00 $10,000.00 0.48102 $4,810.17 + CF

-$31,203.42 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(0.05,NET CF FOR t=1,15) PW = -$31,203.42 =E7+NPV(0.05,E8:E22) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(0.05,15,-NET CF FOR t=1,15) PW = -$31,203.42 =E7+PV(0.05,15,-E8) SOLUTION USING FACTOR TABLES PW = -$135,000 + $10,000(P|A 5%,15) PW = -$135,000 + $10,000(10.37966) PW = -$31,203.40 b

DECISION RULE IF PW >= 0, ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD NOT BUY THE GANG PUNCH

PROBLEM 5.11 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

6.00% - CF NET CF (P|F i%,n) PW OF CF -$100,000.00 -$100,000.00 1.00000 -$100,000.00 $12,000.00 -$2,000.00 $10,000.00 0.94340 $9,433.96 $12,000.00 -$2,000.00 $10,000.00 0.89000 $8,899.96 $12,000.00 -$2,000.00 $10,000.00 0.83962 $8,396.19 $12,000.00 -$2,000.00 $10,000.00 0.79209 $7,920.94 $12,000.00 -$2,000.00 $10,000.00 0.74726 $7,472.58 $12,000.00 -$2,000.00 $10,000.00 0.70496 $7,049.61 $12,000.00 -$2,000.00 $10,000.00 0.66506 $6,650.57 $12,000.00 -$2,000.00 $10,000.00 0.62741 $6,274.12 $12,000.00 -$2,000.00 $10,000.00 0.59190 $5,918.98 $12,000.00 -$2,000.00 $10,000.00 0.55839 $5,583.95 $12,000.00 -$2,000.00 $10,000.00 0.52679 $5,267.88 $12,000.00 -$2,000.00 $10,000.00 0.49697 $4,969.69 $12,000.00 -$2,000.00 $10,000.00 0.46884 $4,688.39 $12,000.00 -$2,000.00 $10,000.00 0.44230 $4,423.01 $12,000.00 -$2,000.00 $10,000.00 0.41727 $4,172.65 + CF

-$2,877.51 SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(0.06,NET CF FOR t=1,15) PW = -$2,877.51 =E7+NPV(0.06,E8:E22) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(0.06,15,-NET CF FOR t=1,15) PW = -$2,877.51 =E7+PV(0.06,15,-E8) SOLUTION USING FACTOR TABLES PW = -$100,000 + $10,000(P|A 6%,15) PW = -$100,000 + $10,000(9.71225) PW = -$2,877.50 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD NOT BUY THE GANG PUNCH

<- PW

PROBLEM 5.12 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5

+ CF

- CF -$75,000.00

$18,500.00 $18,500.00 $18,500.00 $18,500.00 $18,500.00

10.00% NET CF (P|F i%,n) PW OF CF -$75,000.00 1.00000 -$75,000.00 $18,500.00 0.90909 $16,818.18 $18,500.00 0.82645 $15,289.26 $18,500.00 0.75131 $13,899.32 $18,500.00 0.68301 $12,635.75 $18,500.00 0.62092 $11,487.04 -$4,870.44 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$4,870.44 =E7+NPV(0.1,E8:E12) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-CF FOR t=1,n) PW = -$4,870.44 =E7+PV(0.1,5,-E8) SOLUTION USING FACTOR TABLES PW = -$75,000 + $18,500(P|A 10%,5) PW = -$75,000 + $18,500(3.79079) PW = -$4,870.39 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

CARLISLE SHOULD REJECT THE FILTER BASED ON ITS ECONOMIC MERITS

THE ENVIRONMENTAL ISSUE OF REDUCING EMISSIONS IS A NON-ECONOMIC FACTOR TO BE CONSIDERED (I.E., THE "GREEN" ISSUE).

PROBLEM 5.13 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5

0.00% - CF NET CF (P|F i%,n) PW OF CF -$75,000.00 -$75,000.00 1.00000 -$75,000.00 $18,500.00 $18,500.00 1.00000 $18,500.00 $18,500.00 $18,500.00 1.00000 $18,500.00 $18,500.00 $18,500.00 1.00000 $18,500.00 $18,500.00 $18,500.00 1.00000 $18,500.00 $18,500.00 $18,500.00 1.00000 $18,500.00 + CF

$17,500.00 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $17,500.00 =E7+NPV(0,E8:E12) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = $17,500.00 =E7+PV(0,5,-E8) SOLUTION USING FACTOR TABLES PW = -$75,000 + $18,500(P|A 0%,5) PW = -$75,000 + $18,500(5.00000) PW = $17,500.00 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

CARLISLE SHOULD INSTALL THE FILTER

PROBLEM 5.14 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5

+ CF

$2,000.00 $4,000.00 $3,000.00 $1,600.00

- CF -$5,000.00 -$200.00 -$300.00 -$600.00 -$1,000.00 -$1,500.00

6.00% NET CF (P|F i%,n) PW OF CF -$5,000.00 1.00000 -$5,000.00 -$200.00 0.94340 -$188.68 $1,700.00 0.89000 $1,512.99 $3,400.00 0.83962 $2,854.71 $2,000.00 0.79209 $1,584.19 $100.00 0.74726 $74.73 $837.93 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $837.93 =E7+NPV(0.06,E8:E12) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE PW. b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

DURATECH SHOULD IMPLEMENT THE PROCESS IMPROVEMENT

PROBLEM 5.15 CURRENT ANNUAL INSURANCE PREMIUM = ($700,000/$100)*$1.00 = $7,000 NEW ANNUAL INSURANCE PREMIUM = ($720,000/$100)*$0.40 = $2,880 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

+ CF $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00 $4,120.00

- CF -$20,000.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00

15.00% NET CF (P|F i%,n) -$20,000.00 1.00000 $3,720.00 0.86957 $3,720.00 0.75614 $3,720.00 0.65752 $3,720.00 0.57175 $3,720.00 0.49718 $3,720.00 0.43233 $3,720.00 0.37594 $3,720.00 0.32690 $3,720.00 0.28426 $3,720.00 0.24718 $3,720.00 0.21494 $3,720.00 0.18691 $3,720.00 0.16253 $3,720.00 0.14133 $3,720.00 0.12289 $3,720.00 0.10686 $3,720.00 0.09293 $3,720.00 0.08081 $3,720.00 0.07027 $3,720.00 0.06110

PW OF CF -$20,000.00 $3,234.78 $2,812.85 $2,445.96 $2,126.92 $1,849.50 $1,608.26 $1,398.49 $1,216.07 $1,057.46 $919.53 $799.59 $695.29 $604.60 $525.74 $457.17 $397.54 $345.68 $300.60 $261.39 $227.29 $3,284.71 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $3,284.71 =E10+NPV(0.15,E11:E30) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = $3,284.71 =E10+PV(0.15,20,-E11) SOLUTION USING FACTOR TABLES PW = -$20,000 + $3,720(P|A 15%,20) PW = -$20,000 + $3,720(6.25933) PW = $3,284.71 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

EDDIE SHOULD BUY THE SPRINKLER SYSTEM

PROBLEM 5.16 THE MAXIMUM AMOUNT THAT FABCO SHOULD BE WILLING TO SPEND IS THE AMOUNT THAT SETS THE PW TO ZERO WHICH IS THE PW OF THE SAVINGS. SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF

- CF $0.00

$10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

7.00% NET CF (P|F i%,n) $0.00 1.00000 $10,000.00 0.93458 $10,000.00 0.87344 $10,000.00 0.81630 $10,000.00 0.76290 $10,000.00 0.71299 $10,000.00 0.66634 $10,000.00 0.62275 $10,000.00 0.58201 $10,000.00 0.54393 $10,000.00 0.50835 $10,000.00 0.47509 $10,000.00 0.44401

PW OF CF $0.00 $9,345.79 $8,734.39 $8,162.98 $7,628.95 $7,129.86 $6,663.42 $6,227.50 $5,820.09 $5,439.34 $5,083.49 $4,750.93 $4,440.12 $79,426.86 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $79,426.86 =E10+NPV(0.07,E11:E22) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = $79,426.86 =E10+PV(7%,12,-E11) SOLUTION USING FACTOR TABLES PW = $10,000(P|A 7%,12) PW = $10,000(7.94269) PW = $79,426.90 THE MAXIMUM AMOUNT FABCO SHOULD BE WILLING TO PAY IS $79,426.86

PROBLEM 5.17 YEAR 5 ADDITION = $5,000 COMPUTER SALVAGE VALUE LOAN PAYMENTS = 25000(A|P 15%,3) = 25000(0.43798) = $10,949.50 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5

+ INV CF

- INV CF + LOAN CF - LOAN CF -$100,000.00 $25,000.00 $55,000.00 -$25,000.00 -$10,949.50 $55,000.00 -$25,000.00 -$10,949.50 $55,000.00 -$25,000.00 -$10,949.50 $55,000.00 -$25,000.00 $60,000.00 -$25,000.00

18.00% NET CF (P|F i%,n) PW OF CF -$75,000.00 1.00000 -$75,000.00 $19,050.50 0.84746 $16,144.49 $19,050.50 0.71818 $13,681.77 $19,050.50 0.60863 $11,594.72 $30,000.00 0.51579 $15,473.67 $35,000.00 0.43711 $15,298.82 -$2,806.52 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$2,806.52 =G10+NPV(0.18,G11:G15) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,5,-30000,-5000)-PV(i,3,-19050.50) PW = -$2,806.52 =G10+PV(0.18,5,-G14,-G15+G14)+PV(0.18,3,30000-19050.5) SOLUTION USING FACTOR TABLES PW = -$75,000 + $30,000(P|A 18%,5) - $10,949.50(P|A 18%,3) + $5,000(P|F 18%,5) PW = -$75,000 + $30,000(3.12717) - $10,949.50(2.17427) + $5,000(0.43711) PW = -$2,806.52 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

GALVANIZED PRODUCTS SHOULD NOT PURCHASE THE NEW COMPUTER SYSTEM

PROBLEM 5.18 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

+ CF

- CF -$1,400.00

$0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 -$1,000.00 -$2,000.00 -$3,000.00 $1,400.00

13.50% NET CF (P|F i%,n) -$1,400.00 1.00000 $0.00 0.88106 $500.00 0.77626 $500.00 0.68393 $500.00 0.60258 $500.00 0.53091 $0.00 0.46776 $500.00 0.41213 $600.00 0.36311 $700.00 0.31992 $800.00 0.28187 $900.00 0.24834 -$1,000.00 0.21880 -$2,000.00 0.19278 -$3,000.00 0.16985 $1,400.00 0.14964

PW OF CF -$1,400.00 $0.00 $388.13 $341.97 $301.29 $265.45 $0.00 $206.06 $217.86 $223.94 $225.49 $223.51 -$218.80 -$385.55 -$509.54 $209.50 $89.32 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $89.32 =E7+NPV(0.135,E8:E22) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE PW. b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

QRU SHOULD INVEST

PROBLEM 5.19 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7

+ CF

- CF -$12.00 -$1.00

$5.00 $2.00 $5.00 $5.00 $2.00 $5.00

18.00% NET CF (P|F i%,n) -$12.00 1.00000 -$1.00 0.84746 $5.00 0.71818 $2.00 0.60863 $5.00 0.51579 $5.00 0.43711 $2.00 0.37043 $5.00 0.31393

PW OF CF -$12.00 -$0.85 $3.59 $1.22 $2.58 $2.19 $0.74 $1.57 -$0.96 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$0.96 =E7+NPV(0.18,E8:E14) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE PW. b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

IMAGINEERING SHOULD NOT INVEST

PROBLEM 5.20 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$2.00 -$10.00 -$12.00 -$14.00 -$16.00 -$18.00

$200.00 -$10.00 -$12.00 -$14.00 -$100.00

12.00% NET CF (P|F i%,n) -$2.00 1.00000 -$10.00 0.89286 -$12.00 0.79719 -$14.00 0.71178 -$16.00 0.63552 -$18.00 0.56743 $200.00 0.50663 -$10.00 0.45235 -$12.00 0.40388 -$14.00 0.36061 -$100.00 0.32197

PW OF CF -$2.00 -$8.93 -$9.57 -$9.96 -$10.17 -$10.21 $101.33 -$4.52 -$4.85 -$5.05 -$32.20 $3.87 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $3.87 =E7+NPV(0.12,E8:E17) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE PW. b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

JUPITER'S SHOULD INVEST

PROBLEM 5.21 YEAR 7 ADDITION = $7,500 SYSTEM SALVAGE VALUE LOAN PAYMENTS = 20000*(F|P 8%,1)*(A|P 8%,3) = 20000*(1.08000)*(0.38803) = 8381.45 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6 7

+ INV CF $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $19,500.00

- INV CF + LOAN CF - LOAN CF -$40,000.00 $20,000.00 -$2,000.00 -$2,000.00 -$8,381.45 -$2,000.00 -$8,381.45 -$2,000.00 -$8,381.45 -$2,000.00 -$2,000.00 -$2,000.00

10.00% NET CF (P|F i%,n) PW OF CF -$20,000.00 1.00000 -$20,000.00 $10,000.00 0.90909 $9,090.91 $1,618.55 0.82645 $1,337.64 $1,618.55 0.75131 $1,216.04 $1,618.55 0.68301 $1,105.49 $10,000.00 0.62092 $6,209.21 $10,000.00 0.56447 $5,644.74 $17,500.00 0.51316 $8,980.27 $13,584.31 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $13,584.31 =I10+NPV(0.1,G11:G17) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$20,000 + $10,000(P|A 10%,7) - $8,381.45(P|A 10%,3)(P|F 10%,1) + $7,500(P|F 10%,7) PW = -$20,000 + $10,000(4.86842) - $8,381.45(2.48685)(0.90909) + $7,500(0.51316) PW = $13,584.37 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

AEROTRON ELECTRONICS SHOULD PURCHASE THE WATER FILTRATION SYSTEM

PROBLEM 5.22 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5

+ CF $600.00 $600.00 $700.00 $700.00 $700.00

- CF -$1,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

10.00% NET CF (P|F i%,n) PW OF CF -$1,000.00 1.00000 -$1,000.00 $300.00 0.90909 $272.73 $300.00 0.82645 $247.93 $400.00 0.75131 $300.53 $400.00 0.68301 $273.21 $400.00 0.62092 $248.37 $342.76 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $342.76 =E7+NPV(0.1,E8:E12) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,5,-400) + PV(i,2,100) PW = $342.76 =E7+PV(10%,5,-400)+PV(10%,2,100) SOLUTION USING FACTOR TABLES PW = -$1,000 + $400(P|A 10%,5) - $100(P|A 8%,2) PW = -$1,000 + $400(3.79079) - $100(1.73554) PW = $342.76 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

HOME INNOVATION SHOULD PURSUE THE NEW PRODUCT

PROBLEM 5.23 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3 4 5 6

+ CF $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $3,000.00

- CF -$6,000.00

NET CF -$6,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $3,000.00

8.00% (P|F i%,n) 1.00000 0.92593 0.85734 0.79383 0.73503 0.68058 0.63017

PW OF CF -$6,000.00 $925.93 $857.34 $793.83 $735.03 $680.58 $1,890.51 -$116.78

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$116.78 =E7+NPV(0.08,E8:E13) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-1000 NET CF FOR t=1,6,-2000 NET CF FOR t=6) PW = -$116.78 =E7+PV(8%,6,-1000,-2000) SOLUTION USING FACTOR TABLES PW = -$6,000 + $1,000(P|A 8%,6) + $2,000(P|F 8%,6) PW = -$6,000 + $1,000(4.62288) + $2,000(0.63017) PW = -$116.78 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

MAYBERRY SHOULD NOT IMPLEMENT THE DESIGN CHANGE

<- PW

PROBLEM 5.24 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS

EOY 0 1 2 3

+ CF $30,000.00 $30,000.00 $33,000.00

- CF -$10,000.00 -$25,000.00 -$25,000.00 -$25,000.00

24.00% NET CF (P|F i%,n) -$10,000.00 1.00000 $5,000.00 0.80645 $5,000.00 0.65036 $8,000.00 0.52449

PW OF CF -$10,000.00 $4,032.26 $3,251.82 $4,195.90 $1,479.98 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $1,479.98 =E7+NPV(0.24,E8:E10) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-5000 NET CF FOR t=1,3,-3000 NET CF FOR t=3) PW = $1,479.98 =E7+PV(24%,3,-5000,-3000) SOLUTION USING FACTOR TABLES PW = -$10,000 + $5,000(P|A 24%,3) + $3,000(P|F 24%,3) PW = -$10,000 + $5,000(1.98130) + $3,000(0.52449) PW = $1,479.97 b

DECISION RULE IF PW > 0, ACCEPT; OTHERWISE, REJECT

NANCY SHOULD BUY THE TRUCK

PROBLEM 5.25 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS VENDOR A SOFTWARE EOY 0 1 2 3 4

+ CF

- CF -$380,000.00

$125,000.00 $125,000.00 $125,000.00 $125,000.00

10.00% NET CF (P|F i%,n) -$380,000.00 1.00000 $125,000.00 0.90909 $125,000.00 0.82645 $125,000.00 0.75131 $125,000.00 0.68301

PW OF CF -$380,000.00 $113,636.36 $103,305.79 $93,914.35 $85,376.68 $16,233.18 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = $16,233.18 =E8+NPV(0.1,E9:E12) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = $16,233.18 =E8+PV(0.1,4,-E9) SOLUTION USING FACTOR TABLES PW = -$380,000 + $125,000(P|A 10%,4) PW = -$380,000 + $125,000(3.16987) PW = $16,233.75 VENDOR B SOFTWARE EOY 0 1 2 3 4

+ CF

- CF -$280,000.00

$95,000.00 $95,000.00 $95,000.00 $95,000.00

NET CF (P|F i%,n) -$280,000.00 1.00000 $95,000.00 0.90909 $95,000.00 0.82645 $95,000.00 0.75131 $95,000.00 0.68301

PW OF CF -$280,000.00 $86,363.64 $78,512.40 $71,374.91 $64,886.28 $21,137.22 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $21,137.22 =G32+NPV(0.1,E33:E36) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = $21,137.22 =E32+PV(0.1,4,-E33) SOLUTION USING FACTOR TABLES PW = -$280,000 + $95,000(P|A 10%,4) PW = -$280,000 + $95,000(3.16987) PW = $21,137.65 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST PW

MANUEL'S MANUFACTURING SHOULD BUY FROM VENDOR B

PROBLEM 5.26 ORDER OF INVESTMENTS: B, A SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS VENDOR B SOFTWARE 10.00% EOY + CF - CF NET CF (P|F i%,n) 0 -$280,000.00 -$280,000.00 1.00000 1 $95,000.00 $95,000.00 0.90909 2 $95,000.00 $95,000.00 0.82645 3 $95,000.00 $95,000.00 0.75131 4 $95,000.00 $95,000.00 0.68301

PW OF CF -$280,000.00 $86,363.64 $78,512.40 $71,374.91 $64,886.28 $21,137.22 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $21,137.22 =E8+NPV(0.1,E9:E12) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = $21,137.22 =E8+PV(0.1,4,-E9) SOLUTION USING FACTOR TABLES PW = -$280,000 + $95,000(P|A 10%,4) PW = -$280,000 + $95,000(3.16987) PW = $21,137.65 PW OF B IS GREATER THAN ZERO SO ANALYZE INCREMENTAL CASH FLOWS OF A-B INCREMENTAL ANALYSIS OF A-B EOY 0 1 2 3 4

+ CF

- CF -$100,000.00

$30,000.00 $30,000.00 $30,000.00 $30,000.00

NET CF (P|F i%,n) -$100,000.00 1.00000 $30,000.00 0.90909 $30,000.00 0.82645 $30,000.00 0.75131 $30,000.00 0.68301

PW OF CF -$100,000.00 $27,272.73 $24,793.39 $22,539.44 $20,490.40 -$4,904.04 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = -$4,904.04 =E34+NPV(0.1,E35:E38) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = -$4,904.04 =E34+PV(0.1,4,-E35) SOLUTION USING FACTOR TABLES PW = -$100,000 + $30,000(P|A 10%,4) PW = -$100,000 + $30,000(3.16987) PW = -$4,903.90 PW OF INCREMENT A-B IS NEGATIVE SO REJECT THE INCREMENT; STAY WITH VENDOR B SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, VENDOR B IS RECOMMENDED

PROBLEM 5.27 PW(A) = $30,000 PW(B) = ($1,000 + 0.5X)(P|A 10%,10) FOR NADINE TO BE INDIFFERENT, THE PW MUST BE EQUAL, THEREFORE, ($1,000 + 0.5X)(P|A 10%,10) = $30,000.00 ($1,000 + 0.5X)(6.14457) = $30,000.00 3.07229X = 23,855.43 X = 7,764.7 OR APPROXIMATELY 7,765 UNITS

PROBLEM 5.28 NOTE THAT THE ESTIMATED LIVES ARE DIFFERENT SO A COMMON PLANNING HORIZON MUST BE ESTABLISHED. 10 YEARS IS SELECTED IN THE ANALYSIS BELOW. a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS MODEL 127B EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $29,400.00

- CF -$50,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00

8.00% NET CF (P|F i%,n) -$50,000.00 1.00000 $9,400.00 0.92593 $9,400.00 0.85734 $9,400.00 0.79383 $9,400.00 0.73503 $9,400.00 0.68058 $9,400.00 0.63017 $9,400.00 0.58349 $9,400.00 0.54027 $9,400.00 0.50025 $19,400.00 0.46319

PW OF CF -$50,000.00 $8,703.70 $8,058.98 $7,462.02 $6,909.28 $6,397.48 $5,923.59 $5,484.81 $5,078.53 $4,702.34 $8,985.95 $17,706.70 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = $17,706.70 =E11+NPV(0.08,E12:E21) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-CF FOR t=1,10,-10000) PW = $17,706.70 =E11+PV(0.08,10,-9400,-10000) SOLUTION USING FACTOR TABLES PW = -$50,000 + $9,400(P|A 8%,10) + $10,000(P|F 8%,10) PW = -$50,000 + $9,400(6.7101) + $10,000(0.4632) PW = $17,706.94 MODEL 334A SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00

- CF -$80,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$86,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00

NET CF (P|F i%,n) -$80,000.00 1.00000 $20,000.00 0.92593 $20,000.00 0.85734 $20,000.00 0.79383 $20,000.00 0.73503 -$60,000.00 0.68058 $20,000.00 0.63017 $20,000.00 0.58349 $20,000.00 0.54027 $20,000.00 0.50025 $20,000.00 0.46319

PW OF CF -$80,000.00 $18,518.52 $17,146.78 $15,876.64 $14,700.60 -$40,834.99 $12,603.39 $11,669.81 $10,805.38 $10,004.98 $9,263.87 -$245.03 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$245.03 SOLUTION USING EXCEL'S PV FUNCTIONS PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-INVESTMENT)+PV(i,n,,-PV(I,n,-CF FOR t=6)) PW = -$245.03 =E43+PV(0.08,5,-20000,80000)+PV(0.08,5,,-PV(0.08,5,-20000)) SOLUTION USING FACTOR TABLES PW = -$80,000 - $80,000(P|F 8%,5) + $20,000(P|A 8%,10) PW = -$80,000 - $80,000(0.6806) + $20,000(6.7101) PW = -$246.00 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST PW

OCTAVIA'S BAKERY SHOULD BUY MODEL 127B

PROBLEM 5.29 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS 127B, 334A SINCE "NULL" IS NOT IDENTIFIED AS AN OPTION, 127B BECOMES THE "CURRENT BEST" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 334A - 127B ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

334A -$80,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 -$60,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

127B -$50,000.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $19,400.00

8.00% INCR. CF (P|F i%,n) -$30,000.00 1.00000 $10,600.00 0.92593 $10,600.00 0.85734 $10,600.00 0.79383 $10,600.00 0.73503 -$69,400.00 0.68058 $10,600.00 0.63017 $10,600.00 0.58349 $10,600.00 0.54027 $10,600.00 0.50025 $600.00 0.46319

PW -$30,000.00 $9,814.81 $9,087.79 $8,414.62 $7,791.32 -$47,232.47 $6,679.80 $6,185.00 $5,726.85 $5,302.64 $277.92 -$17,951.73 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INCR INVESTMENT + NPV(i,INCR CF FOR t=1,n) PW = -$17,951.73 =E12+NPV(0.08,E13:E22) SOLUTION USING EXCEL'S PV FUNCTIONS PW = INCR INVESTMENT + PV(i,n,-INCR CF FOR t=1,10000)+PV(i,5,,80000) PW = -$17,951.73 =E12+PV(0.08,10,-E13,10000)+PV(8%,5,,80000) SOLUTION USING FACTOR TABLES PW = -$30,000 + $10,600(P|A 8%,10) - $80,000(P|F 8%,5) - $10,000(P|F 8%,10) PW = -$30,000 + $10,600(6.71008) - $80,000(0.68058) - $10,000(0.46319) PW = -$17,951.45 SINCE THE PW OF THE INCREMENT IS NEGATIVE, THE INCREMENTAL INVESTMENT IS REJECTED 127B REMAINS CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, 127B IS PREFERRED

PROBLEM 5.30 HEAT LOSS WITH NO INSULATION = $1.50/YR/FT HEAT LOSS WITH 1 INCH INSULATION IS 1.50 * (1 - 0.89) = $0.165/YR/FT HEAT LOSS WITH 2 INCH INSULATION IS 1.50 * (1 - 0.92) = $0.12/YR/FT

NO INSULATION ANNUAL HEAT LOSS = 1.50 * 250,000 = $375,000 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS 10.00% EOY + CF - CF NET CF (P|F i%,n) 0 $0.00 $0.00 1.00000 1 $0.00 -$375,000.00 -$375,000.00 0.90909 2 $0.00 -$375,000.00 -$375,000.00 0.82645 3 $0.00 -$375,000.00 -$375,000.00 0.75131 4 $0.00 -$375,000.00 -$375,000.00 0.68301 5 $0.00 -$375,000.00 -$375,000.00 0.62092 6 $0.00 -$375,000.00 -$375,000.00 0.56447 7 $0.00 -$375,000.00 -$375,000.00 0.51316 8 $0.00 -$375,000.00 -$375,000.00 0.46651 9 $0.00 -$375,000.00 -$375,000.00 0.42410 10 $0.00 -$375,000.00 -$375,000.00 0.38554

PW OF CF $0.00 -$340,909.09 -$309,917.36 -$281,743.05 -$256,130.05 -$232,845.50 -$211,677.72 -$192,434.29 -$174,940.27 -$159,036.61 -$144,578.73 -$2,304,212.66 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$2,304,212.66 =E14+NPV(0.1,E15:E24) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = -$2,304,212.66 =E14+PV(0.1,10,-E15) SOLUTION USING FACTOR TABLES PW = -$375,000(P|A 10%,10) PW = -$375,000(6.1446) PW = -$2,304,225.00 1 INCH INSULATION ANNUAL HEAT LOSS = 0.165 * 250,000 = $41,250 INSULATION COST = 0.40 * 250,000 = $100,000 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

- CF -$100,000.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00

NET CF (P|F i%,n) -$100,000.00 1.00000 -$41,250.00 0.90909 -$41,250.00 0.82645 -$41,250.00 0.75131 -$41,250.00 0.68301 -$41,250.00 0.62092 -$41,250.00 0.56447 -$41,250.00 0.51316 -$41,250.00 0.46651 -$41,250.00 0.42410 -$41,250.00 0.38554

PW OF CF -$100,000.00 -$37,500.00 -$34,090.91 -$30,991.74 -$28,174.31 -$25,613.00 -$23,284.55 -$21,167.77 -$19,243.43 -$17,494.03 -$15,903.66

-$353,463.39 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$353,463.39 =E48+NPV(0.1,E49:E58) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = -$353,463.39 =E48+PV(0.1,10,-E49) SOLUTION USING FACTOR TABLES PW = -$100,000 - $41,250(P|A 10%,10) PW = -$100,000 - $41,250(6.1446) PW = -$353,464.75 2 INCH INSULATION ANNUAL HEAT LOSS = 0.12 * 250,000 = $30,000 INSULATION COST = 0.85 * 250,000 = $212,500 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

- CF -$212,500.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00

NET CF (P|F i%,n) -$212,500.00 1.00000 -$30,000.00 0.90909 -$30,000.00 0.82645 -$30,000.00 0.75131 -$30,000.00 0.68301 -$30,000.00 0.62092 -$30,000.00 0.56447 -$30,000.00 0.51316 -$30,000.00 0.46651 -$30,000.00 0.42410 -$30,000.00 0.38554

PW OF CF -$212,500.00 -$27,272.73 -$24,793.39 -$22,539.44 -$20,490.40 -$18,627.64 -$16,934.22 -$15,394.74 -$13,995.22 -$12,722.93 -$11,566.30 -$396,837.01 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = -$396,837.01 =E82+NPV(0.1,E83:E92) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,n) PW = -$396,837.01 =E82+PV(0.1,10,-E83) SOLUTION USING FACTOR TABLES PW = -$212,500 - $30,000(P|A 10%,10) PW = -$212,500 - $30,000(6.1446) PW = -$396,838.00 THE HIGHEST PRESENT WORTH IS THE 1 INCH INSULATION, THEREFORE, IT IS RECOMMENDED.

PROBLEM 5.31 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, 1-INCH, 2-INCH NULL BECOMES THE "CURRENT BEST" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 1-INCH - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

10.00% 1-INCH NULL INCR. CF (P|F i%,n) -$100,000.00 $0.00 -$100,000.00 1.00000 -$41,250.00 -$375,000.00 $333,750.00 0.90909 -$41,250.00 -$375,000.00 $333,750.00 0.82645 -$41,250.00 -$375,000.00 $333,750.00 0.75131 -$41,250.00 -$375,000.00 $333,750.00 0.68301 -$41,250.00 -$375,000.00 $333,750.00 0.62092 -$41,250.00 -$375,000.00 $333,750.00 0.56447 -$41,250.00 -$375,000.00 $333,750.00 0.51316 -$41,250.00 -$375,000.00 $333,750.00 0.46651 -$41,250.00 -$375,000.00 $333,750.00 0.42410 -$41,250.00 -$375,000.00 $333,750.00 0.38554

PW -$100,000.00 $303,409.09 $275,826.45 $250,751.31 $227,955.74 $207,232.49 $188,393.17 $171,266.52 $155,696.84 $141,542.58 $128,675.07 $1,950,749.27 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW(INCR CF) = INCR INVESTMENT + NPV(i,INCR CF FOR t=1,n) PW = $1,950,749.27 =E12+NPV(0.1,E13:E22) SOLUTION USING EXCEL'S PV FUNCTION PW(INCR CF) = INCR INVESTMENT + PV(i,n,-INCR CF FOR t=1,n) PW(INCR CF) = $1,950,749.27 =E12+PV(0.1,10,-E13) SOLUTION USING FACTOR TABLES PW = -$100,000 + $333,750(P|A 10%,10) PW = -$100,000 + $333,750(6.14457) PW = $1,950,750.24

SINCE THE PW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. 1-INCH BECOMES THE NEW CURRENT BEST 2-INCH BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR 2-INCH - 1-INCH ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

2-INCH 1-INCH INCR. CF (P|F i%,n) -$212,500.00 -$100,000.00 -$112,500.00 1.00000 -$30,000.00 -$41,250.00 $11,250.00 0.90909 -$30,000.00 -$41,250.00 $11,250.00 0.82645 -$30,000.00 -$41,250.00 $11,250.00 0.75131 -$30,000.00 -$41,250.00 $11,250.00 0.68301 -$30,000.00 -$41,250.00 $11,250.00 0.62092 -$30,000.00 -$41,250.00 $11,250.00 0.56447 -$30,000.00 -$41,250.00 $11,250.00 0.51316 -$30,000.00 -$41,250.00 $11,250.00 0.46651 -$30,000.00 -$41,250.00 $11,250.00 0.42410 -$30,000.00 -$41,250.00 $11,250.00 0.38554

PW -$112,500.00 $10,227.27 $9,297.52 $8,452.29 $7,683.90 $6,985.36 $6,350.33 $5,773.03 $5,248.21 $4,771.10 $4,337.36 -$43,373.62 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INCR INVESTMENT + NPV(i,INCR CF FOR t=1,n) PW = -$43,373.62 =E47+NPV(0.1,E48:E57) SOLUTION USING EXCEL'S PV FUNCTION

PW = INCR INVESTMENT + PV(i,n,-INCR CF FOR t=1,n) PW = -$43,373.62 =E47+PV(0.1,10,-E48) SOLUTION USING FACTOR TABLES PW = -$112,500 + $11,250(P|A 10%,10) PW = -$112,500 + $11,250(6.14457) PW = -$43,373.59

SINCE THE PW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. 1-INCH REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, 1-INCH IS RECOMMENDED.

PROBLEM 5.32 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS LAGRANGE EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF

- CF -$1,260,000.00

$480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

15.00% NET CF (P|F i%,n) -$1,260,000.00 1.00000 $480,000.00 0.86957 $480,000.00 0.75614 $480,000.00 0.65752 $480,000.00 0.57175 $480,000.00 0.49718 $480,000.00 0.43233 $480,000.00 0.37594 $480,000.00 0.32690 $480,000.00 0.28426 $480,000.00 0.24718 $480,000.00 0.21494 $480,000.00 0.18691

PW OF CF -$1,260,000.00 $417,391.30 $362,948.96 $315,607.79 $274,441.56 $238,644.83 $207,517.25 $180,449.78 $156,912.85 $136,445.96 $118,648.66 $103,172.75 $89,715.43 $1,341,897.12 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = $1,341,897.12 SOLUTION USING FACTOR TABLES PW = -$1,260,000 + $480,000(P|A 15%,12) PW = -$1,260,000 + $480,000(5.42062) PW = $1,341,897.60 AUBURN EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

- CF -$1,000,000.00

NET CF (P|F i%,n) -$1,000,000.00 1.00000 $410,000.00 0.86957 $410,000.00 0.75614 $410,000.00 0.65752 $410,000.00 0.57175 $410,000.00 0.49718 $410,000.00 0.43233 $410,000.00 0.37594 $410,000.00 0.32690 $410,000.00 0.28426 $410,000.00 0.24718 $410,000.00 0.21494 $410,000.00 0.18691

PW OF CF -$1,000,000.00 $356,521.74 $310,018.90 $269,581.66 $234,418.83 $203,842.46 $177,254.31 $154,134.19 $134,029.73 $116,547.59 $101,345.73 $88,126.72 $76,631.93 $1,222,453.79 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = $1,222,453.79 =E36+NPV(0.15,E37:E48) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1)

PW =

$1,222,453.79 =E36+PV(0.15,12,-E37)

SOLUTION USING FACTOR TABLES PW = -$1,000,000 + $410,000(P|A 15%,12) PW = -$1,000,000 + $410,000(5.42062) PW = $1,222,454.20 ANNISTON EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF

- CF -$1,620,000.00

$520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00

NET CF (P|F i%,n) -$1,620,000.00 1.00000 $520,000.00 0.86957 $520,000.00 0.75614 $520,000.00 0.65752 $520,000.00 0.57175 $520,000.00 0.49718 $520,000.00 0.43233 $520,000.00 0.37594 $520,000.00 0.32690 $520,000.00 0.28426 $520,000.00 0.24718 $520,000.00 0.21494 $520,000.00 0.18691

PW OF CF -$1,620,000.00 $452,173.91 $393,194.71 $341,908.44 $297,311.69 $258,531.90 $224,810.35 $195,487.26 $169,988.92 $147,816.45 $128,536.05 $111,770.48 $97,191.72 $1,198,721.88 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $1,198,721.88 =E68+NPV(0.15,E69:E80) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $1,198,721.88 =E68+PV(0.15,12,-E69) SOLUTION USING FACTOR TABLES PW = -$1,620,000 + $520,000(P|A 15%,12) PW = -$1,620,000 + $520,000(5.42062) PW = $1,198,722.40 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST PW

QUANTUM LOGISTICS SHOULD BUILD IN LAGRANGE

PROBLEM 5.33 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, AUBURN, LAGRANGE, ANNISTON NULL BECOMES THE "CURRENT BEST" AND AUBURN THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR AUBURN - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

AUBURN -$1,000,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

15.00% NULL INCR. CF (P|F i%,n) PW $0.00 -$1,000,000.00 1.00000 -$1,000,000.00 $0.00 $410,000.00 0.86957 $356,521.74 $0.00 $410,000.00 0.75614 $310,018.90 $0.00 $410,000.00 0.65752 $269,581.66 $0.00 $410,000.00 0.57175 $234,418.83 $0.00 $410,000.00 0.49718 $203,842.46 $0.00 $410,000.00 0.43233 $177,254.31 $0.00 $410,000.00 0.37594 $154,134.19 $0.00 $410,000.00 0.32690 $134,029.73 $0.00 $410,000.00 0.28426 $116,547.59 $0.00 $410,000.00 0.24718 $101,345.73 $0.00 $410,000.00 0.21494 $88,126.72 $0.00 $410,000.00 0.18691 $76,631.93 $1,222,453.79 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INCR INVESTMENT + NPV(i,INCR CF FOR t=1,n) PW = $1,222,453.79 =E12+NPV(0.15,E13:E24) SOLUTION USING EXCEL'S PV FUNCTION PW = INCR INVESTMENT + PV(i,n,-INCR CF FOR t=1,n) PW = $1,222,453.79 =E12+PV(0.15,12,-E13) SOLUTION USING FACTOR TABLES PW = -$1,000,000 + $410,000(P|A 15%,12) PW = -$1,000,000 + $410,000(5.42062) PW = $1,222,454.20 SINCE THE PW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. AUBURN BECOMES THE NEW CURRENT BEST LAGRANGE BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR LAGRANGE - AUBURN ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

LAGRANGE AUBURN -$1,260,000.00 -$1,000,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00 $480,000.00 $410,000.00

INCR. CF (P|F i%,n) -$260,000.00 1.00000 $70,000.00 0.86957 $70,000.00 0.75614 $70,000.00 0.65752 $70,000.00 0.57175 $70,000.00 0.49718 $70,000.00 0.43233 $70,000.00 0.37594 $70,000.00 0.32690 $70,000.00 0.28426 $70,000.00 0.24718 $70,000.00 0.21494 $70,000.00 0.18691

PW -$260,000.00 $60,869.57 $52,930.06 $46,026.14 $40,022.73 $34,802.37 $30,262.93 $26,315.59 $22,883.12 $19,898.37 $17,302.93 $15,046.03 $13,083.50 $119,443.33 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INCR INVESTMENT + NPV(i,INCR CF FOR t=1,n) PW = $119,443.33 =E48+NPV(0.15,E49:E60)

PROBLEM 5.34 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS MACHINE 7745 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

$1,000.00

- CF -$10,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

6.00% NET CF (P|F i%,n) -$10,000.00 1.00000 -$300.00 0.94340 -$300.00 0.89000 -$300.00 0.83962 -$300.00 0.79209 -$300.00 0.74726 -$300.00 0.70496 -$300.00 0.66506 -$300.00 0.62741 -$300.00 0.59190 $700.00 0.55839

PW OF CF -$10,000.00 -$283.02 -$267.00 -$251.89 -$237.63 -$224.18 -$211.49 -$199.52 -$188.22 -$177.57 $390.88 -$11,649.63 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = -$11,649.63 =E8+NPV(0.06,E9:E18) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-1000) PW = -$11,649.63 =E8+PV(0.06,10,-E9,-1000) SOLUTION USING FACTOR TABLES PW = -$10,000 - $300(P|A 6%,10) + $1,000(P|F 6%,10) PW = -$10,000 - $300(7.36009) + $1,000(0.55839) PW = -$11,649.64 MACHINE A37Y EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$8,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

NET CF (P|F i%,n) -$8,000.00 1.00000 -$300.00 0.94340 -$300.00 0.89000 -$300.00 0.83962 -$300.00 0.79209 -$300.00 0.74726 -$300.00 0.70496 -$300.00 0.66506 -$300.00 0.62741 -$300.00 0.59190 -$300.00 0.55839

PW OF CF -$8,000.00 -$283.02 -$267.00 -$251.89 -$237.63 -$224.18 -$211.49 -$199.52 -$188.22 -$177.57 -$167.52 -$10,208.03 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION

PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$10,208.03 =E38+NPV(0.06,E39:E48) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = -$10,208.03 =E38+PV(0.06,10,-E39) SOLUTION USING FACTOR TABLES PW = -$8,000 - $300(P|A 6%,10) PW = -$8,000 - $300(7.36009) PW = -$10,208.03 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST PW

MACHINE A37Y SHOULD BE PURCHASED

PROBLEM 5.35 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS MACHINE A37Y, MACHINE 7745 NULL IS NOT AN OPTION SINCE THE PROBLEM STATES THAT A MACHINE MUST BE PURCHASED A37Y BECOMES THE "CURRENT BEST" AND 7745 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 7745 - A37Y ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

6.00% 7745 A37Y INCR. CF (P|F i%,n) PW -$10,000.00 -$8,000.00 -$2,000.00 1.00000 -$2,000.00 -$300.00 -$300.00 $0.00 0.94340 $0.00 -$300.00 -$300.00 $0.00 0.89000 $0.00 -$300.00 -$300.00 $0.00 0.83962 $0.00 -$300.00 -$300.00 $0.00 0.79209 $0.00 -$300.00 -$300.00 $0.00 0.74726 $0.00 -$300.00 -$300.00 $0.00 0.70496 $0.00 -$300.00 -$300.00 $0.00 0.66506 $0.00 -$300.00 -$300.00 $0.00 0.62741 $0.00 -$300.00 -$300.00 $0.00 0.59190 $0.00 $700.00 -$300.00 $1,000.00 0.55839 $558.39 -$1,441.61 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INCR INVESTMENT + NPV(i,INCR CF FOR t=1,n) PW = -$1,441.61 =E13+NPV(0.06,E14:E23) SOLUTION USING EXCEL'S PV FUNCTION PW = INCR INVESTMENT + PV(i,n,-INCR CF FOR t=1,-INCR CF FOR t=n) PW = -$1,441.61 =E13+PV(0.06,10,,-E23) SOLUTION USING FACTOR TABLES PW = -$2,000 + $1,000(P|F 6%,10) PW = -$2,000 + $1,000(0.52679) PW = -$1,473.21 SINCE THE PW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. A37Y REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, A37Y IS RECOMMENDED.

PROBLEM 5.36 A COMMON PLANNING HORIZON TO 24 YEARS IS USED IN THE ANALYSIS a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS STRUCTURE Y EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

+ CF

- CF -$4,500.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$5,500.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00

5.00% NET CF (P|F i%,n) PW OF CF -$4,500.00 1.00000 -$4,500.00 -$1,000.00 0.95238 -$952.38 -$1,000.00 0.90703 -$907.03 -$1,000.00 0.86384 -$863.84 -$1,000.00 0.82270 -$822.70 -$1,000.00 0.78353 -$783.53 -$1,000.00 0.74622 -$746.22 -$1,000.00 0.71068 -$710.68 -$1,000.00 0.67684 -$676.84 -$1,000.00 0.64461 -$644.61 -$1,000.00 0.61391 -$613.91 -$1,000.00 0.58468 -$584.68 -$5,500.00 0.55684 -$3,062.61 -$1,000.00 0.53032 -$530.32 -$1,000.00 0.50507 -$505.07 -$1,000.00 0.48102 -$481.02 -$1,000.00 0.45811 -$458.11 -$1,000.00 0.43630 -$436.30 -$1,000.00 0.41552 -$415.52 -$1,000.00 0.39573 -$395.73 -$1,000.00 0.37689 -$376.89 -$1,000.00 0.35894 -$358.94 -$1,000.00 0.34185 -$341.85 -$1,000.00 0.32557 -$325.57 -$1,000.00 0.31007 -$310.07 -$20,804.41 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$20,804.41 =E10+NPV(0.05,E11:E34) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1)+PV(i,12,,4500) PW = -$20,804.41 =E38+PV(0.06,10,-E39) SOLUTION USING FACTOR TABLES PW = -$4,500 - $1,000(P|A 5%,24) - $4,500(P|F 5%,12) PW = -$4,500 - $1,000(13.79864) - $4,500(0.55684) PW = -$20,804.42 STRUCTURE Z

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$10,000.00 -$10,000.00 1.00000 -$10,000.00 -$720.00 -$720.00 0.95238 -$685.71 -$720.00 -$720.00 0.90703 -$653.06 -$720.00 -$720.00 0.86384 -$621.96 -$720.00 -$720.00 0.82270 -$592.35 -$720.00 -$720.00 0.78353 -$564.14 -$720.00 -$720.00 0.74622 -$537.28 -$720.00 -$720.00 0.71068 -$511.69 -$720.00 -$720.00 0.67684 -$487.32 -$720.00 -$720.00 0.64461 -$464.12 -$720.00 -$720.00 0.61391 -$442.02 -$720.00 -$720.00 0.58468 -$420.97 -$720.00 -$720.00 0.55684 -$400.92 -$720.00 -$720.00 0.53032 -$381.83 -$720.00 -$720.00 0.50507 -$363.65 -$720.00 -$720.00 0.48102 -$346.33 -$720.00 -$720.00 0.45811 -$329.84 -$720.00 -$720.00 0.43630 -$314.13 -$720.00 -$720.00 0.41552 -$299.17 -$720.00 -$720.00 0.39573 -$284.93 -$720.00 -$720.00 0.37689 -$271.36 -$720.00 -$720.00 0.35894 -$258.44 -$720.00 -$720.00 0.34185 -$246.13 -$720.00 -$720.00 0.32557 -$234.41 $1,800.00 -$720.00 $1,080.00 0.31007 $334.87 -$19,376.90 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = -$19,376.90 SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1)+PV(i,24,,-1800) PW = -$19,376.90 =E38+PV(0.06,10,-E39) SOLUTION USING FACTOR TABLES PW = -$10,000 - $720(P|A 5%,24) + $1,800(P|F 5%,24) PW = -$10,000 - $720(13.79864) + $1,800(0.31007) PW = -$19,376.89 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST PW

THE MILITARY BASE SHOULD SELECT STRUCTURE Z

PROBLEM 5.37 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS PROJECT A EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

12.00% + CF - CF NET CF (P|F i%,n) PW OF CF -$50,000.00 -$50,000.00 1.00000 -$50,000.00 $20,000.00 -$12,500.00 $7,500.00 0.89286 $6,696.43 $20,000.00 -$12,500.00 $7,500.00 0.79719 $5,978.95 $20,000.00 -$12,500.00 $7,500.00 0.71178 $5,338.35 $20,000.00 -$12,500.00 $7,500.00 0.63552 $4,766.39 $20,000.00 -$12,500.00 $7,500.00 0.56743 $4,255.70 $20,000.00 -$12,500.00 $7,500.00 0.50663 $3,799.73 $20,000.00 -$12,500.00 $7,500.00 0.45235 $3,392.62 $20,000.00 -$12,500.00 $7,500.00 0.40388 $3,029.12 $20,000.00 -$12,500.00 $7,500.00 0.36061 $2,704.58 $20,000.00 -$12,500.00 $7,500.00 0.32197 $2,414.80 $20,000.00 -$12,500.00 $7,500.00 0.28748 $2,156.07 $20,000.00 -$12,500.00 $7,500.00 0.25668 $1,925.06 $20,000.00 -$12,500.00 $7,500.00 0.22917 $1,718.81 $20,000.00 -$12,500.00 $7,500.00 0.20462 $1,534.65 $20,000.00 -$12,500.00 $7,500.00 0.18270 $1,370.22 $20,000.00 -$12,500.00 $7,500.00 0.16312 $1,223.41 $20,000.00 -$12,500.00 $7,500.00 0.14564 $1,092.33 $20,000.00 -$12,500.00 $7,500.00 0.13004 $975.30 $20,000.00 -$12,500.00 $7,500.00 0.11611 $870.80 $20,000.00 -$12,500.00 $7,500.00 0.10367 $777.50 $6,020.83 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $6,020.83 =E8+NPV(0.12,E9:E28) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $6,020.83 =E8+PV(0.12,20,-E9) SOLUTION USING FACTOR TABLES PW = -$50,000 + $7,500(P|A 12,20) PW = -$50,000 + $7,500(7.46944) PW = $6,020.80 PROJECT B EOY 0 1 2 3

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$75,000.00 -$75,000.00 1.00000 -$75,000.00 $28,000.00 -$18,000.00 $10,000.00 0.89286 $8,928.57 $28,000.00 -$18,000.00 $10,000.00 0.79719 $7,971.94 $28,000.00 -$18,000.00 $10,000.00 0.71178 $7,117.80

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00 $28,000.00 -$18,000.00

$10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

0.63552 0.56743 0.50663 0.45235 0.40388 0.36061 0.32197 0.28748 0.25668 0.22917 0.20462 0.18270 0.16312 0.14564 0.13004 0.11611 0.10367

$6,355.18 $5,674.27 $5,066.31 $4,523.49 $4,038.83 $3,606.10 $3,219.73 $2,874.76 $2,566.75 $2,291.74 $2,046.20 $1,826.96 $1,631.22 $1,456.44 $1,300.40 $1,161.07 $1,036.67 -$305.56 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = -$305.56 =E48+NPV(0.12,E49:E68) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = -$305.56 =E48+PV(0.12,20,-E49) SOLUTION USING FACTOR TABLES PW = -$75,000 + $10,000(P|A 12,20) PW = -$75,000 + $10,000(7.46944) PW = -$305.60 b

TEMPURA SHOULD PURSUE PROJECT A

PROBLEM 5.38 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS POLISHER 1 EOY 0 1 2 3 4 5 6 7 8 9 10

15.00% + CF - CF NET CF (P|F i%,n) PW OF CF -$20,000.00 -$20,000.00 1.00000 -$20,000.00 $4,465.00 $4,465.00 0.86957 $3,882.61 $4,465.00 $4,465.00 0.75614 $3,376.18 $4,465.00 $4,465.00 0.65752 $2,935.81 $4,465.00 $4,465.00 0.57175 $2,552.88 $4,465.00 $4,465.00 0.49718 $2,219.89 $4,465.00 $4,465.00 0.43233 $1,930.34 $4,465.00 $4,465.00 0.37594 $1,678.56 $4,465.00 $4,465.00 0.32690 $1,459.62 $4,465.00 $4,465.00 0.28426 $1,269.23 $4,465.00 $4,465.00 0.24718 $1,103.68 $2,408.80 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $2,408.80 =E8+NPV(0.15,E9:E18) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-INCR CF FOR t=n) PW = $2,408.80 =E8+PV(0.15,10,-E9) SOLUTION USING FACTOR TABLES PW = -$20,000 + $4,465(P|A 15,10) PW = -$20,000 + $4,465(5.01877) PW = $2,408.81

POLISHER 2 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$10,000.00 -$10,000.00 1.00000 -$10,000.00 $1,770.00 $1,770.00 0.86957 $1,539.13 $1,770.00 $1,770.00 0.75614 $1,338.37 $1,770.00 $1,770.00 0.65752 $1,163.80 $1,770.00 $1,770.00 0.57175 $1,012.00 $1,770.00 $1,770.00 0.49718 $880.00 $1,770.00 $1,770.00 0.43233 $765.22 $1,770.00 $1,770.00 0.37594 $665.41 $1,770.00 $1,770.00 0.32690 $578.62 $1,770.00 $1,770.00 0.28426 $503.14 $1,770.00 $1,770.00 0.24718 $437.52 -$1,116.78 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$1,116.78 =E39+NPV(0.15,E40:E49) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-INCR CF FOR t=n) PW = -$1,116.78 =E39+PV(0.15,10,-E40) SOLUTION USING FACTOR TABLES PW = -$10,000 + $1,770(P|A 15,10) PW = -$10,000 + $1,770(5.01877) PW = -$1,116.78

POLISHER 3 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$15,000.00 -$15,000.00 1.00000 -$15,000.00 $3,580.00 $3,580.00 0.86957 $3,113.04 $3,580.00 $3,580.00 0.75614 $2,706.99 $3,580.00 $3,580.00 0.65752 $2,353.91 $3,580.00 $3,580.00 0.57175 $2,046.88 $3,580.00 $3,580.00 0.49718 $1,779.89 $3,580.00 $3,580.00 0.43233 $1,547.73 $3,580.00 $3,580.00 0.37594 $1,345.85 $3,580.00 $3,580.00 0.32690 $1,170.31 $3,580.00 $3,580.00 0.28426 $1,017.66 $3,580.00 $3,580.00 0.24718 $884.92 $2,967.19 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,CF FOR t=1,n) PW = $2,967.19 =E70+NPV(0.15,E71:E80) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-INCR CF FOR t=n) PW = $2,967.19 =E70+PV(0.15,10,-E71) SOLUTION USING FACTOR TABLES PW = -$15,000 + $3,580(P|A 15,10) PW = -$15,000 + $3,580(5.01877) PW = $2,967.20

FINAL FINISHING SHOULD PURCHASE POLISHER 3

PROBLEM 5.39 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS A001 EOY 0 1 2 3 4

+ CF

- CF -$210.00

$80.00 $90.00 $100.00 $110.00

10.00% NET CF (P|F i%,n) PW OF CF -$210.00 1.00000 -$210.00 $80.00 0.90909 $72.73 $90.00 0.82645 $74.38 $100.00 0.75131 $75.13 $110.00 0.68301 $75.13 $87.37 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $87.37 =E8+NPV(0.1,E9:E12) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$210 + $80(P|A 10%,4) + $10(P|G 10%,4) PW = -$210 + $80(3.16987) + $10(4.37812) PW = $87.37

B002 EOY 0 1 2 3 4

+ CF $60.00 $60.00 $60.00 $70.00

- CF -$110.00

NET CF (P|F i%,n) PW OF CF -$110.00 1.00000 -$110.00 $60.00 0.90909 $54.55 $60.00 0.82645 $49.59 $60.00 0.75131 $45.08 $70.00 0.68301 $47.81 $87.02 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $87.02 =E32+NPV(0.1,E33:E36) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-INCR CF FOR t=n) PW = $87.02 =E32+PV(0.1,4,-E33,-10) SOLUTION USING FACTOR TABLES PW = -$110 + $60(P|A 10%,4) + $10(P|F 10%,4) PW = -$110 + $60(3.16987) + $10(0.68301) PW = $87.02

C003 EOY 0 1 2 3 4

+ CF $80.00 $80.00 $80.00 $80.00

- CF -$160.00

NET CF (P|F i%,n) PW OF CF -$160.00 1.00000 -$160.00 $80.00 0.90909 $72.73 $80.00 0.82645 $66.12 $80.00 0.75131 $60.11 $80.00 0.68301 $54.64 $93.59 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $93.59 =E57+NPV(0.1,E58:E61) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $93.59 =E57+PV(0.1,4,-E58) SOLUTION USING FACTOR TABLES PW = -$160 + $80(P|A 10%,4) PW = -$160 + $80(3.16987) PW = $93.59

XANADU SHOULD ACCEPT ALTERNATIVE C003

PROBLEM 5.40 THE STUDENT IS EXPECTED TO DEDUCE THAT THE SAVINGS ACCOUNT INTEREST RATE, 12%/YR COMPOUNDED MONTHLY, SHOULD BE USED FOR MARR. THIS LEADS TO A PERIOD INTEREST RATE OF 1% PER MONTH. a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS SAVINGS CERTIFICATE EOM 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

1.00% + CF - CF NET CF (P|F i%,n) PW OF CF -$12,000.00 -$12,000.00 1.00000 -$12,000.00 $100.00 $100.00 0.99010 $99.01 $100.00 $100.00 0.98030 $98.03 $100.00 $100.00 0.97059 $97.06 $100.00 $100.00 0.96098 $96.10 $100.00 $100.00 0.95147 $95.15 $100.00 $100.00 0.94205 $94.20 $100.00 $100.00 0.93272 $93.27 $100.00 $100.00 0.92348 $92.35 $100.00 $100.00 0.91434 $91.43 $100.00 $100.00 0.90529 $90.53 $100.00 $100.00 0.89632 $89.63 $100.00 $100.00 0.88745 $88.74 $100.00 $100.00 0.87866 $87.87 $100.00 $100.00 0.86996 $87.00 $100.00 $100.00 0.86135 $86.13 $100.00 $100.00 0.85282 $85.28 $100.00 $100.00 0.84438 $84.44 $100.00 $100.00 0.83602 $83.60 $100.00 $100.00 0.82774 $82.77 $100.00 $100.00 0.81954 $81.95 $100.00 $100.00 0.81143 $81.14 $100.00 $100.00 0.80340 $80.34 $100.00 $100.00 0.79544 $79.54 $100.00 $100.00 0.78757 $78.76 $100.00 $100.00 0.77977 $77.98 $100.00 $100.00 0.77205 $77.20 $100.00 $100.00 0.76440 $76.44 $100.00 $100.00 0.75684 $75.68 $100.00 $100.00 0.74934 $74.93 $100.00 $100.00 0.74192 $74.19 $100.00 $100.00 0.73458 $73.46 $100.00 $100.00 0.72730 $72.73 $100.00 $100.00 0.72010 $72.01 $100.00 $100.00 0.71297 $71.30 $100.00 $100.00 0.70591 $70.59 $100.00 $100.00 0.69892 $69.89 $100.00 $100.00 0.69200 $69.20 $100.00 $100.00 0.68515 $68.52 $100.00 $100.00 0.67837 $67.84 $100.00 $100.00 0.67165 $67.17 $100.00 $100.00 0.66500 $66.50 $100.00 $100.00 0.65842 $65.84 $100.00 $100.00 0.65190 $65.19 $100.00 $100.00 0.64545 $64.54 $100.00 $100.00 0.63905 $63.91 $100.00 $100.00 0.63273 $63.27

47 48 49 50 51 52 53 54 55 56 57 58 59 60

$100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $13,100.00

0.62646 0.62026 0.61412 0.60804 0.60202 0.59606 0.59016 0.58431 0.57853 0.57280 0.56713 0.56151 0.55595 0.55045

$62.65 $62.03 $61.41 $60.80 $60.20 $59.61 $59.02 $58.43 $57.85 $57.28 $56.71 $56.15 $55.60 $7,210.89 -$348.65 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$348.65 =E12+NPV(0.01,E13:E72) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-13000) PW = -$348.65 =E12+PV(0.01,60,-E13,-13000) SOLUTION USING FACTOR TABLES PW = -$12,000 + $100(P|A 1%,60) + $13,000(P|F 1%,60) PW = -$12,000 + $100(44.95504) + $13,000(0.55045) PW = -$348.65

RACE HORSE EOM 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$12,000.00 -$12,000.00 1.00000 -$12,000.00 $0.00 $0.00 0.99010 $0.00 $0.00 $0.00 0.98030 $0.00 $0.00 $0.00 0.97059 $0.00 $0.00 $0.00 0.96098 $0.00 $0.00 $0.00 0.95147 $0.00 $0.00 $0.00 0.94205 $0.00 $0.00 $0.00 0.93272 $0.00 $0.00 $0.00 0.92348 $0.00 $0.00 $0.00 0.91434 $0.00 $0.00 $0.00 0.90529 $0.00 $0.00 $0.00 0.89632 $0.00 $0.00 $0.00 0.88745 $0.00 $0.00 $0.00 0.87866 $0.00 $0.00 $0.00 0.86996 $0.00 $0.00 $0.00 0.86135 $0.00 $0.00 $0.00 0.85282 $0.00 $0.00 $0.00 0.84438 $0.00 $0.00 $0.00 0.83602 $0.00 $0.00 $0.00 0.82774 $0.00 $0.00 $0.00 0.81954 $0.00 $0.00 $0.00 0.81143 $0.00 $0.00 $0.00 0.80340 $0.00 $0.00 $0.00 0.79544 $0.00 $0.00 $0.00 0.78757 $0.00

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.77977 $0.00 0.77205 $0.00 0.76440 $0.00 0.75684 $0.00 0.74934 $0.00 0.74192 $0.00 0.73458 $0.00 0.72730 $0.00 0.72010 $0.00 0.71297 $0.00 0.70591 $0.00 0.69892 $0.00 0.69200 $0.00 0.68515 $0.00 0.67837 $0.00 0.67165 $0.00 0.66500 $0.00 0.65842 $0.00 0.65190 $0.00 0.64545 $0.00 0.63905 $0.00 0.63273 $0.00 0.62646 $0.00 0.62026 $0.00 0.61412 $0.00 0.60804 $0.00 0.60202 $0.00 0.59606 $0.00 0.59016 $0.00 0.58431 $0.00 0.57853 $0.00 0.57280 $0.00 0.56713 $0.00 0.56151 $0.00 0.55595 $0.00 0.55045 $11,008.99 -$991.01 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$991.01 =E93+NPV(0.01,E94:E153) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,,-NET CF FOR t=n) PW = -$991.01 =E93+PV(0.01,60,-E94,-20000) SOLUTION USING FACTOR TABLES PW = -$12,000 + $20,000(P|F 1%,60) PW = -$12,000 + $20,000(0.55045) PW = -$991.00

SAVINGS ACCOUNT THE PRESENT WORTH OF THE SAVINGS ACCOUNT IS ZERO SINCE IT EARNS EXACTLY MARR YANI SHOULD PREFER THE SAVINGS ACCOUNT.

PROBLEM 5.41 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS DRILL PRESS T EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

10.00% - CF NET CF (P|F i%,n) -$20,000.00 -$20,000.00 1.00000 -$14,000.00 -$14,000.00 0.90909 -$14,000.00 -$14,000.00 0.82645 -$14,000.00 -$14,000.00 0.75131 -$14,000.00 -$14,000.00 0.68301 -$14,000.00 -$14,000.00 0.62092 -$14,000.00 -$14,000.00 0.56447 -$14,000.00 -$14,000.00 0.51316 -$14,000.00 -$14,000.00 0.46651 -$14,000.00 -$14,000.00 0.42410 -$9,000.00 -$9,000.00 0.38554

PW OF CF -$20,000.00 -$12,727.27 -$11,570.25 -$10,518.41 -$9,562.19 -$8,692.90 -$7,902.64 -$7,184.21 -$6,531.10 -$5,937.37 -$3,469.89 -$104,096.22 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$104,096.22 =E8+NPV(0.1,E9:E18) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$104,096.22 =E8+PV(0.1,10,-E9,-5000) SOLUTION USING FACTOR TABLES PW = -$20,000 - $14,000(P|A 10%,10) + $5,000(P|F 10%,10) PW = -$20,000 - $14,000(6.14457) + $5,000(0.38554) PW = -$104,096.28

DRILL PRESS M EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) -$30,000.00 -$30,000.00 1.00000 -$10,000.00 -$10,000.00 0.90909 -$10,000.00 -$10,000.00 0.82645 -$10,000.00 -$10,000.00 0.75131 -$10,000.00 -$10,000.00 0.68301 -$10,000.00 -$10,000.00 0.62092 -$10,000.00 -$10,000.00 0.56447 -$10,000.00 -$10,000.00 0.51316 -$10,000.00 -$10,000.00 0.46651 -$10,000.00 -$10,000.00 0.42410 -$3,000.00 -$3,000.00 0.38554

PW OF CF -$30,000.00 -$9,090.91 -$8,264.46 -$7,513.15 -$6,830.13 -$6,209.21 -$5,644.74 -$5,131.58 -$4,665.07 -$4,240.98 -$1,156.63 -$88,746.87 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$88,746.87 =E39+NPV(0.1,E40:E49) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$88,746.87 =E39+PV(0.1,10,-E40,-7000) SOLUTION USING FACTOR TABLES PW = -$30,000 - $10,000(P|A 10%,10) + $7,000(P|F 10%,10) PW = -$30,000 - $10,000(6.14457) + $7,000(0.38554) PW = -$88,746.92

ZUNNI'S MANUFACTURING SHOULD PURCHASE DRILL M

PROBLEM 5.42 IF THE EQUIPMENT IS PURCHASED, THE SERVICE COST IS SAVED AND THUS LOOKS LIKE A REVENUE TO THE PROJECT. a

AT A PRODUCTION RATE OF 200 UNITS/YEAR THE SERVICE WOULD COST $18,000/YR AT A PRODUCTION RATE OF 200 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $5,000/YR SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS AT 200 UNITS/YEAR EOY 0 1 2 3 4 5 6 7 8 9 10

12.00% + CF - CF NET CF (P|F i%,n) PW OF CF -$100,000.00 -$100,000.00 1.00000 -$100,000.00 $18,000.00 -$12,000.00 $6,000.00 0.89286 $5,357.14 $18,000.00 -$12,000.00 $6,000.00 0.79719 $4,783.16 $18,000.00 -$12,000.00 $6,000.00 0.71178 $4,270.68 $18,000.00 -$12,000.00 $6,000.00 0.63552 $3,813.11 $18,000.00 -$12,000.00 $6,000.00 0.56743 $3,404.56 $18,000.00 -$12,000.00 $6,000.00 0.50663 $3,039.79 $18,000.00 -$12,000.00 $6,000.00 0.45235 $2,714.10 $18,000.00 -$12,000.00 $6,000.00 0.40388 $2,423.30 $18,000.00 -$12,000.00 $6,000.00 0.36061 $2,163.66 $18,000.00 -$12,000.00 $6,000.00 0.32197 $1,931.84 -$66,098.66 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$66,098.66 =E14+NPV(0.12,E15:E24) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = -$66,098.66 =E14+PV(0.12,10,-E15) SOLUTION USING FACTOR TABLES PW = -$100,000 + $6,000(P|A 12%,10) PW = -$100,000 + $6,000(5.65022) PW = -$66,098.68 THEREFORE, THE SERVICE CONTRACT IS PREFERRED OVER THE EQUIPMENT

AT A PRODUCTION RATE OF 500 UNITS/YEAR THE SERVICE WOULD COST $45,000/YR AT A PRODUCTION RATE OF 500 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $12,500/YR SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS AT 500 UNITS/YEAR EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$100,000.00 -$100,000.00 1.00000 -$100,000.00 $45,000.00 -$19,500.00 $25,500.00 0.89286 $22,767.86 $45,000.00 -$19,500.00 $25,500.00 0.79719 $20,328.44 $45,000.00 -$19,500.00 $25,500.00 0.71178 $18,150.40 $45,000.00 -$19,500.00 $25,500.00 0.63552 $16,205.71 $45,000.00 -$19,500.00 $25,500.00 0.56743 $14,469.38 $45,000.00 -$19,500.00 $25,500.00 0.50663 $12,919.09 $45,000.00 -$19,500.00 $25,500.00 0.45235 $11,534.90 $45,000.00 -$19,500.00 $25,500.00 0.40388 $10,299.02 $45,000.00 -$19,500.00 $25,500.00 0.36061 $9,195.56 $45,000.00 -$19,500.00 $25,500.00 0.32197 $8,210.32 $44,080.69 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $44,080.69 =E52+NPV(0.12,E53:E62) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $44,080.69 =E52+PV(0.12,10,-E53) SOLUTION USING FACTOR TABLES PW = -$100,000 + $25,500(P|A 12%,10) PW = -$100,000 + $25,500(5.65022) PW = $44,080.61 THEREFORE, THE EQUIPMENT IS PREFERRED OVER THE SERVICE CONTRACT

FOR BREAKEVEN THE PRESENT WORTH OF BENEFITS MUST EQUAL THE PRESENT WORTH OF COSTS 90X(P|A 12%,10) = 100,000 + (7,000+(25X))(P|A 12%,10) 90X(5.65022) = 100,000 + (7,000+(25X))(5.65022) 508.52(X) = 100,000 + 39,551.54 + 141.26(X) 367.26(X) = 139,551.54 X = 379.98 OR APPROXIMATELY 380 UNITS/YR

PROBLEM 5.43 a

A LIST OF POSSIBLE ALTERNATIVES WILL BE CREATED AND THEN THE INFEASIBLE ALTERNATIVES WILL BE ELIMINATED. IN THE TABLE BELOW, A ONE INDICATES THAT A PROPOSAL IS INCLUDED; A ZERO INDICATES THAT IT IS NOT. THERE ARE A TOTAL OF 16 (2^4) POSSIBLE COMBINATIONS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

X1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1

X2 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1

Y1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1

Y2 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1

FEASIBLE YES YES YES NO NO NO YES NO NO YES NO NO NO NO NO NO

REASON

Y1 CONTINGENT ON X1 Y2 CONTINGENT ON X2 X1 & X2 ARE ME Y2 CONTINGENT ON X2 Y1 CONTINGENT ON X1 Y1 & Y2 ARE ME X1 & X2 ARE ME X1 & X2 ARE ME Y1 & Y2 ARE ME Y1 & Y2 ARE ME X1 & X2 ARE ME

FEASIBLE COMBINATIONS ARE: NULL, X1 ONLY, X2 ONLY, X1&Y1, X2&Y2 b

ALTERNATIVE: NULL THE PRESENT WORTH OF NULL IS ZERO ALTERNATIVE: X1 ONLY EOY 0 1 2 3 4 5 6 7 8

+ CF

- CF -$10,000.00

$1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00

10.00% NET CF (P|F i%,n) -$10,000.00 1.00000 $1,600.00 0.90909 $1,600.00 0.82645 $1,600.00 0.75131 $1,600.00 0.68301 $1,600.00 0.62092 $1,600.00 0.56447 $1,600.00 0.51316 $1,600.00 0.46651

PW OF CF -$10,000.00 $1,454.55 $1,322.31 $1,202.10 $1,092.82 $993.47 $903.16 $821.05 $746.41 -$1,464.12 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$1,464.12 =E14+NPV(0.12,E15:E24) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = -$1,464.12 =E14+PV(0.12,10,-E15) SOLUTION USING FACTOR TABLES PW = -$10,000 + $1,600(P|A 10%,8) PW = -$10,000 + $1,600(5.33493) PW = -$1,464.11

ALTERNATIVE: X2 ONLY EOY 0 1 2 3 4 5 6 7 8

+ CF

- CF -$15,000.00

$2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00

NET CF (P|F i%,n) -$15,000.00 1.00000 $2,600.00 0.90909 $2,600.00 0.82645 $2,600.00 0.75131 $2,600.00 0.68301 $2,600.00 0.62092 $2,600.00 0.56447 $2,600.00 0.51316 $2,600.00 0.46651

PW OF CF -$15,000.00 $2,363.64 $2,148.76 $1,953.42 $1,775.83 $1,614.40 $1,467.63 $1,334.21 $1,212.92 -$1,129.19 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$1,129.19 =E62+NPV(0.1,E63:E70) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = -$1,129.19 =E62+PV(0.1,8,-E63) SOLUTION USING FACTOR TABLES PW = -$15,000 + $2,600(P|A 10%,8) PW = -$15,000 + $2,600(5.33493) PW = -$1,129.18 ALTERNATIVE: X1&Y1 EOY 0 1 2 3 4 5 6 7 8

+ CF

- CF -$16,000.00

$4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00

NET CF (P|F i%,n) -$16,000.00 1.00000 $4,100.00 0.90909 $4,100.00 0.82645 $4,100.00 0.75131 $4,100.00 0.68301 $4,100.00 0.62092 $4,100.00 0.56447 $4,100.00 0.51316 $4,100.00 0.46651

PW OF CF -$16,000.00 $3,727.27 $3,388.43 $3,080.39 $2,800.36 $2,545.78 $2,314.34 $2,103.95 $1,912.68 $5,873.20 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $5,873.20 =E90+NPV(0.1,E91:E98) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $5,873.20 =E90+PV(0.1,8,-E91) SOLUTION USING FACTOR TABLES PW = -$16,000 + $4,100(P|A 10%,8) PW = -$16,000 + $4,100(5.33493) PW = $5,873.21 ALTERNATIVE: X2&Y2 EOY

+ CF

- CF

NET CF

(P|F i%,n)

PW OF CF

0 1 2 3 4 5 6 7 8

-$24,000.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00

1.00000 0.90909 0.82645 0.75131 0.68301 0.62092 0.56447 0.51316 0.46651

-$24,000.00 $5,545.45 $5,041.32 $4,583.02 $4,166.38 $3,787.62 $3,443.29 $3,130.26 $2,845.70 $8,543.05 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $8,543.05 =E118+NPV(0.1,E119:E126) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $8,543.05 =E118+PV(0.1,8,-E119) SOLUTION USING FACTOR TABLES PW = -$24,000 + $6,100(P|A 10%,8) PW = -$24,000 + $6,100(5.33493) PW = $8,543.07 THE COMBINATION X2&Y2 HAS THE HIGHEST PRESENT WORTH AND IS THEREFORE PREFERRED.

PROBLEM 5.44 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS TELESCOPE T1 25.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$600,000.00 -$600,000.00 1.00000 -$600,000.00 1 $400,000.00 -$130,000.00 $270,000.00 0.80000 $216,000.00 2 $400,000.00 -$130,000.00 $270,000.00 0.64000 $172,800.00 3 $400,000.00 -$130,000.00 $270,000.00 0.51200 $138,240.00 4 $400,000.00 -$130,000.00 $270,000.00 0.40960 $110,592.00 5 $400,000.00 -$130,000.00 $270,000.00 0.32768 $88,473.60 6 $400,000.00 -$130,000.00 $270,000.00 0.26214 $70,778.88 7 $400,000.00 -$130,000.00 $270,000.00 0.20972 $56,623.10 8 $400,000.00 -$130,000.00 $270,000.00 0.16777 $45,298.48 9 $400,000.00 -$130,000.00 $270,000.00 0.13422 $36,238.79 10 $470,000.00 -$130,000.00 $340,000.00 0.10737 $36,507.22 $371,552.08 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $371,552.08 =E7+NPV(0.25,E8:E17) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $371,552.08 =E7+PV(0.25,10,-E8,-70000) SOLUTION USING FACTOR TABLES PW = -$600,000 + $270,000(P|A 25%,10) + $70,000(P|F 25%,10) PW = -$600,000 + $270,000(3.57050) + $70,000(0.10737) PW = $371,550.90 TELESCOPE T2 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$800,000.00 -$800,000.00 1.00000 -$800,000.00 $600,000.00 -$270,000.00 $330,000.00 0.80000 $264,000.00 $600,000.00 -$270,000.00 $330,000.00 0.64000 $211,200.00 $600,000.00 -$270,000.00 $330,000.00 0.51200 $168,960.00 $600,000.00 -$270,000.00 $330,000.00 0.40960 $135,168.00 $600,000.00 -$270,000.00 $330,000.00 0.32768 $108,134.40 $600,000.00 -$270,000.00 $330,000.00 0.26214 $86,507.52 $600,000.00 -$270,000.00 $330,000.00 0.20972 $69,206.02 $600,000.00 -$270,000.00 $330,000.00 0.16777 $55,364.81 $600,000.00 -$270,000.00 $330,000.00 0.13422 $44,291.85 $730,000.00 -$270,000.00 $460,000.00 0.10737 $49,392.12 $392,224.72 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $392,224.72 =E37+NPV(0.25,E38:E47) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $392,224.72 =E37+PV(0.25,10,-E38,-130000) SOLUTION USING FACTOR TABLES PW = -$800,000 + $330,000(P|A 25%,10) + $130,000(P|F 25%,10) PW = -$800,000 + $330,000(3.57050) + $130,000(0.10737) PW = $392,223.10

TELESCOPE T3 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$470,000.00 -$470,000.00 1.00000 -$470,000.00 $260,000.00 -$70,000.00 $190,000.00 0.80000 $152,000.00 $260,000.00 -$70,000.00 $190,000.00 0.64000 $121,600.00 $260,000.00 -$70,000.00 $190,000.00 0.51200 $97,280.00 $260,000.00 -$70,000.00 $190,000.00 0.40960 $77,824.00 $260,000.00 -$70,000.00 $190,000.00 0.32768 $62,259.20 $260,000.00 -$70,000.00 $190,000.00 0.26214 $49,807.36 $260,000.00 -$70,000.00 $190,000.00 0.20972 $39,845.89 $260,000.00 -$70,000.00 $190,000.00 0.16777 $31,876.71 $260,000.00 -$70,000.00 $190,000.00 0.13422 $25,501.37 $325,000.00 -$70,000.00 $255,000.00 0.10737 $27,380.42 $215,374.94 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $215,374.94 =E67+NPV(0.25,E68:E77) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $215,374.94 =E67+PV(0.25,10,-E68,-65000) SOLUTION USING FACTOR TABLES PW = -$470,000 + $190,000(P|A 25%,10) + $65,000(P|F 25%,10) PW = -$470,000 + $190,000(3.57050) + $65,000(0.10737) PW = $215,374.05 TELESCOPE T4 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$540,000.00 -$540,000.00 1.00000 -$540,000.00 $320,000.00 -$120,000.00 $200,000.00 0.80000 $160,000.00 $320,000.00 -$120,000.00 $200,000.00 0.64000 $128,000.00 $320,000.00 -$120,000.00 $200,000.00 0.51200 $102,400.00 $320,000.00 -$120,000.00 $200,000.00 0.40960 $81,920.00 $320,000.00 -$120,000.00 $200,000.00 0.32768 $65,536.00 $320,000.00 -$120,000.00 $200,000.00 0.26214 $52,428.80 $320,000.00 -$120,000.00 $200,000.00 0.20972 $41,943.04 $320,000.00 -$120,000.00 $200,000.00 0.16777 $33,554.43 $320,000.00 -$120,000.00 $200,000.00 0.13422 $26,843.55 $520,000.00 -$120,000.00 $400,000.00 0.10737 $42,949.67 $195,575.49 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $195,575.49 =E97+NPV(0.25,E98:E107) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $195,575.49 =E97+PV(0.25,10,-E98,-200000) SOLUTION USING FACTOR TABLES PW = -$540,000 + $200,000(P|A 25%,10) + $200,000(P|F 25%,10) PW = -$540,000 + $200,000(3.57050) + $200,000(0.10737) PW = $195,574.00

TELESCOPE T2 HAS THE HIGHEST PRESENT WORTH AND IS THEREFORE PREFERRED.

TELESCOPE T1 EOY 0 1 2 3 4 5 6 7 8 9 10

42.00% - CF NET CF (P|F i%,n) PW OF CF -$600,000.00 -$600,000.00 1.00000 -$600,000.00 $400,000.00 -$130,000.00 $270,000.00 0.70423 $190,140.85 $400,000.00 -$130,000.00 $270,000.00 0.49593 $133,902.00 $400,000.00 -$130,000.00 $270,000.00 0.34925 $94,297.19 $400,000.00 -$130,000.00 $270,000.00 0.24595 $66,406.47 $400,000.00 -$130,000.00 $270,000.00 0.17320 $46,765.12 $400,000.00 -$130,000.00 $270,000.00 0.12197 $32,933.18 $400,000.00 -$130,000.00 $270,000.00 0.08590 $23,192.38 $400,000.00 -$130,000.00 $270,000.00 0.06049 $16,332.66 $400,000.00 -$130,000.00 $270,000.00 0.04260 $11,501.88 $470,000.00 -$130,000.00 $340,000.00 0.03000 $10,199.89 + CF

$25,671.61 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $25,671.61 =E131+NPV(0.42,E132:E141) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $25,671.61 =E131+PV(0.42,10,-E132,-70000) SOLUTION USING FACTOR TABLES PW = -$600,000 + $270,000(P|A 42%,10) + $70,000(P|F 42%,10) PW = -$600,000 + $270,000(2.30952) + $70,000(0.03000) PW = $25,670.40 TELESCOPE T2 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$800,000.00 -$800,000.00 1.00000 -$800,000.00 $600,000.00 -$270,000.00 $330,000.00 0.70423 $232,394.37 $600,000.00 -$270,000.00 $330,000.00 0.49593 $163,658.00 $600,000.00 -$270,000.00 $330,000.00 0.34925 $115,252.12 $600,000.00 -$270,000.00 $330,000.00 0.24595 $81,163.46 $600,000.00 -$270,000.00 $330,000.00 0.17320 $57,157.37 $600,000.00 -$270,000.00 $330,000.00 0.12197 $40,251.67 $600,000.00 -$270,000.00 $330,000.00 0.08590 $28,346.24 $600,000.00 -$270,000.00 $330,000.00 0.06049 $19,962.14 $600,000.00 -$270,000.00 $330,000.00 0.04260 $14,057.85 $730,000.00 -$270,000.00 $460,000.00 0.03000 $13,799.85 -$33,956.93 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$33,956.93 =E161+NPV(0.42,E162:E171) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$33,956.93 =E161+PV(0.42,10,-E162,-130000) SOLUTION USING FACTOR TABLES PW = -$800,000 + $330,000(P|A 42%,10) + $130,000(P|F 42%,10) PW = -$800,000 + $330,000(2.30952) + $130,000(0.03000) PW = -$33,958.40

TELESCOPE T3 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$470,000.00 -$470,000.00 1.00000 -$470,000.00 $260,000.00 -$70,000.00 $190,000.00 0.70423 $133,802.82 $260,000.00 -$70,000.00 $190,000.00 0.49593 $94,227.34 $260,000.00 -$70,000.00 $190,000.00 0.34925 $66,357.28 $260,000.00 -$70,000.00 $190,000.00 0.24595 $46,730.48 $260,000.00 -$70,000.00 $190,000.00 0.17320 $32,908.79 $260,000.00 -$70,000.00 $190,000.00 0.12197 $23,175.20 $260,000.00 -$70,000.00 $190,000.00 0.08590 $16,320.57 $260,000.00 -$70,000.00 $190,000.00 0.06049 $11,493.36 $260,000.00 -$70,000.00 $190,000.00 0.04260 $8,093.91 $325,000.00 -$70,000.00 $255,000.00 0.03000 $7,649.92 -$29,240.35 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$29,240.35 =E191+NPV(0.42,E192:E201) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$29,240.35 =E191+PV(0.42,10,-E192,-65000) SOLUTION USING FACTOR TABLES PW = -$470,000 + $190,000(P|A 42%,10) + $65,000(P|F 42%,10) PW = -$470,000 + $190,000(2.30952) + $65,000(0.03000) PW = -$29,241.20 TELESCOPE T4 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF NET CF (P|F i%,n) PW OF CF -$540,000.00 -$540,000.00 1.00000 -$540,000.00 $320,000.00 -$120,000.00 $200,000.00 0.70423 $140,845.07 $320,000.00 -$120,000.00 $200,000.00 0.49593 $99,186.67 $320,000.00 -$120,000.00 $200,000.00 0.34925 $69,849.77 $320,000.00 -$120,000.00 $200,000.00 0.24595 $49,189.98 $320,000.00 -$120,000.00 $200,000.00 0.17320 $34,640.83 $320,000.00 -$120,000.00 $200,000.00 0.12197 $24,394.95 $320,000.00 -$120,000.00 $200,000.00 0.08590 $17,179.54 $320,000.00 -$120,000.00 $200,000.00 0.06049 $12,098.27 $320,000.00 -$120,000.00 $200,000.00 0.04260 $8,519.91 $520,000.00 -$120,000.00 $400,000.00 0.03000 $11,999.87 -$72,095.15 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$72,095.15 =E221+NPV(0.42,E222:E231) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$72,095.15 =E221+PV(0.42,10,-E222,-200000) SOLUTION USING FACTOR TABLES PW = -$540,000 + $200,000(P|A 25%,10) + $200,000(P|F 25%,10) PW = -$540,000 + $200,000(2.30952) + $200,000(0.03000) PW = -$72,096.00 TELESCOPE T1 HAS THE HIGHEST PRESENT WORTH AND IS THEREFORE PREFERRED.

PROBLEM 5.45 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, T3, T4, T1, T2 a

NULL BECOMES THE "CURRENT BEST" AND T3 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR T3 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

25.00% NULL INCR. CF (P|F i%,n) PW $0.00 -$470,000.00 1.00000 -$470,000.00 $0.00 $190,000.00 0.80000 $152,000.00 $0.00 $190,000.00 0.64000 $121,600.00 $0.00 $190,000.00 0.51200 $97,280.00 $0.00 $190,000.00 0.40960 $77,824.00 $0.00 $190,000.00 0.32768 $62,259.20 $0.00 $190,000.00 0.26214 $49,807.36 $0.00 $190,000.00 0.20972 $39,845.89 $0.00 $190,000.00 0.16777 $31,876.71 $0.00 $190,000.00 0.13422 $25,501.37 $0.00 $255,000.00 0.10737 $27,380.42 $215,374.94 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $215,374.94 =E7+NPV(0.25,E8:E17) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $215,374.94 =E7+PV(0.25,10,-E8,-70000) SOLUTION USING FACTOR TABLES PW = -$470,000 + $190,000(P|A 25%,10) + $65,000(P|F 25%,10) PW = -$470,000 + $190,000(3.57050) + $65,000(0.10737) PW = $215,374.05 SINCE THE PW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T3 BECOMES THE NEW CURRENT BEST T4 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T4 - T3 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T4 T3 INCR. CF (P|F i%,n) -$540,000.00 -$470,000.00 -$70,000.00 1.00000 $200,000.00 $190,000.00 $10,000.00 0.80000 $200,000.00 $190,000.00 $10,000.00 0.64000 $200,000.00 $190,000.00 $10,000.00 0.51200 $200,000.00 $190,000.00 $10,000.00 0.40960 $200,000.00 $190,000.00 $10,000.00 0.32768 $200,000.00 $190,000.00 $10,000.00 0.26214 $200,000.00 $190,000.00 $10,000.00 0.20972 $200,000.00 $190,000.00 $10,000.00 0.16777 $200,000.00 $190,000.00 $10,000.00 0.13422 $400,000.00 $255,000.00 $145,000.00 0.10737

PW -$70,000.00 $8,000.00 $6,400.00 $5,120.00 $4,096.00 $3,276.80 $2,621.44 $2,097.15 $1,677.72 $1,342.18 $15,569.26 -$19,799.45 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$19,799.45 =E46+NPV(0.25,E47:E56) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$19,799.45 =E46+PV(0.25,10,-E47,-135000) SOLUTION USING FACTOR TABLES PW = -$70,000 + $10,000(P|A 25%,10) + $135,000(P|F 25%,10) PW = -$70,000 + $10,000(3.57050) + $135,000(0.10737) PW = -$19,800.05

SINCE THE PW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. T3 REMAINS THE CURRENT BEST T1 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T1 - T3 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T1 T3 INCR. CF (P|F i%,n) PW -$600,000.00 -$470,000.00 -$130,000.00 1.00000 -$130,000.00 $270,000.00 $190,000.00 $80,000.00 0.80000 $64,000.00 $270,000.00 $190,000.00 $80,000.00 0.64000 $51,200.00 $270,000.00 $190,000.00 $80,000.00 0.51200 $40,960.00 $270,000.00 $190,000.00 $80,000.00 0.40960 $32,768.00 $270,000.00 $190,000.00 $80,000.00 0.32768 $26,214.40 $270,000.00 $190,000.00 $80,000.00 0.26214 $20,971.52 $270,000.00 $190,000.00 $80,000.00 0.20972 $16,777.22 $270,000.00 $190,000.00 $80,000.00 0.16777 $13,421.77 $270,000.00 $190,000.00 $80,000.00 0.13422 $10,737.42 $340,000.00 $255,000.00 $85,000.00 0.10737 $9,126.81 $156,177.13 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $156,177.13 =E80+NPV(0.25,E81:E90) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $156,177.13 =E80+PV(0.25,10,-E81,-5000) SOLUTION USING FACTOR TABLES PW = -$130,000 + $80,000(P|A 25%,10) + $5,000(P|F 25%,10) PW = -$130,000 + $80,000(3.57050) + $5,000(0.10737) PW = $156,176.85 SINCE THE PW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T1 BECOMES THE NEW CURRENT BEST T2 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T2 - T1 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T2 T1 INCR. CF (P|F i%,n) PW -$800,000.00 -$600,000.00 -$200,000.00 1.00000 -$200,000.00 $330,000.00 $270,000.00 $60,000.00 0.80000 $48,000.00 $330,000.00 $270,000.00 $60,000.00 0.64000 $38,400.00 $330,000.00 $270,000.00 $60,000.00 0.51200 $30,720.00 $330,000.00 $270,000.00 $60,000.00 0.40960 $24,576.00 $330,000.00 $270,000.00 $60,000.00 0.32768 $19,660.80 $330,000.00 $270,000.00 $60,000.00 0.26214 $15,728.64 $330,000.00 $270,000.00 $60,000.00 0.20972 $12,582.91 $330,000.00 $270,000.00 $60,000.00 0.16777 $10,066.33 $330,000.00 $270,000.00 $60,000.00 0.13422 $8,053.06 $460,000.00 $340,000.00 $120,000.00 0.10737 $12,884.90 $20,672.65 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $20,672.65 =E114+NPV(0.25,E115:E124) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $20,672.65 =E114+PV(0.25,10,-E115,-60000) SOLUTION USING FACTOR TABLES PW = -$200,000 + $60,000(P|A 25%,10) + $60,000(P|F 25%,10) PW = -$200,000 + $60,000(3.57050) + $60,000(0.10737) PW = $20,672.20 SINCE THE PW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T2 BECOMES THE NEW CURRENT BEST

THERE ARE NO MORE CHALLENGERS SO T2 IS PREFERRED. b

NULL BECOMES THE "CURRENT BEST" AND T3 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR T3 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

42.00% NULL INCR. CF (P|F i%,n) PW $0.00 -$470,000.00 1.00000 -$470,000.00 $0.00 $190,000.00 0.70423 $133,802.82 $0.00 $190,000.00 0.49593 $94,227.34 $0.00 $190,000.00 0.34925 $66,357.28 $0.00 $190,000.00 0.24595 $46,730.48 $0.00 $190,000.00 0.17320 $32,908.79 $0.00 $190,000.00 0.12197 $23,175.20 $0.00 $190,000.00 0.08590 $16,320.57 $0.00 $190,000.00 0.06049 $11,493.36 $0.00 $190,000.00 0.04260 $8,093.91 $0.00 $255,000.00 0.03000 $7,649.92 -$29,240.35 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$29,240.35 =E151+NPV(0.42,E152:E161) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$29,240.35 =E151+PV(0.42,10,-E152,-65000) SOLUTION USING FACTOR TABLES PW = -$470,000 + $190,000(P|A 42%,10) + $65,000(P|F 42%,10) PW = -$470,000 + $190,000(2.30952) + $65,000(0.03000) PW = -$29,241.20 SINCE THE PW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. NULL REMAINS THE NEW CURRENT BEST T4 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T4 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T4 -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $400,000.00

NULL INCR. CF (P|F i%,n) PW $0.00 -$540,000.00 1.00000 -$540,000.00 $0.00 $200,000.00 0.70423 $140,845.07 $0.00 $200,000.00 0.49593 $99,186.67 $0.00 $200,000.00 0.34925 $69,849.77 $0.00 $200,000.00 0.24595 $49,189.98 $0.00 $200,000.00 0.17320 $34,640.83 $0.00 $200,000.00 0.12197 $24,394.95 $0.00 $200,000.00 0.08590 $17,179.54 $0.00 $200,000.00 0.06049 $12,098.27 $0.00 $200,000.00 0.04260 $8,519.91 $0.00 $400,000.00 0.03000 $11,999.87 -$72,095.15 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$72,095.15 =E185+NPV(0.42,E186:E195) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$72,095.15 =E185+PV(0.42,10,-E186,-200000) SOLUTION USING FACTOR TABLES PW = -$540,000 + $200,000(P|A 42%,10) + $200,000(P|F 42%,10) PW = -$540,000 + $200,000(2.30952) + $200,000(0.03000) PW = -$72,096.00 SINCE THE PW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. NULL REMAINS THE CURRENT BEST

T1 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T1 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T1 -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

NULL INCR. CF (P|F i%,n) PW $0.00 -$600,000.00 1.00000 -$600,000.00 $0.00 $270,000.00 0.70423 $190,140.85 $0.00 $270,000.00 0.49593 $133,902.00 $0.00 $270,000.00 0.34925 $94,297.19 $0.00 $270,000.00 0.24595 $66,406.47 $0.00 $270,000.00 0.17320 $46,765.12 $0.00 $270,000.00 0.12197 $32,933.18 $0.00 $270,000.00 0.08590 $23,192.38 $0.00 $270,000.00 0.06049 $16,332.66 $0.00 $270,000.00 0.04260 $11,501.88 $0.00 $340,000.00 0.03000 $10,199.89 $25,671.61 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $25,671.61 =E219+NPV(0.42,E220:E229) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $25,671.61 =E219+PV(0.42,10,-E220,-70000) SOLUTION USING FACTOR TABLES PW = -$600,000 + $270,000(P|A 42%,10) + $70,000(P|F 42%,10) PW = -$600,000 + $270,000(2.30952) + $70,000(0.03000) PW = $25,670.40 SINCE THE PW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T1 BECOMES THE NEW CURRENT BEST T2 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T2 - T1 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T2 T1 INCR. CF (P|F i%,n) PW -$800,000.00 -$600,000.00 -$200,000.00 1.00000 -$200,000.00 $330,000.00 $270,000.00 $60,000.00 0.70423 $42,253.52 $330,000.00 $270,000.00 $60,000.00 0.49593 $29,756.00 $330,000.00 $270,000.00 $60,000.00 0.34925 $20,954.93 $330,000.00 $270,000.00 $60,000.00 0.24595 $14,756.99 $330,000.00 $270,000.00 $60,000.00 0.17320 $10,392.25 $330,000.00 $270,000.00 $60,000.00 0.12197 $7,318.48 $330,000.00 $270,000.00 $60,000.00 0.08590 $5,153.86 $330,000.00 $270,000.00 $60,000.00 0.06049 $3,629.48 $330,000.00 $270,000.00 $60,000.00 0.04260 $2,555.97 $460,000.00 $340,000.00 $120,000.00 0.03000 $3,599.96 -$59,628.54 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$59,628.54 =E253+NPV(0.42,E254:E263) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$59,628.54 =E253+PV(0.42,10,-E254,-60000) SOLUTION USING FACTOR TABLES PW = -$200,000 + $60,000(P|A 42%,10) + $60,000(P|F 42%,10) PW = -$200,000 + $60,000(2.30952) + $60,000(0.03000) PW = -$59,628.80 SINCE THE PW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. T1 REMAINS THE CURRENT BEST THERE ARE NO MORE CHALLENGERS SO T1 IS PREFERRED.

PROBLEM 5.46 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS DELIVERY VAN EOY 0 1 2 3 4 5 6

VAN -$18,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $500.00

LOAN $12,000.00 -$3,305.88 -$3,305.88 -$3,305.88 -$3,305.88

O&M

SAVINGS

-$700.00 $3,800.00 -$700.00 $3,800.00 -$700.00 $3,800.00 -$700.00 $3,800.00 -$700.00 $3,800.00 -$700.00 $3,800.00

6.00% NET CF (P|F i%,n) PW OF CF -$6,000.00 1.00000 -$6,000.00 -$205.88 0.94340 -$194.23 -$205.88 0.89000 -$183.23 -$205.88 0.83962 -$172.86 -$205.88 0.79209 -$163.08 $3,100.00 0.74726 $2,316.50 $3,600.00 0.70496 $2,537.86 -$1,859.04 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$1,859.04 =G7+NPV(0.06,G8:G13) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$1,859.04 =G7+PV(0.06,6,-G12,-500)+PV(0.06,4,G12-G8) SOLUTION USING FACTOR TABLES PW = -$6,000 - $205.88(P|A 6%,4) + $3,100(P|F 6%,5) + $3,600(P|F 6%,6) PW = -$6,000 - $205.88(3.46511) + $3,100(0.74726) + $3,600(0.70496) PW = -$1,859.03

PURCHASING THE DELIVERY VAN IS NOT ATTRACTIVE

PROBLEM 5.47 PW OF LOTTERY PAYOUT (IN M$) SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS 6.00% EOY CF (P|F i%,n) PW OF CF 0 $1.00 1.00000 $1.00 1 $1.30 0.94340 $1.23 2 $1.30 0.89000 $1.16 3 $1.30 0.83962 $1.09 4 $1.30 0.79209 $1.03 5 $1.30 0.74726 $0.97 6 $1.30 0.70496 $0.92 7 $1.30 0.66506 $0.86 8 $1.30 0.62741 $0.82 9 $1.30 0.59190 $0.77 10 $1.30 0.55839 $0.73 11 $1.30 0.52679 $0.68 12 $1.30 0.49697 $0.65 13 $1.30 0.46884 $0.61 14 $1.30 0.44230 $0.57 15 $1.30 0.41727 $0.54 16 $1.30 0.39365 $0.51 17 $1.30 0.37136 $0.48 18 $1.30 0.35034 $0.46 19 $1.30 0.33051 $0.43 20 $1.30 0.31180 $0.41 $15.91 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $15.91 =C7+NPV(0.06,C8:C27) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $15.91 =C7+PV(0.06,20,-C8) SOLUTION USING FACTOR TABLES PW = $1.00 + $1.30(P|A 6%,20) PW = $1.00 + $1.30(11.46992) PW = $15.91 DECISION: SINCE THE PW OF THE ONE-TIME IS LOWER THAN THE PW OF THE PAYOUT, THE STATE SHOULD PREFER THE ONE-TIME.

PROBLEM 5.48 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS MACHINE 1 (IN K$) 12.00% EOY MACHINE O&M NET CF (P|F i%,n) PW OF CF 0 -$800.00 -$800.00 1.00000 -$800.00 1 -$50.00 -$50.00 0.89286 -$44.64 2 -$50.00 -$50.00 0.79719 -$39.86 3 -$50.00 -$50.00 0.71178 -$35.59 4 $40.00 -$50.00 -$10.00 0.63552 -$6.36 -$926.45 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$926.45 =E7+NPV(0.12,E8:E11) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$926.45 =E7+PV(0.12,4,-E8,-40) SOLUTION USING FACTOR TABLES PW = -$800 - $50(P|A 12%,4) + $40(P|F 12%,4) PW = -$800 - $50(3.03735) + $40(0.63552) PW = -$926.45 MACHINE 2 (IN K$) EOY 0 1 2 3 4

MACHINE -$650.00

O&M -$90.00 -$90.00 -$90.00 -$90.00

$32.50

NET CF (P|F i%,n) PW OF CF -$650.00 1.00000 -$650.00 -$90.00 0.89286 -$80.36 -$90.00 0.79719 -$71.75 -$90.00 0.71178 -$64.06 -$57.50 0.63552 -$36.54 -$902.71 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$902.71 =E31+NPV(0.12,E32:E35) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$902.71 =E31+PV(0.12,4,-E32,-32.5) SOLUTION USING FACTOR TABLES PW = -$650 - $90(P|A 12%,4) + $32.50(P|F 12%,4) PW = -$650 - $90(3.03735) + $32.50(0.63552) PW = -$902.71 MACHINE 3 (IN K$) EOY

MACHINE

O&M

NET CF

(P|F i%,n) PW OF CF

0 1 2 3 4

-$575.00

$28.75

-$105.00 -$105.00 -$105.00 -$105.00

-$575.00 -$105.00 -$105.00 -$105.00 -$76.25

1.00000 0.89286 0.79719 0.71178 0.63552

-$575.00 -$93.75 -$83.71 -$74.74 -$48.46 -$875.65 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$875.65 =E55+NPV(0.12,E56:E59) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$875.65 =E55+PV(0.12,4,-E56,-28.75) SOLUTION USING FACTOR TABLES PW = -$575 - $105(P|A 12%,4) + $28.75(P|F 12%,4) PW = -$575 - $105(3.03735) + $28.75(0.63552) PW = -$875.65

DECISION: PREFER MACHINE 3

PROBLEM 5.49 GATE 1 EOY 0 1 2 3 4 5

GATE -$15,000.00

$0.00

O&M -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00

NET CF -$15,000.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00

20.00% (P|F i%,n) 1.00000 0.83333 0.69444 0.57870 0.48225 0.40188

PW OF CF -$15,000.00 -$5,416.67 -$4,513.89 -$3,761.57 -$3,134.65 -$2,612.20 -$34,438.98 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$34,438.98 =E6+NPV(0.2,E7:E11) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$34,438.98 =E6+PV(0.2,5,-E7) SOLUTION USING FACTOR TABLES PW = -$15,000 - $6,500(P|A 20%,5) PW = -$15,000 - $6,500(2.99061) PW = -$34,438.97 GATE 2 EOY 0 1 2 3 4 5

GATE -$19,000.00

$2,000.00

O&M -$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00

NET CF -$19,000.00 -$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00 -$3,600.00

(P|F i%,n) 1.00000 0.83333 0.69444 0.57870 0.48225 0.40188

PW OF CF -$19,000.00 -$4,666.67 -$3,888.89 -$3,240.74 -$2,700.62 -$1,446.76 -$34,943.67 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$34,943.67 =E31+NPV(0.2,E32:E36) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$34,943.67 =E31+PV(0.2,5,-E32,-2000) SOLUTION USING FACTOR TABLES PW = -$19,000 - $5,600(P|A 20%,5) + $2,000(P|F 20%,5) PW = -$19,000 - $5,600(2.99061) + $2,000(0.40188) PW = -$34,943.66 GATE 3 EOY 0 1 2 3 4 5

GATE -$24,000.00

$5,000.00

O&M -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00

NET CF -$24,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 $1,000.00

(P|F i%,n) 1.00000 0.83333 0.69444 0.57870 0.48225 0.40188

PW OF CF -$24,000.00 -$3,333.33 -$2,777.78 -$2,314.81 -$1,929.01 $401.88 -$33,953.06 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$33,953.06 =E56+NPV(0.2,E57:E61) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$33,953.06 =E56+PV(0.2,5,-E57,-5000) SOLUTION USING FACTOR TABLES PW = -$24,000 - $4,000(P|A 20%,5) + $5,000(P|F 20%,5) PW = -$24,000 - $4,000(2.99061) + $5,000(0.40188) PW = -$33,953.04

DECISION: PREFER GATE 3

PROBLEM 5.50 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS SPRINKLER SYSTEM EOY 0 1 2 3 4 5 6 7 8 9

SPRINKLERS LOAN O&M SAVINGS -$30,000.00 $30,000.00 -$9,877.03 -$9,000.00 $15,000.00 -$9,877.03 -$9,000.00 $15,000.00 -$9,877.03 -$9,000.00 $15,000.00 -$9,877.03 -$9,000.00 $15,000.00 -$9,000.00 $15,000.00 -$9,000.00 $15,000.00 -$9,000.00 $15,000.00 -$9,000.00 $15,000.00 $2,000.00 -$9,000.00 $15,000.00

15.00% NET CF (P|F i%,n) PW OF CF $0.00 1.00000 $0.00 -$3,877.03 0.86957 -$3,371.33 -$3,877.03 0.75614 -$2,931.59 -$3,877.03 0.65752 -$2,549.21 -$3,877.03 0.57175 -$2,216.71 $6,000.00 0.49718 $2,983.06 $6,000.00 0.43233 $2,593.97 $6,000.00 0.37594 $2,255.62 $6,000.00 0.32690 $1,961.41 $8,000.00 0.28426 $2,274.10 $999.31 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $999.31 =G7+NPV(0.15,G8:G16) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = $999.31 =G7+PV(0.15,9,-G12,-G16+G15)-PV(0.15,4,-G12+G11) SOLUTION USING FACTOR TABLES PW = $6,000(P|A 15%,9) - $9,877.03(P|A 15%,4) + $2,000(P|F 15%,9) PW = $6,000(4.77158) - $9,877.03(2.85498) + $2,000(0.28426) PW = $999.28 PURCHASING THE SPRINKLER SYSTEM IS ATTRACTIVE

PROBLEM 5.51 LIGHT BAR EOY 0 1 2 3 4 5 6

BAR REVENUE -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

10.00% NET CF (P|F i%,n) PW OF CF -$6,000.00 1.00000 -$6,000.00 $2,000.00 0.90909 $1,818.18 $2,000.00 0.82645 $1,652.89 $2,000.00 0.75131 $1,502.63 $2,000.00 0.68301 $1,366.03 $2,000.00 0.62092 $1,241.84 $2,000.00 0.56447 $1,128.95 $2,710.52 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $2,710.52 =E6+NPV(0.1,E7:E12) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = $2,710.52 =E6+PV(0.1,6,-E7) SOLUTION USING FACTOR TABLES PW = -$6,000 + $2,000(P|A 10%,6) PW = -$6,000 + $2,000(4.35526) PW = $2,710.52 SLIDING SPOTS EOY 0 1 2 3 4 5 6

SPOTS REVENUE NET CF (P|F i%,n) PW OF CF -$14,000.00 -$14,000.00 1.00000 -$14,000.00 $3,500.00 $3,500.00 0.90909 $3,181.82 $3,500.00 $3,500.00 0.82645 $2,892.56 $3,500.00 $3,500.00 0.75131 $2,629.60 $3,500.00 $3,500.00 0.68301 $2,390.55 $3,500.00 $3,500.00 0.62092 $2,173.22 $3,500.00 $3,500.00 0.56447 $1,975.66 $1,243.41 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $1,243.41 =E6+NPV(0.1,E7:E12) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = $1,243.41 =E6+PV(0.1,6,-E7) SOLUTION USING FACTOR TABLES PW = -$14,000 + $3,500(P|A 10%,6) PW = -$14,000 + $3,500(4.35526)

PW =

$1,243.41

REFLECTED BEAM EOY 0 1 2 3 4 5 6

BEAM REVENUE NET CF (P|F i%,n) PW OF CF -$20,000.00 -$20,000.00 1.00000 -$20,000.00 $0.00 $0.00 0.90909 $0.00 $2,300.00 $2,300.00 0.82645 $1,900.83 $4,600.00 $4,600.00 0.75131 $3,456.05 $6,900.00 $6,900.00 0.68301 $4,712.79 $9,200.00 $9,200.00 0.62092 $5,712.48 $11,500.00 $11,500.00 0.56447 $6,491.45 $2,273.59 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $2,273.59 =E58+NPV(0.1,E59:E64) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$20,000 + $2,300(P|G 10%,6) PW = -$20,000 + $2,300(9.68417) PW = $2,273.59 DECISION: LIGHT BAR IS PREFERRED

PROBLEM 5.52 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS DESIGN 1 (IN M$) 10.00% EOY NET CF (P|F i%,n) PW OF CF 0 -$15.00 1.00000 -$15.00 1 -$2.50 0.90909 -$2.27 2 -$2.50 0.82645 -$2.07 3 -$2.50 0.75131 -$1.88 -$21.22 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$21.22 =C7+NPV(0.1,C8:C10) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$21.22 =C7+PV(0.1,3,-C8) SOLUTION USING FACTOR TABLES PW = -$15 - $2.50(P|A 10%,3) PW = -$15 - $2.50(2.48685) PW = -$21.22 DESIGN 2 (IN M$) EOY 0 1 2 3

NET CF (P|F i%,n) PW OF CF -$20.00 1.00000 -$20.00 -$1.50 0.90909 -$1.36 -$1.50 0.82645 -$1.24 -$1.50 0.75131 -$1.13 -$23.73 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$23.73 =C30+NPV(0.1,C31:C33) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$23.73 =C30+PV(0.1,3,-C31) SOLUTION USING FACTOR TABLES PW = -$20 - $1.50(P|A 10%,3) PW = -$20 - $1.50(2.48685) PW = -$23.73 DECISION: PREFER DESIGN 1

PROBLEM 5.53 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS FIRST SATELLITE ONLY (IN K$) EOY 0 1 2 3 4 5

10.00% EQUIPMENT DEVELOPMENT VEHICLE PAYMENT NET CF (P|F i%,n) PW OF CF -$750.00 -$750.00 1.00000 -$750.00 -$150.00 -$150.00 0.90909 -$136.36 -$150.00 -$150.00 0.82645 -$123.97 -$150.00 -$150.00 0.75131 -$112.70 -$150.00 -$150.00 0.68301 -$102.45 -$150.00 -$275.00 $2,500.00 $2,075.00 0.62092 $1,288.41 $62.93 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $62.93 =G7+NPV(0.1,G8:G12) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = $62.93 =G7+PV(0.1,5,-G8,-2225) SOLUTION USING FACTOR TABLES PW = -$750 - $150(P|A 10%,4) + $2,075(P|F 10%,5) PW = -$750 - $150(3.16987) + $2,075(0.62092) PW = $62.93 SECOND SATELLITE ONLY (IN K$) EOY 0 1 2 3 4 5

EQUIPMENT DEVELOPMENT VEHICLE PAYMENT NET CF (P|F i%,n) PW OF CF -$850.00 -$850.00 1.00000 -$850.00 -$120.00 -$120.00 0.90909 -$109.09 -$120.00 -$120.00 0.82645 -$99.17 -$120.00 -$120.00 0.75131 -$90.16 -$120.00 -$120.00 0.68301 -$81.96 -$120.00 -$275.00 $2,500.00 $2,105.00 0.62092 $1,307.04 $76.66 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $76.66 =G32+NPV(0.1,G33:G37) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = $76.66 =G32+PV(0.1,5,-G33,-2225) SOLUTION USING FACTOR TABLES PW = -$850 - $120(P|A 10%,4) + $2,105(P|F 10%,5) PW = -$850 - $120(3.16987) + $2,105(0.62092) PW = $76.65 BOTH SATELLITES (IN K$) EOY 0 1 2 3 4 5

EQUIPMENT DEVELOPMENT VEHICLE PAYMENT NET CF (P|F i%,n) PW OF CF -$1,750.00 -$1,750.00 1.00000 -$1,750.00 -$400.00 -$400.00 0.90909 -$363.64 -$400.00 -$400.00 0.82645 -$330.58 -$400.00 -$400.00 0.75131 -$300.53 -$400.00 -$400.00 0.68301 -$273.21 -$400.00 -$350.00 $6,000.00 $5,250.00 0.62092 $3,259.84

$241.89 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $241.89 =G57+NPV(0.1,G58:G62) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = $241.89 =G57+PV(0.1,5,-G58,-5650) SOLUTION USING FACTOR TABLES PW = -$1,750 - $400(P|A 10%,4) + $5,250(P|F 10%,5) PW = -$1,750 - $400(3.16987) + $5,250(0.62092) PW = $241.88 DECISION: PREFER BOTH SATELLITES

PROBLEM 5.54 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS IN K$ EOY 0 1 2 3 4 5 6 7 8 9 10

FILTER -$100.00

$10.00

LOAN $50.00 -$14.92 -$14.92 -$14.92 -$14.92 -$14.92

12.00% SAVINGS NET CF (P|F i%,n) PW OF CF -$50.00 1.00000 -$50.00 -$20.00 $50.00 $15.08 0.89286 $13.47 -$21.50 $50.00 $13.58 0.79719 $10.83 -$23.00 $50.00 $12.08 0.71178 $8.60 -$24.50 $50.00 $10.58 0.63552 $6.73 -$26.00 $50.00 $9.08 0.56743 $5.15 -$27.50 $50.00 $22.50 0.50663 $11.40 -$29.00 $50.00 $21.00 0.45235 $9.50 -$30.50 $50.00 $19.50 0.40388 $7.88 -$32.00 $50.00 $18.00 0.36061 $6.49 -$33.50 $50.00 $26.50 0.32197 $8.53 O&M

$38.58 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $38.58 =G7+NPV(0.12,G8:G17) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = (-$100 + $50) + $10(P|F 12%,10) - $14.92(P|A 12%,5) - $20(P|A 12%,10) - $1.50(P|G 12%,10) + $50(P|A 12%,10) PW = (-$100 + $50) + $10(0.32197) - $14.92(3.60478) - $20(5.65022) - $1.50(20.25409) + $50(5.65022) PW = $38.56 DECISION: FILTER IS ECONOMICALLY JUSTIFIED

PROBLEM 5.55 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS IN K$ EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BUILDING FURNITURE -$8,000.00 -$700.00

$900.00

O&M

-$800.00 -$800.00 -$800.00 -$800.00 -$700.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$700.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00

REVENUE $1,460.00 $1,752.00 $2,044.00 $2,336.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00

12.00% NET CF (P|F i%,n) PW OF CF -$8,700.00 1.00000 -$8,700.00 $660.00 0.89286 $589.29 $952.00 0.79719 $758.93 $1,244.00 0.71178 $885.45 $1,536.00 0.63552 $976.16 $1,128.00 0.56743 $640.06 $1,828.00 0.50663 $926.12 $1,828.00 0.45235 $826.89 $1,828.00 0.40388 $738.30 $1,828.00 0.36061 $659.20 $1,128.00 0.32197 $363.19 $1,828.00 0.28748 $525.51 $1,828.00 0.25668 $469.20 $1,828.00 0.22917 $418.93 $1,828.00 0.20462 $374.05 $2,728.00 0.18270 $498.40 $949.66 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $949.66 =G7+NPV(0.12,G8:G22) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE PW. DECISION: MOTEL IS ECONOMICALLY ATTRACTIVE

PROBLEM 5.56 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS IN K$ 20.00% EOY CF (P|F i%,n) PW OF CF 0 -$70,000.00 1.00000 -$70,000.00 1 $20,000.00 0.83333 $16,666.67 2 $19,000.00 0.69444 $13,194.44 3 $18,000.00 0.57870 $10,416.67 4 $17,000.00 0.48225 $8,198.30 5 $16,000.00 0.40188 $6,430.04 6 $15,000.00 0.33490 $5,023.47 7 $14,000.00 0.27908 $3,907.14 8 $13,000.00 0.23257 $3,023.38 9 $12,000.00 0.19381 $2,325.68 10 $11,000.00 0.16151 $1,776.56 11 $10,000.00 0.13459 $1,345.88 12 $9,000.00 0.11216 $1,009.41 13 $8,000.00 0.09346 $747.71 14 $7,000.00 0.07789 $545.21 15 $6,000.00 0.06491 $389.43 16 $5,000.00 0.05409 $270.44 17 $4,000.00 0.04507 $180.29 18 $3,000.00 0.03756 $112.68 19 $2,000.00 0.03130 $62.60 20 $1,000.00 0.02608 $26.08 $5,652.10 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $5,652.10 =C7+NPV(0.2,C8:C27) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$70,000 + $20,000(P|A 20%,20) - $1,000(P|G 20%,20) PW = -$70,000 + $20,000(4.86958) - $1,000(21.73949) PW = $5,652.11

(1) PW = $5,652.10 (2) INVESTMENT IS ATTRACTIVE (3) IF PW >= 0, THEN ATTRACTIVE; OTHERWISE, UNATTRACTIVE

PROBLEM 5.57 IN K$ EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

CF -$70,000.00 $20,000.00 $19,000.00 $18,000.00 $17,000.00 $16,000.00 $15,000.00 $14,000.00 $13,000.00 $12,000.00 $11,000.00 $10,000.00 $9,000.00 $8,000.00 $7,000.00 $6,000.00 $5,000.00 $4,000.00 $3,000.00 $2,000.00 $1,000.00

MARR 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40

NPV $140,000 $125,445 $112,428 $100,751 $90,242 $80,756 $72,168 $64,371 $57,273 $50,794 $44,864 $39,424 $34,421 $29,810 $25,549 $21,604 $17,945 $14,543 $11,374 $8,417 $5,652 $3,063 $635 -$1,646 -$3,793 -$5,816 -$7,724 -$9,528 -$11,235 -$12,852 -$14,386 -$15,843 -$17,228 -$18,546 -$19,802 -$21,000 -$22,144 -$23,237 -$24,283 -$25,284 -$26,243

Nu Things Investment PW versus MARR

$160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $0 -$20,000 0% -$40,000 -$60,000

10%

20%

30%

MARR

=NPV(B30,$C$7:$C$26)+$C$6 =NPV(B31,$C$7:$C$26)+$C$6 SUBSEQUENT EQUATIONS ARE SIMILAR

40%

50%

60%

0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50

-$27,162 -$28,045 -$28,892 -$29,707 -$30,491 -$31,245 -$31,972 -$32,672 -$33,347 -$33,999

Y-AXIS INTERCEPT IS THE UNDISCOUNTED SUM OF CASH FLOWS

X-AXIS INTERCEPT IS THE POINT WHERE PW IS ZERO (INTERNAL RATE OF RETURN)

PROBLEM 5.58 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS PURCHASE 10.00% EOY PURCHASE SAVINGS NET CF (P|F i%,n) PW OF CF 0 -$60,000.00 -$60,000.00 1.00000 -$60,000.00 1 $23,000.00 $23,000.00 0.90909 $20,909.09 2 $23,000.00 $23,000.00 0.82645 $19,008.26 3 $10,000.00 $23,000.00 $33,000.00 0.75131 $24,793.39 $4,710.74 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $4,710.74 =E7+NPV(0.1,E8:E10) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = $4,710.74 =E7+PV(0.1,3,-E8,-10000) SOLUTION USING FACTOR TABLES PW = -$60,000 + $23,000(P|A 10%,3) + $10,000(P|F 10%,3) PW = -$60,000 + $23,000(2.48685) + $10,000(0.75131) PW = $4,710.65 LEASE EOY 0 1 2 3

LEASE SAVINGS NET CF (P|F i%,n) PW OF CF -$21,000.00 -$21,000.00 1.00000 -$21,000.00 -$21,000.00 $23,000.00 $2,000.00 0.90909 $1,818.18 -$21,000.00 $23,000.00 $2,000.00 0.82645 $1,652.89 $23,000.00 $23,000.00 0.75131 $17,280.24 -$248.69 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$248.69 =E30+NPV(0.1,E31:E33) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV t=n) PW = -$248.69 =E30+PV(0.1,3,-E31,-21000) SOLUTION USING FACTOR TABLES PW = -$21,000 + $2,000(P|A 10%,3) + $21,000(P|F 10%,3) PW = -$21,000 + $2,000(2.48685) + $21,000(0.75131) PW = -$248.79 DECISION: PURCHASE IS PREFERRED

PROBLEM 5.59 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS TANK 20.00% EOY TANK O&M NET CF (P|F i%,n) PW OF CF 0 -$426,000.00 -$426,000.00 1.00000 -$426,000.00 1 -$6,400.00 -$6,400.00 0.83333 -$5,333.33 2 -$6,400.00 -$6,400.00 0.69444 -$4,444.44 3 -$6,400.00 -$6,400.00 0.57870 -$3,703.70 4 -$6,400.00 -$6,400.00 0.48225 -$3,086.42 5 -$6,400.00 -$6,400.00 0.40188 -$2,572.02 6 -$6,400.00 -$6,400.00 0.33490 -$2,143.35 7 -$6,400.00 -$6,400.00 0.27908 -$1,786.12 8 -$6,400.00 -$6,400.00 0.23257 -$1,488.44 9 -$6,400.00 -$6,400.00 0.19381 -$1,240.36 10 -$6,400.00 -$6,400.00 0.16151 -$1,033.64 11 -$6,400.00 -$6,400.00 0.13459 -$861.36 12 -$6,400.00 -$6,400.00 0.11216 -$717.80 13 -$6,400.00 -$6,400.00 0.09346 -$598.17 14 -$6,400.00 -$6,400.00 0.07789 -$498.47 15 -$6,400.00 -$6,400.00 0.06491 -$415.40 16 -$6,400.00 -$6,400.00 0.05409 -$346.16 17 -$6,400.00 -$6,400.00 0.04507 -$288.47 18 -$6,400.00 -$6,400.00 0.03756 -$240.39 19 -$6,400.00 -$6,400.00 0.03130 -$200.33 20 -$6,400.00 -$6,400.00 0.02608 -$166.94 -$457,165.31 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$457,165.31 =E7+NPV(0.2,E8:E27) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = -$457,165.31 =E7+PV(0.2,20,-E25) SOLUTION USING FACTOR TABLES PW = -$426,000 - $6,400(P|A 20%,20) PW = -$426,000 - $6,400(4.86958) PW = -$457,165.31

POND EOY 0 1 2 3

TANK -$270,000.00

O&M

NET CF (P|F i%,n) PW OF CF -$270,000.00 1.00000 -$270,000.00 -$17,000.00 -$17,000.00 0.83333 -$14,166.67 -$17,000.00 -$17,000.00 0.69444 -$11,805.56 -$17,000.00 -$17,000.00 0.57870 -$9,837.96

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

-$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00 -$17,000.00

0.48225 0.40188 0.33490 0.27908 0.23257 0.19381 0.16151 0.13459 0.11216 0.09346 0.07789 0.06491 0.05409 0.04507 0.03756 0.03130 0.02608

-$8,198.30 -$6,831.92 -$5,693.27 -$4,744.39 -$3,953.66 -$3,294.71 -$2,745.59 -$2,288.00 -$1,906.66 -$1,588.89 -$1,324.07 -$1,103.39 -$919.49 -$766.25 -$638.54 -$532.11 -$443.43 -$352,782.86 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$352,782.86 =E48+NPV(0.2,E49:E68) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = -$352,782.86 =E48+PV(0.2,20,-E66) SOLUTION USING FACTOR TABLES PW = -$270,000 - $17,000(P|A 20%,20) PW = -$270,000 - $17,000(4.86958) PW = -$352,782.86 DECISION: POND IS PREFERRED

PROBLEM 5.60 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS PUMP A 12.00% EOY PUMP O&M NET CF (P|F i%,n) PW OF CF 0 -$19,400.00 -$19,400.00 1.00000 -$19,400.00 1 -$7,000.00 -$7,000.00 0.89286 -$6,250.00 2 -$7,000.00 -$7,000.00 0.79719 -$5,580.36 3 -$7,000.00 -$7,000.00 0.71178 -$4,982.46 4 -$7,000.00 -$7,000.00 0.63552 -$4,448.63 5 -$7,000.00 -$7,000.00 0.56743 -$3,971.99 6 -$7,000.00 -$7,000.00 0.50663 -$3,546.42 7 -$7,000.00 -$7,000.00 0.45235 -$3,166.44 8 -$7,000.00 -$7,000.00 0.40388 -$2,827.18 9 -$7,000.00 -$7,000.00 0.36061 -$2,524.27 10 $1,940.00 -$7,000.00 -$5,060.00 0.32197 -$1,629.18 -$58,326.93 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$58,326.93 =E7+NPV(0.12,E8:E17) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$58,326.93 =E7+PV(0.12,10,-E8,-1940) SOLUTION USING FACTOR TABLES PW = -$19,400 - $7,000(P|A 12%,10) + $1,940(P|F 12%,10) PW = -$19,400 - $7,000( 5.65022) + $1,940(0.32197) PW = -$58,326.92 PUMP B EOY 0 1 2 3 4 5 6 7 8 9 10

PUMP -$15,000.00

$1,500.00

O&M -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00

NET CF (P|F i%,n) -$15,000.00 1.00000 -$8,400.00 0.89286 -$8,400.00 0.79719 -$8,400.00 0.71178 -$8,400.00 0.63552 -$8,400.00 0.56743 -$8,400.00 0.50663 -$8,400.00 0.45235 -$8,400.00 0.40388 -$8,400.00 0.36061 -$6,900.00 0.32197

PW OF CF -$15,000.00 -$7,500.00 -$6,696.43 -$5,978.95 -$5,338.35 -$4,766.39 -$4,255.70 -$3,799.73 -$3,392.62 -$3,029.12 -$2,221.62 -$61,978.91 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = -$61,978.91 =E37+NPV(0.12,E38:E47) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = -$61,978.91 =E37+PV(0.12,10,-E38,-1500) SOLUTION USING FACTOR TABLES PW = -$15,000 - $8,400(P|A 12%,10) + $1,500(P|F 12%,10) PW = -$15,000 - $8,400( 5.65022) + $1,500(0.32197) PW = -$61,978.89 DECISION: PUMP A IS PREFERRED

PROBLEM 5.61 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS ALTERNATIVE W 11.00% EOY CF (P|F i%,n) PW OF CF 0 -$100,000.00 1.00000 -$100,000.00 1 $20,000.00 0.90090 $18,018.02 2 $20,000.00 0.81162 $16,232.45 3 $50,000.00 0.73119 $36,559.57 4 $80,000.00 0.65873 $52,698.48 5 $110,000.00 0.59345 $65,279.65 $88,788.16 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $88,788.16 =C7+NPV(0.11,C8:C12) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$100,000 + $20,000(P|A 11%,5) + $30,000(P|G 11%,4)(P|F 11%,1) PW = -$100,000 + $20,000(3.69590) + $30,000(4.25020)(0.90090) PW = $88,788.16 ALTERNATIVE X EOY 0 1 2 3 4 5 6 7

CF (P|F i%,n) PW OF CF -$150,000.00 1.00000 -$150,000.00 $40,000.00 0.90090 $36,036.04 $45,000.00 0.81162 $36,523.01 $50,000.00 0.73119 $36,559.57 $55,000.00 0.65873 $36,230.20 $60,000.00 0.59345 $35,607.08 $65,000.00 0.53464 $34,751.65 $70,000.00 0.48166 $33,716.09 $99,423.64 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $99,423.64 =C31+NPV(0.11,C32:C38) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$150,000 + $40,000(P|A 11%,7) + $5,000(P|G 11%,7) PW = -$150,000 + $40,000(4.71220) + $5,000(12.18716) PW = $99,423.80

ALTERNATIVE X IS PREFERRED

PROBLEM 5.62 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS OPTION 1 12.00% EOY CF (P|F i%,n) PW OF CF 0 -$100,000.00 1.00000 -$100,000.00 1 $16,500.00 0.89286 $14,732.14 2 $16,500.00 0.79719 $13,153.70 3 $16,500.00 0.71178 $11,744.37 4 $16,500.00 0.63552 $10,486.05 5 $16,500.00 0.56743 $9,362.54 6 $16,500.00 0.50663 $8,359.41 7 $16,500.00 0.45235 $7,463.76 8 $16,500.00 0.40388 $6,664.07 9 $16,500.00 0.36061 $5,950.07 10 $16,500.00 0.32197 $5,312.56 11 $16,500.00 0.28748 $4,743.36 12 $16,500.00 0.25668 $4,235.14 $2,207.17 <- PW SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $2,207.17 =C7+NPV(0.12,C8:C19) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $2,207.17 =C7+PV(0.12,12,-C8) SOLUTION USING FACTOR TABLES PW = -$100,000 - $16,500(P|A 12%,12) PW = -$100,000 + $16,500(6.19437) PW = $2,207.11 OPTION 2 EOY 0 1 2 3 4 5 6 7 8 9

CF (P|F i%,n) -$75,000.00 1.00000 $14,300.00 0.89286 $14,300.00 0.79719 $14,300.00 0.71178 $14,300.00 0.63552 $14,300.00 0.56743 $14,300.00 0.50663 $14,300.00 0.45235 $14,300.00 0.40388 $14,300.00 0.36061

PW OF CF -$75,000.00 $12,767.86 $11,399.87 $10,178.46 $9,087.91 $8,114.20 $7,244.83 $6,468.59 $5,775.53 $5,156.72 $1,193.97 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $1,193.97 =C39+NPV(0.12,C40:C48) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1) PW = $1,193.97 =C39+PV(0.12,9,-C40) SOLUTION USING FACTOR TABLES PW = -$75,000 + $14,300(P|A 12%,9) PW = -$75,000 + $14,300(5.32825) PW = $1,193.97 OPTION 1 IS PREFERRED

PROBLEM 5.63 E SERIES EOY 0 1 2 3 4 5 6 7

8.00% (P|F i%,n) 1.00000 0.92593 0.85734 0.79383 0.73503 0.68058 0.63017 0.58349

CF -$40,000.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $19,400.00

PW OF CF -$40,000.00 $8,703.70 $8,058.98 $7,462.02 $6,909.28 $6,397.48 $5,923.59 $11,319.71 $14,774.78 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $14,774.78 =D6+NPV(0.08,D7:D13) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $14,774.78 =D6+PV(0.08,7,-D7,-10000) SOLUTION USING FACTOR TABLES PW = -$40,000 + $9,400(P|A 8%,7) + $10,000(P|F 8%,7) PW = -$40,000 + $9,400(5.20637) + $10,000(0.58349) PW = $14,774.78 M SERIES EOY 0 1 2 3 4 5 6 7

(P|F i%,n) 1.00000 0.92593 0.85734 0.79383 0.73503 0.68058 0.63017 0.58349

CF -$60,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $0.00 $0.00

PW OF CF -$60,000.00 $18,518.52 $17,146.78 $15,876.64 $14,700.60 $13,611.66 $0.00 $0.00 $19,854.20 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $19,854.20 =D33+NPV(0.08,D34:D40) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n) PW = $19,854.20 =D33+PV(0.08,5,-D34) SOLUTION USING FACTOR TABLES PW = -$60,000 + $20,000(P|A 8%,5) PW = -$60,000 + $20,000(3.99271) PW = $19,854.20 M SERIES IS PREFERRED

PROBLEM 5.64 ALTERNATIVE 1 10.00% EOY (P|F i%,n) 0 1.00000 1 0.90909 2 0.82645 3 0.75131 4 0.68301 5 0.62092

CF -$50,000.00 $40,000.00 $50,000.00 $60,000.00 $0.00 $0.00

PW OF CF -$50,000.00 $36,363.64 $41,322.31 $45,078.89 $0.00 $0.00 $72,764.84 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $72,764.84 =D6+NPV(0.1,D7:D11) SOLUTION USING EXCEL'S PV FUNCTION PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-INCR CF FOR t=n)+PV(i,2,,-10000) PW = $72,764.84 =D6+PV(0.1,3,-D7,-20000)+PV(0.1,2,,-10000) SOLUTION USING FACTOR TABLES PW = -$50,000 + $40,000(P|A 10%,3) + $10,000(P|F 10%,2) + $20,000(P|F 10%,3) PW = -$50,000 + $40,000(2.48685) + $10,000(0.82645) + $20,000(0.75131) PW = $72,764.70 ALTERNATIVE 2 EOY 0 1 2 3 4 5

(P|F i%,n) 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092

CF -$90,000.00 $35,000.00 $40,000.00 $45,000.00 $50,000.00 $55,000.00

PW OF CF -$90,000.00 $31,818.18 $33,057.85 $33,809.17 $34,150.67 $34,150.67 $76,986.54 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $76,986.54 =D31+NPV(0.1,D32:D36) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$90,000 + $35,000(P|A 10%,5) + $5,000(P|G 10%,5) PW = -$90,000 + $35,000(3.79079) + $5,000(6.86180) PW = $76,986.65 ALTERNATIVE 3 EOY 0 1 2 3 4 5

(P|F i%,n) CF PW OF CF 1.00000 -$100,000.00 -$100,000.00 0.90909 $70,000.00 $63,636.36 0.82645 $65,000.00 $53,719.01 0.75131 $60,000.00 $45,078.89 0.68301 $55,000.00 $37,565.74 0.62092 $0.00 $0.00 $100,000.00 <- PW

SOLUTION USING EXCEL'S NPV FUNCTION PW = INVESTMENT + NPV(i,NET CF FOR t=1,n) PW = $100,000.00 =D55+NPV(0.1,D56:D60) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PV FUNCTION IS NOT USED TO COMPUTE PW. SOLUTION USING FACTOR TABLES PW = -$100,000 + $70,000(P|A 10%,4) - $5,000(P|G 10%,4) PW = -$100,000 + $70,000(3.16987) - $5,000(4.37812) PW = $100,000.30

ALTERNATIVE 3 IS PREFERRED

PROBLEM 5.65 a EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

5.00% CUMULATIVE + CF - CF NET CF (P|F i%,n) PW OF CF PW OF CF -$100,000.00 -$100,000.00 1.00000 -$100,000.00 -$100,000.00 $12,000.00 -$2,000.00 $10,000.00 0.95238 $9,523.81 -$90,476.19 $12,000.00 -$2,000.00 $10,000.00 0.90703 $9,070.29 -$81,405.90 $12,000.00 -$2,000.00 $10,000.00 0.86384 $8,638.38 -$72,767.52 $12,000.00 -$2,000.00 $10,000.00 0.82270 $8,227.02 -$64,540.49 $12,000.00 -$2,000.00 $10,000.00 0.78353 $7,835.26 -$56,705.23 $12,000.00 -$2,000.00 $10,000.00 0.74622 $7,462.15 -$49,243.08 $12,000.00 -$2,000.00 $10,000.00 0.71068 $7,106.81 -$42,136.27 $12,000.00 -$2,000.00 $10,000.00 0.67684 $6,768.39 -$35,367.87 $12,000.00 -$2,000.00 $10,000.00 0.64461 $6,446.09 -$28,921.78 $12,000.00 -$2,000.00 $10,000.00 0.61391 $6,139.13 -$22,782.65 $12,000.00 -$2,000.00 $10,000.00 0.58468 $5,846.79 -$16,935.86 $12,000.00 -$2,000.00 $10,000.00 0.55684 $5,568.37 -$11,367.48 $12,000.00 -$2,000.00 $10,000.00 0.53032 $5,303.21 -$6,064.27 $12,000.00 -$2,000.00 $10,000.00 0.50507 $5,050.68 -$1,013.59 $12,000.00 -$2,000.00 $10,000.00 0.48102 $4,810.17 $3,796.58

LINEAR INTERPOLATION OF DPBP: SOLUTION USING EXCEL'S NPER FUNCTION DPBP = NPER(i,NET CF FOR t=1,INVESTMENT) DPBP = 14.21 =NPER(5%,10000,-100000) b

DECISION RULE IF DPBP <= 3, ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD NOT BUY THE GANG PUNCH

14.21

<- DPBP

=(ABS(H20)/(H21-H20))+B20

PROBLEM 5.66 a

UNDISCOUNTED PBP IS EQUIVALENT TO DPBP WITH AN INTEREST RATE OF ZERO.

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.00% CUMULATIVE - CF NET CF (P|F i%,n) PW OF CF PW OF CF -$100,000.00 -$100,000.00 1.00000 -$100,000.00 -$100,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$90,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$80,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$70,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$60,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$50,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$40,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$30,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$20,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 -$10,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 $0.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 $12,000.00 -$2,000.00 $10,000.00 1.00000 $10,000.00 + CF

10.00 <- PBP SOLUTION USING EXCEL'S NPER FUNCTION PBP = NPER(0%,NET CF FOR t=1,INVESTMENT) PBP = 10.00 =NPER(0%,E8,E7) b

DECISION RULE IF PBP <= 3, ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD NOT BUY THE GANG PUNCH

USING PW, THE RECOMMENDATION WAS TO BUY THE GANG PUNCH USING DPBP, THE RECOMMENDATION WAS TO NOT BUY THE GANG PUNCH USING PBP, THE RECOMMENDATION WAS TO NOT BUY THE GANG PUNCH THE DECISIONS ARE INCONSISTENT PW IS THE PREFERRED METHOD TO PROPERLY ACCOUNT FOR THE TIME VALUE OF MONEY, THEREFORE THE RECOMMENDATION SHOULD BE TO BUY THE GANG PUNCH

PROBLEM 5.67 a

EOY 0 1 2 3 4 5

+ CF $600.00 $600.00 $700.00 $700.00 $700.00

- CF -$1,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

10.00% CUMULATIVE NET CF (P|F i%,n) PW OF CF PW OF CF -$1,000.00 1.00000 -$1,000.00 -$1,000.00 $300.00 0.90909 $272.73 -$727.27 $300.00 0.82645 $247.93 -$479.34 $400.00 0.75131 $300.53 -$178.81 $400.00 0.68301 $273.21 $94.39 $400.00 0.62092 $248.37

LINEAR INTERPOLATION OF DPBP:

3.65 <- DPBP

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S NPER FUNCTION IS NOT USED TO COMPUTE DPBP. b

DECISION RULE IF DPBP <= 3, ACCEPT; OTHERWISE, REJECT

HOME INNOVATIONS SHOULD NOT PURSUE THE NEW PRODUCT SINCE THE NET CF SERIES IS NOT A UNIFORM SERIES, EXCEL'S NPER FUNCTION CANNOT BE USED TO COMPUTE DPBP

=(ABS(H10)/(H11-H10))+B10

PROBLEM 5.68

UNDISCOUNTED PBP IS EQUIVALENT TO DPBP WITH AN INTEREST RATE OF ZERO.

EOY 0 1 2 3 4 5

+ CF $600.00 $600.00 $700.00 $700.00 $700.00

- CF -$1,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

0.00% NET CF (P|F i%,n) -$1,000.00 1.00000 $300.00 1.00000 $300.00 1.00000 $400.00 1.00000 $400.00 1.00000 $400.00 1.00000

PW OF CF -$1,000.00 $300.00 $300.00 $400.00 $400.00 $400.00

CUMULATIVE PW OF CF -$1,000.00 -$700.00 -$400.00 $0.00

3.00 <- PBP DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S NPER FUNCTION IS NOT USED TO COMPUTE PBP. b

DECISION RULE IF PBP <= 3, ACCEPT; OTHERWISE, REJECT

LENGTHY LOUNGERS SHOULD PURSUE THE NEW PRODUCT

USING PW, THE RECOMMENDATION WAS PURSUE THE NEW PRODUCT USING DPBP, THE RECOMMENDATION WAS TO NOT PURSUE THE NEW PRODUCT USING PBP, THE RECOMMENDATION WAS TO PURSUE THE NEW PRODUCT THE DECISIONS ARE INCONSISTENT PW IS THE PREFERRED METHOD TO PROPERLY ACCOUNT FOR THE TIME VALUE OF MONEY, THEREFORE, THE RECOMMENDATION SHOULD BE TO PURSUE THE NEW PRODUCT

PROBLEM 5.69 a

VENDOR A SOFTWARE EOY 0 1 2 3 4

10.00% CUMULATIVE + CF - CF NET CF (P|F i%,n) PW OF CF PW OF CF -$380,000.00 -$380,000.00 1.00000 -$380,000.00 -$380,000.00 $125,000.00 $125,000.00 0.90909 $113,636.36 -$266,363.64 $125,000.00 $125,000.00 0.82645 $103,305.79 -$163,057.85 $125,000.00 $125,000.00 0.75131 $93,914.35 -$69,143.50 $125,000.00 $125,000.00 0.68301 $85,376.68 $16,233.18

LINEAR INTERPOLATION OF DPBP:

3.81

<- DPBP

=(ABS(H9)/(H10-H9))+B9

<- DPBP

=(ABS(H25)/(H26-H25))+B25

SOLUTION USING EXCEL'S NPER FUNCTION DPBP = NPER(i,NET CF FOR t=1,INVESTMENT) DPBP = 3.802 =NPER(10%,E7,E6)

VENDOR B SOFTWARE EOY 0 1 2 3 4

CUMULATIVE + CF - CF NET CF (P|F i%,n) PW OF CF PW OF CF -$280,000.00 -$280,000.00 1.00000 -$280,000.00 -$280,000.00 $95,000.00 $95,000.00 0.90909 $86,363.64 -$193,636.36 $95,000.00 $95,000.00 0.82645 $78,512.40 -$115,123.97 $95,000.00 $95,000.00 0.75131 $71,374.91 -$43,749.06 $95,000.00 $95,000.00 0.68301 $64,886.28 $21,137.22

LINEAR INTERPOLATION OF DPBP:

3.67

SOLUTION USING EXCEL'S NPER FUNCTION DPBP = NPER(i,NET CF FOR t=1,INVESTMENT) DPBP = 3.664 =NPER(10%,E23,E22) b

SHORTEST DPBP IS VENDOR B

THIS DECISION AGREES WITH THE RECOMMENDATION FROM THE PW ANALYSIS

PROBLEM 5.70 a

NOTE THAT THE ESTIMATED LIVES ARE DIFFERENT SO A COMMON PLANNING HORIZON MUST BE ESTABLISHED. 10 YEARS IS SELECTED IN THE ANALYSIS BELOW.

MODEL 127B EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $29,400.00

- CF -$50,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00

8.00% CUMULATIVE NET CF (P|F i%,n) PW OF CF PW OF CF -$50,000.00 1.00000 -$50,000.00 -$50,000.00 $9,400.00 0.92593 $8,703.70 -$41,296.30 $9,400.00 0.85734 $8,058.98 -$33,237.31 $9,400.00 0.79383 $7,462.02 -$25,775.29 $9,400.00 0.73503 $6,909.28 -$18,866.01 $9,400.00 0.68058 $6,397.48 -$12,468.53 $9,400.00 0.63017 $5,923.59 -$6,544.93 $9,400.00 0.58349 $5,484.81 -$1,060.12 $9,400.00 0.54027 $5,078.53 $4,018.41 $9,400.00 0.50025 $4,702.34 $8,720.75 $19,400.00 0.46319 $8,985.95 $17,706.70

LINEAR INTERPOLATION OF DPBP:

7.21

<- DPBP

=(ABS(H17)/(H18-H17))+B17

BY REVIEWING THE CUMULATIVE PW OF CF COLUMN, WE CAN SEE THAT THE DPBP OCCURS PRIOR TO YEAR 10 WHERE THE NON-UNIFORM CASH FLOW OCCURS, SO WE CAN USE THE NPER FUNCTION TO DETERMINE THE VALUE OF DPBP SOLUTION USING EXCEL'S NPER FUNCTION DPBP = NPER(i,NET CF FOR t=1,INVESTMENT) DPBP = 7.202 =NPER(8%,E11,E10)

MODEL 334A

EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00

- CF -$80,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$86,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00

CUMULATIVE NET CF (P|F i%,n) PW OF CF PW OF CF -$80,000.00 1.00000 -$80,000.00 -$80,000.00 $20,000.00 0.92593 $18,518.52 -$61,481.48 $20,000.00 0.85734 $17,146.78 -$44,334.71 $20,000.00 0.79383 $15,876.64 -$28,458.06 $20,000.00 0.73503 $14,700.60 -$13,757.46 -$60,000.00 0.68058 -$40,834.99 -$54,592.46 $20,000.00 0.63017 $12,603.39 -$41,989.06 $20,000.00 0.58349 $11,669.81 -$30,319.25 $20,000.00 0.54027 $10,805.38 -$19,513.88 $20,000.00 0.50025 $10,004.98 -$9,508.90 $20,000.00 0.46319 $9,263.87 -$245.03

BY REVIEWING THE CUMULATIVE PW OF CF COLUMN, WE CAN SEE THAT THIS INVESTMENT DOES NOT ACHIEVE DPBP WITHIN ITS PLANNING HORIZON.

OCTAVIA'S BAKERY SHOULD BUY MODEL 127B

THIS DECISION AGREES WITH THE RECOMMENDATION FROM THE PW ANALYSIS

PROBLEM 5.71

LAGRANGE EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

15.00% CUMULATIVE - CF NET CF (P|F i%,n) PW OF CF PW OF CF -$1,260,000.00 -$1,260,000.00 1.00000 -$1,260,000.00 -$1,260,000.00 $480,000.00 0.86957 $417,391.30 -$842,608.70 $480,000.00 0.75614 $362,948.96 -$479,659.74 $480,000.00 0.65752 $315,607.79 -$164,051.94 $480,000.00 0.57175 $274,441.56 $110,389.61 $480,000.00 0.49718 $238,644.83 $349,034.45 $480,000.00 0.43233 $207,517.25 $556,551.69 $480,000.00 0.37594 $180,449.78 $737,001.47 $480,000.00 0.32690 $156,912.85 $893,914.32 $480,000.00 0.28426 $136,445.96 $1,030,360.28 $480,000.00 0.24718 $118,648.66 $1,149,008.94 $480,000.00 0.21494 $103,172.75 $1,252,181.69 $480,000.00 0.18691 $89,715.43 $1,341,897.12

LINEAR INTERPOLATION OF DPBP:

3.60

<- DPBP

=(ABS(H10)/(H11-H10))+B10

<- DPBP

=(ABS(H32)/(H33-H32))+B32

<- DPBP

=(ABS(H57)/(H58-H57))+B57

SOLUTION USING EXCEL'S NPER FUNCTION DPBP = NPER(i,NET CF FOR t=1,INVESTMENT) DPBP = 3.581 =NPER(15%,E8,E7) AUBURN EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

CUMULATIVE - CF NET CF (P|F i%,n) PW OF CF PW OF CF -$1,000,000.00 -$1,000,000.00 1.00000 -$1,000,000.00 -$1,000,000.00 $410,000.00 0.86957 $356,521.74 -$643,478.26 $410,000.00 0.75614 $310,018.90 -$333,459.36 $410,000.00 0.65752 $269,581.66 -$63,877.70 $410,000.00 0.57175 $234,418.83 $170,541.13 $410,000.00 0.49718 $203,842.46 $374,383.59 $410,000.00 0.43233 $177,254.31 $551,637.90 $410,000.00 0.37594 $154,134.19 $705,772.09 $410,000.00 0.32690 $134,029.73 $839,801.82 $410,000.00 0.28426 $116,547.59 $956,349.41 $410,000.00 0.24718 $101,345.73 $1,057,695.14 $410,000.00 0.21494 $88,126.72 $1,145,821.86 $410,000.00 0.18691 $76,631.93 $1,222,453.79

LINEAR INTERPOLATION OF DPBP:

3.24

SOLUTION USING EXCEL'S NPER FUNCTION DPBP = NPER(i,NET CF FOR t=1,INVESTMENT) DPBP = 3.259 =NPER(15%,E31,E30) ANNISTON EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00

CUMULATIVE - CF NET CF (P|F i%,n) PW OF CF PW OF CF -$1,620,000.00 -$1,620,000.00 1.00000 -$1,620,000.00 -$1,620,000.00 $520,000.00 0.86957 $452,173.91 -$1,167,826.09 $520,000.00 0.75614 $393,194.71 -$774,631.38 $520,000.00 0.65752 $341,908.44 -$432,722.94 $520,000.00 0.57175 $297,311.69 -$135,411.25 $520,000.00 0.49718 $258,531.90 $123,120.65 $520,000.00 0.43233 $224,810.35 $347,931.00 $520,000.00 0.37594 $195,487.26 $543,418.26 $520,000.00 0.32690 $169,988.92 $713,407.18 $520,000.00 0.28426 $147,816.45 $861,223.64 $520,000.00 0.24718 $128,536.05 $989,759.69 $520,000.00 0.21494 $111,770.48 $1,101,530.16 $520,000.00 0.18691 $97,191.72 $1,198,721.88

LINEAR INTERPOLATION OF DPBP: SOLUTION USING EXCEL'S NPER FUNCTION DPBP = NPER(i,NET CF FOR t=1,INVESTMENT) DPBP = 4.506 =NPER(15%,E54,E53) b

AUBURN IS PREFERRED

THIS DECISION IS INCONSISTENT WITH PW ANALYSIS

4.52

PROBLEM 5.72 CC(CONSTRUCTION) = $10,000,000 CC(ANNUAL MAINTENANCE) = ($700,000+$75,000(A|G 4%,5))/0.04 CC(ANNUAL MAINTENANCE) = ($700,000+$75,000(1.92161))/0.04 = $21,103,018 USING EXCEL, CC(ANNUAL MAINTENANCE) =1000*PMT(4%,5,-NPV(4%,700,775,850,925,1000))/0.04 CC(ANNUAL MAINTENANCE) = $21,103,020.28 CC(MAJOR REPAIRS) = ($2,000,000(A|F 4%,5))/0.04 CC(MAJOR REPAIRS) = ($2,000,000(0.18463))/0.04 = $9,231,500 USING EXCEL, CC(MAJOR REPAIRS) =PMT(4%,5,,-2000000)/0.04 CC(MAJOR REPAIRS) = $9,231,355.67 TOTAL CC = $10,000,000 + $21,103,018 + $9,231,500 = $40,334,518. USING EXCEL, TOTAL CC = $10,000,000 + $21,103,020.28 + $9,231,355.67 = $40,334,375.95.

PROBLEM 5.73 DESIGN A CC(INITIAL COST) = $2,500,000 CC(ANNUAL MAINTENANCE) = $800,000/0.05 = $16,000,000 CC(MAJOR REPAIRS) = ($1,250,000(A|F 5%,5))/0.05 CC(MAJOR REPAIRS) = ($1,250,000(0.18097))/0.05 = $4,524,250 USING EXCEL, CC(MAJOR REPAIRS) =PMT(5%,5,,-1250000)/0.05 CC(MAJOR REPAIRS) = $4,524,369.95 TOTAL CC = $2,500,000 + $16,000,000 + $4,524,250 = $23,024,250 USING EXCEL, TOTAL CC = $2,500,000 + $16,000,000 + $4,524,369.95 = $23,024,369.95

DESIGN B CC(INITIAL COST) = $5,750,000 CC(ANNUAL MAINTENANCE) = $600,000/0.05 = $12,000,000 CC(MAJOR REPAIRS) = ($3,000,000(A|F 5%,10))/0.05 CC(MAJOR REPAIRS) = ($3,000,000(0.7950))/0.05 = $4,770,000 USING EXCEL, CC(MAJOR REPAIRS) =PMT(5%,10,,-3000000)/0.05 CC(MAJOR REPAIRS) = $4,770,274.50 TOTAL CC = $5,750,000 + $12,000,000 + $4,770,000 = $22,520,000 USING EXCEL, TOTAL CC = $5,750,000 + $12,000,000 + $4,770,274.50 = $22,520,274.50 DESIGN B IS PREFERRED

PROBLEM 5.74 CC(CONSTRUCTION) = $2,000,000 CC(ANNUAL MAINTENANCE) = $50,000/0.10 = $500,000 CC(INSPECTION) = $250,000(A|F 10%,5)/0.10 = 250,000(0.16380)/0.10 = $409,500 USING EXCEL, CC(INSPECTION) =PMT(10%,5,,-250000)/0.1 CC(INSPECTION) = $409,493.70 TOTAL CC = $2,000,000 + $500,000 + $409,500 = $2,909,500 USING EXCEL, TOTAL CC = $2,000,000 + $500,000 + $409,493.70 = $2,909,493.70

PROBLEM 5.75 CC = ($1,000 + $1,000(A|G 0.5%,12))/0.005 CC = ($1,000 + $1,000(5.44057))/0.005 CC = 1,288,114 USING EXCEL, CC =1000*PMT(0.005,12,-NPV(0.5%,1,2,3,4,5,6,7,8,9,10,11,12))/0.005 CC = $1,288,113.74

MINIMUM TICKET PRICE = 1,288,114 / 1,000,000 = $1.288114 OR APPROXIMATELY $1.29

PROBLEM 5.76 a

A = $500,000(A|P 4%,20) A = $500,000(0.07358) A = $36,790 USING EXCEL, A =PMT(4%,20,-500000) A= $36,790.88

A = $500,000(A|P 4%,30) A = $500,000(0.05783) A = $28,915 USING EXCEL, A =PMT(4%,30,-500000) A= $28,915.05

A = $500,000(A|P 4%,50) A = $500,000(0.04655) A = $23,275 USING EXCEL, A =PMT(4%,50,-500000) A= $23,275.10

A=P*I A = $500,000 (0.04) A = $20,000

PROBLEM 5.77

YEARS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

$500,000 4.00% (A|P 4%,n) 1.04000 0.53020 0.36035 0.27549 0.22463 0.19076 0.16661 0.14853 0.13449 0.12329 0.11415 0.10655 0.10014 0.09467 0.08994 0.08582 0.08220 0.07899 0.07614 0.07358 0.07128 0.06920 0.06731 0.06559 0.06401 0.06257 0.06124 0.06001 0.05888 0.05783 0.05686 0.05595 0.05510 0.05431 0.05358 0.05289 0.05224 0.05163 0.05106 0.05052 0.05002 0.04954 0.04909 0.04866 0.04826 0.04788 0.04752 0.04718 0.04686 0.04655 0.04626 0.04598 0.04572 0.04547 0.04523 0.04500 0.04479 0.04458 0.04439 0.04420 0.04402 0.04385 0.04369 0.04354 0.04339 0.04325 0.04311 0.04299 0.04286 0.04275 0.04263 0.04252 0.04242 0.04232 0.04223 0.04214 0.04205 0.04197 0.04189 0.04181 0.04174 0.04167 0.04160 0.04154 0.04148 0.04142 0.04136 0.04131 0.04126 0.04121 0.04116 0.04111 0.04107 0.04103 0.04099 0.04095 0.04091 0.04088 0.04084 0.04081

SCHOLARSHIPS $520,000 $265,098 $180,174 $137,745 $112,314 $95,381 $83,305 $74,264 $67,246 $61,645 $57,075 $53,276 $50,072 $47,334 $44,971 $42,910 $41,099 $39,497 $38,069 $36,791 $35,640 $34,599 $33,655 $32,793 $32,006 $31,284 $30,619 $30,006 $29,440 $28,915 $28,428 $27,974 $27,552 $27,157 $26,789 $26,443 $26,120 $25,816 $25,530 $25,262 $25,009 $24,770 $24,545 $24,332 $24,131 $23,941 $23,761 $23,590 $23,429 $23,275 $23,129 $22,991 $22,860 $22,735 $22,616 $22,502 $22,395 $22,292 $22,194 $22,101 $22,012 $21,927 $21,846 $21,769 $21,695 $21,625 $21,557 $21,493 $21,431 $21,373 $21,316 $21,262 $21,211 $21,162 $21,115 $21,069 $21,026 $20,985 $20,945 $20,907 $20,871 $20,836 $20,802 $20,770 $20,740 $20,710 $20,682 $20,655 $20,629 $20,604 $20,580 $20,557 $20,535 $20,514 $20,494 $20,474 $20,456 $20,438 $20,420 $20,404

Scholarship Dollars versus Endowment Life for a $500,000 Endowment $600,000

$500,000

$400,000

Dollars

P= i=

$300,000

$200,000

$100,000

$0 0

Endowment Life (years)

100

PROBLEM 5.78

EOY 0 1 2 3 4 5

+ CF $100.00 $300.00 $500.00 $400.00 $350.00 $250.00

- CF -$1,100.00 -$50.00 -$250.00 -$150.00 -$100.00 $0.00

NET CF -$1,000.00 $250.00 $250.00 $250.00 $250.00 $250.00

EQUIVALENT ANNUAL WORTH = -$1,000(A|P 6%,5) + $250 EQUIVALENT ANNUAL WORTH = -$1,000(0.23740) + $250 EQUIVALENT ANNUAL WORTH = $12.60 USING EXCEL, AW =250+PMT(6%,5,1000) AW = $12.60 CC = AW / i CC = $12.60 / 0.06 CC = $210.00

PROBLEM 5.79 THERE WILL BE 40 DEPOSITS OF $4,000 THE AMOUNT IN THE ACCOUNT AT THE TIME OF THE LAST DEPOSIT IS: F = $4,000(F|A 8%,40) F = $4,000(259.05652) F = $1,036,226.08 USING EXCEL, F =FV(8%,40,-4000) F= $1,036,226.07 THIS AMOUNT WILL DRAW INTEREST FOR 2 YEARS TO POSITION IT ONE PERIOD BEFORE THE FIRST WITHDRAWAL F = $1,036,226.08(F|P 8%,2) F = $1,036,226.08(1.16640) F = $1,208,654.10 USING EXCEL, F =FV(8%,2,,FV(8%,40,4000)) F= $1,208,654.09 a

WITHDRAWALS FOR 20 YEARS A = $1,208,654.10(A|P 8%,20) A = $1,208,654.10(0.10185) A = $123,101.42 USING EXCEL, A =PMT(8%,20,-FV(8%,2,,FV(8%,40,4000))) A= $123,104.09

WITHDRAWALS FOR 30 YEARS A = $1,208,654.10(A|P 8%,30) A = $1,208,654.10(0.08883) A = $107,364.74 USING EXCEL, A =PMT(8%,30,-FV(8%,2,,FV(8%,40,4000))) A= $107,361.64

WITHDRAWALS FOREVER A = $1,208,654.10 * i A = $1,208,654.10 * 0.08 A = $96,692.33 USING EXCEL, A = $1,208,654.09*i A = $1,208,654.09(0.08) A = $96,692.33

PROBLEM 5.80 PAY-ME-NOW CC = $5,000 PAY-ME-LATER CC = $1,000(A|P 6%,5) / i CC = $1,000(0.23740) / 0.06 CC = $3,956.67 USING EXCEL, CC =PMT(6%,5,-1000)/0.06 CC = $3,956.61 PAY-ME-FOREVER CC = $250 / i CC = $250 / 0.06 CC = $4,166.67 DECISION: PAY-ME-LATER IS PREFERRED

PROBLEM 6.1 COMPARE BOTH TERMS ARE ASSOCIATED WITH TIME VALUE OF MONEY CALCULATIONS AND MOVING MONEY IN TIME TO DETERMINE AN EQUIVALENT AMOUNT OF MONEY AT A DIFFERENT POINT IN TIME. CONTRAST DISCOUNTING IS GENERALLY ASSOCIATED WITH MOVING MONEY BACKWARD IN TIME. COMPOUNDING IS GENERALLY ASSOCIATED WITH MOVING MONEY FORWARD FORWARD IN TIME.

PROBLEM 6.2 a b c d e f

TRUE TRUE TRUE TRUE FALSE FALSE

PROBLEM 6.3 a b c

THE FUTURE WORTH OF THE PROJECT WILL BE GREATER THAN ZERO THE FUTURE WORTH OF THE PROJECT WILL BE EQUAL TO ZERO THE FUTURE WORTH OF THE PROJECT WILL BE LESS THAN ZERO

PROBLEM 6.4 a

A = $2,000,000(A|F 10.4%,40) = 2000000(0.00203) = $4,060 USING EXCEL'S PMT FUNCTION A= $4,052.10 =PMT(10.4%,40,,-2000000)

A = $2,000,000(P|F 10.4%,1)(A|F 10.4%,40) = 2000000(0.90580)(0.00203) = $3,677.55 USING EXCEL FUNCTIONS A = NPV(10.4%,PMT(10.4%,40,,-2000000)) A= $3,670.38 = NPV(10.4%,PMT(10.4%,40,,-2000000)) OR A=PV(10.4%,1,PMT(10.4%,40,,2000000)) A= $3,670.38 =PV(10.4%,1,PMT(10.4%,40,,2000000))

(i)

(ii) d

(i)

(ii)

$2,000,000 = (A + 200(A|G 10.4%,40))(F|A 10.4%,40) $2,000,000 = (A + 200(8.83614))(493.57183) A = FIRST DEPOSIT = $2,284.87 DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FUNCTIONS ARE NOT USED TO COMPUTE DEPOSITS. LAST DEPOSIT = $2,284.87 + 39(200) = $10,084.87 $2,000,000 = A(F|A1 10.4%, 5%, 40) $2,000,000 = A(838.73114) A = FIRST DEPOSIT = $2,384.55 DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FUNCTIONS ARE NOT USED TO COMPUTE DEPOSITS. LAST DEPOSIT = $2,284.87(1.05)^39 = $15,319.48

PROBLEM 6.5 a

A = $2,000,000(A|F 10.4%/12,40*12) = 2000000(A|F 0.8667%,480) = 2000000(0.00014) = $280 USING EXCEL'S PMT FUNCTION A= $279.87 =PMT(10.4%/12,40*12,,-2000000)

THIS QUESTION PRESUMES THE STARTING DEPOSIT IS $280 PER MONTH AS CALCULATED IN PART a. THE AMOUNT OF THE DEPOSIT IS INCREASED BY 4% AFTER EACH YEAR. THE SUM AT THE BOTTOM OF THE FW COLUMN BELOW REPRESENTS THE ACCOUNT BALANCE; A TOTAL OF $2,965,261.

MONTH 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

CF $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $291.20 $291.20 $291.20 $291.20 $291.20 $291.20 $291.20 $291.20 $291.20 $291.20 $291.20 $291.20 $302.85 $302.85 $302.85 $302.85 $302.85 $302.85 $302.85 $302.85 $302.85 $302.85 $302.85 $302.85 $314.96 $314.96 $314.96 $314.96 $314.96 $314.96 $314.96 $314.96 $314.96 $314.96 $314.96 $314.96 $327.56 $327.56 $327.56 $327.56 $327.56 $327.56 $327.56 $327.56 $327.56 $327.56

0.87% (F|P i%,480-t) 62.39265 61.85656 61.32508 60.79816 60.27577 59.75787 59.24442 58.73538 58.23071 57.73038 57.23435 56.74258 56.25504 55.77168 55.29248 54.81740 54.34639 53.87944 53.41650 52.95753 52.50251 52.05140 51.60416 51.16077 50.72118 50.28538 49.85332 49.42497 49.00030 48.57928 48.16187 47.74806 47.33780 46.93106 46.52782 46.12804 45.73170 45.33876 44.94920 44.56299 44.18010 43.80049 43.42415 43.05104 42.68114 42.31441 41.95084 41.59039 41.23304 40.87875 40.52752 40.17930 39.83407 39.49180 39.15248 38.81608 38.48256 38.15191

FW OF CF $17,469.94 $17,319.84 $17,171.02 $17,023.48 $16,877.22 $16,732.20 $16,588.44 $16,445.91 $16,304.60 $16,164.51 $16,025.62 $15,887.92 $16,381.47 $16,240.71 $16,101.17 $15,962.83 $15,825.67 $15,689.69 $15,554.88 $15,421.23 $15,288.73 $15,157.37 $15,027.13 $14,898.02 $15,360.81 $15,228.83 $15,097.98 $14,968.25 $14,839.64 $14,712.14 $14,585.73 $14,460.40 $14,336.16 $14,212.98 $14,090.86 $13,969.79 $14,403.74 $14,279.98 $14,157.29 $14,035.65 $13,915.05 $13,795.49 $13,676.95 $13,559.44 $13,442.93 $13,327.43 $13,212.92 $13,099.39 $13,506.31 $13,390.26 $13,275.21 $13,161.15 $13,048.06 $12,935.95 $12,824.80 $12,714.61 $12,605.36 $12,497.06

59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130

$327.56 $327.56 $340.66 $340.66 $340.66 $340.66 $340.66 $340.66 $340.66 $340.66 $340.66 $340.66 $340.66 $340.66 $354.29 $354.29 $354.29 $354.29 $354.29 $354.29 $354.29 $354.29 $354.29 $354.29 $354.29 $354.29 $368.46 $368.46 $368.46 $368.46 $368.46 $368.46 $368.46 $368.46 $368.46 $368.46 $368.46 $368.46 $383.20 $383.20 $383.20 $383.20 $383.20 $383.20 $383.20 $383.20 $383.20 $383.20 $383.20 $383.20 $398.53 $398.53 $398.53 $398.53 $398.53 $398.53 $398.53 $398.53 $398.53 $398.53 $398.53 $398.53 $414.47 $414.47 $414.47 $414.47 $414.47 $414.47 $414.47 $414.47 $414.47 $414.47

37.82410 37.49911 37.17691 36.85748 36.54079 36.22683 35.91556 35.60696 35.30102 34.99771 34.69700 34.39888 34.10332 33.81029 33.51979 33.23178 32.94625 32.66316 32.38252 32.10428 31.82843 31.55496 31.28383 31.01503 30.74855 30.48435 30.22242 29.96274 29.70530 29.45006 29.19702 28.94616 28.69744 28.45087 28.20641 27.96406 27.72379 27.48558 27.24942 27.01528 26.78316 26.55304 26.32489 26.09870 25.87445 25.65214 25.43173 25.21321 24.99658 24.78180 24.56887 24.35777 24.14848 23.94099 23.73529 23.53135 23.32916 23.12871 22.92999 22.73297 22.53764 22.34400 22.15201 21.96168 21.77298 21.58590 21.40043 21.21655 21.03426 20.85352 20.67435 20.49671

$12,389.68 $12,283.22 $12,664.79 $12,555.97 $12,448.09 $12,341.13 $12,235.10 $12,129.97 $12,025.75 $11,922.42 $11,819.98 $11,718.42 $11,617.73 $11,517.91 $11,875.70 $11,773.66 $11,672.50 $11,572.21 $11,472.78 $11,374.20 $11,276.47 $11,179.58 $11,083.53 $10,988.30 $10,893.88 $10,800.28 $11,135.78 $11,040.10 $10,945.24 $10,851.20 $10,757.96 $10,665.53 $10,573.89 $10,483.03 $10,392.96 $10,303.66 $10,215.13 $10,127.36 $10,441.96 $10,352.24 $10,263.29 $10,175.11 $10,087.68 $10,001.00 $9,915.07 $9,829.88 $9,745.42 $9,661.69 $9,578.67 $9,496.37 $9,791.37 $9,707.24 $9,623.83 $9,541.14 $9,459.16 $9,377.89 $9,297.31 $9,217.42 $9,138.23 $9,059.71 $8,981.87 $8,904.69 $9,181.31 $9,102.42 $9,024.21 $8,946.67 $8,869.80 $8,793.59 $8,718.03 $8,643.13 $8,568.86 $8,495.24

131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202

$414.47 $414.47 $431.05 $431.05 $431.05 $431.05 $431.05 $431.05 $431.05 $431.05 $431.05 $431.05 $431.05 $431.05 $448.29 $448.29 $448.29 $448.29 $448.29 $448.29 $448.29 $448.29 $448.29 $448.29 $448.29 $448.29 $466.22 $466.22 $466.22 $466.22 $466.22 $466.22 $466.22 $466.22 $466.22 $466.22 $466.22 $466.22 $484.87 $484.87 $484.87 $484.87 $484.87 $484.87 $484.87 $484.87 $484.87 $484.87 $484.87 $484.87 $504.26 $504.26 $504.26 $504.26 $504.26 $504.26 $504.26 $504.26 $504.26 $504.26 $504.26 $504.26 $524.43 $524.43 $524.43 $524.43 $524.43 $524.43 $524.43 $524.43 $524.43 $524.43

20.32060 20.14600 19.97290 19.80129 19.63115 19.46248 19.29525 19.12946 18.96510 18.80215 18.64060 18.48043 18.32164 18.16422 18.00815 17.85342 17.70002 17.54794 17.39716 17.24768 17.09949 16.95257 16.80691 16.66250 16.51933 16.37739 16.23667 16.09717 15.95886 15.82173 15.68579 15.55101 15.41740 15.28493 15.15360 15.02339 14.89431 14.76634 14.63946 14.51367 14.38897 14.26534 14.14277 14.02125 13.90078 13.78134 13.66293 13.54553 13.42914 13.31376 13.19936 13.08595 12.97352 12.86204 12.75153 12.64197 12.53335 12.42566 12.31889 12.21305 12.10811 12.00407 11.90093 11.79868 11.69730 11.59680 11.49715 11.39837 11.30043 11.20333 11.10707 11.01164

$8,422.25 $8,349.88 $8,609.26 $8,535.29 $8,461.95 $8,389.25 $8,317.16 $8,245.70 $8,174.85 $8,104.61 $8,034.98 $7,965.94 $7,897.49 $7,829.64 $8,072.86 $8,003.49 $7,934.72 $7,866.55 $7,798.96 $7,731.95 $7,665.51 $7,599.65 $7,534.35 $7,469.61 $7,405.43 $7,341.81 $7,569.87 $7,504.83 $7,440.35 $7,376.42 $7,313.04 $7,250.20 $7,187.91 $7,126.15 $7,064.92 $7,004.22 $6,944.03 $6,884.37 $7,098.23 $7,037.24 $6,976.77 $6,916.83 $6,857.39 $6,798.47 $6,740.06 $6,682.15 $6,624.73 $6,567.81 $6,511.38 $6,455.43 $6,655.97 $6,598.78 $6,542.08 $6,485.87 $6,430.14 $6,374.89 $6,320.12 $6,265.81 $6,211.98 $6,158.60 $6,105.69 $6,053.22 $6,241.26 $6,187.64 $6,134.47 $6,081.76 $6,029.51 $5,977.70 $5,926.34 $5,875.42 $5,824.94 $5,774.89

203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274

$524.43 $524.43 $545.41 $545.41 $545.41 $545.41 $545.41 $545.41 $545.41 $545.41 $545.41 $545.41 $545.41 $545.41 $567.23 $567.23 $567.23 $567.23 $567.23 $567.23 $567.23 $567.23 $567.23 $567.23 $567.23 $567.23 $589.92 $589.92 $589.92 $589.92 $589.92 $589.92 $589.92 $589.92 $589.92 $589.92 $589.92 $589.92 $613.51 $613.51 $613.51 $613.51 $613.51 $613.51 $613.51 $613.51 $613.51 $613.51 $613.51 $613.51 $638.06 $638.06 $638.06 $638.06 $638.06 $638.06 $638.06 $638.06 $638.06 $638.06 $638.06 $638.06 $663.58 $663.58 $663.58 $663.58 $663.58 $663.58 $663.58 $663.58 $663.58 $663.58

10.91702 10.82322 10.73023 10.63803 10.54663 10.45601 10.36617 10.27710 10.18880 10.10125 10.01446 9.92842 9.84311 9.75853 9.67469 9.59156 9.50915 9.42744 9.34644 9.26613 9.18652 9.10759 9.02933 8.95175 8.87483 8.79858 8.72298 8.64803 8.57373 8.50006 8.42702 8.35462 8.28283 8.21167 8.14111 8.07116 8.00181 7.93306 7.86489 7.79732 7.73032 7.66390 7.59805 7.53277 7.46804 7.40388 7.34026 7.27719 7.21467 7.15268 7.09122 7.03029 6.96988 6.91000 6.85062 6.79176 6.73341 6.67555 6.61819 6.56133 6.50495 6.44906 6.39365 6.33871 6.28425 6.23025 6.17672 6.12365 6.07104 6.01887 5.96716 5.91589

$5,725.27 $5,676.07 $5,852.40 $5,802.11 $5,752.26 $5,702.83 $5,653.83 $5,605.26 $5,557.09 $5,509.35 $5,462.01 $5,415.08 $5,368.55 $5,322.42 $5,487.76 $5,440.61 $5,393.86 $5,347.52 $5,301.57 $5,256.02 $5,210.86 $5,166.08 $5,121.70 $5,077.69 $5,034.06 $4,990.81 $5,145.84 $5,101.63 $5,057.79 $5,014.34 $4,971.25 $4,928.54 $4,886.19 $4,844.21 $4,802.58 $4,761.32 $4,720.41 $4,679.85 $4,825.23 $4,783.77 $4,742.66 $4,701.91 $4,661.51 $4,621.46 $4,581.75 $4,542.39 $4,503.36 $4,464.66 $4,426.30 $4,388.27 $4,524.59 $4,485.71 $4,447.17 $4,408.96 $4,371.08 $4,333.52 $4,296.28 $4,259.37 $4,222.77 $4,186.49 $4,150.52 $4,114.86 $4,242.68 $4,206.23 $4,170.09 $4,134.26 $4,098.73 $4,063.52 $4,028.60 $3,993.99 $3,959.67 $3,925.65

275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346

$663.58 $663.58 $690.12 $690.12 $690.12 $690.12 $690.12 $690.12 $690.12 $690.12 $690.12 $690.12 $690.12 $690.12 $717.73 $717.73 $717.73 $717.73 $717.73 $717.73 $717.73 $717.73 $717.73 $717.73 $717.73 $717.73 $746.43 $746.43 $746.43 $746.43 $746.43 $746.43 $746.43 $746.43 $746.43 $746.43 $746.43 $746.43 $776.29 $776.29 $776.29 $776.29 $776.29 $776.29 $776.29 $776.29 $776.29 $776.29 $776.29 $776.29 $807.34 $807.34 $807.34 $807.34 $807.34 $807.34 $807.34 $807.34 $807.34 $807.34 $807.34 $807.34 $839.64 $839.64 $839.64 $839.64 $839.64 $839.64 $839.64 $839.64 $839.64 $839.64

5.86506 5.81466 5.76470 5.71517 5.66606 5.61738 5.56911 5.52126 5.47382 5.42679 5.38016 5.33394 5.28811 5.24267 5.19762 5.15296 5.10869 5.06479 5.02128 4.97813 4.93536 4.89295 4.85091 4.80923 4.76791 4.72694 4.68633 4.64606 4.60614 4.56657 4.52733 4.48843 4.44986 4.41163 4.37372 4.33614 4.29889 4.26195 4.22533 4.18903 4.15303 4.11735 4.08197 4.04690 4.01213 3.97765 3.94348 3.90959 3.87600 3.84270 3.80968 3.77695 3.74450 3.71232 3.68043 3.64880 3.61745 3.58637 3.55555 3.52500 3.49472 3.46469 3.43492 3.40541 3.37615 3.34714 3.31838 3.28987 3.26160 3.23358 3.20579 3.17825

$3,891.92 $3,858.48 $3,978.34 $3,944.15 $3,910.27 $3,876.67 $3,843.36 $3,810.34 $3,777.60 $3,745.14 $3,712.96 $3,681.06 $3,649.43 $3,618.07 $3,730.46 $3,698.41 $3,666.63 $3,635.13 $3,603.90 $3,572.93 $3,542.23 $3,511.80 $3,481.62 $3,451.71 $3,422.05 $3,392.65 $3,498.04 $3,467.98 $3,438.18 $3,408.64 $3,379.35 $3,350.32 $3,321.53 $3,292.99 $3,264.70 $3,236.65 $3,208.84 $3,181.27 $3,280.09 $3,251.91 $3,223.96 $3,196.26 $3,168.80 $3,141.57 $3,114.58 $3,087.82 $3,061.29 $3,034.99 $3,008.91 $2,983.05 $3,075.72 $3,049.29 $3,023.09 $2,997.12 $2,971.37 $2,945.84 $2,920.52 $2,895.43 $2,870.55 $2,845.89 $2,821.44 $2,797.19 $2,884.09 $2,859.31 $2,834.74 $2,810.38 $2,786.23 $2,762.29 $2,738.56 $2,715.03 $2,691.70 $2,668.57

347 $839.64 348 $839.64 349 $873.22 350 $873.22 351 $873.22 352 $873.22 353 $873.22 354 $873.22 355 $873.22 356 $873.22 357 $873.22 358 $873.22 359 $873.22 360 $873.22 361 $908.15 362 $908.15 363 $908.15 364 $908.15 365 $908.15 366 $908.15 367 $908.15 368 $908.15 369 $908.15 370 $908.15 371 $908.15 372 $908.15 373 $944.48 374 $944.48 375 $944.48 376 $944.48 377 $944.48 378 $944.48 379 $944.48 380 $944.48 381 $944.48 382 $944.48 383 $944.48 384 $944.48 385 $982.26 386 $982.26 387 $982.26 388 $982.26 389 $982.26 390 $982.26 391 $982.26 392 $982.26 393 $982.26 394 $982.26 395 $982.26 396 $982.26 397 $1,021.55 398 $1,021.55 399 $1,021.55 400 $1,021.55 401 $1,021.55 402 $1,021.55 403 $1,021.55 404 $1,021.55 405 $1,021.55 406 $1,021.55 407 $1,021.55 408 $1,021.55 409 $1,062.41 410 $1,062.41 411 $1,062.41 412 $1,062.41 413 $1,062.41 414 $1,062.41 415 $1,062.41 416 $1,062.41 417 $1,062.41 418 $1,062.41

3.15094 3.12387 3.09702 3.07041 3.04403 3.01788 2.99195 2.96624 2.94075 2.91549 2.89044 2.86560 2.84098 2.81657 2.79237 2.76838 2.74459 2.72101 2.69763 2.67445 2.65147 2.62869 2.60610 2.58371 2.56151 2.53950 2.51768 2.49605 2.47460 2.45334 2.43226 2.41136 2.39064 2.37010 2.34974 2.32955 2.30953 2.28969 2.27001 2.25051 2.23117 2.21200 2.19300 2.17415 2.15547 2.13695 2.11859 2.10039 2.08234 2.06445 2.04671 2.02913 2.01169 1.99441 1.97727 1.96028 1.94344 1.92674 1.91018 1.89377 1.87750 1.86137 1.84537 1.82952 1.81380 1.79821 1.78276 1.76745 1.75226 1.73720 1.72228 1.70748

$2,645.64 $2,622.91 $2,704.39 $2,681.15 $2,658.12 $2,635.28 $2,612.64 $2,590.19 $2,567.93 $2,545.87 $2,523.99 $2,502.31 $2,480.81 $2,459.49 $2,535.89 $2,514.10 $2,492.50 $2,471.09 $2,449.85 $2,428.80 $2,407.94 $2,387.25 $2,366.73 $2,346.40 $2,326.24 $2,306.25 $2,377.89 $2,357.46 $2,337.20 $2,317.12 $2,297.21 $2,277.48 $2,257.91 $2,238.51 $2,219.27 $2,200.20 $2,181.30 $2,162.56 $2,229.74 $2,210.58 $2,191.58 $2,172.75 $2,154.08 $2,135.58 $2,117.23 $2,099.04 $2,081.00 $2,063.12 $2,045.39 $2,027.82 $2,090.81 $2,072.85 $2,055.04 $2,037.38 $2,019.87 $2,002.52 $1,985.31 $1,968.25 $1,951.34 $1,934.58 $1,917.95 $1,901.47 $1,960.54 $1,943.70 $1,927.00 $1,910.44 $1,894.02 $1,877.75 $1,861.62 $1,845.62 $1,829.76 $1,814.04

419 $1,062.41 420 $1,062.41 421 $1,104.90 422 $1,104.90 423 $1,104.90 424 $1,104.90 425 $1,104.90 426 $1,104.90 427 $1,104.90 428 $1,104.90 429 $1,104.90 430 $1,104.90 431 $1,104.90 432 $1,104.90 433 $1,149.10 434 $1,149.10 435 $1,149.10 436 $1,149.10 437 $1,149.10 438 $1,149.10 439 $1,149.10 440 $1,149.10 441 $1,149.10 442 $1,149.10 443 $1,149.10 444 $1,149.10 445 $1,195.07 446 $1,195.07 447 $1,195.07 448 $1,195.07 449 $1,195.07 450 $1,195.07 451 $1,195.07 452 $1,195.07 453 $1,195.07 454 $1,195.07 455 $1,195.07 456 $1,195.07 457 $1,242.87 458 $1,242.87 459 $1,242.87 460 $1,242.87 461 $1,242.87 462 $1,242.87 463 $1,242.87 464 $1,242.87 465 $1,242.87 466 $1,242.87 467 $1,242.87 468 $1,242.87 469 $1,292.58 470 $1,292.58 471 $1,292.58 472 $1,292.58 473 $1,292.58 474 $1,292.58 475 $1,292.58 476 $1,292.58 477 $1,292.58 478 $1,292.58 479 $1,292.58 480 $1,292.58

1.69281 1.67826 1.66384 1.64955 1.63537 1.62132 1.60739 1.59358 1.57989 1.56631 1.55286 1.53951 1.52629 1.51317 1.50017 1.48728 1.47450 1.46183 1.44927 1.43682 1.42447 1.41223 1.40010 1.38807 1.37614 1.36432 1.35260 1.34098 1.32945 1.31803 1.30671 1.29548 1.28435 1.27331 1.26237 1.25152 1.24077 1.23011 1.21954 1.20906 1.19867 1.18837 1.17816 1.16804 1.15800 1.14806 1.13819 1.12841 1.11872 1.10910 1.09957 1.09013 1.08076 1.07147 1.06227 1.05314 1.04409 1.03512 1.02623 1.01741 1.00867 1.00000

$1,798.45 $1,783.00 $1,838.39 $1,822.59 $1,806.93 $1,791.41 $1,776.02 $1,760.76 $1,745.63 $1,730.63 $1,715.76 $1,701.02 $1,686.40 $1,671.91 $1,723.85 $1,709.04 $1,694.35 $1,679.79 $1,665.36 $1,651.05 $1,636.86 $1,622.80 $1,608.86 $1,595.03 $1,581.33 $1,567.74 $1,616.44 $1,602.55 $1,588.78 $1,575.13 $1,561.60 $1,548.18 $1,534.88 $1,521.69 $1,508.62 $1,495.65 $1,482.80 $1,470.06 $1,515.73 $1,502.70 $1,489.79 $1,476.99 $1,464.30 $1,451.72 $1,439.25 $1,426.88 $1,414.62 $1,402.47 $1,390.42 $1,378.47 $1,421.29 $1,409.08 $1,396.97 $1,384.97 $1,373.07 $1,361.27 $1,349.57 $1,337.98 $1,326.48 $1,315.08 $1,303.78 $1,292.58 $2,965,260.56 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW. DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE FW.

PROBLEM 6.6 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 5.00% EOY CF (F|P i%,n-t) FW OF CF 10 $1,000.00 1.47746 $1,477.46 11 $1,000.00 1.40710 $1,407.10 12 $2,000.00 1.34010 $2,680.19 13 $1,500.00 1.27628 $1,914.42 14 -$1,500.00 1.21551 -$1,823.26 15 $3,000.00 1.15763 $3,472.88 16 $2,500.00 1.10250 $2,756.25 17 $2,000.00 1.05000 $2,100.00 18 $2,000.00 1.00000 $2,000.00 $15,985.04 <- FW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $15,985.04 =FV(5%,9,,-NPV(5%,C6:C14)) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE FW.

A = $15,985(A|F 5%,9) = $15,985(0.09069) = $1,449.68 SOLUTION USING EXCEL'S PMT FUNCTION A= $1,449.68 = PMT(5%,9,,-15985.04)

A = $15,985(A|F 5%,18) = $15,985(0.03555) = $568.27 SOLUTION USING EXCEL'S PMT FUNCTION A= $568.21 = PMT(5%,18,,-15985.04)

PROBLEM 6.7 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 12.00% EOY CF (F|P i%,n-t) FW OF CF 0 -$30,000.00 1.57352 -$47,205.58 1 $6,000.00 1.40493 $8,429.57 2 $13,500.00 1.25440 $16,934.40 3 $0.00 1.12000 $0.00 4 $13,500.00 1.00000 $13,500.00 -$8,341.61 <- FW WITHOUT YEAR 3 RETURN DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = -$8,341.61 =FV(12%,5,,-NPV(12%,C6:C10)) THE FUTURE WORTH WITHOUT THE YEAR 3 RETURN IS -$8,341.61. TO BE MINIMALLY ATTRACTIVE, THE FUTURE WORTH OF THE YEAR 3 RETURN MUST BRING THE TOTAL FUTURE WORTH TO ZERO. LET X EQUAL THE YEAR 3 CASH FLOW, THEN (F|P 12%,1)(X) = $8,341.61 (1.12000)(X) = 8341.61 X = $7,447.87 EXCEL'S SOLVER CAN BE USED TO SOLVE FOR X. LET THE TARGET CELL BE E12 AND SET IT EQUAL TO A VALUE OF ZERO. DESIGNATE C9 AS THE CHANGE CELL. SOLVER PROVIDES AN ANSWER OF $7,447.87.

PROBLEM 6.8 FW = $10,000(F|P 4%,1)(F|P 6%,1)(F|P 8%,2)(F|P 12%,1) FW = $10,000(1.04000)(1.06000)(1.16640)(1.12000) FW = 14401.401 SOLUTION USING EXCEL'S FV FUNCTION FW = $14,401.40 =FV(12%,1,,FV(8%,2,,FV(6%,1,,FV(4%,1,,10000)))) SOLUTION USING EXCEL'S FVSCHEDULE FUNCTION FW = $14,401.40 =FVSCHEDULE(10000,{0.04,0.06,0.08,0.08,0.12})

PROBLEM 6.9 a

F = $200(F|A 9%/12,30*12) = $200(F|A 0.75%2,360) = $200(1830.74348) = $366,148.70 SOLUTION USING EXCEL'S FV FUNCTION FW = $366,148.70 =FV(9%/12,30*12,-200)

F = $366,148.70(F|P 12%/12,23) = $366,148.70(F|P 1%,23) = $366,148.70(1.25716) = $460,307.50 SOLUTION USING EXCEL'S FV FUNCTION FW = $460,308.60 =FV(12%/12,23,,FV(9%/12,30*12,-200))

A = $460,307.50(A|P 1%,180) = $460,307.50*(0.01200) = $5,523.69 SOLUTION USING EXCEL'S FUNCTIONS A= $5,524.48 =PMT(1%,180,FV(12%/12,23,,FV(9%/12,30*12,-200)))

A = $460,307.50(i) = $460,307.50(0.01) = $4,603.08 SOLUTION USING EXCEL'S FV FUNCTION A= $4,603.09 =1%*-FV(12%/12,23,,FV(9%/12,30*12,-200))

PROBLEM 6.10 a

F = $2,000(F|A 10%,42) = $2,000(537.63699) = $1,075,273.98 SOLUTION USING EXCEL'S FV FUNCTION FW = $1,075,273.98 =FV(10%,42,-2000)

A = $1,075273.98(A|P 10%,15) = $1,075273.98(0.13147) = $141,366.27 SOLUTION USING EXCEL'S FUNCTIONS A= $141,370.33 =PMT(10%,15,-FV(10%,42,-2000))

A = $1,075273.98(A|P 10%,20) = $1,075,273.98(0.11746) = $126,301.68 SOLUTION USING EXCEL'S FUNCTIONS A= $126,301.28 =PMT(10%,20,-FV(10%,42,-2000))

A = $1,075273.98(A|P 10%,25) = $1,075,273.98(0.11017) = $118,462.93 SOLUTION USING EXCEL'S FUNCTIONS A= $118,460.86 =PMT(10%,25,-FV(10%,42,-2000))

PROBLEM 6.11 SOLUTION USING FACTOR TABLES A = $2,000(F|A 8%,40)(F|P 8%,2)(A|P 8%,30) A = $2,000(259.05652)(1.16640)(0.08883) A= $53,682.37 SOLUTION USING EXCEL'S FUNCTIONS A= $53,680.82 =PMT(8%,30,FV(8%,2,,FV(8%,40,-2000)))

PROBLEM 6.12 PERIODIC INTEREST RATE = 8%/12 = 0.6667% BALANCE IN THE ACCOUNT 1 MONTH PRIOR TO FIRST WITHDRAWAL IS GIVEN BY F = $225(F|A 0.6667%, 360)(F|P 0.6667%,11) F = $225(1490.35945)(1.07583) = $360,759.02 BALANCE USING EXCEL'S FUNCTIONS F= $360,758.12 =FV(8%/12,11,,FV(8%/12,360,225)) a

A = 360,759.02(A|P 0.6667%,180) = 360,759.02(0.00956) = $3,448.86 SOLUTION USING EXCEL'S PMT FUNCTION A= $3,447.59 =PMT(8%/12,180,FV(8%/12,11,,FV(8%/12,360,-225)))

A = 360,759.02(A|P 0.6667%,300) = 360,759.02(0.00772) = $2,785.06 SOLUTION USING EXCEL'S PMT FUNCTION A= $2,784.39 =PMT(8%/12,300,FV(8%/12,11,,FV(8%/12,360,-225)))

A = 360,759.02(A|P 0.6667%,480) = 360,759.02(0.00695) = $2,507.28 SOLUTION USING EXCEL'S PMT FUNCTION A= $2,508.39 =PMT(8%/12,480,FV(8%/12,11,,FV(8%/12,360,-225)))

A = 360,759.02(i) = 360,759.02(0.006667) = $2,405.18 SOLUTION USING EXCEL'S FUNCTIONS A= $2,405.05 =8%/12*-FV(8%/12,11,,FV(8%/12,360,-225))

PROBLEM 6.13 FIRST STEP: DETERMINE WHEN THE BALANCE WILL EXCEED $20,000 FIND THE LOWEST VALUE OF n SUCH THAT (F|P 7%,n) >= $20,000/$10,000 OR >= 2.0000 THIS OCCURS AT n=11; THE VALUE AT t=11 IS F = $10,000(F|P 7%,11) = 10000(2.10485) = $21,048.50 SECOND STEP: DETERMINE WHEN THE BALANCE WILL EXCEED $40,000 FIND THE LOWEST VALUE OF n SUCH THAT (F|P 10%/4,n) >= $40,000/$21,048.50 OR > = 1.90037 THIS OCCURS AT n=26 WHICH IS 6.5 YEARS THE ACCOUNT IS ONLY REVIEWED ANNUALLY SO IT WILL EXCEED $40,000 AFTER 7 YEARS THE VALUE AFTER 7 MORE YEARS IS F = $21,048.50(F|P 2.5%,28) = $21,048.50(1.99650) = $42,023.33 FINAL STEP: DETERMINE VALUE AT t=25 THE ACCOUNT WILL BE OPEN 7 MORE YEARS (A TOTAL OF 25 YEARS) THE VALUE AT t=25 IS F = $42,023.33(F|P 12%/12,7*12) = $42,023.33(F|P 1%,84) = $42,023.33(2.30672) = $96,936.06

PROBLEM 6.14 a

F = $10,000(F|P 14%,1)(F|P 15.5%,1)(F|P 14%,1)(F|P 3.75%,4) F = $10,000(1.14000)(1.155000)(1.14000)(1.15865) F= 17391.777 SOLUTION USING EXCEL'S FV FUNCTION F= $17,391.78 =FV(3.75%,4,,FV(14%,1,,FV(15.5%,1,,FV(14%,1,,10000)))) SOLUTION USING EXCEL'S FVSCHEDULE FUNCTION F= $17,391.78 =FVSCHEDULE(10000,{0.14,0.155,0.14,0.0375,0.0375,0.0375,0.0375})

ORDER OF FACTORS DOES NOT MATTER (COMMUTATIVE LAW OF MULTIPLICATION) F = $17,391.78 NO NEED TO SWITCH BANKS

PROBLEM 6.15 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

j i 8.00% 5.00% CF (F|P i%,n-t) FW OF CF $0.00 2.40662 $0.00 $300.00 2.29202 $687.61 $324.00 2.18287 $707.25 $349.92 2.07893 $727.46 $377.91 1.97993 $748.24 $408.15 1.88565 $769.62 $440.80 1.79586 $791.61 $476.06 1.71034 $814.23 $514.15 1.62889 $837.49 $555.28 1.55133 $861.42 $599.70 1.47746 $886.03 $647.68 1.40710 $911.35 $699.49 1.34010 $937.39 $755.45 1.27628 $964.17 $815.89 1.21551 $991.72 $881.16 1.15763 $1,020.05 $951.65 1.10250 $1,049.19 $1,027.78 1.05000 $1,079.17 $1,110.01 1.00000 $1,110.01 $15,894.00 <- FW

SOLUTION USING FACTOR TABLES F = $300(F|A1 i%,j%,n) = $300(F|A1 5%,8%,18) = $300(52.98001) = $15,894.00 DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $15,894.00 =FV(5%,18,,-NPV(5%,C9:C26))

PROBLEM 6.16 SOLUTION USING CALCULATED FACTOR VALUES

FIRST DEPOSIT 25 30 35 40 45 50 55 60 65

NUMBER OF DEPOSITS 41 36 31 26 21 16 11 6 1

10.00% (A|F i%,n) 0.00205 0.00334 0.00550 0.00916 0.01562 0.02782 0.05396 0.12961 1.00000

1000000 ANNUAL DEPOSIT 2049.802782 3343.063818 5496.214003 9159.038568 15624.38981 27816.6207 53963.14202 129607.3804 1000000

SOLUTION USING EXCEL'S PMT FUNCTION

FIRST DEPOSIT 25 30 35 40 45 50 55 60 65

NUMBER OF DEPOSITS 41 36 31 26 21 16 11 6 1

1000000 ANNUAL DEPOSIT 2049.802782 =PMT(10%,C21,,-D$19) 3343.063818 =PMT(10%,C22,,-D$19) 5496.214003 =PMT(10%,C23,,-D$19) 9159.038568 =PMT(10%,C24,,-D$19) 15624.38981 =PMT(10%,C25,,-D$19) 27816.6207 =PMT(10%,C26,,-D$19) 53963.14202 =PMT(10%,C27,,-D$19) 129607.3804 =PMT(10%,C28,,-D$19) 1000000 =PMT(10%,C29,,-D$19)

PROBLEM 6.16 THE DESIRED F IS $1,000,000 A TOTAL OF 40 DEPOSITS WILL BE MADE SOLUTION USING CALCULATED FACTOR VALUES INTEREST RATE 4.00% 5.00% 6.00% 7.00% 8.00% 9.00%

(A|F i%,40) 0.01052 0.00828 0.00646 0.00501 0.00386 0.00296

DEPOSIT $10,523.49 $8,278.16 $6,461.54 $5,009.14 $3,860.16 $2,959.61

SOLUTION USING EXCEL'S PMT FUNCTION INTEREST RATE 4.00% 5.00% 6.00% 7.00% 8.00% 9.00%

DEPOSIT $10,523.49 =PMT(B20,40,,-1000000) $8,278.16 =PMT(B21,40,,-1000000) $6,461.54 =PMT(B22,40,,-1000000) $5,009.14 =PMT(B23,40,,-1000000) $3,860.16 =PMT(B24,40,,-1000000) $2,959.61 =PMT(B25,40,,-1000000)

PROBLEM 6.18 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

+ CF $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00

- CF -$100,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00

NET CF -$100,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

5.00% (F|P i%,n-t) 2.07893 1.97993 1.88565 1.79586 1.71034 1.62889 1.55133 1.47746 1.40710 1.34010 1.27628 1.21551 1.15763 1.10250 1.05000 1.00000

FW OF CF -$207,892.82 $19,799.32 $18,856.49 $17,958.56 $17,103.39 $16,288.95 $15,513.28 $14,774.55 $14,071.00 $13,400.96 $12,762.82 $12,155.06 $11,576.25 $11,025.00 $10,500.00 $10,000.00 $7,892.82 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $7,892.82 =FV(5%,15,-10000,100000) SOLUTION USING FACTOR TABLES FW = -$100,000(F|P 5%,15) + $10,000(F|A 5%,15) FW = -$100,000(2.07893) + $10,000(21.57856) FW = $7,892.60 b

DECISION RULE IF FW >= 0, ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD BUY THE GANG PUNCH

PROBLEM 6.19 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5

+ CF $18,500.00 $18,500.00 $18,500.00 $18,500.00 $18,500.00

- CF -$75,000.00

10.00% NET CF (F|P i%,n-t) FW OF CF -$75,000.00 1.61051 -$120,788.25 $18,500.00 1.46410 $27,085.85 $18,500.00 1.33100 $24,623.50 $18,500.00 1.21000 $22,385.00 $18,500.00 1.10000 $20,350.00 $18,500.00 1.00000 $18,500.00 -$7,843.90 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$7,843.90 =FV(10%,5,-18500,75000) SOLUTION USING FACTOR TABLES FW = -$75,000(F|P 10%,5) + $18,500(F|A 10%,5) FW = -$75,000(1.61051) + $18,500(6.10510) FW = -$7,843.90 b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

CARLISLE SHOULD REJECT THE FILTER BASED ON ITS ECONOMIC MERITS

PROBLEM 6.20 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5

+ CF

$2,000.00 $4,000.00 $3,000.00 $1,600.00

- CF -$5,000.00 -$200.00 -$300.00 -$600.00 -$1,000.00 -$1,500.00

6.00% NET CF (F|P i%,n-t) FW OF CF -$5,000.00 1.33823 -$6,691.13 -$200.00 1.26248 -$252.50 $1,700.00 1.19102 $2,024.73 $3,400.00 1.12360 $3,820.24 $2,000.00 1.06000 $2,120.00 $100.00 1.00000 $100.00 $1,121.34 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $1,121.34 =FV(6%,5,,-NPV(6%,E8:E12)-E7) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE FW. b

DECISION RULE IF FW >= 0, ACCEPT; OTHERWISE, REJECT

DURATECH SHOULD IMPLEMENT THE PROCESS IMPROVEMENT

PROBLEM 6.21 CURRENT ANNUAL INSURANCE PREMIUM = ($700,000/$100)*$1.00 = $7,000 NEW ANNUAL INSURANCE PREMIUM = ($720,000/$100)*$0.40 = $2,880 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

- CF -$20,000.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00

NET CF -$20,000.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00 $3,720.00

15.00% (F|P i%,n-t) FW OF CF 16.36654 -$327,330.75 14.23177 $52,942.19 12.37545 $46,036.69 10.76126 $40,031.90 9.35762 $34,810.35 8.13706 $30,269.87 7.07571 $26,321.63 6.15279 $22,888.37 5.35025 $19,902.93 4.65239 $17,306.90 4.04556 $15,049.47 3.51788 $13,086.50 3.05902 $11,379.57 2.66002 $9,895.27 2.31306 $8,604.59 2.01136 $7,482.25 1.74901 $6,506.30 1.52088 $5,657.66 1.32250 $4,919.70 1.15000 $4,278.00 1.00000 $3,720.00 $53,759.38 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $53,759.38 =FV(15%,20,-3720,20000) SOLUTION USING FACTOR TABLES FW = -$20,000(F|P 15%,20) + $3,720(F|A 15%,20) FW = -$20,000(16.36654) + $3,720(102.44358) FW = $53,759.32 b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

EDDIE SHOULD BUY THE SPRINKLER SYSTEM

PROBLEM 6.22 THE MAXIMUM AMOUNT THAT FABCO SHOULD BE WILLING TO SPEND IS THE AMOUNT THAT SETS THE FW OF THE COST EQUAL TO THE FW OF THE SAVINGS. P*(F|P 7%,12) = $10,000*(F|A 7%,12) P = $10,000*(F|A 7%,12) / (F|P 7%,12) P = $10,000*(17.88845) / (2.25219) P= $79,426.91 SOLUTION USING EXCEL'S FV FUNCTION P= $79,426.86 =FV(7%,12,10000)/FV(7%,12,,1)

PROBLEM 6.23 YEAR 5 ADDITION = $5,000 COMPUTER SALVAGE VALUE LOAN PAYMENTS = 25000*(A|P 15%,3) = 25000*(0.43798) = $10,949.50 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5

+ INV CF $55,000.00 $55,000.00 $55,000.00 $55,000.00 $60,000.00

- INV CF + LOAN CF -$100,000.00 $25,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00

- LOAN CF -$10,949.50 -$10,949.50 -$10,949.50

NET CF -$75,000.00 $19,050.50 $19,050.50 $19,050.50 $30,000.00 $35,000.00

18.00% (F|P i%,n-t) 2.28776 1.93878 1.64303 1.39240 1.18000 1.00000

FW OF CF -$171,581.83 $36,934.69 $31,300.58 $26,525.92 $35,400.00 $35,000.00 -$6,420.65 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = -$6,420.65 =FV(18%,5,,-NPV(18%,G11:G15)-G10) SOLUTION USING FACTOR TABLES FW = -$75,000(F|P 18%,5) + $19,050(F|A 18%,3)(F|P 18%,2) + $30,000(F|P 18%,1) + $35,000 FW = -$75,000(2.28776) + $19,050(3.57240)(1.39240) + $30,000(1.18000) + $35,000 FW = -$6,423.30 b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

GALVANIZED PRODUCTS SHOULD NOT PURCHASE THE NEW COMPUTER SYSTEM

PROBLEM 6.24 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

+ CF

- CF -$1,400.00

$0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 -$1,000.00 -$2,000.00 -$3,000.00 $1,400.00

13.50% NET CF (F|P i%,n-t) -$1,400.00 6.68248 $0.00 5.88765 $500.00 5.18736 $500.00 4.57036 $500.00 4.02675 $500.00 3.54780 $0.00 3.12581 $500.00 2.75402 $600.00 2.42645 $700.00 2.13784 $800.00 1.88356 $900.00 1.65952 -$1,000.00 1.46214 -$2,000.00 1.28823 -$3,000.00 1.13500 $1,400.00 1.00000

FW OF CF -$9,355.48 $0.00 $2,593.68 $2,285.18 $2,013.37 $1,773.90 $0.00 $1,377.01 $1,455.87 $1,496.49 $1,506.85 $1,493.57 -$1,462.14 -$2,576.45 -$3,405.00 $1,400.00 $596.85 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $596.85 =FV(13.5%,15,,-NPV(13.5%,E8:E22)-E7) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE FW. b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

QRU SHOULD INVEST

PROBLEM 6.25 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6 7

+ CF

- CF -$12.00 -$1.00

$5.00 $2.00 $5.00 $5.00 $2.00 $5.00

NET CF -$12.00 -$1.00 $5.00 $2.00 $5.00 $5.00 $2.00 $5.00

18.00% (F|P i%,n) 3.18547 2.69955 2.28776 1.93878 1.64303 1.39240 1.18000 1.00000

FW OF CF -$38.23 -$2.70 $11.44 $3.88 $8.22 $6.96 $2.36 $5.00 -$3.07 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = -$3.07 =FV(18%,7,,-NPV(18%,E8:E14)-E7) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE FW. b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

IMAGINEERING SHOULD NOT INVEST

PROBLEM 6.26 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$2.00 -$10.00 -$12.00 -$14.00 -$16.00 -$18.00

$200.00 -$10.00 -$12.00 -$14.00 -$100.00

NET CF -$2.00 -$10.00 -$12.00 -$14.00 -$16.00 -$18.00 $200.00 -$10.00 -$12.00 -$14.00 -$100.00

12.00% (F|P i%,n-t) FW OF CF 3.10585 -$6.21 2.77308 -$27.73 2.47596 -$29.71 2.21068 -$30.95 1.97382 -$31.58 1.76234 -$31.72 1.57352 $314.70 1.40493 -$14.05 1.25440 -$15.05 1.12000 -$15.68 1.00000 -$100.00 $12.01 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $12.01 =FV(12%,10,,-NPV(12%,E8:E17)-E7) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE FW. b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

JUPITER'S SHOULD INVEST

PROBLEM 6.27 YEAR 7 ADDITION = $7,500 SYSTEM SALVAGE VALUE LOAN PAYMENTS = 20000(F|P 8%,1)(A|P 8%,3) = 20000(1.08000)(0.38803) = 8381.45 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6 7

+ INV CF $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $19,500.00

- INV CF + LOAN CF -$40,000.00 $20,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00

- LOAN CF

-$8,381.45 -$8,381.45 -$8,381.45

NET CF -$20,000.00 $10,000.00 $1,618.55 $1,618.55 $1,618.55 $10,000.00 $10,000.00 $17,500.00

10.00% (F|P i%,n-t) 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$38,974.34 $17,715.61 $2,606.69 $2,369.72 $2,154.29 $12,100.00 $11,000.00 $17,500.00 $26,471.97 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $26,471.97 =FV(10%,7,,-NPV(10%,G11:G17)-G10) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE FW. b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

AEROTRON ELECTRONICS SHOULD PURCHASE THE WATER FILTRATION SYSTEM

PROBLEM 6.28 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5

+ CF $600.00 $600.00 $700.00 $700.00 $700.00

- CF -$1,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

NET CF -$1,000.00 $300.00 $300.00 $400.00 $400.00 $400.00

10.00% (F|P i%,n-t) FW OF CF 1.61051 -$1,610.51 1.46410 $439.23 1.33100 $399.30 1.21000 $484.00 1.10000 $440.00 1.00000 $400.00 $552.02 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $552.02 =FV(10%,5,-300,1000)+FV(10%,3,-100) SOLUTION USING FACTOR TABLES FW = -$1,000(F|P 10%,5) + $300(F|A 10%,5) + $100(F|A 10%,3) FW = -$1,000(1.61051) + $300(6.10510) + $100(3.31000) FW = $552.02 b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

HOME INNOVATION SHOULD PURSUE THE NEW PRODUCT

PROBLEM 6.29 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5 6

+ CF $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $3,000.00

- CF -$6,000.00

NET CF -$6,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $3,000.00

8.00% (F|P i%,n-t) 1.58687 1.46933 1.36049 1.25971 1.16640 1.08000 1.00000

FW OF CF -$9,521.25 $1,469.33 $1,360.49 $1,259.71 $1,166.40 $1,080.00 $3,000.00 -$185.32 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$185.32 =FV(8%,6,-1000,6000)+2000 SOLUTION USING FACTOR TABLES FW = -$6,000(F|P 8%,6) + $1,000(F|A 8%,6) + $2,000 FW = -$6,000(1.58687) + $1,000(7.33593) + $2,000 FW = -$185.29 b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

MAYBERRY SHOULD NOT IMPLEMENT THE DESIGN CHANGE

PROBLEM 6.30 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3

+ CF $30,000.00 $30,000.00 $33,000.00

- CF -$10,000.00 -$25,000.00 -$25,000.00 -$25,000.00

NET CF -$10,000.00 $5,000.00 $5,000.00 $8,000.00

24.00% (F|P i%,n-t) 1.90662 1.53760 1.24000 1.00000

FW OF CF -$19,066.24 $7,688.00 $6,200.00 $8,000.00 $2,821.76 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $2,821.76 =FV(24%,3,-5000,10000)+3000 SOLUTION USING FACTOR TABLES FW = -$10,000(F|P 24%,3) + $5,000(F|A 24%,3) + $3,000 FW = -$10,000(1.90662) + $5,000(3.77760) + $3,000 FW = $2,821.80 b

DECISION RULE IF FW > 0, ACCEPT; OTHERWISE, REJECT

NANCY SHOULD BUY THE TRUCK

PROBLEM 6.31 INVESTMENT 1 EOY CF 0 -$20,000.00 1 $8,000.00 2 $9,000.00 3 $10,000.00 4 $11,000.00

9.00% (F|P i%,n-t) 1.41158 1.29503 1.18810 1.09000 1.00000

FW OF CF -$28,231.63 $10,360.23 $10,692.90 $10,900.00 $11,000.00 $14,721.50 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $14,721.50 =FV(9%,4,,-NPV(9%,C6:C9)-C5) SOLUTION USING FACTOR TABLES FW = -$20,000(F|P 9%,4) + ($8,000 + $1,000(A|G 9%,4))(F|A 9%,4) FW = -$20,000(1.41158) + ($8,000 + $1,000(1.39250))(4.57313) FW = $14,721.52

INVESTMENT 2 EOY CF 0 -$20,000.00 1 $11,000.00 2 $10,000.00 3 $9,000.00 4 $8,000.00

(F|P i%,n-t) 1.41158 1.29503 1.18810 1.09000 1.00000

FW OF CF -$28,231.63 $14,245.32 $11,881.00 $9,810.00 $8,000.00 $15,704.69 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $15,704.69 =FV(9%,4,,-NPV(9%,C27:C30)-C26) SOLUTION USING FACTOR TABLES FW = -$20,000(F|P 9%,4) + ($11,000 - $1,000(A|G 9%,4))(F|A 9%,4) FW = -$20,000(1.41158) + ($11,000 - $1,000(1.39250))(4.57313) FW = $15,704.75

INVESTMENT 3 EOY CF 0 -$20,000.00 1 $9,500.00 2 $9,500.00 3 $9,500.00 4 $9,500.00

(F|P i%,n-t) 1.41158 1.29503 1.18810 1.09000 1.00000

FW OF CF -$28,231.63 $12,302.78 $11,286.95 $10,355.00 $9,500.00 $15,213.09 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $15,213.09 =FV(9%,4,-9500,20000) SOLUTION USING FACTOR TABLES FW = -$20,000(F|P 9%,4) + ($9,500)(F|A 9%,4) FW = -$20,000(1.41158) + ($9,500)(4.57313) FW = $15,213.14 INVESTMENT 2 HAS THE HIGHEST FW AND IS PREFERRED

PROBLEM 6.32 a

FOR EACH INVESTMENT THE SUM OF THE RETURNS IS $38,000; THEREFORE, THE AVERAGE ANNUAL RETURN FOR EACH IS $9,500

PATTERN I VARIES FROM THE AVERAGE USING A POSITIVE GRADIENT PATTERN II VARIES FROM THE AVERAGE USING A NEGATIVE GRADIENT PATTERN III IS A UNIFORM SERIES

YES. FOR A GIVEN LEVEL OF AVERAGE DEPOSIT, YOU ACCUMULATE A BIGGER TOTAL IF YOU DEPOSIT LARGER AMOUNTS EARLIER (NEGATIVE GRADIENT)

PROBLEM 6.33 a

ACCOUNT 1 FW = $10,000(F|P 4%,1)(F|P 6%,1)(F|P 8%,2)(F|P 12%,1) FW = $10,000(1.04000)(1.06000)(1.16640)(1.12000) FW = $14,401.40 SOLUTION USING EXCEL'S FV FUNCTION FW = $14,401.40 =FV(12%,1,,FV(8%,2,,FV(6%,1,,FV(4%,1,,10000)))) SOLUTION USING EXCEL'S FVSCHEDULE FUNCTION FW = $14,401.40 =FVSCHEDULE(10000,{0.04,0.06,0.08,0.08,0.12})

ACCOUNT 2 FW = $10,000(F|P 6%/12,5*12) = $10,000(F|P 0.5%,60) FW = $10,000(1.34885) FW = $13,488.50 SOLUTION USING EXCEL'S FV FUNCTION FW = $13,488.50 =FV(6%/12,5*12,,-10000)

ACCOUNT 3 FW = $10,000(F|P 8%/2,5*2) = $10,000(F|P 4%,10) FW = $10,000(1.48024) FW = $14,802.40 SOLUTION USING EXCEL'S FV FUNCTION FW = $14,802.44 =FV(8%/2,5*2,,-10000) JEFF SHOULD PREFER ACCOUNT 3

PROBLEM 6.34 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS VENDOR A SOFTWARE EOY 0 1 2 3 4

+ CF

- CF -$380,000.00

$125,000.00 $125,000.00 $125,000.00 $125,000.00

NET CF -$380,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00

10.00% (F|P i%,n-t) 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$556,358.00 $166,375.00 $151,250.00 $137,500.00 $125,000.00 $23,767.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $23,767.00 =FV(10%,4,-125000,380000) SOLUTION USING FACTOR TABLES FW = -$380,000(F|P 10%,4) + $125,000(F|A 10%,4) FW = -$380,000(1.4641) + $125,000(4.64100) FW = $23,767.00

VENDOR B SOFTWARE EOY 0 1 2 3 4

+ CF $95,000.00 $95,000.00 $95,000.00 $95,000.00

- CF -$280,000.00

NET CF (F|P i%,n-t) -$280,000.00 1.46410 $95,000.00 1.33100 $95,000.00 1.21000 $95,000.00 1.10000 $95,000.00 1.00000

FW OF CF -$409,948.00 $126,445.00 $114,950.00 $104,500.00 $95,000.00 $30,947.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $30,947.00 =FV(10%,4,-95000,280000) SOLUTION USING FACTOR TABLES FW = -$280,000(F|P 10%,4) + $95,000(F|A 10%,4) FW = -$280,000(1.4641) + $95,000(4.64100) FW = $30,947.00 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST FW

MANUEL'S MANUFACTURING SHOULD BUY FROM VENDOR B

PROBLEM 6.35 ORDER OF INVESTMENTS: B, A SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS VENDOR B SOFTWARE 10.00% EOY + CF - CF NET CF (F|P i%,n-t) 0 -$280,000.00 -$280,000.00 1.46410 1 $95,000.00 $95,000.00 1.33100 2 $95,000.00 $95,000.00 1.21000 3 $95,000.00 $95,000.00 1.10000 4 $95,000.00 $95,000.00 1.00000

FW OF CF -$409,948.00 $126,445.00 $114,950.00 $104,500.00 $95,000.00 $30,947.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FV = $30,947.00 =FV(10%,4,-95000,280000) SOLUTION USING FACTOR TABLES FW = -$280,000(F|P 10%,4) + $95,000(F|A 10%,4) FW = -$280,000(1.46410) + $95,000(4.64100) FW = $30,947.00 FW OF B IS GREATER THAN ZERO SO ANALYZE INCREMENTAL CASH FLOWS OF A-B INCREMENTAL ANALYSIS OF A-B EOY 0 1 2 3 4

+ CF $30,000.00 $30,000.00 $30,000.00 $30,000.00

- CF -$100,000.00

NET CF -$100,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00

10.00% (F|P i%,n-t) 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$146,410.00 $39,930.00 $36,300.00 $33,000.00 $30,000.00 -$7,180.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$7,180.00 =FV(10%,4,-30000,100000) SOLUTION USING FACTOR TABLES FW = -$100,000(F|P 10%,4) + $30,000(F|A 10%,4) FW = -$100,000(1.46410) + $30,000(4.64100) FW = -$7,180.00 FW OF INCREMENT A-B IS NEGATIVE SO REJECT THE INCREMENT; STAY WITH VENDOR B SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, VENDOR B IS RECOMMENDED

PROBLEM 6.36 FW(A) = $30,000*(F|P 10%,10) = $30,000*(2.59374) = $77,812.20 FW(B) = ($1,000 + 0.5X)*(F|A 10%,10) FOR NADINE TO BE INDIFFERENT, THE FW VALUES MUST BE EQUAL, THEREFORE, ($1,000 + 0.5X)*(F|A 10%,10) = $77,812.20 ($1,000 + 0.5X)*(15.93742) = $77,812.20 7.96871X = 61,874.78 X = 7,764.7 OR APPROXIMATELY 7,765 UNITS

PROBLEM 6.37 HEAT LOSS WITH NO INSULATION = $1.50/YR/FT HEAT LOSS WITH 1 INCH INSULATION IS 1.50 * (1 - 0.89) = $0.165/YR/FT HEAT LOSS WITH 2 INCH INSULATION IS 1.50 * (1 - 0.92) = $0.12/YR/FT

NO INSULATION ANNUAL HEAT LOSS = 1.50 * 250,000 = $375,000 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 10.00% EOY + CF - CF NET CF (F|P i%,n-t) 0 $0.00 $0.00 2.59374 1 $0.00 -$375,000.00 -$375,000.00 2.35795 2 $0.00 -$375,000.00 -$375,000.00 2.14359 3 $0.00 -$375,000.00 -$375,000.00 1.94872 4 $0.00 -$375,000.00 -$375,000.00 1.77156 5 $0.00 -$375,000.00 -$375,000.00 1.61051 6 $0.00 -$375,000.00 -$375,000.00 1.46410 7 $0.00 -$375,000.00 -$375,000.00 1.33100 8 $0.00 -$375,000.00 -$375,000.00 1.21000 9 $0.00 -$375,000.00 -$375,000.00 1.10000 10 $0.00 -$375,000.00 -$375,000.00 1.00000

FW OF CF $0.00 -$884,230.38 -$803,845.80 -$730,768.91 -$664,335.38 -$603,941.25 -$549,037.50 -$499,125.00 -$453,750.00 -$412,500.00 -$375,000.00 -$5,976,534.23 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$5,976,534.23 =FV(10%,10,375000) SOLUTION USING FACTOR TABLES FW = -$375,000(F|A 10%,10) FW = -$375,000(15.93742) FW = -$5,976,532.50

1 INCH INSULATION ANNUAL HEAT LOSS = 0.165 * 250,000 = $41,250 INSULATION COST = 0.40 * 250,000 = $100,000 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS 10.00% EOY + CF - CF NET CF (F|P i%,n-t) 0 -$100,000.00 -$100,000.00 2.59374 1 $0.00 -$41,250.00 -$41,250.00 2.35795 2 $0.00 -$41,250.00 -$41,250.00 2.14359 3 $0.00 -$41,250.00 -$41,250.00 1.94872 4 $0.00 -$41,250.00 -$41,250.00 1.77156 5 $0.00 -$41,250.00 -$41,250.00 1.61051 6 $0.00 -$41,250.00 -$41,250.00 1.46410 7 $0.00 -$41,250.00 -$41,250.00 1.33100 8 $0.00 -$41,250.00 -$41,250.00 1.21000 9 $0.00 -$41,250.00 -$41,250.00 1.10000 10 $0.00 -$41,250.00 -$41,250.00 1.00000

FW OF CF -$259,374.25 -$97,265.34 -$88,423.04 -$80,384.58 -$73,076.89 -$66,433.54 -$60,394.13 -$54,903.75 -$49,912.50 -$45,375.00 -$41,250.00 -$916,793.01 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$916,793.01 =FV(10%,10,41250,100000)

SOLUTION USING FACTOR TABLES FW = -$100,000(F|P 10%,10) - $41,250(P|A 10%,10) FW = -$100,000(2.59374) - $41,250(15.93742) FW = -$916,792.58

2 INCH INSULATION ANNUAL HEAT LOSS = 0.12 * 250,000 = $30,000 INSULATION COST = 0.85 * 250,000 = $212,500 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS 10.00% EOY + CF - CF NET CF (F|P i%,n-t) 0 -$212,500.00 -$212,500.00 2.59374 1 $0.00 -$30,000.00 -$30,000.00 2.35795 2 $0.00 -$30,000.00 -$30,000.00 2.14359 3 $0.00 -$30,000.00 -$30,000.00 1.94872 4 $0.00 -$30,000.00 -$30,000.00 1.77156 5 $0.00 -$30,000.00 -$30,000.00 1.61051 6 $0.00 -$30,000.00 -$30,000.00 1.46410 7 $0.00 -$30,000.00 -$30,000.00 1.33100 8 $0.00 -$30,000.00 -$30,000.00 1.21000 9 $0.00 -$30,000.00 -$30,000.00 1.10000 10 $0.00 -$30,000.00 -$30,000.00 1.00000

FW OF CF -$551,170.27 -$70,738.43 -$64,307.66 -$58,461.51 -$53,146.83 -$48,315.30 -$43,923.00 -$39,930.00 -$36,300.00 -$33,000.00 -$30,000.00 -$1,029,293.01 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$1,029,293.01 =FV(10%,10,30000,212500) SOLUTION USING FACTOR TABLES FW = -$212,500(F|P 10%,10) - $30,000(P|A 10%,10) FW = -$212,500(2.59374) - $30,000(15.93742) FW = -$1,029,292.35 THE HIGHEST FUTURE WORTH IS THE 1 INCH INSULATION, THEREFORE, IT IS RECOMMENDED.

PROBLEM 6.38 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, 1-INCH, 2-INCH NULL BECOMES THE "CURRENT BEST" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 1-INCH - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

1-INCH -$100,000.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00

NULL $0.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00

INCR. CF -$100,000.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00

10.00% (F|P i%,n-t) 2.59374 2.35795 2.14359 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$259,374.25 $786,965.04 $715,422.77 $650,384.33 $591,258.48 $537,507.71 $488,643.38 $444,221.25 $403,837.50 $367,125.00 $333,750.00 $5,059,741.21 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $5,059,741.21 =FV(10%,10,-333750,100000) SOLUTION USING FACTOR TABLES FW = -$100,000(F|P 10%,10) + $333,750(F|A 10%,10) FW = -$100,000(2.59374) + $333,750(15.93742) FW = $5,059,739.93 SINCE THE FW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. 1-INCH BECOMES THE NEW CURRENT BEST 2-INCH BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR 2-INCH - 1-INCH ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

2-INCH -$212,500.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00

1-INCH -$100,000.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00

INCR. CF -$112,500.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00

10.00% (F|P i%,n-t) 2.59374 2.35795 2.14359 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$291,796.03 $26,526.91 $24,115.37 $21,923.07 $19,930.06 $18,118.24 $16,471.13 $14,973.75 $13,612.50 $12,375.00 $11,250.00 -$112,500.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$112,500.00 =FV(10%,10,-11250,112500) SOLUTION USING FACTOR TABLES FW = -$112,500(F|P 10%,10) + $11,250(F|A 10%,10) FW = -$112,500(2.59374) + $11,250(15.93742) FW = -$112,499.78 SINCE THE FW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. 1-INCH REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, 1-INCH IS RECOMMENDED.

PROBLEM 6.39 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS LAGRANGE EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

- CF NET CF -$1,260,000.00 -$1,260,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

15.00% (F|P i%,n-t) 5.35025 4.65239 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF -$6,741,315.13 $2,233,147.87 $1,941,867.71 $1,688,580.62 $1,468,330.97 $1,276,809.54 $1,110,269.17 $965,451.45 $839,523.00 $730,020.00 $634,800.00 $552,000.00 $480,000.00 $7,179,485.20 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $7,179,485.20 =FV(15%,12,-480000,1260000) SOLUTION USING FACTOR TABLES FW = -$1,260,000(F|P 15%,12) + $480,000(F|A 15%,12) FW = -$1,260,000(5.35025) + $480,000(29.00167) FW = $7,179,486.60

AUBURN EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

- CF NET CF -$1,000,000.00 -$1,000,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

15.00% (F|P i%,n-t) 5.35025 4.65239 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF -$5,350,250.11 $1,907,480.47 $1,658,678.67 $1,442,329.28 $1,254,199.37 $1,090,608.15 $948,354.91 $824,656.45 $717,092.56 $623,558.75 $542,225.00 $471,500.00 $410,000.00 $6,540,433.52 <- FW

ANNISTON EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00

- CF NET CF -$1,620,000.00 -$1,620,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00

15.00% (F|P i%,n-t) 5.35025 4.65239 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF -$8,667,405.17 $2,419,243.53 $2,103,690.02 $1,829,295.67 $1,590,691.89 $1,383,210.34 $1,202,791.60 $1,045,905.74 $909,483.25 $790,855.00 $687,700.00 $598,000.00 $520,000.00 $6,413,461.86 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $6,413,461.86 =FV(15%,12,-520000,1620000) SOLUTION USING FACTOR TABLES FW = -$1,620,000(F|P 15%,12) + $520,000(F|A 15%,12) FW = -$1,620,000(5.35025) + $520,000(29.00167) FW = $6,413,463.40 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST FW

QUANTUM LOGISTICS SHOULD BUILD IN LAGRANGE

PROBLEM 6.40 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, AUBURN, LAGRANGE, ANNISTON NULL BECOMES THE "CURRENT BEST" AND AUBURN THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR AUBURN - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

AUBURN -$1,000,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR. CF -$1,000,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

15.00% (F|P i%,n-t) 5.35025 4.65239 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF -$5,350,250.11 $1,907,480.47 $1,658,678.67 $1,442,329.28 $1,254,199.37 $1,090,608.15 $948,354.91 $824,656.45 $717,092.56 $623,558.75 $542,225.00 $471,500.00 $410,000.00 $6,540,433.52 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $6,540,433.52 =FV(15%,12,-410000,1000000) SOLUTION USING FACTOR TABLES FW = -$1,000,000(F|P 15%,12) + $410,000(F|A 15%,12) FW = -$1,000,000(5.35025) + $410,000(29.00167) FW = $6,540,434.70 SINCE THE FW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. AUBURN BECOMES THE NEW CURRENT BEST LAGRANGE BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR LAGRANGE - AUBURN ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

LAGRANGE -$1,260,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

AUBURN -$1,000,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

INCR. CF -$260,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00

15.00% (F|P i%,n-t) 5.35025 4.65239 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW -$1,391,065.03 $325,667.40 $283,189.04 $246,251.34 $214,131.60 $186,201.39 $161,914.25 $140,795.00 $122,430.44 $106,461.25 $92,575.00 $80,500.00 $70,000.00 $639,051.69 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $639,051.69 =FV(15%,12,-70000,260000) SOLUTION USING FACTOR TABLES FW = -$260,000(F|P 15%,12) + $70,000(F|A 15%,12) FW = -$260,000(5.35025) + $70,000(29.00167) FW = $639,051.90

SINCE THE FW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED LAGRANGE BECOMES THE NEW CURRENT BEST ANNISTON BECOMES THE NEXT CHALLENGER THUS, THE CASH FLOWS FOR ANNISTON - LAGRANGE ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

ANNISTON -$1,620,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00 $520,000.00

LAGRANGE -$1,260,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

INCR. CF -$360,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00

15.00% (F|P i%,n-t) 5.35025 4.65239 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW -$1,926,090.04 $186,095.66 $161,822.31 $140,715.05 $122,360.91 $106,400.80 $92,522.43 $80,454.29 $69,960.25 $60,835.00 $52,900.00 $46,000.00 $40,000.00 -$766,023.34 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$766,023.34 =FV(15%,12,-40000,360000) SOLUTION USING FACTOR TABLES FW = -$360,000(F|P 15%,12) + $40,000(F|A 15%,12) FW = -$360,000(5.35025) + $40,000(29.00167) FW = -$766,023.20 SINCE THE FW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED LAGRANGE REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, LAGRANGE IS RECOMMENDED.

PROBLEM 6.41 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS MACHINE 7745 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

$1,000.00

- CF -$10,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

NET CF -$10,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 $700.00

6.00% (F|P i%,n-t) 1.79085 1.68948 1.59385 1.50363 1.41852 1.33823 1.26248 1.19102 1.12360 1.06000 1.00000

FW OF CF -$17,908.48 -$506.84 -$478.15 -$451.09 -$425.56 -$401.47 -$378.74 -$357.30 -$337.08 -$318.00 $700.00 -$20,862.72 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$20,862.72 =FV(6%,10,300,10000)+1000 SOLUTION USING FACTOR TABLES FW = -$10,000(F|P 6%,10) - $300(P|A 6%,10) + $1,000 FW = -$10,000(1.79085) - $300(13.18079) + $1,000 FW = -$20,862.74 MACHINE A37Y EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$8,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

NET CF -$8,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

6.00% (F|P i%,n-t) 1.79085 1.68948 1.59385 1.50363 1.41852 1.33823 1.26248 1.19102 1.12360 1.06000 1.00000

FW -$14,326.78 -$506.84 -$478.15 -$451.09 -$425.56 -$401.47 -$378.74 -$357.30 -$337.08 -$318.00 -$300.00 -$18,281.02 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$18,281.02 =FV(6%,10,300,8000) SOLUTION USING FACTOR TABLES FW = -$8,000(F|P 6%,10) - $300(P|A 6%,10) FW = -$8,000(1.79085) - $300(13.18079) FW = -$18,281.04 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST FW

MACHINE A37Y SHOULD BE PURCHASED

PROBLEM 6.42 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS MACHINE A37Y, MACHINE 7745 NULL IS NOT AN OPTION SINCE THE PROBLEM STATES THAT A MACHINE MUST BE PURCHASED A37Y BECOMES THE "CURRENT BEST" AND 7745 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 7745 - A37Y ARE NEEDED SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 6.00% EOY 7745 A37Y INCR. CF (F|P i%,n-t) FW OF CF 0 -$10,000.00 -$8,000.00 -$2,000.00 1.79085 -$3,581.70 1 -$300.00 -$300.00 $0.00 1.68948 $0.00 2 -$300.00 -$300.00 $0.00 1.59385 $0.00 3 -$300.00 -$300.00 $0.00 1.50363 $0.00 4 -$300.00 -$300.00 $0.00 1.41852 $0.00 5 -$300.00 -$300.00 $0.00 1.33823 $0.00 6 -$300.00 -$300.00 $0.00 1.26248 $0.00 7 -$300.00 -$300.00 $0.00 1.19102 $0.00 8 -$300.00 -$300.00 $0.00 1.12360 $0.00 9 -$300.00 -$300.00 $0.00 1.06000 $0.00 10 $700.00 -$300.00 $1,000.00 1.00000 $1,000.00 -$2,581.70 <- FW SOLUTION USING EXCEL'S FV FUNCTION FW = -$2,581.70 =FV(6%,10,,2000)+1000 SOLUTION USING FACTOR TABLES FW = -$2,000(F|P 6%,10) + $1,000 FW = -$2,000(1.79085) + $1,000 FW = -$2,581.70 SINCE THE FW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. A37Y REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, A37Y IS RECOMMENDED.

PROBLEM 6.43 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS PROJECT A EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

+ CF $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

- CF -$50,000.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00 -$12,500.00

NET CF -$50,000.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00

12.00% (F|P i%,n-t) 9.64629 8.61276 7.68997 6.86604 6.13039 5.47357 4.88711 4.36349 3.89598 3.47855 3.10585 2.77308 2.47596 2.21068 1.97382 1.76234 1.57352 1.40493 1.25440 1.12000 1.00000

FW -$482,314.65 $64,595.71 $57,674.74 $51,495.31 $45,977.95 $41,051.74 $36,653.34 $32,726.20 $29,219.82 $26,089.12 $23,293.86 $20,798.09 $18,569.72 $16,580.11 $14,803.67 $13,217.56 $11,801.40 $10,536.96 $9,408.00 $8,400.00 $7,500.00 $58,078.66 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $58,078.66 =FV(12%,20,-7500,50000) SOLUTION USING FACTOR TABLES FW = -$50,000(F|P 12%,20) + $7,500(F|A 12%,20) FW = -$50,000(9.64629) + $7,500(72.05244) FW = $58,078.80 PROJECT B EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

+ CF $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00 $28,000.00

- CF -$75,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00

NET CF -$75,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

12.00% (F|P i%,n-t) 9.64629 8.61276 7.68997 6.86604 6.13039 5.47357 4.88711 4.36349 3.89598 3.47855 3.10585 2.77308 2.47596 2.21068 1.97382 1.76234 1.57352 1.40493 1.25440 1.12000 1.00000

FW -$723,471.98 $86,127.62 $76,899.66 $68,660.41 $61,303.94 $54,735.66 $48,871.12 $43,634.93 $38,959.76 $34,785.50 $31,058.48 $27,730.79 $24,759.63 $22,106.81 $19,738.23 $17,623.42 $15,735.19 $14,049.28 $12,544.00 $11,200.00 $10,000.00 -$2,947.56 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$2,947.56 =FV(12%,20,-10000,75000) SOLUTION USING FACTOR TABLES FW = -$75,000(F|P 12%,20) + $10,000(F|A 12%,20) FW = -$75,000(9.64629) + $10,000(72.05244) FW = -$2,947.35 b

TEMPURA SHOULD PURSUE PROJECT A

PROBLEM 6.44 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS POLISHER 1 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$20,000.00

$4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00

NET CF -$20,000.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00

15.00% (F|P i%,n-t) 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF -$80,911.15 $15,707.32 $13,658.54 $11,876.99 $10,327.82 $8,980.71 $7,809.31 $6,790.71 $5,904.96 $5,134.75 $4,465.00 $9,744.95 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $9,744.95 =FV(15%,10,-4465,20000) SOLUTION USING FACTOR TABLES FW = -$20,000(F|P 15%,10) + $4,465(F|A 15%,10) FW = -$20,000(4.04556) + $4,465(20.30372) FW = $9,744.91

POLISHER 2 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$10,000.00

$1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00

NET CF -$10,000.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00

(F|P i%,n-t) 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF -$40,455.58 $6,226.64 $5,414.47 $4,708.24 $4,094.12 $3,560.10 $3,095.74 $2,691.95 $2,340.83 $2,035.50 $1,770.00 -$4,518.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$4,518.00 =FV(15%,10,-1770,10000) SOLUTION USING FACTOR TABLES FW = -$10,000(F|P 15%,10) + $1,770(F|A 15%,10) FW = -$10,000(4.04556) + $1,770(20.30372) FW = -4518.0156

POLISHER 3 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00

- CF -$15,000.00

NET CF -$15,000.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00

(F|P i%,n-t) 4.04556 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF -$60,683.37 $12,594.00 $10,951.30 $9,522.87 $8,280.76 $7,200.66 $6,261.44 $5,444.73 $4,734.55 $4,117.00 $3,580.00 $12,003.95 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $12,003.95 =FV(15%,10,-3580,15000) SOLUTION USING FACTOR TABLES FW = -$15,000(F|P 15%,10) + $3,580(F|A 15%,10) FW = -$15,000(4.04556) + $3,580(20.30372) FW = $12,003.92

FINAL FINISHING SHOULD PURCHASE POLISHER 3

PROBLEM 6.45 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS A001 EOY 0 1 2 3 4

+ CF

- CF -$210.00

$80.00 $90.00 $100.00 $110.00

NET CF -$210.00 $80.00 $90.00 $100.00 $110.00

10.00% (F|P i%,n-t) 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$307.46 $106.48 $108.90 $110.00 $110.00 $127.92 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $127.92 =FV(10%,4,,-NPV(10%,E9:E12)-E8) SOLUTION USING FACTOR TABLES FW = -$210(F|P 10%,4) + $80(F|A 10%,4) + $10(A|G 10%,4)(F|A 10%,4) FW = -$210(1.46410) + $80(4.64100) + $10(1.3817)(4.64100) FW = $127.94

B002 EOY 0 1 2 3 4

+ CF

- CF -$110.00

$60.00 $60.00 $60.00 $70.00

NET CF -$110.00 $60.00 $60.00 $60.00 $70.00

10.00% (F|P i%,n-t) 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$161.05 $79.86 $72.60 $66.00 $70.00 $127.41 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $127.41 =FV(10%,4,-60,110)+10 SOLUTION USING FACTOR TABLES FW = -$110(F|P 10%,4) + $60(F|A 10%,4) + $10 FW = -$110(1.46410) + $60(4.64100) + $10 FW = $127.41

C003 EOY 0 1 2 3 4

+ CF

- CF -$160.00

$80.00 $80.00 $80.00 $80.00

NET CF -$160.00 $80.00 $80.00 $80.00 $80.00

10.00% (F|P i%,n-t) 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$234.26 $106.48 $96.80 $88.00 $80.00 $137.02 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $137.02 =FV(10%,4,-80,160) SOLUTION USING FACTOR TABLES FW = -$160(F|P 10%,4) + $80(F|A 10%,4) FW = -$160(1.46410) + $80(4.64100) FW = $137.02

XANADU SHOULD ACCEPT ALTERNATIVE C003

PROBLEM 6.46 THE STUDENT IS EXPECTED TO DEDUCE THAT THE SAVINGS ACCOUNT INTEREST RATE, 12%/YR COMPOUNDED MONTHLY, SHOULD BE USED FOR MARR. THIS LEADS TO A PERIOD INTEREST RATE OF 1% PER MONTH. SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS SAVINGS CERTIFICATE EOM 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

+ CF $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $13,100.00

- CF -$12,000.00

NET CF -$12,000.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $100.00 $13,100.00

1.00% (F|P i%,n-t) 1.81670 1.79871 1.78090 1.76327 1.74581 1.72852 1.71141 1.69447 1.67769 1.66108 1.64463 1.62835 1.61223 1.59626 1.58046 1.56481 1.54932 1.53398 1.51879 1.50375 1.48886 1.47412 1.45953 1.44508 1.43077 1.41660 1.40258 1.38869 1.37494 1.36133 1.34785 1.33450 1.32129 1.30821 1.29526 1.28243 1.26973 1.25716 1.24472 1.23239 1.22019 1.20811 1.19615 1.18430 1.17258 1.16097 1.14947 1.13809 1.12683 1.11567 1.10462 1.09369 1.08286 1.07214 1.06152 1.05101 1.04060 1.03030 1.02010 1.01000 1.00000

FW OF CF -$21,800.36 $179.87 $178.09 $176.33 $174.58 $172.85 $171.14 $169.45 $167.77 $166.11 $164.46 $162.83 $161.22 $159.63 $158.05 $156.48 $154.93 $153.40 $151.88 $150.38 $148.89 $147.41 $145.95 $144.51 $143.08 $141.66 $140.26 $138.87 $137.49 $136.13 $134.78 $133.45 $132.13 $130.82 $129.53 $128.24 $126.97 $125.72 $124.47 $123.24 $122.02 $120.81 $119.61 $118.43 $117.26 $116.10 $114.95 $113.81 $112.68 $111.57 $110.46 $109.37 $108.29 $107.21 $106.15 $105.10 $104.06 $103.03 $102.01 $101.00 $13,100.00 -$633.39 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$633.39 =FV(1%,60,-100,12000)+13000 SOLUTION USING FACTOR TABLES FW = -$12,000(F|P 1%,60) + $100(F|A 1%,60) + $13,000 FW = -$12,000(1.81670) + $100(81.66967) + $13,000 FW = -$633.43

RACE HORSE

EOM 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

+ CF

- CF -$12,000.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $20,000.00

NET CF -$12,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $20,000.00

FW OF CF -$21,800.36 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $20,000.00 -$1,800.36 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$1,800.36 =FV(1%,60,,12000)+20000 SOLUTION USING FACTOR TABLES FW = -$12,000(F|P 1%,60) + $20,000 FW = -$12,000(1.81670) + $20,000 FW = -$1,800.40

SAVINGS ACCOUNT THE FUTURE WORTH OF THE SAVINGS ACCOUNT IS ZERO SINCE IT EARNS EXACTLY MARR YANI SHOULD PREFER THE SAVINGS ACCOUNT.

PROBLEM 6.47 a

SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS DRILL PRESS T EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$20,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$9,000.00

NET CF -$20,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$9,000.00

10.00% (F|P i%,n-t) 2.59374 2.35795 2.14359 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$51,874.85 -$33,011.27 -$30,010.24 -$27,282.04 -$24,801.85 -$22,547.14 -$20,497.40 -$18,634.00 -$16,940.00 -$15,400.00 -$9,000.00 -$269,998.79 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$269,998.79 =FV(10%,10,14000,20000)+5000 SOLUTION USING FACTOR TABLES FW = -$20,000(F|P 10%,10) - $14,000(F|A 10%,10) + $5,000 FW = -$20,000(2.59374) - $14,000(15.93742) + $5,000 FW = -$269,998.68

DRILL PRESS M EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$30,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$3,000.00

NET CF -$30,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$3,000.00

10.00% (F|P i%,n-t) 2.59374 2.35795 2.14359 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$77,812.27 -$23,579.48 -$21,435.89 -$19,487.17 -$17,715.61 -$16,105.10 -$14,641.00 -$13,310.00 -$12,100.00 -$11,000.00 -$3,000.00 -$230,186.52 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$230,186.52 =FV(10%,10,10000,30000)+7000 SOLUTION USING FACTOR TABLES FW = -$30,000(F|P 10%,10) - $10,000(F|A 10%,10) + $7,000 FW = -$30,000(2.59374) - $10,000(15.93742) + $7,000 FW = -$230,186.40

ZUNNI'S MANUFACTURING SHOULD PURCHASE DRILL M

PROBLEM 6.48 IF THE EQUIPMENT IS PURCHASED, THE SERVICE COST IS SAVED AND THUS LOOKS LIKE A REVENUE TO THE PROJECT. a

AT A PRODUCTION RATE OF 200 UNITS/YEAR THE SERVICE WOULD COST $18,000/YR AT A PRODUCTION RATE OF 200 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $5,000/YR SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS AT 200 UNITS/YEAR EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00

- CF -$100,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00

NET CF -$100,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00

12.00% (F|P i%,n-t) 3.10585 2.77308 2.47596 2.21068 1.97382 1.76234 1.57352 1.40493 1.25440 1.12000 1.00000

FW OF CF -$310,584.82 $16,638.47 $14,855.78 $13,264.09 $11,842.94 $10,574.05 $9,441.12 $8,429.57 $7,526.40 $6,720.00 $6,000.00 -$205,292.41 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$205,292.41 =FV(12%,10,-6000,100000) SOLUTION USING FACTOR TABLES FW = -$100,000(F|P 12%,10) + 6,000(F|A 12%,10) FW = -$100,000(3.10585) + 6,000(17.54874) FW = -$205,292.56 THEREFORE, THE SERVICE CONTRACT IS PREFERRED OVER THE EQUIPMENT

+ CF $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00

- CF -$100,000.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00

NET CF -$100,000.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00

(F|P i%,n-t) 3.10585 2.77308 2.47596 2.21068 1.97382 1.76234 1.57352 1.40493 1.25440 1.12000 1.00000

FW OF CF -$310,584.82 $70,713.51 $63,137.06 $56,372.38 $50,332.48 $44,939.71 $40,124.74 $35,825.66 $31,987.20 $28,560.00 $25,500.00 $136,907.92 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $136,907.92 =FV(12%,10,-25500,100000) SOLUTION USING FACTOR TABLES FW = -$100,000(F|P 12%,10) + 25,500(F|A 12%,10) FW = -$100,000(3.10585) + 25,500(17.54874) FW = $136,907.87 THEREFORE, THE EQUIPMENT IS PREFERRED OVER THE SERVICE CONTRACT

FOR BREAKEVEN THE FUTURE WORTH OF BENEFITS MUST EQUAL THE FUTURE WORTH OF COSTS (90)(X)(F|A 12%,10) = 100,000(F|P 12%,10) + (7,000+(25*X))(F|A 12%,10) (90)(X)(17.54874) = 100,000(3.10585) + (7,000+(25*X))(17.54874) 1,579.3866(X) = 310,585 + 122,841.18 + 438.7185(X) 1,140.6681(X) = 433,426.18 X = 379.98 OR APPROXIMATELY 380 UNITS/YR

PROBLEM 6.49 a

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

X1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1

X2 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1

Y1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1

Y2 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1

FEASIBLE YES YES YES NO NO NO YES NO NO YES NO NO NO NO NO NO

REASON

Y1 CONTINGENT ON X1 Y2 CONTINGENT ON X2 X1 & X2 ARE ME Y2 CONTINGENT ON X2 Y1 CONTINGENT ON X1 Y1 & Y2 ARE ME X1 & X2 ARE ME X1 & X2 ARE ME Y1 & Y2 ARE ME Y1 & Y2 ARE ME X1 & X2 ARE ME

FEASIBLE COMBINATIONS ARE: NULL, X1 ONLY, X2 ONLY, X1&Y1, X2&Y2 b

ALTERNATIVE: NULL THE PRESENT WORTH OF NULL IS ZERO ALTERNATIVE: X1 ONLY SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 10.00% EOY + CF - CF NET CF (F|P i%,n-t) 0 -$10,000.00 -$10,000.00 2.14359 1 $1,600.00 $1,600.00 1.94872 2 $1,600.00 $1,600.00 1.77156 3 $1,600.00 $1,600.00 1.61051 4 $1,600.00 $1,600.00 1.46410 5 $1,600.00 $1,600.00 1.33100 6 $1,600.00 $1,600.00 1.21000 7 $1,600.00 $1,600.00 1.10000 8 $1,600.00 $1,600.00 1.00000

FW OF CF -$21,435.89 $3,117.95 $2,834.50 $2,576.82 $2,342.56 $2,129.60 $1,936.00 $1,760.00 $1,600.00 -$3,138.47 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$3,138.47 =FV(10%,8,-1600,10000) SOLUTION USING FACTOR TABLES FW = -$10,000(F|P 10%,8) + $1,600(F|A 10%,8) FW = -$10,000(2.14359) + $1,600(11.43589) FW = -$3,138.48

ALTERNATIVE: X2 ONLY EOY 0 1 2 3 4 5 6 7

+ CF $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00

- CF -$15,000.00

NET CF -$15,000.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00

10.00% (F|P i%,n-t) 2.14359 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000

FW OF CF -$32,153.83 $5,066.66 $4,606.06 $4,187.33 $3,806.66 $3,460.60 $3,146.00 $2,860.00

$2,600.00

1.00000

$2,600.00 -$2,420.52 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$2,420.52 =FV(10%,8,-2600,15000) SOLUTION USING FACTOR TABLES FW = -$15,000(F|P 10%,8) + $2,600(F|A 10%,8) FW = -$15,000(2.14359) + $2,600(11.43589) FW = -$2,420.54

ALTERNATIVE: X1&Y1 EOY 0 1 2 3 4 5 6 7 8

+ CF

- CF -$16,000.00

$4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00

NET CF -$16,000.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00

10.00% (F|P i%,n-t) 2.14359 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$34,297.42 $7,989.74 $7,263.40 $6,603.09 $6,002.81 $5,457.10 $4,961.00 $4,510.00 $4,100.00 $12,589.72 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $12,589.72 =FV(10%,8,-4100,16000) SOLUTION USING FACTOR TABLES FW = -$16,000(F|P 10%,8) + $4,100(F|A 10%,8) FW = -$16,000(2.14359) + $4,100(11.43589) FW = $12,589.71

ALTERNATIVE: X2&Y2 EOY 0 1 2 3 4 5 6 7 8

+ CF $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00

- CF -$24,000.00

NET CF -$24,000.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00 $6,100.00

10.00% (F|P i%,n-t) 2.14359 1.94872 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$51,446.13 $11,887.17 $10,806.52 $9,824.11 $8,931.01 $8,119.10 $7,381.00 $6,710.00 $6,100.00 $18,312.79 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $18,312.79 =FV(10%,8,-6100,24000) SOLUTION USING FACTOR TABLES FW = -$24,000(F|P 10%,8) + $6,100(F|A 10%,8) FW = -$24,000(2.14359) + $6,100(11.43589) FW = $18,312.77

THE COMBINATION X2&Y2 HAS THE HIGHEST FUTURE WORTH AND IS THEREFORE PREFERRED.

PROBLEM 6.50 a

TELESCOPE T1 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $470,000.00

- CF -$600,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00

NET CF -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

25.00% (F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$5,587,935.45 $2,011,656.76 $1,609,325.41 $1,287,460.33 $1,029,968.26 $823,974.61 $659,179.69 $527,343.75 $421,875.00 $337,500.00 $340,000.00 $3,460,348.36 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $3,460,348.36 =FV(25%,10,-270000,600000)+70000 SOLUTION USING FACTOR TABLES FW = -$600,000(F|P 25%,10) + $270,000(F|A 25%,10) + $70,000 FW = -$600,000(9.31323) + $270,000(33.25290) + $70,000 FW = $3,460,345.00

TELESCOPE T2 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $600,000.00 $600,000.00 $600,000.00 $600,000.00 $600,000.00 $600,000.00 $600,000.00 $600,000.00 $600,000.00 $730,000.00

- CF -$800,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00

NET CF -$800,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $460,000.00

(F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$7,450,580.60 $2,458,691.60 $1,966,953.28 $1,573,562.62 $1,258,850.10 $1,007,080.08 $805,664.06 $644,531.25 $515,625.00 $412,500.00 $460,000.00 $3,652,877.39 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $3,652,877.39 =FV(25%,10,-330000,800000)+130000 SOLUTION USING FACTOR TABLES FW = -$800,000(F|P 25%,10) + $330,000(F|A 25%,10) + $130,000 FW = -$800,000(9.31323) + $330,000(33.25290) + $130,000 FW = $3,652,873.00

TELESCOPE T3 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $325,000.00

- CF -$470,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00

NET CF -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

(F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$4,377,216.10 $1,415,610.31 $1,132,488.25 $905,990.60 $724,792.48 $579,833.98 $463,867.19 $371,093.75 $296,875.00 $237,500.00 $255,000.00 $2,005,835.47 <- FW

TELESCOPE T4 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $520,000.00

- CF -$540,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00

NET CF -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $400,000.00

(F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$5,029,141.90 $1,490,116.12 $1,192,092.90 $953,674.32 $762,939.45 $610,351.56 $488,281.25 $390,625.00 $312,500.00 $250,000.00 $400,000.00 $1,821,438.69 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $1,821,438.69 =FV(25%,10,-200000,540000)+200000 SOLUTION USING FACTOR TABLES FW = -$540,000(F|P 25%,10) + $200,000(F|A 25%,10) + $200,000 FW = -$540,000(9.31323) + $200,000(33.25290) + $200,000 FW = $1,821,435.80

TELESCOPE T2 HAS THE HIGHEST FUTURE WORTH AND IS THEREFORE PREFERRED.

TELESCOPE T1 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $470,000.00

- CF -$600,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00

NET CF -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

42.00% (F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175 8.19842 5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

FW OF CF -$20,000,216.38 $6,338,096.74 $4,463,448.41 $3,143,273.53 $2,213,572.91 $1,558,854.16 $1,097,784.62 $773,087.76 $544,428.00 $383,400.00 $340,000.00 $855,729.74 <- FW

TELESCOPE T2 EOY 0 1 2 3

+ CF $600,000.00 $600,000.00 $600,000.00

- CF -$800,000.00 -$270,000.00 -$270,000.00 -$270,000.00

NET CF -$800,000.00 $330,000.00 $330,000.00 $330,000.00

(F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175

FW OF CF -$26,666,955.17 $7,746,562.68 $5,455,325.83 $3,841,778.75

4 5 6 7 8 9 10

$600,000.00 $600,000.00 $600,000.00 $600,000.00 $600,000.00 $600,000.00 $730,000.00

-$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00 -$270,000.00

$330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $460,000.00

8.19842 5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

$2,705,478.00 $1,905,266.19 $1,341,736.76 $944,885.04 $665,412.00 $468,600.00 $460,000.00 -$1,131,909.91 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$1,131,909.91 =FV(42%,10,-330000,800000)+130000 SOLUTION USING FACTOR TABLES FW = -$800,000(F|P 42%,10) + $330,000(F|A 42%,10) + $130,000 FW = -$800,000(33.33369) + $330,000(76.98499) + $130,000 FW = -$1,131,905.30

TELESCOPE T3 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $325,000.00

- CF -$470,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00 -$70,000.00

NET CF -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

(F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175 8.19842 5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

FW OF CF -$15,666,836.16 $4,460,142.15 $3,140,945.18 $2,211,933.22 $1,557,699.45 $1,096,971.45 $772,515.10 $544,024.72 $383,116.00 $269,800.00 $255,000.00 -$974,688.89 <- FW

TELESCOPE T4 EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $320,000.00 $520,000.00

- CF -$540,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00

NET CF -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $400,000.00

(F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175 8.19842 5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

FW OF CF -$18,000,194.74 $4,694,886.47 $3,306,258.08 $2,328,350.76 $1,639,683.63 $1,154,706.78 $813,173.79 $572,657.60 $403,280.00 $284,000.00 $400,000.00 -$2,403,197.61 <- FW

TELESCOPE T1 HAS THE HIGHEST FUTURE WORTH AND IS THEREFORE PREFERRED.

PROBLEM 6.51 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, T3, T4, T1, T2 a

NULL BECOMES THE "CURRENT BEST" AND T3 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR T3 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR. CF -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

25.00% (F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$4,377,216.10 $1,415,610.31 $1,132,488.25 $905,990.60 $724,792.48 $579,833.98 $463,867.19 $371,093.75 $296,875.00 $237,500.00 $255,000.00 $2,005,835.47 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $2,005,835.47 =FV(25%,10,-190000,470000)+65000 SOLUTION USING FACTOR TABLES FW = -$470,000(F|P 25%,10) + $190,000(F|A 25%,10) + $65,000 FW = -$470,000(9.31323) + $190,000(33.25290) + $65,000 FW = $2,005,832.90 SINCE THE FW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T3 BECOMES THE NEW CURRENT BEST T4 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T4 - T3 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T4 -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $400,000.00

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

INCR. CF -$70,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $145,000.00

(F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$651,925.80 $74,505.81 $59,604.64 $47,683.72 $38,146.97 $30,517.58 $24,414.06 $19,531.25 $15,625.00 $12,500.00 $145,000.00 -$184,396.77 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$184,396.77 =FV(25%,10,-10000,70000)+135000 SOLUTION USING FACTOR TABLES FW = -$70,000(F|P 25%,10) + $10,000(F|A 25%,10) + $135,000 FW = -$70,000(9.31323) + $10,000(33.25290) + $135,000 FW = -$184,397.10 SINCE THE FW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. T3 REMAINS THE CURRENT BEST T1 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T1 - T3 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T1 -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

INCR. CF -$130,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $85,000.00

(F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$1,210,719.35 $596,046.45 $476,837.16 $381,469.73 $305,175.78 $244,140.63 $195,312.50 $156,250.00 $125,000.00 $100,000.00 $85,000.00 $1,454,512.89 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $1,454,512.89 =FV(25%,10,-80000,130000)+5000 SOLUTION USING FACTOR TABLES FW = -$130,000(F|P 25%,10) + $80,000(F|A 25%,10) + $5,000 FW = -$130,000(9.31323) + $80,000(33.25290) + $5,000 FW = $1,454,512.10 SINCE THE FW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T1 BECOMES THE NEW CURRENT BEST T2 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T2 - T1 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T2 -$800,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $460,000.00

T1 -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

INCR. CF -$200,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $120,000.00

(F|P i%,n-t) 9.31323 7.45058 5.96046 4.76837 3.81470 3.05176 2.44141 1.95313 1.56250 1.25000 1.00000

FW OF CF -$1,862,645.15 $447,034.84 $357,627.87 $286,102.29 $228,881.84 $183,105.47 $146,484.38 $117,187.50 $93,750.00 $75,000.00 $120,000.00 $192,529.03 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $192,529.03 =FV(25%,10,-60000,200000)+60000 SOLUTION USING FACTOR TABLES FW = -$200,000(F|P 25%,10) + $60,000(F|A 25%,10) + $60,000 FW = -$200,000(9.31323) + $60,000(33.25290) + $60,000 FW = $192,528.00 SINCE THE FW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T2 BECOMES THE NEW CURRENT BEST THERE ARE NO MORE CHALLENGERS SO T2 IS PREFERRED. b

NULL BECOMES THE "CURRENT BEST" AND T3 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR T3 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR. CF -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

42.00% (F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175 8.19842 5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

FW OF CF -$15,666,836.16 $4,460,142.15 $3,140,945.18 $2,211,933.22 $1,557,699.45 $1,096,971.45 $772,515.10 $544,024.72 $383,116.00 $269,800.00 $255,000.00 -$974,688.89 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$974,688.89 =FV(42%,10,-190000,470000)+65000 SOLUTION USING FACTOR TABLES FW = -$470,000(F|P 42%,10) + $190,000(F|A 42%,10) + $65,000 FW = -$470,000(33.33369) + $190,000(76.98499) + $65,000 FW = -$974,686.20 SINCE THE FW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. NULL REMAINS THE NEW CURRENT BEST T4 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T4 - NULL ARE NEEDED

EOY 0 1 2 3 4

T4 -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00

INCR. CF -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00

(F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175 8.19842

FW OF CF -$18,000,194.74 $4,694,886.47 $3,306,258.08 $2,328,350.76 $1,639,683.63

5 6 7 8 9 10

$200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $400,000.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $400,000.00

5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

$1,154,706.78 $813,173.79 $572,657.60 $403,280.00 $284,000.00 $400,000.00 -$2,403,197.61 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$2,403,197.61 =FV(42%,10,-200000,540000)+200000 SOLUTION USING FACTOR TABLES FW = -$540,000(F|P 42%,10) + $200,000(F|A 42%,10) + $200,000 FW = -$540,000(33.33369) + $200,000(76.98499) + $200,000 FW = -$2,403,194.60 SINCE THE FW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. NULL REMAINS THE CURRENT BEST T1 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T1 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T1 -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR. CF -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

(F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175 8.19842 5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

FW OF CF -$20,000,216.38 $6,338,096.74 $4,463,448.41 $3,143,273.53 $2,213,572.91 $1,558,854.16 $1,097,784.62 $773,087.76 $544,428.00 $383,400.00 $340,000.00 $855,729.74 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $855,729.74 =FV(42%,10,-270000,600000)+70000 SOLUTION USING FACTOR TABLES FW = -$600,000(F|P 42%,10) + $270,000(F|A 42%,10) + $70,000 FW = -$600,000(33.33369) + $270,000(76.98499) + $70,000 FW = $855,733.30 SINCE THE FW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. T1 BECOMES THE NEW CURRENT BEST T2 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T2 - T1 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T2 -$800,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $330,000.00 $460,000.00

T1 -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

INCR. CF -$200,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $120,000.00

(F|P i%,n-t) 33.33369 23.47443 16.53129 11.64175 8.19842 5.77353 4.06587 2.86329 2.01640 1.42000 1.00000

FW OF CF -$6,666,738.79 $1,408,465.94 $991,877.42 $698,505.23 $491,905.09 $346,412.04 $243,952.14 $171,797.28 $120,984.00 $85,200.00 $120,000.00 -$1,987,639.65 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$1,987,639.65 =FV(42%,10,-60000,200000)+60000 SOLUTION USING FACTOR TABLES FW = -$200,000(F|P 42%,10) + $60,000(F|A 42%,10) + $60,000 FW = -$200,000(33.33369) + $60,000(76.98499) + $60,000 FW = -$1,987,638.60 SINCE THE FW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. T1 REMAINS THE CURRENT BEST THERE ARE NO MORE CHALLENGERS SO T1 IS PREFERRED.

PROBLEM 6.52 DELIVERY VAN SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS EOY 0 1 2 3 4 5 6

VAN -$18,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $500.00

LOAN $12,000.00 -$3,305.88 -$3,305.88 -$3,305.88 -$3,305.88

O&M -$700.00 -$700.00 -$700.00 -$700.00 -$700.00 -$700.00

SAVINGS $3,800.00 $3,800.00 $3,800.00 $3,800.00 $3,800.00 $3,800.00

NET CF -$6,000.00 -$205.88 -$205.88 -$205.88 -$205.88 $3,100.00 $3,600.00

6.00% (F|P i%,n-t) 1.41852 1.33823 1.26248 1.19102 1.12360 1.06000 1.00000

FW OF CF -$8,511.11 -$275.51 -$259.92 -$245.21 -$231.33 $3,286.00 $3,600.00 -$2,637.08 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$2,637.08 =FV(6%,6,,6000)+FV(6%,2,,FV(6%,4,-205.88))+FV(6%,2,-3100)+500 SOLUTION USING FACTOR TABLES FW = -$6,000(F|P 6%,6) - $205.88(F|A 6%,4)(F|P 6%,2) + $3,100(F|A 6%,2) + $500 FW = -$6,000(1.41852) - $205.88(4.37462)(1.12360) + $3,100(2.06000) + $500 FW = -$2,637.09 DECISION: SINCE THE FW IS NEGATIVE, DO NOT PURCHASE THE VAN

PROBLEM 6.53 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS FW OF LOTTERY PAYOUT (IN M$)

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

CF $1.00 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30

6.00% (F|P i%,n-t) 3.20714 3.02560 2.85434 2.69277 2.54035 2.39656 2.26090 2.13293 2.01220 1.89830 1.79085 1.68948 1.59385 1.50363 1.41852 1.33823 1.26248 1.19102 1.12360 1.06000 1.00000

FW OF CF $3.21 $3.93 $3.71 $3.50 $3.30 $3.12 $2.94 $2.77 $2.62 $2.47 $2.33 $2.20 $2.07 $1.95 $1.84 $1.74 $1.64 $1.55 $1.46 $1.38 $1.30 $51.03 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $51.03 =FV(6%,20,-1.3,-1) SOLUTION USING FACTOR TABLES FW = $1.0(F|P 6%,20) + $1.3(F|A 6%,20) FW = $1.0(3.20714) + $1.3(36.78559) FW = $51.03

FW OF ONE-TIME PAYMENT (IN M$) FW = $46.18 =FV(6%,20,,-14.4) OR FW = $14.4(F|P 6%,20) = $14.4(3.20714) = $46.18

DECISION: SINCE THE FW OF THE ONE-TIME IS LOWER THAN THE FW OF THE PAYOUT, THE STATE SHOULD PREFER THE ONE-TIME PAYMENT.

PROBLEM 6.54 MACHINE 1 (IN K$) SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 12.00% EOY MACHINE O&M NET CF (F|P i%,n-t) FW OF CF 0 -$800.00 -$800.00 1.57352 -$1,258.82 1 -$50.00 -$50.00 1.40493 -$70.25 2 -$50.00 -$50.00 1.25440 -$62.72 3 -$50.00 -$50.00 1.12000 -$56.00 4 $40.00 -$50.00 -$10.00 1.00000 -$10.00 -$1,457.78 <- FW SOLUTION USING EXCEL'S FV FUNCTION FW = -$1,457.78 =FV(12%,4,50,800)+40 SOLUTION USING FACTOR TABLES FW = -$800(F|P 12%,4) - $50(F|A 12%,4) + $40 FW = -$800(1.57352) - $50(4.7793) + $40 FW = -$1,457.78

MACHINE 2 (IN K$) EOY 0 1 2 3 4

MACHINE -$650.00

$32.50

O&M -$90.00 -$90.00 -$90.00 -$90.00

NET CF (F|P i%,n-t) -$650.00 1.57352 -$90.00 1.40493 -$90.00 1.25440 -$90.00 1.12000 -$57.50 1.00000

FW OF CF -$1,022.79 -$126.44 -$112.90 -$100.80 -$57.50 -$1,420.43 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$1,420.43 =FV(12%,4,90,650)+32.5 SOLUTION USING FACTOR TABLES FW = -$650(F|P 12%,4) - $90(F|A 12%,4) + $32.50 FW = -$650(1.57352) - $90(4.7793) + $32.50 FW = -$1,420.43

MACHINE 3 (IN K$) EOY 0 1 2 3 4

MACHINE -$575.00

$28.75

O&M -$105.00 -$105.00 -$105.00 -$105.00

NET CF (F|P i%,n-t) -$575.00 1.57352 -$105.00 1.40493 -$105.00 1.25440 -$105.00 1.12000 -$76.25 1.00000

FW OF CF -$904.77 -$147.52 -$131.71 -$117.60 -$76.25 -$1,377.85 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$1,377.85 =FV(12%,4,105,575)+28.75 SOLUTION USING FACTOR TABLES FW = -$575(F|P 12%,4) - $105(F|A 12%,4) + $28.75 FW = -$575(1.57352) - $105(4.7793) + $28.75 FW = -$1,377.85

DECISION: PREFER MACHINE 3, IT HAS THE HIGHEST (LEAST NEGATIVE) FW.

PROBLEM 6.55 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS GATE 1 20.00% EOY GATE O&M NET CF (F|P i%,n-t) FW OF CF 0 -$15,000.00 -$15,000.00 2.48832 -$37,324.80 1 -$6,500.00 -$6,500.00 2.07360 -$13,478.40 2 -$6,500.00 -$6,500.00 1.72800 -$11,232.00 3 -$6,500.00 -$6,500.00 1.44000 -$9,360.00 4 -$6,500.00 -$6,500.00 1.20000 -$7,800.00 5 $0.00 -$6,500.00 -$6,500.00 1.00000 -$6,500.00 -$85,695.20 <- FW SOLUTION USING EXCEL'S FV FUNCTION FW = -$85,695.20 =FV(20%,5,6500,15000) SOLUTION USING FACTOR TABLES FW = -$15,000(F|P 20%,5) - $6,500(F|A 20%,5) FW = -$15,000(2.48832) - $6,500(7.44160) FW = -$85,695.20

GATE 2 EOY 0 1 2 3 4 5

GATE -$19,000.00

$2,000.00

O&M -$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00

NET CF (F|P i%,n-t) -$19,000.00 2.48832 -$5,600.00 2.07360 -$5,600.00 1.72800 -$5,600.00 1.44000 -$5,600.00 1.20000 -$3,600.00 1.00000

FW OF CF -$47,278.08 -$11,612.16 -$9,676.80 -$8,064.00 -$6,720.00 -$3,600.00 -$86,951.04 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$86,951.04 =FV(20%,5,5600,19000)+2000 SOLUTION USING FACTOR TABLES FW = -$19,000(F|P 20%,5) - $5,600(F|A 20%,5) + $2,000 FW = -$19,000(2.48832) - $5,600(7.44160) + $2,000 FW = -$86,951.04

GATE 3 EOY 0 1 2 3 4 5

GATE -$24,000.00

$5,000.00

O&M -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00

NET CF (F|P i%,n-t) -$24,000.00 2.48832 -$4,000.00 2.07360 -$4,000.00 1.72800 -$4,000.00 1.44000 -$4,000.00 1.20000 $1,000.00 1.00000

FW OF CF -$59,719.68 -$8,294.40 -$6,912.00 -$5,760.00 -$4,800.00 $1,000.00 -$84,486.08 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$84,486.08 =FV(20%,5,4000,24000)+5000 SOLUTION USING FACTOR TABLES FW = -$24,000(F|P 20%,5) - $4,000(F|A 20%,5) + $5,000 FW = -$24,000(2.48832) - $4,000(7.44160) + $5,000 FW = -$84,486.08

DECISION: PREFER GATE 3, IT HAS THE HIGHEST (LEAST NEGATIVE) FW.

PROBLEM 6.56

LOAN PAYMENT = $30,000(A|P 12%,4) = $30,000(0.32923) = $9876.90 OR USING EXCEL'S PMT FUNCTION PMT = $9,877.03 =PMT(12%,4,-30000) SPRINKLER SYSTEM SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS EOY 0 1 2 3 4 5 6 7 8 9

SPRINKLERS -$30,000.00

$2,000.00

LOAN $30,000.00 -$9,877.03 -$9,877.03 -$9,877.03 -$9,877.03

O&M

SAVINGS

-$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00

$15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00

NET CF $0.00 -$3,877.03 -$3,877.03 -$3,877.03 -$3,877.03 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $8,000.00

15.00% (F|P i%,n-t) 3.51788 3.05902 2.66002 2.31306 2.01136 1.74901 1.52088 1.32250 1.15000 1.00000

FW OF CF $0.00 -$11,859.93 -$10,312.99 -$8,967.81 -$7,798.10 $10,494.04 $9,125.25 $7,935.00 $6,900.00 $8,000.00 $3,515.46 <- FW

SOLUTION USING EXCEL'S FUNCTIONS FW = $3,515.46 =FV(15%,5,-6000)+FV(15%,5,,FV(15%,4,PMT(12%,4,30000)+6000))+2000 SOLUTION USING FACTOR TABLES FW = -$3,877.03(F|A 15%,4)(F|P 15%,5) + $6,000(F|A 15%,5) + $2,000 FW = -$3,877.03(4.99338)(2.01136) + $6,000(6.74238) + $2,000 FW = $3,515.39 DECISION: SINCE THE FW IS POSITIVE, THE SPRINKLER SYSTEM IS ECONOMICALLY ATTRACTIVE

PROBLEM 6.57 LIGHT BAR SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 10.00% EOY BAR REVENUE NET CF (F|P i%,n-t) 0 -$6,000.00 -$6,000.00 1.77156 1 $2,000.00 $2,000.00 1.61051 2 $2,000.00 $2,000.00 1.46410 3 $2,000.00 $2,000.00 1.33100 4 $2,000.00 $2,000.00 1.21000 5 $2,000.00 $2,000.00 1.10000 6 $2,000.00 $2,000.00 1.00000

FW OF CF -$10,629.37 $3,221.02 $2,928.20 $2,662.00 $2,420.00 $2,200.00 $2,000.00 $4,801.85 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $4,801.85 =FV(10%,6,-2000,6000) SOLUTION USING FACTOR TABLES FW = -$6,000(F|P 10%,6) + $2,000(F|A 10%,6) FW = -$6,000(1.77156) + $2,000(7.71561) FW = $4,801.86

SLIDING SPOTS EOY 0 1 2 3 4 5 6

SPOTS -$14,000.00

REVENUE $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00

NET CF -$14,000.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00

(F|P i%,n-t) 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$24,801.85 $5,636.79 $5,124.35 $4,658.50 $4,235.00 $3,850.00 $3,500.00 $2,202.78 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $2,202.78 =FV(10%,6,-3500,14000) SOLUTION USING FACTOR TABLES FW = -$14,000(F|P 10%,6) + $3,500(F|A 10%,6) FW = -$14,000(1.77156) + $3,500(7.71561) FW = $2,202.80

REFLECTED BEAM EOY 0 1 2 3 4 5 6

BEAM -$20,000.00

REVENUE $0.00 $2,300.00 $4,600.00 $6,900.00 $9,200.00 $11,500.00

NET CF -$20,000.00 $0.00 $2,300.00 $4,600.00 $6,900.00 $9,200.00 $11,500.00

(F|P i%,n-t) 1.77156 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$35,431.22 $0.00 $3,367.43 $6,122.60 $8,349.00 $10,120.00 $11,500.00 $4,027.81 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $4,027.81 =FV(10%,6,,-NPV(10%,E52:E57)-E51) SOLUTION USING FACTOR TABLES FW = -$20,000(F|P 10%,6) + $2,300(A|G 10%,6)(F|A 10%,6) FW = -$20,000(1.77156) + $2,300(2.22356)(7.71561) FW = $4,027.88

DECISION: LIGHT BAR IS PREFERRED SINCE IT HAS THE HIGHEST FW.

PROBLEM 6.58 DESIGN 1 (IN M$) SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3

NET CF -$15.00 -$2.50 -$2.50 -$2.50

10.00% (F|P i%,n-t) 1.33100 1.21000 1.10000 1.00000

FW OF CF -$19.97 -$3.03 -$2.75 -$2.50 -$28.24 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$28.24 =FV(10%,3,2.5,15) SOLUTION USING FACTOR TABLES FW = -$15.00(F|P 10%,3) - $2.50(F|A 10%,3) FW = -$15.00(1.33100) - $2.50(3.31000) FW = -$28.24

DESIGN 2 (IN M$) EOY 0 1 2 3

NET CF -$20.00 -$1.50 -$1.50 -$1.50

10.00% (F|P i%,n-t) 1.33100 1.21000 1.10000 1.00000

FW OF CF -$26.62 -$1.82 -$1.65 -$1.50 -$31.59 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -$31.59 =FV(10%,3,1.5,20) SOLUTION USING FACTOR TABLES FW = -$20.00(F|P 10%,3) - $1.50(F|A 10%,3) FW = -$20.00(1.33100) - $1.50(3.31000) FW = -$31.59

DECISION: PREFER DESIGN 1, IT HAS THE HIGHEST (LEAST NEGATIVE) FW

PROBLEM 6.59 FIRST SATELLITE ONLY (IN K$) SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS

EOY 0 1 2 3 4 5

EQUIPMENT -$750.00

DEVELOPMENT

VEHICLE

-$150.00 -$150.00 -$150.00 -$150.00 -$150.00

-$275.00

PAYMENT

$2,500.00

NET CF -$750.00 -$150.00 -$150.00 -$150.00 -$150.00 $2,075.00

10.00% (F|P i%,n-t) 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$1,207.88 -$219.62 -$199.65 -$181.50 -$165.00 $2,075.00 $101.35 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $101.35 =FV(10%,5,150,750)+2225 SOLUTION USING FACTOR TABLES FW = -$750(F|P 10%,5) - $150(F|A 10%,5) + $2,225 FW = -$750(1.61051) - $150(6.10510) + $2,225 FW = $101.35

SECOND SATELLITE ONLY (IN K$) EOY 0 1 2 3 4 5

EQUIPMENT -$850.00

DEVELOPMENT

VEHICLE

-$120.00 -$120.00 -$120.00 -$120.00 -$120.00

-$275.00

PAYMENT

$2,500.00

NET CF -$850.00 -$120.00 -$120.00 -$120.00 -$120.00 $2,105.00

(F|P i%,n-t) 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$1,368.93 -$175.69 -$159.72 -$145.20 -$132.00 $2,105.00 $123.45 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $123.45 =FV(10%,5,120,850)+2225 SOLUTION USING FACTOR TABLES FW = -$850(F|P 10%,5) - $120(F|A 10%,5) + $2,225 FW = -$850(1.61051) - $120(6.10510) + $2,225 FW = $123.45

BOTH SATELLITES (IN K$) EOY 0 1 2 3 4 5

EQUIPMENT -$1,750.00

DEVELOPMENT

VEHICLE

-$400.00 -$400.00 -$400.00 -$400.00 -$400.00

-$350.00

PAYMENT

$6,000.00

NET CF -$1,750.00 -$400.00 -$400.00 -$400.00 -$400.00 $5,250.00

(F|P i%,n-t) 1.61051 1.46410 1.33100 1.21000 1.10000 1.00000

FW OF CF -$2,818.39 -$585.64 -$532.40 -$484.00 -$440.00 $5,250.00 $389.57 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $389.57 =FV(10%,5,400,1750)+5650 SOLUTION USING FACTOR TABLES FW = -$1,750(F|P 10%,5) - $400(F|A 10%,5) + $5,650 FW = -$1,750(1.61051) - $400(6.10510) + $5,650 FW = $389.57

DECISION: PREFER BOTH SATELLITES SINCE IT HAS THE HIGHEST FW

PROBLEM 6.60 LOAN PAYMENT = $50(A|P 15%,5) = $50(0.29832) = $14.92 OR USING EXCEL'S PMT FUNCTION PMT = $14.92 =PMT(15%,5,-50) SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS CASH FLOWS IN K$ EOY 0 1 2 3 4 5 6 7 8 9 10

FILTER -$100.00

$10.00

LOAN $50.00 -$14.92 -$14.92 -$14.92 -$14.92 -$14.92

O&M -$20.00 -$21.50 -$23.00 -$24.50 -$26.00 -$27.50 -$29.00 -$30.50 -$32.00 -$33.50

SAVINGS $50.00 $50.00 $50.00 $50.00 $50.00 $50.00 $50.00 $50.00 $50.00 $50.00

NET CF -$50.00 $15.08 $13.58 $12.08 $10.58 $9.08 $22.50 $21.00 $19.50 $18.00 $26.50

12.00% (F|P i%,n-t) 3.10585 2.77308 2.47596 2.21068 1.97382 1.76234 1.57352 1.40493 1.25440 1.12000 1.00000

FW OF CF -$155.29 $41.83 $33.63 $26.71 $20.89 $16.01 $35.40 $29.50 $24.46 $20.16 $26.50 $119.82 <- FW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $119.82 =FV(12%,10,,-NPV(12%,G13:G22)-G12) SOLUTION USING FACTOR TABLES FW = -$50(F|P 12%,10) -$14.92(F|A 12%,5)(F|P 12%,5) -($20 - $1.50(A|G 12%,10) + $50))(F|A 12%,10) + $10 FW = -$50(3.10585) -$14.92(6.35285)(1.76234) + (-$20 - $1.50(3.58465) + $50)(17.54874) + $10 FW = $119.77

DECISION: FILTER IS ECONOMICALLY JUSTIFIED SINCE THE FW IS POSITIVE

PROBLEM 6.61 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS IN K$ EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BUILDING FURNITURE -$8,000.00 -$700.00

-$700.00

$900.00

O&M -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00

REVENUE $1,460.00 $1,752.00 $2,044.00 $2,336.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00

NET CF -$8,700.00 $660.00 $952.00 $1,244.00 $1,536.00 $1,128.00 $1,828.00 $1,828.00 $1,828.00 $1,828.00 $1,128.00 $1,828.00 $1,828.00 $1,828.00 $1,828.00 $2,728.00

12.00% (F|P i%,n-t) 5.47357 4.88711 4.36349 3.89598 3.47855 3.10585 2.77308 2.47596 2.21068 1.97382 1.76234 1.57352 1.40493 1.25440 1.12000 1.00000

FW OF CF -$47,620.02 $3,225.49 $4,154.05 $4,846.59 $5,343.05 $3,503.40 $5,069.19 $4,526.06 $4,041.13 $3,608.15 $1,987.92 $2,876.39 $2,568.21 $2,293.04 $2,047.36 $2,728.00 $5,198.01 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = $5,198.01 =FV(12%,15,800,8700)+FV(12%,10,,700)+FV(12%,5,,700)+FV(12%,14,,-1460)+FV(12%,13,,-1752)+ FV(12%,12,,-2044)+FV(12%,11,-2628,-2336)+900 SOLUTION USING FACTOR TABLES FW = -$8,700(F|P 12%,15) - $700(F|P 12%,10) - $700(F|P 12%,5) - $800(F|A 12%,15) + $1,460(F|P 12%,14) + $1,752(F|P 12%,13) + $2,044(F|P 12%,12) + $2,336(F|P 12%,11) + $2,628(F|A 12%,11) + $900 FW = -$8,700(5.47357) - $700(3.10585) - $700(1.76234) - $800(37.27971) + $1,460(4.88711) + $1,752(4.36349) + $2,044(3.89598) + $2,336(3.47855) + $2,628(20.65458) + $900 FW = $5,197.97 DECISION: MOTEL IS ECONOMICALLY ATTRACTIVE SINCE THE FW IS POSITIVE.

PROBLEM 6.62 SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS IN K$ 20.00% EOY CF (F|P i%,n-t) FW OF CF 0 -$70,000.00 38.33760 -$2,683,631.99 1 $20,000.00 31.94800 $638,960.00 2 $19,000.00 26.62333 $505,843.33 3 $18,000.00 22.18611 $399,350.00 4 $17,000.00 18.48843 $314,303.24 5 $16,000.00 15.40702 $246,512.35 6 $15,000.00 12.83918 $192,587.77 7 $14,000.00 10.69932 $149,790.49 8 $13,000.00 8.91610 $115,909.31 9 $12,000.00 7.43008 $89,161.00 10 $11,000.00 6.19174 $68,109.10 11 $10,000.00 5.15978 $51,597.80 12 $9,000.00 4.29982 $38,698.35 13 $8,000.00 3.58318 $28,665.45 14 $7,000.00 2.98598 $20,901.89 15 $6,000.00 2.48832 $14,929.92 16 $5,000.00 2.07360 $10,368.00 17 $4,000.00 1.72800 $6,912.00 18 $3,000.00 1.44000 $4,320.00 19 $2,000.00 1.20000 $2,400.00 20 $1,000.00 1.00000 $1,000.00 $216,688.00 <- FW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $216,688.00 =FV(20%,20,,-NPV(20%,C8:C27)-C7) SOLUTION USING FACTOR TABLES FW = -$70,000(F|P 20%,20) + ($20,000 - $1,000(A|G 20%,20))(F|A 20%,20) FW = -$70,000(38.33760) + ($20,000 - $1,000(4.46435))(186.68800) FW = 216687.4272 (1) FW = $216,688.00 (2) INVESTMENT IS ATTRACTIVE (3) IF FW >= 0, THEN ATTRACTIVE; OTHERWISE, UNATTRACTIVE

PROBLEM 6.63 GRAPH OF FW VERSUS i% IN K$ CF -$70,000.00 $20,000.00 $19,000.00 $18,000.00 $17,000.00 $16,000.00 $15,000.00 $14,000.00 $13,000.00 $12,000.00 $11,000.00 $10,000.00 $9,000.00 $8,000.00 $7,000.00 $6,000.00 $5,000.00 $4,000.00 $3,000.00 $2,000.00 $1,000.00

FW $140,000 $153,066 $167,063 $181,967 $197,731 $214,269 $231,452 $249,096 $266,948 $284,670 $301,825 $317,851 $332,038 $343,499 $351,133 $353,590 $349,218 $336,014 $311,558 $272,943 $216,688 $138,646 $33,890 -$103,413 -$280,147 -$504,417 -$785,734 -$1,135,235 -$1,565,933 -$2,092,991 -$2,734,050 -$3,509,585 -$4,443,319 -$5,562,685 -$6,899,356 -$8,489,833 -$10,376,115 -$12,606,455 -$15,236,204 -$18,328,766 -$21,956,667 -$26,202,755 -$31,161,546 -$36,940,727 -$43,662,841 -$51,467,173 -$60,511,843 -$70,976,158 -$83,063,218 -$97,002,827 -$113,054,729

Nu Things Investment FW versus MARR $20,000,000 $0 -$20,000,000

10%

20%

30%

40%

50%

60%

25%

30%

-$40,000,000

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

-$60,000,000 -$80,000,000

-$100,000,000 -$120,000,000 MARR

Nu Things Investment FW versus MARR Zoom of 0% to 30% Region $500,000 $0 -$500,000

10%

15%

-$1,000,000

-$1,500,000 -$2,000,000 -$2,500,000 -$3,000,000 MARR

Y-AXIS INTERCEPT IS THE UNDISCOUNTED SUM OF CASH FLOWS

X-AXIS INTERCEPT IS THE POINT WHERE FW IS ZERO (INTERNAL RATE OF RETURN)

20%

PROBLEM 6.64 PURCHASE SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS 10.00% EOY PURCHASE SAVINGS NET CF (F|P i%,n-t) 0 -$60,000.00 -$60,000.00 1.33100 1 $23,000.00 $23,000.00 1.21000 2 $23,000.00 $23,000.00 1.10000 3 $10,000.00 $23,000.00 $33,000.00 1.00000

FW OF CF -$79,860.00 $27,830.00 $25,300.00 $33,000.00 $6,270.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = 6270 =FV(10%,3,-23000,60000)+10000 SOLUTION USING FACTOR TABLES FW = -$60,000(F|P 10%,3) + $23,000(F|A 10%,3) + $10,000 FW = -$60,000(1.33100) + $23,000(3.31000) + $10,000 FW = 6270

LEASE EOY 0 1 2 3

LEASE -$21,000.00 -$21,000.00 -$21,000.00

SAVINGS $23,000.00 $23,000.00 $23,000.00

NET CF -$21,000.00 $2,000.00 $2,000.00 $23,000.00

(F|P i%,n-t) 1.33100 1.21000 1.10000 1.00000

FW OF CF -$27,951.00 $2,420.00 $2,200.00 $23,000.00 -$331.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -331 =FV(10%,3,-2000,21000)+21000 SOLUTION USING FACTOR TABLES FW = -$21,000(F|P 10%,3) + $2,000(F|A 10%,3) + $21,000 FW = -$21,000(1.33100) + $2,000(3.31000) + $21,000 FW = -331

DECISION: PURCHASE IS PREFERRED SINCE IT HAS A HIGHER FW.

PROBLEM 6.65 OPTION 1: $100,000 IN CD, $0 IN VENTURES, $0 IN BANK ACCOUNT SOLUTION USING EXCEL'S FV FUNCTION FW = $146,410.00 =FV(10%,4,,-100000) SOLUTION USING FACTOR TABLES FW = $100,000(F|P 10%,4) FW = $100,000(1.46410) FW = $146,410.00

OPTION 2: $0 IN CD, $35,000 IN BV01, $65,000 IN BANK ACCOUNT BV01 CASH FLOWS = -$35,000; $0; $0; $0; $50,000 SOLUTION USING EXCEL'S FV FUNCTION FW = $135,201.74 =50000+FV(7%,4,,-65000) SOLUTION USING FACTOR TABLES FW = $50,000 + $65,000(F|P 7%,4) FW = $50,000 + $65,000(1.31080) FW = $135,202.00

OPTION 3: $0 IN CD, $80,000 IN BV02, $20,000 IN BANK ACCOUNT BV02 CASH FLOWS = -$80,000; $10,000; $10,000; $10,000; $90,000 SOLUTION USING EXCEL'S FV FUNCTION FW = $150,615.35 =FV(7%,4,-10000)+80000+FV(7%,4,,-20000) SOLUTION USING FACTOR TABLES FW = $10,000(F|A 7%,4) + $80,000 + $20,000(F|P 7%,4) FW = $10,000(4.43994) + $80,000 + $20,000(1.31080) FW = $150,615.40

OPTION 4: $0 IN CD, $60,000 IN BV03, $40,000 IN BANK ACCOUNT BV03 CASH FLOWS = -$60,000; $0; $40,000; $0; $40,000 SOLUTION USING EXCEL'S FV FUNCTION FW = $138,227.84 =FV(7%,2,,-40000)+40000+FV(7%,4,,-40000) SOLUTION USING FACTOR TABLES FW = $40,000(F|P 7%,2) + $40,000 + $40,000(F|P 7%,4) FW = $40,000(1.14490) + $40,000 + $40,000(1.31080) FW = $138,228.00

OPTION 3 WHICH INCLUDES $0 IN THE CD, $80,000 IN BUSINESS VENTURE 2, AND $20,000 IN THE BANK ACCOUNT IS PREFERRED BECAUSE IT HAS THE HIGHEST PORTFOLIO VALUE.

PROBLEM 6.66 a

MONEY AVAILABLE FOR LIGHTING ENHANCEMENT IS $20,000 SINCE THIS IS THE COST OF THE MOST EXPENSIVE ALTERNATIVE. SOLUTION APPROACH IS TO SUM THE FW OF THE INVESTMENT RETURNS PLUS THE FW OF THE RESIDUAL INVESTMENT TO DETERMINE TOTAL PORTFOLIO VALUE OPTION 1: LIGHT BAR, CASH FLOWS = -$6,000; $2,000; $2,000; $2,000; $2,000; $2,000; $2,000, BANK ACCOUNT = $14,000 SOLUTION USING EXCEL'S FV FUNCTION FW = $40,233.07 =FV(10%,6,-2000) + FV(,10%,6,,-14000) SOLUTION USING FACTOR TABLES FW = $2,000(F|A 10%,6) + $14,000(F|P 10%,6) FW = $2,000(7.71561) + $14,000(1.77156) FW = $40,233.06

OPTION 2: SLIDING SPOTS, CASH FLOWS = -$14,000; $3,500; $3,500; $3,500; $3,500; $3,500; $3,500, BANK ACCOUNT = $6,000 SOLUTION USING EXCEL'S FV FUNCTION FW = $37,634.00 =FV(10%,6,-2000) + FV(,10%,6,,-14000) SOLUTION USING FACTOR TABLES FW = $3,500(F|A 10%,6) + $6,000(F|P 10%,6) FW = $3,500(7.71561) + $6,000(1.77156) FW = $37,634.00

OPTION 3: REFLECTED BEAM, CASH FLOWS = -$20,000; $0; $2,300; $4,600; $6,900; $9,200; $11,500, BANK ACCOUNT = $0 DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S FV FUNCTION IS NOT USED TO COMPUTE FW DIRECTLY. SOLUTION USING EXCEL'S NPV AND FV FUNCTIONS FW = $39,459.03 =FV(10%,6,,-NPV(10%,0,2300,4600,6900,9200,11500)) SOLUTION USING FACTOR TABLES FW = $2,300(A|G 10%,6)(F|A 10%,6) FW = $2,300(2.22356)(7.71561) FW = $39,459.08

DECISION: OPTION 1, THE LIGHT BAR IS PREFERRED SINCE IT HAS THE HIGHEST PORTFOLIO VALUE.

FW ANALYSIS AND TOTAL PORTFOLIO VALUE ANALYSIS PRODUCE A CONSISTENT DECISION.

PROBLEM 6.67 NOTE THAT THE ESTIMATED LIVES ARE DIFFERENT SO A COMMON PLANNING HORIZON MUST BE ESTABLISHED. THERE IS NO INDICATION THAT EITHER INVESTMENT IS A ONE-SHOT INVESTMENT A 10 YEAR HORIZON IS SELECTED IN THE ANALYSIS BELOW. a

MODEL 127B SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $19,400.00 $29,400.00

- CF -$50,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00

NET CF -$50,000.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $19,400.00

8.00% (F|P i%,n-t) 2.15892 1.99900 1.85093 1.71382 1.58687 1.46933 1.36049 1.25971 1.16640 1.08000 1.00000

FW OF CF -$107,946.25 $18,790.64 $17,398.74 $16,109.95 $14,916.62 $13,811.68 $12,788.60 $11,841.29 $10,964.16 $10,152.00 $19,400.00 $38,227.44 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = 38227.43732 =FV(8%,10,-9400,50000)+10000 SOLUTION USING FACTOR TABLES FW = -$50,000(F|P 8%,10) + $9,400(F|A 8%,10) + $10,000 FW = -$50,000(2.15892) + $9,400(14.48656) + $10,000 FW = 38227.664 MODEL 334A SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00 $26,000.00

- CF -$80,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$86,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00

NET CF -$80,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 -$60,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

(F|P i%,n-t) 2.15892 1.99900 1.85093 1.71382 1.58687 1.46933 1.36049 1.25971 1.16640 1.08000 1.00000

FW OF CF -$172,714.00 $39,980.09 $37,018.60 $34,276.49 $31,737.49 -$88,159.68 $27,209.78 $25,194.24 $23,328.00 $21,600.00 $20,000.00 -$529.00 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -528.996608 =FV(8%,10,-20000,80000)+FV(8%,5,,80000) SOLUTION USING FACTOR TABLES FW = -$80,000(F|P 8%,10) - $80,000(F|P 8%,5) + $20,000(F|A 8%,10) FW = -$80,000(2.15892) - $80,000(1.46933) + $20,000(14.48656) FW = -528.8 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST FW

OCTAVIA'S BAKERY SHOULD BUY MODEL 127B

PROBLEM 6.68 FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS 127B, 334A SINCE "NULL" IS NOT IDENTIFIED AS AN OPTION, 127B BECOMES THE "CURRENT BEST" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 334A - 127B ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

334A -$80,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$86,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00

127B -$50,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00

INCR. CF -$30,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 -$76,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00

8.00% (F|P i%,n-t) 2.15892 1.99900 1.85093 1.71382 1.58687 1.46933 1.36049 1.25971 1.16640 1.08000 1.00000

FW OF CF -$64,767.75 $7,996.02 $7,403.72 $6,855.30 $6,347.50 -$111,668.93 $5,441.96 $5,038.85 $4,665.60 $4,320.00 $4,000.00 -$124,367.75 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -124367.7462 =FV(8%,10,-4000,30000)+FV(8%,5,,80000) SOLUTION USING FACTOR TABLES FW = -$30,000(F|P 8%,10) + $4,000(F|A 8%,10) - $80,000(F|P 8%,5) FW = -$30,000(2.15892) + $4,000(14.48656) - $80,000(1.46933) FW = -124367.76 SINCE THE FW OF THE INCREMENT IS NEGATIVE, THE INCREMENTAL INVESTMENT IS REJECTED 127B REMAINS CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, 127B IS PREFERRED

PROBLEM 6.69 A COMMON PLANNING HORIZON TO 24 YEARS IS USED IN THE ANALYSIS REPETITION OF STRUCTURE Y IS ASSUMED SINCE THERE IS NO INDICATION OF A ONE-SHOT INVESTMENT a

STRUCTURE Y SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

+ CF

5.00% NET CF (F|P i%,n-t) -$4,500.00 3.22510 -$1,000.00 3.07152 -$1,000.00 2.92526 -$1,000.00 2.78596 -$1,000.00 2.65330 -$1,000.00 2.52695 -$1,000.00 2.40662 -$1,000.00 2.29202 -$1,000.00 2.18287 -$1,000.00 2.07893 -$1,000.00 1.97993 -$1,000.00 1.88565 -$5,500.00 1.79586 -$1,000.00 1.71034 -$1,000.00 1.62889 -$1,000.00 1.55133 -$1,000.00 1.47746 -$1,000.00 1.40710 -$1,000.00 1.34010 -$1,000.00 1.27628 -$1,000.00 1.21551 -$1,000.00 1.15763 -$1,000.00 1.10250 -$1,000.00 1.05000 -$1,000.00 1.00000

FW OF CF -$14,512.95 -$3,071.52 -$2,925.26 -$2,785.96 -$2,653.30 -$2,526.95 -$2,406.62 -$2,292.02 -$2,182.87 -$2,078.93 -$1,979.93 -$1,885.65 -$9,877.21 -$1,710.34 -$1,628.89 -$1,551.33 -$1,477.46 -$1,407.10 -$1,340.10 -$1,276.28 -$1,215.51 -$1,157.63 -$1,102.50 -$1,050.00 -$1,000.00 -$67,096.30 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -67096.30209 =FV(5%,24,1000,4500)+FV(5%,12,,4500) SOLUTION USING FACTOR TABLES FW = -$4,500(F|P 5%,24) - $1,000(F|A 5%,24) - $4,500(F|P 5%,12) FW = -$4,500(3.22510) - $1,000(44.50200) - $4,500(1.79586) FW = -67096.32 STRUCTURE Z EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

+ CF

- CF -$10,000.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00

NET CF -$10,000.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00

(F|P i%,n-t) 3.22510 3.07152 2.92526 2.78596 2.65330 2.52695 2.40662 2.29202 2.18287 2.07893 1.97993 1.88565 1.79586 1.71034 1.62889 1.55133 1.47746 1.40710

FW OF CF -$32,251.00 -$2,211.50 -$2,106.19 -$2,005.89 -$1,910.37 -$1,819.40 -$1,732.77 -$1,650.25 -$1,571.67 -$1,496.83 -$1,425.55 -$1,357.67 -$1,293.02 -$1,231.44 -$1,172.80 -$1,116.96 -$1,063.77 -$1,013.11

18 19 20 21 22 23 24

$1,800.00

-$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00

-$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 $1,080.00

1.34010 1.27628 1.21551 1.15763 1.10250 1.05000 1.00000

-$964.87 -$918.92 -$875.16 -$833.49 -$793.80 -$756.00 $1,080.00 -$62,492.44 <- FW

SOLUTION USING EXCEL'S FV FUNCTION FW = -62492.43863 =FV(5%,24,720,10000)+1800 SOLUTION USING FACTOR TABLES FW = -$10,000(F|P 5%,24) - $720(F|A 5%,24) + $1,800 FW = -$10,000(3.22510) - $720(44.50200) + $1,800 FW = -62492.44 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST FW

THE MILITARY BASE SHOULD SELECT STRUCTURE Z

PROBLEM 7.1 a b c d e f

ANNUAL WORTH OF THE PROJECT WILL BE GREATER THAN ZERO ANNUAL WORTH OF THE PROJECT WILL BE EQUAL TO ZERO ANNUAL WORTH OF THE PROJECT WILL BE LESS THAN ZERO ANNUAL WORTH OF THE PROJECT WILL BE GREATER THAN ZERO ANNUAL WORTH OF THE PROJECT WILL BE EQUAL TO ZERO ANNUAL WORTH OF THE PROJECT WILL BE LESS THAN ZERO

PROBLEM 7.2 a b c d e f

TRUE FALSE TRUE TRUE FALSE FALSE

PROBLEM 7.3

PROBLEM 7.4 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 0.1 EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$70,000.00 -$70,000.00 1.00000 -$70,000.00 1 $30,000.00 $30,000.00 0.90909 $27,272.73 2 $30,000.00 $30,000.00 0.82645 $24,793.39 3 $30,000.00 $30,000.00 0.75131 $22,539.44 4 $30,000.00 $30,000.00 0.68301 $20,490.40 5 $30,000.00 $30,000.00 0.62092 $18,627.64 6 $32,000.00 $32,000.00 0.56447 $18,063.17 $61,786.77 <- PW 0.22961 <- (A|P i%,n) $14,186.70 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $14,186.70 =30000+PMT(10%,6,70000,-2000) SOLUTION USING FACTOR TABLES AW = $30,000 -$70,000(A|P 10%,6) + $2,000(A|F 10%,6) AW = $30,000 -$70,000(0.22961) + $2,000(0.12961) AW = $14,186.52 b

IF AW >= 0 THEN ACCEPT; OTHERWISE, REJECT

PROJECT IS ECONOMICALLY JUSTIFIED

PROBLEM 7.5 a

RATE = ($70,000 - $2,000)/6 = $11,333.33 PER YEAR

GEOMETRIC SALVAGE VALUE DECLINE RATE $2,000 = $70,000((1-RATE)^6) 0.02857 = (1-RATE)^6 (1-RATE) = 0.55291 RATE = 1 - 0.55291 = 0.44709

c HORIZON 0 1 2 3 4 5 6

10.00% AW GEOMETRIC

SVGEOMETRIC

CF -$70,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00

$70,000.00 $38,703.70 $21,399.66 $11,832.09 $6,542.08 $3,617.18 $1,999.98

SVGRADIENT

N/A -$8,296.30 -$143.02 $5,426.61 $9,326.67 $12,126.66 $14,186.69

AW GRADIENT

$70,000.00 $58,666.67 $47,333.34 $36,000.01 $24,666.68 $13,333.35 $2,000.02

N/A $11,666.67 $12,206.35 $12,728.10 $13,231.99 $13,718.15 $14,186.70

SVVENDOR

AW VENDOR

$70,000.00 $50,000.00 $30,000.00 $20,000.00 $10,000.00 $5,000.00 $2,000.00

N/A $3,000.00 $3,952.38 $7,894.26 $10,071.75 $12,353.16 $14,186.70

FORMULAS IN TABLE COLUMNS CF PROBLEM STATEMENT SVGEOMETRIC EACH ROW ENTRY AFTER THE FIRST IS (1-0.44709) TIMES THE PRECEDING ROW ENTRY AW GEOMETRIC FOR CELL B14: =PMT($E$11,B14,-$C$13,-D14)+C14, OTHERS ARE SIMILAR SVGRADIENT

EACH ROW ENTRY AFTER THE FIRST IS $11,333.33 LESS THAN THE PRECEDING ROW ENTRY

AW GRADIENT

FOR CELL G14: =PMT($E$11,B14,-$C$13,-F14)+C14, OTHERS ARE SIMILAR

SVVENDOR

PROBLEM STATEMENT

AW VENDOR

FOR CELL I14: =PMT($E$11,B14,-$C$13,-H14)+C14, OTHERS ARE SIMILAR

$20,000.00

ANNUAL WORTH

$15,000.00 $10,000.00 GEOMETRIC

$5,000.00

GRADIENT VENDOR

$0.00

-$5,000.00 -$10,000.00

PLANNING HORIZON

PROBLEM 7.6 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 20.00% EOY CF (P|F i%,n) PW OF CF 0 -$70,000.00 1.00000 -$70,000.00 1 $20,000.00 0.83333 $16,666.67 2 $19,000.00 0.69444 $13,194.44 3 $18,000.00 0.57870 $10,416.67 4 $17,000.00 0.48225 $8,198.30 5 $16,000.00 0.40188 $6,430.04 6 $15,000.00 0.33490 $5,023.47 7 $14,000.00 0.27908 $3,907.14 8 $13,000.00 0.23257 $3,023.38 9 $12,000.00 0.19381 $2,325.68 10 $11,000.00 0.16151 $1,776.56 11 $10,000.00 0.13459 $1,345.88 12 $9,000.00 0.11216 $1,009.41 13 $8,000.00 0.09346 $747.71 14 $7,000.00 0.07789 $545.21 15 $6,000.00 0.06491 $389.43 16 $5,000.00 0.05409 $270.44 17 $4,000.00 0.04507 $180.29 18 $3,000.00 0.03756 $112.68 19 $2,000.00 0.03130 $62.60 20 $1,000.00 0.02608 $26.08 $5,652.10 <- PW 0.20536 <- (A|P i%,n) $1,160.70 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $1,160.70 =-PMT(20%,20,NPV(20%,C7:C26)+C6) SOLUTION USING FACTOR TABLES AW = -$70,000(A|P 20%,20) + $20,000 - $1,000(A|G 20%,20) AW = -$70,000(0.20536) + $20,000 - $1,000(4.46435) AW = $1,160.45 (1) AW = $1,161 (2) INVESTMENT IS ATTRACTIVE (3) IF AW >= 0, THEN ATTRACTIVE; OTHERWISE, UNATTRACTIVE

PROBLEM 7.7

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

20.00% (P|F i%,n) 1.00000 0.83333 0.69444 0.57870 0.48225 0.40188 0.33490 0.27908 0.23257 0.19381 0.16151 0.13459 0.11216 0.09346 0.07789 0.06491 0.05409 0.04507 0.03756 0.03130 0.02608

PW OF CF -$70,000.00 $16,666.67 $13,194.44 $10,416.67 $8,198.30 $6,430.04 $5,023.47 $3,907.14 $3,023.38 $2,325.68 $1,776.56 $1,345.88 $1,009.41 $747.71 $545.21 $389.43 $270.44 $180.29 $112.68 $62.60 $26.08 $5,652.10 <- PW 0.20536 <- (A|P i%,n) $1,160.70 <- AW

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38

AW $7,000.00 =-PMT(B31,20,NPV(B31,$C$6:$C$25)+$C$5) $6,951.56 =-PMT(B32,20,NPV(B32,$C$6:$C$25)+$C$5) $6,875.75 SIMILAR FORMULAS REPEAT $6,772.04 $6,640.15 $6,480.05 $6,291.93 $6,076.19 $5,833.40 $10,000.00 $5,564.30 $5,269.75 $5,000.00 $4,950.73 $0.00 $4,608.28 0% 10% 20% $4,243.51 -$5,000.00 $3,857.55 $3,451.56 -$10,000.00 $3,026.69 -$15,000.00 $2,584.07 $2,124.82 -$20,000.00 $1,650.02 $1,160.70 $657.84 $142.40 -$384.74 -$922.75 -$1,470.84 -$2,028.28 -$2,594.39 -$3,168.54 -$3,750.13 -$4,338.62 -$4,933.52 -$5,534.34 -$6,140.67 -$6,752.11 -$7,368.30 -$7,988.90 -$8,613.60 -$9,242.11

Nu Things Investment

MARR

… 30%

MARR

40%

50%

60%

0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5

-$9,874.19 -$10,509.57 -$11,148.05 -$11,789.42 -$12,433.49 -$13,080.08 -$13,729.04 -$14,380.22 -$15,033.47 -$15,688.68 -$16,345.73 -$17,004.51

Y-AXIS INTERCEPT IS THE AVERAGE ANNUAL UNDISCOUNTED CASH FLOWS

X-AXIS INTERCEPT IS THE POINT WHERE AW IS ZERO (INTERNAL RATE OF RETURN)

PROBLEM 7.8

AW = PW(A|P 12%,4) = PW(0.32923) PW = -30,000 + 6,000(P|F 12%,1) + 13,500(P|F 12%,2) + X(P|F 12%,3) + 13,500(P|F 12%,4) PW = -30,000 + 6,000(0.89286) + 13,500(0.79719) + X(0.71178) + 13,500(0.63552) PW = -5,301.255 + 0.71178X AW = (-5,301.255 + 0.71178X)(0.32923) AW = -1,745.33 + 0.23434(X) SETTING AW TO ZERO AND SOLVING FOR X X = $7,447.85

PROBLEM 7.9 NOTE: IN THIS PROBLEM, AND MANY THAT FOLLOW, THE ANSWER TO AN AW QUESTION INVOLVES THE CALCULATION OF A VALUE FOR PW. IN SOME CASES, THE NON-UNIFORM NATURE OF THE CASH FLOWS OR A CHANGING INTEREST RATE MAKES THIS ONE OF THE MOST DIRECT APPROACHES FOR SOLVING THE PROBLEM. IN OTHER CASES, IT IS DONE TO MAINTAIN CONSISTENCY IN THE VARIETY OF SOLUTION APPROACHES DOCUMENTED FOR EACH PROBLEM WITHIN THIS SOLUTIONS FILE.

PW = $200(P|F 10%,1)-$200(P|F 10%,2)+$300(P|F 8%,1)(P|F 10%,2)+$200(P|F 12%,1)(P|F 8%,2)(P|F 10%,2) PW = $200(0.90909)-$200(0.82645)+$300(0.92593)(0.82645)+$200(0.89286)(0.85734)(0.82645) PW = $372.63 NOW, SET UP THE EXPRESSION FOR PW ASSUMING EQUAL ANNUAL CASH FLOWS OF SIZE X PW = X(P|F 10%,1) + X(P|F 10%,2) + X(P|F 8%,1)(P|F 10%,2) + X(P|F 8%,2)(P|F 10%,2) + X(P|F 12%,1)(P|F 8%,2)(P|F 10%,2) PW = X(0.90909) + X(0.82645) + X(0.92953)(0.82645) + X(0.85734)(0.82645) + X(0.89286)(0.85734)(0.82645) PW = 3.84493X SETTING THE TWO PWs EQUAL AND SOLVING FOR X 3.84493X = 372.63 X = $96.91

PROBLEM 7.10 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 0.05 EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$100,000.00 -$100,000.00 1.00000 -$100,000.00 1 $12,000.00 -$2,000.00 $10,000.00 0.95238 $9,523.81 2 $12,000.00 -$2,000.00 $10,000.00 0.90703 $9,070.29 3 $12,000.00 -$2,000.00 $10,000.00 0.86384 $8,638.38 4 $12,000.00 -$2,000.00 $10,000.00 0.82270 $8,227.02 5 $12,000.00 -$2,000.00 $10,000.00 0.78353 $7,835.26 6 $12,000.00 -$2,000.00 $10,000.00 0.74622 $7,462.15 7 $12,000.00 -$2,000.00 $10,000.00 0.71068 $7,106.81 8 $12,000.00 -$2,000.00 $10,000.00 0.67684 $6,768.39 9 $12,000.00 -$2,000.00 $10,000.00 0.64461 $6,446.09 10 $12,000.00 -$2,000.00 $10,000.00 0.61391 $6,139.13 11 $12,000.00 -$2,000.00 $10,000.00 0.58468 $5,846.79 12 $12,000.00 -$2,000.00 $10,000.00 0.55684 $5,568.37 13 $12,000.00 -$2,000.00 $10,000.00 0.53032 $5,303.21 14 $12,000.00 -$2,000.00 $10,000.00 0.50507 $5,050.68 15 $12,000.00 -$2,000.00 $10,000.00 0.48102 $4,810.17 $3,796.58 <- PW 0.09634 <- (A|P i%,n) $365.77 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $365.77 =10000+PMT(5%,15,100000) SOLUTION USING FACTOR TABLES AW = $10,000 - $100,000(A|P 5%,15) AW = $10,000 - $100,000(0.09634) AW = $366.00

DECISION RULE IF AW >= 0, ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD BUY THE GANG PUNCH

PROBLEM 7.11 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$75,000.00 -$75,000.00 1.00000 -$75,000.00 1 $18,500.00 $18,500.00 0.90909 $16,818.18 2 $18,500.00 $18,500.00 0.82645 $15,289.26 3 $18,500.00 $18,500.00 0.75131 $13,899.32 4 $18,500.00 $18,500.00 0.68301 $12,635.75 5 $18,500.00 $18,500.00 0.62092 $11,487.04 -$4,870.44 <- PW 0.26380 <- (A|P i%,n) -$1,284.81 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$1,284.81 =18500+PMT(10%,5,75000) SOLUTION USING FACTOR TABLES AW = $18,500 - $75,000(A|P 10%,5) AW = $18,500 - $75,000(0.26380) AW = -$1,285.00 b

DECISION RULE IF AW > 0, ACCEPT; OTHERWISE, REJECT

CARLISLE SHOULD REJECT THE FILTER BASED ON ITS ECONOMIC MERITS

PROBLEM 7.12 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 6.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$5,000.00 -$5,000.00 1.00000 -$5,000.00 1 -$200.00 -$200.00 0.94340 -$188.68 2 $2,000.00 -$300.00 $1,700.00 0.89000 $1,512.99 3 $4,000.00 -$600.00 $3,400.00 0.83962 $2,854.71 4 $3,000.00 -$1,000.00 $2,000.00 0.79209 $1,584.19 5 $1,600.00 -$1,500.00 $100.00 0.74726 $74.73 $837.93 <- PW 0.23740 <- (A|P i%,n) $198.92 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $198.92 =-PMT(6%,5,NPV(6%,E7:E11)+E6) SOLUTION USING FACTOR TABLES AW = (-$5,000-$200(P|F 6%,1)+$1,700(P|F 6%,2)+$3,400(P|F 6%,3)+$2,000(P|F 6%,4)+$100(P|F 6%,5))(A|P 6%,5) AW = (-$5,000-$200(0.94340)+$1,700(0.89000)+$3,400(0.83962)+$2,000(0.79209)+$100(0.74726))(0.23740) AW = $198.93

DECISION RULE IF AW >= 0, ACCEPT; OTHERWISE, REJECT

DURATECH SHOULD IMPLEMENT THE PROCESS IMPROVEMENT

PROBLEM 7.13 NEW ANNUAL INSURANCE PREMIUM = ($720,000/$100)($0.40) = $2,880 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

- CF -$20,000.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00

15.00% (P|F i%,n) 1.00000 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 0.28426 0.24718 0.21494 0.18691 0.16253 0.14133 0.12289 0.10686 0.09293 0.08081 0.07027 0.06110

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $524.77 =3720+PMT(15%,20,20000) SOLUTION USING FACTOR TABLES AW = $3,720 - $20,000(A|P 15%,20) AW = $3,720 - $20,000(0.15976) AW = $524.80 b

DECISION RULE IF AW > 0, ACCEPT; OTHERWISE, REJECT

EDDIE SHOULD BUY THE SPRINKLER SYSTEM

PROBLEM 7.14 THE MAXIMUM AMOUNT IS THE ONE THAT SETS THE AW OF THE PAYMENT EQUAL TO AW OF THE BENEFITS. LET X BE THE AMOUNT PAID SOLUTION USING FACTOR TABLES X(A|P 7%,12) = $10,000 X = $10,000 / (A|P 7%,12) X = $10,000 / (0.12590) X= $79,428.12 SOLUTION USING EXCEL'S PMT FUNCTION X= $79,426.86 =-10000/PMT(7%,12,1) SOLUTION USING EXCEL'S SOLVER EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

0.07 - CF NET CF (P|F i%,n) PW OF CF -$79,426.86 -$79,426.86 1.00000 -$79,426.86 $10,000.00 $10,000.00 0.93458 $9,345.79 $10,000.00 $10,000.00 0.87344 $8,734.39 $10,000.00 $10,000.00 0.81630 $8,162.98 $10,000.00 $10,000.00 0.76290 $7,628.95 $10,000.00 $10,000.00 0.71299 $7,129.86 $10,000.00 $10,000.00 0.66634 $6,663.42 $10,000.00 $10,000.00 0.62275 $6,227.50 $10,000.00 $10,000.00 0.58201 $5,820.09 $10,000.00 $10,000.00 0.54393 $5,439.34 $10,000.00 $10,000.00 0.50835 $5,083.49 $10,000.00 $10,000.00 0.47509 $4,750.93 $10,000.00 $10,000.00 0.44401 $4,440.12

+ CF

$0.00 <- PW $0.00 <- AW TO IMPLEMENT SOLVER: (1) SET TARGET CELL: G30 (2) EQUAL TO: VALUE OF: ZERO (3) BY CHANGING CELLS: D15

THE AW THE TARGET AW VALUE THE PURCHASE PRICE TO BE DETERMINED

MAXIMUM PURCHASE PRICE IS $79,426.86

=-PMT(7%,12,G34)

PROBLEM 7.15 LOAN PAYMENTS = $25,000*(A|P 15%,3) = 25000*(0.43798) = $10,949.50 USING EXCEL'S PMT FUNCTION PMT = $10,949.42 =-PMT(15%,3,25000) a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR

EOY 0 1 2 3 4 5

+ INV CF $55,000.00 $55,000.00 $55,000.00 $55,000.00 $60,000.00

- INV CF -$100,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00

+ LOAN CF $25,000.00

- LOAN CF -$10,949.50 -$10,949.50 -$10,949.50

0.18 NET CF (P|F i%,n) -$75,000.00 1.00000 $19,050.50 0.84746 $19,050.50 0.71818 $19,050.50 0.60863 $30,000.00 0.51579 $35,000.00 0.43711

PW OF CF -$75,000.00 $16,144.49 $13,681.77 $11,594.72 $15,473.67 $15,298.82 -$2,806.52 <- PW 0.31978 <- (A|P i%,n) -$897.46 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = -$897.46 =-PMT(18%,5,NPV(18%,G12:G16)+G11) SOLUTION USING FACTOR TABLES AW = (-$75,000+$19,050.50(P|A 18%,3)+$30,000(P|F 18%,4)+$35,000(P|F 18%,5))(A|P 18%,5) AW = (-$75,000+$19,050.50(2.17427)+$30,000(0.51579)+$35,000(0.43711))(0.31978) AW = -$897.47 b

DECISION RULE IF AW > 0, ACCEPT; OTHERWISE, REJECT

GALVANIZED PRODUCTS SHOULD NOT PURCHASE THE NEW COMPUTER SYSTEM

PROBLEM 7.16 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 13.50% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$1,400.00 -$1,400.00 1.00000 -$1,400.00 1 $0.00 $0.00 0.88106 $0.00 2 $500.00 $500.00 0.77626 $388.13 3 $500.00 $500.00 0.68393 $341.97 4 $500.00 $500.00 0.60258 $301.29 5 $500.00 $500.00 0.53091 $265.45 6 $0.00 $0.00 0.46776 $0.00 7 $500.00 $500.00 0.41213 $206.06 8 $600.00 $600.00 0.36311 $217.86 9 $700.00 $700.00 0.31992 $223.94 10 $800.00 $800.00 0.28187 $225.49 11 $900.00 $900.00 0.24834 $223.51 12 -$1,000.00 -$1,000.00 0.21880 -$218.80 13 -$2,000.00 -$2,000.00 0.19278 -$385.55 14 -$3,000.00 -$3,000.00 0.16985 -$509.54 15 $1,400.00 $1,400.00 0.14964 $209.50 $89.32 <- PW 0.15876 <- (A|P i%,n) $14.18 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $14.18 =-PMT(13.5%,15,NPV(13.5%,E7:E21)+E6) SOLUTION USING FACTOR TABLES AW = (-$1,400+$500(P|A 13.5%,4)(P|F 13.5%,1)+($500(P|A 13.5%,5)+$100(P|G 13.5%,5))(P|F 13.5%,6)+ (-$1,000(P|A 13.5%,3)-$1,000(P|G 13.5%,3))(P|F 13.5%,11)+$1,400(P|F 13.5%,15))(A|P 13.5%,15) AW = (-$1,400+$500(2.94383)(0.88106)+{$500(3.47474)+$100(6.07551))(0.46776)+ (-$1,000(2.34125)-$1,000(2.14412))(0.24834)+$1,400(0.14964)0(0.15876) AW = $14.18

DECISION RULE IF AW >= 0, ACCEPT; OTHERWISE, REJECT

QRU SHOULD INVEST

PROBLEM 7.17 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR

EOY 0 1 2 3 4 5 6 7

+ CF

- CF -$12.00 -$1.00

$5.00 $2.00 $5.00 $5.00 $2.00 $5.00

NET CF -$12.00 -$1.00 $5.00 $2.00 $5.00 $5.00 $2.00 $5.00

18.00% (P|F i%,n) 1.00000 0.84746 0.71818 0.60863 0.51579 0.43711 0.37043 0.31393

PW OF CF -$12.00 -$0.85 $3.59 $1.22 $2.58 $2.19 $0.74 $1.57 -$0.96 <- PW 0.26236 <- (A|P i%,n) -$0.25 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = -$0.25 =-PMT(18%,7,NPV(18%,E8:E14)+E7) SOLUTION USING FACTOR TABLES AW = (-$12-$1(P|F 18%,1)+$5(P|F 18%,2)+$2(P|F 18%,3)+$5(P|F 18%,4)+$5(P|F 18%,5)+$2(P|F 18%,6)+$5(P|F 18%,7))(A|P 18%,7) AW = (-$12-$1(0.84746)+$5(0.71818)+$2(0.60863)+$5(0.51579)+$5(0.43711)+$2(0.3704)+$5(0.31393))(0.26236) AW = -$0.25 b

DECISION RULE IF AW > 0, ACCEPT; OTHERWISE, REJECT

IMAGINEERING SHOULD NOT INVEST

PROBLEM 7.18 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 12.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$2.00 -$2.00 1.00000 -$2.00 1 -$10.00 -$10.00 0.89286 -$8.93 2 -$12.00 -$12.00 0.79719 -$9.57 3 -$14.00 -$14.00 0.71178 -$9.96 4 -$16.00 -$16.00 0.63552 -$10.17 5 -$18.00 -$18.00 0.56743 -$10.21 6 $200.00 $200.00 0.50663 $101.33 7 -$10.00 -$10.00 0.45235 -$4.52 8 -$12.00 -$12.00 0.40388 -$4.85 9 -$14.00 -$14.00 0.36061 -$5.05 10 -$100.00 -$100.00 0.32197 -$32.20 $3.87 <- PW 0.17698 <- (A|P i%,n) $0.68 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $0.68 =-PMT(12%,10,NPV(12%,E7:E16)+E6) SOLUTION USING FACTOR TABLES AW = (-$2-$10(P|A 12%,5)-$2(P|G 12%,5)+$200(P|F 12%,6)+(-$10(P|A 12%,3)-$2(P|G 12%,3))(P|F 12%,6)-$100(P|F 12%,10)0(A|P 12%,10) AW = (-$2-$10(3.60478)-$2(6.39702)+$200(0.50663)+(-$10(2.40183)-$2(2.22075))(0.50663)-$100(0.32197))(0.17698) AW = $0.68

DECISION RULE IF AW >= 0, ACCEPT; OTHERWISE, REJECT

JUPITER SHOULD INVEST

PROBLEM 7.19 LOAN PAYMENTS = $20,000(F|P 8%,1)(A|P 8%,3) = $20,000(1.08000)(0.38803) = $8,381.45 USING EXCEL'S PMT FUNCTION PMT = $8,381.52 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY + INV CF - INV CF + LOAN CF - LOAN CF NET CF (P|F i%,n) 0 -$40,000.00 $20,000.00 -$20,000.00 1.00000 1 $12,000.00 -$2,000.00 $10,000.00 0.90909 2 $12,000.00 -$2,000.00 -$8,381.45 $1,618.55 0.82645 3 $12,000.00 -$2,000.00 -$8,381.45 $1,618.55 0.75131 4 $12,000.00 -$2,000.00 -$8,381.45 $1,618.55 0.68301 5 $12,000.00 -$2,000.00 $10,000.00 0.62092 6 $12,000.00 -$2,000.00 $10,000.00 0.56447 7 $19,500.00 -$2,000.00 $17,500.00 0.51316

PW OF CF -$20,000.00 $9,090.91 $1,337.64 $1,216.04 $1,105.49 $6,209.21 $5,644.74 $8,980.27 $13,584.31 <- PW 0.20541 <- (A|P i%,n) $2,790.29 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $2,790.29 =-PMT(10%,7,NPV(10%,G11:G17)+G10) SOLUTION USING FACTOR TABLES AW = $10,000-$20,0000(A|P 10%,7)-($10,000-$1,618.55)(P|A 10%,3)(P|F 10%,1))(A|P 10%,7)+$7,500(A|F 10%,7) AW = $10,000-$20,0000(0.20541)-($10,000-$1,618.55)(2.48685)(0.90909))(0.20541)+$7,500(0.10541) AW = $2,790.16 b

DECISION RULE IF AW > 0, ACCEPT; OTHERWISE, REJECT

AEROTRON ELECTRONICS SHOULD PURCHASE THE WATER FILTRATION SYSTEM

PROBLEM 7.20 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$1,000.00 -$1,000.00 1.00000 -$1,000.00 1 $600.00 -$300.00 $300.00 0.90909 $272.73 2 $600.00 -$300.00 $300.00 0.82645 $247.93 3 $700.00 -$300.00 $400.00 0.75131 $300.53 4 $700.00 -$300.00 $400.00 0.68301 $273.21 5 $700.00 -$300.00 $400.00 0.62092 $248.37 $342.76 <- PW 0.26380 <- (A|P i%,n) $90.42 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $90.42 =-PMT(10%,5,NPV(10%,E7:E11)+E6) ALTERNATIVELY, AW = -$1,000(A|P 10%,5) + $300 + $100(F|A 10%,3)(A|F 10%,5) AW = -$1,000(0.26380) + $300 + $100(3.31000)(0.16380) AW = $90.42 b

DECISION RULE IF AW >= 0, ACCEPT; OTHERWISE, REJECT

HOME INNOVATION SHOULD PURSUE THE NEW PRODUCT

PROBLEM 7.21 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 8.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$6,000.00 -$6,000.00 1.00000 -$6,000.00 1 $1,000.00 $1,000.00 0.92593 $925.93 2 $1,000.00 $1,000.00 0.85734 $857.34 3 $1,000.00 $1,000.00 0.79383 $793.83 4 $1,000.00 $1,000.00 0.73503 $735.03 5 $1,000.00 $1,000.00 0.68058 $680.58 6 $3,000.00 $3,000.00 0.63017 $1,890.51 -$116.78 <- PW 0.21632 <- (A|P i%,n) -$25.26 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$25.26 =1000+PMT(8%,6,6000,-2000) SOLUTION USING FACTOR TABLES AW = $1,000 - $6,000(A|P 8%,6) + $2,000(A|F 8%,6) AW = $1,000 - $6,000(0.21632) + $2,000(0.13632) AW = -$25.28 b

DECISION RULE IF AW > 0, ACCEPT; OTHERWISE, REJECT

MAYBERRY SHOULD NOT IMPLEMENT THE DESIGN CHANGE

PROBLEM 7.22 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 24.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$10,000.00 -$10,000.00 1.00000 -$10,000.00 1 $30,000.00 -$25,000.00 $5,000.00 0.80645 $4,032.26 2 $30,000.00 -$25,000.00 $5,000.00 0.65036 $3,251.82 3 $33,000.00 -$25,000.00 $8,000.00 0.52449 $4,195.90 $1,479.98 <- PW 0.50472 <- (A|P i%,n) $746.97 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $746.97 =5000+PMT(24%,3,10000,-3000) SOLUTION USING FACTOR TABLES AW = $5,000 - $10,000(A|P 24%,3) + $3,000(A|F 24%,3) AW = $5,000 - $10,000(0.50472) + $3,000(0.26472) AW = $746.96 b

DECISION RULE IF AW >= 0, ACCEPT; OTHERWISE, REJECT

NANCY SHOULD BUY THE TRUCK

PROBLEM 7.23 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR VENDOR A SOFTWARE 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$380,000.00 -$380,000.00 1.00000 -$380,000.00 1 $125,000.00 $125,000.00 0.90909 $113,636.36 2 $125,000.00 $125,000.00 0.82645 $103,305.79 3 $125,000.00 $125,000.00 0.75131 $93,914.35 4 $125,000.00 $125,000.00 0.68301 $85,376.68 $16,233.18 <- PW 0.31547 <- (A|P i%,n) $5,121.09 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $5,121.09 =125000+PMT(10%,4,380000) SOLUTION USING FACTOR TABLES AW = $125,000 - $380,000(A|P 10%,4) AW = $125,000 - $380,000(0.31547) AW = $5,121.40

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR VENDOR B SOFTWARE EOY 0 1 2 3 4

+ CF

- CF -$280,000.00

$95,000.00 $95,000.00 $95,000.00 $95,000.00

NET CF -$280,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00

(P|F i%,n) 1.00000 0.90909 0.82645 0.75131 0.68301

PW OF CF -$280,000.00 $86,363.64 $78,512.40 $71,374.91 $64,886.28 $21,137.22 <- PW 0.31547 <- (A|P i%,n) $6,668.17 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $6,668.17 =95000+PMT(10%,4,280000) SOLUTION USING FACTOR TABLES AW = $95,000 - $280,000(A|P 10%,4) AW = $95,000 - $280,000(0.31547) AW = $6,668.40 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST AW

MANUEL'S MANUFACTURING SHOULD BUY FROM VENDOR B

PROBLEM 7.24 ORDER OF INVESTMENTS: B, A SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR VENDOR B SOFTWARE 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$280,000.00 -$280,000.00 1.00000 -$280,000.00 1 $95,000.00 $95,000.00 0.90909 $86,363.64 2 $95,000.00 $95,000.00 0.82645 $78,512.40 3 $95,000.00 $95,000.00 0.75131 $71,374.91 4 $95,000.00 $95,000.00 0.68301 $64,886.28 $21,137.22 <- PW 0.31547 <- (A|P i%,n) $6,668.17 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $6,668.17 =95000+PMT(10%,4,280000) SOLUTION USING FACTOR TABLES AW = $95,000 - $280,000(A|P 10%,4) AW = $95,000 - $280,000(0.31547) AW = $6,668.40 AW OF B IS GREATER THAN ZERO SO ANALYZE INCREMENTAL CASH FLOWS OF A-B SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR INCREMENTAL ANALYSIS OF A-B EOY 0 1 2 3 4

+ CF

- CF -$100,000.00

$30,000.00 $30,000.00 $30,000.00 $30,000.00

NET CF (P|F i%,n) -$100,000.00 1.00000 $30,000.00 0.90909 $30,000.00 0.82645 $30,000.00 0.75131 $30,000.00 0.68301

PW OF CF -$100,000.00 $27,272.73 $24,793.39 $22,539.44 $20,490.40 -$4,904.04 <- PW 0.31547 <- (A|P i%,n) -$1,547.08 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$1,547.08 =30000+PMT(10%,4,100000) SOLUTION USING FACTOR TABLES AW = $30,000 - $100,000(A|P 10%,4) AW = $30,000 - $100,000(0.31547) AW = -$1,547.00 AW OF INCREMENT A-B IS NEGATIVE SO REJECT THE INCREMENT; STAY WITH VENDOR B SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, VENDOR B IS RECOMMENDED

PROBLEM 7.25 LET X BE THE NUMBER OF UNITS SOLD ANNUALLY AW(B) = $1,000 + 0.5X NEXT, SOLVE FOR AW(A) USING EXCEL'S PMT FUNCTION AW = 4882.361846 =-PMT(10%,10,30000) USING FACTOR TABLES AW = $30,000(A|P 10%,10) = $30,000(0.16275) = $4,882.50 FOR NADINE TO BE INDIFFERENT, AW(A) AND AW(B) MUST BE EQUAL, THEREFORE, $4,882.50 = $1,000 + $0.50(X) 0.5X = 3,882.51 X = 7,765.02 OR APPROXIMATELY 7,765 UNITS

PROBLEM 7.26 HEAT LOSS WITH NO INSULATION = $1.50/YR/FT HEAT LOSS WITH 1 INCH INSULATION IS (1.50)(1 - 0.89) = $0.165/YR/FT HEAT LOSS WITH 2 INCH INSULATION IS (1.50)(1 - 0.92) = $0.12/YR/FT

NO INSULATION ANNUAL HEAT LOSS = (1.50)(250,000) = $375,000 SINCE THERE IS NO INVESTMENT, THE AW = -$375,000

1 INCH INSULATION ANNUAL HEAT LOSS =( 0.165)(250,000) = $41,250 INSULATION COST = (0.40)(250,000) = $100,000 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$100,000.00 -$100,000.00 1.00000 -$100,000.00 1 $0.00 -$41,250.00 -$41,250.00 0.90909 -$37,500.00 2 $0.00 -$41,250.00 -$41,250.00 0.82645 -$34,090.91 3 $0.00 -$41,250.00 -$41,250.00 0.75131 -$30,991.74 4 $0.00 -$41,250.00 -$41,250.00 0.68301 -$28,174.31 5 $0.00 -$41,250.00 -$41,250.00 0.62092 -$25,613.00 6 $0.00 -$41,250.00 -$41,250.00 0.56447 -$23,284.55 7 $0.00 -$41,250.00 -$41,250.00 0.51316 -$21,167.77 8 $0.00 -$41,250.00 -$41,250.00 0.46651 -$19,243.43 9 $0.00 -$41,250.00 -$41,250.00 0.42410 -$17,494.03 10 $0.00 -$41,250.00 -$41,250.00 0.38554 -$15,903.66 -$353,463.39 <- PW 0.16275 <- (A|P i%,n) -$57,524.54 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$57,524.54 =-41250+PMT(10%,10,100000) SOLUTION USING FACTOR TABLES AW = -$41,250 - $100,000(A|P 10%,10) AW = -$41,250 - $100,000(0.16275) = -$57,525 AW = -$57,525.00

2 INCH INSULATION ANNUAL HEAT LOSS = (0.12)(250,000) = $30,000 INSULATION COST = (0.85)(250,000) = $212,500 SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

- CF -$212,500.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00

PW OF CF -$212,500.00 -$27,272.73 -$24,793.39 -$22,539.44 -$20,490.40 -$18,627.64 -$16,934.22 -$15,394.74 -$13,995.22 -$12,722.93 -$11,566.30 -$396,837.01 <- PW 0.16275 <- (A|P i%,n) -$64,583.40 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$64,583.40 =-30000+PMT(10%,10,212500) SOLUTION USING FACTOR TABLES AW = -$30,000 - $212,500(A|P 10%,10) AW = -$30,000 - $212,500(0.16275) = -$64,584.38 AW = -$64,584.38

THE HIGHEST ANNUAL WORTH IS THE 1 INCH INSULATION, THEREFORE, IT IS RECOMMENDED.

PROBLEM 7.27 ORDER IS NULL, 1-INCH, 2-INCH NULL BECOMES THE "CURRENT BEST" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 1-INCH - NULL ARE NEEDED SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY 1-INCH NULL INCR. CF (P|F i%,n) PW 0 -$100,000.00 $0.00 -$100,000.00 1.00000 -$100,000.00 1 -$41,250.00 -$375,000.00 $333,750.00 0.90909 $303,409.09 2 -$41,250.00 -$375,000.00 $333,750.00 0.82645 $275,826.45 3 -$41,250.00 -$375,000.00 $333,750.00 0.75131 $250,751.31 4 -$41,250.00 -$375,000.00 $333,750.00 0.68301 $227,955.74 5 -$41,250.00 -$375,000.00 $333,750.00 0.62092 $207,232.49 6 -$41,250.00 -$375,000.00 $333,750.00 0.56447 $188,393.17 7 -$41,250.00 -$375,000.00 $333,750.00 0.51316 $171,266.52 8 -$41,250.00 -$375,000.00 $333,750.00 0.46651 $155,696.84 9 -$41,250.00 -$375,000.00 $333,750.00 0.42410 $141,542.58 10 -$41,250.00 -$375,000.00 $333,750.00 0.38554 $128,675.07 $1,950,749.27 <- PW 0.16275 <- (A|P i%,n) $317,475.46 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $317,475.46 =333750+PMT(10%,10,100000) SOLUTION USING FACTOR TABLES AW = $333,750.00 - $100,000.00(A|P 10%,10) AW = $333,750.00 - $100,000.00(0.16275) = $317,475.00 AW = $317,475.00 SINCE THE AW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. 1-INCH BECOMES THE NEW CURRENT BEST 2-INCH BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR 2-INCH - 1-INCH ARE NEEDED SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY 0 1 2 3 4 5 6 7 8 9 10

2-INCH -$212,500.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00

1-INCH -$100,000.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00

INCR. CF -$112,500.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00

(P|F i%,n) 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092 0.56447 0.51316 0.46651 0.42410 0.38554

PW -$112,500.00 $10,227.27 $9,297.52 $8,452.29 $7,683.90 $6,985.36 $6,350.33 $5,773.03 $5,248.21 $4,771.10 $4,337.36 -$43,373.62 <- PW 0.16275 <- (A|P i%,n) -$7,058.86 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$7,058.86 =11250+PMT(10%,10,112500) SOLUTION USING FACTOR TABLES AW = $11,250.00 - $112,500.00(A|P 10%,10) AW = $11,250 - $112,500(0.16275) AW = -$7,059.38 SINCE THE AW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. 1-INCH REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, 1-INCH IS RECOMMENDED.

PROBLEM 7.28

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR LAGRANGE 15.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$1,260,000.00 -$1,260,000.00 1.00000 -$1,260,000.00 1 $480,000.00 $480,000.00 0.86957 $417,391.30 2 $480,000.00 $480,000.00 0.75614 $362,948.96 3 $480,000.00 $480,000.00 0.65752 $315,607.79 4 $480,000.00 $480,000.00 0.57175 $274,441.56 5 $480,000.00 $480,000.00 0.49718 $238,644.83 6 $480,000.00 $480,000.00 0.43233 $207,517.25 7 $480,000.00 $480,000.00 0.37594 $180,449.78 8 $480,000.00 $480,000.00 0.32690 $156,912.85 9 $480,000.00 $480,000.00 0.28426 $136,445.96 10 $480,000.00 $480,000.00 0.24718 $118,648.66 11 $480,000.00 $480,000.00 0.21494 $103,172.75 12 $480,000.00 $480,000.00 0.18691 $89,715.43 $1,341,897.12 <- PW 0.18448 <- (A|P i%,n) $247,554.22 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $247,554.22 =480000+PMT(15%,12,1260000) SOLUTION USING FACTOR TABLES AW = $480,000.00 - $1,260,000(A|P 15%,12) AW = $480,000.00 - $1,260,000(0.18448) AW = $247,555.20

AUBURN SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$1,000,000.00 -$1,000,000.00 1.00000 -$1,000,000.00 1 $410,000.00 $410,000.00 0.86957 $356,521.74 2 $410,000.00 $410,000.00 0.75614 $310,018.90 3 $410,000.00 $410,000.00 0.65752 $269,581.66 4 $410,000.00 $410,000.00 0.57175 $234,418.83 5 $410,000.00 $410,000.00 0.49718 $203,842.46 6 $410,000.00 $410,000.00 0.43233 $177,254.31 7 $410,000.00 $410,000.00 0.37594 $154,134.19 8 $410,000.00 $410,000.00 0.32690 $134,029.73 9 $410,000.00 $410,000.00 0.28426 $116,547.59 10 $410,000.00 $410,000.00 0.24718 $101,345.73 11 $410,000.00 $410,000.00 0.21494 $88,126.72 12 $410,000.00 $410,000.00 0.18691 $76,631.93 $1,222,453.79 <- PW 0.18448 <- (A|P i%,n) $225,519.22 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $225,519.22 =410000+PMT(15%,12,1000000) SOLUTION USING FACTOR TABLES AW = $410,000.00 - $1,000,000(A|P 15%,12) AW = $410,000.00 - $1,000,000(0.18448) = $225,520.00 AW = $225,520.00

ANNISTON SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$1,620,000.00 -$1,620,000.00 1.00000 -$1,620,000.00 1 $520,000.00 $520,000.00 0.86957 $452,173.91 2 $520,000.00 $520,000.00 0.75614 $393,194.71 3 $520,000.00 $520,000.00 0.65752 $341,908.44 4 $520,000.00 $520,000.00 0.57175 $297,311.69 5 $520,000.00 $520,000.00 0.49718 $258,531.90 6 $520,000.00 $520,000.00 0.43233 $224,810.35 7 $520,000.00 $520,000.00 0.37594 $195,487.26 8 $520,000.00 $520,000.00 0.32690 $169,988.92 9 $520,000.00 $520,000.00 0.28426 $147,816.45 10 $520,000.00 $520,000.00 0.24718 $128,536.05 11 $520,000.00 $520,000.00 0.21494 $111,770.48 12 $520,000.00 $520,000.00 0.18691 $97,191.72 $1,198,721.88 <- PW 0.18448 <- (A|P i%,n) $221,141.14 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $221,141.14 =520000+PMT(15%,12,1620000) SOLUTION USING FACTOR TABLES AW = $520,000.00 - $1,620,000(A|P 15%,12) AW = $520,000.00 - $1,620,000(0.18448) = $221,142.40 AW = $221,142.40 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST AW

QUANTUM LOGISTICS SHOULD BUILD IN LAGRANGE

PROBLEM 7.29 ORDER IS NULL, AUBURN, LAGRANGE, ANNISTON NULL BECOMES THE "CURRENT BEST" AND AUBURN THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR AUBURN - NULL ARE NEEDED SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 15.00% EOY AUBURN NULL INCR. CF (P|F i%,n) PW 0 -$1,000,000.00 $0.00 -$1,000,000.00 1.00000 -$1,000,000.00 1 $410,000.00 $0.00 $410,000.00 0.86957 $356,521.74 2 $410,000.00 $0.00 $410,000.00 0.75614 $310,018.90 3 $410,000.00 $0.00 $410,000.00 0.65752 $269,581.66 4 $410,000.00 $0.00 $410,000.00 0.57175 $234,418.83 5 $410,000.00 $0.00 $410,000.00 0.49718 $203,842.46 6 $410,000.00 $0.00 $410,000.00 0.43233 $177,254.31 7 $410,000.00 $0.00 $410,000.00 0.37594 $154,134.19 8 $410,000.00 $0.00 $410,000.00 0.32690 $134,029.73 9 $410,000.00 $0.00 $410,000.00 0.28426 $116,547.59 10 $410,000.00 $0.00 $410,000.00 0.24718 $101,345.73 11 $410,000.00 $0.00 $410,000.00 0.21494 $88,126.72 12 $410,000.00 $0.00 $410,000.00 0.18691 $76,631.93 $1,222,453.79 <- PW 0.18448 <- (A|P i%,n) $225,519.22 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $225,519.22 =410000+PMT(15%,12,1000000) SOLUTION USING FACTOR TABLES AW = $410,000.00 - $1,000,000(A|P 15%,12) AW = $410,000.00 - $1,000,000(0.18448) AW = $225,520.00 SINCE THE AW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED. AUBURN BECOMES THE NEW CURRENT BEST LAGRANGE BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR LAGRANGE - AUBURN ARE NEEDED SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

INCR. CF -$260,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00

(P|F i%,n) 1.00000 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 0.28426 0.24718 0.21494 0.18691

PW -$260,000.00 $60,869.57 $52,930.06 $46,026.14 $40,022.73 $34,802.37 $30,262.93 $26,315.59 $22,883.12 $19,898.37 $17,302.93 $15,046.03 $13,083.50 $119,443.33 <- PW 0.18448 <- (A|P i%,n) $22,035.00 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $22,035.00 =70000+PMT(15%,12,260000) SOLUTION USING FACTOR TABLES

AW = $70,000.00 - $260,000(A|P 15%,12) AW = $70,000.00 - $260,000(0.18448) AW = $22,035.20 SINCE THE AW OF THE INCREMENT IS POSITIVE THE INCREMENTAL INVESTMENT IS ACCEPTED LAGRANGE BECOMES THE NEW CURRENT BEST ANNISTON BECOMES THE NEXT CHALLENGER THUS, THE CASH FLOWS FOR ANNISTON - LAGRANGE ARE NEEDED SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

ANNISTON LAGRANGE -$1,620,000.00 -$1,260,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00 $520,000.00 $480,000.00

INCR. CF -$360,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00

(P|F i%,n) 1.00000 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 0.28426 0.24718 0.21494 0.18691

PW -$360,000.00 $34,782.61 $30,245.75 $26,300.65 $22,870.13 $19,887.07 $17,293.10 $15,037.48 $13,076.07 $11,370.50 $9,887.39 $8,597.73 $7,476.29 -$143,175.24 <- PW 0.18448 <- (A|P i%,n) -$26,413.08 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$26,413.08 =40000+PMT(15%,12,360000) SOLUTION USING FACTOR TABLES AW = $40,000.00 - $360,000(A|P 15%,12) AW = $40,000.00 - $360,000(0.18448) AW = -$26,412.80 SINCE THE AW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED LAGRANGE REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, LAGRANGE IS RECOMMENDED.

PROBLEM 7.30 a

MACHINE 7745 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 6.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$10,000.00 -$10,000.00 1.00000 -$10,000.00 1 -$300.00 -$300.00 0.94340 -$283.02 2 -$300.00 -$300.00 0.89000 -$267.00 3 -$300.00 -$300.00 0.83962 -$251.89 4 -$300.00 -$300.00 0.79209 -$237.63 5 -$300.00 -$300.00 0.74726 -$224.18 6 -$300.00 -$300.00 0.70496 -$211.49 7 -$300.00 -$300.00 0.66506 -$199.52 8 -$300.00 -$300.00 0.62741 -$188.22 9 -$300.00 -$300.00 0.59190 -$177.57 10 $1,000.00 -$300.00 $700.00 0.55839 $390.88 -$11,649.63 <- PW 0.13587 <- (A|P i%,n) -$1,582.81 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$1,582.81 =-300+PMT(6%,10,10000,-1000) SOLUTION USING FACTOR TABLES AW = -$300.00 -$10,000.00(A|P 6%,10) + $400.00(A|F 6%,10) AW = -$300.00 -$10,000.00(0.13587) + $1,000.00(0.07587) AW = -$1,582.83 MACHINE A37Y SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$8,000.00 -$8,000.00 1.00000 -$8,000.00 1 -$300.00 -$300.00 0.94340 -$283.02 2 -$300.00 -$300.00 0.89000 -$267.00 3 -$300.00 -$300.00 0.83962 -$251.89 4 -$300.00 -$300.00 0.79209 -$237.63 5 -$300.00 -$300.00 0.74726 -$224.18 6 -$300.00 -$300.00 0.70496 -$211.49 7 -$300.00 -$300.00 0.66506 -$199.52 8 -$300.00 -$300.00 0.62741 -$188.22 9 -$300.00 -$300.00 0.59190 -$177.57 10 -$300.00 -$300.00 0.55839 -$167.52 -$10,208.03 <- PW 0.13587 <- (A|P i%,n) -$1,386.94 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$1,386.94 =-300+PMT(6%,10,8000) SOLUTION USING FACTOR TABLES AW = -$300.00 -$8,000.00(A|P 6%,10) AW = -$300.00 -$8,000.00(0.13587) AW = -$1,386.96

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST AW

MACHINE A37Y SHOULD BE PURCHASED

PROBLEM 7.31 ORDER IS MACHINE A37Y, MACHINE 7745 NULL IS NOT AN OPTION SINCE THE PROBLEM STATES THAT A MACHINE MUST BE PURCHASED A37Y BECOMES THE "CURRENT BEST" AND 7745 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 7745 - A37Y ARE NEEDED SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 6.00% EOY 7745 A37Y INCR. CF (P|F i%,n) PW 0 -$10,000.00 -$8,000.00 -$2,000.00 1.00000 -$2,000.00 1 -$300.00 -$300.00 $0.00 0.94340 $0.00 2 -$300.00 -$300.00 $0.00 0.89000 $0.00 3 -$300.00 -$300.00 $0.00 0.83962 $0.00 4 -$300.00 -$300.00 $0.00 0.79209 $0.00 5 -$300.00 -$300.00 $0.00 0.74726 $0.00 6 -$300.00 -$300.00 $0.00 0.70496 $0.00 7 -$300.00 -$300.00 $0.00 0.66506 $0.00 8 -$300.00 -$300.00 $0.00 0.62741 $0.00 9 -$300.00 -$300.00 $0.00 0.59190 $0.00 10 $700.00 -$300.00 $1,000.00 0.55839 $558.39 -$1,441.61 <- PW 0.13587 <- (A|P i%,n) -$195.87 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$195.87 =PMT(6%,10,2000,-1000) SOLUTION USING FACTOR TABLES AW = -$2,000.00(A|P 6%,10) + $1,000.00(A|F 6%,10) AW = -$2,000.00(0.13587) + $1,000.00(0.07587) = -$195.87 AW = -$195.87 SINCE THE AW OF THE INCREMENT IS NEGATIVE THE INCREMENTAL INVESTMENT IS REJECTED. A37Y REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, A37Y IS RECOMMENDED.

PROBLEM 7.32

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR PROJECT A 12.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$50,000.00 -$50,000.00 1.00000 -$50,000.00 1 $20,000.00 -$12,500.00 $7,500.00 0.89286 $6,696.43 2 $20,000.00 -$12,500.00 $7,500.00 0.79719 $5,978.95 3 $20,000.00 -$12,500.00 $7,500.00 0.71178 $5,338.35 4 $20,000.00 -$12,500.00 $7,500.00 0.63552 $4,766.39 5 $20,000.00 -$12,500.00 $7,500.00 0.56743 $4,255.70 6 $20,000.00 -$12,500.00 $7,500.00 0.50663 $3,799.73 7 $20,000.00 -$12,500.00 $7,500.00 0.45235 $3,392.62 8 $20,000.00 -$12,500.00 $7,500.00 0.40388 $3,029.12 9 $20,000.00 -$12,500.00 $7,500.00 0.36061 $2,704.58 10 $20,000.00 -$12,500.00 $7,500.00 0.32197 $2,414.80 11 $20,000.00 -$12,500.00 $7,500.00 0.28748 $2,156.07 12 $20,000.00 -$12,500.00 $7,500.00 0.25668 $1,925.06 13 $20,000.00 -$12,500.00 $7,500.00 0.22917 $1,718.81 14 $20,000.00 -$12,500.00 $7,500.00 0.20462 $1,534.65 15 $20,000.00 -$12,500.00 $7,500.00 0.18270 $1,370.22 16 $20,000.00 -$12,500.00 $7,500.00 0.16312 $1,223.41 17 $20,000.00 -$12,500.00 $7,500.00 0.14564 $1,092.33 18 $20,000.00 -$12,500.00 $7,500.00 0.13004 $975.30 19 $20,000.00 -$12,500.00 $7,500.00 0.11611 $870.80 20 $20,000.00 -$12,500.00 $7,500.00 0.10367 $777.50 $6,020.83 <- PW 0.13388 <- (A|P i%,n) $806.06 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $806.06 =7500+PMT(12%,20,50000) SOLUTION USING FACTOR TABLES AW = $7,500.00 - $50,000(A|P 12%,20) AW = $7,500.00 - $50,000(0.13388) AW = $806.00 PROJECT B SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$75,000.00 -$75,000.00 1.00000 -$75,000.00 1 $28,000.00 -$18,000.00 $10,000.00 0.89286 $8,928.57 2 $28,000.00 -$18,000.00 $10,000.00 0.79719 $7,971.94 3 $28,000.00 -$18,000.00 $10,000.00 0.71178 $7,117.80 4 $28,000.00 -$18,000.00 $10,000.00 0.63552 $6,355.18 5 $28,000.00 -$18,000.00 $10,000.00 0.56743 $5,674.27 6 $28,000.00 -$18,000.00 $10,000.00 0.50663 $5,066.31 7 $28,000.00 -$18,000.00 $10,000.00 0.45235 $4,523.49 8 $28,000.00 -$18,000.00 $10,000.00 0.40388 $4,038.83 9 $28,000.00 -$18,000.00 $10,000.00 0.36061 $3,606.10 10 $28,000.00 -$18,000.00 $10,000.00 0.32197 $3,219.73 11 $28,000.00 -$18,000.00 $10,000.00 0.28748 $2,874.76 12 $28,000.00 -$18,000.00 $10,000.00 0.25668 $2,566.75 13 $28,000.00 -$18,000.00 $10,000.00 0.22917 $2,291.74 14 $28,000.00 -$18,000.00 $10,000.00 0.20462 $2,046.20 15 $28,000.00 -$18,000.00 $10,000.00 0.18270 $1,826.96 16 $28,000.00 -$18,000.00 $10,000.00 0.16312 $1,631.22 17 $28,000.00 -$18,000.00 $10,000.00 0.14564 $1,456.44 18 $28,000.00 -$18,000.00 $10,000.00 0.13004 $1,300.40 19 $28,000.00 -$18,000.00 $10,000.00 0.11611 $1,161.07 20 $28,000.00 -$18,000.00 $10,000.00 0.10367 $1,036.67 -$305.56 <- PW 0.13388 <- (A|P i%,n) -$40.91 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$40.91 =10000+PMT(12%,20,75000) ALTERNATIVELY, AW = $10,000.00 - $75,000(A|P 12%,20) AW = $10,000.00 - $75,000(0.13388) AW = -$41.00

TEMPURA SHOULD PURSUE PROJECT A SINCE IT HAS THE HIGHEST AW

PROBLEM 7.33 POLISHER 1 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 15.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$20,000.00 -$20,000.00 1.00000 -$20,000.00 1 $4,465.00 $4,465.00 0.86957 $3,882.61 2 $4,465.00 $4,465.00 0.75614 $3,376.18 3 $4,465.00 $4,465.00 0.65752 $2,935.81 4 $4,465.00 $4,465.00 0.57175 $2,552.88 5 $4,465.00 $4,465.00 0.49718 $2,219.89 6 $4,465.00 $4,465.00 0.43233 $1,930.34 7 $4,465.00 $4,465.00 0.37594 $1,678.56 8 $4,465.00 $4,465.00 0.32690 $1,459.62 9 $4,465.00 $4,465.00 0.28426 $1,269.23 10 $4,465.00 $4,465.00 0.24718 $1,103.68 $2,408.80 <- PW 0.19925 <- (A|P i%,n) $479.96 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $479.96 =4465+PMT(15%,10,20000) SOLUTION USING FACTOR TABLES AW = $4,465.00 - $20,000(A|P 15%,10) AW = $4,465.00 - $20,000(0.19925) AW = $480.00 POLISHER 2 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$10,000.00 -$10,000.00 1.00000 -$10,000.00 1 $1,770.00 $1,770.00 0.86957 $1,539.13 2 $1,770.00 $1,770.00 0.75614 $1,338.37 3 $1,770.00 $1,770.00 0.65752 $1,163.80 4 $1,770.00 $1,770.00 0.57175 $1,012.00 5 $1,770.00 $1,770.00 0.49718 $880.00 6 $1,770.00 $1,770.00 0.43233 $765.22 7 $1,770.00 $1,770.00 0.37594 $665.41 8 $1,770.00 $1,770.00 0.32690 $578.62 9 $1,770.00 $1,770.00 0.28426 $503.14 10 $1,770.00 $1,770.00 0.24718 $437.52 -$1,116.78 <- PW 0.19925 <- (A|P i%,n) -$222.52 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$222.52 =1770+PMT(15%,10,10000) SOLUTION USING FACTOR TABLES AW = $1,770.00 - $10,000(A|P 15%,10) AW = $1,770.00 - $10,000(0.19925) AW = -$222.50 POLISHER 3 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF

0 1 2 3 4 5 6 7 8 9 10

-$15,000.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00

1.00000 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 0.28426 0.24718

-$15,000.00 $3,113.04 $2,706.99 $2,353.91 $2,046.88 $1,779.89 $1,547.73 $1,345.85 $1,170.31 $1,017.66 $884.92 $2,967.19 <- PW 0.19925 <- (A|P i%,n) $591.22 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $591.22 =3580+PMT(15%,10,15000) SOLUTION USING FACTOR TABLES AW = $3,580.00 - $15,000(A|P 15%,10) AW = $3,580.00 - $15,000(0.19925) AW = $591.25

FINAL FINISHING SHOULD PURCHASE POLISHER 3 SINCE IT HAS THE HIGHEST AW

PROBLEM 7.34 a

SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR A001 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$210.00 -$210.00 1.00000 -$210.00 1 $80.00 $80.00 0.90909 $72.73 2 $90.00 $90.00 0.82645 $74.38 3 $100.00 $100.00 0.75131 $75.13 4 $110.00 $110.00 0.68301 $75.13 $87.37 <- PW 0.31547 <- (A|P i%,n) $27.56 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $27.56 =-PMT(10%,4,NPV(10%,E8:E11)+E7) SOLUTION USING FACTOR TABLES AW = $80.00 - $210.00(A|P 10%,4) + $10.00(A|G 10%,4) AW = $80.00 - $210.00(0.31547) + $10.00(1.38117) AW = $27.56 B002 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$110.00 -$110.00 1.00000 -$110.00 1 $60.00 $60.00 0.90909 $54.55 2 $60.00 $60.00 0.82645 $49.59 3 $60.00 $60.00 0.75131 $45.08 4 $70.00 $70.00 0.68301 $47.81 $87.02 <- PW 0.31547 <- (A|P i%,n) $27.45 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $27.45 =60+PMT(10%,4,110,-10) SOLUTION USING FACTOR TABLES AW = $60.00 - $110.00(A|P 10%,4) + $10.00(A|F 10%,4) AW = $60.00 - $110.00(0.31547) + $10.00(0.21547) = $27.45 AW = $27.45 C003 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$160.00 -$160.00 1.00000 -$160.00 1 $80.00 $80.00 0.90909 $72.73 2 $80.00 $80.00 0.82645 $66.12 3 $80.00 $80.00 0.75131 $60.11 4 $80.00 $80.00 0.68301 $54.64 $93.59 <- PW 0.31547 <- (A|P i%,n) $29.52 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $29.52 =80+PMT(10%,4,160) SOLUTION USING FACTOR TABLES AW = $80.00 - $160.00(A|P 10%,4) AW = $80.00 - $160.00(0.31547) AW = $29.52

XANADU SHOULD ACCEPT ALTERNATIVE C003 SINCE IT HAS THE HIGHEST AW

PROBLEM 7.35 12%/YR COMPOUNDED MONTHLY, SHOULD BE USED FOR MARR. THIS LEADS TO A PERIOD INTEREST RATE OF 1% PER MONTH. SAVINGS CERTIFICATE SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 1.00% EOM + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$12,000.00 -$12,000.00 1.00000 -$12,000.00 1 $100.00 $100.00 0.99010 $99.01 2 $100.00 $100.00 0.98030 $98.03 3 $100.00 $100.00 0.97059 $97.06 4 $100.00 $100.00 0.96098 $96.10 5 $100.00 $100.00 0.95147 $95.15 6 $100.00 $100.00 0.94205 $94.20 7 $100.00 $100.00 0.93272 $93.27 8 $100.00 $100.00 0.92348 $92.35 9 $100.00 $100.00 0.91434 $91.43 10 $100.00 $100.00 0.90529 $90.53 11 $100.00 $100.00 0.89632 $89.63 12 $100.00 $100.00 0.88745 $88.74 13 $100.00 $100.00 0.87866 $87.87 14 $100.00 $100.00 0.86996 $87.00 15 $100.00 $100.00 0.86135 $86.13 16 $100.00 $100.00 0.85282 $85.28 17 $100.00 $100.00 0.84438 $84.44 18 $100.00 $100.00 0.83602 $83.60 19 $100.00 $100.00 0.82774 $82.77 20 $100.00 $100.00 0.81954 $81.95 21 $100.00 $100.00 0.81143 $81.14 22 $100.00 $100.00 0.80340 $80.34 23 $100.00 $100.00 0.79544 $79.54 24 $100.00 $100.00 0.78757 $78.76 25 $100.00 $100.00 0.77977 $77.98 26 $100.00 $100.00 0.77205 $77.20 27 $100.00 $100.00 0.76440 $76.44 28 $100.00 $100.00 0.75684 $75.68 29 $100.00 $100.00 0.74934 $74.93 30 $100.00 $100.00 0.74192 $74.19 31 $100.00 $100.00 0.73458 $73.46 32 $100.00 $100.00 0.72730 $72.73 33 $100.00 $100.00 0.72010 $72.01 34 $100.00 $100.00 0.71297 $71.30 35 $100.00 $100.00 0.70591 $70.59 36 $100.00 $100.00 0.69892 $69.89 37 $100.00 $100.00 0.69200 $69.20 38 $100.00 $100.00 0.68515 $68.52 39 $100.00 $100.00 0.67837 $67.84 40 $100.00 $100.00 0.67165 $67.17 41 $100.00 $100.00 0.66500 $66.50 42 $100.00 $100.00 0.65842 $65.84 43 $100.00 $100.00 0.65190 $65.19 44 $100.00 $100.00 0.64545 $64.54 45 $100.00 $100.00 0.63905 $63.91 46 $100.00 $100.00 0.63273 $63.27 47 $100.00 $100.00 0.62646 $62.65 48 $100.00 $100.00 0.62026 $62.03 49 $100.00 $100.00 0.61412 $61.41 50 $100.00 $100.00 0.60804 $60.80 51 $100.00 $100.00 0.60202 $60.20 52 $100.00 $100.00 0.59606 $59.61 53 $100.00 $100.00 0.59016 $59.02 54 $100.00 $100.00 0.58431 $58.43 55 $100.00 $100.00 0.57853 $57.85 56 $100.00 $100.00 0.57280 $57.28 57 $100.00 $100.00 0.56713 $56.71 58 $100.00 $100.00 0.56151 $56.15 59 $100.00 $100.00 0.55595 $55.60 60 $13,100.00 $13,100.00 0.55045 $7,210.89 -$348.65 <- PW 0.02224 <- (A|P i%,n) -$7.76 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$7.76 =100+PMT(1%,60,12000,-13000) SOLUTION USING FACTOR TABLES AW = $100.00 - $12,000.00(A|P 1%,60) + $13,000.00(A|F 1%,60) AW = $100.00 - $12,000.00(0.02224) + $13,000.00(0.01224) AW = -$7.76

RACE HORSE SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOM + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$12,000.00 -$12,000.00 1.00000 -$12,000.00 1 $0.00 $0.00 0.99010 $0.00 2 $0.00 $0.00 0.98030 $0.00 3 $0.00 $0.00 0.97059 $0.00 4 $0.00 $0.00 0.96098 $0.00 5 $0.00 $0.00 0.95147 $0.00 6 $0.00 $0.00 0.94205 $0.00 7 $0.00 $0.00 0.93272 $0.00 8 $0.00 $0.00 0.92348 $0.00 9 $0.00 $0.00 0.91434 $0.00 10 $0.00 $0.00 0.90529 $0.00 11 $0.00 $0.00 0.89632 $0.00 12 $0.00 $0.00 0.88745 $0.00 13 $0.00 $0.00 0.87866 $0.00 14 $0.00 $0.00 0.86996 $0.00 15 $0.00 $0.00 0.86135 $0.00 16 $0.00 $0.00 0.85282 $0.00 17 $0.00 $0.00 0.84438 $0.00 18 $0.00 $0.00 0.83602 $0.00 19 $0.00 $0.00 0.82774 $0.00 20 $0.00 $0.00 0.81954 $0.00 21 $0.00 $0.00 0.81143 $0.00 22 $0.00 $0.00 0.80340 $0.00 23 $0.00 $0.00 0.79544 $0.00 24 $0.00 $0.00 0.78757 $0.00 25 $0.00 $0.00 0.77977 $0.00 26 $0.00 $0.00 0.77205 $0.00 27 $0.00 $0.00 0.76440 $0.00 28 $0.00 $0.00 0.75684 $0.00 29 $0.00 $0.00 0.74934 $0.00 30 $0.00 $0.00 0.74192 $0.00 31 $0.00 $0.00 0.73458 $0.00 32 $0.00 $0.00 0.72730 $0.00 33 $0.00 $0.00 0.72010 $0.00 34 $0.00 $0.00 0.71297 $0.00 35 $0.00 $0.00 0.70591 $0.00 36 $0.00 $0.00 0.69892 $0.00 37 $0.00 $0.00 0.69200 $0.00 38 $0.00 $0.00 0.68515 $0.00 39 $0.00 $0.00 0.67837 $0.00 40 $0.00 $0.00 0.67165 $0.00 41 $0.00 $0.00 0.66500 $0.00 42 $0.00 $0.00 0.65842 $0.00 43 $0.00 $0.00 0.65190 $0.00 44 $0.00 $0.00 0.64545 $0.00 45 $0.00 $0.00 0.63905 $0.00 46 $0.00 $0.00 0.63273 $0.00 47 $0.00 $0.00 0.62646 $0.00 48 $0.00 $0.00 0.62026 $0.00 49 $0.00 $0.00 0.61412 $0.00 50 $0.00 $0.00 0.60804 $0.00 51 $0.00 $0.00 0.60202 $0.00 52 $0.00 $0.00 0.59606 $0.00 53 $0.00 $0.00 0.59016 $0.00 54 $0.00 $0.00 0.58431 $0.00 55 $0.00 $0.00 0.57853 $0.00 56 $0.00 $0.00 0.57280 $0.00 57 $0.00 $0.00 0.56713 $0.00 58 $0.00 $0.00 0.56151 $0.00 59 $0.00 $0.00 0.55595 $0.00 60 20000 20000 0.55044962 $11,008.99 -991.00768 <- PW $0.02 <- (A|P i%,n) -$22.04 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$22.04 =PMT(1%,60,12000,-20000) SOLUTION USING FACTOR TABLES AW = -$12,000.00(A|P 1%,60) + $20,000.00(A|F 1%,60) AW = -$12,000.00(0.02224) + $20,000.00(0.01224) AW = -$22.08 SAVINGS ACCOUNT THE ANNUAL WORTH OF THE SAVINGS ACCOUNT IS ZERO SINCE IT EARNS EXACTLY MARR

YANI SHOULD PREFER THE SAVINGS ACCOUNT SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.36

DRILL PRESS T SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$20,000.00 -$20,000.00 1.00000 -$20,000.00 1 -$14,000.00 -$14,000.00 0.90909 -$12,727.27 2 -$14,000.00 -$14,000.00 0.82645 -$11,570.25 3 -$14,000.00 -$14,000.00 0.75131 -$10,518.41 4 -$14,000.00 -$14,000.00 0.68301 -$9,562.19 5 -$14,000.00 -$14,000.00 0.62092 -$8,692.90 6 -$14,000.00 -$14,000.00 0.56447 -$7,902.64 7 -$14,000.00 -$14,000.00 0.51316 -$7,184.21 8 -$14,000.00 -$14,000.00 0.46651 -$6,531.10 9 -$14,000.00 -$14,000.00 0.42410 -$5,937.37 10 -$9,000.00 -$9,000.00 0.38554 -$3,469.89 -$104,096.22 <- PW 0.16275 <- (A|P i%,n) -$16,941.18 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$16,941.18 =-14000+PMT(10%,10,20000,-5000) SOLUTION USING FACTOR TABLES AW = -$14,000.00 -$20,000(A|P 10%,10) + $5,000(A|F 10%,10) AW = -$14,000.00 -$20,000(0.16275) + $5,000(0.06275) AW = -$16,941.25

DRILL PRESS M SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$30,000.00 -$30,000.00 1.00000 -$30,000.00 1 -$10,000.00 -$10,000.00 0.90909 -$9,090.91 2 -$10,000.00 -$10,000.00 0.82645 -$8,264.46 3 -$10,000.00 -$10,000.00 0.75131 -$7,513.15 4 -$10,000.00 -$10,000.00 0.68301 -$6,830.13 5 -$10,000.00 -$10,000.00 0.62092 -$6,209.21 6 -$10,000.00 -$10,000.00 0.56447 -$5,644.74 7 -$10,000.00 -$10,000.00 0.51316 -$5,131.58 8 -$10,000.00 -$10,000.00 0.46651 -$4,665.07 9 -$10,000.00 -$10,000.00 0.42410 -$4,240.98 10 -$3,000.00 -$3,000.00 0.38554 -$1,156.63 -$88,746.87 <- PW 0.16275 <- (A|P i%,n) -$14,443.14 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$14,443.14 =-10000+PMT(10%,10,30000,-7000) SOLUTION USING FACTOR TABLES AW = -$10,000.00 -$30,000(A|P 10%,10) + $7,000(A|F 10%,10) AW = -$10,000.00 -$30,000(0.16275) + $7,000(0.06275) AW = -$14,443.25

ZUNNI'S MANUFACTURING SHOULD PURCHASE DRILL M SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.37 a

AT A PRODUCTION RATE OF 200 UNITS/YEAR THE SERVICE WOULD COST $18,000/YR. IF THE EQUIPMENT IS PURCHASED THE SAVED SERVICE COST LOOKS LIKE A REVENUE. AT A PRODUCTION RATE OF 200 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $5,000/YR AT 200 UNITS/YEAR SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00 $18,000.00

- CF -$100,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00

NET CF -$100,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00

12.00% (P|F i%,n) 1.00000 0.89286 0.79719 0.71178 0.63552 0.56743 0.50663 0.45235 0.40388 0.36061 0.32197

PW OF CF -$100,000.00 $5,357.14 $4,783.16 $4,270.68 $3,813.11 $3,404.56 $3,039.79 $2,714.10 $2,423.30 $2,163.66 $1,931.84 -$66,098.66 <- PW 0.17698 <- (A|P i%,n) -$11,698.42 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$11,698.42 =6000+PMT(12%,10,100000) SOLUTION USING FACTOR TABLES AW = $6,000.00 -$100,000(A|P 12%,10) AW = $6,000.00 -$100,000(0.17698) = -$11,698.00 AW = -$11,698.00 SINCE THE AW IS NEGATIVE, THE SERVICE CONTRACT IS PREFERRED OVER THE EQUIPMENT

AT A PRODUCTION RATE OF 500 UNITS/YEAR THE SERVICE WOULD COST $45,000/YR AT A PRODUCTION RATE OF 500 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $12,500/YR AT 500 UNITS/YEAR SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS EOY + CF - CF NET CF (P|F i%,n) 0 -$100,000.00 -$100,000.00 1.00000 1 $45,000.00 -$19,500.00 $25,500.00 0.89286 2 $45,000.00 -$19,500.00 $25,500.00 0.79719 3 $45,000.00 -$19,500.00 $25,500.00 0.71178 4 $45,000.00 -$19,500.00 $25,500.00 0.63552 5 $45,000.00 -$19,500.00 $25,500.00 0.56743 6 $45,000.00 -$19,500.00 $25,500.00 0.50663 7 $45,000.00 -$19,500.00 $25,500.00 0.45235 8 $45,000.00 -$19,500.00 $25,500.00 0.40388 9 $45,000.00 -$19,500.00 $25,500.00 0.36061 10 $45,000.00 -$19,500.00 $25,500.00 0.32197

PW OF CF -$100,000.00 $22,767.86 $20,328.44 $18,150.40 $16,205.71 $14,469.38 $12,919.09 $11,534.90 $10,299.02 $9,195.56 $8,210.32 $44,080.69 <- PW 0.17698 <- (A|P i%,n) $7,801.58 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $7,801.58 =25500+PMT(12%,10,100000) SOLUTION USING FACTOR TABLES AW = $25,500.00 - $100,000(A|P 12%,10) AW = $25,500.00 - $100,000(0.17698) AW = $7,802.00 SINCE THE AW IS POSITIVE, THE EQUIPMENT IS PREFERRED OVER THE SERVICE CONTRACT

FOR BREAKEVEN THE ANNUAL WORTH OF BENEFITS MUST EQUAL THE ANNUAL WORTH OF COSTS 90(X) = 100,000(A|P 12%,10) + (7,000+25(X)) 90(X) = 100,000(0.17698) + (7,000+25(X)) 90X = 17,698 + 7,000 + 25X 65X = 24,698 X = 379.97 OR APPROXIMATELY 380 UNITS/YR

PROBLEM 7.38 a

X1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1

X2 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1

Y1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1

Y2 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1

FEASIBLE YES YES YES NO NO NO YES NO NO YES NO NO NO NO NO NO

REASON

Y1 CONTINGENT ON X1 Y2 CONTINGENT ON X2 X1 & X2 ARE ME Y2 CONTINGENT ON X2 Y1 CONTINGENT ON X1 Y1 & Y2 ARE ME X1 & X2 ARE ME X1 & X2 ARE ME Y1 & Y2 ARE ME Y1 & Y2 ARE ME X1 & X2 ARE ME

FEASIBLE COMBINATIONS ARE: NULL, X1 ONLY, X2 ONLY, X1&Y1, X2&Y2 b

ALTERNATIVE: NULL THE ANNUAL WORTH OF NULL IS ZERO ALTERNATIVE: X1 ONLY SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$10,000.00 -$10,000.00 1.00000 -$10,000.00 1 $1,600.00 $1,600.00 0.90909 $1,454.55 2 $1,600.00 $1,600.00 0.82645 $1,322.31 3 $1,600.00 $1,600.00 0.75131 $1,202.10 4 $1,600.00 $1,600.00 0.68301 $1,092.82 5 $1,600.00 $1,600.00 0.62092 $993.47 6 $1,600.00 $1,600.00 0.56447 $903.16 7 $1,600.00 $1,600.00 0.51316 $821.05 8 $1,600.00 $1,600.00 0.46651 $746.41 -$1,464.12 <- PW 0.18744 <- (A|P i%,n) -$274.44 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$274.44 =1600+PMT(10%,8,10000) SOLUTION USING FACTOR TABLES AW = $1,600 - $10,000(A|P 10%,8) AW = $1,600 - $10,000(0.18744) AW = -$274.40

ALTERNATIVE: X2 ONLY SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$15,000.00 -$15,000.00 1.00000 -$15,000.00 1 $2,600.00 $2,600.00 0.90909 $2,363.64 2 $2,600.00 $2,600.00 0.82645 $2,148.76 3 $2,600.00 $2,600.00 0.75131 $1,953.42 4 $2,600.00 $2,600.00 0.68301 $1,775.83 5 $2,600.00 $2,600.00 0.62092 $1,614.40 6 $2,600.00 $2,600.00 0.56447 $1,467.63 7 $2,600.00 $2,600.00 0.51316 $1,334.21

$2,600.00

0.46651

$1,212.92 -$1,129.19 <- PW 0.18744 <- (A|P i%,n) -$211.66 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$211.66 =2600+PMT(10%,8,15000) SOLUTION USING FACTOR TABLES AW = $2,600 - $15,000(A|P 10%,8) AW = $2,600 - $15,000(0.18744) AW = -$211.60

ALTERNATIVE: X1&Y1 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$16,000.00 -$16,000.00 1.00000 -$16,000.00 1 $4,100.00 $4,100.00 0.90909 $3,727.27 2 $4,100.00 $4,100.00 0.82645 $3,388.43 3 $4,100.00 $4,100.00 0.75131 $3,080.39 4 $4,100.00 $4,100.00 0.68301 $2,800.36 5 $4,100.00 $4,100.00 0.62092 $2,545.78 6 $4,100.00 $4,100.00 0.56447 $2,314.34 7 $4,100.00 $4,100.00 0.51316 $2,103.95 8 $4,100.00 $4,100.00 0.46651 $1,912.68 $5,873.20 <- PW 0.18744 <- (A|P i%,n) $1,100.90 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $1,100.90 =4100+PMT(10%,8,16000) SOLUTION USING FACTOR TABLES AW = $4,100 - $16,000(A|P 10%,8) AW = $4,100 - $16,000(0.18744) AW = $1,100.96

ALTERNATIVE: X2&Y2 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$24,000.00 -$24,000.00 1.00000 -$24,000.00 1 $6,100.00 $6,100.00 0.90909 $5,545.45 2 $6,100.00 $6,100.00 0.82645 $5,041.32 3 $6,100.00 $6,100.00 0.75131 $4,583.02 4 $6,100.00 $6,100.00 0.68301 $4,166.38 5 $6,100.00 $6,100.00 0.62092 $3,787.62 6 $6,100.00 $6,100.00 0.56447 $3,443.29 7 $6,100.00 $6,100.00 0.51316 $3,130.26 8 $6,100.00 $6,100.00 0.46651 $2,845.70 $8,543.05 <- PW 0.18744 <- (A|P i%,n) $1,601.34 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $1,601.34 =6100+PMT(10%,8,24000) SOLUTION USING FACTOR TABLES AW = $6,100 - $24,000(A|P 10%,8) AW = $6,100 - $24,000(0.18744) = $1,601.44 AW = $1,601.44

THE COMBINATION X2&Y2 HAS THE HIGHEST ANNUAL WORTH AND IS THEREFORE PREFERRED.

PROBLEM 7.39 TELESCOPE T2 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 25.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$600,000.00 -$600,000.00 1.00000 -$600,000.00 1 $400,000.00 -$130,000.00 $270,000.00 0.80000 $216,000.00 2 $400,000.00 -$130,000.00 $270,000.00 0.64000 $172,800.00 3 $400,000.00 -$130,000.00 $270,000.00 0.51200 $138,240.00 4 $400,000.00 -$130,000.00 $270,000.00 0.40960 $110,592.00 5 $400,000.00 -$130,000.00 $270,000.00 0.32768 $88,473.60 6 $400,000.00 -$130,000.00 $270,000.00 0.26214 $70,778.88 7 $400,000.00 -$130,000.00 $270,000.00 0.20972 $56,623.10 8 $400,000.00 -$130,000.00 $270,000.00 0.16777 $45,298.48 9 $400,000.00 -$130,000.00 $270,000.00 0.13422 $36,238.79 10 $470,000.00 -$130,000.00 $340,000.00 0.10737 $36,507.22 $371,552.08 <- PW 0.28007 <- (A|P i%,n) $104,061.54 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $104,061.54 =270000+PMT(25%,10,600000,-70000) SOLUTION USING FACTOR TABLES AW = $270,000 - $600,000(A|P 25%,10) + $70,000(A|F 25%,10) AW = $270,000 - $600,000(0.28007) + $70,000(0.03007) AW = $104,062.90

TELESCOPE T2 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$800,000.00 -$800,000.00 1.00000 -$800,000.00 1 $600,000.00 -$270,000.00 $330,000.00 0.80000 $264,000.00 2 $600,000.00 -$270,000.00 $330,000.00 0.64000 $211,200.00 3 $600,000.00 -$270,000.00 $330,000.00 0.51200 $168,960.00 4 $600,000.00 -$270,000.00 $330,000.00 0.40960 $135,168.00 5 $600,000.00 -$270,000.00 $330,000.00 0.32768 $108,134.40 6 $600,000.00 -$270,000.00 $330,000.00 0.26214 $86,507.52 7 $600,000.00 -$270,000.00 $330,000.00 0.20972 $69,206.02 8 $600,000.00 -$270,000.00 $330,000.00 0.16777 $55,364.81 9 $600,000.00 -$270,000.00 $330,000.00 0.13422 $44,291.85 10 $730,000.00 -$270,000.00 $460,000.00 0.10737 $49,392.12 $392,224.72 <- PW 0.28007 <- (A|P i%,n) $109,851.38 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $109,851.38 =330000+PMT(25%,10,800000,-130000) SOLUTION USING FACTOR TABLES AW = $330,000 - $800,000(A|P 25%,10) + $130,000(A|F 25%,10) AW = $330,000 - $800,000(0.28007) + $130,000(0.03007) AW = $109,853.10

TELESCOPE T3 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$470,000.00 -$470,000.00 1.00000 -$470,000.00 1 $260,000.00 -$70,000.00 $190,000.00 0.80000 $152,000.00 2 $260,000.00 -$70,000.00 $190,000.00 0.64000 $121,600.00 3 $260,000.00 -$70,000.00 $190,000.00 0.51200 $97,280.00 4 $260,000.00 -$70,000.00 $190,000.00 0.40960 $77,824.00 5 $260,000.00 -$70,000.00 $190,000.00 0.32768 $62,259.20 6 $260,000.00 -$70,000.00 $190,000.00 0.26214 $49,807.36 7 $260,000.00 -$70,000.00 $190,000.00 0.20972 $39,845.89 8 $260,000.00 -$70,000.00 $190,000.00 0.16777 $31,876.71 9 $260,000.00 -$70,000.00 $190,000.00 0.13422 $25,501.37 10 $325,000.00 -$70,000.00 $255,000.00 0.10737 $27,380.42 $215,374.94 <- PW 0.28007 <- (A|P i%,n) $60,320.61 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $60,320.61 =190000+PMT(25%,10,470000,-65000)

SOLUTION USING FACTOR TABLES AW = $190,000 - $470,000(A|P 25%,10) + $65,000(A|F 25%,10) AW = $190,000 - $470,000(0.28007) + $65,000(0.03007) AW = $60,321.65

TELESCOPE T4 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$540,000.00 -$540,000.00 1.00000 -$540,000.00 1 $320,000.00 -$120,000.00 $200,000.00 0.80000 $160,000.00 2 $320,000.00 -$120,000.00 $200,000.00 0.64000 $128,000.00 3 $320,000.00 -$120,000.00 $200,000.00 0.51200 $102,400.00 4 $320,000.00 -$120,000.00 $200,000.00 0.40960 $81,920.00 5 $320,000.00 -$120,000.00 $200,000.00 0.32768 $65,536.00 6 $320,000.00 -$120,000.00 $200,000.00 0.26214 $52,428.80 7 $320,000.00 -$120,000.00 $200,000.00 0.20972 $41,943.04 8 $320,000.00 -$120,000.00 $200,000.00 0.16777 $33,554.43 9 $320,000.00 -$120,000.00 $200,000.00 0.13422 $26,843.55 10 $520,000.00 -$120,000.00 $400,000.00 0.10737 $42,949.67 $195,575.49 <- PW 0.28007 <- (A|P i%,n) $54,775.33 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $54,775.33 =200000+PMT(25%,10,540000,-200000) SOLUTION USING FACTOR TABLES AW = $200,000 - $540,000(A|P 25%,10) + $200,000(A|F 25%,10) AW = $200,000 - $540,000(0.28007) + $200,000(0.03007) AW = $54,776.20

TELESCOPE T2 HAS THE HIGHEST ANNUAL WORTH AND IS THEREFORE PREFERRED.

TELESCOPE T1 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 42.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$600,000.00 -$600,000.00 1.00000 -$600,000.00 1 $400,000.00 -$130,000.00 $270,000.00 0.70423 $190,140.85 2 $400,000.00 -$130,000.00 $270,000.00 0.49593 $133,902.00 3 $400,000.00 -$130,000.00 $270,000.00 0.34925 $94,297.19 4 $400,000.00 -$130,000.00 $270,000.00 0.24595 $66,406.47 5 $400,000.00 -$130,000.00 $270,000.00 0.17320 $46,765.12 6 $400,000.00 -$130,000.00 $270,000.00 0.12197 $32,933.18 7 $400,000.00 -$130,000.00 $270,000.00 0.08590 $23,192.38 8 $400,000.00 -$130,000.00 $270,000.00 0.06049 $16,332.66 9 $400,000.00 -$130,000.00 $270,000.00 0.04260 $11,501.88 10 $470,000.00 -$130,000.00 $340,000.00 0.03000 $10,199.89 $25,671.61 <- PW 0.43299 <- (A|P i%,n) $11,115.54 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $11,115.54 =270000+PMT(42%,10,600000,-70000) SOLUTION USING FACTOR TABLES AW = $270,000 - $600,000(A|P 42%,10) + $70,000(A|F 42%,10) AW = $270,000 - $600,000(0.43299) + $70,000(0.01299) AW = $11,115.30

$730,000.00

-$270,000.00

$460,000.00

0.03000

$13,799.85 -$33,956.93 <- PW 0.43299 <- (A|P i%,n) -$14,703.00 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$14,703.00 =330000+PMT(42%,10,800000,-130000) SOLUTION USING FACTOR TABLES AW = $330,000 - $800,000(A|P 42%,10) + $130,000(A|F 42%,10) AW = $330,000 - $800,000(0.43299) + $130,000(0.01299) AW = -$14,703.30

TELESCOPE T3 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$470,000.00 -$470,000.00 1.00000 -$470,000.00 1 $260,000.00 -$70,000.00 $190,000.00 0.70423 $133,802.82 2 $260,000.00 -$70,000.00 $190,000.00 0.49593 $94,227.34 3 $260,000.00 -$70,000.00 $190,000.00 0.34925 $66,357.28 4 $260,000.00 -$70,000.00 $190,000.00 0.24595 $46,730.48 5 $260,000.00 -$70,000.00 $190,000.00 0.17320 $32,908.79 6 $260,000.00 -$70,000.00 $190,000.00 0.12197 $23,175.20 7 $260,000.00 -$70,000.00 $190,000.00 0.08590 $16,320.57 8 $260,000.00 -$70,000.00 $190,000.00 0.06049 $11,493.36 9 $260,000.00 -$70,000.00 $190,000.00 0.04260 $8,093.91 10 $325,000.00 -$70,000.00 $255,000.00 0.03000 $7,649.92 -$29,240.35 <- PW 0.43299 <- (A|P i%,n) -$12,660.77 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$12,660.77 =190000+PMT(42%,10,470000,-65000) SOLUTION USING FACTOR TABLES AW = $190,000 - $470,000(A|P 42%,10) + $65,000(A|F 42%,10) AW = $190,000 - $470,000(0.43299) + $65,000(0.01299) AW = -$12,660.95

TELESCOPE T4 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$540,000.00 -$540,000.00 1.00000 -$540,000.00 1 $320,000.00 -$120,000.00 $200,000.00 0.70423 $140,845.07 2 $320,000.00 -$120,000.00 $200,000.00 0.49593 $99,186.67 3 $320,000.00 -$120,000.00 $200,000.00 0.34925 $69,849.77 4 $320,000.00 -$120,000.00 $200,000.00 0.24595 $49,189.98 5 $320,000.00 -$120,000.00 $200,000.00 0.17320 $34,640.83 6 $320,000.00 -$120,000.00 $200,000.00 0.12197 $24,394.95 7 $320,000.00 -$120,000.00 $200,000.00 0.08590 $17,179.54 8 $320,000.00 -$120,000.00 $200,000.00 0.06049 $12,098.27 9 $320,000.00 -$120,000.00 $200,000.00 0.04260 $8,519.91 10 $520,000.00 -$120,000.00 $400,000.00 0.03000 $11,999.87 -$72,095.15 <- PW 0.43299 <- (A|P i%,n) -$31,216.45 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$31,216.45 =200000+PMT(42%,10,540000,-200000) SOLUTION USING FACTOR TABLES AW = $200,000 - $540,000(A|P 42%,10) + $200,000(A|F 42%,10) AW = $200,000 - $540,000(0.43299) + $200,000(0.01299) AW = -$31,216.60

TELESCOPE T1 HAS THE HIGHEST ANNUAL WORTH AND IS THEREFORE PREFERRED.

PROBLEM 7.40 DELIVERY VAN SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 6.00% EOY VAN LOAN O&M SAVINGS NET CF (P|F i%,n) 0 -$18,000.00 $12,000.00 -$6,000.00 1.00000 1 $0.00 -$3,305.88 -$700.00 $3,800.00 -$205.88 0.94340 2 $0.00 -$3,305.88 -$700.00 $3,800.00 -$205.88 0.89000 3 $0.00 -$3,305.88 -$700.00 $3,800.00 -$205.88 0.83962 4 $0.00 -$3,305.88 -$700.00 $3,800.00 -$205.88 0.79209 5 $0.00 -$700.00 $3,800.00 $3,100.00 0.74726 6 $500.00 -$700.00 $3,800.00 $3,600.00 0.70496

PW OF CF -$6,000.00 -$194.23 -$183.23 -$172.86 -$163.08 $2,316.50 $2,537.86 -$1,859.04 <- PW 0.20336 <- (A|P i%,n) -$378.06 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = -$378.06 =-PMT(6%,6,NPV(6%,G8:G13)+G7) SOLUTION USING FACTOR TABLES AW = (-$6,000 - $205.88(P|A 6%,4) + $3,100(P|F 6%,5) + $3,600(P|F 6%,6))(A|P 6%,6) AW = (-$6,000 - $205.88(3.46511) + $3,100(0.74726) + $3,600(0.70496))(0.20336) AW = -$378.05 DELTA DAWN'S BAKERY SHOULD NOT PURCHASE THE DELIVERY VAN SINCE THE AW IS NEGATIVE

PROBLEM 7.41 AW OF LOTTERY PAYOUT SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 6.00% EOY CF (P|F i%,n) PW OF CF 0 $1.00 1.00000 $1.00 1 $1.30 0.94340 $1.23 2 $1.30 0.89000 $1.16 3 $1.30 0.83962 $1.09 4 $1.30 0.79209 $1.03 5 $1.30 0.74726 $0.97 6 $1.30 0.70496 $0.92 7 $1.30 0.66506 $0.86 8 $1.30 0.62741 $0.82 9 $1.30 0.59190 $0.77 10 $1.30 0.55839 $0.73 11 $1.30 0.52679 $0.68 12 $1.30 0.49697 $0.65 13 $1.30 0.46884 $0.61 14 $1.30 0.44230 $0.57 15 $1.30 0.41727 $0.54 16 $1.30 0.39365 $0.51 17 $1.30 0.37136 $0.48 18 $1.30 0.35034 $0.46 19 $1.30 0.33051 $0.43 20 $1.30 0.31180 $0.41 $15.91 <- PW 0.08718 <- (A|P i%,n) $1.39 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $1.39 =1.3+PMT(6%,20,-1) ALTERNATIVELY, AW = $1.30 + $1.00(A|P 6%,20) AW = $1.30 + $1.00(0.08718) AW = $1.39

AW OF ONE-TIME PAYMENT SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $1.26 =PMT(6%,20,-14.4) SOLUTION USING FACTOR TABLES AW = $14.4(A|P 6%,20) AW = $14.4(0.08718) = $1.26 AW = $1.26 DECISION: SINCE THE AW OF THE ONE-TIME PAYMENT IS LOWER THAN THE AW OF THE PAYOUT, THE STATE SHOULD PREFER THE ONE-TIME PAYMENT.

PROBLEM 7.42 MACHINE 1 (IN K$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 12.00% EOY MACHINE O&M NET CF (P|F i%,n) PW OF CF 0 -$800.00 -$800.00 1.00000 -$800.00 1 -$50.00 -$50.00 0.89286 -$44.64 2 -$50.00 -$50.00 0.79719 -$39.86 3 -$50.00 -$50.00 0.71178 -$35.59 4 $40.00 -$50.00 -$10.00 0.63552 -$6.36 -$926.45 <- PW 0.32923 <- (A|P i%,n) -$305.02 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$305.02 =-50+PMT(12%,4,800,-40) SOLUTION USING FACTOR TABLES AW = -$50.00 - $800(A|P 12%,4) + $40(A|F 12%,4) AW = -$50.00 - $800(0.32923) + $40(0.20923) AW = -$305.01

MACHINE 2 (IN K$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY MACHINE O&M NET CF (P|F i%,n) PW OF CF 0 -$650.00 -$650.00 1.00000 -$650.00 1 -$90.00 -$90.00 0.89286 -$80.36 2 -$90.00 -$90.00 0.79719 -$71.75 3 -$90.00 -$90.00 0.71178 -$64.06 4 $32.50 -$90.00 -$57.50 0.63552 -$36.54 -$902.71 <- PW 0.32923 <- (A|P i%,n) -$297.20 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$297.20 =-90+PMT(12%,4,650,-32.5) SOLUTION USING FACTOR TABLES AW = -$90.00 - $650(A|P 12%,4) + $32.5(A|F 12%,4) AW = -$90.00 - $650(0.32923) + $32.5(0.20923) AW = -$297.20

MACHINE 3 (IN K$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY MACHINE O&M NET CF (P|F i%,n) PW OF CF 0 -$575.00 -$575.00 1.00000 -$575.00 1 -$105.00 -$105.00 0.89286 -$93.75 2 -$105.00 -$105.00 0.79719 -$83.71 3 -$105.00 -$105.00 0.71178 -$74.74 4 $28.75 -$105.00 -$76.25 0.63552 -$48.46 -$875.65 <- PW 0.32923 <- (A|P i%,n) -$288.29 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$288.29 =-105+PMT(12%,4,575,-28.75) SOLUTION USING FACTOR TABLES AW = -$105.00 - $575(A|P 12%,4) + $28.75(A|F 12%,4) AW = -$105.00 - $575(0.32923) + $28.75(0.20923) AW = -$288.29

DECISION: PREFER MACHINE 3 SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.43 GATE 1 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 20.00% EOY GATE O&M NET CF (P|F i%,n) PW OF CF 0 -$15,000.00 -$15,000.00 1.00000 -$15,000.00 1 -$6,500.00 -$6,500.00 0.83333 -$5,416.67 2 -$6,500.00 -$6,500.00 0.69444 -$4,513.89 3 -$6,500.00 -$6,500.00 0.57870 -$3,761.57 4 -$6,500.00 -$6,500.00 0.48225 -$3,134.65 5 $0.00 -$6,500.00 -$6,500.00 0.40188 -$2,612.20 -$34,438.98 <- PW 0.33438 <- (A|P i%,n) -$11,515.70 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$11,515.70 =-6500+PMT(20%,5,15000) SOLUTION USING FACTOR TABLES AW = -$6,500.00 - $15,000(A|P 20%,5) AW = -$6,500.00 - $15,000(0.33438) AW = -$11,515.70

GATE 2 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY GATE O&M NET CF (P|F i%,n) PW OF CF 0 -$19,000.00 -$19,000.00 1.00000 -$19,000.00 1 -$5,600.00 -$5,600.00 0.83333 -$4,666.67 2 -$5,600.00 -$5,600.00 0.69444 -$3,888.89 3 -$5,600.00 -$5,600.00 0.57870 -$3,240.74 4 -$5,600.00 -$5,600.00 0.48225 -$2,700.62 5 $2,000.00 -$5,600.00 -$3,600.00 0.40188 -$1,446.76 -$34,943.67 <- PW 0.33438 <- (A|P i%,n) -$11,684.45 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$11,684.45 =-5600+PMT(20%,5,19000,-2000) SOLUTION USING FACTOR TABLES AW = -$5,600.00 - $19,000(A|P 20%,5) + $2,000(A|F 20%,5) AW = -$5,600.00 - $19,000(0.33438) + $2,000(0.13438) AW = -$11,684.46

GATE 3 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY GATE O&M NET CF (P|F i%,n) PW OF CF 0 -$24,000.00 -$24,000.00 1.00000 -$24,000.00 1 -$4,000.00 -$4,000.00 0.83333 -$3,333.33 2 -$4,000.00 -$4,000.00 0.69444 -$2,777.78 3 -$4,000.00 -$4,000.00 0.57870 -$2,314.81 4 -$4,000.00 -$4,000.00 0.48225 -$1,929.01 5 $5,000.00 -$4,000.00 $1,000.00 0.40188 $401.88 -$33,953.06 <- PW 0.33438 <- (A|P i%,n) -$11,353.21 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$11,353.21 =-4000+PMT(20%,5,24000,-5000) SOLUTION USING FACTOR TABLES AW = -$4,000.00 - $24,000(A|P 20%,5) + $5,000(A|F 20%,5) AW = -$4,000.00 - $24,000(0.33438) + $5,000(0.13438) = -$11,353.22 AW = -$11,353.22

DECISION: PREFER GATE 3 SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.44 SPRINKLER SYSTEM SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 15.00% EOY SPRINKLERS LOAN O&M SAVINGS NET CF (P|F i%,n) PW OF CF 0 -$30,000.00 $30,000.00 $0.00 1.00000 $0.00 1 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.86957 -$3,371.33 2 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.75614 -$2,931.59 3 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.65752 -$2,549.21 4 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 0.57175 -$2,216.71 5 -$9,000.00 $15,000.00 $6,000.00 0.49718 $2,983.06 6 -$9,000.00 $15,000.00 $6,000.00 0.43233 $2,593.97 7 -$9,000.00 $15,000.00 $6,000.00 0.37594 $2,255.62 8 -$9,000.00 $15,000.00 $6,000.00 0.32690 $1,961.41 9 $2,000.00 -$9,000.00 $15,000.00 $8,000.00 0.28426 $2,274.10 $999.31 <- PW 0.20957 <- (A|P i%,n) $209.43 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE =30000+PMT(10%,6,70000,-2000) AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $209.43 =-PMT(15%,9,NPV(15%,G8:G16)) SOLUTION USING FACTOR TABLES AW = -$3,877.03(P|A 15%,4)(A|P 15%,9)+($6,000(F|A 15%,5)+$2,000)(A|F 15%,9) AW = -$3,877.03(2.85498)(0.20957)+($6,000(6.74238)+$2,000)(0.05957) AW = $209.30 SPRINKLER SYSTEM IS ECONOMICALLY ATTRACTIVE SINCE THE AW IS POSITIVE.

PROBLEM 7.45 LIGHT BAR SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY BAR REVENUE NET CF (P|F i%,n) PW OF CF 0 -$6,000.00 -$6,000.00 1.00000 -$6,000.00 1 $2,000.00 $2,000.00 0.90909 $1,818.18 2 $2,000.00 $2,000.00 0.82645 $1,652.89 3 $2,000.00 $2,000.00 0.75131 $1,502.63 4 $2,000.00 $2,000.00 0.68301 $1,366.03 5 $2,000.00 $2,000.00 0.62092 $1,241.84 6 $2,000.00 $2,000.00 0.56447 $1,128.95 $2,710.52 <- PW 0.22961 <- (A|P i%,n) $622.36 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $622.36 =2000+PMT(10%,6,6000) SOLUTION USING FACTOR TABLES AW = $2,000.00 - $6,000(A|P 10%,6) AW = $2,000.00 - $6,000(0.22961) AW = $622.34

SLIDING SPOTS SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY SPOTS REVENUE NET CF (P|F i%,n) PW OF CF 0 -$14,000.00 -$14,000.00 1.00000 -$14,000.00 1 $3,500.00 $3,500.00 0.90909 $3,181.82 2 $3,500.00 $3,500.00 0.82645 $2,892.56 3 $3,500.00 $3,500.00 0.75131 $2,629.60 4 $3,500.00 $3,500.00 0.68301 $2,390.55 5 $3,500.00 $3,500.00 0.62092 $2,173.22 6 $3,500.00 $3,500.00 0.56447 $1,975.66 $1,243.41 <- PW 0.22961 <- (A|P i%,n) $285.50 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $285.50 =3500+PMT(10%,6,14000) SOLUTION USING FACTOR TABLES AW = $3,500.00 - $14,000(A|P 10%,6) AW = $3,500.00 - $14,000(0.22961) AW = $285.46

REFLECTED BEAM SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY BEAM REVENUE NET CF (P|F i%,n) PW OF CF 0 -$20,000.00 -$20,000.00 1.00000 -$20,000.00 1 $0.00 $0.00 0.90909 $0.00 2 $2,300.00 $2,300.00 0.82645 $1,900.83 3 $4,600.00 $4,600.00 0.75131 $3,456.05 4 $6,900.00 $6,900.00 0.68301 $4,712.79 5 $9,200.00 $9,200.00 0.62092 $5,712.48 6 $11,500.00 $11,500.00 0.56447 $6,491.45 $2,273.59 <- PW 0.22961 <- (A|P i%,n) $522.03 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $522.03 =-PMT(10%,6,NPV(10%,E56:E61)+E55) SOLUTION USING FACTOR TABLES AW = $2,300.00(A|G 10%,6) - $20,000(A|P 10%,6) AW = $2,300.00(2.22356) - $20,000(0.22961) AW = $521.99

DECISION: LIGHT BAR IS PREFERRED SINCE IT HAS THE HIGHEST AW

PROBLEM 7.46 DESIGN 1 (IN M$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY NET CF (P|F i%,n) PW OF CF 0 -$15.00 1.00000 -$15.00 1 -$2.50 0.90909 -$2.27 2 -$2.50 0.82645 -$2.07 3 -$2.50 0.75131 -$1.88 -$21.22 <- PW 0.40211 <- (A|P i%,n) -$8.53 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$8.53 =-2.5+PMT(10%,3,15) SOLUTION USING FACTOR TABLES AW = -$2.50 - $15.00(A|P 10%,3) AW = -$2.50 - $15.00(0.40211) AW = -$8.53

DESIGN 2 (IN M$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY NET CF (P|F i%,n) PW OF CF 0 -$20.00 1.00000 -$20.00 1 -$1.50 0.90909 -$1.36 2 -$1.50 0.82645 -$1.24 3 -$1.50 0.75131 -$1.13 -$23.73 <- PW 0.40211 <- (A|P i%,n) -$9.54 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$9.54 =-1.5+PMT(10%,3,20) SOLUTION USING FACTOR TABLES AW = -$1.50 - $20.00(A|P 10%,3) AW = -$1.50 - $20.00(0.40211) AW = -$9.54

DECISION: PREFER DESIGN 1 SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.47 FIRST SATELLITE ONLY (IN K$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY 0 1 2 3 4 5

EQUIPMENT DEVELOPMENT -$750.00 -$150.00 -$150.00 -$150.00 -$150.00 -$150.00

VEHICLE

-$275.00

PAYMENT

$2,500.00

NET CF -$750.00 -$150.00 -$150.00 -$150.00 -$150.00 $2,075.00

10.00% (P|F i%,n) 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092

PW OF CF -$750.00 -$136.36 -$123.97 -$112.70 -$102.45 $1,288.41 $62.93 <- PW 0.26380 <- (A|P i%,n) $16.60 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $16.60 =-150+PMT(10%,5,750,-2225) SOLUTION USING FACTOR TABLES AW = -$150.00 - $750.00(A|P 10%,5) + ($2,075 - (-$150))(A|F 10%,5) AW = -$150.00 - $750.00(0.26380) + ($2,075 - (-$150))(0.16380) AW = $16.61

SECOND SATELLITE ONLY (IN K$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY EQUIPMENT DEVELOPMENT VEHICLE PAYMENT NET CF (P|F i%,n) 0 -$850.00 -$850.00 1.00000 1 -$120.00 -$120.00 0.90909 2 -$120.00 -$120.00 0.82645 3 -$120.00 -$120.00 0.75131 4 -$120.00 -$120.00 0.68301 5 -$120.00 -$275.00 $2,500.00 $2,105.00 0.62092

PW OF CF -$850.00 -$109.09 -$99.17 -$90.16 -$81.96 $1,307.04 $76.66 <- PW 0.26380 <- (A|P i%,n) $20.22 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $20.22 =-120+PMT(10%,5,850,-2225) SOLUTION USING FACTOR TABLES AW = -$120.00 - $850.00(A|P 10%,5) + ($2,105 - (-$120))(A|F 10%,5) AW = -$120.00 - $850.00(0.26380) + ($2,105 - (-$120))(0.16380) AW = $20.23

BOTH SATELLITES (IN K$) SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY EQUIPMENT DEVELOPMENT VEHICLE PAYMENT NET CF (P|F i%,n) 0 -$1,750.00 -$1,750.00 1.00000 1 -$400.00 -$400.00 0.90909 2 -$400.00 -$400.00 0.82645 3 -$400.00 -$400.00 0.75131 4 -$400.00 -$400.00 0.68301 5 -$400.00 -$350.00 $6,000.00 $5,250.00 0.62092

PW OF CF -$1,750.00 -$363.64 -$330.58 -$300.53 -$273.21 $3,259.84 $241.89 <- PW 0.26380 <- (A|P i%,n) $63.81 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $63.81 =-400+PMT(10%,5,1750,-5650) SOLUTION USING FACTOR TABLES AW = -$400.00 - $1,750.00(A|P 10%,5) + ($5,250 - (-$400))(A|F 10%,5) AW = -$400.00 - $1,750.00(0.26380) + ($5,250 - (-$400))(0.16380) AW = $63.82

DECISION: PREFER BOTH SATELLITES SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.48 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR IN K$ 12.00% EOY FILTER LOAN O&M SAVINGS NET CF (P|F i%,n) 0 -$100.00 $50.00 -$50.00 1.00000 1 -$14.92 -$20.00 $50.00 $15.08 0.89286 2 -$14.92 -$21.50 $50.00 $13.58 0.79719 3 -$14.92 -$23.00 $50.00 $12.08 0.71178 4 -$14.92 -$24.50 $50.00 $10.58 0.63552 5 -$14.92 -$26.00 $50.00 $9.08 0.56743 6 -$27.50 $50.00 $22.50 0.50663 7 -$29.00 $50.00 $21.00 0.45235 8 -$30.50 $50.00 $19.50 0.40388 9 -$32.00 $50.00 $18.00 0.36061 10 $10.00 -$33.50 $50.00 $26.50 0.32197

PW OF CF -$50.00 $13.47 $10.83 $8.60 $6.73 $5.15 $11.40 $9.50 $7.88 $6.49 $8.53 $38.58 <- PW 0.17698 <- (A|P i%,n) $6.83 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE =30000+PMT(10%,6,70000,-2000) AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $6.83 =-PMT(12%,10,NPV(12%,G8:G17)+G7) SOLUTION USING FACTOR TABLES AW = $50-$20-$1.50(A|G 12%,10)+(-50-$14.92(P|A 12%,5))(A|P 12%,10)+$10(A|F 12%,10) AW = $50-$20-$1.50(3.58465)+(-50-$14.92(3.60478))(0.17698)+$10(0.05698) AW = $6.83 DECISION: FILTER IS ECONOMICALLY JUSTIFIED SINCE AW IS POSITIVE.

PROBLEM 7.49 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 12.00% EOY BUILDING FURNITURE O&M REVENUE NET CF (P|F i%,n) 0 -$8,000.00 -$700.00 -$8,700.00 1.00000 1 -$800.00 $1,460.00 $660.00 0.89286 2 -$800.00 $1,752.00 $952.00 0.79719 3 -$800.00 $2,044.00 $1,244.00 0.71178 4 -$800.00 $2,336.00 $1,536.00 0.63552 5 -$700.00 -$800.00 $2,628.00 $1,128.00 0.56743 6 -$800.00 $2,628.00 $1,828.00 0.50663 7 -$800.00 $2,628.00 $1,828.00 0.45235 8 -$800.00 $2,628.00 $1,828.00 0.40388 9 -$800.00 $2,628.00 $1,828.00 0.36061 10 -$700.00 -$800.00 $2,628.00 $1,128.00 0.32197 11 -$800.00 $2,628.00 $1,828.00 0.28748 12 -$800.00 $2,628.00 $1,828.00 0.25668 13 -$800.00 $2,628.00 $1,828.00 0.22917 14 -$800.00 $2,628.00 $1,828.00 0.20462 15 $900.00 -$800.00 $2,628.00 $2,728.00 0.18270

PW OF CF -$8,700.00 $589.29 $758.93 $885.45 $976.16 $640.06 $926.12 $826.89 $738.30 $659.20 $363.19 $525.51 $469.20 $418.93 $374.05 $498.40 $949.66 <- PW 0.14682 <- (A|P i%,n) $139.43 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $139.43 =-PMT(12%,15,NPV(12%,G7:G21)+G6) SOLUTION USING FACTOR TABLES AW = $1,828 - $8,700(A|P 12%,15) + ((-$1,828 + $660)(P|F 12%,1) + (-$1,828 + $952)(P|F 12%,2) + (-$1,828 + $1,244)(P|F 12%,3) + (-$1,828 + $1,536)(P|F 12%,4) + (-$1,828 + $1,128)(P|F 12%,5) + (-$1,828 + $1,128)(P|F 12%,10))(A|P 12%,15) + ($2,728 - $1,828)(A|F 12%,15) AW = $1,828 - $8,700(0.14682) + ((-$1,828 + $660)(0.89286) + (-$1,828 + $952)(0.79719) + (-$1,828 + $1,244)(0.71178) + (-$1,828 + $1,536)(0.63552) + (-$1,828 + $1,128)(0.56743) + (-$1,828 + $1,128)(0.32197))(0.14682) + ($2,728 - $1,828)(0.02682) AW = $139.48 DECISION: MOTEL IS ECONOMICALLY ATTRACTIVE SINCE AW IS POSITIVE.

PROBLEM 7.50 PURCHASE SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY PURCHASE SAVINGS NET CF (P|F i%,n) PW OF CF 0 -$60,000.00 -$60,000.00 1.00000 -$60,000.00 1 $23,000.00 $23,000.00 0.90909 $20,909.09 2 $23,000.00 $23,000.00 0.82645 $19,008.26 3 $10,000.00 $23,000.00 $33,000.00 0.75131 $24,793.39 $4,710.74 <- PW 0.40211 <- (A|P i%,n) $1,894.26 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $1,894.26 =23000+PMT(10%,3,60000,-10000) SOLUTION USING FACTOR TABLES AW = $23,000 - $60,000(A|P 10%,3) + $10,000(A|F 10%,3) AW = $23,000 - $60,000(0.40211) + $10,000(0.30211) AW = $1,894.50

LEASE SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY LEASE SAVINGS NET CF (P|F i%,n) PW OF CF 0 -$21,000.00 -$21,000.00 1.00000 -$21,000.00 1 -$21,000.00 $23,000.00 $2,000.00 0.90909 $1,818.18 2 -$21,000.00 $23,000.00 $2,000.00 0.82645 $1,652.89 3 $23,000.00 $23,000.00 0.75131 $17,280.24 -$248.69 <- PW 0.40211 <- (A|P i%,n) -$100.00 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$100.00 =2000+PMT(10%,3,21000,-21000) SOLUTION USING FACTOR TABLES AW = $2,000 - $21,000(A|P 10%,3) + $21,000(A|F 10%,3) AW = $2,000 - $21,000(0.40211) + $21,000(0.30211) = -$100.00 AW = -$100.00

DECISION: PURCHASE IS PREFERRED SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.51 a

LEAST COMMON MULTIPLE LIFE FOR 3 (=PRIME), 4 (=2*2), AND 6 (=3*2) IS 12 YEARS (=3*2*2)

DETAILS OF THE DEVELOPMENT OF THE CASH FLOWS CAN BE FOUND IN THE SOLUTION TO PROBLEM 4.7 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 8.00% EOY ALT 1 ALT 2 ALT 3 (P|F i%,n) PW CF A1 0 -$20,000.00 -$40,000.00 -$70,000.00 1.00000 -$20,000.00 1 $8,000.00 $20,000.00 $30,000.00 0.92593 $7,407.41 2 $8,000.00 $20,000.00 $30,000.00 0.85734 $6,858.71 3 $8,000.00 $20,000.00 $30,000.00 0.79383 $6,350.66 4 $8,000.00 -$20,000.00 $30,000.00 0.73503 $5,880.24 5 $8,000.00 $20,000.00 $30,000.00 0.68058 $5,444.67 6 $8,000.00 $20,000.00 -$38,000.00 0.63017 $5,041.36 7 $8,000.00 $20,000.00 $30,000.00 0.58349 $4,667.92 8 $8,000.00 -$20,000.00 $30,000.00 0.54027 $4,322.15 9 $8,000.00 $20,000.00 $30,000.00 0.50025 $4,001.99 10 $8,000.00 $20,000.00 $30,000.00 0.46319 $3,705.55 11 $8,000.00 $20,000.00 $30,000.00 0.42888 $3,431.06 12 $28,000.00 $20,000.00 $32,000.00 0.39711 $11,119.19

PW CF A2 -$40,000.00 $18,518.52 $17,146.78 $15,876.64 -$14,700.60 $13,611.66 $12,603.39 $11,669.81 -$10,805.38 $10,004.98 $9,263.87 $8,577.66 $7,942.28

$48,230.90 0.13270 $6,400.00

$59,709.61 0.13270 $7,923.17

PW CF A3 -$70,000.00 $27,777.78 $25,720.16 $23,814.97 $22,050.90 $20,417.50 -$23,946.45 $17,504.71 $16,208.07 $15,007.47 $13,895.80 $12,866.49 $12,707.64 $114,025.03 <- PW 0.13270 <- (A|P i%,n) $15,130.55 <- AW

SOLUTIONS USING EXCEL'S NPV AND PMT FUNCTIONS ALT 1 $6,400.00 =8000+PMT(8%,12,20000,-20000) ALT 2 $7,923.17 =-PMT(8%,12,NPV(8%,D11:D22)+D10) ALT 3 $15,130.55 =-PMT(8%,12,NPV(8%,E11:E22)+E10) SOLUTIONS USING FACTOR TABLES ALT1 AW = $8,000 -$20,000(A|P 8%,12) + $20,000(A|F 8%,12) AW = $8,000 -$20,000(0.13270) + $20,000(0.05270) AW = $6,400.00

ALT2

AW = $20,000 - $40,000(A|P 8%,12) - $40,000(P|F 8%,4)(A|P 8%,12) - $40,000(P|F 8%,8)(A|P 8%,12) AW = $20,000 - $40,000(0.13270) - $40,000(0.73503)(0.13270) - $40,000(0.54027)(0.13270) AW = $7,922.71

ALT3

AW = $30,000 - $70,000(A|P 8%,12) - $38,000(P|F 8%,6)(A|P 8%,12) + $2,000(A|F 8%,12) AW = $30,000 - $70,000(0.13270) - $68,000(0.63017)(0.13270) + $2,000(0.05270) AW = $15,130.00

NATURAL LIFE CASH FLOWS SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY ALT 1 ALT 2 ALT 3 (P|F i%,n) PW CF A1 0 -$20,000.00 -$40,000.00 -$70,000.00 1.00000 -$20,000.00 1 $8,000.00 $20,000.00 $30,000.00 0.92593 $7,407.41 2 $8,000.00 $20,000.00 $30,000.00 0.85734 $6,858.71 3 $28,000.00 $20,000.00 $30,000.00 0.79383 $22,227.30 4 $20,000.00 $30,000.00 0.73503 5 $30,000.00 0.68058 6 $32,000.00 0.63017

PW CF A2 -$40,000.00 $18,518.52 $17,146.78 $15,876.64 $14,700.60

$16,493.42 3 0.38803 $6,400.00

$26,242.54 4 0.30192 $7,923.17

SOLUTIONS USING EXCEL'S NPV AND PMT FUNCTIONS ALT 1 $6,400.00 =8000+PMT(8%,3,20000,-20000) ALT 2 $7,923.17 =20000+PMT(8%,4,40000) ALT 3 $15,130.55 =30000+PMT(8%,6,70000,-2000) SOLUTIONS USING FACTOR TABLES ALT1 AW = $8,000 - $20,000(A|P 8%,3) + $28,000(A|F 8%,3) AW = $8,000 - $20,000(0.38803) + $20,000(0.30803) AW = $6,400.00

ALT2

AW = $20,000 - $40,000(A|P 8%,4) = AW = $20,000 - $40,000(0.30192) AW = $7,923.20

ALT3

AW = $30,000 - $70,000(A|P 8%,6) + $2,000(A|F 8%,6) AW = $30,000 - $70,000(0.21632) + $2,000(0.13632) AW = $15,130.24

THE RESULTS FOR PARTS b AND c AGREE (EXACTLY FOR THE EXCEL SOLUTIONS AND APPROXIMATELY FOR THE FACTOR TABLE SOLUTIONS) THEREFORE CONFIRMING THE CLAIM THAT AW IMPLICITLY ASSUMES A LCM PLANNING HORIZON

PW CF A3 -$70,000.00 $27,777.78 $25,720.16 $23,814.97 $22,050.90 $20,417.50 $20,165.43 $69,946.73 <- PW 6 <- n 0.21632 <- (A|P i%,n) $15,130.55 <- AW

PROBLEM 7.52 a

PLANNING HORIZON FOR LEAST COMMON MULTIPLE = 15

ALTERNATIVE 1 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY CF (P|F i%,n) PW OF CF 0 -$50,000.00 1.00000 -$50,000.00 1 $25,000.00 0.90909 $22,727.27 2 $30,000.00 0.82645 $24,793.39 3 -$15,000.00 0.75131 -$11,269.72 4 $25,000.00 0.68301 $17,075.34 5 $30,000.00 0.62092 $18,627.64 6 -$15,000.00 0.56447 -$8,467.11 7 $25,000.00 0.51316 $12,828.95 8 $30,000.00 0.46651 $13,995.22 9 -$15,000.00 0.42410 -$6,361.46 10 $25,000.00 0.38554 $9,638.58 11 $30,000.00 0.35049 $10,514.82 12 -$15,000.00 0.31863 -$4,779.46 13 $25,000.00 0.28966 $7,241.61 14 $30,000.00 0.26333 $7,899.94 15 $35,000.00 0.23939 $8,378.72 $72,843.72 <- PW 0.13147 <- (A|P i%,n) $9,577.04 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $9,577.04 =-PMT(10%,15,NPV(10%,C10:C24)+C9) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE AW.

ALTERNATIVE 2 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY CF (P|F i%,n) PW OF CF 0 -$80,000.00 1.00000 -$80,000.00 1 $35,000.00 0.90909 $31,818.18 2 $45,000.00 0.82645 $37,190.08 3 $50,000.00 0.75131 $37,565.74 4 $55,000.00 0.68301 $37,565.74 5 -$20,000.00 0.62092 -$12,418.43 6 $35,000.00 0.56447 $19,756.59 7 $45,000.00 0.51316 $23,092.12 8 $50,000.00 0.46651 $23,325.37 9 $55,000.00 0.42410 $23,325.37 10 -$20,000.00 0.38554 -$7,710.87 11 $35,000.00 0.35049 $12,267.29 12 $45,000.00 0.31863 $14,338.39 13 $50,000.00 0.28966 $14,483.22 14 $55,000.00 0.26333 $14,483.22 15 $60,000.00 0.23939 $14,363.52 $203,445.53 <- PW 0.13147 <- (A|P i%,n) $26,747.75 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $26,747.75 =-PMT(10%,15,NPV(10%,C43:C57)+C42) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE AW.

ALTERNATIVE 1 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 10.00% EOY CF (P|F i%,n) PW OF CF 0 -$50,000.00 1.00000 -$50,000.00 1 $25,000.00 0.90909 $22,727.27 2 $30,000.00 0.82645 $24,793.39 3 $35,000.00 0.75131 $26,296.02 $23,816.68 <- PW 0.40211 <- (A|P i%,n) $9,577.04 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $9,577.04 =-PMT(10%,3,NPV(10%,C77:C79)+C76) SOLUTION USING FACTOR TABLES AW = -$50,000(A|P 10%,3) + $25,000 + $5,000(A|G 10%,3) AW = -$50,000(0.40211) + $25,000 + $5,000(0.93656) AW = $9,577.30

ALTERNATIVE 2 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY CF (P|F i%,n) PW OF CF 0 -$80,000.00 1.00000 -$80,000.00 1 $35,000.00 0.90909 $31,818.18 2 $45,000.00 0.82645 $37,190.08 3 $50,000.00 0.75131 $37,565.74 4 $55,000.00 0.68301 $37,565.74 5 $60,000.00 0.62092 $37,255.28 $101,395.02 <- PW 0.26380 <- (A|P i%,n) $26,747.75 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $26,747.75 =-PMT(10%,5,NPV(10%,C100:C104)+C99) SOLUTION USING FACTOR TABLES AW = -$80,000(A|P 10%,5) + $35,000 + ($5,000(P|A 10%,4)(P|F 10%,1)+ $5,000(P|G 10%,5))(A|P 10%,5) AW = -$80,000(0.26380) + $35,000 + ($5,000(3.16987)(0.90909)+ $5,000(6.86180))(0.26380) AW = $26,747.67

PROBLEM 7.53 a

LEAST COMMON MULTIPLE LIFE FOR 4 (=2*2) AND 3 (PRIME) IS 12 YEARS (=2*2*3)

DETAILS OF THE DEVELOPMENT OF THE CASH FLOWS CAN BE FOUND IN THE SOLUTION TO PROBLEM 4.6 SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 8.00% EOY ALT 1 ALT 2 (P|F i%,n) PW CF A1 PW CF A2 0 -$100.00 -$70.00 1.00000 -$100.00 -$70.00 1 $20.00 $30.00 0.92593 $18.52 $27.78 2 $20.00 $40.00 0.85734 $17.15 $34.29 3 $40.00 -$20.00 0.79383 $31.75 -$15.88 4 -$40.00 $30.00 0.73503 -$29.40 $22.05 5 $20.00 $40.00 0.68058 $13.61 $27.22 6 $20.00 -$20.00 0.63017 $12.60 -$12.60 7 $40.00 $30.00 0.58349 $23.34 $17.50 8 -$40.00 $40.00 0.54027 -$21.61 $21.61 9 $20.00 -$20.00 0.50025 $10.00 -$10.00 10 $20.00 $30.00 0.46319 $9.26 $13.90 11 $40.00 $40.00 0.42888 $17.16 $17.16 12 $60.00 $50.00 0.39711 $23.83 $19.86 $26.21 0.13270 $3.48

$92.88 <- PW 0.13270 <- (A|P i%,n) $12.33 <- AW

SOLUTIONS USING EXCEL'S NPV AND PMT FUNCTIONS ALT 1 $3.48 =-PMT(8%,12,NPV(8%,C11:C22)+C10) ALT 2 $12.33 =-PMT(8%,12,NPV(8%,D11:D22)+D10) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, THE FACTOR TABLES ARE NOT USED TO COMPUTE AW.

NATURAL LIFE CASH FLOWS SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY ALT 1 ALT 2 (P|F i%,n) PW CF A1 PW CF A2 0 -$100.00 -$70.00 1.00000 -$100.00 -$70.00 1 $20.00 $30.00 0.92593 $18.52 $27.78 2 $20.00 $40.00 0.85734 $17.15 $34.29 3 $40.00 $50.00 0.79383 $31.75 $39.69 4 $60.00 0.73503 $44.10 $11.52 4 0.30192 $3.48 SOLUTIONS USING EXCEL'S NPV AND PMT FUNCTIONS ALT 1 $3.48 =-PMT(8%,4,NPV(8%,C40:C43)+C39) ALT 2 $12.33 =-PMT(8%,3,NPV(8%,D40:D42)+D39) SOLUTIONS USING FACTOR TABLES ALT1 AW = -$100(A|P 8%,4) + $20 + $20(P|G 8%,3)(P|F 8%,1)(A|P 8%,4) AW = -$100(0.30192) + $20 + $20(2.44500)(0.92593)(0.30192) AW = $3.48 ALT2

AW = -$70(A|P 8%,3) + $30 + $10(A|G 8%,3) AW = -$70(0.38803) + $30 + $10(0.94874) AW = $12.33

$31.76 <- PW 3 <- n 0.38803 <- (A|P i%,n) $12.33 <- AW

PROBLEM 7.54 PIPE A SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 6.00% EOY PIPE EQUIPMENT M&E NET CF (P|F i%,n) 0 -$120,000.00 -$15,000.00 -$135,000.00 1.00000 1 -$3,000.00 -$3,000.00 0.94340 2 -$3,000.00 -$3,000.00 0.89000 3 -$3,000.00 -$3,000.00 0.83962 4 -$3,000.00 -$3,000.00 0.79209 5 -$3,000.00 -$3,000.00 0.74726 6 -$3,000.00 -$3,000.00 0.70496 7 -$3,000.00 -$3,000.00 0.66506 8 -$3,000.00 -$3,000.00 0.62741 9 -$3,000.00 -$3,000.00 0.59190 10 -$3,000.00 -$3,000.00 0.55839 11 -$3,000.00 -$3,000.00 0.52679 12 -$3,000.00 -$3,000.00 0.49697 13 -$3,000.00 -$3,000.00 0.46884 14 -$3,000.00 -$3,000.00 0.44230 15 -$3,000.00 -$3,000.00 0.41727 16 -$3,000.00 -$3,000.00 0.39365 17 -$3,000.00 -$3,000.00 0.37136 18 -$3,000.00 -$3,000.00 0.35034 19 -$3,000.00 -$3,000.00 0.33051 20 -$15,000.00 -$3,000.00 -$18,000.00 0.31180 21 -$3,000.00 -$3,000.00 0.29416 22 -$3,000.00 -$3,000.00 0.27751 23 -$3,000.00 -$3,000.00 0.26180 24 -$3,000.00 -$3,000.00 0.24698 25 -$3,000.00 -$3,000.00 0.23300 26 -$3,000.00 -$3,000.00 0.21981 27 -$3,000.00 -$3,000.00 0.20737 28 -$3,000.00 -$3,000.00 0.19563 29 -$3,000.00 -$3,000.00 0.18456 30 -$3,000.00 -$3,000.00 0.17411 31 -$3,000.00 -$3,000.00 0.16425 32 -$3,000.00 -$3,000.00 0.15496 33 -$3,000.00 -$3,000.00 0.14619 34 -$3,000.00 -$3,000.00 0.13791 35 -$3,000.00 -$3,000.00 0.13011 36 -$3,000.00 -$3,000.00 0.12274 37 -$3,000.00 -$3,000.00 0.11579 38 -$3,000.00 -$3,000.00 0.10924 39 -$3,000.00 -$3,000.00 0.10306 40 -$15,000.00 -$3,000.00 -$18,000.00 0.09722 41 -$3,000.00 -$3,000.00 0.09172 42 -$3,000.00 -$3,000.00 0.08653 43 -$3,000.00 -$3,000.00 0.08163 44 -$3,000.00 -$3,000.00 0.07701 45 -$3,000.00 -$3,000.00 0.07265 46 -$3,000.00 -$3,000.00 0.06854 47 -$3,000.00 -$3,000.00 0.06466 48 -$3,000.00 -$3,000.00 0.06100 49 -$3,000.00 -$3,000.00 0.05755 50 -$3,000.00 -$3,000.00 0.05429 51 -$3,000.00 -$3,000.00 0.05122 52 -$3,000.00 -$3,000.00 0.04832 53 -$3,000.00 -$3,000.00 0.04558 54 -$3,000.00 -$3,000.00 0.04300 55 -$3,000.00 -$3,000.00 0.04057 56 -$3,000.00 -$3,000.00 0.03827 57 -$3,000.00 -$3,000.00 0.03610 58 -$3,000.00 -$3,000.00 0.03406 59 -$3,000.00 -$3,000.00 0.03213 60 -$3,000.00 -$3,000.00 0.03031

PW OF CF -$135,000.00 -$2,830.19 -$2,669.99 -$2,518.86 -$2,376.28 -$2,241.77 -$2,114.88 -$1,995.17 -$1,882.24 -$1,775.70 -$1,675.18 -$1,580.36 -$1,490.91 -$1,406.52 -$1,326.90 -$1,251.80 -$1,180.94 -$1,114.09 -$1,051.03 -$991.54 -$5,612.49 -$882.47 -$832.52 -$785.39 -$740.94 -$699.00 -$659.43 -$622.10 -$586.89 -$553.67 -$522.33 -$492.76 -$464.87 -$438.56 -$413.73 -$390.32 -$368.22 -$347.38 -$327.72 -$309.17 -$1,750.00 -$275.16 -$259.58 -$244.89 -$231.03 -$217.95 -$205.61 -$193.97 -$183.00 -$172.64 -$162.87 -$153.65 -$144.95 -$136.74 -$129.00 -$121.70 -$114.81 -$108.31 -$102.18 -$96.40 -$90.94 -$189,619.69 <- PW 0.06188 <- (A|P i%,n) -$11,732.85 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S PV AND PMT FUNCTIONS AW = -$11,732.85 =-3000+PMT(6%,60,135000+PV(6%,20,,-15000)+PV(6%,40,,-15000)) SOLUTION USING FACTOR TABLES AW = -$3,000 + (-$135,000-$15,000(P|F 6%,20)-$15,000(P|F 6%,40))(A|P 6%,60) AW = -$3,000 + (-$135,000-$15,000(0.31180)-$15,000(0.09722))(0.06188) AW = -$11,733.45

PIPE B SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY PIPE EQUIPMENT M&E NET CF (P|F I%,N) 0 -$80,000.00 -$20,000.00 -$100,000.00 1.00000 1 -$4,000.00 -$4,000.00 0.94340 2 -$4,000.00 -$4,000.00 0.89000 3 -$4,000.00 -$4,000.00 0.83962 4 -$4,000.00 -$4,000.00 0.79209 5 -$4,000.00 -$4,000.00 0.74726 6 -$4,000.00 -$4,000.00 0.70496 7 -$4,000.00 -$4,000.00 0.66506 8 -$4,000.00 -$4,000.00 0.62741 9 -$4,000.00 -$4,000.00 0.59190 10 -$4,000.00 -$4,000.00 0.55839 11 -$4,000.00 -$4,000.00 0.52679 12 -$4,000.00 -$4,000.00 0.49697 13 -$4,000.00 -$4,000.00 0.46884 14 -$4,000.00 -$4,000.00 0.44230 15 -$4,000.00 -$4,000.00 0.41727 16 -$4,000.00 -$4,000.00 0.39365 17 -$4,000.00 -$4,000.00 0.37136 18 -$4,000.00 -$4,000.00 0.35034 19 -$4,000.00 -$4,000.00 0.33051 20 -$20,000.00 -$4,000.00 -$24,000.00 0.31180 21 -$4,000.00 -$4,000.00 0.29416 22 -$4,000.00 -$4,000.00 0.27751 23 -$4,000.00 -$4,000.00 0.26180 24 -$4,000.00 -$4,000.00 0.24698 25 -$4,000.00 -$4,000.00 0.23300 26 -$4,000.00 -$4,000.00 0.21981 27 -$4,000.00 -$4,000.00 0.20737 28 -$4,000.00 -$4,000.00 0.19563 29 -$4,000.00 -$4,000.00 0.18456 30 -$80,000.00 -$4,000.00 -$84,000.00 0.17411 31 -$4,000.00 -$4,000.00 0.16425 32 -$4,000.00 -$4,000.00 0.15496 33 -$4,000.00 -$4,000.00 0.14619 34 -$4,000.00 -$4,000.00 0.13791 35 -$4,000.00 -$4,000.00 0.13011 36 -$4,000.00 -$4,000.00 0.12274 37 -$4,000.00 -$4,000.00 0.11579 38 -$4,000.00 -$4,000.00 0.10924 39 -$4,000.00 -$4,000.00 0.10306 40 -$20,000.00 -$4,000.00 -$24,000.00 0.09722 41 -$4,000.00 -$4,000.00 0.09172 42 -$4,000.00 -$4,000.00 0.08653 43 -$4,000.00 -$4,000.00 0.08163 44 -$4,000.00 -$4,000.00 0.07701 45 -$4,000.00 -$4,000.00 0.07265 46 -$4,000.00 -$4,000.00 0.06854 47 -$4,000.00 -$4,000.00 0.06466 48 -$4,000.00 -$4,000.00 0.06100 49 -$4,000.00 -$4,000.00 0.05755 50 -$4,000.00 -$4,000.00 0.05429 51 -$4,000.00 -$4,000.00 0.05122 52 -$4,000.00 -$4,000.00 0.04832 53 -$4,000.00 -$4,000.00 0.04558 54 -$4,000.00 -$4,000.00 0.04300 55 -$4,000.00 -$4,000.00 0.04057 56 -$4,000.00 -$4,000.00 0.03827 57 -$4,000.00 -$4,000.00 0.03610 58 -$4,000.00 -$4,000.00 0.03406 59 -$4,000.00 -$4,000.00 0.03213 60 -$4,000.00 -$4,000.00 0.03031

PW OF CF -$100,000.00 -$3,773.58 -$3,559.99 -$3,358.48 -$3,168.37 -$2,989.03 -$2,819.84 -$2,660.23 -$2,509.65 -$2,367.59 -$2,233.58 -$2,107.15 -$1,987.88 -$1,875.36 -$1,769.20 -$1,669.06 -$1,574.59 -$1,485.46 -$1,401.38 -$1,322.05 -$7,483.31 -$1,176.62 -$1,110.02 -$1,047.19 -$987.91 -$931.99 -$879.24 -$829.47 -$782.52 -$738.23 -$14,625.25 -$657.02 -$619.83 -$584.74 -$551.65 -$520.42 -$490.96 -$463.17 -$436.96 -$412.22 -$2,333.33 -$366.88 -$346.11 -$326.52 -$308.04 -$290.60 -$274.15 -$258.63 -$243.99 -$230.18 -$217.15 -$204.86 -$193.27 -$182.33 -$172.01 -$162.27 -$153.08 -$144.42 -$136.24 -$128.53 -$121.26 -$186,755.06 <- PW 0.06188 <- (A|P i%,n) -$11,555.60 <- AW

DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S PV AND PMT FUNCTIONS AW = -$11,555.60 =-4000+PMT(6%,60,100000+PV(6%,20,,-20000)+PV(6%,40,,-20000)+PV(6%,30,,-80000)) SOLUTION USING FACTOR TABLES AW = -$4,000 + {-$100,00-$20,000(P|F 6%,20)-$20,000(P|F 6%,40)-$80,000(P|F 6%,30)}(A|P 6%,60) AW = -$4,000 + {-$100,000-$20,000(0.31180)-$20,000(0.09722)-$80,000(0.17411)}(0.06188) AW= -$11,556.12 PIPE B IS PREFERRED SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.55 a

A 7 YEAR PLANNING HORIZON IS USED WITH NO CASH FLOWS FOR ALTERNATIVE W IN YEARS 6 AND 7

ALT W SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 11.00% EOY ALT W (P|F i%,n) PW OF CF 0 -$100,000.00 1.00000 -$100,000.00 1 $20,000.00 0.90090 $18,018.02 2 $20,000.00 0.81162 $16,232.45 3 $50,000.00 0.73119 $36,559.57 4 $80,000.00 0.65873 $52,698.48 5 $110,000.00 0.59345 $65,279.65 6 $0.00 0.53464 $0.00 7 $0.00 0.48166 $0.00 $88,788.16 <- PW 0.21222 <- (A|P i%,n) $18,842.20 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $18,842.20 =-PMT(11%,7,NPV(11%,C11:C17)+C10) SOLUTION USING FACTOR TABLES AW = (-$100,000+$20,000(P|F 11%,1)+$20,000(P|F 11%,2)+$50,000(P|F 11,3)+$80,000(P|F 11%,4)+$110,000(P|F 11%,5))(A|P 11%,7) AW = (-$100,000+$20,000(0.90090)+$20,000(0.81162)+$50,000(0.73119)+$80,000(0.65873)+$110,000(0.59345))(0.21222) AW = $18,842.55

ALT X SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 11.00% EOY ALT W (P|F i%,n) PW OF CF 0 -$150,000.00 1.00000 -$150,000.00 1 $40,000.00 0.90090 $36,036.04 2 $45,000.00 0.81162 $36,523.01 3 $50,000.00 0.73119 $36,559.57 4 $55,000.00 0.65873 $36,230.20 5 $60,000.00 0.59345 $35,607.08 6 $65,000.00 0.53464 $34,751.65 7 $70,000.00 0.48166 $33,716.09 $99,423.64 <- PW 0.21222 <- (A|P i%,n) $21,099.21 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S NPV AND PMT FUNCTIONS AW = $21,099.21 =-PMT(11%,7,NPV(11%,C39:C45)+C38) SOLUTION USING FACTOR TABLES AW(X) = -$150,000(A|P 11%,7)+$40,000+$5,000(A|G 11%,7) AW(X) = -$150,000(0.21222)+$40,000+$5,000(2.58630) AW(X) = $21,098.50

ALTERNATIVE X IS PREFERRED SINCE IT HAS A HIGHER AW.

PROBLEM 7.56 NOTE THAT THE ESTIMATED LIVES ARE DIFFERENT SO A COMMON PLANNING HORIZON MUST BE ESTABLISHED. 10 YEARS IS SELECTED IN THE ANALYSIS BELOW. a

MODEL 127B SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 8.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$50,000.00 -$50,000.00 1.00000 -$50,000.00 1 $19,400.00 -$10,000.00 $9,400.00 0.92593 $8,703.70 2 $19,400.00 -$10,000.00 $9,400.00 0.85734 $8,058.98 3 $19,400.00 -$10,000.00 $9,400.00 0.79383 $7,462.02 4 $19,400.00 -$10,000.00 $9,400.00 0.73503 $6,909.28 5 $19,400.00 -$10,000.00 $9,400.00 0.68058 $6,397.48 6 $19,400.00 -$10,000.00 $9,400.00 0.63017 $5,923.59 7 $19,400.00 -$10,000.00 $9,400.00 0.58349 $5,484.81 8 $19,400.00 -$10,000.00 $9,400.00 0.54027 $5,078.53 9 $19,400.00 -$10,000.00 $9,400.00 0.50025 $4,702.34 10 $29,400.00 -$10,000.00 $19,400.00 0.46319 $8,985.95 $17,706.70 <- PW 0.14903 <- (A|P i%,n) $2,638.82 <- AW SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = $2,638.82 =9400+PMT(8%,10,50000,-10000) SOLUTION USING FACTOR TABLES AW = $9,400 - $50,000(A|P 8%,10) + $10,000(A|F 8%,10) AW = $9,400 - $50,000(0.14903) + $10,000(0.06903) AW = $2,638.80

MODEL 334A SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$80,000.00 -$80,000.00 1.00000 -$80,000.00 1 $26,000.00 -$6,000.00 $20,000.00 0.92593 $18,518.52 2 $26,000.00 -$6,000.00 $20,000.00 0.85734 $17,146.78 3 $26,000.00 -$6,000.00 $20,000.00 0.79383 $15,876.64 4 $26,000.00 -$6,000.00 $20,000.00 0.73503 $14,700.60 5 $26,000.00 -$86,000.00 -$60,000.00 0.68058 -$40,834.99 6 $26,000.00 -$6,000.00 $20,000.00 0.63017 $12,603.39 7 $26,000.00 -$6,000.00 $20,000.00 0.58349 $11,669.81 8 $26,000.00 -$6,000.00 $20,000.00 0.54027 $10,805.38 9 $26,000.00 -$6,000.00 $20,000.00 0.50025 $10,004.98 10 $26,000.00 -$6,000.00 $20,000.00 0.46319 $9,263.87 -$245.03 <- PW 0.14903 <- (A|P i%,n) -$36.52 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S PV AND PMT FUNCTIONS AW = -$36.52 =20000+PMT(8%,10,80000+PV(8%,5,,-80000)) SOLUTION USING FACTOR TABLES AW = $20,000 - $80,000(A|P 8%,10) - $80,000(P|F 8%,5)(A|P 8%,10) AW = $20,000 - $80,000(0.14903) - $80,000(0.68058)(0.14903) = -$36.55 AW = -$36.55 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST AW

OCTAVIA'S BAKERY SHOULD BUY MODEL 127B SINCE IT HAS THE HIGHEST AW.

PROBLEM 7.57 ORDER IS 127B, 334A SINCE "NULL" IS NOT IDENTIFIED AS AN OPTION, 127B BECOMES THE "CURRENT BEST" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 334A - 127B ARE NEEDED SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 8.00% EOY 334A 127B INCR. CF (P|F i%,n) PW 0 -$80,000.00 -$50,000.00 -$30,000.00 1.00000 -$30,000.00 1 $20,000.00 $9,400.00 $10,600.00 0.92593 $9,814.81 2 $20,000.00 $9,400.00 $10,600.00 0.85734 $9,087.79 3 $20,000.00 $9,400.00 $10,600.00 0.79383 $8,414.62 4 $20,000.00 $9,400.00 $10,600.00 0.73503 $7,791.32 5 -$60,000.00 $9,400.00 -$69,400.00 0.68058 -$47,232.47 6 $20,000.00 $9,400.00 $10,600.00 0.63017 $6,679.80 7 $20,000.00 $9,400.00 $10,600.00 0.58349 $6,185.00 8 $20,000.00 $9,400.00 $10,600.00 0.54027 $5,726.85 9 $20,000.00 $9,400.00 $10,600.00 0.50025 $5,302.64 10 $20,000.00 $19,400.00 $600.00 0.46319 $277.92 -$17,951.73 <- PW 0.14903 <- (A|P i%,n) -$2,675.34 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S PV AND PMT FUNCTIONS AW = -$2,675.34 =10600+PMT(8%,10,30000+PV(8%,5,,-80000),10000) SOLUTION USING FACTOR TABLES AW = $10,600 - $30,000(A|P 8%,10) -$80,000(P|F 8%,5)(A|P 8%,10) - $10,000(A|F 8%,10) AW = $10,600 - $30,000(0.14903) - $80,000(0.68058)(0.14903) - $10,000(0.06903) = -$2,675.35 AW = -$2,675.35 SINCE THE AW OF THE INCREMENT IS NEGATIVE, THE INCREMENTAL INVESTMENT IS REJECTED 127B REMAINS CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, 127B IS PREFERRED

PROBLEM 7.58 NOTE THAT THE ESTIMATED LIVES ARE DIFFERENT SO A COMMON PLANNING HORIZON MUST BE ESTABLISHED. 24 YEARS IS SELECTED IN THE ANALYSIS BELOW. SOLVE USING PW AND THEN AW a

STRUCTURE Y SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR 5.00% EOY + CF - CF NET CF (P|F i%,n) PW OF CF 0 -$4,500.00 -$4,500.00 1.00000 -$4,500.00 1 -$1,000.00 -$1,000.00 0.95238 -$952.38 2 -$1,000.00 -$1,000.00 0.90703 -$907.03 3 -$1,000.00 -$1,000.00 0.86384 -$863.84 4 -$1,000.00 -$1,000.00 0.82270 -$822.70 5 -$1,000.00 -$1,000.00 0.78353 -$783.53 6 -$1,000.00 -$1,000.00 0.74622 -$746.22 7 -$1,000.00 -$1,000.00 0.71068 -$710.68 8 -$1,000.00 -$1,000.00 0.67684 -$676.84 9 -$1,000.00 -$1,000.00 0.64461 -$644.61 10 -$1,000.00 -$1,000.00 0.61391 -$613.91 11 -$1,000.00 -$1,000.00 0.58468 -$584.68 12 -$5,500.00 -$5,500.00 0.55684 -$3,062.61 13 -$1,000.00 -$1,000.00 0.53032 -$530.32 14 -$1,000.00 -$1,000.00 0.50507 -$505.07 15 -$1,000.00 -$1,000.00 0.48102 -$481.02 16 -$1,000.00 -$1,000.00 0.45811 -$458.11 17 -$1,000.00 -$1,000.00 0.43630 -$436.30 18 -$1,000.00 -$1,000.00 0.41552 -$415.52 19 -$1,000.00 -$1,000.00 0.39573 -$395.73 20 -$1,000.00 -$1,000.00 0.37689 -$376.89 21 -$1,000.00 -$1,000.00 0.35894 -$358.94 22 -$1,000.00 -$1,000.00 0.34185 -$341.85 23 -$1,000.00 -$1,000.00 0.32557 -$325.57 24 -$1,000.00 -$1,000.00 0.31007 -$310.07 -$20,804.41 <- PW 0.07247 <- (A|P i%,n) -$1,507.71 <- AW DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S PMT FUNCTION IS NOT USED TO COMPUTE AW DIRECTLY. SOLUTION USING EXCEL'S PV AND PMT FUNCTIONS AW = -$1,507.71 =-1000+PMT(5%,24,4500+PV(5%,12,,-4500)) SOLUTION USING FACTOR TABLES AW = -$1,000 - $4,500(A|P 5%,24) - $4,500(P|F 5%,12)(A|P 5%,24) AW = -$1,000 - $4,500(0.07247) - $4,500(0.55684)(0.07247) AW = -$1,507.71

STRUCTURE Z EOY 0 1 2 3 4 5

+ CF

- CF -$10,000.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00

NET CF -$10,000.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00

(P|F i%,n) 1.00000 0.95238 0.90703 0.86384 0.82270 0.78353

PW OF CF -$10,000.00 -$685.71 -$653.06 -$621.96 -$592.35 -$564.14

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

$1,800.00

-$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00

-$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 $1,080.00

0.74622 0.71068 0.67684 0.64461 0.61391 0.58468 0.55684 0.53032 0.50507 0.48102 0.45811 0.43630 0.41552 0.39573 0.37689 0.35894 0.34185 0.32557 0.31007

-$537.28 -$511.69 -$487.32 -$464.12 -$442.02 -$420.97 -$400.92 -$381.83 -$363.65 -$346.33 -$329.84 -$314.13 -$299.17 -$284.93 -$271.36 -$258.44 -$246.13 -$234.41 $334.87 -$19,376.90 <- PW 0.07247 <- (A|P i%,n) -$1,404.26 <- AW

SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY AW = -$1,404.26 =-720+PMT(5%,24,10000,-1800) SOLUTION USING FACTOR TABLES AW = -$720 - $10,000(A|P 5%,24) + $1,800(A|F 5%,24) AW = -$720.00 - $10,000(0.07247) + $1,800(0.02247) AW = -$1,404.25 b

DECISION RULE SELECT THE PROJECT WITH THE HIGHEST AW

THE MILITARY BASE SHOULD SELECT STRUCTURE Z

PROBLEM 7.59 n

PROBLEM 7.60 SOLUTION USING FACTOR VALUES n 1 2 3 4 5 6

P $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00

F $50,000.00 $30,000.00 $20,000.00 $10,000.00 $5,000.00 $2,000.00

8.00% (A|F i%,n) 1.00000 0.48077 0.30803 0.22192 0.17046 0.13632

CR $25,600.00 =((C6-D6)*E6)+(C6*E$4) $24,830.77 =((C7-D7)*E7)+(C7*E$4) $21,001.68 FORMULA REPEATS SIMILARLY $18,915.25 $16,679.67 $14,869.45

SOLUTION USING EXCEL'S PMT FUNCTION n P F CR 1 $70,000.00 $50,000.00 $25,600.00 =-PMT(8%,B16,C16,-D16) 2 $70,000.00 $30,000.00 $24,830.77 =-PMT(8%,B17,C17,-D17) 3 $70,000.00 $20,000.00 $21,001.68 FORMULA REPEATS SIMILARLY 4 $70,000.00 $10,000.00 $18,915.25 5 $70,000.00 $5,000.00 $16,679.67 6 $70,000.00 $2,000.00 $14,869.45

PROBLEM 7.61 n

PROBLEM 7.62 MODEL 127B TABLE OF CASH FLOWS EOY + CF - CF 0 -$50,000.00 1 $19,400.00 -$10,000.00 2 $19,400.00 -$10,000.00 3 $19,400.00 -$10,000.00 4 $19,400.00 -$10,000.00 5 $19,400.00 -$10,000.00 6 $19,400.00 -$10,000.00 7 $19,400.00 -$10,000.00 8 $19,400.00 -$10,000.00 9 $19,400.00 -$10,000.00 10 $29,400.00 -$10,000.00

NET CF -$50,000.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $9,400.00 $19,400.00

SOLUTION USING FACTOR TABLES CR = $50,000(A|P 8%,10) - $10,000(A|F 8%,10) CR = $50,000(0.14903) - $10,000(0.06903) CR = $6,761.20 SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY CR = $6,761.18 = -PMT(8%,10,50000,-10000)

PROBLEM 7.63 MODEL 334A TABLE OF CASH FLOWS EOY + CF 0 1 $26,000.00 2 $26,000.00 3 $26,000.00 4 $26,000.00 5 $26,000.00

- CF -$80,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00

NET CF -$80,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

SOLUTION USING FACTOR TABLES CR = $80,000(A|P 8%,5) - $0(A|F 8%,5) CR = $80,000(0.25046) CR = $20,036.80 SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY CR = $20,036.52 = -PMT(8%,5,80000)

PROBLEM 7.64 SOLUTION USING FACTOR TABLES CR = $70,000(A|P 8%,6) - $2,000(A|F 8%,6) CR = $70,000(0.21632) - $2,000(0.13632) CR = $14,869.76 SOLUTION USING EXCEL'S PMT FUNCTION DIRECTLY CR = $14,869.45 = -PMT(8%,6,70000,-2000)

PROBLEM 7.65 STARTING WITH A VALUE OF n=1 AND INCREASING n IN 1 YEAR INCREMENTS UNTIL CR IS LESS THAN OR EQUAL TO $3,000 YIELDS THE FOLLOWING: SOLUTION USING FACTOR VALUES N 1 2 3 4 5 6 7 8 9 10 11 12 13 14

P $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

F $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00

12.00% (A|F i%,n) 1.00000 0.47170 0.29635 0.20923 0.15741 0.12323 0.09912 0.08130 0.06768 0.05698 0.04842 0.04144 0.03568 0.03087

CR $21,400.00 =((C10-D10)*E10)+(C10*E$8) $11,362.26 =((C11-D11)*E11)+(C11*E$8) $8,030.63 FORMULA REPEATS SIMILARLY $6,375.45 $5,390.78 $4,741.29 $4,283.24 $3,944.75 $3,685.90 $3,482.70 $3,319.89 $3,187.30 $3,077.87 $2,986.55

SOLUTION USING EXCEL'S PMT FUNCTION N P F CR 1 $20,000.00 $1,000.00 $21,400.00 =-PMT(12%,B27,C27,-D27) 2 $20,000.00 $1,000.00 $11,362.26 =-PMT(12%,B28,C28,-D28) 3 $20,000.00 $1,000.00 $8,030.63 FORMULA REPEATS SIMILARLY 4 $20,000.00 $1,000.00 $6,375.45 5 $20,000.00 $1,000.00 $5,390.78 6 $20,000.00 $1,000.00 $4,741.29 7 $20,000.00 $1,000.00 $4,283.24 8 $20,000.00 $1,000.00 $3,944.75 9 $20,000.00 $1,000.00 $3,685.90 10 $20,000.00 $1,000.00 $3,482.70 11 $20,000.00 $1,000.00 $3,319.89 12 $20,000.00 $1,000.00 $3,187.30 13 $20,000.00 $1,000.00 $3,077.87 14 $20,000.00 $1,000.00 $2,986.55

THE ELECTROMAGNET MUST LAST AT LEAST 14 YEARS FOR THE CAPITAL RECOVERY COST TO BE LESS THAN $3,000 PER YEAR

PROBLEM 7.66

8.00% F (A|F i%,n) $1,000.00 1.00000 $1,000.00 0.48077 $1,000.00 0.30803 $1,000.00 0.22192 $1,000.00 0.17046 $1,000.00 0.13632 $1,000.00 0.11207 $1,000.00 0.09401 $1,000.00 0.08008 $1,000.00 0.06903 $1,000.00 0.06008 $1,000.00 0.05270 $1,000.00 0.04652 $1,000.00 0.04130 $1,000.00 0.03683 $1,000.00 0.03298 $1,000.00 0.02963 $1,000.00 0.02670 $1,000.00 0.02413 $1,000.00 0.02185 $1,000.00 0.01983 $1,000.00 0.01803 $1,000.00 0.01642 $1,000.00 0.01498 $1,000.00 0.01368

Capital Recovery

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

PROBLEM 7.67

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

P $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

F $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00

8.00% (A|F i%,n) 1.00000 0.48077 0.30803 0.22192 0.17046 0.13632 0.11207 0.09401 0.08008 0.06903 0.06008 0.05270 0.04652 0.04130 0.03683 0.03298 0.02963 0.02670 0.02413 0.02185 0.01983 0.01803 0.01642 0.01498 0.01368 0.01251 0.01145 0.01049 0.00962 0.00883 0.00811 0.00745 0.00685 0.00630 0.00580 0.00534 0.00492 0.00454 0.00419 0.00386 0.00356 0.00329 0.00303 0.00280 0.00259 0.00239 0.00221 0.00204 0.00189 0.00174 0.00161 0.00149 0.00138 0.00127 0.00118 0.00109 0.00101

CR $20,600.00 =((C6-D6)*E6)+(C6*E$4) OR =-PMT(8%,B6,C6,-D6) $10,734.62 =((C7-D7)*E7)+(C7*E$4) OR =-PMT(8%,B7,C7,-D7) $7,452.64 FORMULA REPEATS SIMILARLY $5,816.50 $4,838.67 $4,189.99 $3,729.38 Capital Recovery Cost versus Life $3,386.28 $3,121.51 P=$20,000; F=various; MARR=8% $2,911.56 $2,741.45 $25,000.00 $2,601.21 $2,483.91 $2,384.64 $20,000.00 $2,299.76 $2,226.56 $15,000.00 $2,162.96 $2,107.34 $10,000.00 $2,058.42 $2,015.19 $1,976.81 $5,000.00 $1,942.61 $1,912.02 $0.00 $1,884.58 0 20 40 60 80 $1,859.90 $1,837.64 Life (years) $1,817.51 $1,799.29 $1,782.75 $1,767.72 $1,754.04 $1,741.57 $1,730.18 $1,719.78 $1,710.26 $1,701.55 $1,693.56 $1,686.24 $1,679.52 $1,673.34 $1,667.67 $1,662.45 $1,657.65 $1,653.23 $1,649.16 $1,645.41 $1,641.95 $1,638.77 $1,635.83 $1,633.11 $1,630.61 $1,628.30 $1,626.17 $1,624.20 $1,622.38 $1,620.70 $1,619.15

Capital Recovery

$1,000 $2,000 $0 $15,000

100

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 b

$1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00

0.00093 0.00086 0.00080 0.00074 0.00068 0.00063 0.00058 0.00054 0.00050 0.00046 0.00043 0.00040 0.00037 0.00034 0.00031 0.00029 0.00027 0.00025 0.00023 0.00021 0.00020 0.00018 0.00017 0.00016 0.00015 0.00013 0.00012 0.00012 0.00011 0.00010 0.00009 0.00008 0.00008 0.00007 0.00007 0.00006 0.00006 0.00005 0.00005 0.00005 0.00004 0.00004 0.00004

$1,617.71 $1,616.39 $1,615.16 $1,614.03 $1,612.98 $1,612.01 $1,611.11 $1,610.29 $1,609.52 $1,608.81 $1,608.15 $1,607.55 $1,606.99 $1,606.47 $1,605.98 $1,605.54 $1,605.13 $1,604.75 $1,604.39 $1,604.07 $1,603.77 $1,603.49 $1,603.23 $1,602.99 $1,602.77 $1,602.56 $1,602.37 $1,602.20 $1,602.03 $1,601.88 $1,601.74 $1,601.61 $1,601.49 $1,601.38 $1,601.28 $1,601.19 $1,601.10 $1,601.02 $1,600.94 $1,600.87 $1,600.81 $1,600.75 $1,600.69

8.00% (A|F i%,n) 1.00000 0.48077 0.30803 0.22192 0.17046 0.13632 0.11207 0.09401 0.08008 0.06903 0.06008 0.05270 0.04652 0.04130

CR $19,600.00 $10,253.85 $7,144.60 $5,594.57 $4,668.22 $4,053.68 $3,617.30 $3,292.27 $3,041.43 $2,842.53 $2,681.37 $2,548.51 $2,437.39 $2,343.34

ESTIMATE OF ASYMPTOTIC LIMIT = $1,600

c N 1 2 3 4 5 6 7 8 9 10 11 12 13 14

P $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

F $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76

$20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00 $20,000.00

$2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

0.03683 0.03298 0.02963 0.02670 0.02413 0.02185 0.01983 0.01803 0.01642 0.01498 0.01368 0.01251 0.01145 0.01049 0.00962 0.00883 0.00811 0.00745 0.00685 0.00630 0.00580 0.00534 0.00492 0.00454 0.00419 0.00386 0.00356 0.00329 0.00303 0.00280 0.00259 0.00239 0.00221 0.00204 0.00189 0.00174 0.00161 0.00149 0.00138 0.00127 0.00118 0.00109 0.00101 0.00093 0.00086 0.00080 0.00074 0.00068 0.00063 0.00058 0.00054 0.00050 0.00046 0.00043 0.00040 0.00037 0.00034 0.00031 0.00029 0.00027 0.00025 0.00023

$2,262.93 $2,193.58 $2,133.33 $2,080.64 $2,034.30 $1,993.34 $1,956.98 $1,924.58 $1,895.60 $1,869.60 $1,846.22 $1,825.13 $1,806.07 $1,788.80 $1,773.13 $1,758.89 $1,745.93 $1,734.11 $1,723.33 $1,713.47 $1,704.46 $1,696.20 $1,688.64 $1,681.70 $1,675.33 $1,669.48 $1,664.11 $1,659.16 $1,654.61 $1,650.43 $1,646.57 $1,643.02 $1,639.74 $1,636.72 $1,633.94 $1,631.37 $1,629.00 $1,626.81 $1,624.79 $1,622.93 $1,621.20 $1,619.61 $1,618.14 $1,616.78 $1,615.52 $1,614.36 $1,613.29 $1,612.30 $1,611.38 $1,610.53 $1,609.74 $1,609.02 $1,608.35 $1,607.72 $1,607.15 $1,606.62 $1,606.13 $1,605.67 $1,605.25 $1,604.86 $1,604.50 $1,604.16

77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

d F $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

0.00021 0.00020 0.00018 0.00017 0.00016 0.00015 0.00013 0.00012 0.00012 0.00011 0.00010 0.00009 0.00008 0.00008 0.00007 0.00007 0.00006 0.00006 0.00005 0.00005 0.00005 0.00004 0.00004 0.00004

$1,603.85 $1,603.57 $1,603.30 $1,603.06 $1,602.83 $1,602.62 $1,602.43 $1,602.25 $1,602.08 $1,601.93 $1,601.78 $1,601.65 $1,601.53 $1,601.41 $1,601.31 $1,601.21 $1,601.12 $1,601.04 $1,600.96 $1,600.89 $1,600.83 $1,600.76 $1,600.71 $1,600.65

CR $21,600.00 $11,215.38 $7,760.67 $6,038.42 $5,009.13 $4,326.31 $3,841.45 $3,480.30 $3,201.59 $2,980.59 $2,801.53 $2,653.90 $2,530.44 $2,425.94 $2,336.59 $2,259.54 $2,192.59 $2,134.04 $2,082.55 $2,037.04 $1,996.65 $1,960.64 $1,928.44 $1,899.56 $1,873.58 $1,850.14 $1,828.96 $1,809.78 $1,792.37 $1,776.55 $1,762.15 $1,749.02 $1,737.03 $1,726.08

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

0.00580 0.00534 0.00492 0.00454 0.00419 0.00386 0.00356 0.00329 0.00303 0.00280 0.00259 0.00239 0.00221 0.00204 0.00189 0.00174 0.00161 0.00149 0.00138 0.00127 0.00118 0.00109 0.00101 0.00093 0.00086 0.00080 0.00074 0.00068 0.00063 0.00058 0.00054 0.00050 0.00046 0.00043 0.00040 0.00037 0.00034 0.00031 0.00029 0.00027 0.00025 0.00023 0.00021 0.00020 0.00018 0.00017 0.00016 0.00015 0.00013 0.00012 0.00012 0.00011 0.00010 0.00009 0.00008 0.00008 0.00007 0.00007 0.00006 0.00006 0.00005 0.00005

$1,716.07 $1,706.89 $1,698.49 $1,690.78 $1,683.70 $1,677.20 $1,671.23 $1,665.74 $1,660.68 $1,656.03 $1,651.75 $1,647.80 $1,644.16 $1,640.81 $1,637.71 $1,634.86 $1,632.22 $1,629.79 $1,627.55 $1,625.47 $1,623.56 $1,621.79 $1,620.16 $1,618.65 $1,617.25 $1,615.96 $1,614.77 $1,613.66 $1,612.64 $1,611.70 $1,610.83 $1,610.02 $1,609.27 $1,608.58 $1,607.94 $1,607.35 $1,606.81 $1,606.30 $1,605.83 $1,605.40 $1,605.00 $1,604.63 $1,604.28 $1,603.96 $1,603.67 $1,603.40 $1,603.15 $1,602.91 $1,602.70 $1,602.50 $1,602.31 $1,602.14 $1,601.98 $1,601.83 $1,601.70 $1,601.57 $1,601.46 $1,601.35 $1,601.25 $1,601.16 $1,601.07 $1,600.99

97 98 99 100

$20,000.00 $20,000.00 $20,000.00 $20,000.00

$0.00 $0.00 $0.00 $0.00

0.00005 0.00004 0.00004 0.00004

$1,600.92 $1,600.85 $1,600.79 $1,600.73

F $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00

CR $6,600.00 $4,003.85 $3,140.17 $2,709.60 $2,452.28 $2,281.58 $2,160.36 $2,070.07 $2,000.40 $1,945.15 $1,900.38 $1,863.48 $1,832.61 $1,806.48 $1,784.15 $1,764.88 $1,748.15 $1,733.51 $1,720.64 $1,709.26 $1,699.16 $1,690.16 $1,682.11 $1,674.89 $1,668.39 $1,662.54 $1,657.24 $1,652.44 $1,648.09 $1,644.14 $1,640.54 $1,637.25 $1,634.26 $1,631.52 $1,629.02 $1,626.72 $1,624.62 $1,622.69 $1,620.93 $1,619.30 $1,617.81 $1,616.43 $1,615.17 $1,614.01 $1,612.94 $1,611.95 $1,611.04 $1,610.20 $1,609.43 $1,608.71 $1,608.06 $1,607.45 $1,606.89 $1,606.37

e N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

$15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00

0.00118 0.00109 0.00101 0.00093 0.00086 0.00080 0.00074 0.00068 0.00063 0.00058 0.00054 0.00050 0.00046 0.00043 0.00040 0.00037 0.00034 0.00031 0.00029 0.00027 0.00025 0.00023 0.00021 0.00020 0.00018 0.00017 0.00016 0.00015 0.00013 0.00012 0.00012 0.00011 0.00010 0.00009 0.00008 0.00008 0.00007 0.00007 0.00006 0.00006 0.00005 0.00005 0.00005 0.00004 0.00004 0.00004

$1,605.89 $1,605.45 $1,605.04 $1,604.66 $1,604.31 $1,603.99 $1,603.69 $1,603.42 $1,603.16 $1,602.92 $1,602.71 $1,602.50 $1,602.32 $1,602.15 $1,601.99 $1,601.84 $1,601.70 $1,601.57 $1,601.46 $1,601.35 $1,601.25 $1,601.16 $1,601.07 $1,600.99 $1,600.92 $1,600.85 $1,600.79 $1,600.73 $1,600.67 $1,600.62 $1,600.58 $1,600.53 $1,600.50 $1,600.46 $1,600.42 $1,600.39 $1,600.36 $1,600.34 $1,600.31 $1,600.29 $1,600.27 $1,600.25 $1,600.23 $1,600.21 $1,600.20 $1,600.18

STARTING WITH EQUATION 7.3 CR = P(A|P i%,n) - F(A|F i%,n) USING THE LIMITING CASES FROM TABLE 2.8 AS n GOES TO INFINITY, P(A|P i%,n) GOES TO P(i) AS n GOES TO INFINITY, F(A|F i%,n) GOES TO ZERO THEREFORE, AS n GOES TO INFINITY CR = P(i) - 0 = P(i)

FOR THE PROBLEM CR = Pi = $20,000(0.08) = $1,600.00 THIS VALUE IS CONSISTENT WITH THE RESULTS FROM PARTS a - e

PROBLEM 8.1 a b c d e f

RANKING APPROACH AND INCREMENTAL APPROACH INCREMENTAL APPROACH ONLY RANKING APPROACH AND INCREMENTAL APPROACH INCREMENTAL APPROACH ONLY INCREMENTAL APPROACH ONLY RANKING APPROACH AND INCREMENTAL APPROACH

PROBLEM 8.2 a b c d e f

DOLLARS PERCENTAGE DOLLARS PERCENTAGE PERCENTAGE DOLLARS

PROBLEM 8.3 a b

ONE SIGN CHANGE, THEREFORE, ONE POSITIVE REAL ROOT EOY 0 1 2 3 4 5 6

CF CUM CF -$100.00 -$100.00 $15.00 -$85.00 $15.00 -$70.00 $15.00 -$55.00 $15.00 -$40.00 $15.00 -$25.00 $15.00 -$10.00

NO SIGN CHANGE, THEREFORE, NO CONCLUSION CAN BE DRAWN c

EOY 0 1 2 3 4 5 6

CF -$100.00 $15.00 $15.00 $15.00 $15.00 $15.00 $15.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = -2.93% =IRR(C17:C23) SOLUTION USING EXCEL'S RATE FUNCTION IRR = -2.93% =RATE(6,15,-100) THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= -2.93% NPV = $0.00 =NPV(C35,C18:C23)+C17 SOLVER PARAMETERS SET TARGET CELL: C36 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C35 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= -2.93% NPV = $0.00 =NPV(C44,C18:C23)+C17 SOLVER PARAMETERS SET TARGET CELL: C45 VALUE OF: 0 BY CHANGING CELL: C44 CLICK "SOLVE" d

IRR < MARR; THEREFORE, NOT ATTRACTIVE

PROBLEM 8.4 a b

ONE SIGN CHANGE, THEREFORE, ONE POSITIVE REAL ROOT EOY 0 1 2 3 4 5 6

CF CUM CF -$100.00 -$100.00 $25.00 -$75.00 $25.00 -$50.00 $25.00 -$25.00 $25.00 $0.00 $25.00 $25.00 $25.00 $50.00

ONE SIGN CHANGE, THEREFORE, UNIQUE POSITIVE REAL ROOT c

EOY 0 1 2 3 4 5 6

CF -$100.00 $25.00 $25.00 $25.00 $25.00 $25.00 $25.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 12.98% =IRR(C17:C23) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 12.98% =RATE(6,25,-100) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 12.00% $2.79 IRR $0.00 15.00% -$5.39 IRR = 13.02% =B33+(B35-B33)*(C34-C33)/(C35-C33) SOLUTION USING EXCEL'S SOLVER i= 12.98% NPV = $0.00 =NPV(C39,C18:C23)+C17 SOLVER PARAMETERS SET TARGET CELL: C40 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C39 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 12.98% NPV = $0.00 =NPV(C48,C18:C23)+C17 SOLVER PARAMETERS SET TARGET CELL: C49 VALUE OF: 0 BY CHANGING CELL: C48 CLICK "SOLVE" d

IRR >= MARR; THEREFORE, ATTRACTIVE

PROBLEM 8.5

THREE SIGN CHANGES, THEREFORE, EITHER 3 OR 1 POSITIVE REAL ROOTS EOY 0 1 2 3 4 5 6

CF CUM CF -$100.00 -$100.00 $25.00 -$75.00 $25.00 -$50.00 $60.00 $10.00 -$30.00 -$20.00 $60.00 $40.00 $25.00 $65.00

MULTIPLE SIGN CHANGES, THEREFORE, NO CONCLUSION CAN BE DRAWN c

EOY 0 1 2 3 4 5 6

CF -$100.00 $25.00 $25.00 $60.00 -$30.00 $60.00 $25.00

THE GRAPH TO THE RIGHT INDICATES THE PRESENCE OF A SINGLE ROOT SOLUTION USING EXCEL'S IRR FUNCTION IRR = 16.31% =IRR(C17:C23) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $3.58 IRR $0.00 18.00% -$4.33 IRR = 16.36% =B35+(B37-B35)*(C36-C35)/(C37-C35) SOLUTION USING EXCEL'S SOLVER i= 16.31% NPV = $0.00 =NPV(C41,C18:C23)+C17 SOLVER PARAMETERS SET TARGET CELL: C42 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C41 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 16.31% NPV = $0.00 =NPV(C50,C18:C23)+C17 SOLVER PARAMETERS SET TARGET CELL: C51 VALUE OF: 0 BY CHANGING CELL: C50 CLICK "SOLVE" d

IRR >= MARR; THEREFORE, ATTRACTIVE

GRAPHIC PRESENTATION OF PW VERSUS i i

PW 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% 12.00% 13.00% 14.00% 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% 21.00% 22.00% 23.00% 24.00% 25.00% 26.00% 27.00% 28.00% 29.00% 30.00% 31.00% 32.00% 33.00% 34.00% 35.00% 36.00% 37.00% 38.00% 39.00% 40.00% 41.00% 42.00% 43.00% 44.00% 45.00% 46.00% 47.00% 48.00% 49.00% 50.00%

$65.00 =$C$17+NPV(K6,$C$18:$C$23) $59.30 =$C$17+NPV(K7,$C$18:$C$23) $53.91 OTHER EQUATIONS ARE SIMILAR $48.78 $43.92 $39.30 $34.91 $30.73 $26.75 $22.96 $80.00 $19.34 $15.90 $12.60 $60.00 $9.46 $6.45 $40.00 $3.58 $0.83 -$1.80 $20.00 -$4.33 -$6.75 $0.00 -$9.07 0% 10% -$11.29 -$13.43 -$20.00 -$15.48 -$17.46 -$40.00 -$19.35 -$21.18 -$22.94 -$60.00 -$24.63 -$26.26 -$27.83 -$29.35 -$30.81 -$32.22 -$33.58 -$34.90 -$36.17 -$37.40 -$38.59 -$39.74 -$40.85 -$41.93 -$42.98 -$43.99 -$44.97 -$45.92 -$46.85 -$47.74 -$48.61 -$49.45 -$50.27 VALUES OF PW

PW VERSUS i

20%

30%

VALUES OF i

40%

50%

60%

PROBLEM 8.6

FOUR SIGN CHANGES, THEREFORE, EITHER 4, 2, OR 0 POSITIVE REAL ROOTS EOY 0 1 2 3 4 5 6

CF CUM CF -$100.00 -$100.00 $25.00 -$75.00 $200.00 $125.00 -$100.00 $25.00 $250.00 $275.00 -$200.00 $75.00 -$100.00 -$25.00

MULTIPLE SIGN CHANGES, THEREFORE, NO CONCLUSION c

EOY 0 1 2 3 4 5 6

CF -$100.00 $25.00 $200.00 -$100.00 $250.00 -$200.00 -$100.00

BY EXAMINING THE GRAPH OF PW VS i, TWO ROOTS ARE APPARENT BY USING THE [GUESS] OPTION OF EXCEL'S IRR FUNCTION, THESE TWO ROOTS CAN BE LOCATED IRR = IRR(CF_COLUMN, GUESS) IRR = 8.08% =IRR(C17:C23,10%) IRR = 37.43% =IRR(C17:C23,40%) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 8.00% -$0.14 IRR $0.00 9.00% $1.55 IRR = 8.08% =B38+(B40-B38)*(C39-C38)/(C40-C38) AND i% NPV 30.00% $5.01 IRR $0.00 40.00% -$1.94 IRR = 37.21% =B44+(B46-B44)*(C45-C44)/(C46-C44) DUE TO MULTIPLE ROOTS EXCEL'S SOLVER IS NOT USED TO COMPUTE IRR DUE TO MULTIPLE ROOTS EXCEL'S GOAL SEEK IS NOT USED TO COMPUTE IRR d

SINCE THE PW OF THE INVESTMENT AT MARR IS POSITIVE, THE INVESTMENT IS ATTRACTIVE

GRAPHIC PRESENTATION OF PW VERSUS i i 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% 12.00% 13.00% 14.00% 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% 21.00% 22.00% 23.00% 24.00% 25.00% 26.00% 27.00% 28.00% 29.00% 30.00% 31.00% 32.00% 33.00% 34.00% 35.00% 36.00% 37.00% 38.00% 39.00% 40.00% 41.00% 42.00% 43.00% 44.00% 45.00% 46.00% 47.00% 48.00% 49.00% 50.00%

PW -$25.00 =NPV(K6,C$7:C$12)+C$6 -$20.50 =NPV(K7,C$7:C$12)+C$6 -$16.47 OTHER EQUATIONS ARE SIMILAR -$12.87 -$9.67 -$6.82 PW versus i -$4.30 -$2.09 -$0.14 $15.00 $1.55 $10.00 $3.01 $4.26 $5.00 $5.31 $6.19 $0.00 $6.91 0% 10% 20% 30% 40% $7.49 -$5.00 $7.92 $8.24 -$10.00 $8.44 -$15.00 $8.54 $8.55 -$20.00 $8.47 $8.32 -$25.00 $8.09 $7.80 -$30.00 $7.45 VALUES OF i $7.05 $6.60 $6.11 $5.57 $5.01 $4.41 $3.78 $3.13 $2.45 $1.76 $1.05 $0.32 -$0.42 -$1.17 -$1.94 -$2.71 -$3.48 -$4.27 -$5.05 -$5.84 -$6.64 -$7.43 -$8.22 -$9.02 -$9.81 VALUES OF PW

50%

60%

a b

SIX SIGN CHANGES, THEREFORE, EITHER 6, 4, 2, OR 0 POSITIVE REAL ROOTS EOY 0 1 2 3 4 5 6

CF CUM CF -$100.00 -$100.00 $800.00 $700.00 -$750.00 -$50.00 $900.00 $850.00 -$950.00 -$100.00 $700.00 $600.00 -$800.00 -$200.00

MULTIPLE SIGN CHANGES, THEREFORE, NO CONCLUSION c

EOY 0 1 2 3 4 5 6

CF -$100.00 $800.00 -$750.00 $900.00 -$950.00 $700.00 -$800.00

BY EXAMINING THE GRAPH OF PW VS i, TWO ROOTS ARE APPARENT BY USING THE [GUESS] OPTION OF EXCEL'S IRR FUNCTION, THESE TWO ROOTS CAN BE LOCATED IRR = IRR(CF_COLUMN, GUESS) IRR = 8.84% =IRR(C17:C23,10%) IRR = 609.77% =IRR(C17:C23,600%) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 8.00% -$13.82 IRR $0.00 9.00% $2.58 IRR = 8.84% =B38+(B40-B38)*(C39-C38)/(C40-C38) THE SECOND ROOT IS OUTSIDE THE RANGE OF THE INTEREST TABLES DUE TO MULTIPLE ROOTS EXCEL'S SOLVER IS NOT USED TO COMPUTE IRR DUE TO MULTIPLE ROOTS EXCEL'S GOAL SEEK IS NOT USED TO COMPUTE IRR d

SINCE THE PW OF THE INVESTMENT AT MARR IS POSITIVE, THE INVESTMENT IS ATTRACTIVE

PRINTING NOTE: DUE TO i VALUES UP TO 700%, THE PRINTOUT IS LONG. CONSIDER PRINTING ONLY THE FIRST 1 OR 2 PAGES. GRAPHIC PRESENTATION OF PW VERSUS i i 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 9.00% 10.00% 11.00% 12.00% 13.00% 14.00% 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% 21.00% 22.00% 23.00% 24.00% 25.00% 26.00% 27.00% 28.00% 29.00% 30.00% 31.00% 32.00% 33.00% 34.00% 35.00% 36.00% 37.00% 38.00% 39.00% 40.00% 41.00% 42.00% 43.00% 44.00% 45.00% 46.00% 47.00% 48.00% 49.00% 50.00% 51.00% 52.00% 53.00%

PW -$200.00 =NPV(K6,C$7:C$12)+C$6 -$170.15 =NPV(K7,C$7:C$12)+C$6 -$142.49 OTHER EQUATIONS ARE SIMILAR -$116.84 -$93.06 -$70.98 PW versus i -$50.50 -$31.48 $250.00 -$13.82 $2.58 $200.00 $17.82 $31.98 $150.00 $45.14 $100.00 $57.37 $68.74 $50.00 $79.31 $89.12 $0.00 0% 100% 200% 300% 400% $98.25 -$50.00 $106.73 $114.60 -$100.00 $121.92 -$150.00 $128.72 $135.02 -$200.00 $140.88 $146.31 -$250.00 $151.34 VALUES OF i $156.00 $160.32 $164.32 $168.01 $171.42 $174.56 $177.45 $180.12 $182.56 $184.81 $186.86 $188.73 $190.43 $191.98 $193.38 $194.64 $195.76 $196.77 $197.66 $198.45 $199.13 $199.72 $200.21 $200.63 $200.96 $201.22 $201.41 $201.53 VALUES OF PW

PROBLEM 8.7

500%

600%

700%

54.00% 55.00% 56.00% 57.00% 58.00% 59.00% 60.00% 61.00% 62.00% 63.00% 64.00% 65.00% 66.00% 67.00% 68.00% 69.00% 70.00% 71.00% 72.00% 73.00% 74.00% 75.00% 76.00% 77.00% 78.00% 79.00% 80.00% 81.00% 82.00% 83.00% 84.00% 85.00% 86.00% 87.00% 88.00% 89.00% 90.00% 91.00% 92.00% 93.00% 94.00% 95.00% 96.00% 97.00% 98.00% 99.00% 100.00% 101.00% 102.00% 103.00% 104.00% 105.00% 106.00% 107.00% 108.00% 109.00% 110.00% 111.00% 112.00%

$201.60 $201.60 $201.55 $201.45 $201.30 $201.11 $200.87 $200.60 $200.28 $199.93 $199.55 $199.14 $198.70 $198.23 $197.73 $197.21 $196.67 $196.11 $195.53 $194.93 $194.31 $193.68 $193.03 $192.37 $191.70 $191.01 $190.31 $189.60 $188.89 $188.16 $187.42 $186.68 $185.93 $185.18 $184.42 $183.65 $182.88 $182.10 $181.33 $180.54 $179.76 $178.97 $178.18 $177.39 $176.59 $175.80 $175.00 $174.20 $173.41 $172.61 $171.81 $171.01 $170.21 $169.42 $168.62 $167.82 $167.03 $166.24 $165.45

113.00% 114.00% 115.00% 116.00% 117.00% 118.00% 119.00% 120.00% 121.00% 122.00% 123.00% 124.00% 125.00% 126.00% 127.00% 128.00% 129.00% 130.00% 131.00% 132.00% 133.00% 134.00% 135.00% 136.00% 137.00% 138.00% 139.00% 140.00% 141.00% 142.00% 143.00% 144.00% 145.00% 146.00% 147.00% 148.00% 149.00% 150.00% 151.00% 152.00% 153.00% 154.00% 155.00% 156.00% 157.00% 158.00% 159.00% 160.00% 161.00% 162.00% 163.00% 164.00% 165.00% 166.00% 167.00% 168.00% 169.00% 170.00% 171.00%

$164.65 $163.87 $163.08 $162.29 $161.51 $160.73 $159.95 $159.17 $158.40 $157.63 $156.86 $156.09 $155.33 $154.56 $153.80 $153.05 $152.29 $151.54 $150.80 $150.05 $149.31 $148.57 $147.83 $147.10 $146.37 $145.64 $144.92 $144.20 $143.48 $142.77 $142.06 $141.35 $140.65 $139.94 $139.25 $138.55 $137.86 $137.17 $136.49 $135.80 $135.13 $134.45 $133.78 $133.11 $132.44 $131.78 $131.12 $130.46 $129.81 $129.16 $128.52 $127.87 $127.23 $126.59 $125.96 $125.33 $124.70 $124.08 $123.46

172.00% 173.00% 174.00% 175.00% 176.00% 177.00% 178.00% 179.00% 180.00% 181.00% 182.00% 183.00% 184.00% 185.00% 186.00% 187.00% 188.00% 189.00% 190.00% 191.00% 192.00% 193.00% 194.00% 195.00% 196.00% 197.00% 198.00% 199.00% 200.00% 201.00% 202.00% 203.00% 204.00% 205.00% 206.00% 207.00% 208.00% 209.00% 210.00% 211.00% 212.00% 213.00% 214.00% 215.00% 216.00% 217.00% 218.00% 219.00% 220.00% 221.00% 222.00% 223.00% 224.00% 225.00% 226.00% 227.00% 228.00% 229.00% 230.00%

$122.84 $122.22 $121.61 $121.00 $120.40 $119.79 $119.19 $118.60 $118.00 $117.41 $116.82 $116.24 $115.65 $115.07 $114.50 $113.92 $113.35 $112.79 $112.22 $111.66 $111.10 $110.54 $109.99 $109.44 $108.89 $108.34 $107.80 $107.26 $106.72 $106.19 $105.65 $105.12 $104.60 $104.07 $103.55 $103.03 $102.51 $102.00 $101.49 $100.98 $100.47 $99.97 $99.47 $98.97 $98.47 $97.97 $97.48 $96.99 $96.50 $96.02 $95.54 $95.06 $94.58 $94.10 $93.63 $93.16 $92.69 $92.22 $91.76

231.00% 232.00% 233.00% 234.00% 235.00% 236.00% 237.00% 238.00% 239.00% 240.00% 241.00% 242.00% 243.00% 244.00% 245.00% 246.00% 247.00% 248.00% 249.00% 250.00% 251.00% 252.00% 253.00% 254.00% 255.00% 256.00% 257.00% 258.00% 259.00% 260.00% 261.00% 262.00% 263.00% 264.00% 265.00% 266.00% 267.00% 268.00% 269.00% 270.00% 271.00% 272.00% 273.00% 274.00% 275.00% 276.00% 277.00% 278.00% 279.00% 280.00% 281.00% 282.00% 283.00% 284.00% 285.00% 286.00% 287.00% 288.00% 289.00%

$91.29 $90.83 $90.38 $89.92 $89.47 $89.01 $88.56 $88.12 $87.67 $87.23 $86.79 $86.35 $85.91 $85.47 $85.04 $84.61 $84.18 $83.75 $83.33 $82.91 $82.48 $82.06 $81.65 $81.23 $80.82 $80.41 $80.00 $79.59 $79.18 $78.78 $78.37 $77.97 $77.57 $77.18 $76.78 $76.39 $75.99 $75.60 $75.22 $74.83 $74.44 $74.06 $73.68 $73.30 $72.92 $72.54 $72.17 $71.79 $71.42 $71.05 $70.68 $70.31 $69.95 $69.58 $69.22 $68.86 $68.50 $68.14 $67.79

290.00% 291.00% 292.00% 293.00% 294.00% 295.00% 296.00% 297.00% 298.00% 299.00% 300.00% 301.00% 302.00% 303.00% 304.00% 305.00% 306.00% 307.00% 308.00% 309.00% 310.00% 311.00% 312.00% 313.00% 314.00% 315.00% 316.00% 317.00% 318.00% 319.00% 320.00% 321.00% 322.00% 323.00% 324.00% 325.00% 326.00% 327.00% 328.00% 329.00% 330.00% 331.00% 332.00% 333.00% 334.00% 335.00% 336.00% 337.00% 338.00% 339.00% 340.00% 341.00% 342.00% 343.00% 344.00% 345.00% 346.00% 347.00% 348.00%

$67.43 $67.08 $66.73 $66.38 $66.03 $65.68 $65.33 $64.99 $64.65 $64.31 $63.96 $63.63 $63.29 $62.95 $62.62 $62.28 $61.95 $61.62 $61.29 $60.96 $60.64 $60.31 $59.99 $59.67 $59.34 $59.02 $58.71 $58.39 $58.07 $57.76 $57.44 $57.13 $56.82 $56.51 $56.20 $55.89 $55.59 $55.28 $54.98 $54.68 $54.37 $54.07 $53.78 $53.48 $53.18 $52.88 $52.59 $52.30 $52.00 $51.71 $51.42 $51.13 $50.85 $50.56 $50.27 $49.99 $49.71 $49.42 $49.14

349.00% 350.00% 351.00% 352.00% 353.00% 354.00% 355.00% 356.00% 357.00% 358.00% 359.00% 360.00% 361.00% 362.00% 363.00% 364.00% 365.00% 366.00% 367.00% 368.00% 369.00% 370.00% 371.00% 372.00% 373.00% 374.00% 375.00% 376.00% 377.00% 378.00% 379.00% 380.00% 381.00% 382.00% 383.00% 384.00% 385.00% 386.00% 387.00% 388.00% 389.00% 390.00% 391.00% 392.00% 393.00% 394.00% 395.00% 396.00% 397.00% 398.00% 399.00% 400.00% 401.00% 402.00% 403.00% 404.00% 405.00% 406.00% 407.00%

$48.86 $48.58 $48.31 $48.03 $47.75 $47.48 $47.20 $46.93 $46.66 $46.39 $46.12 $45.85 $45.58 $45.31 $45.05 $44.78 $44.52 $44.26 $43.99 $43.73 $43.47 $43.21 $42.96 $42.70 $42.44 $42.19 $41.93 $41.68 $41.43 $41.17 $40.92 $40.67 $40.42 $40.17 $39.93 $39.68 $39.44 $39.19 $38.95 $38.70 $38.46 $38.22 $37.98 $37.74 $37.50 $37.26 $37.03 $36.79 $36.55 $36.32 $36.09 $35.85 $35.62 $35.39 $35.16 $34.93 $34.70 $34.47 $34.24

408.00% 409.00% 410.00% 411.00% 412.00% 413.00% 414.00% 415.00% 416.00% 417.00% 418.00% 419.00% 420.00% 421.00% 422.00% 423.00% 424.00% 425.00% 426.00% 427.00% 428.00% 429.00% 430.00% 431.00% 432.00% 433.00% 434.00% 435.00% 436.00% 437.00% 438.00% 439.00% 440.00% 441.00% 442.00% 443.00% 444.00% 445.00% 446.00% 447.00% 448.00% 449.00% 450.00% 451.00% 452.00% 453.00% 454.00% 455.00% 456.00% 457.00% 458.00% 459.00% 460.00% 461.00% 462.00% 463.00% 464.00% 465.00% 466.00%

$34.02 $33.79 $33.57 $33.34 $33.12 $32.89 $32.67 $32.45 $32.23 $32.01 $31.79 $31.57 $31.35 $31.14 $30.92 $30.71 $30.49 $30.28 $30.06 $29.85 $29.64 $29.43 $29.22 $29.01 $28.80 $28.59 $28.38 $28.17 $27.97 $27.76 $27.56 $27.35 $27.15 $26.94 $26.74 $26.54 $26.34 $26.14 $25.94 $25.74 $25.54 $25.34 $25.14 $24.95 $24.75 $24.55 $24.36 $24.16 $23.97 $23.78 $23.58 $23.39 $23.20 $23.01 $22.82 $22.63 $22.44 $22.25 $22.07

467.00% 468.00% 469.00% 470.00% 471.00% 472.00% 473.00% 474.00% 475.00% 476.00% 477.00% 478.00% 479.00% 480.00% 481.00% 482.00% 483.00% 484.00% 485.00% 486.00% 487.00% 488.00% 489.00% 490.00% 491.00% 492.00% 493.00% 494.00% 495.00% 496.00% 497.00% 498.00% 499.00% 500.00% 501.00% 502.00% 503.00% 504.00% 505.00% 506.00% 507.00% 508.00% 509.00% 510.00% 511.00% 512.00% 513.00% 514.00% 515.00% 516.00% 517.00% 518.00% 519.00% 520.00% 521.00% 522.00% 523.00% 524.00% 525.00%

$21.88 $21.69 $21.51 $21.32 $21.13 $20.95 $20.77 $20.58 $20.40 $20.22 $20.04 $19.86 $19.68 $19.50 $19.32 $19.14 $18.96 $18.78 $18.60 $18.43 $18.25 $18.07 $17.90 $17.72 $17.55 $17.38 $17.20 $17.03 $16.86 $16.69 $16.52 $16.35 $16.18 $16.01 $15.84 $15.67 $15.50 $15.33 $15.17 $15.00 $14.83 $14.67 $14.50 $14.34 $14.17 $14.01 $13.85 $13.68 $13.52 $13.36 $13.20 $13.04 $12.88 $12.72 $12.56 $12.40 $12.24 $12.08 $11.92

526.00% 527.00% 528.00% 529.00% 530.00% 531.00% 532.00% 533.00% 534.00% 535.00% 536.00% 537.00% 538.00% 539.00% 540.00% 541.00% 542.00% 543.00% 544.00% 545.00% 546.00% 547.00% 548.00% 549.00% 550.00% 551.00% 552.00% 553.00% 554.00% 555.00% 556.00% 557.00% 558.00% 559.00% 560.00% 561.00% 562.00% 563.00% 564.00% 565.00% 566.00% 567.00% 568.00% 569.00% 570.00% 571.00% 572.00% 573.00% 574.00% 575.00% 576.00% 577.00% 578.00% 579.00% 580.00% 581.00% 582.00% 583.00% 584.00%

$11.77 $11.61 $11.45 $11.30 $11.14 $10.99 $10.83 $10.68 $10.52 $10.37 $10.22 $10.07 $9.91 $9.76 $9.61 $9.46 $9.31 $9.16 $9.01 $8.86 $8.71 $8.56 $8.41 $8.27 $8.12 $7.97 $7.83 $7.68 $7.54 $7.39 $7.25 $7.10 $6.96 $6.81 $6.67 $6.53 $6.39 $6.24 $6.10 $5.96 $5.82 $5.68 $5.54 $5.40 $5.26 $5.12 $4.98 $4.84 $4.71 $4.57 $4.43 $4.29 $4.16 $4.02 $3.89 $3.75 $3.61 $3.48 $3.35

585.00% 586.00% 587.00% 588.00% 589.00% 590.00% 591.00% 592.00% 593.00% 594.00% 595.00% 596.00% 597.00% 598.00% 599.00% 600.00% 601.00% 602.00% 603.00% 604.00% 605.00% 606.00% 607.00% 608.00% 609.00% 610.00% 611.00% 612.00% 613.00% 614.00% 615.00% 616.00% 617.00% 618.00% 619.00% 620.00% 621.00% 622.00% 623.00% 624.00% 625.00% 626.00% 627.00% 628.00% 629.00% 630.00% 631.00% 632.00% 633.00% 634.00% 635.00% 636.00% 637.00% 638.00% 639.00% 640.00% 641.00% 642.00% 643.00%

$3.21 $3.08 $2.94 $2.81 $2.68 $2.55 $2.41 $2.28 $2.15 $2.02 $1.89 $1.76 $1.63 $1.50 $1.37 $1.24 $1.11 $0.99 $0.86 $0.73 $0.60 $0.48 $0.35 $0.22 $0.10 -$0.03 -$0.15 -$0.28 -$0.40 -$0.53 -$0.65 -$0.78 -$0.90 -$1.02 -$1.15 -$1.27 -$1.39 -$1.51 -$1.63 -$1.76 -$1.88 -$2.00 -$2.12 -$2.24 -$2.36 -$2.48 -$2.60 -$2.72 -$2.83 -$2.95 -$3.07 -$3.19 -$3.31 -$3.42 -$3.54 -$3.66 -$3.77 -$3.89 -$4.01

644.00% 645.00% 646.00% 647.00% 648.00% 649.00% 650.00% 651.00% 652.00% 653.00% 654.00% 655.00% 656.00% 657.00% 658.00% 659.00% 660.00% 661.00% 662.00% 663.00% 664.00% 665.00% 666.00% 667.00% 668.00% 669.00% 670.00% 671.00% 672.00% 673.00% 674.00% 675.00% 676.00% 677.00% 678.00% 679.00% 680.00% 681.00% 682.00% 683.00% 684.00% 685.00% 686.00% 687.00% 688.00% 689.00% 690.00% 691.00% 692.00% 693.00% 694.00% 695.00% 696.00% 697.00% 698.00% 699.00% 700.00%

-$4.12 -$4.24 -$4.35 -$4.47 -$4.58 -$4.69 -$4.81 -$4.92 -$5.04 -$5.15 -$5.26 -$5.37 -$5.49 -$5.60 -$5.71 -$5.82 -$5.93 -$6.04 -$6.15 -$6.26 -$6.37 -$6.48 -$6.59 -$6.70 -$6.81 -$6.92 -$7.03 -$7.14 -$7.25 -$7.35 -$7.46 -$7.57 -$7.68 -$7.78 -$7.89 -$8.00 -$8.10 -$8.21 -$8.31 -$8.42 -$8.52 -$8.63 -$8.73 -$8.84 -$8.94 -$9.05 -$9.15 -$9.25 -$9.36 -$9.46 -$9.56 -$9.67 -$9.77 -$9.87 -$9.97 -$10.07 -$10.17

PROBLEM 8.8

CF -$101.00 $411.00 -$558.00 $253.00 $2.00 $8.00 -$14.00

BY EXAMINING THE GRAPH OF PW VS I, THREE ROOTS ARE APPARENT BY USING THE [GUESS] OPTION OF EXCEL'S IRR FUNCTION, THESE THREE ROOTS CAN BE LOCATED IRR = IRR(CF_COLUMN, GUESS) IRR = 9.82% =IRR(C4:C10,10%) IRR = 25.67% =IRR(C4:C10,25%) IRR = 57.45% =IRR(C4:C10,60%) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 9.00% $0.04 10.00% $0.00 10.00% -$0.01 IRR = 9.84% =B26+(B28-B26)*(C27-C26)/(C28-C26) AND i% NPV 25.00% -$0.01 IRR $0.00 30.00% $0.09 IRR = 25.66% =B32+(B34-B32)*(C33-C32)/(C34-C32) THE THIRD ROOT IS OUTSIDE THE RANGE OF THE INTEREST TABLES DUE TO MULTIPLE ROOTS EXCEL'S SOLVER IS NOT USED TO COMPUTE IRR DUE TO MULTIPLE ROOTS EXCEL'S GOAL SEEK IS NOT USED TO COMPUTE IRR

SINCE THE PW OF THE INVESTMENT AT MARR IS NEGATIVE THE INVESTMENT IS NOT ATTRACTIVE

PW $1.00 =NPV(I6,C$5:C$10)+C$4 $0.83 =NPV(I7,C$5:C$10)+C$4 $0.68 OTHER EQUATIONS ARE SIMILAR $0.54 $0.43 $0.32 PW versus i $0.23 $0.16 $1.20 $0.09 $0.04 $1.00 -$0.01 $0.80 -$0.04 -$0.07 $0.60 -$0.09 -$0.11 $0.40 -$0.12 $0.20 -$0.12 -$0.12 $0.00 0% 10% 20% 30% 40% 50% -$0.12 -$0.20 -$0.11 -$0.10 -$0.40 -$0.08 -$0.60 -$0.07 -$0.05 -$0.80 -$0.03 VALUES OF i -$0.01 $0.01 $0.03 $0.05 $0.07 $0.09 $0.11 $0.13 $0.14 $0.16 $0.17 $0.19 $0.20 $0.21 $0.22 $0.23 $0.23 $0.24 $0.24 $0.24 $0.23 $0.23 $0.22 $0.21 $0.20 VALUES OF PW

EOY 0 1 2 3 4 5 6

60%

70%

80%

50.00% 51.00% 52.00% 53.00% 54.00% 55.00% 56.00% 57.00% 58.00% 59.00% 60.00% 61.00% 62.00% 63.00% 64.00% 65.00% 66.00% 67.00% 68.00% 69.00% 70.00%

$0.18 $0.17 $0.15 $0.12 $0.10 $0.07 $0.05 $0.01 -$0.02 -$0.05 -$0.09 -$0.13 -$0.18 -$0.22 -$0.27 -$0.32 -$0.37 -$0.42 -$0.48 -$0.54 -$0.60

PROBLEM 8.9 SINCE THE PW IS NEGATIVE, THE IRR MUST BE LESS THAN 15% (MARR). SINCE THE IRR IS A 2-DIGIT NUMBER, THE FIRST DIGIT MUST BE A 1 (ASSUMING A LEADING ZERO WOULD NOT BE CONSIDERED A 2-DIGIT NUMBER) THEREFORE, THE IRR MUST BE 12%

PROBLEM 8.10 a b c d e f g h i

IRR > MARR IRR = MARR IRR < MARR IRR > MARR IRR = MARR IRR < MARR IRR > MARR IRR = MARR IRR < MARR

PROBLEM 8.11 AN INFINITE NUMBER OF CORRECT RESPONSES ARE POSSIBLE. THE SIMPLEST FORM FOR THE RESPONSE IS A SINGLE DEPOSIT AND A SINGLE WITHDRAWAL. FOR EXAMPLE: P = $100 F = $100(F|P 10%,4) = $100(1.46410) = $146.41 $146.41

$100.00

PROBLEM 8.12 a

EOY 0 1 2 3 4 5 6

CF -$70,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $32,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 36.35% =IRR(C4:C10) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 36.35% =RATE(6,30000,-70000,2000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 30.00% $9,696.73 IRR $0.00 40.00% -$4,695.15 IRR = 36.74% =B20+(B22-B20)*(C21-C20)/(C22-C20) SOLUTION USING EXCEL'S SOLVER i= 36.35% NPV = $0.00 =NPV(C26,C5:C10)+C4 SOLVER PARAMETERS SET TARGET CELL: C27 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C26 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 36.35% NPV = $0.00 =NPV(C35,C5:C10)+C4 SOLVER PARAMETERS SET TARGET CELL: C36 VALUE OF: 0 BY CHANGING CELL: C35 CLICK "SOLVE" b

IF IRR >= MARR (10%), THEN ATTRACTIVE; OTHERWISE, UNATTRACTIVE

INVESTMENT IS JUSTIFIED

PROBLEM 8.13

IN K$ EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 22.27% =IRR(C7:C27) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 20.00% $5,652.10 IRR $0.00 25.00% -$5,815.53 IRR = 22.46% =B37+(B39-B37)*(C38-C37)/(C39-C37) SOLUTION USING EXCEL'S SOLVER i= 22.27% NPV = $0.00 =NPV(C43,C8:C27)+C7 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 22.27% NPV = $0.00 =NPV(C52,C8:C27)+C7 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C44 0 C43

C53 0 C52

(1) IRR =22.27% (2) INVESTMENT IS ATTRACTIVE (3) IF IRR >= MARR (20%), THEN ATTRACTIVE; OTHERWISE, UNATTRACTIVE NU THINGS SHOULD INVEST IN THE BUSINESS VENTURE

PROBLEM 8.14 SOLUTIONS USING EXCEL'S GOAL SEEK EOY 0 1 2 3 4 IRR

CF -$30,000.00 $6,000.00 $13,500.00 $7,447.88 $13,500.00 12.00% CALCULATED

TO IMPLEMENT GOAL SEEK: (1) SET CELL: C12 (2) TO VALUE: MARR VALUE (3) BY CHANGING CELL: C9 a b c d e

$7,413.12 $10,413.52 $20,343.81 $3,717.52 -$3,000.00

12.00% TARGET

THE CALCULATED IRR VALUE THE TARGET IRR VALUE THE CASH FLOW TO BE DETERMINED

RESULTING IRR = 11.96% (12%) RESULTING IRR = 14.99% (15%) RESULTING IRR = 24.00% (24%) RESULTING IRR = 8.01% (8%) SOLVED BY INSPECTION, IRR = 0%

SOLUTIONS USING EXCEL'S SOLVER TO IMPLEMENT SOLVER: (1) SET TARGET CELL: C12 (2) EQUAL TO: VALUE OF: MARR VALUE (3) BY CHANGING CELLS: C9 a b c d e

$7,447.88 $10,427.13 $20,346.05 $3,713.02 -$3,000.00

THE CALCULATED IRR VALUE THE TARGET IRR VALUE THE CASH FLOW TO BE DETERMINED

RESULTING IRR = 12.00% (12%) RESULTING IRR = 15.00% (15%) RESULTING IRR = 24.00% (24%) RESULTING IRR = 8.00% (8%) SOLVED BY INSPECTION, IRR = 0%

NOTE: THE SOLVER SOLUTIONS DETERMINE MORE PRECISE VALUES OF IRR

SOLUTIONS USING FACTOR TABLES a

0 = -$30,000 + $6,000(P|F 12%,1) + $13,500(P|F 12%,2) + X(P|F 12%,3) + $13,500(P|F 12%,4) X = ($30,000 - $6,000(P|F 12%,1) - $13,500(P|F 12%,2) - $13,500(P|F 12%,4)) / (P|F 12%,3) X = ($30,000 - $6,000(0.89286) - $13,500(0.79719) - $13,500(0.63552)) / (0.71178) X= $7,447.88 X = ($30,000 - $6,000(P|F 15%,1) - $13,500(P|F 15%,2) - $13,500(P|F 15%,4)) / (P|F 15%,3) X = ($30,000 - $6,000(0.86957) - $13,500(0.75614) - $13,500(0.57175)) / (0.65752) X= $10,427.16 X = ($30,000 - $6,000(P|F 24%,1) - $13,500(P|F 24%,2) - $13,500(P|F 24%,4)) / (P|F 24%,3) X = ($30,000 - $6,000(0.80645) - $13,500(0.65036) - $13,500(0.42297)) / (0.52449) X= $20,346.14 X = ($30,000 - $6,000(P|F 8%,1) - $13,500(P|F 8%,2) - $13,500(P|F 8%,4)) / (P|F 8%,3) X = ($30,000 - $6,000(0.92593) - $13,500(0.85734) - $13,500(0.73503)) / (0.79383) X= $3,712.92 X = $30,000 - $6,000 - $13,500 - $13,500 X= -$3,000.00

PROBLEM 8.15

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

+ CF $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00

- CF -$100,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00

NET CF -$100,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 5.56% =IRR(E5:E20) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 5.56% =RATE(15,10000,-100000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 5.00% $3,796.58 IRR $0.00 6.00% -$2,877.51 IRR = 5.57% =B31+(B33-B31)*(C32-C31)/(C33-C31) SOLUTION USING EXCEL'S SOLVER i= 5.56% NPV = $0.00 =NPV(C37,E6:E20)+E5 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 5.56% NPV = $0.00 =NPV(C46,E6:E20)+E5 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C38 0 C37

C47 0 C46

DECISION RULE IF IRR (5.56%) >= MARR (5%), ACCEPT; OTHERWISE, REJECT

BAILEY SHOULD BUY THE GANG PUNCH

PROBLEM 8.16

EOY 0 1 2 3 4 5

+ CF

- CF -$75,000.00

$18,500.00 $18,500.00 $18,500.00 $18,500.00 $18,500.00

NET CF -$75,000.00 $18,500.00 $18,500.00 $18,500.00 $18,500.00 $18,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 7.42% =IRR(E5:E10) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 7.42% =RATE(5,18500,-75000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 7.00% $853.65 IRR $0.00 8.00% -$1,134.86 IRR = 7.43% =B21+(B23-B21)*(C22-C21)/(C23-C21) SOLUTION USING EXCEL'S SOLVER i= 7.42% NPV = $0.00 =NPV(C27,E6:E10)+E5 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 7.42% NPV = $0.00 =NPV(C36,E6:E10)+E5 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C28 0 C27

C37 0 C36

DECISION RULE IF IRR (7.42%) > MARR (10%), ACCEPT; OTHERWISE, REJECT

CARLISLE SHOULD REJECT THE FILTER BASED ON ITS ECONOMIC MERITS

PROBLEM 8.17

EOY 0 1 2 3 4 5

+ CF

$2,000.00 $4,000.00 $3,000.00 $1,600.00

- CF -$5,000.00 -$200.00 -$300.00 -$600.00 -$1,000.00 -$1,500.00

NET CF -$5,000.00 -$200.00 $1,700.00 $3,400.00 $2,000.00 $100.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 11.45% =IRR(E6:E11) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 11.00% $62.44 IRR $0.00 12.00% -$75.51 IRR = 11.45% =B22+(B24-B22)*(C23-C22)/(C24-C22) SOLUTION USING EXCEL'S SOLVER i= 11.45% NPV = $0.00 =NPV(C28,E7:E11)+E6 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 11.45% NPV = $0.00 =NPV(C37,E7:E11)+E6 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C29 0 C28

C38 0 C37

DECISION RULE IF IRR >= MARR (6%), ACCEPT; OTHERWISE, REJECT

DURATECH SHOULD IMPLEMENT THE PROCESS IMPROVEMENT

PROBLEM 8.18 a

CURRENT ANNUAL INSURANCE PREMIUM = ($700,000/$100)*$1.00 = $7,000 NEW ANNUAL INSURANCE PREMIUM = ($720,000/$100)*$0.40 = $2,880

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

- CF -$20,000.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00 -$400.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 17.91% =IRR(E9:E29) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 17.91% =RATE(20,3720,-20000,,,0.2); INITIAL GUESS IS REQUIRED FOR CONVERGENCE SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $3,284.71 IRR $0.00 18.00% -$87.78 IRR = 17.92% =B40+(B42-B40)*(C41-C40)/(C42-C40) SOLUTION USING EXCEL'S SOLVER i= 17.91% NPV = $0.00 =NPV(C46,E10:E29)+E9 SOLVER PARAMETERS SET TARGET CELL: C47 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C46 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 17.91% NPV = $0.00 =NPV(C55,E10:E29)+E9 SOLVER PARAMETERS SET TARGET CELL: C56 VALUE OF: 0 BY CHANGING CELL: C55 CLICK "SOLVE" b

DECISION RULE IF IRR >= MARR (15%), ACCEPT; OTHERWISE, REJECT

EDDIE SHOULD BUY THE SPRINKLER SYSTEM

PROBLEM 8.19 THE MAXIMUM AMOUNT THAT FABCO SHOULD BE WILLING TO SPEND IS THE AMOUNT THE SETS THE IRR TO MARR (7%). SOLUTION USING EXCEL'S GOAL SEEK EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

+ CF

- CF -$79,426.95

$10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 IRR

NET CF -$79,426.95 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 7.00% CALCULATED

7.00% TARGET

TO IMPLEMENT GOAL SEEK: (1) SET CELL: E23 THE CALCULATED IRR VALUE (2) TO VALUE: MARR VALUE THE TARGET IRR VALUE (3) BY CHANGING CELL: D9 THE CASH FLOW TO BE DETERMINED THE MAXIMUM AMOUNT FABCO SHOULD BE WILLING TO PAY IS $79,076.00

SOLUTION USING EXCEL'S SOLVER TO IMPLEMENT GOAL SEEK: (1) SET TARGET CELL: E23 (2) EQUAL TO: VALUE OF: MARR VALUE (3) BY CHANGING CELLS: D9

THE CALCULATED IRR VALUE THE TARGET IRR VALUE THE CASH FLOW TO BE DETERMINED

THE MAXIMUM AMOUNT FABCO SHOULD BE WILLING TO PAY IS $79,426.95 SOLUTION USING FACTOR TABLES LET X BE THE AMOUNT PAID 0 = -X + $10,000(P|A 7%,12) 0 = -X + $10,000(7.94269) X = $10,000(7.94269) X= $79,426.90

NOTE: THE SOLVER SOLUTION IS MORE ACCURATE (AS COMPARED TO THE PW SOLUTION OF PROBLEM 5.16) THAN THE GOAL SEEK SOLUTION.

PROBLEM 8.20 a

YEAR 5 ADDITION = $5,000 COMPUTER SALVAGE VALUE LOAN PAYMENTS = 25000*(A|P 15,3) = 25000*(0.43798) = $10,949.50 ALTERNATIVELY, LOAN PAYMENTS = PMT(15%,3,25000) = $10,949.42 THE FACTOR-BASED VALUE IS USED IN THE CASH FLOW PROFILE BELOW

EOY 0 1 2 3 4 5

+ INV CF $55,000.00 $55,000.00 $55,000.00 $55,000.00 $60,000.00

- INV CF -$100,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00

+ LOAN CF $25,000.00

- LOAN CF -$10,949.50 -$10,949.50 -$10,949.50

NET CF -$75,000.00 $19,050.50 $19,050.50 $19,050.50 $30,000.00 $35,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 16.52% =IRR(G12:G17) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $3,050.36 IRR $0.00 18.00% -$2,806.52 IRR = 16.56% =B28+(B30-B28)*(C29-C28)/(C30-C28) SOLUTION USING EXCEL'S SOLVER i= 16.52% NPV = $0.00 =NPV(C34,G13:G17)+G12 SOLVER PARAMETERS SET TARGET CELL: C35 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C34 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 16.52% NPV = $0.00 =NPV(C43,G13:G17)+G12 SOLVER PARAMETERS SET TARGET CELL: C44 VALUE OF: 0 BY CHANGING CELL: C43 CLICK "SOLVE" b

DECISION RULE IF IRR >= MARR (18%), ACCEPT; OTHERWISE, REJECT

GALVANIZED PRODUCTS SHOULD NOT PURCHASE THE NEW COMPUTER SYSTEM

PROBLEM 8.21 a EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

+ CF

- CF -$1,400.00

$0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 -$1,000.00 -$2,000.00 -$3,000.00 $1,400.00

NET CF -$1,400.00 $0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 -$1,000.00 -$2,000.00 -$3,000.00 $1,400.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 16.82% =IRR(E6:E21) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $51.69 IRR $0.00 18.00% -$35.68 IRR = 16.77% =B32+(B34-B32)*(C33-C32)/(C34-C32) SOLUTION USING EXCEL'S SOLVER i= 16.82% NPV = $0.00 =NPV(C38,E7:E21)+E6 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 16.82% NPV = $0.00 =NPV(C47,E7:E21)+E6 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C39 0 C38

C48 0 C47

DECISION RULE IF IRR(16.82%) >= MARR (13.5%), ACCEPT; OTHERWISE, REJECT

QRU SHOULD INVEST

PROBLEM 8.22 a

SOLUTION USING EXCEL'S IRR FUNCTION

EOY 0 1 2 3 4 5 6 7

+ CF

$5.00 $2.00 $5.00 $5.00 $2.00 $5.00

- CF -$12.00 -$1.00

NET CF -$12.00 -$1.00 $5.00 $2.00 $5.00 $5.00 $2.00 $5.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 15.70% =IRR(E7:E14) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $0.32 IRR $0.00 18.00% -$0.96 IRR = 15.74% =B25+(B27-B25)*(C26-C25)/(C27-C25) SOLUTION USING EXCEL'S SOLVER i= 15.70% NPV = $0.00 =NPV(C31,E8:E14)+E7 SOLVER PARAMETERS SET TARGET CELL: C32 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C31 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 15.70% NPV = $0.00 =NPV(C40,E8:E14)+E7 SOLVER PARAMETERS SET TARGET CELL: C41 VALUE OF: 0 BY CHANGING CELL: C40 CLICK "SOLVE" b

DECISION RULE IF IRR (15.70%) >= MARR (18%), ACCEPT; OTHERWISE, REJECT

IMAGINEERING SHOULD NOT INVEST

PROBLEM 8.23

EOY 0 1 2 3 4 5 6 7 8 9 10

+ CF

- CF -$2.00 -$10.00 -$12.00 -$14.00 -$16.00 -$18.00

NET CF -$2.00 -$10.00 -$12.00 -$14.00 -$16.00 -$18.00 $200.00 -$10.00 -$12.00 -$14.00 -$100.00

i 0.00% 1.00% 2.00% $200.00 3.00% -$10.00 4.00% -$12.00 5.00% -$14.00 6.00% -$100.00 7.00% 8.00% SINCE THERE ARE TWO SIGN CHANGES, THERE ARE 2 OR 0 REAL POSITIVE ROOTS 9.00% WE CAN USE A PW VERSUS I GRAPH TO HELP ISOLATE THE ROOTS AND THEN 10.00% USE EXCEL'S IRR FUNCTION. 11.00% BY EXAMINING THE GRAPH OF PW VS i, TWO ROOTS ARE APPARENT 12.00% 13.00% BY USING THE [GUESS] OPTION OF EXCEL'S IRR FUNCTION, 14.00% THESE TWO ROOTS CAN BE LOCATED 15.00% IRR = IRR(CF_COLUMN, GUESS) 16.00% IRR = 3.52% =IRR(E4:E14,5%) 17.00% IRR = 21.68% =IRR(E4:E14,20%) 18.00% 19.00% DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION 20.00% IS NOT USED TO COMPUTE IRR. 21.00% 22.00% SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) 23.00% i% NPV 24.00% 3.00% -$0.82 25.00% IRR $0.00 26.00% 4.00% $0.68 27.00% IRR = 3.55% =B32+(B34-B32)*(C33-C32)/(C34-C32) 28.00% AND 29.00% i% NPV 30.00% 20.00% $0.82 31.00% IRR $0.00 32.00% 25.00% -$1.60 33.00% IRR = 21.69% =B38+(B40-B38)*(C39-C38)/(C40-C38) 34.00% 35.00% DUE TO MULTIPLE ROOTS EXCEL'S SOLVER IS NOT USED TO COMPUTE IRR 36.00% 37.00% DUE TO MULTIPLE ROOTS EXCEL'S GOAL SEEK IS NOT USED TO COMPUTE IRR 38.00% 39.00% SINCE THERE ARE MULTIPLE IRR ROOTS, WE CAN REVERT BACK TO THE PW DECISION RULE 40.00% IF PW >= 0, ACCEPT; OTHERWISE, REJECT 41.00% 42.00% ALTERNATIVELY, WE CAN EXAMINE THE IRR RESULTS TO DETERMINE THE FOLLOWING IRR DECISION RULE 43.00% IF 3.52% <= MARR (12%) <= 21.68%, ACCEPT; OTHERWISE, REJECT 44.00% 45.00% JUPITER'S SHOULD INVEST 46.00% 47.00% 48.00% 49.00% 50.00%

PW -$8.00 =E$4+NPV(K7,E$5:E$14) -$5.08 =E$4+NPV(K8,E$5:E$14) -$2.72 OTHER EQUATIONS ARE SIMILAR -$0.82 $0.68 $1.83 $2.69 $3.31 $3.72 $6.00 $3.96 $4.04 $4.00 $4.01 $3.87 $2.00 $3.65 $0.00 $3.36 0% 10% $3.01 -$2.00 $2.63 $2.20 -$4.00 $1.76 $1.29 -$6.00 $0.82 $0.33 -$8.00 -$0.15 -$0.64 -$10.00 -$1.12 -$1.60 -$2.06 -$2.52 -$2.97 -$3.40 -$3.82 -$4.22 -$4.61 -$4.99 -$5.35 -$5.70 -$6.03 -$6.35 -$6.65 -$6.94 -$7.21 -$7.47 -$7.72 -$7.96 -$8.18 -$8.39 -$8.59 -$8.77 -$8.95 -$9.12 -$9.27 VALUES OF PW

PW VERSUS i

20%

30%

VALUES OF i

40%

50%

60%

PROBLEM 8.24 YEAR 7 ADDITION = $7,500 SYSTEM SALVAGE VALUE LOAN PAYMENTS = 20000(F|P,8,1)(A|P 8,3) = 20000(1.08000)(0.38803) = $8,381.45 ALTERNATIVELY, LOAN PAYMENTS = PMT(8%,3,20000*1.08000) = $8,381.52 THE FACTOR-BASED VALUE IS USED IN THE CASH FLOW PROFILE BELOW a

SOLUTION USING EXCEL'S IRR FUNCTION

EOY 0 1 2 3 4 5 6 7

+ INV CF $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $19,500.00

- INV CF -$40,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00

+ LOAN CF $20,000.00

- LOAN CF

-$8,381.45 -$8,381.45 -$8,381.45

NET CF -$20,000.00 $10,000.00 $1,618.55 $1,618.55 $1,618.55 $10,000.00 $10,000.00 $17,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 25.16% =IRR(G12:G19) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 25.00% $95.78 IRR $0.00 30.00% -$2,492.60 IRR = 25.19% =B30+(B32-B30)*(C31-C30)/(C32-C30) SOLUTION USING EXCEL'S SOLVER i= 25.16% NPV = $0.00 =NPV(C36,G13:G19)+G12 SOLVER PARAMETERS SET TARGET CELL: C37 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C36 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 25.16% NPV = $0.00 =NPV(C45,G13:G19)+G12 SOLVER PARAMETERS SET TARGET CELL: C46 VALUE OF: 0 BY CHANGING CELL: C45 CLICK "SOLVE" b

DECISION RULE IF IRR >= MARR (10%), ACCEPT; OTHERWISE, REJECT

AEROTRON ELECTRONICS SHOULD PURCHASE THE WATER FILTRATION SYSTEM

PROBLEM 8.25

a EOY 0 1 2 3 4 5

+ CF $600.00 $600.00 $700.00 $700.00 $700.00

- CF -$1,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

NET CF -$1,000.00 $300.00 $300.00 $400.00 $400.00 $400.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 21.84% =IRR(E6:E11) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 20.00% $43.47 IRR $0.00 25.00% -$68.29 IRR = 21.94% =B22+(B24-B22)*(C23-C22)/(C24-C22) SOLUTION USING EXCEL'S SOLVER i= 21.84% NPV = $0.00 =NPV(C28,E7:E11)+E6 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 21.84% NPV = $0.00 =NPV(C37,E7:E11)+E6 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C29 0 C28

C38 0 C37

DECISION RULE IF IRR (21.84%) >= MARR (10%), ACCEPT; OTHERWISE, REJECT

HOME INNOVATION SHOULD PURSUE THE NEW PRODUCT

PROBLEM 8.26

a EOY 0 1 2 3 4 5 6

+ CF $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $3,000.00

- CF -$6,000.00

NET CF -$6,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $3,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 7.45% =IRR(E6:E12) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 7.45% =RATE(6,1000,-6000,2000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 7.00% $99.22 IRR $0.00 8.00% -$116.78 IRR = 7.46% =B23+(B25-B23)*(C24-C23)/(C25-C23) SOLUTION USING EXCEL'S SOLVER i= 7.45% NPV = $0.00 =NPV(C29,E7:E12)+E6 SOLVER PARAMETERS SET TARGET CELL: C30 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C29 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 7.45% NPV = $0.00 =NPV(C38,E7:E12)+E6 SOLVER PARAMETERS SET TARGET CELL: C39 VALUE OF: 0 BY CHANGING CELL: C38 CLICK "SOLVE" b

DECISION RULE IF IRR (7.45%) >= MARR (8%), ACCEPT; OTHERWISE, REJECT

MAYBERRY SHOULD NOT IMPLEMENT THE DESIGN CHANGE

PROBLEM 8.27

a EOY 0 1 2 3

+ CF $30,000.00 $30,000.00 $33,000.00

- CF -$10,000.00 -$25,000.00 -$25,000.00 -$25,000.00

NET CF -$10,000.00 $5,000.00 $5,000.00 $8,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 32.91% =IRR(E7:E10) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 32.91% =RATE(3,5000,-10000,3000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 30.00% $446.06 IRR $0.00 40.00% -$962.10 IRR = 33.17% =B21+(B23-B21)*(C22-C21)/(C23-C21) SOLUTION USING EXCEL'S SOLVER i= 32.91% NPV = $0.00 =NPV(C27,E8:E10)+E7 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 32.91% NPV = $0.00 =NPV(C36,E8:E10)+E7 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C28 0 C27

C37 0 C36

DECISION RULE IF IRR (32.91%) >= MARR (24%), ACCEPT; OTHERWISE, REJECT

NANCY SHOULD BUY THE TRUCK

PROBLEM 8.28

DELIVERY VAN EOY 0 1 2 3 4 5 6

VAN -$18,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $500.00

LOAN $12,000.00 -$3,305.88 -$3,305.88 -$3,305.88 -$3,305.88

O&M -$700.00 -$700.00 -$700.00 -$700.00 -$700.00 -$700.00

SAVINGS $3,800.00 $3,800.00 $3,800.00 $3,800.00 $3,800.00 $3,800.00

NET CF -$6,000.00 -$205.88 -$205.88 -$205.88 -$205.88 $3,100.00 $3,600.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = -0.35% =IRR(G7:G13) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= -0.35% NPV = $0.00 =NPV(C26,G8:G13)+G7 SOLVER PARAMETERS SET TARGET CELL: C27 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C26 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= -0.35% NPV = $0.00 =NPV(C35,G8:G13)+G7 SOLVER PARAMETERS SET TARGET CELL: C36 VALUE OF: 0 BY CHANGING CELL: C35 CLICK "SOLVE"

DELTA DAWN'S SHOULD NOT PURCHASE THE DELIVERY VAN SINCE IRR (-0.35%) IS LESS THAN MARR (6%).

PROBLEM 8.29 SOLUTION USING EXCEL'S IRR FUNCTION SPRINKLER SYSTEM EOY 0 1 2 3 4 5 6 7 8 9

SPRINKLERS -$30,000.00

LOAN $30,000.00 -$9,877.03 -$9,877.03 -$9,877.03 -$9,877.03

$2,000.00

O&M

SAVINGS

-$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00 -$9,000.00

$15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00

NET CF $0.00 -$3,877.03 -$3,877.03 -$3,877.03 -$3,877.03 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $8,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 17.23% =IRR(G8:G17) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 18.00% -$300.79 IRR $0.00 20.00% -$995.60 IRR = 17.13% =B28+(B30-B28)*(C29-C28)/(C30-C28) SOLUTION USING EXCEL'S SOLVER i= 17.23% NPV = $0.00 =NPV(C34,G9:G17) SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 17.23% NPV = $0.00 =NPV(C43,G9:G17) SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C35 0 C34

C44 0 C43

REALTURF SHOULD PURCHASE THE SPRINKLER SYSTEM SINCE IRR (17.23%) IS GREATER THAN MARR (15%).

PROBLEM 8.30 SOLUTION USING EXCEL'S IRR FUNCTION EOY 0 1 2 3 4 5 6 7 8 9 10

FILTER -$100,000.00

LOAN $50,000.00 -$14,915.78 -$14,915.78 -$14,915.78 -$14,915.78 -$14,915.78

$10,000.00

O&M

SAVINGS

-$20,000.00 -$21,500.00 -$23,000.00 -$24,500.00 -$26,000.00 -$27,500.00 -$29,000.00 -$30,500.00 -$32,000.00 -$33,500.00

$50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00

NET CF -$50,000.00 $15,084.22 $13,584.22 $12,084.22 $10,584.22 $9,084.22 $22,500.00 $21,000.00 $19,500.00 $18,000.00 $26,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 26.83% =IRR(G6:G16) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 25.00% $3,095.57 IRR $0.00 30.00% -$4,687.64 IRR = 26.99% =B27+(B29-B27)*(C28-C27)/(C29-C27) SOLUTION USING EXCEL'S SOLVER i= 26.83% NPV = $0.00 =NPV(C33,G7:G16)+G6 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 26.83% NPV = $0.00 =NPV(C42,G7:G16)+G6 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C34 0 C33

C43 0 C42

DECISION: BAON CHEMICALS SHOULD PURCHASE THE FILTER SINCE THE IRR (26.83%) IS GREATER THAN MARR (12%).

PROBLEM 8.31

IN K$ EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BUILDING -$8,000.00

FURNITURE -$700.00

O&M

-$700.00

$900.00

REVENUE

-$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00 -$800.00

$1,460.00 $1,752.00 $2,044.00 $2,336.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00 $2,628.00

NET CF -$8,700.00 $660.00 $952.00 $1,244.00 $1,536.00 $1,128.00 $1,828.00 $1,828.00 $1,828.00 $1,828.00 $1,128.00 $1,828.00 $1,828.00 $1,828.00 $1,828.00 $2,728.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 13.68% =IRR(G7:G22) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 12.00% $949.66 IRR $0.00 15.00% -$650.43 IRR = 13.78% =B33+(B35-B33)*(C34-C33)/(C35-C33) SOLUTION USING EXCEL'S SOLVER i= 13.68% NPV = $0.00 =NPV(C39,G8:G22)+G7 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 13.68% NPV = $0.00 =NPV(C48,G8:G22)+G7 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C40 0 C39

C49 0 C48

DECISION: VALUE LODGES SHOULD BUILD THE MOTEL SINCE IRR (13.68%) IS GREATER THAN MARR (12%).

PROBLEM 8.32 ORDER OF COMPARISONS: NULL, A, B, C, D, E, F, G a

MARR = 12% COMPARISON # 1 2 3 4 5 6 7

CURRENT BEST CHALLENGER NULL A NULL B NULL C NULL D NULL E NULL F NULL G

INCREMENT A-NULL B-NULL C-NULL D-NULL E-NULL F-NULL G-NULL

IRR OF INCREMENT 10.00% 9.00% 8.00% 7.00% 6.00% 5.00% 7.00%

WINNER NULL NULL NULL NULL NULL NULL NULL

CURRENT BEST CHALLENGER NULL A A B A C A D A E A F A G

INCREMENT A-NULL B-A C-A D-A E-A F-A G-A

IRR OF INCREMENT 10.00% 7.00% 2.00% 9.00% 5.00% 8.00% 3.00%

WINNER A A A A A A A

CURRENT BEST CHALLENGER NULL A A B A C A D D E D F D G

INCREMENT A-NULL B-A C-A D-A E-D F-D G-D

IRR OF INCREMENT 10.00% 7.00% 2.00% 9.00% 3.00% 5.00% 4.00%

WINNER A A A D D D D

CURRENT BEST CHALLENGER NULL A A B B C B D D E D F F G

INCREMENT A-NULL B-A C-B D-B E-D F-D G-F

IRR OF INCREMENT 10.00% 7.00% 0.10% 5.00% 3.00% 5.00% 2.00%

WINNER A B B D D F F

CURRENT BEST CHALLENGER NULL A A B B C B D D E E F F G

INCREMENT A-NULL B-A C-B D-B E-D F-E G-F

IRR OF INCREMENT 10.00% 7.00% 0.10% 5.00% 3.00% 5.00% 2.00%

WINNER A B B D E F G

PREFER NULL b

MARR = 9.5% COMPARISON # 1 2 3 4 5 6 7 PREFER A

MARR = 8% COMPARISON # 1 2 3 4 5 6 7 PREFER D

MARR = 3.5% COMPARISON # 1 2 3 4 5 6 7 PREFER F

MARR = 1.5% COMPARISON # 1 2 3 4 5 6 7 PREFER G

PROBLEM 8.33 ORDER OF COMPARISON: NULL, C, D, A, B a

MARR = 50% COMPARISON # 1 2 3 4

CURRENT BEST NULL NULL NULL NULL

CHALLENGER C D A B

INCREMENT C-NULL D-NULL A-NULL B-NULL

IRR OF INCREMENT 39.20% 36.00% 44.00% 40.00%

WINNER NULL NULL NULL NULL

CURRENT BEST NULL NULL NULL A

CHALLENGER C D A B

INCREMENT C-NULL D-NULL A-NULL B-A

IRR OF INCREMENT 39.20% 36.00% 44.00% 28.30%

WINNER NULL NULL A A

CURRENT BEST NULL C C A

CHALLENGER C D A B

INCREMENT C-NULL D-C A-C B-A

IRR OF INCREMENT 39.20% 18.40% 61.00% 28.30%

WINNER C C A B

CURRENT BEST NULL C D A

CHALLENGER C D A B

INCREMENT C-NULL D-C A-D B-A

IRR OF INCREMENT 39.20% 18.40% 116.50% 28.30%

WINNER C D A B

PREFER NULL b

MARR = 41% COMPARISON # 1 2 3 4 PREFER A

MARR = 25% COMPARISON # 1 2 3 4 PREFER B

MARR = 10% COMPARISON # 1 2 3 4 PREFER B

PROBLEM 8.34 a

INCREMENTAL CASH FLOW ARE A - C EOY 0 1 2 3 4 5 6 7 8 9 10

A -$600,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $270,000.00 $340,000.00

C -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

INCR CF -$130,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $85,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 61.03% =IRR(E6:E16) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 61.03% =RATE(10,80000,-130000,5000,,50%); INITIAL GUESS IS REQUIRED FOR CONVERGENCE THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE VALUES IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= 61.03% NPV = $0.00 =NPV(C28,E7:E16)+E6 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 61.03% NPV = $0.00 =NPV(C37,E7:E16)+E6 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

MARR = 37% COMPARISON # 1 2 3 4

CURRENT BEST NULL C C A

CHALLENGER C D A B

PREFER A d

IF MARR = 40%, PW(C) < 0 SINCE IRR(C) = 39% IF MARR = 40%, PW(D) < 0 SINCE IRR(D) = 36% IF MARR = 40%, PW(A) > 0 SINCE IRR(A) = 44% IF MARR = 40%, PW(B) = 0 SINCE IRR(B) = 40%

C29 0 C28

C38 0 C37

INCREMENT C-NULL D-C A-C B-A

IRR OF INCREMENT 39.00% 18.00% 61.03% 28.00%

WINNER C C A A

PROBLEM 8.35 a

IF THE ALTERNATIVES ARE INDEPENDENT, WE CAN ACCEPT ALL ALTERNATIVES WHOSE IRR'S ARE GREATER THAN MARR (15.5%) ACCEPT: W (16%) AND Y (29%) REJECT: X (15%) AND Z (14%)

IF THE ALTERNATIVES ARE MUTUALLY EXCLUSIVE THEN WE MUST PERFORM AN INCREMENTAL ANALYSIS TO DETERMINE THE PREFERRED ALTERNATIVE. THE ORDER OF COMPARISON IS Y, X, W, Z MARR = 9.5% COMPARISON # 1 2 3 PREFER Z

CURRENT BEST Y Y Y

CHALLENGER X W Z

INCREMENT X-Y W-Y Z-Y

IRR OF INCREMENT 1.00% 7.00% 10.00%

WINNER Y Y Z

PROBLEM 8.36 IRR COMPARISONS MUST BE DONE INCREMENTALLY MARR IS 10%; ORDER OF INVESTMENTS: NULL, B, A INCREMENTAL ANALYSIS OF B-NULL EOY 0 1 2 3 4

B -$280,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$280,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 13.44% =IRR(E10:E14) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 13.44% =RATE(4,95000,-280000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 12.00% $8,548.19 IRR $0.00 15.00% -$8,777.06 IRR = 13.48% =B24+(B26-B24)*(C25-C24)/(C26-C24) SOLUTION USING EXCEL'S SOLVER i= 13.44% NPV = $0.00 =NPV(C30,E11:E14)+E10 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 13.44% NPV = $0.00 =NPV(C39,E11:E14)+E10 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C31 0 C30

C40 0 C39

IRR OF INCREMENT IS GREATER THAN MARR (10%) SO B IS PREFERRED TO NULL ANALYZE INCREMENTAL CASH FLOWS OF A-B INCREMENTAL ANALYSIS OF A-B EOY 0 1 2 3 4

A -$380,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00

B -$280,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00

INCR CF $100,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 7.71% =IRR(E53:E57) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 7.71% =RATE(4,30000,-100000)

SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 7.00% -$1,616.34 IRR $0.00 8.00% $636.19 IRR = 7.72% =B67+(B69-B67)*(C68-C67)/(C69-C67) SOLUTION USING EXCEL'S SOLVER i= 7.71% NPV = $0.00 =NPV(C73,E54:E57)+E53 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 7.71% NPV = $0.00 =NPV(C82,E54:E57)+E53 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C74 0 C73

C83 0 C82

IRR OF INCREMENT A-B IS LESS THAN MARR (10%), SO REJECT THE INCREMENT; STAY WITH VENDOR B SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, VENDOR B IS RECOMMENDED

PROBLEM 8.37 IRR COMPARISONS MUST BE DONE INCREMENTALLY MARR IS 10%/YEAR FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, 1-INCH, 2-INCH NULL BECOMES THE "CURRENT BEST" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 1-INCH - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

1-INCH -$100,000.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00

NULL $0.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00 -$375,000.00

INCR. CF -$100,000.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00 $333,750.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 333.75% =IRR(E14:E24) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 333.76% =RATE(10,333759,-100000,,,300%); INITIAL GUESS IS REQUIRED FOR CONVERGENCE THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE VALUES IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= 333.75% NPV = $0.00 =NPV(C36,E15:E24)+E14 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 333.75% NPV = $0.00 =NPV(C45,E15:E24)+E14 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C37 0 C36

C46 0 C45

SINCE THE IRR OF THE INCREMENT (333.75%) IS GREATER THAN MARR, THE INCREMENTAL INVESTMENT IS ACCEPTED. 1-INCH BECOMES THE NEW CURRENT BEST 2-INCH BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR 2-INCH - 1-INCH ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

2-INCH -$212,500.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00

1-INCH -$100,000.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00 -$41,250.00

INCR. CF -$112,500.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00 $11,250.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 0.00% =IRR(E60:E70) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 0.00% =RATE(10,11250,-112500) THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE VALUES IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= 0.00% NPV = $0.00 =NPV(C82,E61:E70)+E60 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C83 0 C82

SOLUTION USING EXCEL'S GOAL SEEK GOAL SEEK DOES NOT CONVERGE ON A SOLUTION. SINCE THE IRR OF THE INCREMENT (0.00%) IS LESS THAN MARR, THE INCREMENTAL INVESTMENT IS REJECTED. 1-INCH REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, 1-INCH IS RECOMMENDED.

PROBLEM 8.38 IRR COMPARISONS MUST BE DONE INCREMENTALLY MARR IS 15% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, AUBURN, LAGRANGE, ANNISTON NULL BECOMES THE "CURRENT BEST" AND AUBURN THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR AUBURN - NULL ARE NEEDED EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

AUBURN -$1,000,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

NULL INCR. CF $0.00 -$1,000,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00 $0.00 $410,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 40.29% =IRR(E14:E26) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 40.29% =RATE(12,410000,-1000000,,,50%); INITIAL GUESS IS REQUIRED FOR CONVERGENCE SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 40.00% $6,920.46 IRR $0.00 50.00% -$186,320.02 IRR = 40.36% =B36+(B38-B36)*(C37-C36)/(C38-C36) SOLUTION USING EXCEL'S SOLVER i= 40.29% NPV = $0.00 =NPV(C42,E15:E26)+E14 SOLVER PARAMETERS SET TARGET CELL: C43 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C42 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 40.29% NPV = $0.00 =NPV(C51,E15:E26)+E14 SOLVER PARAMETERS SET TARGET CELL: C52 VALUE OF: 0 BY CHANGING CELL: C51 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED. AUBURN BECOMES THE NEW CURRENT BEST LAGRANGE BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR LAGRANGE - AUBURN ARE NEEDED EOY 0 1

LAGRANGE AUBURN -$1,260,000.00 -$1,000,000.00 $480,000.00 $410,000.00

INCR. CF -$260,000.00 $70,000.00

2 3 4 5 6 7 8 9 10 11 12

$480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

$410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

$70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00 $70,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 25.09% =IRR(E65:E77) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 25.09% =RATE(12,70000,-260000,,,20%); INITIAL GUESS IS REQUIRED FOR CONVERGENCE SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 25.00% $758.55 IRR $0.00 30.00% -$36,681.80 IRR = 25.10% =B87+(B89-B87)*(C88-C87)/(C89-C87) SOLUTION USING EXCEL'S SOLVER i= 25.09% NPV = $0.00 =NPV(C93,E66:E77)+E65 SOLVER PARAMETERS SET TARGET CELL: C94 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C93 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 25.09% NPV = $0.00 =NPV(C102,E66:E77)+E65 SOLVER PARAMETERS SET TARGET CELL: C103 VALUE OF: 0 BY CHANGING CELL: C102 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED. LAGRANGE BECOMES THE NEW CURRENT BEST ANNISTON BECOMES THE NEXT CHALLENGER THUS, THE CASH FLOWS FOR ANNISTON - LAGRANGE ARE NEEDED EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 4.73% =IRR(E116:E128)

INCR. CF -$360,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00 $40,000.00

SOLUTION USING EXCEL'S RATE FUNCTION IRR = 4.73% =RATE(12,40000,-360000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 4.00% $15,402.95 IRR $0.00 5.00% -$5,469.93 IRR = 4.74% =B138+(B140-B138)*(C139-C138)/(C140-C138) SOLUTION USING EXCEL'S SOLVER i= 4.73% NPV = $0.00 =NPV(C144,E117:E128)+E116 SOLVER PARAMETERS SET TARGET CELL: C145 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C144 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 4.73% NPV = $0.00 =NPV(C153,E117:E128)+E116 SOLVER PARAMETERS SET TARGET CELL: C154 VALUE OF: 0 BY CHANGING CELL: C153 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED LAGRANGE REMAINS THE CURRENT BEST

SINCE THERE ARE NO MORE CHALLENGERS, LAGRANGE IS RECOMMENDED.

PROBLEM 8.39 IRR COMPARISONS MUST BE DONE INCREMENTALLY FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS MACHINE A37Y, MACHINE 7745 NULL IS NOT AN OPTION SINCE THE PROBLEM STATES THAT A MACHINE MUST BE PURCHASED MARR IS 6%/YEAR A37Y BECOMES THE "CURRENT BEST" AND 7745 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 7745 - A37Y ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

7745 -$10,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 $700.00

A37Y -$8,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

INCR. CF -$2,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = -6.70% =IRR(E15:E25) SOLUTION USING EXCEL'S RATE FUNCTION IRR = -6.70% =RATE(10,,-2000,1000) THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE RATES IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= -6.70% NPV = $0.00 =NPV(C37,E16:E25)+E15 SOLVER PARAMETERS SET TARGET CELL: C38 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C37 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= -6.70% NPV = $0.00 =NPV(C46,E16:E25)+E15 SOLVER PARAMETERS SET TARGET CELL: C47 VALUE OF: 0 BY CHANGING CELL: C46 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR, THE INCREMENTAL INVESTMENT IS REJECTED. A37Y REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, A37Y IS RECOMMENDED.

PROBLEM 8.40 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS NOT AN OPTION. MARR IS 12% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, A, B NULL BECOMES THE "CURRENT BEST" AND A THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR A-NULL ARE NEEDED PROJECT A EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

A -$50,000.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$50,000.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 13.89% =IRR(E18:E38) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 13.89% =RATE(20,7500,-50000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 12.00% $6,020.83 IRR $0.00 15.00% -$3,055.01 IRR = 13.99% =B48+(B50-B48)*(C49-C48)/(C50-C48) SOLUTION USING EXCEL'S SOLVER i= 13.89% NPV = $0.00 =NPV(C54,E19:E38)+E18 SOLVER PARAMETERS SET TARGET CELL: C55 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C54 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 13.89% NPV = $0.00 =NPV(C63,E19:E38)+E18 SOLVER PARAMETERS SET TARGET CELL: C64 VALUE OF: 0 BY CHANGING CELL: C63 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT (13.89%) IS GREATER THAN MARR (12%) THE INCREMENTAL INVESTMENT IS ACCEPTED A BECOMES THE NEW CURRENT BEST B BECOMES THE CHALLENGER

THUS, THE CASH FLOWS FOR B - A ARE NEEDED B-A EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

B A -$75,000.00 -$50,000.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00 $10,000.00 $7,500.00

INCR CF -$25,000.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 7.75% =IRR(E79:E99) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 7.75% =RATE(20,2500,-25000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 7.00% $1,485.04 IRR $0.00 8.00% -$454.63 IRR = 7.77% =B109+(B111-B109)*(C110-C109)/(C111-C109) SOLUTION USING EXCEL'S SOLVER i= 7.75% NPV = $0.00 =NPV(C115,E80:E99)+E79 SOLVER PARAMETERS SET TARGET CELL: C116 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C115 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 7.75% NPV = $0.00 =NPV(C124,E80:E99)+E79 SOLVER PARAMETERS SET TARGET CELL: C125 VALUE OF: 0 BY CHANGING CELL: C124 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT (7.75%) IS LESS THAN MARR (12%) THE INCREMENTAL INVESTMENT IS REJECTED A REMAINS THE CURRENT BEST

SINCE THERE ARE NO MORE CHALLENGERS, A IS RECOMMENDED.

PROBLEM 8.41 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS NOT AN OPTION. MARR IS 15% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, 2, 3, 1 NULL BECOMES THE "CURRENT BEST" AND 2 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR 2 - NULL ARE NEEDED POLISHER 2 EOY 0 1 2 3 4 5 6 7 8 9 10

2 -$10,000.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$10,000.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00 $1,770.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 12.00% =IRR(E18:E28) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 12.00% =RATE(10,1770,-10000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 12.00% $0.89 IRR $0.00 15.00% -$1,116.78 IRR = 12.00% =B38+(B40-B38)*(C39-C38)/(C40-C38) SOLUTION USING EXCEL'S SOLVER i= 12.00% NPV = $0.00 =NPV(C44,E19:E28)+E18 SOLVER PARAMETERS SET TARGET CELL: C45 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C44 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 12.00% NPV = $0.00 =NPV(C53,E19:E28)+E18 SOLVER PARAMETERS SET TARGET CELL: C54 VALUE OF: 0 BY CHANGING CELL: C53 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED NULL STAYS THE NEW CURRENT BEST 3 BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR 3 - NULL ARE NEEDED POLISHER 3

EOY 0 1 2 3 4 5 6 7 8 9 10

3 -$15,000.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$15,000.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 20.02% =IRR(E69:E79) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 20.02% =RATE(10,3580,-15000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 20.00% $9.05 IRR $0.00 25.00% -$2,217.60 IRR = 20.02% =B89+(B91-B89)*(C90-C89)/(C91-C89) SOLUTION USING EXCEL'S SOLVER i= 20.02% NPV = $0.00 =NPV(C95,E70:E79)+E69 SOLVER PARAMETERS SET TARGET CELL: C96 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C95 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 20.02% NPV = $0.00 =NPV(C104,E70:E79)+E69 SOLVER PARAMETERS SET TARGET CELL: C105 VALUE OF: 0 BY CHANGING CELL: C104 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED 3 BECOMES THE NEW CURRENT BEST 1 BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR 1 - 3 ARE NEEDED POLISHER 1 - POLISHER 3 EOY 0 1 2 3 4 5 6 7 8 9 10

1 -$20,000.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00 $4,465.00

3 -$15,000.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00 $3,580.00

INCR CF -$5,000.00 $885.00 $885.00 $885.00 $885.00 $885.00 $885.00 $885.00 $885.00 $885.00 $885.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 12.00% =IRR(E120:E130)

SOLUTION USING EXCEL'S RATE FUNCTION IRR = 12.00% =RATE(10,885,-5000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 12.00% $0.45 IRR $0.00 15.00% -$558.39 IRR = 12.00% =B140+(B142-B140)*(C141-C140)/(C142-C140) SOLUTION USING EXCEL'S SOLVER i= 12.00% NPV = $0.00 =NPV(C146,E121:E130)+E120 SOLVER PARAMETERS SET TARGET CELL: C147 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C146 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 12.00% NPV = $0.00 =NPV(C155,E121:E130)+E120 SOLVER PARAMETERS SET TARGET CELL: C156 VALUE OF: 0 BY CHANGING CELL: C155 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED 3 STAYS THE NEW CURRENT BEST

THERE ARE NO MORE CHALLENGERS, THUS POLISHER 3 IS RECOMMENDED

PROBLEM 8.42 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS NOT AN OPTION. MARR IS 10% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, B002, C003, A001 NULL BECOMES THE "CURRENT BEST" AND B002 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR B002-NULL ARE NEEDED B002 - NULL EOY 0 1 2 3 4

B002 -$110.00 $60.00 $60.00 $60.00 $70.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00

NET CF -$110.00 $60.00 $60.00 $60.00 $70.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 42.11% =IRR(E18:E22) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 42.11% =RATE(4,60,-110,10) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 40.00% $3.56 IRR $0.00 50.00% -$11.73 IRR = 42.33% =B32+(B34-B32)*(C33-C32)/(C34-C32) SOLUTION USING EXCEL'S SOLVER i= 42.11% NPV = $0.00 =NPV(C38,E19:E22)+E18 SOLVER PARAMETERS SET TARGET CELL: C39 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C38 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 42.11% NPV = $0.00 =NPV(C47,E19:E22)+E18 SOLVER PARAMETERS SET TARGET CELL: C48 VALUE OF: 0 BY CHANGING CELL: C47 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED. B002 BECOMES THE NEW CURRENT BEST C003 BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR C003 - B002 ARE NEEDED C003 - B002 EOY 0 1 2 3 4

C003 -$160.00 $80.00 $80.00 $80.00 $80.00

B002 -$110.00 $60.00 $60.00 $60.00 $70.00

INCR CF -$50.00 $20.00 $20.00 $20.00 $10.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 16.48% =IRR(E63:E67) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 16.48% =RATE(4,20,-50,-10)

SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $1.38 IRR $0.00 18.00% -$1.36 IRR = 16.51% =B77+(B79-B77)*(C78-C77)/(C79-C77) SOLUTION USING EXCEL'S SOLVER i= 16.48% NPV = $0.00 =NPV(C83,E64:E67)+E63 SOLVER PARAMETERS SET TARGET CELL: C84 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C83 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 16.48% NPV = $0.00 =NPV(C92,E64:E67)+E63 SOLVER PARAMETERS SET TARGET CELL: C93 VALUE OF: 0 BY CHANGING CELL: C92 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED. C003 BECOMES THE NEW CURRENT BEST A001 BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR A001 - C003 ARE NEEDED

C003 - B002 EOY 0 1 2 3 4

A001 -$210.00 $80.00 $90.00 $100.00 $110.00

C003 -$160.00 $80.00 $80.00 $80.00 $80.00

INCR CF -$50.00 $0.00 $10.00 $20.00 $30.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 5.65% =IRR(E109:E113) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 5.00% $1.03 IRR $0.00 6.00% -$0.54 IRR = 5.65% =B123+(B125-B123)*(C124-C123)/(C125-C123) SOLUTION USING EXCEL'S SOLVER i= 5.65% NPV = $0.00 =NPV(C129,E110:E113)+E109 SOLVER PARAMETERS SET TARGET CELL: C133 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C132 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 5.65% NPV = $0.00 =NPV(C138,E110:E113)+E109 SOLVER PARAMETERS SET TARGET CELL: C142 VALUE OF: 0 BY CHANGING CELL: C141 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED. SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, C003 IS RECOMMENDED

PROBLEM 8.43 SINCE EACH INVESTMENT REQUIRES A $12,000 INVESTMENT, THE IRRs CAN BE CALCULATED AND COMPARED DIRECTLY. THE LARGEST IRR IS PREFERRED. SAVINGS CERTIFICATE EOM 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

- CF -$12,000.00

SINCE THE CASH FLOWS ARE MONTHLY, THE IRR DETERMINED WILL BE AN EFFECTIVE MONTHLY RATE. A CONVERSION TO EFFECTIVE ANNUAL IS REQUIRED AND PERFORMED BELOW.

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 0.94% =IRR(E9:E69,1%); INITIAL GUESS IS REQUIRED FOR CONVERGENCE SOLUTION USING EXCEL'S RATE FUNCTION IRR = 0.95% =RATE(60,100,-12000,13100) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 0.75% $1,120.43 IRR $0.00 1.00% -$348.65 IRR = 0.94% =B83+(B85-B83)*(C84-C83)/(C85-C83) SOLUTION USING EXCEL'S SOLVER i= 0.94% NPV = $0.00 NPV(C89,E10:E69)+E9 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 0.94% NPV = $0.00 =NPV(C98,E10:E69)+E9 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" MONTHLY IRR = ANNUALIZED IRR =

C90 0 C89

C99 0 C98

0.94% 11.85% =((1+D106)^12)-1

RACE HORSE EOM 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

+ CF $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

- CF -$12,000.00

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $20,000.00

SINCE THE CASH FLOWS ARE MONTHLY, THE IRR DETERMINED WILL BE AN EFFECTIVE MONTHLY RATE. A CONVERSION TO EFFECTIVE ANNUAL IS REQUIRED AND PERFORMED BELOW. SOLUTION USING EXCEL'S IRR FUNCTION IRR = 0.86% =IRR(E113:E173,1%); INITIAL GUESS IS REQUIRED FOR CONVERGENCE SOLUTION USING EXCEL'S RATE FUNCTION IRR = 0.86% =RATE(60,,-12000,20000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 0.75% $773.99 IRR $0.00 1.00% -$991.01 IRR = 0.86% =B187+(B189-B187)*(C188-C187)/(C189-C187) SOLUTION USING EXCEL'S SOLVER i= 0.86% NPV = $0.00 =NPV(C193,E114:E173)+E113 SOLVER PARAMETERS SET TARGET CELL: C198 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C197 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 0.86% NPV = $0.00 =NPV(C202,E114:E173)+E113 SOLVER PARAMETERS SET TARGET CELL: C207 VALUE OF: 0 BY CHANGING CELL: C206 CLICK "SOLVE" MONTHLY IRR = ANNUALIZED IRR =

0.86% 10.76% =((1+D210)^12)-1

SAVINGS ACCOUNT SINCE THE SAVINGS ACCOUNT EARNS MARR, THE IRR IS 12% THE SAVINGS ACCOUNT HAS THE HIGHEST IRR AND IS THEREFORE PREFERRED.

PROBLEM 8.44 a

X1 0 1 0 0 0 1 1 1 0 0 0 1 1 1 0 1

X2 0 0 1 0 0 1 0 0 1 1 0 1 1 0 1 1

Y1 0 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1

Y2 0 0 0 0 1 0 0 1 0 1 1 0 1 1 1 1

FEASIBLE YES YES YES NO NO NO YES NO NO YES NO NO NO NO NO NO

REASON

Y1 CONTINGENT ON X1 Y2 CONTINGENT ON X2 X1 & X2 ARE ME Y2 CONTINGENT ON X2 Y1 CONTINGENT ON X1 Y1 & Y2 ARE ME X1 & X2 ARE ME X1 & X2 ARE ME Y1 & Y2 ARE ME Y1 & Y2 ARE ME X1 & X2 ARE ME

FEASIBLE COMBINATIONS ARE: NULL, X1 ONLY, X2 ONLY, X1&Y1, X2&Y2 b

IRR COMPARISONS MUST BE DONE INCREMENTALLY MARR IS 10% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL ($0), X1 ($10K), X2 ($15K), X1&Y1 ($16K), X2&X2 ($24K) NULL BECOMES THE "CURRENT BEST" AND X1 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED X1 - NULL EOY 0 1 2 3 4 5 6 7 8

X1 -$10,000.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$10,000.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00 $1,600.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 5.84% =IRR(E40:E48) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 5.84% =RATE(8,1600,-10000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 5.00% $341.14 IRR $0.00 6.00% -$64.33 IRR = 5.84% =B58+(B60-B58)*(C59-C58)/(C60-C58) SOLUTION USING EXCEL'S SOLVER i= 5.84% NPV = $0.00 =NPV(C64,E41:E48)+E40 SOLVER PARAMETERS SET TARGET CELL: C65 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C64 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 5.84% NPV = $0.00 =NPV(C73,E41:E48)+E40 SOLVER PARAMETERS SET TARGET CELL: C74 VALUE OF: 0

BY CHANGING CELL: CLICK "SOLVE"

C73

SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED NULL REMAINS THE CURRENT BEST X2 BECOMES THE CHALLENGER X2 - NULL EOY 0 1 2 3 4 5 6 7 8

X2 -$15,000.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$15,000.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00 $2,600.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 7.90% =IRR(E88:E96) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 7.90% =RATE(8,2600,-15000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 7.00% $525.38 IRR $0.00 8.00% -$58.74 IRR = 7.90% =B106+(B108-B106)*(C107-C106)/(C108-C106) SOLUTION USING EXCEL'S SOLVER i= 7.90% NPV = $0.00 =NPV(C112,E89:E96)+E88 SOLVER PARAMETERS SET TARGET CELL: C113 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C112 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 7.90% NPV = $0.00 =NPV(C121,E89:E96)+E88 SOLVER PARAMETERS SET TARGET CELL: C122 VALUE OF: 0 BY CHANGING CELL: C121 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED NULL REMAINS THE CURRENT BEST X1&Y1 BECOMES THE CHALLENGER X1&Y1 - NULL EOY 0 1 2 3 4 5 6 7 8

X1&Y1 -$16,000.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$16,000.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00 $4,100.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 19.44% =IRR(E136:E144) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 19.44% =RATE(8,4100,-16000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 18.00% $718.02

IRR 20.00% IRR =

$0.00 -$267.64 19.46% =B154+(B156-B154)*(C155-C154)/(C156-C154)

SOLUTION USING EXCEL'S SOLVER i= 19.44% NPV = $0.00 =NPV(C160,E137:E144)+E136 SOLVER PARAMETERS SET TARGET CELL: C161 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C160 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 19.44% NPV = $0.00 =NPV(C169,E137:E144)+E136 SOLVER PARAMETERS SET TARGET CELL: C170 VALUE OF: 0 BY CHANGING CELL: C169 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED X1&Y1 BECOMES THE NEW CURRENT BEST X2&Y2 BECOMES THE CHALLENGER X2&Y2 - X1Y1 EOY 0 1 2 3 4 5 6 7 8

X2&Y2 X1&Y1 -$24,000.00 -$16,000.00 $6,100.00 $4,100.00 $6,100.00 $4,100.00 $6,100.00 $4,100.00 $6,100.00 $4,100.00 $6,100.00 $4,100.00 $6,100.00 $4,100.00 $6,100.00 $4,100.00 $6,100.00 $4,100.00

INCR CF -$8,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 18.62% =IRR(E184:E192) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 18.62% =RATE(8,2000,-8000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 18.00% $155.13 IRR $0.00 20.00% -$325.68 IRR = 18.65% =B202+(B204-B202)*(C203-C202)/(C204-C202) SOLUTION USING EXCEL'S SOLVER i= 18.62% NPV = $0.00 =NPV(C208,E185:E192)+E184 SOLVER PARAMETERS SET TARGET CELL: C209 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C208 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 18.62% NPV = $0.00 =NPV(C217,E185:E192)+E184 SOLVER PARAMETERS SET TARGET CELL: C218 VALUE OF: 0 BY CHANGING CELL: C217 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED X2&Y2 BECOMES THE NEW CURRENT BEST SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, X2&Y2 IS RECOMMENDED

PROBLEM 8.45 IRR COMPARISONS MUST BE DONE INCREMENTALLY FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, T3, T4, T1, T2 a

MARR IS 25%/YEAR NULL BECOMES THE "CURRENT BEST" AND T3 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR T3 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR. CF -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 39.14% =IRR(E14:E24) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 39.14% =RATE(10,190000,-470000,65000,,40%); AN INITIAL GUESS IS REQUIRED FOR CONVERGENCE SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 30.00% $122,107.48 IRR $0.00 40.00% -$9,174.36 IRR = 39.30% =B34+(B36-B34)*(C35-C34)/(C36-C34) SOLUTION USING EXCEL'S SOLVER i= 39.14% NPV = $0.00 =NPV(C40,E15:E24)+E14 SOLVER PARAMETERS SET TARGET CELL: C41 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C40 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 39.14% NPV = $0.00 =NPV(C49,E15:E24)+E14 SOLVER PARAMETERS SET TARGET CELL: C50 VALUE OF: 0 BY CHANGING CELL: C49 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (25%) THE INCREMENTAL INVESTMENT IS ACCEPTED. T3 BECOMES THE NEW CURRENT BEST T4 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T4 - T3 ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9

T4 -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00

INCR. CF -$70,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

PROBLEM 8.46 IRR COMPARISONS MUST BE DONE INCREMENTALLY MARR IS 6%; ALL DOLLAR VALUES ARE IN M$ FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS EXTENDED, ONE-TIME EXTENDED BECOMES THE "CURRENT BEST" AND ONE-TIME THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED ONE-TIME - EXTENDED EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

ONE-TIME -$14.40 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

EXTENDED -$1.00 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30 -$1.30

INCR CF -$13.40 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30 $1.30

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 7.36% =IRR(E15:E35) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 7.36% =RATE(20,1.3,-13.4) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 7.00% $0.37 IRR $0.00 8.00% -$0.64 IRR = 7.37% =B45+(B47-B45)*(C46-C45)/(C47-C45) SOLUTION USING EXCEL'S SOLVER i= 7.36% NPV = $0.00 =NPV(C51,E16:E35)+E15 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 7.36% NPV = $0.00 =NPV(C60,E16:E35)+E15 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C52 0 C51

C61 0 C60

SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED ONE-TIME BECOMES THE NEW CURRENT BEST SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, ONE-TIME IS RECOMMENDED

PROBLEM 8.47 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS AN OPTION. MARR IS 20% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS GATE 1, GATE 2, GATE 3 GATE 1 BECOMES THE "CURRENT BEST" AND GATE 2 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR GATE 2 - GATE 1 ARE NEEDED GATE 2 - GATE 1 EOY 0 1 2 3 4 5

GATE 2 -$19,000.00 -$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00 -$3,600.00

GATE 1 -$15,000.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00

INCR CF -$4,000.00 $900.00 $900.00 $900.00 $900.00 $2,900.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 15.10% =IRR(E18:E23) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 15.10% =RATE(5,900,-4000,2000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $11.29 IRR $0.00 18.00% -$311.33 IRR = 15.11% =B33+(B35-B33)*(C34-C33)/(C35-C33) SOLUTION USING EXCEL'S SOLVER i= 15.10% NPV = $0.00 =NPV(C39,E19:E23)+E18 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 15.10% NPV = $0.00 =NPV(C48,E19:E23)+E18 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C40 0 C39

C49 0 C48

SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED. GATE 1 REMAINS THE NEW CURRENT BEST GATE 3 BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR GATE 3 - GATE 1 ARE NEEDED GATE 3 - GATE 1 EOY 0 1

GATE 3 -$24,000.00 -$4,000.00

GATE 1 -$15,000.00 -$6,500.00

INCR CF -$9,000.00 $2,500.00

2 3 4 5

-$4,000.00 -$4,000.00 -$4,000.00 $1,000.00

-$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00

$2,500.00 $2,500.00 $2,500.00 $7,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 22.04% =IRR(E64:E69) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 22.04% =RATE(5,2500,-9000,5000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 20.00% $485.92 IRR $0.00 25.00% -$638.40 IRR = 22.16% =B79+(B81-B79)*(C80-C79)/(C81-C79) SOLUTION USING EXCEL'S SOLVER i= 22.04% NPV = $0.00 =NPV(C85,E65:E69)+E64 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 22.04% NPV = $0.00 =NPV(C94,E65:E69)+E64 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C86 0 C85

C95 0 C94

SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED. GATE 3 BECOMES THE NEW CURRENT BEST THERE ARE NO MORE CHALLENGERS TO CONSIDER. THUS, GATE 3 IS RECOMMENDED.

PROBLEM 8.48 IRR COMPARISONS MUST BE DONE INCREMENTALLY MARR IS 10% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, BAR, SPOT, BEAM NULL BECOMES THE "CURRENT BEST" AND BAR THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED BAR - NULL EOY 0 1 2 3 4 5 6

BAR -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 24.29% =IRR(E15:E21) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 24.29% =RATE(6,2000,-6000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 20.00% $651.02 IRR $0.00 25.00% -$97.15 IRR = 24.35% =B31+(B33-B31)*(C32-C31)/(C33-C31) SOLUTION USING EXCEL'S SOLVER i= 24.29% NPV = $0.00 =NPV(C37,E16:E21)+E15 SOLVER PARAMETERS SET TARGET CELL: C38 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C37 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 24.29% NPV = $0.00 =NPV(C46,E16:E21)+E15 SOLVER PARAMETERS SET TARGET CELL: C47 VALUE OF: 0 BY CHANGING CELL: C46 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED. LIGHT BAR BECOMES THE NEW CURRENT BEST SLIDING SPOTS BECOMES THE CHALLENGER SPOTS - BAR EOY 0 1 2 3 4 5 6

SPOTS -$14,000.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00

BAR -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

INCR CF -$8,000.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 3.47% =IRR(E61:E67) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 3.47% =RATE(6,1500,-8000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 3.00% $125.79

IRR 4.00% IRR =

$0.00 -$136.79 3.48% =B77+(B79-B77)*(C78-C77)/(C79-C77)

SOLUTION USING EXCEL'S SOLVER i= 3.47% NPV = $0.00 =NPV(C83,E62:E67)+E61 SOLVER PARAMETERS SET TARGET CELL: C87 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C86 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 3.47% NPV = $0.00 =NPV(C92,E62:E67)+E61 SOLVER PARAMETERS SET TARGET CELL: C96 VALUE OF: 0 BY CHANGING CELL: C95 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED LIGHT BAR REMAINS THE CURRENT BEST REFLECTED BEAM BECOMES THE CHALLENGER

BEAM - BAR EOY 0 1 2 3 4 5 6

BEAM -$20,000.00 $0.00 $2,300.00 $4,600.00 $6,900.00 $9,200.00 $11,500.00

BAR -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

INCR CF -$14,000.00 -$2,000.00 $300.00 $2,600.00 $4,900.00 $7,200.00 $9,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 9.35% =IRR(E108:E114) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 9.00% $240.65 IRR $0.00 10.00% -$436.93 IRR = 9.36% =B124+(B126-B124)*(C125-C124)/(C126-C124) SOLUTION USING EXCEL'S SOLVER i= 9.35% NPV = $0.00 =NPV(C130,E109:E114)+E108 SOLVER PARAMETERS SET TARGET CELL: C131 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C130 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 9.35% NPV = $0.00 =NPV(C139,E109:E114)+E108 SOLVER PARAMETERS SET TARGET CELL: C140 VALUE OF: 0 BY CHANGING CELL: C139 CLICK "SOLVE"

SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED LIGHT BAR REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, LIGHT BAR IS RECOMMENDED

PROBLEM 8.49 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS AN OPTION. MARR IS 10%; ALL CASH FLOWS ARE IN $K FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS FIRST SATELLITE ONLY, SECOND SATELLITE ONLY, BOTH SATELLITES FIRST ONLY BECOMES THE "CURRENT BEST" AND SECOND ONLY THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED SECOND ONLY - FIRST ONLY EOY 0 1 2 3 4 5

SECOND ONLY -$850.00 -$120.00 -$120.00 -$120.00 -$120.00 $2,105.00

FIRST ONLY -$750.00 -$150.00 -$150.00 -$150.00 -$150.00 $2,075.00

INCR CF -$100.00 $30.00 $30.00 $30.00 $30.00 $30.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 15.24% =IRR(E17:E22) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 15.24% =RATE(5,30,-100) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $0.56 IRR $0.00 18.00% -$6.18 IRR = 15.25% =B32+(B34-B32)*(C33-C32)/(C34-C32) SOLUTION USING EXCEL'S SOLVER i= 15.24% NPV = $0.00 =NPV(C38,E18:E22)+E17 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 15.24% NPV = $0.00 =NPV(C47,E18:E22)+E17 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C39 0 C38

C48 0 C47

SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED SECOND ONLY BECOMES THE NEW CURRENT BEST BOTH BECOMES THE CHALLENGER THUS THE CASH FLOWS OF BOTH - SECOND ONLY ARE NEEDED. BOTH - SECOND ONLY EOY 0 1 2 3 4 5

BOTH -$1,750.00 -$400.00 -$400.00 -$400.00 -$400.00 $5,250.00

SECOND ONLY -$850.00 -$120.00 -$120.00 -$120.00 -$120.00 $2,105.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 12.56% =IRR(E63:E68)

INCR CF -$900.00 -$280.00 -$280.00 -$280.00 -$280.00 $3,145.00

SOLUTION USING EXCEL'S RATE FUNCTION IRR = 12.56% =RATE(5,-280,-900,3425) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 12.00% $34.10 IRR $0.00 15.00% -$135.77 IRR = 12.60% =B78+(B80-B78)*(C79-C78)/(C80-C78) SOLUTION USING EXCEL'S SOLVER i= 12.56% NPV = $0.00 =NPV(C84,E64:E68)+E63 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 12.56% NPV = $0.00 =NPV(C93,E64:E68)+E63 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C85 0 C84

C94 0 C93

SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED BOTH BECOMES THE NEW CURRENT BEST THERE ARE NO MORE CHALLENGERS TO CONSIDER. THUS CONTRACTING FOR BOTH SATELLITES IS PREFERRED.

PROBLEM 8.50 IRR COMPARISONS MUST BE DONE INCREMENTALLY MARR IS 10% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS LEASE, PURCHASE LEASE BECOMES THE "CURRENT BEST" AND PURCHASE THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED PURCHASE - LEASE EOY 0 1 2 3

PURCHASE -$60,000.00 $23,000.00 $23,000.00 $33,000.00

LEASE -$21,000.00 $2,000.00 $2,000.00 $23,000.00

INCR CF -$39,000.00 $21,000.00 $21,000.00 $10,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 17.94% =IRR(E15:E18) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 17.94% =RATE(3,21000,-39000,-11000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 15.00% $1,715.05 IRR $0.00 18.00% -$35.21 IRR = 17.94% =B28+(B30-B28)*(C29-C28)/(C30-C28) SOLUTION USING EXCEL'S SOLVER i= 17.94% NPV = $0.00 =NPV(C34,E16:E18)+E15 SOLVER PARAMETERS SET TARGET CELL: C38 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C37 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 17.94% NPV = $0.00 =NPV(C43,E16:E18)+E15 SOLVER PARAMETERS SET TARGET CELL: C47 VALUE OF: 0 BY CHANGING CELL: C46 CLICK "SOLVE" SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED PURCHASE BECOMES THE NEW CURRENT BEST SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, PURCHASE IS RECOMMENDED

PROBLEM 8.51 MARR IS 10%/YEAR a

EOY 0 1 2 3 4 5 6

CF -$100.00 $15.00 $15.00 $15.00 $15.00 $15.00 $15.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 2.47% =RATE(6,,-100,FV(10%,6,-15)) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 2.47% =MIRR(C6:C12,,10%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 2.00% -$3.12 =FV(B22,6,,-100)+FV(10%,6,15) ERR $0.00 3.00% $3.67 =FV(B24,6,,-100)+FV(10%,6,15) ERR = 2.46% =B22+(B24-B22)*(C23-C22)/(C24-C22) SOLUTION USING EXCEL'S SOLVER i= 2.47% FV = $0.00 =FV(C28,6,,-100)+FV(10%,6,15) SOLVER PARAMETERS SET TARGET CELL: C32 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C31 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 2.47% FV = $0.00 =FV(C37,6,,-100)+FV(10%,6,15) SOLVER PARAMETERS SET TARGET CELL: C41 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C40 CLICK "SOLVE" b

ERR < MARR (10%); THEREFORE, NOT ATTRACTIVE

PROBLEM 8.52 MARR IS 10%/YEAR a

EOY 0 1 2 3 4 5 6

CF -$100.00 $25.00 $25.00 $25.00 $25.00 $25.00 $25.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 11.57% =RATE(6,,-100,FV(10%,6,-25)) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 11.57% =MIRR(C6:C12,,10%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 10.00% -$15.73 =FV(B22,6,,-100)+FV(10%,6,25) ERR $0.00 12.00% $4.49 =FV(B24,6,,-100)+FV(10%,6,25) ERR = 11.56% =B22+(B24-B22)*(C23-C22)/(C24-C22) SOLUTION USING EXCEL'S SOLVER i= 11.57% FV = $0.00 =FV(C28,6,,-100)+FV(10%,6,25) SOLVER PARAMETERS SET TARGET CELL: C29 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C28 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 11.57% FV = $0.00 =FV(C37,6,,-100)+FV(10%,6,25) SOLVER PARAMETERS SET TARGET CELL: C38 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C37 CLICK "SOLVE" b

ERR >= MARR (10%); THEREFORE, ATTRACTIVE

PROBLEM 8.53

MARR IS 10%/YEAR EOY 0 1 2 3 4 5 6

- CF -$100.00 $0.00 $0.00 $0.00 -$30.00 $0.00 $0.00

+ CF $0.00 $25.00 $25.00 $60.00 $0.00 $60.00 $25.00

NET CF -$100.00 $25.00 $25.00 $60.00 -$30.00 $60.00 $25.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 12.00% $12.71 =FV(B25,6,,100)+FV(B25,2,,30)+FV(10%,6,,-NPV(10%,D8:D13)) ERR $0.00 15.00% -$23.26 =FV(B27,6,,-100)+FV(B25,2,,-39)+FV(10%,6,,NPV(10%,D8:D13)) ERR = 13.06% =B25+(B27-B25)*(C26-C25)/(C27-C25) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$100.00 1 $0.00 2 $0.00 3 $0.00 4 -$30.00 5 $0.00 6 $247.73 =FV(10%,6,,-NPV(10%,D8:D13)) ERR = 13.10% =IRR(C32:C38) SOLUTION USING EXCEL'S SOLVER i= 13.10% FV = $0.00 =FV(C42,6,,100)+FV(C42,2,,30)+FV(10%,6,,-NPV(10%,D8:D13)) SOLVER PARAMETERS SET TARGET CELL: C43 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C42 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 13.10% FV = $0.00 =FV(C51,6,,100)+FV(C51,2,,30)+FV(10%,6,,-NPV(10%,D8:D13)) SOLVER PARAMETERS SET TARGET CELL: C52 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C51 CLICK "SOLVE" b

ERR >= MARR (10%); THEREFORE, ATTRACTIVE

PROBLEM 8.54

MARR IS 10%/YEAR EOY 0 1 2 3 4 5 6

- CF -$100.00 $0.00 $0.00 -$100.00 $0.00 -$200.00 -$100.00

+ CF $25.00 $200.00 $0.00 $250.00 $0.00 $0.00

NET CF -$100.00 $25.00 $200.00 -$100.00 $250.00 -$200.00 -$100.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 10.00% $5.33 =FV(B24,6,,100)+FV(B24,3,,100)+FV(B24,1,,200)+(-100)+FV(10%,6,,-NPV(10%,D8:D13)) ERR $0.00 11.00% -$10.22 =FV(B26,6,,100)+FV(B26,3,,100)+FV(B26,1,,200)+(-100)+FV(10%,6,,-NPV(10%,D8:D13)) ERR = 10.34% =B25+(B27-B25)*(C26-C25)/(C27-C25) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$100.00 1 $0.00 2 $0.00 3 -$100.00 4 $0.00 5 -$200.00 6 $535.58 =-100+FV(10%,6,,-NPV(10%,D8:D13)) ERR = 10.35% =IRR(C31:C37) SOLUTION USING EXCEL'S SOLVER i= 10.35% FV = $0.00 =FV(C41,6,,100)+FV(C41,3,,100)+FV(C41,1,,200)+(-100)+FV(10%,6,,-NPV(10%,D8:D13)) SOLVER PARAMETERS SET TARGET CELL: C42 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C41 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 10.35% FV = $0.00 =FV(C50,6,,100)+FV(C50,3,,100)+FV(C50,1,,200)+(-100)+FV(10%,6,,-NPV(10%,D8:D13)) SOLVER PARAMETERS SET TARGET CELL: C51 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C50 CLICK "SOLVE" b

ERR >= MARR (10%); THEREFORE, ATTRACTIVE

PROBLEM 8.55 a

MARR IS 10%/YEAR

EOY 0 1 2 3 4 5 6

- CF -$100.00 $0.00 -$750.00 $0.00 -$950.00 $0.00 -$800.00

+ CF $800.00 $0.00 $900.00 $0.00 $700.00 $0.00

NET CF -$100.00 $800.00 -$750.00 $900.00 -$950.00 $700.00 -$800.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 10.00% $31.58 =FV(B25,6,,100)+FV(B25,4,,750)+FV(B25,2,,950)+(-800)+FV(10%,6,,-NPV(10%,D8:D13)) ERR $0.00 11.00% -$39.78 =FV(B27,6,,100)+FV(B27,4,,750)+FV(B27,2,,950)+(-800)+FV(10%,6,,-NPV(10%,D8:D13)) ERR = 10.44% =B25+(B27-B25)*(C26-C25)/(C27-C25) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$100.00 1 $0.00 2 -$750.00 3 $0.00 4 -$950.00 5 $0.00 6 $2,456.31 =-800+FV(10%,6,,-NPV(10%,D8:D13)) ERR = 10.45% =IRR(C32:C38) SOLUTION USING EXCEL'S SOLVER i= 10.45% FV = $0.00 =FV(C42,6,,100)+FV(C42,4,,750)+FV(C42,2,,950)+(-800)+FV(10%,6,,-NPV(10%,D8:D13)) SOLVER PARAMETERS SET TARGET CELL: C43 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C42 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 10.45% FV = $0.00 =FV(C51,6,,100)+FV(C51,4,,750)+FV(C51,2,,950)+(-800)+FV(10%,6,,-NPV(10%,D8:D13)) SOLVER PARAMETERS SET TARGET CELL: C52 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C51 CLICK "SOLVE" b

ERR (10.45%) >= MARR (10%); THEREFORE, ATTRACTIVE

PROBLEM 8.56

MARR IS 10%/YEAR

EOY 0 1 2 3 4 5 6

- CF -$101.00 $0.00 -$558.00 $0.00 $0.00 $0.00 -$14.00

+ CF $411.00 $0.00 $253.00 $2.00 $8.00 $0.00

NET CF -$101.00 $411.00 -$558.00 $253.00 $2.00 $8.00 -$14.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 9.00% $38.83 =FV(B25,6,,101)+FV(B25,4,,558)+(-14)+FV(10%,6,,-NPV(10%,D9:D14)) ERR $0.00 10.00% -$0.01 =FV(B27,6,,101)+FV(B27,4,,558)+(-14)+FV(10%,6,,-NPV(10%,D9:D14)) ERR = 9.9997% =B25+(B27-B25)*(C26-C25)/(C27-C25) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$101.00 1 $0.00 2 -$558.00 3 $0.00 4 $0.00 5 $0.00 6 $995.88 =-14+FV(10%,6,,-NPV(10%,D9:D14)) ERR = 9.9997% =IRR(C32:C38) SOLUTION USING EXCEL'S SOLVER i= 9.9997% FV = $0.00 =FV(C42,6,,101)+FV(C42,4,,558)+(-14)+FV(10%,6,,-NPV(10%,D9:D14)) SOLVER PARAMETERS SET TARGET CELL: C43 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C42 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 9.9997% FV = $0.00 =FV(C51,6,,101)+FV(C51,4,,558)+(-14)+FV(10%,6,,-NPV(10%,D9:D14)) SOLVER PARAMETERS SET TARGET CELL: C52 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C51 CLICK "SOLVE" b

ERR (9.9997%)< MARR (10%); THEREFORE, NOT ATTRACTIVE NOTE: ALTHOUGH IN A STRICT MATHEMATICAL SENSE, THIS PROJECT IS UNATTRACTIVE FOR PRACTICAL PURPOSES, IT DOES RETURN MARR SO IT WOULD LIKELY BE CONSIDERED BY MANY COMPANIES.

PROBLEM 8.57 CASH FLOWS IN K$ MARR IS 20%/YEAR EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

CF -$70.00 $20.00 $19.00 $18.00 $17.00 $16.00 $15.00 $14.00 $13.00 $12.00 $11.00 $10.00 $9.00 $8.00 $7.00 $6.00 $5.00 $4.00 $3.00 $2.00 $1.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 20.47% =RATE(20,,-70,FV(20%,20,,-NPV(20%,C8:C27)),,20%) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 20.47% =MIRR(C7:C27,,20%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 20.00% $216.69 ERR $0.00 25.00% -$3,171.21 ERR = 20.32% =B38+(B40-B38)*(C39-C38)/(C40-C38) SOLUTION USING EXCEL'S SOLVER i= 20.47% FV = $0.00 =FV(C44,20,,70)+FV(20%,20,,-NPV(20%,C8:C27)) SOLVER PARAMETERS SET TARGET CELL: C45 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C44 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 20.47% FV = $0.00 =FV(C53,20,,70)+FV(20%,20,,-NPV(20%,C8:C27)) SOLVER PARAMETERS SET TARGET CELL: C54 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C53 CLICK "SOLVE"

(1) ERR = 20.47% (2) INVESTMENT IS ATTRACTIVE; NU THINGS SHOULD INVEST IN THE BUSINESS VENTURE (3) IF ERR >= MARR (20%), THEN ATTRACTIVE; OTHERWISE, UNATTRACTIVE

PROBLEM 8.58 NOTE: PROBLEMS 8.58, 8.59, 8.61, AND 8.62 INCLUDE TWO SOLUTIONS. ONE SOLUTION USES THE POSITIVE CASH FLOWS (Rt) AND NEGATIVE CASH FLOWS (Ct) BEFORE NETTING. THE OTHER SOLUTION USES THE CASH FLOWS AFTER NETTING (At = Rt - Ct). IN EACH CASE, THE NUMERIC RESULTS DIFFER BUT THE DECISIONS ARE CONSISTENT. SUBSEQUENT PROBLEMS USE ONLY THE NETTED CASH FLOWS. a

SOLUTION USING Rt AND Ct CASH FLOWS BEFORE NETTING MARR IS 6%/YEAR EOY - CF + CF NET CF 0 -$5,000.00 -$5,000.00 1 -$200.00 $0.00 -$200.00 2 -$300.00 $2,000.00 $1,700.00 3 -$600.00 $4,000.00 $3,400.00 4 -$1,000.00 $3,000.00 $2,000.00 5 -$1,500.00 $1,600.00 $100.00 DUE TO MULTIPLE NEGATIVE VALUES IN THE CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 8.00% $379.94 =FV(B26,5,,5000)+FV(B26,4,,200)+FV(B26,3,,300)+FV(B26,2,,600)+FV(B26,1,,1000)+(-1500)+FV(6%,5,,-NPV(6%,D12:D16)) ERR $0.00 9.00% -$10.37 =FV(B28,5,,5000)+FV(B28,4,,200)+FV(B28,3,,300)+FV(B28,2,,600)+FV(B28,1,,1000)+(-1500)+FV(6%,5,,-NPV(6%,D12:D16)) ERR = 8.97% =B26+(B28-B26)*(C27-C26)/(C28-C26) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$5,000.00 1 -$200.00 2 -$300.00 3 -$600.00 4 -$1,000.00 5 $10,156.43 =-1500+FV(6%,5,,-NPV(6%,D12:D16)) ERR = 8.97% =IRR(C33:C38) SOLUTION USING EXCEL'S SOLVER i= 8.97% FV = $0.00 =FV(C42,5,,5000)+FV(C42,4,,200)+FV(C42,3,,300)+FV(C42,2,,600)+FV(C42,1,,1000)+(-1500)+FV(6%,5,,-NPV(6%,D12:D16)) SOLVER PARAMETERS SET TARGET CELL: C43 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C42 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 8.97% FV = $0.00 =FV(C51,5,,5000)+FV(C51,4,,200)+FV(C51,3,,300)+FV(C51,2,,600)+FV(C51,1,,1000)+(-1500)+FV(6%,5,,-NPV(6%,D12:D16)) SOLVER PARAMETERS SET TARGET CELL: C52 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C51 CLICK "SOLVE"

IF ERR (8.97%) >= MARR (6%), THEN ACCEPT; OTHERWISE, REJECT

DURATECH SHOULD IMPLEMENT THE PROCESS IMPROVEMENT

SOLUTION USING NETTED CASH FLOWS MARR IS 6%/YEAR EOY - CF + CF NET CF 0 -$5,000.00 $0.00 -$5,000.00 1 -$200.00 $0.00 -$200.00 2 -$300.00 $2,000.00 $1,700.00 3 -$600.00 $4,000.00 $3,400.00 4 -$1,000.00 $3,000.00 $2,000.00 5 -$1,500.00 $1,600.00 $100.00

NET - CF -$5,000.00 -$200.00 $0.00 $0.00 $0.00 $0.00

NET + CF $0.00 $0.00 $1,700.00 $3,400.00 $2,000.00 $100.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S

MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 9.00% $89.53 =FV(B82,5,,5000)+FV(B82,4,,200)+FV(6%,5,,-NPV(6%,G68:G72)) ERR $0.00 10.00% -$280.40 =FV(B84,5,,5000)+FV(B84,4,,200)+FV(6%,5,,-NPV(6%,G68:G72)) ERR = 9.24% =B82+(B84-B82)*(C83-C82)/(C84-C82) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$5,000.00 1 -$200.00 2 $0.00 3 $0.00 4 $0.00 5 $8,064.97 =FV(6%,5,,-NPV(6%,G68:G72)) ERR = 9.25% =IRR(C89:C94) SOLUTION USING EXCEL'S SOLVER i= 9.25% FV = $0.00 =FV(C98,5,,5000)+FV(B82,4,,200)+FV(6%,5,,-NPV(6%,G68:G72)) SOLVER PARAMETERS SET TARGET CELL: C99 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C98 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 9.25% FV = $0.00 =FV(C107,5,,5000)+FV(B82,4,,200)+FV(6%,5,,-NPV(6%,G68:G72)) SOLVER PARAMETERS SET TARGET CELL: C108 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C107 CLICK "SOLVE" b

IF ERR (9.25%) >= MARR (6%), THEN ACCEPT; OTHERWISE, REJECT

DURATECH SHOULD IMPLEMENT THE PROCESS IMPROVEMENT

PROBLEM 8.59 NOTE: PROBLEMS 8.58, 8.59, 8.61, AND 8.62 INCLUDE TWO SOLUTIONS. ONE SOLUTION USES THE POSITIVE CASH FLOWS (Rt) AND NEGATIVE CASH FLOWS (Ct) BEFORE NETTING. THE OTHER SOLUTION USES THE CASH FLOWS AFTER NETTING (At = Rt - Ct). IN EACH CASE, THE NUMERIC RESULTS DIFFER BUT THE DECISIONS ARE CONSISTENT. SUBSEQUENT PROBLEMS USE ONLY THE NETTED CASH FLOWS. YEAR 5 ADDITION = $5,000 COMPUTER SALVAGE VALUE LOAN PAYMENTS = 25000*(A|P 15%,3) = 25000*(0.43798) = a

SOLUTION USING Rt AND Ct CASH FLOWS BEFORE NETTING MARR IS 18%/YEAR EOY 0 1 2 3 4 5

+ INV CF $55,000.00 $55,000.00 $55,000.00 $55,000.00 $60,000.00

- INV CF -$100,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00

+ LOAN CF $25,000.00

- LOAN CF -$10,949.50 -$10,949.50 -$10,949.50

NET - CF -$100,000.00 -$35,949.50 -$35,949.50 -$35,949.50 -$25,000.00 -$25,000.00

NET + CF $25,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $60,000.00

NET CF -$75,000.00 $19,050.50 $19,050.50 $19,050.50 $30,000.00 $35,000.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 15.00% $35,695.95 =FV(B30,5,,100000)+FV(B30,4,,35949.5)+FV(B30,3,,35949.5)+FV(B30,2,,35949.5)+FV(B30,1,,25000)+(-25000)+FV(18%,5,,-NPV(18%,H16:H20)-H15) ERR $0.00 18.00% -$6,420.65 =FV(B32,5,,100000)+FV(B32,4,,35949.5)+FV(B32,3,,35949.5)+FV(B32,2,,35949.5)+FV(B32,1,,25000)+(-25000)+FV(18%,5,,-NPV(18%,H16:H20)-H15) ERR = 17.54% =B30+(B32-B30)*(C31-C30)/(C32-C30) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$100,000.00 1 -$35,949.50 2 -$35,949.50 3 -$35,949.50 4 -$25,000.00 6 $430,675.48 =-25000+FV(18%,5,,-NPV(18%,H16:H20)-H15) ERR = 17.56% =IRR(C37:C42) SOLUTION USING EXCEL'S SOLVER i= 17.56% FV = $0.00 =FV(C46,5,,100000)+FV(C46,4,,35949.5)+FV(C46,3,,35949.5)+FV(C46,2,,35949.5)+FV(C46,1,,25000)+(-25000)+FV(18%,5,,-NPV(18%,H16:H20)-H15) SOLVER PARAMETERS SET TARGET CELL: C47 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C46 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 17.56% FV = $0.00 =FV(C55,5,,100000)+FV(C55,4,,35949.5)+FV(C55,3,,35949.5)+FV(C55,2,,35949.5)+FV(C55,1,,25000)+(-25000)+FV(18%,5,,-NPV(18%,H16:H20)-H15) SOLVER PARAMETERS SET TARGET CELL: C56 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C55 CLICK "SOLVE" b

IF ERR (17.56%) >= MARR (18%), THEN ACCEPT; OTHERWISE, REJECT

GALVANIZED PRODUCTS SHOULD NOT PURCHASE THE NEW COMPUTER SYSTEM

SOLUTION USING NETTED CASH FLOWS MARR IS 18%/YEAR EOY 0 1 2 3 4 5

+ INV CF $55,000.00 $55,000.00 $55,000.00 $55,000.00 $60,000.00

- INV CF -$100,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00 -$25,000.00

+ LOAN CF $25,000.00

- LOAN CF -$10,949.50 -$10,949.50 -$10,949.50

NET CF -$75,000.00 $19,050.50 $19,050.50 $19,050.50 $30,000.00 $35,000.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 17.10% =RATE(5,,-75000,FV(18%,5,,-NPV(18%,I73:I77))) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 17.10% =MIRR(G72:G77,,18%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 15.00% $14,309.39 =FV(B87,5,,75000)+FV(18%,5,,-NPV(18%,G73:G77)) ERR $0.00 18.00% -$6,420.65 =FV(B89,5,,75000)+FV(18%,5,,-NPV(18%,G73:G77)) ERR = 17.07% =B87+(B89-B87)*(C88-C87)/(C89-C87) SOLUTION USING EXCEL'S SOLVER i= 17.10%

NET - CF -$75,000.00 $0.00 $0.00 $0.00 $0.00 $0.00

NET + CF $0.00 $19,050.50 $19,050.50 $19,050.50 $30,000.00 $35,000.00

FV = $0.00 =FV(C93,5,,75000)+FV(18%,5,,-NPV(18%,G73:G77)) SOLVER PARAMETERS SET TARGET CELL: C94 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C93 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 17.10% FV = $0.00 =FV(C102,5,,75000)+FV(18%,5,,-NPV(18%,G73:G77)) SOLVER PARAMETERS SET TARGET CELL: C103 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C102 CLICK "SOLVE" b

IF ERR (17.10%) >= MARR (18%), THEN ACCEPT; OTHERWISE, REJECT

GALVANIZED PRODUCTS SHOULD NOT PURCHASE THE NEW COMPUTER SYSTEM

PROBLEM 8.60 a

SOLUTIONS USES GOAL SEEK TO DETERMINE ERR MARR IS 13.5%

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

- CF -$1,400.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 -$1,000.00 -$2,000.00 -$3,000.00 $0.00

+ CF $0.00 $0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 $0.00 $0.00 $0.00 $1,600.00

NET CF -$1,400.00 $0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 -$1,000.00 -$2,000.00 -$3,000.00 $1,600.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 12.00% $2,659.20 =FV(B34,15,,1400)+FV(B34,3,,1000)+FV(B34,2,,2000)+FV(B34,1,,3000)+FV(13.5%,15,,-NPV(13.5%,D9:D23)) ERR $0.00 15.00% -$1,411.85 =FV(B36,15,,1400)+FV(B36,3,,1000)+FV(B36,2,,2000)+FV(B36,1,,3000)+FV(13.5%,15,,-NPV(13.5%,D9:D23)) ERR = 13.96% =B34+(B36-B34)*(C35-C34)/(C36-C34) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$1,400.00 1 $0.00 2 $0.00 3 $0.00 4 $0.00 5 $0.00 6 $0.00 7 $0.00 8 $0.00 9 $0.00 10 $0.00 11 $0.00 12 -$1,000.00 13 -$2,000.00 14 -$3,000.00 15 $17,595.92 =FV(13.5%,15,,-NPV(13.5%,D9:D23)) ERR = 14.0711% =IRR(C41:C56) SOLUTION USING EXCEL'S SOLVER i= 14.07% FV = $0.00 =FV(C60,15,,1400)+FV(C60,3,,1000)+FV(C60,2,,2000)+FV(C60,1,,3000)+FV(13.5%,15,,-NPV(13.5%,D9:D23)) SOLVER PARAMETERS SET TARGET CELL: C61 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C60 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 14.07% FV = $0.00 =FV(C69,15,,1400)+FV(C69,3,,1000)+FV(C69,2,,2000)+FV(C69,1,,3000)+FV(13.5%,15,,-NPV(13.5%,D9:D23)) SOLVER PARAMETERS SET TARGET CELL: C70 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C69 CLICK "SOLVE" b

IF ERR (14.07%) >= MARR (13.5%), THEN ACCEPT; OTHERWISE, REJECT

QRU SHOULD BUY THE NEW PATTERNING ATTACHMENT

PROBLEM 8.61 NOTE: PROBLEMS 8.58, 8.59, 8.61, AND 8.62 INCLUDE TWO SOLUTIONS. ONE SOLUTION USES THE POSITIVE CASH FLOWS (Rt) AND NEGATIVE CASH FLOWS (Ct) BEFORE NETTING. THE OTHER SOLUTION USES THE CASH FLOWS AFTER NETTING (At = Rt - Ct). IN EACH CASE, THE NUMERIC RESULTS DIFFER BUT THE DECISIONS ARE CONSISTENT. SUBSEQUENT PROBLEMS USE ONLY THE NETTED CASH FLOWS. YEAR 7 ADDITION = $7,500 SYSTEM SALVAGE VALUE LOAN PAYMENTS = 20000(F|P 8%,1)(A|P 8%,3) = 20000(1.08000)(0.38803) = $8,381.45 a

SOLUTION USING Rt AND Ct CASH FLOWS BEFORE NETTING MARR IS 10%/YEAR EOY 0 1 2 3 4 5 6 7

+ INV CF $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $19,500.00

- INV CF -$40,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00

+ LOAN CF $20,000.00

- LOAN CF

-$8,381.45 -$8,381.45 -$8,381.45

NET - CF -$40,000.00 -$2,000.00 -$10,381.45 -$10,381.45 -$10,381.45 -$2,000.00 -$2,000.00 -$2,000.00

NET + CF $20,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $19,500.00

NET CF -$20,000.00 $10,000.00 $1,618.55 $1,618.55 $1,618.55 $10,000.00 $10,000.00 $17,500.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 12.00% $11,980.43 =FV(B32,7,,40000)+FV(B32,6,,2000)+FV(B32,5,,10381.45)+FV(B32,4,,10381.45)+FV(B32,3,,10381.45)+FV(B32,2,,2000)+FV(B32,1,,2000)+(-2000)+FV(10%,7,,-NPV(10%,H16:H22)-H15) ERR $0.00 15.00% -$12,478.44 =FV(B34,7,,40000)+FV(B34,6,,2000)+FV(B34,5,,10381.45)+FV(B34,4,,10381.45)+FV(B34,3,,10381.45)+FV(B34,2,,2000)+FV(B34,1,,2000)+(-2000)+FV(10%,7,,-NPV(10%,H16:H22)-H15) ERR = 13.47% =B32+(B34-B32)*(C33-C32)/(C34-C32) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$40,000.00 1 -$2,000.00 2 -$10,381.45 3 -$10,381.45 4 -$10,381.45 5 -$2,000.00 6 -$2,000.00 7 $158,320.39 =-2000+FV(10%,7,,-NPV(10%,H16:H22)-H15) ERR = 13.52% =IRR(C39:C46) SOLUTION USING EXCEL'S SOLVER i= 13.52% FV = $0.00 =FV(C50,7,,40000)+FV(C50,6,,2000)+FV(C50,5,,10381.45)+FV(C50,4,,10381.45)+FV(C50,3,,10381.45)+FV(C50,2,,2000)+FV(C50,1,,2000)+(-2000)+FV(10%,7,,-NPV(10%,H16:H22)-H15) SOLVER PARAMETERS SET TARGET CELL: C51 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C50 CLICK "SOLVE"

SOLUTION USING EXCEL'S GOAL SEEK i= 13.52% FV = $0.00 =FV(C59,7,,40000)+FV(C59,6,,2000)+FV(C59,5,,10381.45)+FV(C59,4,,10381.45)+FV(C59,3,,10381.45)+FV(C59,2,,2000)+FV(C59,1,,2000)+(-2000)+FV(10%,7,,-NPV(10%,H16:H22)-H15) SOLVER PARAMETERS SET TARGET CELL: C60 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C59 CLICK "SOLVE" b

IF ERR (13.52%) >= MARR (10%), THEN ACCEPT; OTHERWISE, REJECT

AEROTRON ELECTRONICS SHOULD PURCHASE THE WATER FILTRATION SYSTEM

SOLUTION USING NETTED CASH FLOWS MARR IS 10%/YEAR EOY 0 1 2 3 4 5 6 7

+ INV CF $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $19,500.00

- INV CF -$40,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00 -$2,000.00

+ LOAN CF $20,000.00

- LOAN CF

-$8,381.45 -$8,381.45 -$8,381.45

NET CF -$20,000.00 $10,000.00 $1,618.55 $1,618.55 $1,618.55 $10,000.00 $10,000.00 $17,500.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 18.45% =RATE(7,,-20000,FV(10%,7,,-NPV(10%,I77:I83))) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 18.45% =MIRR(G76:G83,,10%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 18.00% $1,736.83 =FV(B93,7,,20000)+FV(10%,7,,-NPV(10%,I77:I83)) ERR $0.00 20.00% -$6,217.31 =FV(B95,7,,20000)+FV(10%,7,,-NPV(10%,I77:I83)) ERR = 18.44% =B93+(B95-B93)*(C94-C93)/(C95-C93) SOLUTION USING EXCEL'S SOLVER i= 18.45% FV = $0.00 =FV(C99,7,,20000)+FV(10%,7,,-NPV(10%,I77:I83)) SOLVER PARAMETERS SET TARGET CELL: C100 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C99 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 18.45% FV = $0.00 =FV(C108,7,,20000)+FV(10%,7,,-NPV(10%,I77:I83)) SOLVER PARAMETERS SET TARGET CELL: C109 EQUAL TO: VALUE OF: 0

NET - CF -$20,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

NET + CF $0.00 $10,000.00 $1,618.55 $1,618.55 $1,618.55 $10,000.00 $10,000.00 $17,500.00

BY CHANGING CELL: CLICK "SOLVE"

C108

IF ERR (18.45%) >= MARR (10%), THEN ACCEPT; OTHERWISE, REJECT

AEROTRON ELECTRONICS SHOULD PURCHASE THE WATER FILTRATION SYSTEM

PROBLEM 8.62 NOTE: PROBLEMS 8.58, 8.59, 8.61, AND 8.62 INCLUDE TWO SOLUTIONS. ONE SOLUTION USES THE POSITIVE CASH FLOWS (Rt) AND NEGATIVE CASH FLOWS (Ct) BEFORE NETTING. THE OTHER SOLUTION USES THE CASH FLOWS AFTER NETTING (At = Rt - Ct). IN EACH CASE, THE NUMERIC RESULTS DIFFER BUT THE DECISIONS ARE CONSISTENT. SUBSEQUENT PROBLEMS USE ONLY THE NETTED CASH FLOWS. a

SOLUTION USING Rt AND Ct CASH FLOWS BEFORE NETTING MARR IS 10%/YEAR

EOY 0 1 2 3 4 5

- CF -$1,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

+ CF $600.00 $600.00 $700.00 $700.00 $700.00

NET CF -$1,000.00 $300.00 $300.00 $400.00 $400.00 $400.00

DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. DUE TO MULTIPLE NEGATIVE VALUES IN THE NET CF SERIES, EXCEL'S MIRR FUNCTION IS NOT USED TO COMPUTE ERR DIRECTLY. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 12.00% $325.86 =FV(B28,5,300,1000)+FV(10%,5,,-NPV(10%,D14:D18)) ERR $0.00 15.00% -$40.01 =FV(B30,5,300,1000)+FV(10%,5,,-NPV(10%,D14:D18)) ERR = 14.67% =B28+(B30-B28)*(C29-C28)/(C30-C28) SOLUTION USING EXCEL'S IRR FUNCTION AS IN EXAMPLE 8.10 EOY - CF 0 -$1,000.00 1 -$300.00 2 -$300.00 3 -$300.00 4 -$300.00 5 $3,694.06 =-300+FV(10%,5,,-NPV(10%,D14:D18)) ERR = 14.68% =IRR(C35:C40) SOLUTION USING EXCEL'S SOLVER i= 14.68% FV = $0.00 =FV(C44,5,300,1000)+FV(10%,5,,-NPV(10%,D14:D18)) SOLVER PARAMETERS SET TARGET CELL: C45 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C44 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 14.68% FV = $0.00 =FV(C53,5,300,1000)+FV(10%,5,,-NPV(10%,D14:D18)) SOLVER PARAMETERS SET TARGET CELL: C54 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C53 CLICK "SOLVE" b

IF ERR (14.68%)>= MARR (10%), THEN ACCEPT; OTHERWISE, REJECT

HOME INNOVATION SHOULD PURSUE THE NEW PRODUCT

SOLUTION USING NETTED CASH FLOWS MARR IS 10%/YEAR EOY 0 1 2 3 4 5

- CF -$1,000.00 -$300.00 -$300.00 -$300.00 -$300.00 -$300.00

+ CF $600.00 $600.00 $700.00 $700.00 $700.00

NET CF -$1,000.00 $300.00 $300.00 $400.00 $400.00 $400.00

NET - CF -$1,000.00 $0.00 $0.00 $0.00 $0.00 $0.00

NET + CF $0.00 $300.00 $300.00 $400.00 $400.00 $400.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 16.68% =RATE(5,,-1000,FV(10%,5,,-NPV(10%,G71:G75))) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 16.68% =MIRR(E70:E75,,10%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 15.00% $151.17 =FV(B85,5,,1000)+FV(10%,5,,-NPV(10%,G71:G75)) ERR $0.00 18.00% -$125.23 =FV(B87,5,,1000)+FV(10%,5,,-NPV(10%,G71:G75)) ERR = 16.64% =B85+(B87-B85)*(C86-C85)/(C87-C85) SOLUTION USING EXCEL'S SOLVER i= 16.68% FV = $0.00 =FV(C91,5,,1000)+FV(10%,5,,-NPV(10%,G71:G75)) SOLVER PARAMETERS SET TARGET CELL: C92 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C91 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 16.68% FV = $0.00 =FV(C100,5,,1000)+FV(10%,5,,-NPV(10%,G71:G75)) SOLVER PARAMETERS SET TARGET CELL: C101 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C100 CLICK "SOLVE" b

IF ERR (16.68%)>= MARR (10%), THEN ACCEPT; OTHERWISE, REJECT

HOME INNOVATION SHOULD PURSUE THE NEW PRODUCT

PROBLEM 8.63 ERR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS NOT AN OPTION. MARR IS 10%; ORDER OF INVESTMENTS: NULL, B, A INCREMENTAL ANALYSIS OF B-NULL EOY

+ CF 0 1 2 3 4

- CF -$280,000.00

$95,000.00 $95,000.00 $95,000.00 $95,000.00

NET CF -$280,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 12.02% =RATE(4,,-280000,FV(10%,4,,PV(10%,4,95000))) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 12.02% =MIRR(E12:E16,,10%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 12.00% $309.58 ERR $0.00 15.00% -$48,826.75 ERR = 12.02% =B26+(B28-B26)*(C27-C26)/(C28-C26) SOLUTION USING EXCEL'S SOLVER i= 12.02% FV = $0.00 =FV(C32,4,,280000)+FV(10%,4,,PV(10%,4,95000)) SOLVER PARAMETERS SET TARGET CELL: C36 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C35 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 12.02% FV = $0.00 =FV(C41,4,,280000)+FV(10%,4,,PV(10%,4,95000)) SOLVER PARAMETERS SET TARGET CELL: C45 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C44 CLICK "SOLVE" ERR OF INCREMENT (12.02%) IS GREATER THAN MARR (10%) SO B IS PREFERRED TO NULL ANALYZE INCREMENTAL CASH FLOWS OF A-B INCREMENTAL ANALYSIS OF A-B EOY

+ CF 0 1 2 3 4

$30,000.00 $30,000.00 $30,000.00 $30,000.00

- CF -$100,000.00

8.62 NET CF -$100,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 8.63% =RATE(4,,-100000,FV(10%,4,,PV(10%,4,30000))) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 8.63% =MIRR(E55:E59,,10%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 8.00% $3,181.10 ERR $0.00

9.00% ERR =

-$1,928.16 8.62% =B69+(B71-B69)*(C70-C69)/(C71-C69)

SOLUTION USING EXCEL'S SOLVER i= 8.63% FV = $0.00 =FV(C75,4,,100000)+FV(10%,4,,PV(10%,4,30000)) SOLVER PARAMETERS SET TARGET CELL: C76 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C75 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 8.63% FV = $0.00 =FV(C84,4,,100000)+FV(10%,4,,PV(10%,4,30000)) SOLVER PARAMETERS SET TARGET CELL: C85 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C84 CLICK "SOLVE" IRR OF INCREMENT A-B (8.63%) IS LESS THAN MARR (10%), SO REJECT THE INCREMENT; STAY WITH VENDOR B SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, VENDOR B IS RECOMMENDED

PROBLEM 8.64 ERR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS NOT AN OPTION. MARR IS 12% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, A, B NULL BECOMES THE "CURRENT BEST" AND A THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR A-NULL ARE NEEDED PROJECT A EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 12.64% =RATE(20,,-50000,FV(12%,20,-7500)) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 12.64% =MIRR(E18:E38,,12%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 12.00% $58,078.66 =FV(B48,20,,50000)+FV(12%,20,-7500) ERR $0.00 15.00% -$277,933.55 =FV(B50,20,,50000)+FV(12%,20,-7500) ERR = 12.52% =B48+(B50-B48)*(C49-C48)/(C50-C48) SOLUTION USING EXCEL'S SOLVER i= 12.64% FV = $0.00 =FV(C54,20,,50000)+FV(12%,20,-7500) SOLVER PARAMETERS SET TARGET CELL: C55 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C54 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 12.64% FV = $0.00 =FV(C63,20,,50000)+FV(12%,20,-7500) SOLVER PARAMETERS SET TARGET CELL: C64 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C63

CLICK "SOLVE" SINCE THE ERR OF THE INCREMENT (12.64%) IS GREATER THAN MARR(12%) THE INCREMENTAL INVESTMENT IS ACCEPTED A BECOMES THE NEW CURRENT BEST B BECOMES THE CHALLENGER THUS, THE CASH FLOWS FOR B - A ARE NEEDED PROJECT B-A EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

- CF -$25,000.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00 -$5,500.00

+ CF $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00 $8,000.00

NET CF -$25,000.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 10.38% =RATE(20,,-25000,FV(12%,20,-2500)) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 10.38% =MIRR(E79:E99,,12%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 10.00% $11,943.61 =FV(B109,20,,25000)+FV(12%,20,-2500) ERR $0.00 11.00% -$21,426.68 =FV(B111,20,,25000)+FV(12%,20,-2500) ERR = 10.36% =B109+(B111-B109)*(C110-C109)/(C111-C109) SOLUTION USING EXCEL'S SOLVER i= 10.38% FV = $0.00 =FV(C115,20,,25000)+FV(12%,20,-2500) SOLVER PARAMETERS SET TARGET CELL: C116 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C115 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 10.38% FV = $0.00 =FV(C124,20,,25000)+FV(12%,20,-2500) SOLVER PARAMETERS SET TARGET CELL: C125 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C124 CLICK "SOLVE" SINCE THE ERR OF THE INCREMENT (10.38%) IS LESS THAN MARR (12%) THE INCREMENTAL INVESTMENT IS REJECTED A REMAINS THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, A IS RECOMMENDED.

PROBLEM 8.65 ERR COMPARISONS MUST BE DONE INCREMENTALLY FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, T3, T4, T1, T2 MARR IS 25%/YEAR NULL BECOMES THE "CURRENT BEST" AND T3 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED THUS, THE CASH FLOWS FOR T3 - NULL ARE NEEDED

EOY 0 1 2 3 4 5 6 7 8 9 10

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR. CF -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $255,000.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 29.81% =RATE(10,,-470000,FV(25%,10,-190000)+65000) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 29.81% =MIRR(E14:E24,,25%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 20.00% $3,472,935.45 =FV(B34,10,,470000)+FV(25%,10,-190000)+65000 ERR $0.00 30.00% -$96,297.55 =FV(B36,10,,470000)+FV(25%,10,-190000)+65000 ERR = 29.73% =B34+(B36-B34)*(C35-C34)/(C36-C34) SOLUTION USING EXCEL'S SOLVER i= 29.81% FV = $0.00 =FV(C40,10,,470000)+FV(25%,10,-190000)+65000 SOLVER PARAMETERS SET TARGET CELL: C41 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C40 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 29.81% FV = $0.00 =FV(C49,10,,470000)+FV(25%,10,-190000)+65000 SOLVER PARAMETERS SET TARGET CELL: C50 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C49 CLICK "SOLVE" SINCE THE ERR OF THE INCREMENT (29.81%) IS GREATER THAN MARR (25%) THE INCREMENTAL INVESTMENT IS ACCEPTED. T3 BECOMES THE NEW CURRENT BEST T4 BECOMES THE NEXT CHALLENGER THUS THE CASH FLOWS FOR T4 - T3 ARE NEEDED EOY 0 1 2 3 4 5 6 7 8

T4 -$540,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00 $200,000.00

T3 -$470,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00

INCR. CF -$70,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00

PROBLEM 8.66 ERR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION WHICH IS CONSISTENT WITH THE COST ONLY PROBLEM FORMULATION MARR IS 20% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS GATE1, GATE2, GATE3 GATE1 BECOMES THE "CURRENT BEST" AND GATE2 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED GATE 2 - GATE 1 EOY 0 1 2 3 4 5

GATE 2 -$19,000.00 -$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00 -$3,600.00

GATE 1 -$15,000.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00

INCR CF -$4,000.00 $900.00 $900.00 $900.00 $900.00 $2,900.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 16.81% =RATE(5,,-4000,FV(20%,5,-900)+2000) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 16.81% =MIRR(E17:E22,,20%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 15.00% $652.01 =FV(B32,5,,4000)+FV(20%,5,-900)+2000 ERR $0.00 18.00% -$453.59 =FV(B34,5,,4000)+FV(20%,5,-900)+2000 ERR = 16.77% =B32+(B34-B32)*(C33-C32)/(C34-C32) SOLUTION USING EXCEL'S SOLVER i= 16.81% FV = $0.00 =FV(C38,5,,4000)+FV(20%,5,-900)+2000 SOLVER PARAMETERS SET TARGET CELL: C39 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C38 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 16.81% FV = $0.00 =FV(C47,5,,4000)+FV(20%,5,-900)+2000 SOLVER PARAMETERS SET TARGET CELL: C48 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C47 CLICK "SOLVE" SINCE THE ERR OF THE INCREMENT (16.81%) IS LESS THAN MARR (20%) THE INCREMENTAL INVESTMENT IS REJECTED GATE 1 REMAINS THE CURRENT BEST GATE 3 BECOMES THE CHALLENGER GATE 3 - GATE 1 EOY 0 1 2 3 4 5

GATE 3 -$24,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 $1,000.00

GATE 1 -$15,000.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00 -$6,500.00

NET CF -$9,000.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $7,500.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS

ERR =

21.27% =RATE(5,,-9000,FV(20%,5,-2500)+5000)

SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 21.27% =MIRR(E62:E67,,20%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 20.00% $1,209.12 =FV(B78,5,,9000)+FV(20%,5,-2500)+5000 ERR $0.00 25.00% -$3,861.82 =FV(B80,5,,9000)+FV(20%,5,-2500)+5000 ERR = 21.19% =B78+(B80-B78)*(C79-C78)/(C80-C78) SOLUTION USING EXCEL'S SOLVER i= 21.27% FV = $0.00 =FV(C84,5,,9000)+FV(20%,5,-2500)+5000 SOLVER PARAMETERS SET TARGET CELL: C85 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C84 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 21.27% FV = $0.00 =FV(C93,5,,9000)+FV(20%,5,-2500)+5000 SOLVER PARAMETERS SET TARGET CELL: C94 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C93 CLICK "SOLVE" SINCE THE ERR OF THE INCREMENT (21.27%) IS GREATER THAN MARR (20%) THE INCREMENTAL INVESTMENT IS ACCEPTED GATE 3 BECOMES THE CURRENT BEST SINCE THERE ARE NO MORE CHALLENGERS, GATE 3 IS RECOMMENDED.

PROBLEM 8.67 ERR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS AN OPTION. MARR IS 10%; ALL CASH FLOWS ARE IN $K FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS FIRST SATELLITE ONLY, SECOND SATELLITE ONLY, BOTH SATELLITES FIRST ONLY BECOMES THE "CURRENT BEST" AND SECOND ONLY THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED SECOND ONLY - FIRST ONLY EOY 0 1 2 3 4 5

SECOND ONLY -$850.00 -$120.00 -$120.00 -$120.00 -$120.00 $2,105.00

FIRST ONLY -$750.00 -$150.00 -$150.00 -$150.00 -$150.00 $2,075.00

INCR CF -$100.00 $30.00 $30.00 $30.00 $30.00 $30.00

SOLUTION USING EXCEL'S RATE AND FV FUNCTIONS ERR = 12.87% =RATE(5,,-100,FV(10%,5,-30)) SOLUTION USING EXCEL'S MIRR FUNCTION ERR = 12.87% =MIRR(E17:E22,,10%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S FV FUNCTION) i% FV 12.00% $6.92 =FV(B32,5,,100)+FV(10%,5,-30) ERR $0.00 15.00% -$17.98 =FV(B34,5,,100)+FV(10%,5,-30) ERR = 12.83% =B32+(B34-B32)*(C33-C32)/(C34-C32) SOLUTION USING EXCEL'S SOLVER i= 12.87% FV = $0.00 =FV(C38,5,,100)+FV(10%,5,-30) SOLVER PARAMETERS SET TARGET CELL: C39 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C38 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 12.87% FV = $0.00 =FV(C47,5,,100)+FV(10%,5,-30) SOLVER PARAMETERS SET TARGET CELL: C48 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C47 CLICK "SOLVE" SINCE THE ERR OF THE INCREMENT (12.87%) IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED SECOND ONLY BECOMES THE NEW CURRENT BEST BOTH BECOMES THE CHALLENGER THUS THE CASH FLOWS OF BOTH - SECOND ONLY ARE NEEDED. BOTH - SECOND ONLY EOY 0 1 2 3 4 5

BOTH SECOND ONLY -$1,750.00 -$850.00 -$400.00 -$120.00 -$400.00 -$120.00 -$400.00 -$120.00 -$400.00 -$120.00 $5,250.00 $2,105.00

INCR CF -$900.00 -$280.00 -$280.00 -$280.00 -$280.00 $3,145.00

PROBLEM 8.68 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS AN OPTION. MARR IS 20%/YEAR EOY 0 1 2 3 4

CF 1 -$5,000.00 -$2,200.00 -$2,200.00 -$2,200.00 -$2,200.00

CF 2 -$8,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00

INCR CF -$3,000.00 $1,200.00 $1,200.00 $1,200.00 $1,200.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 21.86% =IRR(E10:E14) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 21.86% =RATE(4,1200,-3000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 20.00% $106.48 IRR $0.00 25.00% -$166.08 IRR = 21.95% =B24+(B26-B24)*(C25-C24)/(C26-C24) SOLUTION USING EXCEL'S SOLVER i= 21.86% NPV = $0.00 =-PV(C30,4,1200)-3000 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 21.86% NPV = $0.00 =-PV(C39,4,1200)-3000 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C31 0 C30

C40 0 C39

SINCE THE IRR OF THE INCREMENT (21.86%) IS GREATER THAN MARR (20%) THE INCREMENTAL INVESTMENT IS ACCEPTED ALTERNATIVE 2 IS PREFERRED

PROBLEM 8.69 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS AN OPTION. MARR IS 10%/YEAR EOY 0 1 2 3 4 5 6 7 8 9 10

DRILL M -$30,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$3,000.00

DRILL T -$20,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$9,000.00

INCR CF -$10,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 $4,000.00 $6,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 38.78% =IRR(E10:E20) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 38.78% =RATE(10,4000,-10000,2000,,30%) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 30.00% $2,511.23 IRR $0.00 40.00% -$276.57 IRR = 39.01% =B30+(B32-B30)*(C31-C30)/(C32-C30) SOLUTION USING EXCEL'S SOLVER i= 38.78% NPV = $0.00 =NPV(C36,E11:E20)+E10 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 38.78% NPV = $0.00 =NPV(C45,E11:E20)+E10 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C37 0 C36

C46 0 C45

SINCE THE IRR OF THE INCREMENT (38.78%) IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED ZUNNI'S SHOULD PURCHASE DRILL PRESS M

PROBLEM 8.70 a

PRODUCTION RATE OF 200 UNITS/YR, THE SERVICE COSTS $18,000/YR AND THE ANNUAL EQUIPMENT O&M COSTS $12,000/YR EOY

SERVICE 0 1 2 3 4 5 6 7 8 9 10

-$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00

EQUIPMENT -$100,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00 -$12,000.00

INCR CF -$100,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = -8.35% =IRR(E7:E17) SOLUTION USING EXCEL'S RATE FUNCTION IRR = -8.35% =RATE(10,6000,-100000) THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE RATES IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= -8.35% NPV = $0.00 =NPV(C29,E8:E17)+E7 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= -8.35% NPV = $0.00 =NPV(C38,E8:E17)+E7 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C30 0 C29

C39 0 C38

SINCE THE IRR OF THE INCREMENT (-8.35%) IS LESS THAN MARR (12%) THE INCREMENTAL INVESTMENT IS REJECTED ALPHA ELECTRONICS SHOULD PURCHASE THE SERVICE b

PRODUCTION RATE OF 500 UNITS/YR, THE SERVICE COSTS $18,000/YR AND THE ANNUAL EQUIPMENT O&M COSTS $12,000/YR EOY

SERVICE 0 1 2 3 4 5 6 7 8 9 10

-$45,000.00 -$45,000.00 -$45,000.00 -$45,000.00 -$45,000.00 -$45,000.00 -$45,000.00 -$45,000.00 -$45,000.00 -$45,000.00

EQUIPMENT -$100,000.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00 -$19,500.00

INCR CF -$100,000.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00 $25,500.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 22.01% =IRR(E53:E63) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 22.01% =RATE(10,25500,-100000) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 20.00% $6,908.04 IRR $0.00

25.00% IRR =

-$8,952.17 22.18% =B73+(B75-B73)*(C74-C73)/(C75-C73)

SOLUTION USING EXCEL'S SOLVER i= 22.01% NPV = $0.00 =NPV(C79,E54:E63)+E53 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 22.01% NPV = $0.00 =NPV(C88,E54:E63)+E53 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C80 0 C79

C89 0 C8

SINCE THE IRR OF THE INCREMENT (22.01%) IS GREATER THAN MARR (12%) THE INCREMENTAL INVESTMENT IS ACCEPTED ALPHA ELECTRONICS SHOULD BUY THE EQUIPMENT

PROBLEM 8.71 IRR COMPARISONS MUST BE DONE INCREMENTALLY NULL IS NOT AN OPTION BASED ON THE PROBLEM STATEMENT MARR IS 12%; ALL CASH FLOWS ARE IN $K FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS MACHINE 3, MACHINE 2, MACHINE 1 M3 BECOMES THE "CURRENT BEST" AND M2 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED M2 - M3 EOY 0 1 2 3 4

M2 -$650.00 -$90.00 -$90.00 -$90.00 -$57.50

M3 -$575.00 -$105.00 -$105.00 -$105.00 -$76.25

INCR CF -$75.00 $15.00 $15.00 $15.00 $18.75

SOLUTION USING EXCEL'S IRR FUNCTION IRR = -6.00% =IRR(E16:E20) SOLUTION USING EXCEL'S RATE FUNCTION IRR = -6.00% =RATE(4,15,-75,3.75) THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE RATES IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= -6.00% NPV = $0.00 =NPV(C32,E17:E20)+E16 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= -6.00% NPV = $0.00 =NPV(C41,E17:E20)+E16 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL:

C33 0 C32

C42 0 C41

SINCE THE IRR OF THE INCREMENT (-6.00%) IS LESS THAN MARR (12%) THE INCREMENTAL INVESTMENT IS REJECTED M3 REMAINS THE CURRENT BEST M1 BECOMES THE CHALLENGER THUS THE CASH FLOWS OF M1 - M3 ARE NEEDED. M1 - M3 EOY 0 1 2 3 4

M1 -$800.00 -$50.00 -$50.00 -$50.00 -$10.00

M3 -$575.00 -$105.00 -$105.00 -$105.00 -$76.25

INCR CF -$225.00 $55.00 $55.00 $55.00 $66.25

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 1.07% =IRR(E56:E60) SOLUTION USING EXCEL'S RATE FUNCTION IRR = 1.07% =RATE(4,55,-225,11.25) SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 1.00% $0.42 IRR $0.00

1.25% IRR =

-$1.00 1.07% =B70+(B72-B70)*(C71-C70)/(C72-C70)

SOLUTION USING EXCEL'S SOLVER i= 1.07% NPV = $0.00 =NPV(C76,E57:E60)+E56 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 1.07% NPV = $0.00 =NPV(C85,E57:E60)+E56 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL:

C77 0 C76

C86 0 C85

SINCE THE IRR OF THE INCREMENT (1.07%) IS LESS THAN MARR (12%) THE INCREMENTAL INVESTMENT IS REJECTED M3 REMAINS THE CURRENT BEST THERE ARE NO MORE ALTERNATIVES TO CONSIDER THUS ALLIED ELECTRONICS SHOULD PURCHASE MACHINE 3

PROBLEM 8.72 COSTS IN $M MARR IS 10%/YEAR EOY 0 1 2 3

DESIGN 1 -$15.00 -$2.50 -$2.50 -$2.50

DESIGN 2 -$20.00 -$1.50 -$1.50 -$1.50

INCR CF -$5.00 $1.00 $1.00 $1.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = -21.76% =IRR(E7:E10) SOLUTION USING EXCEL'S RATE FUNCTION IRR = -21.76% =RATE(3,1,-5) THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE RATES IS NOT PERFORMED. SOLUTION USING EXCEL'S SOLVER i= -21.76% NPV = $0.00 =NPV(C22,E8:E10)+E7 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= -21.76% NPV = $0.00 =NPV(C31,E8:E10)+E7 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL:

C23 0 C22

C32 0 C31

SINCE THE IRR OF THE INCREMENT (-21.76%) IS LESS THAN MARR (10%) THE INCREMENTAL INVESTMENT IS REJECTED DEEP SEA SUBMARINE SHOULD SELECT DESIGN 1

PROBLEM 8.73 IRR COMPARISONS MUST BE DONE INCREMENTALLY NULL IS NOT AN OPTION BASED ON THE PROBLEM STATEMENT MARR IS 6%/YEAR PIPE B IS CURRENT BEST; PIPE A IS THE CHALLENGER INCREMENTAL CASH FLOWS FOR PIPE A - PIPE B EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

PIPE A -$135,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$18,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$18,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00 -$3,000.00

PIPE B -$100,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$24,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$84,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$24,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00 -$4,000.00

INCR CF -$35,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $6,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $81,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $6,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00 $1,000.00

-$3,000.00

-$4,000.00

$1,000.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 5.60% =IRR(E11:E71) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE RATES IS NOT PERFORMED. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 5.00% $5,034.16 IRR $0.00 6.00% -$2,864.63 IRR = 5.64% =B84+(B86-B84)*(C85-C84)/(C86-C84)

SOLUTION USING EXCEL'S SOLVER i= 5.60% NPV = $0.00 =NPV(C91,E12:E71)+E11 SOLVER PARAMETERS SET TARGET CELL: EQUAL TO: VALUE OF: BY CHANGING CELL: CLICK "SOLVE"

C92 0 C91

SOLUTION USING EXCEL'S GOAL SEEK i= 5.60% NPV = $0.00 =NPV(C100,E12:E71)+E11 SOLVER PARAMETERS SET TARGET CELL: C101 VALUE OF: 0 BY CHANGING CELL: C100 SINCE THE IRR OF THE INCREMENT (5.60%) IS LESS THAN MARR (6%) THE INCREMENTAL INVESTMENT IS REJECT PIPE B REMAINS THE CURRENT BEST AND THERE ARE NO MORE ALTERNATIVES TO CONSIDER THEREFORE, THE UNIVERSITY SHOULD SELECT PIPE B FOR THE WATER LINE

PROBLEM 8.74 IRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS AN OPTION. MARR IS 5%/YEAR STRUCTURE Y IS THE FIRST CURRENT BEST; STRUCTURE Z IS THE CHALLENGER INCREMENTAL CASH FLOWS FOR Z - Y EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Y -$4,500.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$5,500.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00 -$1,000.00

Z -$10,000.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 -$720.00 $1,080.00

INCR CF -$5,500.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $4,780.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $280.00 $2,080.00

SOLUTION USING EXCEL'S IRR FUNCTION IRR = 7.11% =IRR(E12:E36) DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL'S RATE FUNCTION IS NOT USED TO COMPUTE IRR. THE IRR SOLUTION IS OUTSIDE THE RANGE OF THE INTEREST TABLES. THEREFORE, INTERPOLATION OF THE TABLE RATES IS NOT PERFORMED. SOLUTION INTERPOLATING INTEREST TABLE RATES (WITH EXCEL'S NPV FUNCTION) i% NPV 7.00% $64.33 IRR $0.00 8.00% -$481.08 IRR = 7.12% =B49+(B51-B49)*(C50-C49)/(C51-C49) SOLUTION USING EXCEL'S SOLVER i= 7.11% NPV = $0.00 =NPV(C55,E13:E36)+E12 SOLVER PARAMETERS SET TARGET CELL: C56 EQUAL TO: VALUE OF: 0 BY CHANGING CELL: C55 CLICK "SOLVE" SOLUTION USING EXCEL'S GOAL SEEK i= 7.11% NPV = $0.00 PV(C64,E13:E36)+E12 SOLVER PARAMETERS SET TARGET CELL: VALUE OF: BY CHANGING CELL:

C65 0 C64

SINCE THE IRR OF THE INCREMENT (7.11%) IS GREATER THAN MARR (5%) THE INCREMENTAL INVESTMENT IS ACCEPTED STRUCTURE Z BECOMES THE NEW CURRENT BEST THERE ARE NO MORE ALTERNATIVES TO CONSIDER THUS, THE MILITARY SHOULD PREFER STORAGE STRUCTURE Z

PROBLEM 8.75

MARR = 10%; FINANCE RATE = 4%

EOY 0 1 2 3 4 5 6

CF -$100.00 $25.00 $200.00 -$100.00 $250.00 -$200.00 -$100.00

- CF -$100.00 $0.00 $0.00 -$100.00 $0.00 -$200.00 -$100.00

4.00% PW(-) -$100.00 $0.00 $0.00 -$88.90 $0.00 -$164.39 -$79.03

+ CF $0.00 $25.00 $200.00 $0.00 $250.00 $0.00 $0.00

-$432.32 <- PW

10.00% FW(+) $0.00 $40.26 $292.82 $0.00 $302.50 $0.00 $0.00 $635.58 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 6.63% =MIRR(C8:C14,4%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 6.63% =RATE(6,,E16,G16) SINCE THE MIRR (6.63%) IS LESS THAN MARR (10%) THE PROJECT IS NOT ATTRACTIVE

PROBLEM 8.76 SOLUTIONS USES EXCEL'S MIRR FUNCTION MARR = 10%; FINANCE RATE = 4%

EOY 0 1 2 3 4 5 6

CF -$100.00 $25.00 $25.00 $60.00 -$30.00 $60.00 $25.00

- CF -$100.00 $0.00 $0.00 $0.00 -$30.00 $0.00 $0.00

4.00% PW(-) -$100.00 $0.00 $0.00 $0.00 -$25.64 $0.00 $0.00

+ CF $0.00 $25.00 $25.00 $60.00 $0.00 $60.00 $25.00

-$125.64 <- PW

10.00% FW(+) $0.00 $40.26 $36.60 $79.86 $0.00 $66.00 $25.00 $247.73 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 11.98% =MIRR(C8:C14,4%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 11.98% =RATE(6,,E16,G16) SINCE THE MIRR (11.98%) IS GREATER THAN MARR (10%) THE PROJECT IS ATTRACTIVE

PROBLEM 8.77 MARR = 10%; FINANCE RATE = 4%

EOY 0 1 2 3 4 5 6

CF -$101.00 $411.00 -$558.00 $253.00 $2.00 $8.00 -$14.00

- CF -$101.00 $0.00 -$558.00 $0.00 $0.00 $0.00 -$14.00

4.00% PW(-) -$101.00 $0.00 -$515.90 $0.00 $0.00 $0.00 -$11.06

+ CF $0.00 $411.00 $0.00 $253.00 $2.00 $8.00 $0.00

-$627.97 <- PW

10.00% FW(+) $0.00 $661.92 $0.00 $336.74 $2.42 $8.80 $0.00 $1,009.88 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 8.24% =MIRR(C7:C13,4%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 8.24% =RATE(6,,E15,G15) SINCE THE MIRR (8.24%) IS LESS THAN MARR (10%) THE PROJECT IS NOT ATTRACTIVE

PROBLEM 8.78 MARR = 10%; FINANCE RATE = 4%

EOY 0 1 2 3 4 5 6

CF -$100.00 $800.00 -$750.00 $900.00 -$950.00 $700.00 -$800.00

- CF -$100.00 $0.00 -$750.00 $0.00 -$950.00 $0.00 -$800.00

4.00% PW(-) -$100.00 $0.00 -$693.42 $0.00 -$812.06 $0.00 -$632.25

+ CF $0.00 $800.00 $0.00 $900.00 $0.00 $700.00 $0.00

-$2,237.73 <- PW

10.00% FW(+) $0.00 $1,288.41 $0.00 $1,197.90 $0.00 $770.00 $0.00 $3,256.31 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 6.45% =MIRR(C7:C13,4%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 6.45% =RATE(6,,E15,G15) SINCE THE MIRR (6.45%) IS LESS THAN MARR (10%) THE PROJECT IS NOT ATTRACTIVE

PROBLEM 8.79 MIRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS AN OPTION SINCE THIS IS ALLOWED BY THE PROBLEM STATEMENT MARR IS 10%; FINANCE RATE IS 5% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS NULL, LIGHT BAR, SLIDING SPOTS, REFLECTED BEAM NULL BECOMES THE "CURRENT BEST" AND LIGHT BAR THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED LIGHT BAR - NULL EOY 0 1 2 3 4 5 6

LIGHT BAR -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

NULL $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

INCR CF -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

- CF -$6,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

5.00% PW(-) -$6,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

+ CF $0.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

-$6,000.00 <- PW

10.00% FW(+) $0.00 $3,221.02 $2,928.20 $2,662.00 $2,420.00 $2,200.00 $2,000.00 $15,431.22 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 17.05% =MIRR(E16:E22,5%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 17.05% =RATE(6,,G24,I24) SINCE THE MIRR OF THE INCREMENT (17.05%) IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED LIGHT BAR BECOMES THE NEW CURRENT BEST SLIDING SPOTS BECOMES THE CHALLENGER THUS THE CASH FLOWS OF SLIDING SPOTS - LIGHT BAR ARE NEEDED. SLIDING SPOTS - LIGHT BAR EOY 0 1 2 3 4 5 6

SLIDING SPOTS -$14,000.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00 $3,500.00

LIGHT BAR -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

INCR CF -$8,000.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00

- CF -$8,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

5.00% PW(-) -$8,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

+ CF $0.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00

-$8,000.00 <- PW

10.00% FW(+) $0.00 $2,415.77 $2,196.15 $1,996.50 $1,815.00 $1,650.00 $1,500.00 $11,573.42 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 6.35% =MIRR(E39:E45,5%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 6.35% =RATE(6,,G47,I47) SINCE THE MIRR OF THE INCREMENT (6.35%) IS LESS THAN MARR (10%) THE INCREMENTAL INVESTMENT IS REJECTED LIGHT BAR REMAINS THE CURRENT BEST REFLECTED BEAM BECOMES THE CHALLENGER THUS THE CASH FLOWS OF REFLECTED BEAM - LIGHT BAR ARE NEEDED. REFLECTED BEAM - LIGHT BAR EOY 0 1 2 3 4 5 6

REFLECTED BEAM -$20,000.00 $0.00 $2,300.00 $4,600.00 $6,900.00 $9,200.00 $11,500.00

LIGHT BAR -$6,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

INCR CF -$14,000.00 -$2,000.00 $300.00 $2,600.00 $4,900.00 $7,200.00 $9,500.00

- CF -$14,000.00 -$2,000.00 $0.00 $0.00 $0.00 $0.00 $0.00

5.00% PW(-) -$14,000.00 -$1,904.76 $0.00 $0.00 $0.00 $0.00 $0.00

+ CF $0.00 $0.00 $300.00 $2,600.00 $4,900.00 $7,200.00 $9,500.00

-$15,904.76 <- PW

10.00% FW(+) $0.00 $0.00 $439.23 $3,460.60 $5,929.00 $7,920.00 $9,500.00 $27,248.83 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 9.39% =MIRR(E62:E68,5%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 9.39% =RATE(6,,G70,I70) SINCE THE MIRR OF THE INCREMENT (9.39%) IS LESS THAN MARR (10%) THE INCREMENTAL INVESTMENT IS REJECTED LIGHT BAR REMAINS THE CURRENT BEST THERE ARE NO MORE ALTERNATIVES TO CONSIDER. THUS, ORPHEUM PRODUCTIONS SHOULD IMPLEMENTED THE LIGHT BAR ENHANCEMENT

PROBLEM 8.80 a

MARR = 13.5%; FINANCE RATE = 6%

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

CF -$1,400.00 $0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 -$1,000.00 -$2,000.00 -$3,000.00 $1,400.00

- CF -$1,400.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 -$1,000.00 -$2,000.00 -$3,000.00 $0.00

6.00% PW(-) -$1,400.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 -$496.97 -$937.68 -$1,326.90 $0.00

+ CF $0.00 $0.00 $500.00 $500.00 $500.00 $500.00 $0.00 $500.00 $600.00 $700.00 $800.00 $900.00 $0.00 $0.00 $0.00 $1,400.00

-$4,161.55 <- PW SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 10.01% =MIRR(C7:C22,6%,13.5%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 10.01% =RATE(15,,E24,G24) b

IF MIRR (10.01%) >= MARR (13.5%), THEN ACCEPT; OTHERWISE REJECT

INVESTMENT IS NOT ATTRACTIVE QRU SHOULD NOT BUY THE PATTERNING ATTACHMENT

13.50% FW(+) $0.00 $0.00 $2,593.68 $2,285.18 $2,013.37 $1,773.90 $0.00 $1,377.01 $1,455.87 $1,496.49 $1,506.85 $1,493.57 $0.00 $0.00 $0.00 $1,400.00 $17,395.92 <- FW

PROBLEM 8.81 MIRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION BASED ON THE PROBLEM STATEMENT MARR IS 20%; FINANCE RATE IS 10% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS ALTERNATIVE 1, ALTERNATIVE 2, ALTERNATIVE 3 ALTERNATIVE 1 BECOMES THE "CURRENT BEST" AND ALTERNATIVE 2 THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED ALT 2 - ALT 1 EOY 0 1 2 3 4 5

ALTERNATIVE 2 -$19,000.00 $7,600.00 $7,600.00 $7,600.00 $7,600.00 $7,600.00

ALTERNATIVE 1 -$15,000.00 $6,500.00 $6,500.00 $6,500.00 $6,500.00 $6,500.00

INCR CF -$4,000.00 $1,100.00 $1,100.00 $1,100.00 $1,100.00 $1,100.00

- CF -$4,000.00 $0.00 $0.00 $0.00 $0.00 $0.00

10.00% PW(-) -$4,000.00 $0.00 $0.00 $0.00 $0.00 $0.00

+ CF $0.00 $1,100.00 $1,100.00 $1,100.00 $1,100.00 $1,100.00

-$4,000.00 <- PW

20.00% FW(+) $0.00 $2,280.96 $1,900.80 $1,584.00 $1,320.00 $1,100.00 $8,185.76 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 15.40% =MIRR(E16:E21,10%,20%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 15.40% =RATE(5,,G23,I23) SINCE THE MIRR OF THE INCREMENT (15.40%) IS LESS THAN MARR (20%) THE INCREMENTAL INVESTMENT IS REJECTED ALTERNATIVE 1 REMAINS THE CURRENT BEST ALTERNATIVE 3 BECOMES THE CHALLENGER THUS THE CASH FLOWS OF ALTERNATIVE 3 - ALTERNATIVE 1 ARE NEEDED. ALT 3 - ALT 1 EOY 0 1 2 3 4 5

ALTERNATIVE 3 -$24,000.00 $4,000.00 $6,000.00 $10,000.00 $15,000.00 $18,000.00

ALTERNATIVE 1 -$15,000.00 $6,500.00 $6,500.00 $6,500.00 $6,500.00 $6,500.00

INCR CF -$9,000.00 -$2,500.00 -$500.00 $3,500.00 $8,500.00 $11,500.00

- CF -$9,000.00 -$2,500.00 -$500.00 $0.00 $0.00 $0.00

10.00% PW(-) -$9,000.00 -$2,272.73 -$413.22 $0.00 $0.00 $0.00

+ CF $0.00 $0.00 $0.00 $3,500.00 $8,500.00 $11,500.00

-$11,685.95 <- PW

20.00% FW(+) $0.00 $0.00 $0.00 $5,040.00 $10,200.00 $11,500.00 $26,740.00 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 18.00% =MIRR(E38:E43,10%,20%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 18.00% =RATE(5,,G45,I45) SINCE THE MIRR OF THE INCREMENT (18.00%) IS LESS THAN MARR (20%) THE INCREMENTAL INVESTMENT IS REJECTED ALTERNATIVE 1 REMAINS THE CURRENT BEST THERE ARE NO MORE ALTERNATIVES TO CONSIDER THUS, MANAGEMENT SHOULD IMPLEMENT ALTERNATIVE 1

PROBLEM 8.82 MIRR COMPARISONS MUST BE DONE INCREMENTALLY THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED ASSUMING THAT NULL IS AN OPTION. MARR IS 10%; FINANCE RATE IS 5% FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED. ORDER IS FIRST ONLY, SECOND ONLY, BOTH FIRST ONLY BECOMES THE "CURRENT BEST" AND SECOND ONLY THE "CHALLENGER" NEXT, THE INCREMENTAL CASH FLOWS FOR "CHALLENGER" - "CURRENT BEST" MUST BE DETERMINED SECOND ONLY - FIRST ONLY EOY 0 1 2 3 4 5

SECOND ONLY CF -$850.00 -$120.00 -$120.00 -$120.00 -$120.00 $2,105.00

FIRST ONLY CF -$750.00 -$150.00 -$150.00 -$150.00 -$150.00 $2,075.00

INCR CF -$100.00 $30.00 $30.00 $30.00 $30.00 $30.00

- CF -$100.00 $0.00 $0.00 $0.00 $0.00 $0.00

5.00% PW(-) -$100.00 $0.00 $0.00 $0.00 $0.00 $0.00

+ CF $0.00 $30.00 $30.00 $30.00 $30.00 $30.00

-$100.00 <- PW

10.00% FW(+) $0.00 $43.92 $39.93 $36.30 $33.00 $30.00 $183.15 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 12.87% =MIRR(E17:E22,5%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 12.87% =RATE(5,,G24,I24) SINCE THE MIRR OF THE INCREMENT (12.87%) IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED SECOND ONLY BECOMES THE NEW CURRENT BEST BOTH BECOMES THE CHALLENGER BOTH - SECOND ONLY EOY 0 1 2 3 4 5

BOTH CF SECOND ONLY CF -$1,750.00 -$850.00 -$400.00 -$120.00 -$400.00 -$120.00 -$400.00 -$120.00 -$400.00 -$120.00 $5,250.00 $2,105.00

INCR CF -$900.00 -$280.00 -$280.00 -$280.00 -$280.00 $3,145.00

- CF -$900.00 -$280.00 -$280.00 -$280.00 -$280.00 $0.00

5.00% PW(-) -$900.00 -$266.67 -$253.97 -$241.87 -$230.36 $0.00

+ CF $0.00 $0.00 $0.00 $0.00 $0.00 $3,145.00

-$1,892.87 <- PW

10.00% FW(+) $0.00 $0.00 $0.00 $0.00 $0.00 $3,145.00 $3,145.00 <- FW

SOLUTION USING EXCEL'S MIRR FUNCTION MIRR = 10.69% =MIRR(E38:E43,5%,10%) SOLUTION USING EXCEL'S RATE FUNCTION AS IN EXAMPLE 8.A.1 MIRR = 10.69% =RATE(5,,G45,I45) SINCE THE MIRR OF THE INCREMENT (10.69%) IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED BOTH BECOMES THE NEW CURRENT BEST THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED. CALISTO LAUNCH SERVICES SHOULD CONTRACT FOR BOTH SATELLITES.

A B C 1 MODIFIED ACRS RATES - GDS

7-YR

10-YR

15-YR

20-YR

2 3

MACRS CL

3-YR

5-YR

ADR

<=4

200%

150%

33.33%

20.00%

14.29%

10.00%

5.00%

3.750%

44.45%

32.00%

24.49%

18.00%

9.50%

7.219%

14.81%

19.20%

17.49%

14.40%

8.55%

6.677%

7.41%

11.52%

12.49%

11.52%

7.70%

6.177%

11.52%

8.93%

9.22%

6.93%

5.713%

5.76%

8.92%

7.37%

6.23%

5.285%

8.93%

6.55%

5.90%

4.888%

4.46%

6.55%

5.90%

4.522%

6.56%

5.91%

4.462%

6.55%

5.90%

4.461%

3.28%

5.91%

4.462%

5.90%

4.461%

5.91%

4.462%

5.90%

4.461%

5.91%

4.462%

2.95%

4.461%

4.462%

4.461%

4.462%

4.461%

2.231%

>4 to <10 >=10 to <16 .=16 to <20 >=20 to <25

>=25

28 29

SUM

100.00% 100.00%

100.00%

100.000%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS $500,000.00 INTEREST 10.00% ANN DEPOSIT $28,235.43 EST SALV $50,000.00 USEFUL LIFE 10 RCVD SALV $50,000.00 PERIODS 10 dt

0 1 2 3 4 5 6 7 8 9 10

$28,235.43 $31,058.97 $34,164.87 $37,581.35 $41,339.49 $45,473.44 $50,020.78 $55,022.86 $60,525.15 $66,577.66

$500,000.00 $471,764.57 $440,705.60 $406,540.73 $368,959.38 $327,619.89 $282,146.45 $232,125.67 $177,102.81 $116,577.66 $50,000.00

SUM DEPR

$450,000.00

EOY

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS $500,000.00 EST SALV $50,000.00 USEFUL LIFE 10 RCVD SALV $50,000.00 PERIODS 10 EOY

0 1 2 3 4 5 6 7 8 9 10

$45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00

$500,000.00 $455,000.00 $410,000.00 $365,000.00 $320,000.00 $275,000.00 $230,000.00 $185,000.00 $140,000.00 $95,000.00 $50,000.00

SUM DEPR

$450,000.00

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS $500,000.00 RATE EST SALV $50,000.00 USEFUL LIFE RCVD SALV $50,000.00 PERIODS

20.5672% 10 10

EOY

EXC FUNC 0 1 2 3 4 5 6 7 8 9 10

$103,000.00 $81,782.00 $64,934.91 $51,558.32 $40,937.30 $32,504.22 $25,808.35 $20,491.83 $16,270.51 $12,918.79

SUM DEPR $450,206.23

EXC FUNC CALC CALC $500,000.00 $500,000.00 $397,000.00 $102,835.88 $397,164.12 $315,218.00 $81,685.45 $315,478.67 $250,283.09 $64,885.06 $250,593.62 $198,724.78 $51,540.03 $199,053.59 $157,787.47 $40,939.70 $158,113.88 $125,283.25 $32,519.56 $125,594.32 $99,474.90 $25,831.21 $99,763.12 $78,983.07 $20,518.46 $79,244.66 $62,712.56 $16,298.39 $62,946.27 $49,793.77 $12,946.27 $50,000.00 SUM DEPR

$450,000.00

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS $500,000.00 RATE EST SALV $50,000.00 USEFUL LIFE RCVD SALV $50,000.00 PERIODS

20.0000% 10 10

EOY

EXC FUNC 0 1 2 3 4 5 6 7 8 9 10

$100,000.00 $80,000.00 $64,000.00 $51,200.00 $40,960.00 $32,768.00 $26,214.40 $20,971.52 $16,777.22 $13,421.77

SUM DEPR $446,312.91

EXC FUNC CALC CALC $500,000.00 $500,000.00 $400,000.00 $100,000.00 $400,000.00 $320,000.00 $80,000.00 $320,000.00 $256,000.00 $64,000.00 $256,000.00 $204,800.00 $51,200.00 $204,800.00 $163,840.00 $40,960.00 $163,840.00 $131,072.00 $32,768.00 $131,072.00 $104,857.60 $26,214.40 $104,857.60 $83,886.08 $20,971.52 $83,886.08 $67,108.86 $16,777.22 $67,108.86 $53,687.09 $13,421.77 $53,687.09 SUM DEPR

$446,312.91

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS $500,000.00 RATE EST SALV $50,000.00 USEFUL LIFE RCVD SALV $50,000.00 PERIODS EOY 0 1 2 3 4 5 6 7 8 9 10

20.0000% 10 10

EXC FUNC

CALC

SLN

DDB-SLN

$100,000.00 $80,000.00 $64,000.00 $51,200.00 $40,960.00 $32,768.00 $26,214.40 $20,971.52 $16,777.22 $13,421.77

SUM DEPR

$450,000.00

DDB-SLN $500,000.00 $45,000.00 $100,000.00 $400,000.00 $38,888.89 $80,000.00 $320,000.00 $33,750.00 $64,000.00 $256,000.00 $29,428.57 $51,200.00 $204,800.00 $25,800.00 $40,960.00 $163,840.00 $22,768.00 $32,768.00 $131,072.00 $20,268.00 $26,214.40 $104,857.60 $18,285.87 $20,971.52 $83,886.08 $16,943.04 $16,943.04 $66,943.04 $16,943.04 $16,943.04 $50,000.00

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS $500,000.00 RATE 20.0000% EST SALV $50,000.00 USEFUL LIFE 10 RCVD SALV $50,000.00 PERIODS 10 EOY 0 1 2 3 4 5 6 7 8 9 10

EXC FUNC

EXC FUNC $500,000.00 $400,000.00 $320,000.00 $256,000.00 $204,800.00 $163,840.00 $131,072.00 $104,857.60 $83,886.08 $66,943.04 $50,000.00

$100,000.00 $80,000.00 $64,000.00 $51,200.00 $40,960.00 $32,768.00 $26,214.40 $20,971.52 $16,943.04 $16,943.04

SUM DEPR $450,000.00

BASIS

$500,000.00

SYD

EST SALV

RCVD SALV $50,000.00

1 2 $50,000.00 USEFUL LIFE

PERIODS

FORMULA

EXC FUNC

FORMULA

6 7

EOY

8 9

$500,000.00

$81,818.18

$81,818.18 $418,181.82

$73,636.36

$73,636.36 $344,545.45

$65,454.55

$65,454.55 $279,090.91

$57,272.73

$57,272.73 $221,818.18

$49,090.91

$49,090.91 $172,727.27

$40,909.09

$40,909.09 $131,818.18

$32,727.27

$99,090.91

$24,545.45

$74,545.45

$16,363.64

$58,181.82

$8,181.82

$50,000.00

20 21

SUM DEPR $450,000.00

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS $500,000.00 EST SALV $50,000.00 USEFUL LIFE RCVD SALV $50,000.00 PERIODS EOY

0 1 2 3 4 5 6 7 8 9 10

$71,450.00 $122,450.00 $87,450.00 $62,450.00 $44,650.00 $44,600.00 $44,650.00 $22,300.00 $0.00 $0.00

$500,000.00 $428,550.00 $306,100.00 $218,650.00 $156,200.00 $111,550.00 $66,950.00 $22,300.00 $0.00 $0.00 $0.00

SUM DEPR

$500,000.00

8 8 MACRS-GDS

14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BASIS $500,000.00 EST SALV $50,000.00 USEFUL LIFE 8 RCVD SALV $50,000.00 PERIODS 8 EOY dt Bt MACRS-ADS 0 1 2 3 4 5 6 7 8 9 10

$31,250.00 $62,500.00 $62,500.00 $62,500.00 $62,500.00 $62,500.00 $62,500.00 $62,500.00 $31,250.00 $0.00

SUM DEPR $500,000.00

$500,000.00 $468,750.00 $406,250.00 $343,750.00 $281,250.00 $218,750.00 $156,250.00 $93,750.00 $31,250.00 $0.00 $0.00 SUM %

6.25% 12.50% 12.50% 12.50% 12.50% 12.50% 12.50% 12.50% 6.25%

100.00%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

MACRS-GDS BASIS $300,000.00 EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS MARR

5 6 10.00%

EOY

MACRS-GDS(5)

0 1 2 3 4 5 6

$60,000.00 $96,000.00 $57,600.00 $34,560.00 $34,560.00 $17,280.00

$300,000.00 $240,000.00 $144,000.00 $86,400.00 $51,840.00 $17,280.00 $0.00

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

SUM DEPR PW DEPR

$300,000.00 $231,978.13

$300,000.00 RATE $0.00 USEFUL LIFE $0.00 PERIODS MARR

40.0000% 5 6 10.00%

200% DBH BASIS EST SALV RCVD SALV

EOY

0 1 2 3 4 5 6

$60,000.00 $96,000.00 $57,600.00 $34,560.00 $20,736.00 $7,776.00

$300,000.00 $240,000.00 $144,000.00 $86,400.00 $51,840.00 $31,104.00 $23,328.00

SUM DEPR PW DEPR

$276,672.00 $218,029.75

DDB BASIS EST SALV RCVD SALV

$300,000.00 RATE $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1

$120,000.00

$300,000.00 $180,000.00

40.0000% 5 5 10.00%

A 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

B 2 3 4 5 6

C $72,000.00 $43,200.00 $25,920.00 $15,552.00 $0.00

SUM DEPR PW DEPR

$276,672.00 $228,412.12

DDB-SL BASIS EST SALV RCVD SALV

D $108,000.00 $64,800.00 $38,880.00 $23,328.00 $23,328.00

$300,000.00 RATE $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1 2 3 4 5 6

$120,000.00 $72,000.00 $43,200.00 $32,400.00 $32,400.00 $0.00

$300,000.00 $180,000.00 $108,000.00 $64,800.00 $32,400.00 $0.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $243,299.33

SLN BASIS EST SALV RCVD SALV

$300,000.00 $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1 2 3 4 5 6

$60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $0.00

$300,000.00 $240,000.00 $180,000.00 $120,000.00 $60,000.00 $0.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $227,447.21

SLH BASIS EST SALV

$300,000.00 $0.00 USEFUL LIFE

40.0000% 5 5 10.00%

5 5 10.00%

A 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

B RCVD SALV

C $0.00

D PERIODS MARR

EOY

0 1 2 3 4 5 6

$30,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $30,000.00

$300,000.00 $270,000.00 $210,000.00 $150,000.00 $90,000.00 $30,000.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $217,108.70

SYD BASIS EST SALV RCVD SALV

EOY

$300,000.00 SYD $0.00 USEFUL LIFE $0.00 PERIODS MARR dt

EXC FUNC

EXC FUNC $300,000.00 $200,000.00 $120,000.00 $60,000.00 $20,000.00 $0.00 $0.00

0 1 2 3 4 5 6

$100,000.00 $80,000.00 $60,000.00 $40,000.00 $20,000.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $241,842.65

E 6 10.00%

15 5 5 10.00%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

ORIG BASIS $350,000.00 INCOME/UNIT EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS EOY 0 1 2 3 4 5 6

UNITS SOLD

15000 13000 10000 6000 3000 1000

GROSS INC

$50.00 48000 6

FIXED COST VAR COST PERCENT DEPL

$12.50 $7.50 15.00%

OPERATING COST

-$350,000.00 $750,000.00 $187,500.00 $650,000.00 $260,000.00 $500,000.00 $275,000.00 $300,000.00 $210,000.00 $150,000.00 $127,500.00 $50,000.00 $50,000.00

TAXABLE INC 50% OF TI BEFORE DEPL BEFORE DEPL -$350,000.00 $562,500.00 $281,250.00 $390,000.00 $195,000.00 $225,000.00 $112,500.00 $90,000.00 $45,000.00 $22,500.00 $11,250.00 $0.00 $0.00

H I J K L 1 2 3 4 5 6 7 PERCENTAGE COST DEPLETION ADJ COST UNITS 8 DEPLETION (15%) DEPLETION USED BASIS REMAINING 9 $350,000.00 48,000 10 $112,500.00 $109,375.00 $112,500.00 $237,500.00 33,000 11 $97,500.00 $93,560.61 $97,500.00 $140,000.00 20,000 12 $75,000.00 $70,000.00 $75,000.00 $65,000.00 10,000 13 $45,000.00 $39,000.00 $45,000.00 $20,000.00 4,000 14 $11,250.00 $15,000.00 $15,000.00 $5,000.00 1,000 15 $0.00 $5,000.00 $5,000.00 $0.00 0

A B C 1 PROBLEM 9.1 2 3 a SALES $300,000,000.00 4 EXPENSES $250,000,000.00 5 NET $50,000,000.00 6 7 NEW MILLS $14,000,000.00 8 9 FINANCIAL GAIN $36,000,000.00 10 11 THIS WOULD BE A FINANCIAL GAIN OF $36,000,000; HOWEVER, IT IS NOT A FAIR REPRESENTAT 12 OF PERFORMANCE SINCE $14M OF THE $50M IS AN INVESTMENT OVER 7 YEARS. 13 14 b SALES $300,000,000.00 15 EXPENSES $250,000,000.00 16 NET $50,000,000.00 17 18 NEW MILLS $2,000,000.00 19 20 FINANCIAL GAIN $48,000,000.00

D 1 2 3 4 5 6 7 8 9 LOOKING STRICTLY AT CASH FLOWS 10 FINANCIAL GAIN 11 OF $36,000,000; HOWEVER, IT IS NOT A FAIR REPRESENTATION E SINCE $14M12OF THE $50M IS AN INVESTMENT OVER 7 YEARS. 13 14 15 16 17 18 1ST OF 7 YEAR EQUAL WRITEOFF OF $14M ASSET 19 20 AMORTIZING THE $14M INVESTMENT EQUALLY OVER 7 YEARS.

1 2 3 4 5 6 7 8 9

A PROBLEM 9.2 a

B 1 2 3 4 5 6 7 8 9

CAPITAL INVESTMENT OUTFLOWS ARE NOT ALLOWED TO BE SIMPLY SUBTRACTED FOR SEVERAL REASONS: 1. U.S. TAX LAW PROHIBITS SIMPLY SUBTRACTING THE INVESTMENT ALL AT ONE TIME (WITH CERTAIN EXCEP 2. AMORTIZING THE COST OF THESE ASSETS PRESENTS A REASONABLY ACCURATE REPORT FOR THE OWNE 3. AMORTIZING THE COST ALSO ALLOWS REASONABLE ESTIMES TO BE MADE OF THE COST OF DOING BUSIN

DEPRECIATION CHARGES, WHILE NOT CASH FLOWS, CAN BE TREATED AS EXPENSES FOR THE PURPOSE OF THE SPECIFIC DEPRECIATION METHOD USED CAN AFFECT THE AMOUNT OF TAXABLE INCOME AND HENCE TH

C D E F G 1 2 3 IME (WITH CERTAIN 4 EXCEPTIONS COVERED IN CHAPTER 10). TE REPORT FOR 5 THE OWNERS OF THE VALUE OF THE BUSINESS. 6 7 8 9

1 2 3 4 5 6

A PROBLEM 9.3 a b

B 1 2 3 THE CURRENT $600,000 / YEAR MANUAL COST MAY ALL BE SUBTRACTED FROM INCOME FOR FINANCIAL REPO 4 5 THE $80,000 / YEAR OPERATIONAL COST MAY ALL BE SUBTRACTED FROM INCOME FOR FINANCIAL REPORTIN 6 THE $3.75 MILLION INVESTMENT MUST BE DEPRECIATED AND WRITTEN OFF OVER THE COURSE OF SEVERAL

C D E F 1 2 COME FOR FINANCIAL 3 REPORTING AND TAXABLE INCOME. 4 5 6

A 1 PROBLEM 9.4 2 3 4 a 5 b 6 c 7 d 8 e 9 f 10 g 11 h 12 i 13 14 15 16 17 18 19 20 21 22

WHAT MELT INDEXER IN RESEARCH LAB COMPUTER FOR PERSONAL USE PLOT OF LAND FOR PRODUCTION OF INCOME FILE CABINET IN BUSINESS OFFICE RESTAURANT FRANCHISE COMMERCIAL DELIVERY TRUCK AMATUER RADIO TOWER ATTACHED TO LAND AN OFFICE COMPLEX FOR BUSINESS FENCING AND LANDSCAPE AROUND AN OFFICE COMPLEX

TANGIBLE X X X X X X X X

NOTE (FROM WIKI)! IN ACCOUNTING, AMORTIZATION REFERS TO EXPENSING THE ACQUISITIO OF INTANGIBLE ASSETS SUCH AS TRADEMARKS AND COPYRIGHTS IN A SYSTEMATIC MANNER ECONOMIC LIVES SO AS TO REFLECT THEIR CONSUMPTION, EXPIRATION, OBSOLESCENCE OR RESULT OF USE OR THE PASSAGE OF TIME.

A CORRESPONDING CONCEPT FOR TANGIBLE ASSETS IS DEPRECIATION. METHODOLOGIES FO EACH ACCOUNTING PERIOD ARE GENERALLY THE SAME AS FOR DEPRECIATION. HOWEVER, M AS GOODWILL OR CERTAIN BRANDS MAY BE DEEMED TO HAVE AN INDEFINITE USEFUL LIFE AN TO AMORTIZATION.

D E F G H 1 2 3 INTANGIBLE PERSONAL REAL DEPRECIABLE NONDEPRECIABLE 4 X X 5 X X 6 X X 7 X X 8 X X X (SEE NOTE) 9 X X 10 X X 11 X X 12 X X 13 TO EXPENSING 14 THE ACQUISITION COST LESS THE RESIDUAL VALUE GHTS IN A SYSTEMATIC 15 MANNER OVER THEIR ESTIMATED USEFUL EXPIRATION, 16 OBSOLESCENCE OR OTHER DECLINE IN VALUE AS A 17 18 RECIATION. METHODOLOGIES 19 FOR ALLOCATING AMORTIZATION TO OR DEPRECIATION. 20 HOWEVER, MANY INTANGIBLE ASSETS SUCH E AN INDEFINITE 21 USEFUL LIFE AND ARE THEREFORE NOT SUBJECT 22

A 1 PROBLEM 9.5 2 3 4 a 5 b 6 c 7 d 8 e 9 f 10 g 11 h 12 i 13 14 15 16 17 18 19 20 21 22

WHAT A CELL PHONE TOWER A TRACTOR-TRAILER RIG (18-WHEELER) A PLOT OF LAND FOR YOUR PERSONAL USE. A COPYRIGHT A COMPUTER USED IN YOUR JOB AN ALL-IN-ONE COPIER, SCANNER, FAX MACHINE USED IN YOUR BUSINESS. A MOONEY VISCOMETER USED IN A POLYMERS LAB. A RENTAL HOME FOR THE PURPOSE OF GENERATING RENTAL INCOME AN ELECTRIC GENERATOR PURCHASED BY A PUBLIC UTILITY

C D E F G H 1 2 3 TANGIBLE INTANGIBLE PERSONAL REAL DEPRECIABLE NONDEPRECIABLE 4 X X X 5 X X X 6 X X X 7 X X X (SEE NOTE) 8 X X X 9 X X X 10 X X X 11 X X X 12 X X X 13 EXPENSING14 THE ACQUISITION COST LESS THE RESIDUAL VALUE TS IN A SYSTEMATIC 15 MANNER OVER THEIR ESTIMATED USEFUL IRATION, OBSOLESCENCE 16 OR OTHER DECLINE IN VALUE AS A 17 18 CIATION. METHODOLOGIES 19 FOR ALLOCATING AMORTIZATION TO DEPRECIATION. 20 HOWEVER, MANY INTANGIBLE ASSETS SUCH N INDEFINITE21USEFUL LIFE AND ARE THEREFORE NOT SUBJECT 22

A B 1 PROBLEM 9.6 2 3 BASIS 4 EST SALV 5 RCVD SALV 6 7 EOY 8 0 9 1 10 2 11 3 12 4 13 5 14 6 15 7 16 8 17 18 SUM DEPR 19 20 a ANNUAL DEPOSIT= 21 22 b INCR IN ACCOUNT VALUE(6)= 23 24 c SINKING FUND DEPRECIATION 25 26 d TOTAL VALUE(8)=

$120,000.00 INTEREST 9.00% $10,000.00 USEFUL LIFE 8 $10,000.00 PERIODS 8 dt

$9,974.18 $10,871.86 $11,850.33 $12,916.85 $14,079.37 $15,346.51 $16,727.70 $18,233.19

$110,025.82 $99,153.96 $87,303.64 $74,386.78 $60,307.41 $44,960.90 $28,233.19 $10,000.00

$110,000.00 $9,974.18 $15,346.51

$110,000.00

A B 1 PROBLEM 9.7 2 3 BASIS 4 EST SALV 5 RCVD SALV 6 7 EOY 8 0 9 1 10 2 11 3 12 4 13 5 14 15 SUM DEPR

$18,000.00 INTEREST 12.00% ANN DEPOSIT $2,518.56 $2,000.00 USEFUL LIFE 5 $2,000.00 PERIODS 5 dt $2,518.56 $2,820.78 $3,159.28 $3,538.39 $3,963.00 $16,000.00

Bt $15,481.44 $12,660.66 $9,501.39 $5,963.00 $2,000.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

A PROBLEM 9.8 a

BASIS $60,000.00 INTEREST 10.00% ANN DEPOSIT $10,574.02 EST SALV $25,000.00 USEFUL LIFE 3 RCVD SALV $25,000.00 PERIODS 3 dt

EOY 0 1 2 3

$10,574.02 $11,631.42 $12,794.56

SUM DEPR

$35,000.00

Bt $49,425.98 $37,794.56 $25,000.00

IT IS BACK END LOADED SINCE LESS DEPRECIATION OCCURS IN THE EARLY YEARS AND MO

BECAUSE IT IS BACK-END LOADED AND INDUSTRY PREFERS ACCELERATED METHODS TO D

H I J K L M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 URS IN THE EARLY 15 YEARS AND MORE IN THE "BACK END" OR LATER YEARS. 16 RS ACCELERATED 17 METHODS TO DEPRECIATE MORE IN THE EARLY YEARS.

A B 1 PROBLEM 9.9 2 3 a SLN 4 BASIS 5 EST SALV 6 RCVD SALV 7 8 EOY 9 0 10 1 11 2 12 3 13 4 14 5 15 6 16 17 SUM DEPR 18 19 b DB 20 BASIS 21 EST SALV 22 RCVD SALV 23 24 EOY 25 26 0 27 1 28 2 29 3 30 4 31 5 32 6 33 34 SUM DEPR 35 36 c DDB 37 BASIS 38 EST SALV 39 RCVD SALV 40 41 EOY 42 43 0 44 1 45 2 46 3 47 4 48 5 49 6 50

$17,000.00 $3,500.00 USEFUL LIFE $3,500.00 PERIODS dt $2,250.00 $2,250.00 $2,250.00 $2,250.00 $2,250.00 $2,250.00

6 6

Bt $17,000.00 $14,750.00 $12,500.00 $10,250.00 $8,000.00 $5,750.00 $3,500.00

$13,500.00

$17,000.00 RATE $3,500.00 USEFUL LIFE $3,500.00 PERIODS

23.1572% 6 6

EXC FUNC

CALC

$3,944.00 $3,028.99 $2,326.27 $1,786.57 $1,372.09 $1,053.76

$13,056.00 $10,027.01 $7,700.74 $5,914.17 $4,542.08 $3,488.32

$3,936.72 $13,063.28 $3,025.09 $10,038.19 $2,324.56 $7,713.62 $1,786.26 $5,927.36 $1,372.61 $4,554.75 $1,054.75 $3,500.00

$13,511.68

SUM DEPR

$13,500.00

$17,000.00 RATE $3,500.00 USEFUL LIFE $3,500.00 PERIODS

33.3333% 6 6

EXC FUNC

EXC FUNC $17,000.00 $11,333.33 $7,555.56 $5,037.04 $3,500.00 $3,500.00 $3,500.00

CALC

$5,666.67 $3,777.78 $2,518.52 $1,537.04 $0.00 $0.00

CALC $17,000.00 $5,666.67 $11,333.33 $3,777.78 $7,555.56 $2,518.52 $5,037.04 $1,679.01 $3,358.02 $1,119.34 $2,238.68 $746.23 $1,492.46

SEE NOTE SEE NOTE SEE NOTE

A 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89

B SUM DEPR

C $13,500.00

D SUM DEPR

E $15,507.54

NOTE! THE MANUALLY CALCULATED VALUES OF dt WOULD NORMALLY BE ADJUSTED SUCH THAT Bt DOES NOT GO BELOW THE SALVAGE VALUE d

DDB-SLN BASIS EST SALV RCVD SALV EOY

$17,000.00 RATE $3,500.00 USEFUL LIFE $3,500.00 PERIODS dt

EXC FUNC

EXC FUNC $17,000.00 $11,333.33 $7,555.56 $5,037.04 $3,500.00 $3,500.00 $3,500.00

0 1 2 3 4 5 6

$5,666.67 $3,777.78 $2,518.52 $1,537.04 $0.00 $0.00

SUM DEPR

$13,500.00

SYD BASIS $17,000.00 SYD EST SALV $3,500.00 USEFUL LIFE RCVD SALV $3,500.00 PERIODS EOY

EXC FUNC

EXC FUNC $17,000.00 $13,142.86 $9,928.57 $7,357.14 $5,428.57 $4,142.86 $3,500.00

0 1 2 3 4 5 6

$3,857.14 $3,214.29 $2,571.43 $1,928.57 $1,285.71 $642.86

SUM DEPR

$13,500.00

33.3333% 6 6

21 6 6

A B 1 PROBLEM 9.10 2 3 a SLN 4 BASIS 5 EST SALV 6 RCVD SALV 7 8 EOY 9 0 10 1 11 2 12 3 13 4 14 5 15 16 SUM DEPR 17 18 b DB 19 BASIS 20 EST SALV 21 RCVD SALV 22 23 EOY 24 25 0 26 1 27 2 28 3 29 4 30 5 31 32 SUM DEPR 33 34 c DDB 35 BASIS 36 EST SALV 37 RCVD SALV 38 39 EOY 40 41 0 42 1 43 2 44 3 45 4 46 5 47 48 SUM DEPR 49 50 d DDB-SLN

$1,600,000.00 $100,000.00 USEFUL LIFE $100,000.00 PERIODS dt

5 5

$1,600,000.00 $300,000.00 $1,300,000.00 $300,000.00 $1,000,000.00 $300,000.00 $700,000.00 $300,000.00 $400,000.00 $300,000.00 $100,000.00 $1,500,000.00

$1,600,000.00 RATE $100,000.00 USEFUL LIFE $100,000.00 PERIODS

42.5651% 5 5

EXC FUNC

CALC

$681,600.00 $391,238.40 $224,570.84 $128,903.66 $73,990.70

$918,400.00 $527,161.60 $302,590.76 $173,687.10 $99,696.39

$681,041.32 $391,155.52 $224,659.85 $129,033.20 $74,110.11

$918,958.68 $527,803.16 $303,143.31 $174,110.11 $100,000.00

$1,500,303.61

SUM DEPR

$1,500,000.00

$1,600,000.00 RATE $100,000.00 USEFUL LIFE $100,000.00 PERIODS dt

EXC FUNC

EXC FUNC $1,600,000.00 $640,000.00 $960,000.00 $384,000.00 $576,000.00 $230,400.00 $345,600.00 $138,240.00 $207,360.00 $82,944.00 $124,416.00

$1,475,584.00

SUM DEPR

40.0000% 5 5 dt CALC

CALC $1,600,000.00 $640,000.00 $960,000.00 $384,000.00 $576,000.00 $230,400.00 $345,600.00 $138,240.00 $207,360.00 $82,944.00 $124,416.00 $1,475,584.00

A 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

B C D BASIS $1,600,000.00 RATE EST SALV $100,000.00 USEFUL LIFE RCVD SALV $100,000.00 PERIODS EOY

E 40.0000% 5 5

EXC FUNC 0 1 2 3 4 5 SUM DEPR e

EXC FUNC $1,600,000.00 $640,000.00 $960,000.00 $384,000.00 $576,000.00 $230,400.00 $345,600.00 $138,240.00 $207,360.00 $107,360.00 $100,000.00

$1,500,000.00

SYD BASIS $1,600,000.00 SYD EST SALV $100,000.00 USEFUL LIFE RCVD SALV $100,000.00 PERIODS EOY

dt EXC FUNC

0 1 2 3 4 5 SUM DEPR

EXC FUNC $1,600,000.00 $500,000.00 $1,100,000.00 $400,000.00 $700,000.00 $300,000.00 $400,000.00 $200,000.00 $200,000.00 $100,000.00 $100,000.00

$1,500,000.00

15 5 5

A B C D E F 1 PROBLEM 9.11 2 3 a SLN 4 BASIS $90,000.00 5 EST SALV $4,000.00 USEFUL LIFE 6 6 RCVD SALV $4,000.00 PERIODS 6 7 dt Bt 8 EOY 9 0 $90,000.00 10 1 $14,333.33 $75,666.67 11 2 $14,333.33 $61,333.33 12 3 $14,333.33 $47,000.00 13 4 $14,333.33 $32,666.67 14 5 $14,333.33 $18,333.33 15 6 $14,333.33 $4,000.00 16 17 SUM DEPR $86,000.00 18 19 b DB 20 BASIS $90,000.00 RATE 40.4837% 21 EST SALV $4,000.00 USEFUL LIFE 6 22 RCVD SALV $4,000.00 PERIODS 6 23 dt Bt dt Bt 24 EOY 25 EXC FUNC EXC FUNC CALC CALC 26 0 27 1 $36,450.00 $53,550.00 $36,435.29 $53,564.71 28 2 $21,687.75 $31,862.25 $21,684.95 $31,879.76 29 3 $12,904.21 $18,958.04 $12,906.09 $18,973.67 30 4 $7,678.01 $11,280.03 $7,681.23 $11,292.43 31 5 $4,568.41 $6,711.62 $4,571.59 $6,720.84 32 6 $2,718.21 $3,993.41 $2,720.84 $4,000.00 33 34 SUM DEPR $86,006.59 SUM DEPR $86,000.00 35 36 c DDB 37 BASIS $90,000.00 RATE 33.3333% 38 EST SALV $4,000.00 USEFUL LIFE 6 39 RCVD SALV $4,000.00 PERIODS 6 40 dt Bt dt Bt 41 EOY 42 EXC FUNC EXC FUNC CALC CALC 43 0 $90,000.00 $90,000.00 44 1 $30,000.00 $60,000.00 $30,000.00 $60,000.00 45 2 $20,000.00 $40,000.00 $20,000.00 $40,000.00 46 3 $13,333.33 $26,666.67 $13,333.33 $26,666.67 47 4 $8,888.89 $17,777.78 $8,888.89 $17,777.78 48 5 $5,925.93 $11,851.85 $5,925.93 $11,851.85 49 6 $3,950.62 $7,901.23 $3,950.62 $7,901.23 50

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

B C SUM DEPR $82,098.77

DDB-SLN BASIS $90,000.00 RATE 33.3333% EST SALV $4,000.00 USEFUL LIFE 6 RCVD SALV $4,000.00 PERIODS 6 EOY 0 1 2 3 4 5 6

D SUM DEPR

EXC FUNC

EXC FUNC $90,000.00 $60,000.00 $40,000.00 $26,666.67 $17,777.78 $10,888.89 $4,000.00

$30,000.00 $20,000.00 $13,333.33 $8,888.89 $6,888.89 $6,888.89

E $82,098.77

SUM DEPR $86,000.00 e

SYD BASIS $90,000.00 SYD EST SALV $4,000.00 USEFUL LIFE RCVD SALV $4,000.00 PERIODS EOY 0 1 2 3 4 5 6

EXC FUNC

EXC FUNC $90,000.00 $65,428.57 $44,952.38 $28,571.43 $16,285.71 $8,095.24 $4,000.00

$24,571.43 $20,476.19 $16,380.95 $12,285.71 $8,190.48 $4,095.24

SUM DEPR $86,000.00

21 6 6

A B C D E 1 PROBLEM 9.12 2 3 a COST BASIS= $35,000+$3,000= $38,000.00 4 5 b NET MKT VAL= $2,000-$500= $1,500.00 6 7 SLN 8 BASIS $38,000.00 9 EST SALV $1,000.00 USEFUL LIFE 5 10 RCVD SALV $1,500.00 PERIODS 3 11 dt Bt 12 EOY 13 14 0 $38,000.00 15 1 $7,400.00 $30,600.00 16 2 $7,400.00 $23,200.00 17 3 $7,400.00 $15,800.00 18 4 $7,400.00 $8,400.00 19 5 $7,400.00 $1,000.00 20 21 SUM DEPR $37,000.00 22 B3-NMV3= 23 c $14,300.00

DB BASIS EST SALV RCVD SALV EOY 0 1 2 3 4 5 SUM DEPR

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

$38,000.00 RATE $1,000.00 USEFUL LIFE $1,500.00 PERIODS

EXC FUNC

CALC

$37,001.11 $2,781.79

$18,354.00 $19,641.94 $18,358.06 $8,864.98 $9,489.16 $8,868.91 $4,281.79 $4,584.28 $4,284.63 $2,068.10 $2,214.70 $2,069.94 $998.89 $1,069.94 $1,000.00 SUM DEPR

$37,000.00

DDB BASIS $38,000.00 RATE EST SALV $1,000.00 USEFUL LIFE RCVD SALV $1,500.00 PERIODS

51.6893% 5 3

$19,646.00 $9,489.02 $4,583.20 $2,213.68 $1,069.21

EXC FUNC $15,200.00 $9,120.00 $5,472.00 $3,283.20 $1,969.92

EXC FUNC $38,000.00 $22,800.00 $13,680.00 $8,208.00 $4,924.80 $2,954.88

SUM DEPR $35,045.12

SUM DEPR

EOY 0 1 2 3 4 5

$6,708.00

P Q 1 2 3 4 5 6 7 8 40.0000% 9 5 10 3 11 dt Bt 12 13 CALC CALC 14 $38,000.00 15 $15,200.00 $22,800.00 16 $9,120.00 $13,680.00 17 $5,472.00 $8,208.00 18 $3,283.20 $4,924.80 19 $1,969.92 $2,954.88 20 21 $35,045.12 22 23

DDB-SLN BASIS $38,000.00 RATE 40.0000% EST SALV $1,000.00 USEFUL LIFE 5 RCVD SALV $1,500.00 PERIODS 3 EOY 0 1 2 3 4 5

EXC FUNC

EXC FUNC $38,000.00 $22,800.00 $13,680.00 $8,208.00 $4,604.00 $1,000.00

$15,200.00 $9,120.00 $5,472.00 $3,604.00 $3,604.00

SUM DEPR $37,000.00 $6,708.00

X Y Z AA 1 2 3 4 5 6 7 SYD 8 BASIS $38,000.00 SYD 15 9 EST SALV $1,000.00 USEFUL LIFE 5 10 RCVD SALV $1,500.00 PERIODS 3 11 dt Bt 12 EOY 13 EXC FUNC EXC FUNC 14 0 $38,000.00 15 1 $12,333.33 $25,666.67 16 2 $9,866.67 $15,800.00 17 3 $7,400.00 $8,400.00 18 4 $4,933.33 $3,466.67 19 5 $2,466.67 $1,000.00 20 21 SUM DEPR $37,000.00 22 23 $6,900.00

A B C D E F 1 PROBLEM 9.13 2 3 a SLN 4 BASIS $190,000.00 5 EST SALV $5,000.00 USEFUL LIFE 12 6 RCVD SALV $5,000.00 PERIODS 12 7 dt Bt 8 EOY 9 10 0 $190,000.00 11 1 $15,416.67 $174,583.33 12 2 $15,416.67 $159,166.67 13 3 $15,416.67 $143,750.00 14 4 $15,416.67 $128,333.33 15 5 $15,416.67 $112,916.67 16 6 $15,416.67 $97,500.00 17 7 $15,416.67 $82,083.33 18 8 $15,416.67 $66,666.67 19 9 $15,416.67 $51,250.00 20 10 $15,416.67 $35,833.33 21 11 $15,416.67 $20,416.67 22 12 $15,416.67 $5,000.00 23 24 SUM DEPR $185,000.00 25 26 b DB 27 BASIS $190,000.00 RATE 26.1499% 28 EST SALV $5,000.00 USEFUL LIFE 12 29 RCVD SALV $5,000.00 PERIODS 12 30 dt Bt dt Bt 31 EOY 32 EXC FUNC EXC FUNC CALC CALC 33 0 34 1 $49,590.00 $140,410.00 $49,684.72 $140,315.28 35 2 $36,647.01 $103,762.99 $36,692.24 $103,623.04 36 3 $27,082.14 $76,680.85 $27,097.27 $76,525.77 37 4 $20,013.70 $56,667.15 $20,011.38 $56,514.39 38 5 $14,790.13 $41,877.02 $14,778.43 $41,735.96 39 6 $10,929.90 $30,947.12 $10,913.89 $30,822.07 40 7 $8,077.20 $22,869.92 $8,059.93 $22,762.14 41 8 $5,969.05 $16,900.87 $5,952.27 $16,809.88 42 9 $4,411.13 $12,489.74 $4,395.76 $12,414.12 43 10 $3,259.82 $9,229.92 $3,246.27 $9,167.85 44 11 $2,409.01 $6,820.91 $2,397.38 $6,770.47 45 12 $1,780.26 $5,040.65 $1,770.47 $5,000.00 46 47 SUM DEPR $184,959.35 SUM DEPR $185,000.00 48 49 c DDB 50 BASIS $190,000.00 RATE 16.6667%

A 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

B EST SALV RCVD SALV

C $5,000.00 $5,000.00

D USEFUL LIFE PERIODS

E 12 12

EOY

EXC FUNC

CALC

$31,666.67 $26,388.89 $21,990.74 $18,325.62 $15,271.35 $12,726.12 $10,605.10 $8,837.59 $7,364.65 $6,137.21 $5,114.34 $4,261.95

EXC FUNC $190,000.00 $158,333.33 $131,944.44 $109,953.70 $91,628.09 $76,356.74 $63,630.62 $53,025.51 $44,187.93 $36,823.27 $30,686.06 $25,571.72 $21,309.76

CALC $190,000.00 $31,666.67 $158,333.33 $26,388.89 $131,944.44 $21,990.74 $109,953.70 $18,325.62 $91,628.09 $15,271.35 $76,356.74 $12,726.12 $63,630.62 $10,605.10 $53,025.51 $8,837.59 $44,187.93 $7,364.65 $36,823.27 $6,137.21 $30,686.06 $5,114.34 $25,571.72 $4,261.95 $21,309.76

SUM DEPR $168,690.24

SUM DEPR

$168,690.24

DDB-SLN BASIS $190,000.00 RATE EST SALV $5,000.00 USEFUL LIFE RCVD SALV $5,000.00 PERIODS

16.6667% 12 12

0 1 2 3 4 5 6 7 8 9 10 11 12

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

EXC FUNC

EXC FUNC $190,000.00 $158,333.33 $131,944.44 $109,953.70 $91,628.09 $76,356.74 $63,630.62 $53,025.51 $43,420.41 $33,815.31 $24,210.21 $14,605.10 $5,000.00

$31,666.67 $26,388.89 $21,990.74 $18,325.62 $15,271.35 $12,726.12 $10,605.10 $9,605.10 $9,605.10 $9,605.10 $9,605.10 $9,605.10

SUM DEPR $185,000.00 e

SYD BASIS $190,000.00 SYD EST SALV $5,000.00 USEFUL LIFE RCVD SALV $5,000.00 PERIODS EOY

78 12 12

A 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116

B 0 1 2 3 4 5 6 7 8 9 10 11 12

C EXC FUNC $28,461.54 $26,089.74 $23,717.95 $21,346.15 $18,974.36 $16,602.56 $14,230.77 $11,858.97 $9,487.18 $7,115.38 $4,743.59 $2,371.79

SUM DEPR $185,000.00

D EXC FUNC $190,000.00 $161,538.46 $135,448.72 $111,730.77 $90,384.62 $71,410.26 $54,807.69 $40,576.92 $28,717.95 $19,230.77 $12,115.38 $7,371.79 $5,000.00

A B C D E F 1 PROBLEM 9.14 2 3 a SLN 4 BASIS $120,000.00 5 EST SALV $0.00 USEFUL LIFE 5 6 RCVD SALV $0.00 PERIODS 5 7 dt Bt 8 EOY 9 10 0 $120,000.00 11 1 $24,000.00 $96,000.00 12 2 $24,000.00 $72,000.00 13 3 $24,000.00 $48,000.00 14 4 $24,000.00 $24,000.00 15 5 $24,000.00 $0.00 16 17 SUM DEPR $120,000.00 18 19 b DB 20 BASIS $120,000.00 RATE 99.9999% 21 EST SALV $0.00 USEFUL LIFE 5 22 RCVD SALV $0.00 PERIODS 5 23 dt Bt dt Bt 24 EOY 25 EXC FUNC EXC FUNC CALC CALC 26 0 27 1 $120,000.00 $0.00 $119,999.93 $0.07 28 2 $0.00 $0.00 $0.07 $0.00 29 3 $0.00 $0.00 $0.00 $0.00 30 4 $0.00 $0.00 $0.00 $0.00 31 5 $0.00 $0.00 $0.00 $0.00 32 33 SUM DEPR $120,000.00 SUM DEPR $120,000.00 34 35 c DDB 36 BASIS $120,000.00 RATE 40.0000% 37 EST SALV $0.00 USEFUL LIFE 5 38 RCVD SALV $0.00 PERIODS 5 39 dt Bt dt Bt 40 EOY 41 EXC FUNC EXC FUNC CALC CALC 42 0 $120,000.00 $120,000.00 43 1 $48,000.00 $72,000.00 $48,000.00 $72,000.00 44 2 $28,800.00 $43,200.00 $28,800.00 $43,200.00 45 3 $17,280.00 $25,920.00 $17,280.00 $25,920.00 46 4 $10,368.00 $15,552.00 $10,368.00 $15,552.00 47 5 $6,220.80 $9,331.20 $6,220.80 $9,331.20 48 49 SUM DEPR $110,668.80 SUM DEPR $110,668.80 50

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

A d

B C D DDB-SLN BASIS $120,000.00 RATE EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS EOY 0 1 2 3 4 5

EXC FUNC

EXC FUNC $120,000.00 $72,000.00 $43,200.00 $25,920.00 $12,960.00 $0.00

$48,000.00 $28,800.00 $17,280.00 $12,960.00 $12,960.00

E 40.0000% 5 5

SUM DEPR $120,000.00 e

SYD BASIS $120,000.00 SYD EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS EOY 0 1 2 3 4 5

EXC FUNC

EXC FUNC $120,000.00 $80,000.00 $48,000.00 $24,000.00 $8,000.00 $0.00

$40,000.00 $32,000.00 $24,000.00 $16,000.00 $8,000.00

SUM DEPR $120,000.00

15 5 5

A B C D E 1 PROBLEM 9.15 2 3 BASIS $220,000.00 4 EST SALV $0.00 USEFUL LIFE 11 5 RCVD SALV $0.00 PERIODS 12 6 dt Bt 7 EOY MACRS-ADS 8 9 0 $220,000.00 10 1 $10,000.00 $210,000.00 4.5455% 11 2 $20,000.00 $190,000.00 9.0909% 12 3 $20,000.00 $170,000.00 9.0909% 13 4 $20,000.00 $150,000.00 9.0909% 14 5 $20,000.00 $130,000.00 9.0909% 15 6 $20,000.00 $110,000.00 9.0909% 16 7 $20,000.00 $90,000.00 9.0909% 17 8 $20,000.00 $70,000.00 9.0909% 18 9 $20,000.00 $50,000.00 9.0909% 19 10 $20,000.00 $30,000.00 9.0909% 20 11 $20,000.00 $10,000.00 9.0909% 21 12 $10,000.00 $0.00 4.5455% 22 23 SUM DEPR $220,000.00 SUM % 100.0000%

A B C D E 1 PROBLEM 9.16 2 3 BASIS $88,000.00 4 EST SALV $0.00 USEFUL LIFE 40 5 RCVD SALV $0.00 PERIODS 40 6 dt 7 EOY MACRS-ADS 8 9 0 10 1 $1,558.33 1.7708% 11 5 $2,200.00 2.5000% 12 41 $641.67 0.7292%

A B C D E F G 1 PROBLEM 9.17 2 3 BASIS $1.00 RATE 66.6667% =2/USEFUL LIFE*100% 4 EST SALV $0.00 USEFUL LIFE 3 5 RCVD SALV $0.00 PERIODS 3 6 7 MACRS-GDS IS BASED UPON DDB SWITCHING TO SLN (DDB-SLN) DEPR 8 HALF-YEAR CONVENTION IS USED IN YEARS 1 AND 4 9 USING $1.00 AS THE BASIS - COULD BE ANY AMOUNT 10 11 DDB-SLN DDB-SLN MACRS-GDS 12 DDB SLN MACRS-GDS MACRS-GDS PERCENTAGES dt dt dt Bt dt/B0*100% 13 EOY 14 0 $1.0000 15 1 $0.3333 $0.1667 $0.3333 $0.6667 33.33% 16 2 $0.4444 $0.2667 $0.4444 $0.2222 44.44% 17 3 $0.1481 $0.1481 $0.1481 $0.0741 14.81% 18 4 $0.0247 $0.0741 $0.0741 $0.0000 7.41% 19 20 SUM DEPR $1.00 21 DDB DEPR FOR YR 1 IS CALCULATED AS 0.5*RATE*B0 22 DDB DEPR FOR YR 2 IS CALCULATED AS RATE*B1 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

DDB DEPR FOR YR 4 IS CALCULATED AS 0.5*RATE*B3 SLN DEPR FOR YR 1 IS CALCULATED AS 0.5*SLN(1,0,3) SLN DEPR FOR YR 2 IS CALCULATED AS SLN(0.80,0,2.5) SLN DEPR FOR YR 4 IS CALCULATED AS 0.5*SLN(0.0741,0,0.5) DDB-SLN DEPR IS LARGER OF DDB OR SLN FOR THE YR DDB-SLN DEPR IS ALSO MACRS-GDS DEPRECIATION OR, COULD WORK USING VDB FUNCTION AS FOLLOWS

EOY 0 1 2 3 4 SUM DEPR

VDB dt $0.3333 =VDB(1,0,5,0,0.5) $0.4444 =VDB(1,0,5,0.5,1.5) $0.1481 =VDB(1,0,5,1.5,2.5) $0.0741 =VDB(1,0,5,2.5,3) $1.00

DDB-SLN MACRS-GDS MACRS-GDS PERCENTAGES Bt dt/B0*100% $1.0000 $0.6667 $0.2222 $0.0741 $0.0000

33.33% 44.44% 14.81% 7.41%

A B C D E F G 1 PROBLEM 9.18 2 3 BASIS $1.00 RATE 40.0000% =2/USEFUL LIFE*100% 4 EST SALV $0.00 USEFUL LIFE 5 5 RCVD SALV $0.00 PERIODS 5 6 7 MACRS-GDS IS BASED UPON DDB SWITCHING TO SLN (DDB-SLN) DEPR 8 HALF-YEAR CONVENTION IS USED IN YEARS 1 AND 6 9 USING $1.00 AS THE BASIS - COULD BE ANY AMOUNT 10 11 DDB-SLN DDB-SLN MACRS-GDS 12 DDB SLN MACRS-GDS MACRS-GDS PERCENTAGES dt dt dt Bt dt/B0*100% 13 EOY 14 0 $1.0000 15 1 $0.2000 $0.1000 $0.2000 $0.8000 20.00% 16 2 $0.3200 $0.1778 $0.3200 $0.4800 32.00% 17 3 $0.1920 $0.1371 $0.1920 $0.2880 19.20% 18 4 $0.1152 $0.1152 $0.1152 $0.1728 11.52% 19 5 $0.0691 $0.1152 $0.1152 $0.0576 11.52% 20 6 $0.0115 $0.0576 $0.0576 $0.0000 5.76% 21 22 SUM DEPR $1.00 23 DDB DEPR FOR YR 1 IS CALCULATED AS 0.5*RATE*B0 24 DDB DEPR FOR YR 2 IS CALCULATED AS RATE*B1 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

DDB DEPR FOR YR 6 IS CALCULATED AS 0.5*RATE*B5 SLN DEPR FOR YR 1 IS CALCULATED AS 0.5*SLN(1,0,5) SLN DEPR FOR YR 2 IS CALCULATED AS SLN(0.80,0,4.5) SLN DEPR FOR YR 6 IS CALCULATED AS 0.5*SLN(0.0576,0,0.5) DDB-SLN DEPR IS LARGER OF DDB OR SLN FOR THE YR DDB-SLN DEPR IS ALSO MACRS-GDS DEPRECIATION OR, COULD WORK USING VDB FUNCTION AS FOLLOWS

EOY 0 1 2 3 4 5 6 SUM DEPR

VDB dt $0.2000 =VDB(1,0,5,0,0.5) $0.3200 =VDB(1,0,5,0.5,1.5) $0.1920 =VDB(1,0,5,1.5,2.5) $0.1152 =VDB(1,0,5,2.5,3.5) $0.1152 =VDB(1,0,5,3.5,4.5) $0.0576 =VDB(1,0,5,4.5,5) $1.00

DDB-SLN MACRS-GDS MACRS-GDS PERCENTAGES Bt dt/B0*100% $1.0000 $0.8000 $0.4800 $0.2880 $0.1728 $0.0576 $0.0000

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

A B C D E F G 1 PROBLEM 9.19 2 3 BASIS $1.00 RATE 100.0000% =2/USEFUL LIFE*100% 4 EST SALV $0.00 USEFUL LIFE 2 5 RCVD SALV $0.00 PERIODS 2 6 7 MACRS-GDS IS BASED UPON DDB SWITCHING TO SLN (DDB-SLN) DEPR 8 HALF-YEAR CONVENTION IS USED IN YEARS 1 AND 3 9 USING $1.00 AS THE BASIS - COULD BE ANY AMOUNT 10 11 DDB-SLN DDB-SLN MACRS-GDS 12 DDB SLN MACRS-GDS MACRS-GDS PERCENTAGES dt dt dt Bt dt/B0*100% 13 EOY 14 0 $1.0000 15 1 $0.5000 $0.2500 $0.5000 $0.5000 50.00% 16 2 $0.5000 $0.3333 $0.5000 $0.0000 50.00% 17 3 $0.0000 $0.0000 $0.0000 $0.0000 0.00% 18 19 SUM DEPR $1.00 20 DDB DEPR FOR YR 1 IS CALCULATED AS 0.5*RATE*B0 21 DDB DEPR FOR YR 2 IS CALCULATED AS RATE*B1 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

DDB DEPR FOR YR 3 IS CALCULATED AS 0.5*RATE*B2 SLN DEPR FOR YR 1 IS CALCULATED AS 0.5*SLN(1,0,2) SLN DEPR FOR YR 2 IS CALCULATED AS SLN(0.5,0,1.5) SLN DEPR FOR YR 3 IS CALCULATED AS 0.5*SLN(0,0,0.5) DDB-SLN DEPR IS LARGER OF DDB OR SLN FOR THE YR DDB-SLN DEPR IS ALSO MACRS-GDS DEPRECIATION OR, COULD WORK USING VDB FUNCTION AS FOLLOWS

EOY 0 1 2 3 SUM DEPR

VDB dt $0.50 =VDB(1,0,2,0,0.5) $0.50 =VDB(1,0,2,0.5,1.5) $0.00 =VDB(1,0,2,1.5,2) $1.00

DDB-SLN MACRS-GDS MACRS-GDS PERCENTAGES Bt dt/B0*100% $1.0000 $0.5000 $0.0000 $0.0000

50.00% 50.00% 0.00%

A B C D E F G 1 PROBLEM 9.20 2 3 BASIS $1.00 RATE 50.0000% =2/USEFUL LIFE*100% 4 EST SALV $0.00 USEFUL LIFE 4 5 RCVD SALV $0.00 PERIODS 4 6 7 MACRS-GDS IS BASED UPON DDB SWITCHING TO SLN (DDB-SLN) DEPR 8 HALF-YEAR CONVENTION IS USED IN YEARS 1 AND 5 9 USING $1.00 AS THE BASIS - COULD BE ANY AMOUNT 10 11 DDB-SLN DDB-SLN MACRS-GDS 12 DDB SLN MACRS-GDS MACRS-GDS PERCENTAGES dt dt dt Bt dt/B0*100% 13 EOY 14 0 $1.0000 15 1 $0.2500 $0.1250 $0.2500 $0.7500 25.00% 16 2 $0.3750 $0.2143 $0.3750 $0.3750 37.50% 17 3 $0.1875 $0.1500 $0.1875 $0.1875 18.75% 18 4 $0.0938 $0.1250 $0.1250 $0.0625 12.50% 19 5 $0.0156 $0.0625 $0.0625 $0.0000 6.25% 20 21 SUM DEPR $1.00 22 DDB DEPR FOR YR 1 IS CALCULATED AS 0.5*RATE*B0 23 DDB DEPR FOR YR 2 IS CALCULATED AS RATE*B1 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

DDB DEPR FOR YR 5 IS CALCULATED AS 0.5*RATE*B4 SLN DEPR FOR YR 1 IS CALCULATED AS 0.5*SLN(1,0,4) SLN DEPR FOR YR 2 IS CALCULATED AS SLN(0.75,0,3.5) SLN DEPR FOR YR 5 IS CALCULATED AS 0.5*SLN(0.0625,0,0.5) DDB-SLN DEPR IS LARGER OF DDB OR SLN FOR THE YR DDB-SLN DEPR IS ALSO MACRS-GDS DEPRECIATION OR, COULD WORK USING VDB FUNCTION AS FOLLOWS

EOY 0 1 2 3 4 5 SUM DEPR

VDB dt $0.2500 =VDB(1,0,4,0,0.5) $0.3750 =VDB(1,0,4,0.5,1.5) $0.1875 =VDB(1,0,4,1.5,2.5) $0.1250 =VDB(1,0,4,2.5,3.5) $0.0625 =VDB(1,0,4,3.5,4) $1.00

DDB-SLN MACRS-GDS MACRS-GDS PERCENTAGES Bt dt/B0*100% $1.0000 $0.7500 $0.3750 $0.1875 $0.0625 $0.0000

25.00% 37.50% 18.75% 12.50% 6.25%

A 1 PROBLEM 9.21 2 3 4 a 5 b 6 c 7 d 8 e 9 f 10 g 11 h 12 i 13 14 15 16 17 18 19 20 21 22

TANGIBLE X X X X X X X X

NOTE (FROM WIKI)! IN ACCOUNTING, AMORTIZATION REFERS TO EXPENSING THE ACQUISITI OF INTANGIBLE ASSETS SUCH AS TRADEMARKS AND COPYRIGHTS IN A SYSTEMATIC MANNE ECONOMIC LIVES SO AS TO REFLECT THEIR CONSUMPTION, EXPIRATION, OBSOLESCENCE O RESULT OF USE OR THE PASSAGE OF TIME.

A CORRESPONDING CONCEPT FOR TANGIBLE ASSETS IS DEPRECIATION. METHODOLOGIES F EACH ACCOUNTING PERIOD ARE GENERALLY THE SAME AS FOR DEPRECIATION. HOWEVER, AS GOODWILL OR CERTAIN BRANDS MAY BE DEEMED TO HAVE AN INDEFINITE USEFUL LIFE A TO AMORTIZATION.

D E F G H I 1 2 MACRS 3 INTANGIBLE PERSONAL REAL DEPRECIABLE NONDEPRECIABLE PROP CLASS 4 X X 5 5 X X NA 6 X X NA 7 X X 7 8 X X X (SEE NOTE) NA 9 X X 5 10 X X NA 11 X X 39 12 X X 15 13 RS TO EXPENSING 14 THE ACQUISITION COST LESS THE RESIDUAL VALUE RIGHTS IN A 15 SYSTEMATIC MANNER OVER THEIR ESTIMATED USEFUL N, EXPIRATION, 16 OBSOLESCENCE OR OTHER DECLINE IN VALUE AS A 17 18 EPRECIATION. 19METHODOLOGIES FOR ALLOCATING AMORTIZATION TO FOR DEPRECIATION. 20 HOWEVER, MANY INTANGIBLE ASSETS SUCH AVE AN INDEFINITE 21 USEFUL LIFE AND ARE THEREFORE NOT SUBJECT 22

J SPECIFIC DEPR METH 200% DBSLH NA NA 200% DBSLH NA 200% DBSLH NA SLM 150% DBSLH

A 1 PROBLEM 9.22 2 3 4 a 5 b 6 c 7 d 8 e 9 f 10 g 11 h 12 i 13 14 15 16 17 18 19 20 21 22

WHAT A CELL PHONE TOWER A TRACTOR (PART OF TRACTOR-TRAILER RIG - 18-WHEELER) A PLOT OF LAND FOR YOUR PERSONAL USE. A COPYRIGHT A COMPUTER USED IN YOUR JOB AN ALL-IN-ONE COPIER, SCANNER, FAX MACHINE USED IN YOUR BUSINESS. A MOONEY VISCOMETER USED IN A POLYMERS LAB. A RENTAL HOME FOR THE PURPOSE OF GENERATING RENTAL INCOME AN ELECTRIC GENERATOR PURCHASED BY A PUBLIC UTILITY

C D E F G H I 1 2 MACRS 3 TANGIBLE INTANGIBLE PERSONAL REAL DEPRECIABLE NONDEPRECIABLE PROP CLASS 4 X X X 20 5 X X X 3 6 X X X NA 7 X X X (SEE NOTE) NA 8 X X X 5 9 X X X 5 10 X X X 5 11 X X X 27.5 12 X X X 20 13 EXPENSING14 THE ACQUISITION COST LESS THE RESIDUAL VALUE TS IN A SYSTEMATIC 15 MANNER OVER THEIR ESTIMATED USEFUL IRATION, OBSOLESCENCE 16 OR OTHER DECLINE IN VALUE AS A 17 18 CIATION. METHODOLOGIES 19 FOR ALLOCATING AMORTIZATION TO DEPRECIATION. 20 HOWEVER, MANY INTANGIBLE ASSETS SUCH N INDEFINITE21USEFUL LIFE AND ARE THEREFORE NOT SUBJECT 22

J 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

SPECIFIC DEPR METH 150% DBSLH 200% DBSLH NA NA 200% DBSLH 200% DBSLH 200% DBSLH SLM 150% DBSLH

A B C D E 1 PROBLEM 9.23 2 3 NOTE THAT THE LOAN INFORMATION IS IRRELEVANT 4 d3= 5 a $122,430.00 6 B3= 7 b $306,110.00 8 9 BASIS $700,000.00 10 EST SALV $75,000.00 USEFUL LIFE 10 11 RCVD SALV $75,000.00 PERIODS 10 12 dt Bt 13 EOY MACRS-GDS(7) 14 15 0 $700,000.00 16 1 $100,030.00 $599,970.00 14.29% 17 2 $171,430.00 $428,540.00 24.49% 18 3 $122,430.00 $306,110.00 17.49% 19 4 $87,430.00 $218,680.00 12.49% 20 5 $62,510.00 $156,170.00 8.93% 21 6 $62,440.00 $93,730.00 8.92% 22 7 $62,510.00 $31,220.00 8.93% 23 8 $31,220.00 $0.00 4.46% 24 9 $0.00 $0.00 25 10 $0.00 $0.00 26 27 SUM DEPR $700,000.00 28 d3= 29 c $61,215.00 30 31 BASIS $700,000.00 32 EST SALV $75,000.00 USEFUL LIFE 10 33 RCVD SALV $75,000.00 PERIODS 10 34 35 EOY dt Bt MACRS-GDS(7) 36 37 0 $700,000.00 38 1 $100,030.00 $599,970.00 14.29% 39 2 $171,430.00 $428,540.00 24.49% 40 3 $61,215.00 $367,325.00 8.75% 41 42 SUM DEPR $332,675.00

A B C D E 1 PROBLEM 9.24 2 B4= 3 a $800,000.00 4 5 BASIS $1,200,000.00 6 EST SALV $0.00 USEFUL LIFE 12 7 RCVD SALV $0.00 PERIODS 12 d B 8 EOY t t 9 10 0 $1,200,000.00 11 1 $100,000.00 $1,100,000.00 12 2 $100,000.00 $1,000,000.00 13 3 $100,000.00 $900,000.00 14 4 $100,000.00 $800,000.00 15 16 B4= 17 b $449,820.00 MACRS-GDS(7) 18 19 BASIS $1,200,000.00 20 EST SALV $0.00 USEFUL LIFE 12 21 RCVD SALV $0.00 PERIODS 12 dt Bt 22 EOY MACRS-GDS(7) 23 24 0 $1,200,000.00 25 1 $171,480.00 $1,028,520.00 14.290% 26 2 $293,880.00 $734,640.00 24.490% 27 3 $209,880.00 $524,760.00 17.490% 28 4 $74,940.00 $449,820.00 6.245%

A B C D E 1 PROBLEM 9.25 2 3 a MACRS-GDS(7) 4 5 b, c BASIS $800,000.00 6 EST SALV $130,000.00 USEFUL LIFE 10 7 RCVD SALV $130,000.00 PERIODS 10 8 dt Bt 9 EOY MACRS-GDS(7) 10 11 0 $800,000.00 12 1 $114,320.00 $685,680.00 14.29% 13 2 $195,920.00 $489,760.00 24.49% 14 3 $139,920.00 $349,840.00 17.49% 15 4 $99,920.00 $249,920.00 12.49% 16 5 $71,440.00 $178,480.00 8.93% 17 6 $71,360.00 $107,120.00 8.92% 18 7 $71,440.00 $35,680.00 8.93% 19 8 $35,680.00 $0.00 4.46% 20 9 $0.00 $0.00 21 10 $0.00 $0.00 22 23 SUM DEPR $800,000.00

A B C D E 1 PROBLEM 9.26 2 3 a MACRS-GDS(5) 4 5 b, c BASIS $350,000.00 6 EST SALV $30,000.00 USEFUL LIFE 8 7 RCVD SALV $30,000.00 PERIODS 8 8 dt Bt 9 EOY MACRS-GDS(5) 10 11 0 $350,000.00 12 1 $70,000.00 $280,000.00 20.00% 13 2 $112,000.00 $168,000.00 32.00% 14 3 $67,200.00 $100,800.00 19.20% 15 4 $40,320.00 $60,480.00 11.52% 16 5 $40,320.00 $20,160.00 11.52% 17 6 $20,160.00 $0.00 5.76% 18 7 $0.00 $0.00 19 8 $0.00 $0.00 20 21 SUM DEPR $350,000.00

G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

A B C D E 1 PROBLEM 9.27 2 3 NOTE! THE SALVAGE VALUE OF $10,000 DOES NOT COME 4 INTO PLAY IN DETERMINING MACRS DEPRECIATION. 5 IT WILL BE A FACTOR IN AFTER-TAX CASH FLOW ANALYSIS. 6 7 a MACRS-GDS(7) 8 9 b BASIS $120,000.00 10 EST SALV $10,000.00 USEFUL LIFE 8 11 RCVD SALV $10,000.00 PERIODS 8 12 dt Bt 13 EOY MACRS-GDS(7) 14 15 0 $120,000.00 16 1 $17,148.00 $102,852.00 14.29% 17 2 $29,388.00 $73,464.00 24.49% 18 3 $20,988.00 $52,476.00 17.49% 19 4 $14,988.00 $37,488.00 12.49% 20 5 $10,716.00 $26,772.00 8.93% 21 6 $10,704.00 $16,068.00 8.92% 22 7 $10,716.00 $5,352.00 8.93% 23 8 $5,352.00 $0.00 4.46% 24 25 SUM DEPR $120,000.00 26 27 28 c BASIS $120,000.00 29 EST SALV $10,000.00 USEFUL LIFE 8 30 RCVD SALV $10,000.00 PERIODS 8 31 dt Bt 32 EOY MACRS-GDS(7) 33 34 0 $120,000.00 35 1 $17,148.00 $102,852.00 14.29% 36 2 $29,388.00 $73,464.00 24.49% 37 3 $20,988.00 $52,476.00 17.49% 38 4 $14,988.00 $37,488.00 12.49% 39 5 $10,716.00 $26,772.00 8.93% 40 6 $5,352.00 $21,420.00 4.46% 41 42 SUM DEPR $98,580.00

A B C D E 1 PROBLEM 9.28 2 3 a MACRS-GDS(3) 4 5 b BASIS $90,000.00 6 EST SALV $4,000.00 USEFUL LIFE 6 7 RCVD SALV $4,000.00 PERIODS 6 8 dt Bt 9 EOY MACRS-GDS(3) 10 11 0 $90,000.00 12 1 $29,997.00 $60,003.00 33.33% 13 2 $40,005.00 $19,998.00 44.45% 14 3 $13,329.00 $6,669.00 14.81% 15 4 $6,669.00 $0.00 7.41% 16 5 $0.00 $0.00 0.00% 17 6 $0.00 $0.00 0.00% 18 19 SUM DEPR $90,000.00 20 21 22 c BASIS $90,000.00 23 EST SALV $4,000.00 USEFUL LIFE 6 24 RCVD SALV $4,000.00 PERIODS 4 25 dt Bt 26 EOY MACRS-GDS(3) 27 28 0 $90,000.00 29 1 $29,997.00 $60,003.00 33.33% 30 2 $40,005.00 $19,998.00 44.45% 31 3 $13,329.00 $6,669.00 14.81% 32 4 $3,334.50 $3,334.50 3.705% 33 34 SUM DEPR $86,665.50 35 36 37 d BASIS $90,000.00 38 EST SALV $4,000.00 USEFUL LIFE 6 39 RCVD SALV $4,000.00 PERIODS 3 40 dt Bt 41 EOY MACRS-GDS(3) 42 43 0 $90,000.00 44 1 $29,997.00 $60,003.00 33.33% 45 2 $40,005.00 $19,998.00 44.45% 46 3 $6,664.50 $13,333.50 7.405% 47 48 SUM DEPR $76,666.50

A B C D E 1 PROBLEM 9.29 2 3 a BASIS $28,500.00 4 EST SALV $0.00 USEFUL LIFE 9 5 RCVD SALV $0.00 PERIODS 9 6 dt Bt 7 EOY MACRS-GDS(5) 8 9 0 $28,500.00 10 1 $5,700.00 $22,800.00 20.00% 11 2 $9,120.00 $13,680.00 32.00% 12 3 $5,472.00 $8,208.00 19.20% 13 4 $3,283.20 $4,924.80 11.52% 14 5 $3,283.20 $1,641.60 11.52% 15 6 $1,641.60 $0.00 5.76% 16 7 $0.00 $0.00 0.00% 17 8 $0.00 $0.00 0.00% 18 9 $0.00 $0.00 0.00% 19 20 SUM DEPR $28,500.00 21 22 23 b BASIS $28,500.00 24 EST SALV $0.00 USEFUL LIFE 9 25 RCVD SALV $0.00 PERIODS 9 26 dt Bt 27 EOY 28 29 0 $28,500.00 30 1 $3,166.67 $25,333.33 31 2 $3,166.67 $22,166.67 32 3 $3,166.67 $19,000.00 33 4 $3,166.67 $15,833.33 34 5 $3,166.67 $12,666.67 35 6 $3,166.67 $9,500.00 36 7 $3,166.67 $6,333.33 37 8 $3,166.67 $3,166.67 38 9 $3,166.67 $0.00 39 40 SUM DEPR $28,500.00

A B C D E 1 PROBLEM 9.30 2 3 a MACRS-GDS(5) 4 5 b BASIS $1,600,000.00 6 EST SALV $0.00 USEFUL LIFE 6 7 RCVD SALV $0.00 PERIODS 6 8 dt Bt 9 EOY MACRS-GDS(5) 10 11 0 $1,600,000.00 12 1 $320,000.00 $1,280,000.00 20.00% 13 2 $512,000.00 $768,000.00 32.00% 14 3 $307,200.00 $460,800.00 19.20% 15 4 $184,320.00 $276,480.00 11.52% 16 5 $184,320.00 $92,160.00 11.52% 17 6 $92,160.00 $0.00 5.76% 18 19 SUM DEPR $1,600,000.00 20 21 22 c BASIS $1,600,000.00 23 EST SALV $0.00 USEFUL LIFE 6 24 RCVD SALV $0.00 PERIODS 3 25 dt Bt 26 EOY MACRS-GDS(5) 27 28 0 $1,600,000.00 29 1 $320,000.00 $1,280,000.00 20.00% 30 2 $512,000.00 $768,000.00 32.00% 31 3 $153,600.00 $614,400.00 9.600% 32 33 SUM DEPR $985,600.00

A B C D E 1 PROBLEM 9.31 2 3 a MACRS-GDS(7) 4 5 b BASIS $190,000.00 6 EST SALV $0.00 USEFUL LIFE 12 7 RCVD SALV $0.00 PERIODS 12 8 dt Bt 9 EOY MACRS-GDS(7) 10 11 0 $190,000.00 12 1 $27,151.00 $162,849.00 14.29% 13 2 $46,531.00 $116,318.00 24.49% 14 3 $33,231.00 $83,087.00 17.49% 15 4 $23,731.00 $59,356.00 12.49% 16 5 $16,967.00 $42,389.00 8.93% 17 6 $16,948.00 $25,441.00 8.92% 18 7 $16,967.00 $8,474.00 8.93% 19 8 $8,474.00 $0.00 4.46% 20 9 $0.00 $0.00 0.00% 21 10 $0.00 $0.00 0.00% 22 11 $0.00 $0.00 0.00% 23 12 $0.00 $0.00 0.00% 24 25 SUM DEPR $190,000.00 26 27 28 c BASIS $190,000.00 29 EST SALV $0.00 USEFUL LIFE 12 30 RCVD SALV $0.00 PERIODS 5 31 dt Bt 32 EOY MACRS-GDS(7) 33 34 0 $190,000.00 35 1 $27,151.00 $162,849.00 14.29% 36 2 $46,531.00 $116,318.00 24.49% 37 3 $33,231.00 $83,087.00 17.49% 38 4 $23,731.00 $59,356.00 12.49% 39 5 $8,483.50 $50,872.50 4.465% 40 41 SUM DEPR $139,127.50

A B C D E 1 PROBLEM 9.32 2 d1= 3 a $4,400.00 4 d3= 5 $4,224.00 6 d6= 7 $1,267.20 8 9 BASIS $22,000.00 10 EST SALV $2,000.00 USEFUL LIFE 6 11 RCVD SALV $2,000.00 PERIODS 6 dt Bt 12 EOY MACRS-GDS(5) 13 14 0 $22,000.00 15 1 $4,400.00 $17,600.00 20.00% 16 2 $7,040.00 $10,560.00 32.00% 17 3 $4,224.00 $6,336.00 19.20% 18 4 $2,534.40 $3,801.60 11.52% 19 5 $2,534.40 $1,267.20 11.52% 20 6 $1,267.20 $0.00 5.76% 21 22 SUM DEPR $22,000.00 23 24 d1= 25 b $4,400.00 26 d3= 27 $4,224.00 28 d4= 29 $1,267.20 30 31 BASIS $22,000.00 32 EST SALV $2,000.00 USEFUL LIFE 6 33 RCVD SALV $2,000.00 PERIODS 4 dt Bt 34 EOY MACRS-GDS(5) 35 36 0 $22,000.00 37 1 $4,400.00 $17,600.00 20.00% 38 2 $7,040.00 $10,560.00 32.00% 39 3 $4,224.00 $6,336.00 19.20% 40 4 $1,267.20 $5,068.80 5.76% 41 42 SUM DEPR $16,931.20

A B C D E 1 PROBLEM 9.33 2 3 a MACRS-GDS(10) 4 5 b BASIS $75,000.00 6 EST SALV $0.00 USEFUL LIFE 10 7 RCVD SALV $0.00 PERIODS 5 8 dt Bt 9 EOY MACRS-GDS(10) 10 11 0 $75,000.00 12 1 $7,500.00 $67,500.00 10.00% 13 2 $13,500.00 $54,000.00 18.00% 14 3 $10,800.00 $43,200.00 14.40% 15 4 $8,640.00 $34,560.00 11.52% 16 5 $3,457.50 $31,102.50 4.610% 17 18 SUM DEPR $43,897.50 19 20 21 c BASIS $75,000.00 22 EST SALV $0.00 USEFUL LIFE 10 23 RCVD SALV $0.00 PERIODS 6 24 dt Bt 25 EOY MACRS-GDS(10) 26 27 0 $75,000.00 28 1 $7,500.00 $67,500.00 10.00% 29 2 $13,500.00 $54,000.00 18.00% 30 3 $10,800.00 $43,200.00 14.40% 31 4 $8,640.00 $34,560.00 11.52% 32 5 $6,915.00 $27,645.00 9.22% 33 6 $2,763.75 $24,881.25 3.685% 34 35 SUM DEPR $50,118.75

A B C D E 1 PROBLEM 3.34 2 3 a MACRS-GDS(10) 4 5 b BASIS $250,000.00 6 EST SALV $0.00 USEFUL LIFE 10 7 RCVD SALV $0.00 PERIODS 6 8 dt Bt 9 EOY MACRS-GDS(10) 10 11 0 $250,000.00 12 1 $25,000.00 $225,000.00 10.00% 13 2 $45,000.00 $180,000.00 18.00% 14 3 $36,000.00 $144,000.00 14.40% 15 4 $28,800.00 $115,200.00 11.52% 16 5 $23,050.00 $92,150.00 9.22% 17 6 $9,212.50 $82,937.50 3.685% 18 19 SUM DEPR $167,062.50 20 21 22 c BASIS $250,000.00 23 EST SALV $0.00 USEFUL LIFE 10 24 RCVD SALV $0.00 PERIODS 7 25 dt Bt 26 EOY MACRS-GDS(10) 27 28 0 $250,000.00 29 1 $25,000.00 $225,000.00 10.00% 30 2 $45,000.00 $180,000.00 18.00% 31 3 $36,000.00 $144,000.00 14.40% 32 4 $28,800.00 $115,200.00 11.52% 33 5 $23,050.00 $92,150.00 9.22% 34 6 $18,425.00 $73,725.00 7.37% 35 7 $8,187.50 $65,537.50 3.275% 36 37 SUM DEPR $184,462.50

A B C D E 1 PROBLEM 9.35 2 3 a MACRS-GDS(20) 4 dt Bt 5 b EOY 6 7 1 $112,500.00 $2,887,500.00 8 2 $216,570.00 $2,670,930.00 9 3 $200,310.00 $2,470,620.00 10 4 $185,310.00 $2,285,310.00 11 12 FOR ALL YEARS, SEE BELOW 13 14 BASIS $3,000,000.00 15 EST SALV $250,000.00 USEFUL LIFE 30 16 RCVD SALV $0.00 PERIODS 21 17 dt Bt 18 EOY MACRS-GDS(20) 19 20 0 $3,000,000.00 21 1 $112,500.00 $2,887,500.00 3.750% 22 2 $216,570.00 $2,670,930.00 7.219% 23 3 $200,310.00 $2,470,620.00 6.677% 24 4 $185,310.00 $2,285,310.00 6.177% 25 5 $171,390.00 $2,113,920.00 5.713% 26 6 $158,550.00 $1,955,370.00 5.285% 27 7 $146,640.00 $1,808,730.00 4.888% 28 8 $135,660.00 $1,673,070.00 4.522% 29 9 $133,860.00 $1,539,210.00 4.462% 30 10 $133,830.00 $1,405,380.00 4.461% 31 11 $133,860.00 $1,271,520.00 4.462% 32 12 $133,830.00 $1,137,690.00 4.461% 33 13 $133,860.00 $1,003,830.00 4.462% 34 14 $133,830.00 $870,000.00 4.461% 35 15 $133,860.00 $736,140.00 4.462% 36 16 $133,830.00 $602,310.00 4.461% 37 17 $133,860.00 $468,450.00 4.462% 38 18 $133,830.00 $334,620.00 4.461% 39 19 $133,860.00 $200,760.00 4.462% 40 20 $133,830.00 $66,930.00 4.461% 41 21 $66,930.00 $0.00 2.231% 42 22 $0.00 $0.00 0.000% 43 23 $0.00 $0.00 0.000% 44 24 $0.00 $0.00 0.000% 45 25 $0.00 $0.00 0.000% 46 26 $0.00 $0.00 0.000% 47 27 $0.00 $0.00 0.000% 48 28 $0.00 $0.00 0.000% 49 29 $0.00 $0.00 0.000% 50 30 $0.00 $0.00 0.000%

A 51 52

B SUM DEPR

C $3,000,000.00

A B C D E 1 PROBLEM 9.36 2 3 a MACRS-GDS(10) 4 5 b BASIS $2,700,000.00 6 EST SALV $0.00 USEFUL LIFE 18 7 RCVD SALV $0.00 PERIODS 18 8 dt Bt 9 EOY MACRS-GDS(10) 10 11 0 $2,700,000.00 12 1 $270,000.00 $2,430,000.00 10.00% 13 2 $486,000.00 $1,944,000.00 18.00% 14 3 $388,800.00 $1,555,200.00 14.40% 15 4 $311,040.00 $1,244,160.00 11.52% 16 5 $248,940.00 $995,220.00 9.22% 17 6 $198,990.00 $796,230.00 7.37% 18 7 $176,850.00 $619,380.00 6.55% 19 8 $176,850.00 $442,530.00 6.55% 20 9 $177,120.00 $265,410.00 6.56% 21 10 $176,850.00 $88,560.00 6.55% 22 11 $88,560.00 $0.00 3.28% 23 12 $0.00 $0.00 24 13 $0.00 $0.00 25 14 $0.00 $0.00 26 15 $0.00 $0.00 27 16 $0.00 $0.00 28 17 $0.00 $0.00 29 18 $0.00 $0.00 30 31 SUM DEPR $2,700,000.00

A B C D E 1 PROBLEM 9.37 2 3 a MACRS-GDS(20) 4 d1= B1= 5 b $637,500.00 $16,362,500.00 6 d5= B5= 7 $971,210.00 $11,978,880.00 8 d21= B21= 9 $379,270.00 $0.00 10 11 BASIS $17,000,000.00 12 EST SALV $1,700,000.00 USEFUL LIFE 30 13 RCVD SALV $1,700,000.00 PERIODS 30 14 dt Bt 15 EOY MACRS-GDS(20) 16 17 0 $17,000,000.00 18 1 $637,500.00 $16,362,500.00 3.750% 19 2 $1,227,230.00 $15,135,270.00 7.219% 20 3 $1,135,090.00 $14,000,180.00 6.677% 21 4 $1,050,090.00 $12,950,090.00 6.177% 22 5 $971,210.00 $11,978,880.00 5.713% 23 6 $898,450.00 $11,080,430.00 5.285% 24 7 $830,960.00 $10,249,470.00 4.888% 25 8 $768,740.00 $9,480,730.00 4.522% 26 9 $758,540.00 $8,722,190.00 4.462% 27 10 $758,370.00 $7,963,820.00 4.461% 28 11 $758,540.00 $7,205,280.00 4.462% 29 12 $758,370.00 $6,446,910.00 4.461% 30 13 $758,540.00 $5,688,370.00 4.462% 31 14 $758,370.00 $4,930,000.00 4.461% 32 15 $758,540.00 $4,171,460.00 4.462% 33 16 $758,370.00 $3,413,090.00 4.461% 34 17 $758,540.00 $2,654,550.00 4.462% 35 18 $758,370.00 $1,896,180.00 4.461% 36 19 $758,540.00 $1,137,640.00 4.462% 37 20 $758,370.00 $379,270.00 4.461% 38 21 $379,270.00 $0.00 2.231% 39 22 $0.00 $0.00 40 23 $0.00 $0.00 41 24 $0.00 $0.00 42 25 $0.00 $0.00 43 26 $0.00 $0.00 44 27 $0.00 $0.00 45 28 $0.00 $0.00 46 29 $0.00 $0.00 47 30 $0.00 $0.00 48 49 SUM DEPR $17,000,000.00

A B C D E 1 PROBLEM 9.38 2 3 a MACRS-GDS(39) 4 d1= B1= 5 $15,996.50 $634,003.50 6 d4= B4= 7 $16,666.00 $584,005.50 8 d7= B7= 9 $16,666.00 $534,007.50 10 11 b BASIS $650,000.00 12 EST SALV $0.00 USEFUL LIFE 40 13 RCVD SALV $0.00 PERIODS 40 14 dt Bt 15 EOY MACRS-GDS(39) 16 17 0 $650,000.00 18 1 $15,996.50 $634,003.50 2.461% 19 2 $16,666.00 $617,337.50 2.564% 20 3 $16,666.00 $600,671.50 2.564% 21 4 $16,666.00 $584,005.50 2.564% 22 5 $16,666.00 $567,339.50 2.564% 23 6 $16,666.00 $550,673.50 2.564% 24 7 $16,666.00 $534,007.50 2.564% 25 8 $16,666.00 $517,341.50 2.564% 26 9 $16,666.00 $500,675.50 2.564% 27 10 $16,666.00 $484,009.50 2.564% 28 11 $16,666.00 $467,343.50 2.564% 29 12 $16,666.00 $450,677.50 2.564% 30 13 $16,666.00 $434,011.50 2.564% 31 14 $16,666.00 $417,345.50 2.564% 32 15 $16,666.00 $400,679.50 2.564% 33 16 $16,666.00 $384,013.50 2.564% 34 17 $16,666.00 $367,347.50 2.564% 35 18 $16,666.00 $350,681.50 2.564% 36 19 $16,666.00 $334,015.50 2.564% 37 20 $16,666.00 $317,349.50 2.564% 38 21 $16,666.00 $300,683.50 2.564% 39 22 $16,666.00 $284,017.50 2.564% 40 23 $16,666.00 $267,351.50 2.564% 41 24 $16,666.00 $250,685.50 2.564% 42 25 $16,666.00 $234,019.50 2.564% 43 26 $16,666.00 $217,353.50 2.564% 44 27 $16,666.00 $200,687.50 2.564% 45 28 $16,666.00 $184,021.50 2.564% 46 29 $16,666.00 $167,355.50 2.564% 47 30 $16,666.00 $150,689.50 2.564% 48 31 $16,666.00 $134,023.50 2.564% 49 32 $16,666.00 $117,357.50 2.564% 50 33 $16,666.00 $100,691.50 2.564%

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

B 34 35 36 37 38 39 40

C $16,666.00 $16,666.00 $16,666.00 $16,666.00 $16,666.00 $16,666.00 $695.50

d1=

$15,996.50

B1=

$634,003.50

d4=

$16,666.00

B4=

$584,005.50

d7=

$9,027.42

B7=

$541,646.08

BASIS EST SALV RCVD SALV

D $84,025.50 $67,359.50 $50,693.50 $34,027.50 $17,361.50 $695.50 $0.00

$650,000.00 $0.00 USEFUL LIFE $0.00 PERIODS

E 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 0.107%

40 40

EOY

MACRS-GDS(39)

0 1 2 3 4 5 6 7

$15,996.50 $16,666.00 $16,666.00 $16,666.00 $16,666.00 $16,666.00 $9,027.42

$650,000.00 $634,003.50 $617,337.50 $600,671.50 $584,005.50 $567,339.50 $550,673.50 $541,646.08

2.461% 2.564% 2.564% 2.564% 2.564% 2.564% 1.389%

NORMALLY, BUILDING OWNERS (E.G., DOCTORS) WILL TURN (SELL) A PROPERTY AFTER A FE

G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

G 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

A B C D E 1 PROBLEM 9.39 2 3 a MACRS-GDS(39) 4 d1= 5 b $6,099.00 6 d4= 7 $7,692.00 8 d8= 9 $7,692.00 10 11 BASIS $300,000.00 12 EST SALV $0.00 USEFUL LIFE 40 13 RCVD SALV $0.00 PERIODS 40 14 dt Bt 15 EOY MACRS-GDS(39) 16 17 0 $300,000.00 18 1 $6,099.00 $293,901.00 2.033% 19 2 $7,692.00 $286,209.00 2.564% 20 3 $7,692.00 $278,517.00 2.564% 21 4 $7,692.00 $270,825.00 2.564% 22 5 $7,692.00 $263,133.00 2.564% 23 6 $7,692.00 $255,441.00 2.564% 24 7 $7,692.00 $247,749.00 2.564% 25 8 $7,692.00 $240,057.00 2.564% 26 9 $7,692.00 $232,365.00 2.564% 27 10 $7,692.00 $224,673.00 2.564% 28 11 $7,692.00 $216,981.00 2.564% 29 12 $7,692.00 $209,289.00 2.564% 30 13 $7,692.00 $201,597.00 2.564% 31 14 $7,692.00 $193,905.00 2.564% 32 15 $7,692.00 $186,213.00 2.564% 33 16 $7,692.00 $178,521.00 2.564% 34 17 $7,692.00 $170,829.00 2.564% 35 18 $7,692.00 $163,137.00 2.564% 36 19 $7,692.00 $155,445.00 2.564% 37 20 $7,692.00 $147,753.00 2.564% 38 21 $7,692.00 $140,061.00 2.564% 39 22 $7,692.00 $132,369.00 2.564% 40 23 $7,692.00 $124,677.00 2.564% 41 24 $7,692.00 $116,985.00 2.564% 42 25 $7,692.00 $109,293.00 2.564% 43 26 $7,692.00 $101,601.00 2.564% 44 27 $7,692.00 $93,909.00 2.564% 45 28 $7,692.00 $86,217.00 2.564% 46 29 $7,692.00 $78,525.00 2.564% 47 30 $7,692.00 $70,833.00 2.564% 48 31 $7,692.00 $63,141.00 2.564% 49 32 $7,692.00 $55,449.00 2.564% 50 33 $7,692.00 $47,757.00 2.564%

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

B 34 35 36 37 38 39 40

C $7,692.00 $7,692.00 $7,692.00 $7,692.00 $7,692.00 $7,692.00 $1,605.00

d1=

$6,099.00

d4=

$7,692.00

d8=

$4,807.50

BASIS EST SALV RCVD SALV

D $40,065.00 $32,373.00 $24,681.00 $16,989.00 $9,297.00 $1,605.00 $0.00

$300,000.00 $0.00 USEFUL LIFE $0.00 PERIODS

E 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 0.535%

40 40

EOY

MACRS-GDS(39)

0 1 2 3 4 5 6 7 8

$6,099.00 $7,692.00 $7,692.00 $7,692.00 $7,692.00 $7,692.00 $7,692.00 $4,807.50

$300,000.00 $293,901.00 $286,209.00 $278,517.00 $270,825.00 $263,133.00 $255,441.00 $247,749.00 $242,941.50

2.033% 2.564% 2.564% 2.564% 2.564% 2.564% 2.564% 1.603%

NORMALLY, BUILDING OWNERS WILL TURN (SELL) A PROPERTY AFTER A FEW YEARS, SEEKIN

G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

G 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

A B C D E 1 PROBLEM 9.40 2 3 a MACRS-GDS(27.5) 4 5 b, c BASIS $530,000.00 6 EST SALV $0.00 USEFUL LIFE 28 7 RCVD SALV $0.00 PERIODS 28 8 dt Bt 9 EOY MACRS-GDS(27.5) 10 11 0 $530,000.00 12 1 $16,864.60 $513,135.40 3.182% 13 2 $19,270.80 $493,864.60 3.636% 14 3 $19,270.80 $474,593.80 3.636% 15 4 $19,270.80 $455,323.00 3.636% 16 5 $19,270.80 $436,052.20 3.636% 17 6 $19,270.80 $416,781.40 3.636% 18 7 $4,014.75 $412,766.65 0.758%

A B C D E 1 PROBLEM 9.41 2 3 a MACRS-GDS(39) 4 5 b, c BASIS $240,000.00 6 EST SALV $0.00 USEFUL LIFE 40 7 RCVD SALV $0.00 PERIODS 40 8 dt Bt 9 EOY MACRS-GDS(39) 10 11 0 $240,000.00 12 1 $2,824.80 $237,175.20 1.177% 13 2 $6,153.60 $231,021.60 2.564% 14 3 $6,153.60 $224,868.00 2.564% 15 4 $6,153.60 $218,714.40 2.564% 16 5 $6,153.60 $212,560.80 2.564% 17 6 $2,307.60 $210,253.20 0.962%

A B C D E 1 PROBLEM 9.42 2 3 a MACRS-GDS(27.5) 4 5 6 b, c BASIS $85,000.00 7 EST SALV $0.00 USEFUL LIFE 28 8 RCVD SALV $0.00 PERIODS 28 9 dt Bt 10 EOY MACRS-GDS(27.5) 11 12 0 $85,000.00 13 1 $1,932.05 $83,067.95 2.273% 14 2 $3,090.60 $79,977.35 3.636% 15 3 $3,090.60 $76,886.75 3.636% 16 4 $3,090.60 $73,796.15 3.636% 17 5 $2,189.18 $71,606.98 2.576%

A B C D E 1 PROBLEM 9.43 2 3 a MACRS-GDS 4 BASIS $300,000.00 5 EST SALV $0.00 USEFUL LIFE 5 6 RCVD SALV $0.00 PERIODS 6 7 MARR 10.00% 8 dt Bt 9 EOY MACRS-GDS(5) 10 11 0 $300,000.00 12 1 $60,000.00 $240,000.00 20.00% 13 2 $96,000.00 $144,000.00 32.00% 14 3 $57,600.00 $86,400.00 19.20% 15 4 $34,560.00 $51,840.00 11.52% 16 5 $34,560.00 $17,280.00 11.52% 17 6 $17,280.00 $0.00 5.76% 18 19 SUM DEPR $300,000.00 20 PW DEPR $231,978.13 21 22 b 200% DBH 23 BASIS $300,000.00 RATE 40.0000% 24 EST SALV $0.00 USEFUL LIFE 5 25 RCVD SALV $0.00 PERIODS 6 26 MARR 10.00% 27 dt Bt 28 EOY 29 30 0 $300,000.00 31 1 $60,000.00 $240,000.00 32 2 $96,000.00 $144,000.00 33 3 $57,600.00 $86,400.00 34 4 $34,560.00 $51,840.00 35 5 $20,736.00 $31,104.00 36 6 $7,776.00 $23,328.00 37 38 SUM DEPR $276,672.00 39 PW DEPR $218,029.75 40 41 c DDB 42 BASIS $300,000.00 RATE 40.0000% 43 EST SALV $0.00 USEFUL LIFE 5 44 RCVD SALV $0.00 PERIODS 5 45 MARR 10.00% 46 dt Bt 47 EOY 48 49 0 $300,000.00 50 1 $120,000.00 $180,000.00

A 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

B 2 3 4 5 6

C $72,000.00 $43,200.00 $25,920.00 $15,552.00 $0.00

SUM DEPR PW DEPR

$276,672.00 $228,412.12

DDB-SL BASIS EST SALV RCVD SALV

D $108,000.00 $64,800.00 $38,880.00 $23,328.00 $23,328.00

$300,000.00 RATE $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1 2 3 4 5 6

$120,000.00 $72,000.00 $43,200.00 $32,400.00 $32,400.00 $0.00

$300,000.00 $180,000.00 $108,000.00 $64,800.00 $32,400.00 $0.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $243,299.33

SLN BASIS EST SALV RCVD SALV

$300,000.00 $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1 2 3 4 5 6

$60,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $0.00

$300,000.00 $240,000.00 $180,000.00 $120,000.00 $60,000.00 $0.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $227,447.21

SLH BASIS EST SALV

$300,000.00 $0.00 USEFUL LIFE

40.0000% 5 5 10.00%

5 5 10.00%

A 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134

B RCVD SALV

C $0.00

D PERIODS MARR

EOY

0 1 2 3 4 5 6

$30,000.00 $60,000.00 $60,000.00 $60,000.00 $60,000.00 $30,000.00

$300,000.00 $270,000.00 $210,000.00 $150,000.00 $90,000.00 $30,000.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $217,108.70

SYD BASIS EST SALV RCVD SALV

EOY

$300,000.00 SYD $0.00 USEFUL LIFE $0.00 PERIODS MARR dt

EXC FUNC

EXC FUNC $300,000.00 $200,000.00 $120,000.00 $60,000.00 $20,000.00 $0.00 $0.00

0 1 2 3 4 5 6

$100,000.00 $80,000.00 $60,000.00 $40,000.00 $20,000.00 $0.00

SUM DEPR PW DEPR

$300,000.00 $241,842.65

E 6 10.00%

15 5 5 10.00%

A B C D E 1 PROBLEM 9.44 2 3 a MACRS-GDS 4 BASIS $850,000.00 5 EST SALV $0.00 USEFUL LIFE 3 6 RCVD SALV $0.00 PERIODS 4 7 MARR 11.00% 8 dt Bt 9 EOY MACRS-GDS(3) 10 11 0 $850,000.00 12 1 $283,305.00 $566,695.00 33.33% 13 2 $377,825.00 $188,870.00 44.45% 14 3 $125,885.00 $62,985.00 14.81% 15 4 $62,985.00 $0.00 7.41% 16 17 SUM DEPR $850,000.00 18 PW DEPR $695,417.17 19 20 b 200% DBH 21 BASIS $850,000.00 RATE 66.6667% 22 EST SALV $0.00 USEFUL LIFE 3 23 RCVD SALV $0.00 PERIODS 4 24 MARR 11.00% 25 dt Bt 26 EOY 27 28 0 $850,000.00 29 1 $283,333.33 $566,666.67 30 2 $377,777.78 $188,888.89 31 3 $125,925.93 $62,962.96 32 4 $31,481.48 $31,481.48 33 34 SUM DEPR $818,518.52 35 PW DEPR $674,681.95 36 37 c DDB 38 BASIS $850,000.00 RATE 66.6667% 39 EST SALV $0.00 USEFUL LIFE 3 40 RCVD SALV $0.00 PERIODS 3 41 MARR 11.00% 42 dt Bt 43 EOY 44 45 0 $850,000.00 46 1 $566,666.67 $283,333.33 47 2 $188,888.89 $94,444.44 48 3 $62,962.96 $31,481.48 49 4 $0.00 $31,481.48 50

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

B SUM DEPR PW DEPR

DDB-SL BASIS EST SALV RCVD SALV

C $818,518.52 $709,854.95

$850,000.00 RATE $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1 2 3 4

$566,666.67 $188,888.89 $94,444.44 $0.00

$850,000.00 $283,333.33 $94,444.44 $0.00 $0.00

SUM DEPR PW DEPR

$850,000.00 $732,873.93

SLN BASIS EST SALV RCVD SALV

$850,000.00 $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1 2 3 4

$283,333.33 $283,333.33 $283,333.33 $0.00

$850,000.00 $566,666.67 $283,333.33 $0.00 $0.00

SUM DEPR PW DEPR

$850,000.00 $692,385.84

SLH BASIS EST SALV RCVD SALV

$850,000.00 $0.00 USEFUL LIFE $0.00 PERIODS MARR

EOY

0 1 2 3 4

$141,666.67 $283,333.33 $283,333.33 $141,666.67

$850,000.00 $708,333.33 $425,000.00 $141,666.67 $0.00

66.6667% 3 3 11.00%

3 3 11.00%

3 4 11.00%

A 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

SUM DEPR PW DEPR

$850,000.00 $658,078.43

SYD BASIS EST SALV RCVD SALV

EOY

$850,000.00 SYD $0.00 USEFUL LIFE $0.00 PERIODS MARR dt

EXC FUNC

EXC FUNC $850,000.00 $425,000.00 $141,666.67 $0.00 $0.00

0 1 2 3 4

$425,000.00 $283,333.33 $141,666.67 $0.00

SUM DEPR PW DEPR

$850,000.00 $716,428.02

6 3 3 11.00%

A B C D E 1 PROBLEM 9.45 2 3 a MACRS-GDS 4 BASIS $1,200,000.00 5 EST SALV $0.00 USEFUL LIFE 10 6 RCVD SALV $0.00 PERIODS 11 7 MARR 9.00% 8 dt Bt 9 EOY MACRS-GDS(10) 10 11 0 $1,200,000.00 12 1 $120,000.00 $1,080,000.00 10.00% 13 2 $216,000.00 $864,000.00 18.00% 14 3 $172,800.00 $691,200.00 14.40% 15 4 $138,240.00 $552,960.00 11.52% 16 5 $110,640.00 $442,320.00 9.22% 17 6 $88,440.00 $353,880.00 7.37% 18 7 $78,600.00 $275,280.00 6.55% 19 8 $78,600.00 $196,680.00 6.55% 20 9 $78,720.00 $117,960.00 6.56% 21 10 $78,600.00 $39,360.00 6.55% 22 11 $39,360.00 $0.00 3.28% 23 24 SUM DEPR $1,200,000.00 25 PW DEPR $815,046.16 26 27 b 200% DBH 28 BASIS $1,200,000.00 RATE 20.0000% 29 EST SALV $0.00 USEFUL LIFE 10 30 RCVD SALV $0.00 PERIODS 11 31 MARR 9.00% 32 dt Bt 33 EOY 34 35 0 $1,200,000.00 36 1 $120,000.00 $1,080,000.00 37 2 $216,000.00 $864,000.00 38 3 $172,800.00 $691,200.00 39 4 $138,240.00 $552,960.00 40 5 $110,592.00 $442,368.00 41 6 $88,473.60 $353,894.40 42 7 $70,778.88 $283,115.52 43 8 $56,623.10 $226,492.42 44 9 $45,298.48 $181,193.93 45 10 $36,238.79 $144,955.15 46 11 $16,106.13 $128,849.02 47 48 SUM DEPR $1,071,150.98 49 PW DEPR $757,433.44 50

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

A c

B C D DDB BASIS $1,200,000.00 RATE EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS MARR EOY 0 1 2 3 4 5 6 7 8 9 10 11 SUM DEPR PW DEPR

E 20.0000% 10 10 9.00%

$1,200,000.00 $240,000.00 $960,000.00 $192,000.00 $768,000.00 $153,600.00 $614,400.00 $122,880.00 $491,520.00 $98,304.00 $393,216.00 $78,643.20 $314,572.80 $62,914.56 $251,658.24 $50,331.65 $201,326.59 $40,265.32 $161,061.27 $32,212.25 $128,849.02 $0.00 $128,849.02 $1,071,150.98 $790,050.19

DDB-SL BASIS $1,200,000.00 RATE EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS MARR EOY

0 1 2 3 4 5 6 7 8 9 10 11

$240,000.00 $192,000.00 $153,600.00 $122,880.00 $98,304.00 $78,643.20 $78,643.20 $78,643.20 $78,643.20 $78,643.20 $0.00

$1,200,000.00 $960,000.00 $768,000.00 $614,400.00 $491,520.00 $393,216.00 $314,572.80 $235,929.60 $157,286.40 $78,643.20 $0.00 $0.00

SUM DEPR PW DEPR

$1,200,000.00 $850,146.09

SLN BASIS

$1,200,000.00

20.0000% 10 10 9.00%

A 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

B EST SALV RCVD SALV

C $0.00 $0.00

D USEFUL LIFE PERIODS MARR

EOY

0 1 2 3 4 5 6 7 8 9 10 11 SUM DEPR PW DEPR f

0 1 2 3 4 5 6 7 8 9 10 11 SUM DEPR PW DEPR g

$1,200,000.00 $120,000.00 $1,080,000.00 $120,000.00 $960,000.00 $120,000.00 $840,000.00 $120,000.00 $720,000.00 $120,000.00 $600,000.00 $120,000.00 $480,000.00 $120,000.00 $360,000.00 $120,000.00 $240,000.00 $120,000.00 $120,000.00 $120,000.00 $0.00 $0.00 $0.00 $1,200,000.00 $770,118.92

SLH BASIS $1,200,000.00 EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS MARR EOY

E 10 10 9.00%

10 11 9.00%

$1,200,000.00 $60,000.00 $1,140,000.00 $120,000.00 $1,020,000.00 $120,000.00 $900,000.00 $120,000.00 $780,000.00 $120,000.00 $660,000.00 $120,000.00 $540,000.00 $120,000.00 $420,000.00 $120,000.00 $300,000.00 $120,000.00 $180,000.00 $120,000.00 $60,000.00 $60,000.00 $0.00 $1,200,000.00 $738,325.02

SYD BASIS $1,200,000.00 SYD EST SALV $0.00 USEFUL LIFE RCVD SALV $0.00 PERIODS

55 10 10

A 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169

D MARR

EOY

EXC FUNC 0 1 2 3 4 5 6 7 8 9 10 11 SUM DEPR PW DEPR

EXC FUNC $1,200,000.00 $218,181.82 $981,818.18 $196,363.64 $785,454.55 $174,545.45 $610,909.09 $152,727.27 $458,181.82 $130,909.09 $327,272.73 $109,090.91 $218,181.82 $87,272.73 $130,909.09 $65,454.55 $65,454.55 $43,636.36 $21,818.18 $21,818.18 $0.00 $0.00 $0.00

$1,200,000.00 $868,446.62

E 9.00%

A 1 PROBLEM 9.46 2 3 4 a 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 b

EOY

USAGE (PARTS)

0 1 2 3 4

1,599.99 9,350.01 7,599.99 1,190.01

FULL TABLE BELOW BASIS EST SALV RCVD SALV

$16,000.00 $2,000.00 $2,000.00

USEFUL LIFE PERIODS

24,000.00 4

EOY

USAGE (PARTS)

0 1 2 3 4

$933.33 $5,454.17 $4,433.33 $694.17

SUM DEPR

$11,515.00

USAGE REMAINING (PARTS)

4260.0

$16,000.00 $15,066.67 $9,612.50 $5,179.17 $4,485.00

1,599.99 9,350.01 7,599.99 1,190.01

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

USAGE REMAINING (PARTS) 24,000.00 22,400.01 13,050.00 5,450.01 4,260.00

A B C D E 1 PROBLEM 9.47 2 3 CURRENT BV= $4,555.56 4 5 FULL TABLE BELOW 6 7 BASIS $20,000.00 8 EST SALV $0.00 USEFUL LIFE 18,000 9 RCVD SALV $0.00 PERIODS 4 10 dt Bt 11 EOY USAGE (HOURS) 12 13 0 $20,000.00 14 1 $2,777.78 $17,222.22 2,500 15 2 $5,000.00 $12,222.22 4,500 16 3 $3,333.33 $8,888.89 3,000 17 4 $4,333.33 $4,555.56 3,900 18 19 SUM DEPR $15,444.44

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

USAGE REMAINING (HOURS) 18,000 15,500 11,000 8,000 4,100

A B C D E 1 PROBLEM 9.48 2 3 RECALL THAT 6 MINUTES IS 0.1 HOUR 4 5 a BASIS= $380,000.00 6 7 b SALVAGE VALUE= $60,000.00 8 9 c USEFUL LIFE YRS= 4 10 11 d SEE TABLE BELOW FOR YEARLY DEPRECIATION 12 13 BASIS $380,000.00 14 EST SALV $60,000.00 USEFUL LIFE 24,000 15 RCVD SALV $60,000.00 PERIODS 4 16 dt Bt 17 EOY USAGE (HOURS) 18 19 0 $380,000.00 20 1 $32,000.00 $348,000.00 2,400 21 2 $64,000.00 $284,000.00 4,800 22 3 $96,000.00 $188,000.00 7,200 23 4 $128,000.00 $60,000.00 9,600 24 25 SUM DEPR $320,000.00

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 USAGE REMAINING 18 19 24,000 20 21,600 21 16,800 22 9,600 23 0 24 25

A 1 PROBLEM 9.49 2 3 a

d1=

$6,000.00

d2=

$4,500.00

d3=

$4,000.00

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 b

d4=

$2,500.00

BASIS EST SALV RCVD SALV

$20,000.00 $2,000.00 USEFUL LIFE $2,000.00 PERIODS

EOY

0 1 2 3 4

$6,000.00 $4,500.00 $4,000.00 $2,500.00

SUM DEPR

$17,000.00

ADDN INCOME EXPECTED=

$4,000.00

Bt $20,000.00 $14,000.00 $9,500.00 $5,500.00 $3,000.00

$72,000.00 4 USAGE ($ INCOME)

$24,000.00 $18,000.00 $16,000.00 $10,000.00

F 1 2 3 4 5 6 7 8 9 10 11 12 USAGE REMAINING 13 14 $72,000.00 15 $48,000.00 16 $30,000.00 17 $14,000.00 18 $4,000.00 19 20 21 22

A B C D E 1 PROBLEM 9.50 2 3 a COST DEPLETION = $200,000.00 =($1,200,000/1,800,000)*300,000 4 5 b PERCENTAGE DELPLETION = $148,500.00 =MIN($990,000*0.15; $165,000) 6 7 FULL TABLE BELOW 8 NOTE! DATA WERE GIVEN ONLY FOR YEAR 1. TO CONSTRUCT THE FOLLOWING TABLE, 9 UNITS SOLD WERE ASSUMED TO BE THE SAME FOR EACH OF THE OTHER YEARS. 10 11 ORIG BASIS $1,200,000.00 INCOME/UNIT $3.30 12 EST SALV $0.00 USEFUL LIFE 1,800,000 13 RCVD SALV $0.00 PERIODS 6 14 15 EOY UNITS SOLD GROSS INC OPERATING 16 COST 17 0 -$1,200,000.00 18 1 300,000 $990,000.00 $660,000.00 19 2 300,000 $990,000.00 $660,000.00 20 3 300,000 $990,000.00 $660,000.00 21 4 300,000 $990,000.00 $660,000.00 22 5 300,000 $990,000.00 $660,000.00 23 6 300,000 $990,000.00 $660,000.00

F G H I J K 1 2 1,800,000)*300,000 3 4 00*0.15; $165,000) 5 6 7 UCT THE FOLLOWING 8 TABLE, OF THE OTHER 9 YEARS. 10 11 FIXED COST $2.20 12 VAR COST $0.00 13 PERCENT DEPL 15.00% 14 15 TAXABLE INC 50% OF TI PERCENTAGE COST DEPLETION ADJ COST 16 BEFORE DEPL BEFORE DEPL DEPLETION (15%) DEPLETION USED BASIS 17 -$1,200,000.00 $1,200,000.00 18 $330,000.00 $165,000.00 $148,500.00 $200,000.00 $200,000.00 $1,000,000.00 19 $330,000.00 $165,000.00 $148,500.00 $200,000.00 $200,000.00 $800,000.00 20 $330,000.00 $165,000.00 $148,500.00 $200,000.00 $200,000.00 $600,000.00 21 $330,000.00 $165,000.00 $148,500.00 $200,000.00 $200,000.00 $400,000.00 22 $330,000.00 $165,000.00 $148,500.00 $200,000.00 $200,000.00 $200,000.00 23 $330,000.00 $165,000.00 $148,500.00 $200,000.00 $200,000.00 $0.00

L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 UNITS 16 REMAINING 17 1,800,000 18 1,500,000 19 1,200,000 20 900,000 21 600,000 22 300,000 23 0

A B C D E F 1 PROBLEM 9.51 2 3 ORIG BASIS $62,000,000.00 INCOME/UNIT $60.00 FIXED COST 4 EST SALV $0.00 USEFUL LIFE 6,000,000 VAR COST 5 RCVD SALV $0.00 PERIODS 3 PERCENT DEPL 6 7 EOY UNITS SOLD GROSS INC OPERATING TAXABLE INC 8 COST BEFORE DEPL 9 0 -$62,000,000.00 -$62,000,000.00 10 1 300,000 $18,000,000.00 $13,500,000.00 $4,500,000.00 11 2 600,000 $36,000,000.00 $27,000,000.00 $9,000,000.00 12 3 500,000 $30,000,000.00 $22,500,000.00 $7,500,000.00

G H I J K L 1 2 3 $45.00 4 $0.00 5 10.00% 6 7 50% OF TI PERCENTAGE COST DEPLETION ADJ COST UNITS 8 BEFORE DEPL DEPLETION (10%) DEPLETION USED BASIS REMAINING 9 $62,000,000.00 6,000,000 10 $2,250,000.00 $1,800,000.00 $3,100,000.00 $3,100,000.00 $58,900,000.00 5,700,000 11 $4,500,000.00 $3,600,000.00 $6,200,000.00 $6,200,000.00 $52,700,000.00 5,100,000 12 $3,750,000.00 $3,000,000.00 $5,166,666.67 $5,166,666.67 $47,533,333.33 4,600,000

A 1 PROBLEM 9.52 2 3 a 4 5 b 6 7 8 9 10 11 12 13 14 15

COST DEPLETION =

$255,555.56

PERCENTAGE DEPLETION =

$202,500.00

ORIG BASIS EST SALV RCVD SALV

$2,300,000.00 INCOME/OZ $0.00 USEFUL LIFE $0.00 PERIODS

EOY

UNITS SOLD

0 1

3,000

GROSS INC

$450.00 27,000 1 OPERATING COST

-$2,300,000.00 $1,350,000.00 $750,000.00

F G H I J K 1 2 3 4 5 6 7 8 FIXED COST $250.00 9 VAR COST $0.00 10 PERCENT DEPL 15.00% 11 12 TAXABLE INC 50% OF TI PERCENTAGE COST DEPLETION ADJ COST 13 BEFORE DEPL BEFORE DEPL DEPLETION (15%) DEPLETION USED BASIS 14 -$2,300,000.00 $2,300,000.00 15 $600,000.00 $300,000.00 $202,500.00 $255,555.56 $255,555.56 $2,044,444.44

L 1 2 3 4 5 6 7 8 9 10 11 12 UNITS 13 REMAINING 14 27,000 15 24,000

MODIFIED ACRS RATES - GDS MACRS CL ADR %

3-YR <=4 200%

5-YR 7-YR 10-YR 15-YR >4 to <10 >=10 to <16 .=16 to <20 >=20 to <25 200% 200% 200% 150%

20-YR >=25 150%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

33.33% 44.45% 14.81% 7.41%

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

5.00% 9.50% 8.55% 7.70% 6.93% 6.23% 5.90% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91% 2.95%

3.750% 7.219% 6.677% 6.177% 5.713% 5.285% 4.888% 4.522% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 2.231%

SUM

100.00% 100.00%

100.00%

100.000%

BASIS $1,400,000.00 EST SALV $200,000.00 RCVD SALV $200,000.00 EOY 0 1 2 3 4 5 6 7 8

BTCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

BTCF $400,000.00 TAX RATE MARRAT = USEFUL LIFE 8 PERIODS 8 DWO

$150,000.00 $250,000.00 $100,000.00 $150,000.00 $250,000.00 $100,000.00 $150,000.00 $250,000.00 $100,000.00 $150,000.00 $250,000.00 $100,000.00 $150,000.00 $250,000.00 $100,000.00 $150,000.00 $250,000.00 $100,000.00 $150,000.00 $250,000.00 $100,000.00 $150,000.00 $250,000.00 $100,000.00 MARRAT = SUM DEPR

ATCF -$1,400,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $500,000.00 10%

PW AT =

$293,779.34

BOOK VALUE

FW AT =

$629,742.10

$200,000.00

AW AT =

$55,067.18

IRRAT =

15.24%

ERRAT =

12.65%

$1,200,000.00

40.00% 10.00%

BASIS $1,400,000.00 EST SALV $200,000.00 RCVD SALV $200,000.00 EOY 0 1 2 3 4 5 6 7 8

BTCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

BTCF $400,000.00 TAX RATE MARRAT = USEFUL LIFE 8 PERIODS 8 DWO

$280,000.00 $120,000.00 $48,000.00 $448,000.00 -$48,000.00 -$19,200.00 $268,800.00 $131,200.00 $52,480.00 $161,280.00 $238,720.00 $95,488.00 $161,280.00 $238,720.00 $95,488.00 $80,640.00 $319,360.00 $127,744.00 $0.00 $400,000.00 $160,000.00 $0.00 $600,000.00 $240,000.00 MARRAT = SUM DEPR

ATCF -$1,400,000.00 $352,000.00 $419,200.00 $347,520.00 $304,512.00 $304,512.00 $272,256.00 $240,000.00 $360,000.00 10%

$1,400,000.00

PW AT =

$369,389.01

BOOK VALUE

FW AT =

$791,818.14

$0.00

40.00% 10.00%

AW AT =

$69,239.76

IRRAT =

17.34%

ERRAT =

13.27%

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

BASIS

$1,400,000.00

BTCF

$400,000.00 TAX RATE MARRAT = USEFUL LIFE 8

EST SALV

$200,000.00

RCVD SALV

$200,000.00

PERIODS

EOY

BTCF

DWO

-$1,400,000.00

$400,000.00

$350,000.00

$50,000.00

$20,000.00

$380,000.00

$400,000.00

$262,500.00 $137,500.00

$55,000.00

$345,000.00

$400,000.00

$196,875.00 $203,125.00

$81,250.00

$318,750.00

$400,000.00

$147,656.25 $252,343.75 $100,937.50

$299,062.50

$400,000.00

$110,742.19 $289,257.81 $115,703.13

$284,296.88

$400,000.00

$83,056.64 $316,943.36 $126,777.34

$273,222.66

$400,000.00

$49,169.92 $350,830.08 $140,332.03

$259,667.97

$600,000.00

$0.00 $400,000.00 $160,000.00 MARRAT =

$440,000.00

$1,200,000.00

PW AT =

$343,590.85

BOOK VALUE

FW AT =

$736,517.50

$200,000.00

AW AT =

$64,404.05

IRRAT =

16.61%

ERRAT =

13.06%

40.00% 10.00%

ATCF -$1,400,000.00

SUM DEPR

10%

COST

$400,000.00

BTCF

$85,000.00

BONUS@END

$30,000.00

PERIODS

EOY 0 1 2 3 4 5 6 7 8

TAX RATE MARRAT =

BTCF TI T ATCF -$400,000.00 -$400,000.00 -$160,000.00 -$240,000.00 $85,000.00 $85,000.00 $34,000.00 $51,000.00 $85,000.00 $85,000.00 $34,000.00 $51,000.00 $85,000.00 $85,000.00 $34,000.00 $51,000.00 $85,000.00 $85,000.00 $34,000.00 $51,000.00 $85,000.00 $85,000.00 $34,000.00 $51,000.00 $85,000.00 $85,000.00 $34,000.00 $51,000.00 $85,000.00 $85,000.00 $34,000.00 $51,000.00 $115,000.00 $115,000.00 $46,000.00 $69,000.00 MARRAT = 10% PW AT = $40,478.37 FW AT =

$86,768.98

AW AT =

$7,587.43

IRRAT =

14.35%

ERRAT =

12.16%

40.00% 10.00%

COST/BEG OF YR

$4,000.00

BONUS@END

$0.00

EOY 0 1 2 3 4 5

BTCF

$15,000.00 TAX RATE 40.00% MARRAT = 9.00% PERIODS 5

BTCF TI T -$4,000.00 -$4,000.00 -$1,600.00 $11,000.00 $11,000.00 $4,400.00 $11,000.00 $11,000.00 $4,400.00 $11,000.00 $11,000.00 $4,400.00 $11,000.00 $11,000.00 $4,400.00 $15,000.00 $15,000.00 $6,000.00 MARRAT =

ATCF -$2,400.00 $6,600.00 $6,600.00 $6,600.00 $6,600.00 $9,000.00 9%

PW AT = $24,831.53 FW AT = $38,206.39 AW AT =

$6,384.00

IRRAT =

275.00%

ERRAT =

77.17%

BASIS $500,000.00 LOAN PRINC $300,000.00 BTCF $124,166.67 EST SALV $50,000.00 LOAN PERIOD 10 USEFUL LIFE 10 RCVD SALV $50,000.00 LOAN INT 12.00% PERIODS 10 EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

PPMT -$300,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $300,000.00

IPMT $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00

DWO

$100,000.00 -$11,833.33 $160,000.00 -$71,833.33 $96,000.00 -$7,833.33 $57,600.00 $30,566.67 $57,600.00 $30,566.67 $28,800.00 $59,366.67 $0.00 $88,166.67 $0.00 $88,166.67 $0.00 $88,166.67 $0.00 $138,166.67 SUM DEPR $500,000.00 BOOK VALUE $0.00

TAX RATE MARRAT METHOD

40.00% 10.00% 1

ATCF ATCF+ ATCFATCF MACRS(5) -$200,000.00 $0.00 $200,000.00 -$200,000.00 -$4,733.33 $92,900.00 $92,900.00 $0.00 $0.00 20.00% -$28,733.33 $116,900.00 $116,900.00 $0.00 $0.00 32.00% -$3,133.33 $91,300.00 $91,300.00 $0.00 $0.00 19.20% $12,226.67 $75,940.00 $75,940.00 $0.00 $0.00 11.52% $12,226.67 $75,940.00 $75,940.00 $0.00 $0.00 11.52% $23,746.67 $64,420.00 $64,420.00 $0.00 $0.00 5.76% $35,266.67 $52,900.00 $52,900.00 $0.00 $0.00 $35,266.67 $52,900.00 $52,900.00 $0.00 $0.00 $35,266.67 $52,900.00 $52,900.00 $0.00 $0.00 $55,266.67 -$217,100.00 $0.00 $217,100.00 $974,217.47 MARRAT = 10% PW AT = $175,603.01 FW AT = $455,468.98 AW AT = $28,578.58 IRRAT =

41.54%

ERRAT =

17.16%

BASIS $500,000.00 LOAN PRINC $300,000.00 BTCF $124,166.67 EST SALV $50,000.00 LOAN PERIOD 10 USEFUL LIFE 10 RCVD SALV $50,000.00 LOAN INT 12.00% PERIODS 10 EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

PPMT -$300,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00

IPMT $36,000.00 $32,400.00 $28,800.00 $25,200.00 $21,600.00 $18,000.00 $14,400.00 $10,800.00 $7,200.00 $3,600.00

DWO

$100,000.00 -$11,833.33 $160,000.00 -$68,233.33 $96,000.00 -$633.33 $57,600.00 $41,366.67 $57,600.00 $44,966.67 $28,800.00 $77,366.67 $0.00 $109,766.67 $0.00 $113,366.67 $0.00 $116,966.67 $0.00 $170,566.67 SUM DEPR $500,000.00 BOOK VALUE $0.00

TAX RATE MARRAT METHOD

40.00% 10.00% 2

ATCF ATCF+ ATCFATCF MACRS(5) -$200,000.00 $0.00 $200,000.00 -$200,000.00 -$4,733.33 $62,900.00 $62,900.00 $0.00 $0.00 20.00% -$27,293.33 $89,060.00 $89,060.00 $0.00 $0.00 32.00% -$253.33 $65,620.00 $65,620.00 $0.00 $0.00 19.20% $16,546.67 $52,420.00 $52,420.00 $0.00 $0.00 11.52% $17,986.67 $54,580.00 $54,580.00 $0.00 $0.00 11.52% $30,946.67 $45,220.00 $45,220.00 $0.00 $0.00 5.76% $43,906.67 $35,860.00 $35,860.00 $0.00 $0.00 $45,346.67 $38,020.00 $38,020.00 $0.00 $0.00 $46,786.67 $40,180.00 $40,180.00 $0.00 $0.00 $68,226.67 $72,340.00 $72,340.00 $0.00 $924,343.10 MARRAT = 10% PW AT = $156,374.28 FW AT = $405,594.61 AW AT = $25,449.19 IRRAT =

28.51%

ERRAT =

16.54%

BASIS $500,000.00 LOAN PRINC $300,000.00 BTCF $124,166.67 EST SALV $50,000.00 LOAN PERIOD 10 USEFUL LIFE 10 RCVD SALV $50,000.00 LOAN INT 12.00% PERIODS 10 EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

PPMT -$300,000.00 $17,095.25 $19,146.68 $21,444.28 $24,017.59 $26,899.71 $30,127.67 $33,742.99 $37,792.15 $42,327.21 $47,406.47

IPMT $36,000.00 $33,948.57 $31,650.97 $29,077.65 $26,195.54 $22,967.58 $19,352.26 $15,303.10 $10,768.04 $5,688.78

DWO

$100,000.00 -$11,833.33 $160,000.00 -$69,781.90 $96,000.00 -$3,484.30 $57,600.00 $37,489.02 $57,600.00 $40,371.13 $28,800.00 $72,399.09 $0.00 $104,814.41 $0.00 $108,863.57 $0.00 $113,398.63 $0.00 $168,477.89 SUM DEPR $500,000.00 BOOK VALUE $0.00

TAX RATE MARRAT METHOD

40.00% 10.00% 3

ATCF ATCF+ ATCFATCF MACRS(5) -$200,000.00 $0.00 $200,000.00 -$200,000.00 -$4,733.33 $75,804.75 $75,804.75 $0.00 $0.00 20.00% -$27,912.76 $98,984.18 $98,984.18 $0.00 $0.00 32.00% -$1,393.72 $72,465.14 $72,465.14 $0.00 $0.00 19.20% $14,995.61 $56,075.81 $56,075.81 $0.00 $0.00 11.52% $16,148.45 $54,922.97 $54,922.97 $0.00 $0.00 11.52% $28,959.64 $42,111.78 $42,111.78 $0.00 $0.00 5.76% $41,925.76 $29,145.66 $29,145.66 $0.00 $0.00 $43,545.43 $27,525.99 $27,525.99 $0.00 $0.00 $45,359.45 $25,711.97 $25,711.97 $0.00 $0.00 $67,391.16 $53,680.26 $53,680.26 $0.00 $935,653.41 MARRAT = 10% PW AT = $160,734.89 FW AT = $416,904.92 AW AT = $26,158.86 IRRAT =

31.65%

ERRAT =

16.68%

BASIS $500,000.00 LOAN PRINC $300,000.00 BTCF $124,166.67 EST SALV $50,000.00 LOAN PERIOD 10 USEFUL LIFE 10 RCVD SALV $50,000.00 LOAN INT 12.00% PERIODS 10 EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

PPMT IPMT -$300,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $300,000.00 $631,754.46

DWO

$100,000.00 $24,166.67 $160,000.00 -$35,833.33 $96,000.00 $28,166.67 $57,600.00 $66,566.67 $57,600.00 $66,566.67 $28,800.00 $95,366.67 $0.00 $124,166.67 $0.00 $124,166.67 $0.00 $124,166.67 $0.00 -$457,587.79 SUM DEPR $500,000.00 BOOK VALUE $0.00

TAX RATE MARRAT METHOD

40.00% 10.00% 4

ATCF ATCF+ ATCFATCF MACRS(5) -$200,000.00 $0.00 $200,000.00 -$200,000.00 $9,666.67 $114,500.00 $114,500.00 $0.00 $0.00 20.00% -$14,333.33 $138,500.00 $138,500.00 $0.00 $0.00 32.00% $11,266.67 $112,900.00 $112,900.00 $0.00 $0.00 19.20% $26,626.67 $97,540.00 $97,540.00 $0.00 $0.00 11.52% $26,626.67 $97,540.00 $97,540.00 $0.00 $0.00 11.52% $38,146.67 $86,020.00 $86,020.00 $0.00 $0.00 5.76% $49,666.67 $74,500.00 $74,500.00 $0.00 $0.00 $49,666.67 $74,500.00 $74,500.00 $0.00 $0.00 $49,666.67 $74,500.00 $74,500.00 $0.00 $0.00 -$183,035.12 -$574,552.68 $0.00 $574,552.68 $939,413.16 MARRAT = 10% PW AT = $162,184.44 FW AT = $420,664.67 AW AT = $26,394.77 IRRAT =

53.49%

ERRAT =

16.73%

PROBLEM 10.1 a

LOAN INTEREST PAID INCOME TAX

PROBLEM 10.2 1 2 3

PERFORM AFTER-TAX ANALYSES, NOT BEFORE-TAX ANALYSES, EXCEPT IN UNUSUAL SITUATIONS

IN GENERAL, THE FASTER AN INVESTMENT IS DEPRECIATED OR AMORTIZED, THE GREATER ITS AFTER-TAX PRES

IF INVESTMENT CAPITAL CAN BE BORROWED AT RATES LESS THAN THE MINIMUM ATTRACTIVE RATE OF RETURN ONE MINUS THE INCOME TAX RATE, IT IS ECONOMIC TO DO SO

R ITS AFTER-TAX PRESENT WORTH

TIVE RATE OF RETURN DIVIDED BY

PROBLEM 10.3

AD VALOREM TAX (PROPERTY) SALES TAX EXCISE TAX (A TAX ON THE MANUFACTURE, SALE, OR CONSUMPTION OF A COMMODITY) INCOME TAX INCOME TAXES TEND TO HAVE THE MOST SIGNIFICANT EFFECT

PROBLEM 10.4 a b c d e

GROSS INCOME - A COMPANY'S INCOME BEFORE TAKING DEDUCTIONS OR TAXES INTO ACCOUNT. EXPENSES - DECREASES IN ECONOMIC BENEFITS DURING THE ACCOUNTING PERIOD DEPRECIATION - METHOD OF ATTRIBUTING COST OF ASSET ACROSS ITS USEFUL LIFE INTEREST - THE "RENT" PAID TO BORROW MONEY PROPERTY DISPOSITION - THE OFFERING OR SELLING OF PROPERTY FOR TENDER

PROBLEM 10.5 a

TI $15,000.00

TAX $2,250.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$15,000.00 EFFECTIVE MARGINAL

$2,250.00 15.00% 15.00%

TI $50,000.00 $25,000.00 $13,000.00

TAX $7,500.00 $6,250.00 $4,420.00 $0.00 $0.00 $0.00 $0.00 $0.00

$88,000.00 EFFECTIVE MARGINAL

$18,170.00 20.65% 34.00%

TI $50,000.00 $25,000.00 $25,000.00 $80,000.00

TAX $7,500.00 $6,250.00 $8,500.00 $31,200.00 $0.00 $0.00 $0.00 $0.00

$180,000.00 EFFECTIVE MARGINAL

$53,450.00 29.69% 39.00%

TI $50,000.00 $25,000.00 $25,000.00 $235,000.00 $65,000.00

TAX $7,500.00 $6,250.00 $8,500.00 $91,650.00 $22,100.00 $0.00 $0.00

TOTALS

$0.00 $400,000.00 EFFECTIVE MARGINAL e

$136,000.00 34.00% 34.00%

TOTALS

TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $9,665,000.00 $3,286,100.00 $5,000,000.00 $1,750,000.00 $1,700,000.00 $646,000.00 $0.00 $16,700,000.00 $5,796,000.00 TOTALS EFFECTIVE 34.71% MARGINAL 38.00%

PROBLEM 10.6 a

TI $12,000.00

TAX $1,800.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$12,000.00 EFFECTIVE MARGINAL

$1,800.00 15.00% 15.00%

TI $50,000.00 $15,000.00

TAX $7,500.00 $3,750.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$65,000.00 EFFECTIVE MARGINAL

$11,250.00 17.31% 25.00%

TI $50,000.00 $25,000.00 $25,000.00 $120,000.00

TAX $7,500.00 $6,250.00 $8,500.00 $46,800.00 $0.00 $0.00 $0.00 $0.00

$220,000.00 EFFECTIVE MARGINAL

$69,050.00 31.39% 39.00%

TI $50,000.00 $25,000.00 $25,000.00 $235,000.00 $665,000.00

TAX $7,500.00 $6,250.00 $8,500.00 $91,650.00 $226,100.00 $0.00 $0.00

TOTALS

$0.00 $1,000,000.00 EFFECTIVE MARGINAL e

$340,000.00 34.00% 34.00%

TOTALS

TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $9,665,000.00 $3,286,100.00 $5,000,000.00 $1,750,000.00 $3,333,333.00 $1,266,666.54 $966,667.00 $338,333.45 $19,300,000.00 $6,754,999.99 TOTALS EFFECTIVE 35.00% MARGINAL 35.00%

PROBLEM 10.7 a

TI $22,000.00

TAX $3,300.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$22,000.00 EFFECTIVE MARGINAL

$3,300.00 15.00% 15.00%

TI $50,000.00 $25,000.00 $18,000.00

TAX $7,500.00 $6,250.00 $6,120.00 $0.00 $0.00 $0.00 $0.00 $0.00

$93,000.00 EFFECTIVE MARGINAL

$19,870.00 21.37% 34.00%

TI $50,000.00 $25,000.00 $25,000.00 $125,000.00

TAX $7,500.00 $6,250.00 $8,500.00 $48,750.00 $0.00 $0.00 $0.00 $0.00

$225,000.00 EFFECTIVE MARGINAL

$71,000.00 31.56% 39.00%

TI $50,000.00 $25,000.00 $25,000.00 $235,000.00 $3,065,000.00

TAX $7,500.00 $6,250.00 $8,500.00 $91,650.00 $1,042,100.00 $0.00 $0.00

TOTALS

$0.00

$3,400,000.00 EFFECTIVE MARGINAL

$1,156,000.00 TOTALS 34.00% 34.00%

TI $50,000.00 $25,000.00 $25,000.00 $235,000.00 $9,665,000.00 $5,000,000.00 $3,333,333.00 $18,221,667.00

TAX $7,500.00 $6,250.00 $8,500.00 $91,650.00 $3,286,100.00 $1,750,000.00 $1,266,666.54 $6,377,583.45

$36,555,000.00 $12,794,249.99 TOTALS EFFECTIVE 35.00% MARGINAL 35.00%

PROBLEM 10.8 a

TI=

$100,001.00

TI=

$335,000.000

TI $50,000.00 $25,000.00 $25,000.00 $235,000.000

TAX $7,500.00 $6,250.00 $8,500.00 $91,650.00 $0.00 $0.00 $0.00 $0.00

$335,000.000

$113,900.00 34.0000000% TOTALS

TI=

$18,333,333.33

TI $50,000.00 $25,000.00 $25,000.00 $235,000.00 $9,665,000.00 $5,000,000.00 $3,333,333.33

TAX $7,500.00 $6,250.00 $8,500.00 $91,650.00 $3,286,100.00 $1,750,000.00 $1,266,666.67 $0.00

$18,333,333.33

$6,416,666.67 35.0000000% TOTALS

PROBLEM 10.9 a

$50,001.00

TI=

$83,928.580

TI $50,000.00 $25,000.00 $8,928.58

TAX $7,500.00 $6,250.00 $3,035.72 $0.00 $0.00 $0.00 $0.00 $0.00

$83,928.580

$16,785.72 20.0000014% TOTALS

TI=

$119,642.86

TI $50,000.00 $25,000.00 $25,000.00 $19,642.86

TAX $7,500.00 $6,250.00 $8,500.00 $7,660.72 $0.00 $0.00 $0.00 $0.00

$119,642.86

$29,910.72 25.0000003% TOTALS

PROBLEM 10.10 LAST YR TI TAX $41,000.00 $6,150.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

THIS YR TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $116,000.00 $45,240.00 $0.00 $0.00 $0.00 $0.00

$41,000.00 $6,150.00 TOTALS

$216,000.00 $67,490.00 TOTALS

15.00%

31.25%

35.05%

39.00%

LAST $ IS TAXED AT 39%

PROBLEM 10.11 LAST YR TI TAX $30,000.00 $4,500.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

THIS YR TI $50,000.00 $20,000.00 $0.00 $0.00

$30,000.00 $4,500.00 TOTALS

$70,000.00 $12,500.00 TOTALS

15.00%

17.86%

20.00%

25.00%

LAST $ IS TAXED AT 25%

TAX $7,500.00 $5,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

PROBLEM 10.12 BASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $9,665,000.00 $3,286,100.00 $5,000,000.00 $1,750,000.00 $3,333,333.00 $1,266,666.54 $866,667.00 $303,333.45 $19,200,000.00 $6,719,999.99 TOTALS a

35.00%

WITH INCREASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $9,665,000.00 $3,286,100.00 $5,000,000.00 $1,750,000.00 $3,333,333.00 $1,266,666.54 $7,366,667.00 $2,578,333.45 $25,700,000.00 $8,994,999.99

TOTALS

PROBLEM 10.13 BASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $385,000.00 $130,900.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

TAX RATE 15% 25% 34% 39% 34% 35% 38% 35%

$720,000.00 $244,800.00 TOTALS a

34.00%

WITH INCREASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $525,000.00 $178,500.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

TAX RATE 15% 25% 34% 39% 34% 35% 38% 35%

$860,000.00 $292,400.00 TOTALS

PROBLEM 10.14

SINCE THE INCREMENTAL TAX RATE IS 34.4%, 60% OF THE $5,000,000 INCREASE WAS IN THE 34% BASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $225,000.00 $87,750.00 $7,000,000.00 $2,380,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $7,325,000.00 $2,490,000.00 TOTALS a

$7,325,000.00

$4,210,000.00

WITH INCREASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $225,000.00 $87,750.00 $10,000,000.00 $3,400,000.00 $2,000,000.00 $700,000.00 $0.00 $0.00 $0.00 $0.00 $12,325,000.00 $4,210,000.00

00 INCREASE WAS IN THE 34% BRACKET; 40% IN THE 35% BRACKET

TOTALS

PROBLEM 10.15 SINCE THE INCREMENTAL TAX RATE IS 36.5%, 50% OF THE $150,000 INCREASE WAS IN THE 39% BASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $150,000.00 $58,500.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

TAX RATE 15% 25% 34% 39% 34% 35% 38% 35%

$250,000.00 $80,750.00 TOTALS a

$250,000.00

$135,500.00

WITH INCREASE TI $50,000.00 $25,000.00 $25,000.00 $225,000.00 $75,000.00 $0.00 $0.00 $0.00

TAX $7,500.00 $6,250.00 $8,500.00 $87,750.00 $25,500.00 $0.00 $0.00 $0.00

TAX RATE 15% 25% 34% 39% 34% 35% 38% 35%

$400,000.00 $135,500.00 TOTALS

CREASE WAS IN THE 39% BRACKET; 50% IN THE 34% BRACKET

PROBLEM 10.16 SINCE THE INCREMENTAL TAX RATE IS 31.75%, 25% OF THE $20,000 INCREASE WAS IN THE 25% BASE TI $50,000.00 $20,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

TAX $7,500.00 $5,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$70,000.00 $12,500.00 TOTALS a

$70,000.00

$18,850.00

WITH INCREASE TI $50,000.00 $25,000.00 $15,000.00 $0.00 $0.00 $0.00 $0.00 $0.00

TAX $7,500.00 $6,250.00 $5,100.00 $0.00 $0.00 $0.00 $0.00 $0.00

$90,000.00 $18,850.00 TOTALS

INCREASE WAS IN THE 25% BRACKET; 75% IN THE 34% BRACKET

PROBLEM 10.17

SINCE THE INCREMENTAL TAX RATE IS 34.33%, 33.33% OF THE $3,000,000 DECREASE WAS IN TH BASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $9,665,000.00 $3,286,100.00 $1,000,000.00 $350,000.00 $0.00 $0.00 $0.00 $0.00 $11,000,000.00 $3,750,000.00 TOTALS a

$11,000,000.00

$2,720,000.00

WITH DECREASE TI TAX $50,000.00 $7,500.00 $25,000.00 $6,250.00 $25,000.00 $8,500.00 $235,000.00 $91,650.00 $7,665,000.00 $2,606,100.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $8,000,000.00 $2,720,000.00

000 DECREASE WAS IN THE 35% BRACKET; 66.67% IN THE 34% BRACKET

TOTALS

PROBLEM 10.18 BASIS $1,400,000.00 EST SALV $200,000.00 RCVD SALV $200,000.00 a

SLN EOY 0 1 2 3 4 5 6 7 8

BTCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

BTCF USE LIFE PERIODS

DWO

$400,000.00 TAX RATE MARRAT = 8 8

ATCF -$1,400,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $300,000.00 $500,000.00 10%

$1,200,000.00

PW AT =

$293,779.34

BOOK VALUE

FW AT =

$629,742.10

$200,000.00

MACRS(5) EOY 0 1 2 3 4 5 6 7 8

BTCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

DDB EOY BTCF 0 -$1,400,000.00 1 $400,000.00 2 $400,000.00

DWO

40.00% 10.00%

AW AT =

$55,067.18

IRRAT =

15.24%

ERRAT =

12.65%

ATCF -$1,400,000.00 $352,000.00 $419,200.00 $347,520.00 $304,512.00 $304,512.00 $272,256.00 $240,000.00 $360,000.00 10% $369,389.01

BOOK VALUE

FW AT =

$791,818.14

$0.00

AW AT =

$69,239.76

IRRAT =

17.34%

ERRAT =

13.27%

DWO

$350,000.00 $50,000.00 $262,500.00 $137,500.00

ATCF -$1,400,000.00 $20,000.00 $380,000.00 $55,000.00 $345,000.00

3 4 5 6 7 8

$400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

$196,875.00 $203,125.00 $81,250.00 $147,656.25 $252,343.75 $100,937.50 $110,742.19 $289,257.81 $115,703.13 $83,056.64 $316,943.36 $126,777.34 $49,169.92 $350,830.08 $140,332.03 $0.00 $400,000.00 $160,000.00 MARRAT = SUM DEPR

$318,750.00 $299,062.50 $284,296.88 $273,222.66 $259,667.97 $440,000.00 10%

$1,200,000.00

PW AT =

$343,590.85

BOOK VALUE

FW AT =

$736,517.50

$200,000.00

AW AT =

$64,404.05

IRRAT =

16.61%

ERRAT =

13.06%

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

PROBLEM 10.19 BASIS $3,000,000.00 EST SALV $250,000.00 RCVD SALV $550,000.00 a

SLN EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF -$3,000,000.00 $500,000.00 $512,000.00 $524,288.00 $536,870.91 $549,755.81 $562,949.95 $576,460.75 $590,295.81 $604,462.91 $1,168,970.02

BTCF USE LIFE PERIODS

$500,000.00 30 10

TAX RATE MARRAT =

DWO

$91,666.67 $408,333.33 $163,333.33 $91,666.67 $420,333.33 $168,133.33 $91,666.67 $432,621.33 $173,048.53 $91,666.67 $445,204.25 $178,081.70 $91,666.67 $458,089.15 $183,235.66 $91,666.67 $471,283.29 $188,513.31 $91,666.67 $484,794.09 $193,917.63 $91,666.67 $498,629.14 $199,451.66 $91,666.67 $512,796.24 $205,118.50 $91,666.67 -$1,006,029.98 -$402,411.99 MARRAT = SUM DEPR PW AT = $916,666.67 BOOK VALUE

FW AT =

$2,083,333.33

AW AT = IRRAT = ERRAT =

MACRS(20) EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF -$3,000,000.00 $500,000.00 $512,000.00 $524,288.00 $536,870.91 $549,755.81 $562,949.95 $576,460.75 $590,295.81 $604,462.91 $1,168,970.02

DWO

$112,500.00 $216,570.00 $200,310.00 $185,310.00 $171,390.00 $158,550.00 $146,640.00 $135,660.00 $133,860.00 $66,915.00 SUM DEPR

$387,500.00 $155,000.00 $295,430.00 $118,172.00 $323,978.00 $129,591.20 $351,560.91 $140,624.36 $378,365.81 $151,346.33 $404,399.95 $161,759.98 $429,820.75 $171,928.30 $454,635.81 $181,854.32 $470,602.91 $188,241.16 -$370,239.98 -$148,095.99 MARRAT =

$1,527,705.00

PW AT =

BOOK VALUE

FW AT =

$1,472,295.00

AW AT = IRRAT = ERRAT =

DDB EOY 0

BTCF -$3,000,000.00

DWO

1 2 3 4 5 6 7 8 9 10

$500,000.00 $512,000.00 $524,288.00 $536,870.91 $549,755.81 $562,949.95 $576,460.75 $590,295.81 $604,462.91 $1,168,970.02

$200,000.00 $186,666.67 $174,222.22 $162,607.41 $151,766.91 $141,649.12 $132,205.84 $123,392.12 $115,165.98 $107,488.25 SUM DEPR

$300,000.00 $120,000.00 $325,333.33 $130,133.33 $350,065.78 $140,026.31 $374,263.50 $149,705.40 $397,988.90 $159,195.56 $421,300.83 $168,520.33 $444,254.91 $177,701.96 $466,903.69 $186,761.48 $489,296.93 $195,718.77 -$443,353.70 -$177,341.48 MARRAT =

$1,495,164.52

PW AT =

BOOK VALUE

FW AT =

$1,504,835.48

AW AT = IRRAT = ERRAT =

40.00% 9.00%

ATCF -$3,000,000.00 $336,666.67 $343,866.67 $351,239.47 $358,789.21 $366,520.15 $374,436.64 $382,543.12 $390,844.15 $399,344.41 $1,571,382.01 9% -$161,778.19 -$382,987.81 -$25,208.29 7.98% 8.40%

ATCF MACRS(20) -$3,000,000.00 $345,000.00 3.750% $393,828.00 7.219% $394,696.80 6.677% $396,246.55 6.177% $398,409.49 5.713% $401,189.97 5.285% $404,532.45 4.888% $408,441.49 4.522% $416,221.75 4.462% $1,317,066.01 2.231% 9% -$94,105.31 -$222,781.49 -$14,663.50 8.38% 8.65%

ATCF -$3,000,000.00

$380,000.00 $381,866.67 $384,261.69 $387,165.51 $390,560.25 $394,429.62 $398,758.79 $403,534.33 $408,744.14 $1,346,311.50 9% -$92,396.74 -$218,736.69 -$14,397.27 8.39% 8.66%

PROBLEM 10.20 BASIS $1,350,000.00 EST SALV $0.00 RCVD SALV $900,000.00 a

SLN EOY 0 1 2 3 4

BTCF -$1,350,000.00 $300,000.00 $300,000.00 $300,000.00 $1,200,000.00

BTCF USE LIFE PERIODS

DWO

$300,000.00 TAX RATE MARRAT = 12 4

$75,000.00 $75,000.00 $75,000.00 $75,000.00 MARRAT =

ATCF -$1,350,000.00 $225,000.00 $225,000.00 $225,000.00 $1,125,000.00 9%

PW AT =

$16,519.66

BOOK VALUE

FW AT =

$23,318.85

$900,000.00

AW AT =

$5,099.10

IRRAT =

9.42%

ERRAT =

9.33%

$112,500.00 $187,500.00 $112,500.00 $187,500.00 $112,500.00 $187,500.00 $112,500.00 $187,500.00 SUM DEPR $450,000.00

MACRS(7) EOY 0 1 2 3 4

DDB EOY 0 1 2 3 4

BTCF -$1,350,000.00 $300,000.00 $300,000.00 $300,000.00 $1,200,000.00

DWO

40.00% 9.00%

$192,915.00 $107,085.00 $42,834.00 $330,615.00 -$30,615.00 -$12,246.00 $236,115.00 $63,885.00 $25,554.00 $84,307.50 $609,645.00 $243,858.00 MARRAT = SUM DEPR PW AT = $843,952.50

ATCF -$1,350,000.00 $257,166.00 $312,246.00 $274,446.00 $956,142.00 9% $38,021.09

BOOK VALUE

FW AT =

$53,669.87

$506,047.50

AW AT =

$11,735.92

IRRAT =

10.03%

ERRAT =

9.76%

DWO

$225,000.00 $75,000.00 $30,000.00 $187,500.00 $112,500.00 $45,000.00 $156,250.00 $143,750.00 $57,500.00 $130,208.33 $418,750.00 $167,500.00 MARRAT = SUM DEPR

ATCF -$1,350,000.00 $270,000.00 $255,000.00 $242,500.00 $1,032,500.00 9%

PW AT =

$31,038.34

BOOK VALUE

FW AT =

$43,813.16

$651,041.67

AW AT =

$9,580.56

IRRAT =

9.83%

ERRAT =

9.62%

$698,958.33

MACRS(7) 14.29% 24.49% 17.49% 6.245%

PROBLEM 10.21 BASIS $400,000.00 EST SALV $30,000.00 RCVD SALV $30,000.00 a

SLN EOY 0 1 2 3 4 5 6 7 8

BTCF -$400,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $125,000.00

BTCF USE LIFE PERIODS

$95,000.00 8 8

TAX RATE MARRAT =

DWO

$46,250.00 $46,250.00 $46,250.00 $46,250.00 $46,250.00 $46,250.00 $46,250.00 $46,250.00 SUM DEPR

$48,750.00 $48,750.00 $48,750.00 $48,750.00 $48,750.00 $48,750.00 $48,750.00 $48,750.00

$370,000.00 BOOK VALUE $30,000.00

MACRS(5) EOY 0 1 2 3 4 5 6 7 8

BTCF -$400,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00 $125,000.00

DWO

$0.00

DDB EOY 0 1 2 3 4

BTCF -$400,000.00 $95,000.00 $95,000.00 $95,000.00 $95,000.00

ATCF -$400,000.00 $19,500.00 $75,500.00 $19,500.00 $75,500.00 $19,500.00 $75,500.00 $19,500.00 $75,500.00 $19,500.00 $75,500.00 $19,500.00 $75,500.00 $19,500.00 $75,500.00 $19,500.00 $105,500.00 MARRAT = 12% PW AT = -$12,826.70 FW AT =

-$31,758.44

AW AT =

-$2,582.05

IRRAT =

11.11%

ERRAT =

11.54%

ATCF -$400,000.00 $80,000.00 $15,000.00 $6,000.00 $89,000.00 $128,000.00 -$33,000.00 -$13,200.00 $108,200.00 $76,800.00 $18,200.00 $7,280.00 $87,720.00 $46,080.00 $48,920.00 $19,568.00 $75,432.00 $46,080.00 $48,920.00 $19,568.00 $75,432.00 $23,040.00 $71,960.00 $28,784.00 $66,216.00 $0.00 $95,000.00 $38,000.00 $57,000.00 $0.00 $125,000.00 $50,000.00 $75,000.00 MARRAT = SUM DEPR 12% PW AT = $400,000.00 $8,520.80 BOOK VALUE

40.00% 12.00%

DWO

$100,000.00 $75,000.00 $56,250.00 $42,187.50

-$5,000.00 $20,000.00 $38,750.00 $52,812.50

FW AT =

$21,097.19

AW AT =

$1,715.26

IRRAT =

12.66%

ERRAT =

12.30%

ATCF -$400,000.00 -$2,000.00 $97,000.00 $8,000.00 $87,000.00 $15,500.00 $79,500.00 $21,125.00 $73,875.00

5 6 7 8

$95,000.00 $95,000.00 $95,000.00 $125,000.00

$31,640.63 $23,730.47 $17,797.85 $13,348.39 SUM DEPR

$63,359.38 $71,269.53 $77,202.15 $71,606.45

$25,343.75 $28,507.81 $30,880.86 $28,642.58 MARRAT =

$69,656.25 $66,492.19 $64,119.14 $96,357.42 12%

$359,954.83

PW AT =

$631.67

BOOK VALUE

FW AT =

$1,563.98

$40,045.17

AW AT =

$127.16

IRRAT =

12.05%

ERRAT =

12.02%

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

PROBLEM 10.22 a

COST

$400,000.00

BTCF

$95,000.00

BONUS@END

$30,000.00

PERIODS

EOY 0 1 2 3 4 5 6 7 8

TAX RATE MARRAT =

40.00% 12.00%

BTCF TI T ATCF -$400,000.00 -$400,000.00 -$160,000.00 -$240,000.00 $95,000.00 $95,000.00 $38,000.00 $57,000.00 $95,000.00 $95,000.00 $38,000.00 $57,000.00 $95,000.00 $95,000.00 $38,000.00 $57,000.00 $95,000.00 $95,000.00 $38,000.00 $57,000.00 $95,000.00 $95,000.00 $38,000.00 $57,000.00 $95,000.00 $95,000.00 $38,000.00 $57,000.00 $95,000.00 $95,000.00 $38,000.00 $57,000.00 $125,000.00 $125,000.00 $50,000.00 $75,000.00 MARRAT = 12% PW AT = $50,425.36 FW AT = $124,851.35 AW AT = $10,150.77

IRRAT =

17.63%

ERRAT =

14.70%

PW HERE IS $50,425.36 VERSUS ONLY $8,520.80 WHERE MACRS-GDS(5) IS USED. EXPENSING THE ENTIRE INVESTMENT IN YEAR 0 IS FAR MORE ATTRACTIVE THAN DEPRECIATING IT OVER YEARS 1-6.

GDS(5) IS USED.

PROBLEM 10.23 BASIS $90,000.00 EST SALV $4,000.00 RCVD SALV $6,000.00

SLN EOY 0 1 2 3 4

BTCF -$90,000.00 $37,000.00 $37,000.00 $37,000.00 $43,000.00

BTCF USE LIFE PERIODS

DWO

$37,000.00 TAX RATE MARRAT = 6 4

$14,333.33 $22,666.67 $14,333.33 $22,666.67 $14,333.33 $22,666.67 $14,333.33 -$4,000.00 SUM DEPR $57,333.33 $32,666.67

MACRS(3) EOY 0 1 2 3 4

BTCF -$90,000.00 $37,000.00 $37,000.00 $37,000.00 $43,000.00

DWO

BTCF -$90,000.00 $37,000.00 $37,000.00 $37,000.00 $43,000.00

AW AT =

$3,132.14

IRRAT =

14.63%

ERRAT =

12.92%

DWO

$30,000.00 $7,000.00 $20,000.00 $17,000.00 $13,333.33 $23,666.67 $8,888.89 $16,333.33 SUM DEPR $72,222.22 BOOK VALUE $17,777.78

FW AT = $18,726.38 AW AT = $4,034.99

$0.00

DDB EOY 0 1 2 3 4

ATCF -$90,000.00 $9,066.67 $27,933.33 $9,066.67 $27,933.33 $9,066.67 $27,933.33 -$1,600.00 $44,600.00 MARRAT = 10% PW AT = $9,928.47

ATCF -$90,000.00 $29,997.00 $7,003.00 $2,801.20 $34,198.80 $40,005.00 -$3,005.00 -$1,202.00 $38,202.00 $13,329.00 $23,671.00 $9,468.40 $27,531.60 $6,669.00 $36,331.00 $14,532.40 $28,467.60 MARRAT = SUM DEPR 10% PW = $90,000.00 $12,790.37 AT BOOK VALUE

FW AT = $14,536.27

BOOK VALUE

40.00% 10.00%

IRRAT =

16.72%

ERRAT =

13.72%

ATCF -$90,000.00 $2,800.00 $34,200.00 $6,800.00 $30,200.00 $9,466.67 $27,533.33 $6,533.33 $36,466.67 MARRAT = 10% PW AT = $11,643.01 FW AT = $17,046.53 AW AT = $3,673.03 IRRAT =

15.84%

ERRAT =

13.40%

MACRS(3) 33.33% 44.45% 14.81% 7.41%

PROBLEM 10.24 COST BONUS@END a

EOY 0 1 2 3 4

$90,000.00

BTCF

$6,000.00 PERIODS

$37,000.00 TAX RATE 40.00% MARRAT = 10.00% 4

BTCF TI T ATCF -$90,000.00 -$90,000.00 -$36,000.00 -$54,000.00 $37,000.00 $37,000.00 $14,800.00 $22,200.00 $37,000.00 $37,000.00 $14,800.00 $22,200.00 $37,000.00 $37,000.00 $14,800.00 $22,200.00 $43,000.00 $43,000.00 $17,200.00 $25,800.00 MARRAT = 10% PW AT = $18,829.86 FW AT = $27,568.80 AW AT = $5,940.27

IRRAT =

24.90%

ERRAT =

18.54%

BOTH INVESTMENTS ARE DESIRABLE. THE METRICS FOR THE 100-DAY SHORT-TERM PROJECT ARE SUBSTANTIALLY BETTER, DUE TO THE EXPENSING OF THE PROJECT VS. DEPRECIATION OF THE TRACTOR OVER 4 YEARS.

PROBLEM 10.25 BASIS $190,000.00 EST SALV $5,000.00 RCVD SALV $5,000.00 a

SLN EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

BTCF -$190,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $50,000.00

BTCF USE LIFE PERIODS

DWO

$45,000.00 TAX RATE MARRAT = 12 12

ATCF -$190,000.00 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $33,166.67 $15,416.67 $29,583.33 $11,833.33 $38,166.67 MARRAT = SUM DEPR 10% PW = $185,000.00 $37,580.60 AT $5,000.00

MACRS(7) EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

BTCF -$190,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $50,000.00

DWO

FW AT = $117,944.02

BOOK VALUE

40.00% 10.00%

$5,515.45

IRRAT =

13.85%

ERRAT =

11.67%

ATCF -$190,000.00 $27,151.00 $17,849.00 $7,139.60 $37,860.40 $46,531.00 -$1,531.00 -$612.40 $45,612.40 $33,231.00 $11,769.00 $4,707.60 $40,292.40 $23,731.00 $21,269.00 $8,507.60 $36,492.40 $16,967.00 $28,033.00 $11,213.20 $33,786.80 $16,948.00 $28,052.00 $11,220.80 $33,779.20 $16,967.00 $28,033.00 $11,213.20 $33,786.80 $8,474.00 $36,526.00 $14,610.40 $30,389.60 $0.00 $45,000.00 $18,000.00 $27,000.00 $0.00 $45,000.00 $18,000.00 $27,000.00 $0.00 $45,000.00 $18,000.00 $27,000.00 $0.00 $50,000.00 $20,000.00 $30,000.00 MARRAT = SUM DEPR 10% PW AT = $49,755.75 $190,000.00 BOOK VALUE $0.00

AW AT =

FW AT = $156,154.86 AW AT =

$7,302.32

IRRAT =

15.61%

ERRAT =

12.15%

DDB EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

BTCF -$190,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $50,000.00

DWO

ATCF -$190,000.00 $31,666.67 $13,333.33 $5,333.33 $39,666.67 $26,388.89 $18,611.11 $7,444.44 $37,555.56 $21,990.74 $23,009.26 $9,203.70 $35,796.30 $18,325.62 $26,674.38 $10,669.75 $34,330.25 $15,271.35 $29,728.65 $11,891.46 $33,108.54 $12,726.12 $32,273.88 $12,909.55 $32,090.45 $10,605.10 $34,394.90 $13,757.96 $31,242.04 $8,837.59 $36,162.41 $14,464.97 $30,535.03 $7,364.65 $37,635.35 $15,054.14 $29,945.86 $6,137.21 $38,862.79 $15,545.12 $29,454.88 $5,114.34 $39,885.66 $15,954.26 $29,045.74 $4,261.95 $24,428.28 $9,771.31 $40,228.69 MARR = SUM DEPR 10% AT PW AT = $43,444.06 $168,690.24 BOOK VALUE $21,309.76

FW AT = $136,346.08 AW AT =

$6,375.99

IRRAT =

14.70%

ERRAT =

11.90%

MACRS(7) 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

PROBLEM 10.26

COST

$190,000.00

BTCF

$45,000.00

BONUS@END

$5,000.00

PERIODS

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 MARRBT =

TAX RATE MARRAT =

PW BT =

BTCF TI T ATCF -$190,000.00 -$190,000.00 -$76,000.00 -$114,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $45,000.00 $45,000.00 $18,000.00 $27,000.00 $50,000.00 $50,000.00 $20,000.00 $30,000.00 MARRAT = 16.667% 10% PW = $38,324.16 $70,925.57 AT

FW BT =

$131,536.69

AW BT =

$9,013.51

IRRBT =

21.44%

IRRAT =

21.44%

ERRBT =

18.47%

ERRAT =

14.53%

FW AT = $152,035.26 AW AT = $13,294.57

BOTH INVESTMENTS ARE DESIRABLE. THE METRICS FOR THE DESIGN PORTFOLIO ARE SUBSTANTIALLY BETTER, DUE TO THE EXPENSING OF THE PORTFOLIO VS. DEPRECIATION OF THE ROUTER OVER 8 YEARS.

40.00% 10.00%

PROBLEM 10.27 PORTABLE CONCRETE TEST INSTRUMENT BASIS $22,000.00 BTCF -$9,500.00 TAX RATE MARRAT = EST SALV $2,000.00 USE LIFE 6 RCVD SALV $2,000.00 PERIODS 6 MACRS(5) EOY 0 1 2 3 4 5 6

BTCF -$22,000.00 -$9,500.00 -$9,500.00 -$9,500.00 -$9,500.00 -$9,500.00 -$7,500.00

DWO

ATCF -$22,000.00 $4,400.00 -$13,900.00 -$5,560.00 -$3,940.00 $7,040.00 -$16,540.00 -$6,616.00 -$2,884.00 $4,224.00 -$13,724.00 -$5,489.60 -$4,010.40 $2,534.40 -$12,034.40 -$4,813.76 -$4,686.24 $2,534.40 -$12,034.40 -$4,813.76 -$4,686.24 $1,267.20 -$8,767.20 -$3,506.88 -$3,993.12 MARRAT = SUM DEPR 12% PW AT = -$38,331.82 $22,000.00 BOOK VALUE $0.00

40.00% 12.00%

FW AT = -$75,660.21 AW AT =

-$9,323.28

THE MORE AUTOMATED INSTRUMENT COSTING $29,000 IS MARGINALLY MORE DESIRABLE IN TE

AUTOMATED CONCRETE TEST INSTRUMENT BASIS $29,000.00 BTCF -$7,500.00 TAX RATE MARRAT = EST SALV $3,000.00 USE LIFE 6 RCVD SALV $3,000.00 PERIODS 6

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

MACRS(5) EOY 0 1 2 3 4 5 6

BTCF -$29,000.00 -$7,500.00 -$7,500.00 -$7,500.00 -$7,500.00 -$7,500.00 -$4,500.00

GINALLY MORE DESIRABLE IN TERMS OF AW.

DWO

ATCF -$29,000.00 $5,800.00 -$13,300.00 -$5,320.00 -$2,180.00 $9,280.00 -$16,780.00 -$6,712.00 -$788.00 $5,568.00 -$13,068.00 -$5,227.20 -$2,272.80 $3,340.80 -$10,840.80 -$4,336.32 -$3,163.68 $3,340.80 -$10,840.80 -$4,336.32 -$3,163.68 $1,670.40 -$6,170.40 -$2,468.16 -$2,031.84 MARRAT = SUM DEPR 12% PW AT = -$38,027.48 $29,000.00 BOOK VALUE $0.00

40.00% 12.00%

FW AT = -$75,059.50 AW AT =

-$9,249.26

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

PROBLEM 10.28

BASIS EST SALV RCVD SALV

$58,500.00 $0.00 $0.00

BTCF USE LIFE PERIODS

MACRS(5) EOY 0 1 2 3 4 5 6 7 8 9

BTCF -$58,500.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00

DWO

-$150,000.00 TAX RATE MARRAT = 9 9

$11,700.00 -$161,700.00 -$64,680.00 $18,720.00 -$168,720.00 -$67,488.00 $11,232.00 -$161,232.00 -$64,492.80 $6,739.20 -$156,739.20 -$62,695.68 $6,739.20 -$156,739.20 -$62,695.68 $3,369.60 -$153,369.60 -$61,347.84 $0.00 -$150,000.00 -$60,000.00 $0.00 -$150,000.00 -$60,000.00 $0.00 -$150,000.00 -$60,000.00 MARRAT = SUM DEPR PW AT = $58,500.00

40.00% 10.00%

ATCF -$58,500.00 -$85,320.00 -$82,512.00 -$85,507.20 -$87,304.32 -$87,304.32 -$88,652.16 -$90,000.00 -$90,000.00 -$90,000.00 10% -$558,717.85

FW AT = -$1,317,427.46 AW AT = -$97,016.07

BOOK VALUE $0.00

SELECT THE VIRTUAL MOLD APPARATUS COSTING $87,500. b

SLN EOY 0 1 2 3 4 5 6 7 8 9

BTCF -$58,500.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00

DWO

$6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 $6,500.00 -$156,500.00 -$62,600.00 MARRAT = SUM DEPR

ATCF -$58,500.00 -$87,400.00 -$87,400.00 -$87,400.00 -$87,400.00 -$87,400.00 -$87,400.00 -$87,400.00 -$87,400.00 -$87,400.00 10%

PW AT =

-$561,838.68

$58,500.00 BOOK VALUE $0.00

FW AT = -$1,324,786.22 AW AT =

SELECT THE VIRTUAL MOLD APPARATUS COSTING $87,500.

-$97,557.97

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

BASIS EST SALV RCVD SALV

$87,500.00 $0.00 $0.00

BTCF USE LIFE PERIODS

EOY 0 1 2 3 4 5 6 7 8 9

BTCF -$87,500.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00

DWO

EOY 0 1 2 3 4 5 6 7 8 9

BTCF -$87,500.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00

-$125,000.00 TAX RATE MARRAT = 9 9

$17,500.00 -$142,500.00 -$57,000.00 $28,000.00 -$153,000.00 -$61,200.00 $16,800.00 -$141,800.00 -$56,720.00 $10,080.00 -$135,080.00 -$54,032.00 $10,080.00 -$135,080.00 -$54,032.00 $5,040.00 -$130,040.00 -$52,016.00 $0.00 -$125,000.00 -$50,000.00 $0.00 -$125,000.00 -$50,000.00 $0.00 -$125,000.00 -$50,000.00 MARRAT = SUM DEPR PW AT = $87,500.00 BOOK VALUE

FW AT =

$0.00

AW AT =

DWO

$9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 $9,722.22 -$134,722.22 -$53,888.89 MARRAT = SUM DEPR $87,500.00

PW AT =

BOOK VALUE

FW AT =

$0.00

AW AT =

40.00% 10.00%

ATCF MACRS(5) -$87,500.00 -$68,000.00 20.00% -$63,800.00 32.00% -$68,280.00 19.20% -$70,968.00 11.52% -$70,968.00 11.52% -$72,984.00 5.76% -$75,000.00 -$75,000.00 -$75,000.00 10% -$492,362.67 -$1,160,965.42 -$85,494.12

ATCF -$87,500.00 -$71,111.11 -$71,111.11 -$71,111.11 -$71,111.11 -$71,111.11 -$71,111.11 -$71,111.11 -$71,111.11 -$71,111.11 10% -$497,030.58 -$1,171,972.11 -$86,304.66

PROBLEM 10.29 a

BASIS $70,000.00 EST SALV $3,000.00 RCVD SALV $3,000.00 MACRS(10) EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

BTCF -$70,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$15,000.00

BTCF USE LIFE PERIODS

-$18,000.00 TAX RATE MARRAT = 16 16

DWO

$7,000.00 -$25,000.00 -$10,000.00 $12,600.00 -$30,600.00 -$12,240.00 $10,080.00 -$28,080.00 -$11,232.00 $8,064.00 -$26,064.00 -$10,425.60 $6,454.00 -$24,454.00 -$9,781.60 $5,159.00 -$23,159.00 -$9,263.60 $4,585.00 -$22,585.00 -$9,034.00 $4,585.00 -$22,585.00 -$9,034.00 $4,592.00 -$22,592.00 -$9,036.80 $4,585.00 -$22,585.00 -$9,034.00 $2,296.00 -$20,296.00 -$8,118.40 $0.00 -$18,000.00 -$7,200.00 $0.00 -$18,000.00 -$7,200.00 $0.00 -$18,000.00 -$7,200.00 $0.00 -$18,000.00 -$7,200.00 $0.00 -$15,000.00 -$6,000.00 MARRAT = SUM DEPR

40.00% 9.00%

ATCF -$70,000.00 -$8,000.00 -$5,760.00 -$6,768.00 -$7,574.40 -$8,218.40 -$8,736.40 -$8,966.00 -$8,966.00 -$8,963.20 -$8,966.00 -$9,881.60 -$10,800.00 -$10,800.00 -$10,800.00 -$10,800.00 -$9,000.00 9%

PW AT = -$140,304.52

$70,000.00

FW AT = -$557,051.86

BOOK VALUE

AW AT =

$0.00

-$16,878.62

SELECT THE CONVEYOR COSTING $70,000.

IN THIS PROBLEM, WE ARE SEEKING THE COST OF THE SECOND CONVEYOR THAT MAKES THE TWO ALTERNATIVES EQUIVALENT IN TERMS OF PW, FW, OR AW. DUE TO THE COMPLEXITY OF THE ANALYSIS, IT IS MUCH EASIER TO USE A SEARCH PROCEDURE TO FIND THIS COST. USING EXCEL, THE LOGICAL CHOICES FOR SEARCH ARE EITHER "SOLVER" OR "GOAL SEEK." BELOW, "GOAL SEEK" IS USED AND THE CRITERION IS TO TARGET THE VALUE OF "AW" TO EQUAL THAT O THE FIRST ALTERNATIVE. THE "CHANGED CELL" IS THE BASIS (OR COST). BASIS $97,599.56 GOAL SEEK CHANGED CELL EST SALV $4,000.00 RCVD SALV $4,000.00 MACRS(10) EOY 0 1 2 3

BTCF -$97,599.56 -$14,000.00 -$14,000.00 -$14,000.00

DWO

BTCF USE LIFE PERIODS

$9,759.96 -$23,759.96 -$9,503.98 $17,567.92 -$31,567.92 -$12,627.17 $14,054.34 -$28,054.34 -$11,221.73

ATCF -$97,599.56 -$4,496.02 -$1,372.83 -$2,778.27

4 5 6 7 8 9 10 11 12 13 14 15 16

-$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$10,000.00

$11,243.47 -$25,243.47 -$10,097.39 $8,998.68 -$22,998.68 -$9,199.47 $7,193.09 -$21,193.09 -$8,477.23 $6,392.77 -$20,392.77 -$8,157.11 $6,392.77 -$20,392.77 -$8,157.11 $6,402.53 -$20,402.53 -$8,161.01 $6,392.77 -$20,392.77 -$8,157.11 $3,201.27 -$17,201.27 -$6,880.51 $0.00 -$14,000.00 -$5,600.00 $0.00 -$14,000.00 -$5,600.00 $0.00 -$14,000.00 -$5,600.00 $0.00 -$14,000.00 -$5,600.00 $0.00 -$10,000.00 -$4,000.00 MARRAT = SUM DEPR

-$3,902.61 -$4,800.53 -$5,522.77 -$5,842.89 -$5,842.89 -$5,838.99 -$5,842.89 -$7,119.49 -$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$6,000.00 9%

$97,599.56

PW AT = -$140,304.51

BOOK VALUE

FW AT = -$557,051.83

$0.00

AW AT =

-$16,878.62

THE COST OF THE MORE EXPENSIVE CONVEYOR MUST BE $97,599.56 FOR THE TWO TO BE EQU

BASIS $110,000.00 EST SALV $4,000.00 RCVD SALV $4,000.00

MACRS(10) 10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

MACRS(10) EOY BTCF 0 -$110,000.00 1 -$14,000.00 2 -$14,000.00 3 -$14,000.00 4 -$14,000.00 5 -$14,000.00 6 -$14,000.00 7 -$14,000.00 8 -$14,000.00 9 -$14,000.00 10 -$14,000.00 11 -$14,000.00 12 -$14,000.00 13 -$14,000.00 14 -$14,000.00 15 -$14,000.00 16 -$10,000.00

BTCF USE LIFE PERIODS

DWO

$0.00

-$14,000.00 TAX RATE MARRAT = 16 16

MACRS(10) 10.00% 18.00% 14.40%

40.00% 9.00%

ATCF -$110,000.00 $11,000.00 -$25,000.00 -$10,000.00 -$4,000.00 $19,800.00 -$33,800.00 -$13,520.00 -$480.00 $15,840.00 -$29,840.00 -$11,936.00 -$2,064.00 $12,672.00 -$26,672.00 -$10,668.80 -$3,331.20 $10,142.00 -$24,142.00 -$9,656.80 -$4,343.20 $8,107.00 -$22,107.00 -$8,842.80 -$5,157.20 $7,205.00 -$21,205.00 -$8,482.00 -$5,518.00 $7,205.00 -$21,205.00 -$8,482.00 -$5,518.00 $7,216.00 -$21,216.00 -$8,486.40 -$5,513.60 $7,205.00 -$21,205.00 -$8,482.00 -$5,518.00 $3,608.00 -$17,608.00 -$7,043.20 -$6,956.80 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$10,000.00 -$4,000.00 -$6,000.00 MARRAT = SUM DEPR 9% PW AT = -$149,335.98 $110,000.00 BOOK VALUE

CONVEYOR THAT MAKES THE DUE TO THE COMPLEXITY OF E TO FIND THIS COST. USING R" OR "GOAL SEEK." BELOW, LUE OF "AW" TO EQUAL THAT OF R COST).

-$14,000.00 TAX RATE MARRAT = 16 16

FW AT = -$592,909.50 AW AT =

-$17,965.10

11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

GOAL SEEK SET CELL

9.56 FOR THE TWO TO BE EQUIVALENT.

MACRS(10) 10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

PROBLEM 10.30 BASIS $22,000.00 EST SALV $2,000.00 RCVD SALV $2,000.00 MACRS(3) EOY 0 1 2 3 4 5 6

BTCF -$22,000.00 -$9,500.00 -$9,500.00 -$9,500.00 -$9,500.00 -$9,500.00 -$7,500.00

BTCF USE LIFE PERIODS

DWO

-$9,500.00 TAX RATE MARRAT = 6 6

ATCF -$22,000.00 $7,332.60 -$16,832.60 -$6,733.04 -$2,766.96 $9,779.00 -$19,279.00 -$7,711.60 -$1,788.40 $3,258.20 -$12,758.20 -$5,103.28 -$4,396.72 $1,630.20 -$11,130.20 -$4,452.08 -$5,047.92 $0.00 -$9,500.00 -$3,800.00 -$5,700.00 $0.00 -$7,500.00 -$3,000.00 -$4,500.00 MARRAT = SUM DEPR 12% PW AT = -$37,747.92 $22,000.00 BOOK VALUE $0.00

40.00% 12.00%

FW AT = -$74,507.70 AW AT =

-$9,181.26

THE REGULAR INSTRUMENT COSTING $22,000 IS MARGINALLY MORE DESIRABLE IN TERMS OF A

BASIS $29,000.00 EST SALV $3,000.00 RCVD SALV $3,000.00

MACRS(3) 33.33% 44.45% 14.81% 7.41%

MACRS(5) EOY 0 1 2 3 4 5 6

MORE DESIRABLE IN TERMS OF AW.

BTCF -$29,000.00 -$7,500.00 -$7,500.00 -$7,500.00 -$7,500.00 -$7,500.00 -$4,500.00

BTCF USE LIFE PERIODS

DWO

-$7,500.00 TAX RATE MARRAT = 6 6

40.00% 12.00%

FW AT = -$75,059.50 AW AT =

-$9,249.26

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

PROBLEM 10.31 a

BASIS EST SALV RCVD SALV

$58,500.00 $0.00 $0.00

BTCF USE LIFE PERIODS

MACRS(3) EOY 0 1 2 3 4 5 6 7 8 9

BTCF -$58,500.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$150,000.00

DWO

-$150,000.00 TAX RATE MARRAT = 9 9

$19,498.05 -$169,498.05 -$67,799.22 $26,003.25 -$176,003.25 -$70,401.30 $8,663.85 -$158,663.85 -$63,465.54 $4,334.85 -$154,334.85 -$61,733.94 $0.00 -$150,000.00 -$60,000.00 $0.00 -$150,000.00 -$60,000.00 $0.00 -$150,000.00 -$60,000.00 $0.00 -$150,000.00 -$60,000.00 $0.00 -$150,000.00 -$60,000.00 MARRAT = SUM DEPR PW AT = $58,500.00

40.00% 10.00%

ATCF -$58,500.00 -$82,200.78 -$79,598.70 -$86,534.46 -$88,266.06 -$90,000.00 -$90,000.00 -$90,000.00 -$90,000.00 -$90,000.00 10% -$557,337.81

FW AT = -$1,314,173.41 AW AT = -$96,776.44

BOOK VALUE $0.00

SELECT THE VIRTUAL MOLD APPARATUS COSTING $87,500. b

BASIS EST SALV RCVD SALV

$87,500.00 $0.00 $0.00

BTCF USE LIFE PERIODS

MACRS(7) EOY 0 1 2 3 4 5 6 7 8 9

BTCF -$87,500.00 -$143,279.07 -$143,279.07 -$143,279.07 -$143,279.07 -$143,279.07 -$143,279.07 -$143,279.07 -$143,279.07 -$143,279.07

DWO

-$143,279.07 GOAL SEEK CHANGED CELL 9 9

$12,503.75 -$155,782.82 -$62,313.13 $21,428.75 -$164,707.82 -$65,883.13 $15,303.75 -$158,582.82 -$63,433.13 $10,928.75 -$154,207.82 -$61,683.13 $7,813.75 -$151,092.82 -$60,437.13 $7,805.00 -$151,084.07 -$60,433.63 $7,813.75 -$151,092.82 -$60,437.13 $3,902.50 -$147,181.57 -$58,872.63 $0.00 -$143,279.07 -$57,311.63 MARRAT = SUM DEPR

ATCF -$87,500.00 -$80,965.94 -$77,395.94 -$79,845.94 -$81,595.94 -$82,841.94 -$82,845.44 -$82,841.94 -$84,406.44 -$85,967.44 10%

PW AT =

-$557,337.82

$87,500.00 BOOK VALUE $0.00

FW AT = -$1,314,173.43 AW AT =

-$96,776.44

THE COST OF OPERATING MUST BE $143,279.07/YEAR FOR THE TWO ALTERNATIVES TO BE EQU

MACRS(3) 33.33% 44.45% 14.81% 7.41%

ANGED CELL

BASIS EST SALV RCVD SALV

$87,500.00 $0.00 $0.00

BTCF USE LIFE PERIODS

MACRS(7) EOY 0 1 2 3 4 5 6 7 8 9

BTCF -$87,500.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00 -$125,000.00

DWO

TAX RATE MARRAT =

MACRS(7) 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

GOAL SEEK SET CELL

ALTERNATIVES TO BE EQUIVALENT.

40.00% 10.00%

-$125,000.00 TAX RATE MARRAT = 9 9

$12,503.75 -$137,503.75 -$55,001.50 $21,428.75 -$146,428.75 -$58,571.50 $15,303.75 -$140,303.75 -$56,121.50 $10,928.75 -$135,928.75 -$54,371.50 $7,813.75 -$132,813.75 -$53,125.50 $7,805.00 -$132,805.00 -$53,122.00 $7,813.75 -$132,813.75 -$53,125.50 $3,902.50 -$128,902.50 -$51,561.00 $0.00 -$125,000.00 -$50,000.00 MARRAT = SUM DEPR PW AT = $87,500.00 BOOK VALUE

FW AT =

$0.00

AW AT =

40.00% 10.00%

ATCF MACRS(7) -$87,500.00 -$69,998.50 14.29% -$66,428.50 24.49% -$68,878.50 17.49% -$70,628.50 12.49% -$71,874.50 8.93% -$71,878.00 8.92% -$71,874.50 8.93% -$73,439.00 4.46% -$75,000.00 10% -$494,176.05 -$1,165,241.27 -$85,809.00

PROBLEM 10.32 a

BASIS EST SALV RCVD SALV

$70,000.00 $3,000.00 $3,000.00

BTCF USE LIFE PERIODS

MACRS(10) EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

DWO

-$18,000.00 TAX RATE MARRAT = 16 16

40.00% 9.00%

ATCF -$70,000.00 -$8,000.00 -$5,760.00 -$6,768.00 -$7,574.40 -$8,218.40 -$8,736.40 -$8,966.00 -$8,966.00 -$8,963.20 -$8,966.00 -$9,881.60 -$10,800.00 -$10,800.00 -$10,800.00 -$10,800.00 -$9,000.00 9%

PW AT = -$140,304.52

$70,000.00

FW AT = -$557,051.86

BOOK VALUE

AW AT =

$0.00

-$16,878.62

SELECT THE INVESTMENT COSTING $70,000. b

BASIS $104,039.51 GOAL SEEK CHANGED CELL EST SALV $4,000.00 RCVD SALV $4,000.00 MACRS(5) EOY 0 1 2 3 4 5 6 7 8 9 10 11

BTCF -$104,039.51 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00

DWO

BTCF USE LIFE PERIODS

ATCF -$104,039.51 $20,807.90 -$34,807.90 -$13,923.16 -$76.84 $33,292.64 -$47,292.64 -$18,917.06 $4,917.06 $19,975.59 -$33,975.59 -$13,590.23 -$409.77 $11,985.35 -$25,985.35 -$10,394.14 -$3,605.86 $11,985.35 -$25,985.35 -$10,394.14 -$3,605.86 $5,992.68 -$19,992.68 -$7,997.07 -$6,002.93 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00

12 13 14 15 16

-$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$10,000.00

$0.00 -$14,000.00 $0.00 -$14,000.00 $0.00 -$14,000.00 $0.00 -$14,000.00 $0.00 -$10,000.00 SUM DEPR

-$5,600.00 -$5,600.00 -$5,600.00 -$5,600.00 -$4,000.00 MARRAT =

-$8,400.00 -$8,400.00 -$8,400.00 -$8,400.00 -$6,000.00 9%

$104,039.51

PW AT = -$140,304.51

BOOK VALUE

FW AT = -$557,051.83

$0.00

AW AT =

-$16,878.62

THE COST OF THE MORE EXPENSIVE CONVEYOR MUST BE $104,039.51 FOR THE TWO TO BE EQU

BASIS $110,000.00 EST SALV $4,000.00 RCVD SALV $4,000.00

MACRS(10) 10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

MACRS(5) EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

BTCF -$110,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$14,000.00 -$10,000.00

BTCF USE LIFE PERIODS

DWO

$0.00

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

40.00% 9.00%

ATCF -$110,000.00 $22,000.00 -$36,000.00 -$14,400.00 $400.00 $35,200.00 -$49,200.00 -$19,680.00 $5,680.00 $21,120.00 -$35,120.00 -$14,048.00 $48.00 $12,672.00 -$26,672.00 -$10,668.80 -$3,331.20 $12,672.00 -$26,672.00 -$10,668.80 -$3,331.20 $6,336.00 -$20,336.00 -$8,134.40 -$5,865.60 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$14,000.00 -$5,600.00 -$8,400.00 $0.00 -$10,000.00 -$4,000.00 -$6,000.00 MARRAT = SUM DEPR 9% PW AT = -$144,376.93 $110,000.00 BOOK VALUE

-$14,000.00 TAX RATE MARRAT = 16 16

FW AT = -$573,220.57 AW AT =

-$17,368.53

GOAL SEEK SET CELL

9.51 FOR THE TWO TO BE EQUIVALENT.

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

PROBLEM 10.33 a

PURCHASE BASIS EST SALV RCVD SALV EOY 0 1 2 3 4 5

MACRS(7) $21,000.00 $5,000.00 $5,000.00 BTCF -$21,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $20,000.00

BTCF USE LIFE PERIODS DWO

$15,000.00 TAX RATE MARRAT = 12 5 TI

$3,000.90 $11,999.10 $5,142.90 $9,857.10 $3,672.90 $11,327.10 $2,622.90 $12,377.10 $937.65 $13,439.60 SUM DEPR $15,377.25 $5,622.75

CONTINUE WITH CURRENT EQUIPMENT COST $0.00 BTCF

$5,000.00

BONUS@END

$0.00

PERIODS

EOY 0 1 2 3 4 5

BTCF $0.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00

T $0.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00 MARRAT =

$0.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00 $5,000.00

ATCF -$21,000.00 $4,799.64 $10,200.36 $3,942.84 $11,057.16 $4,530.84 $10,469.16 $4,950.84 $10,049.16 $5,375.84 $14,624.16 MARRAT = 9% PW AT = $22,372.61 FW AT = $34,423.03

BOOK VALUE

40.00% 9.00%

AW AT =

$5,751.83

IRRAT =

42.91%

ERRAT =

26.02%

TAX RATE MARRAT =

40.00% 9.00%

ATCF $0.00 $3,000.00 $3,000.00 $3,000.00 $3,000.00 $3,000.00 9%

PW AT = $11,668.95 FW AT = $17,954.13 AW AT = c

LEASE (PREFERRED) COST/BEG OF YR $4,000.00 BONUS@END

$0.00

EOY 0 1 2 3 4

BTCF -$4,000.00 $11,000.00 $11,000.00 $11,000.00 $11,000.00

BTCF PERIODS

$3,000.00

$15,000.00 TAX RATE MARRAT = 5

TI T -$4,000.00 -$1,600.00 $11,000.00 $4,400.00 $11,000.00 $4,400.00 $11,000.00 $4,400.00 $11,000.00 $4,400.00

ATCF -$2,400.00 $6,600.00 $6,600.00 $6,600.00 $6,600.00

40.00% 9.00%

$15,000.00

$6,000.00 MARRAT =

$9,000.00 9%

PW AT = $24,831.53 FW AT = $38,206.39

AW AT =

$6,384.00

IRRAT =

275.00%

ERRAT =

77.17%

ANNUAL LEASE COST OF $4,966.62 COST/BEG OF YR $4,966.62 GOAL SEEK CHANGED CELL BONUS@END

$0.00

EOY 0 1 2 3 4 5

BTCF -$4,966.62 $10,033.38 $10,033.38 $10,033.38 $10,033.38 $15,000.00

BTCF PERIODS

TI T -$4,966.62 -$1,986.65 $10,033.38 $4,013.35 $10,033.38 $4,013.35 $10,033.38 $4,013.35 $10,033.38 $4,013.35 $15,000.00 $6,000.00 MARRAT =

ATCF -$2,979.97 $6,020.03 $6,020.03 $6,020.03 $6,020.03 $9,000.00 9%

PW AT = $22,372.61 FW AT = $34,423.04 AW AT =

$5,751.83 GOAL SEEK SET CELL

IRRAT =

202.02%

ERRAT =

67.26%

MACRS(7) 14.29% 24.49% 17.49% 12.49% 4.465%

$15,000.00 TAX RATE MARRAT = 5

GOAL SEEK SET CELL

40.00% 9.00%

PROBLEM 10.34 a

BUY BUILDING BASIS EST SALV RCVD SALV

MACRS(39) $240,000.00 $0.00 $120,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF -$240,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$130,000.00 -$10,000.00

BTCF USE LIFE PERIODS

-$130,000.00 39 10

TAX RATE MARRAT =

DWO

$5,906.40 -$135,906.40 $6,153.60 -$136,153.60 $6,153.60 -$136,153.60 $6,153.60 -$136,153.60 $6,153.60 -$136,153.60 $6,153.60 -$136,153.60 $6,153.60 -$136,153.60 $6,153.60 -$136,153.60 $6,153.60 -$136,153.60 $5,897.20 -$194,864.80 SUM DEPR

-$54,362.56 -$54,461.44 -$54,461.44 -$54,461.44 -$54,461.44 -$54,461.44 -$54,461.44 -$54,461.44 -$54,461.44 -$77,945.92 MARRAT =

$61,032.40

PW AT =

BOOK VALUE

FW AT =

$178,967.60

AW AT =

LEASE COST/BEG OF YR

$15,000.00

BTCF

-$134,000.00

BONUS@END

$0.00

PERIODS

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF -$15,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$134,000.00

TI -$15,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$149,000.00 -$134,000.00

T -$6,000.00 -$59,600.00 -$59,600.00 -$59,600.00 -$59,600.00 -$59,600.00 -$59,600.00 -$59,600.00 -$59,600.00 -$59,600.00 -$53,600.00 MARRAT =

ATCF -$9,000.00 -$89,400.00 -$89,400.00 -$89,400.00 -$89,400.00 -$89,400.00 -$89,400.00 -$89,400.00 -$89,400.00 -$89,400.00 -$80,400.00 12%

PW AT =

-$511,232.18

TAX RATE MARRAT =

FW AT = -$1,587,809.55 AW AT = c

CONTRACT OUT COST

-$45,000.00

BTCF

-$170,000.00

-$90,480.00

TAX RATE MARRAT =

BONUS@END

$0.00

PERIODS

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF $45,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00

TI $45,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00 -$170,000.00

T $18,000.00 -$68,000.00 -$68,000.00 -$68,000.00 -$68,000.00 -$68,000.00 -$68,000.00 -$68,000.00 -$68,000.00 -$68,000.00 -$68,000.00 MARRAT =

ATCF $27,000.00 -$102,000.00 -$102,000.00 -$102,000.00 -$102,000.00 -$102,000.00 -$102,000.00 -$102,000.00 -$102,000.00 -$102,000.00 -$102,000.00 12%

PW AT =

-$549,322.75

FW AT = -$1,706,113.08 AW AT = -$97,221.43 d

CONTRACT OUT COST

-$45,000.00

BTCF

BONUS@END

$0.00

PERIODS

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF $45,000.00 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29

TI $45,000.00 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29 -$158,764.29

T $18,000.00 -$63,505.71 -$63,505.71 -$63,505.71 -$63,505.71 -$63,505.71 -$63,505.71 -$63,505.71 -$63,505.71 -$63,505.71 -$63,505.71 MARRAT =

-$158,764.29 GOAL SEEK CHANGED CELL

ATCF $27,000.00 -$95,258.57 -$95,258.57 -$95,258.57 -$95,258.57 -$95,258.57 -$95,258.57 -$95,258.57 -$95,258.57 -$95,258.57 -$95,258.57 12%

PW AT =

-$511,232.18 FW AT = -$1,587,809.55 AW AT = -$90,480.00 CONTRACT PRICE IS $158,764.29 FOR EQUIVALENCE BETWEEN CONTRACTING AND LEASING.

40.00% 12.00%

ATCF MACRS(39) -$240,000.00 -$75,637.44 2.461% -$75,538.56 2.564% -$75,538.56 2.564% -$75,538.56 2.564% -$75,538.56 2.564% -$75,538.56 2.564% -$75,538.56 2.564% -$75,538.56 2.564% -$75,538.56 2.564% $67,945.92 2.457% =(11.5/12.0)*2.564% 12% MID MONTH CONV -$620,699.83 -$1,927,799.47 -$109,854.04

40.00% 12.00%

AL SEEK CHANGED CELL

TAX RATE MARRAT =

GOAL SEEK SET CELL

CONTRACTING AND LEASING.

40.00% 12.00%

PROBLEM 10.35 a

NEW TECHNOLOGY BASIS EST SALV RCVD SALV

MACRS(7) $2,500,000.00 $0.00 $300,000.00

EOY 0 1 2 3 4 5 6 7 8

BTCF -$2,500,000.00 -$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 $190,000.00

BTCF USEFUL PERIODS

-$110,000.00 8 8

TAX RATE MARRAT =

DWO

$357,250.00 -$467,250.00 $612,250.00 -$722,250.00 $437,250.00 -$547,250.00 $312,250.00 -$422,250.00 $223,250.00 -$333,250.00 $223,000.00 -$333,000.00 $223,250.00 -$333,250.00 $111,500.00 $78,500.00 SUM DEPR

-$186,900.00 -$288,900.00 -$218,900.00 -$168,900.00 -$133,300.00 -$133,200.00 -$133,300.00 $31,400.00 MARRAT =

$2,500,000.00

PW AT =

BOOK VALUE

FW AT =

$0.00

AW AT =

MANUAL MIXING COST

$0.00

BTCF

BONUS@END

$0.00

PERIODS

EOY 0 1 2 3 4 5 6 7 8

BTCF $0.00 -$600,000.00 -$600,000.00 -$600,000.00 -$600,000.00 -$600,000.00 -$600,000.00 -$600,000.00 -$600,000.00

-$600,000.00

TAX RATE MARRAT =

T $0.00 $0.00 -$600,000.00 -$240,000.00 -$600,000.00 -$240,000.00 -$600,000.00 -$240,000.00 -$600,000.00 -$240,000.00 -$600,000.00 -$240,000.00 -$600,000.00 -$240,000.00 -$600,000.00 -$240,000.00 -$600,000.00 -$240,000.00 MARRAT =

ATCF $0.00 -$360,000.00 -$360,000.00 -$360,000.00 -$360,000.00 -$360,000.00 -$360,000.00 -$360,000.00 -$360,000.00 10%

PW AT = -$1,920,573.43 FW AT = -$4,116,919.72 AW AT = c

NEW TECHNOLOGY BASIS EST SALV RCVD SALV EOY 0

-$360,000.00

MACRS(7) $2,317,306.09 GOAL SEEK CHANGED CELL $0.00 $300,000.00 BTCF -$2,317,306.09

DWO

1 2 3 4 5 6 7 8

-$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 -$110,000.00 $190,000.00

$331,143.04 -$441,143.04 $567,508.26 -$677,508.26 $405,296.83 -$515,296.83 $289,431.53 -$399,431.53 $206,935.43 -$316,935.43 $206,703.70 -$316,703.70 $0.00 -$110,000.00 $0.00 -$120,287.29 SUM DEPR

-$176,457.22 -$271,003.30 -$206,118.73 -$159,772.61 -$126,774.17 -$126,681.48 -$44,000.00 -$48,114.91 MARRAT =

$2,007,018.80

PW AT =

BOOK VALUE

FW AT =

$310,287.29

AW AT =

AN INVESTMENT OF $2,317,306.09 WOULD MAKE THE TWO ALTERNATIVES EQUIVALENT.

40.00% 10.00%

ATCF -$2,500,000.00 $76,900.00 $178,900.00 $108,900.00 $58,900.00 $23,300.00 $23,200.00 $23,300.00 $158,600.00 10%

MACRS(7) 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

-$2,046,684.08 -$4,387,249.09 -$383,638.69

40.00% 10.00%

BTCF USEFUL PERIODS ATCF -$2,317,306.09

-$110,000.00 TAX RATE 40.00% 8 MARRAT = 10.00% 8 MACRS(7)

$66,457.22 $161,003.30 $96,118.73 $49,772.61 $16,774.17 $16,681.48 -$66,000.00 $238,114.91 10%

14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

-$1,920,573.43 -$4,116,919.72 -$360,000.00 GOAL SEEK SET CELL

TIVES EQUIVALENT.

PROBLEM 10.36

WHEN WE USE BTCF, THAT MEANS WE HAVE NOT YET DEDUCTED TAXES FROM THE CASH FLOW. (ALS

WHEN WE USE BTLCF, THAT MEANS WE HAVE NOT YET DEDUCTED TAXES, LOAN INTEREST, OR LOAN P

IN BOTH CASES, BTCF OR BTLCF IS CONSIDERED GROSS INCOME LESS EXPENSE DEDUCTIONS, WITH N

FROM THE CASH FLOW. (ALSO, THERE IS NO CASH FLOW DUE TO A LOAN CONSIDERED.)

PROBLEM 10.37 BASIS

$850,000.00

TAX RATE

40.00%

$750,000.00

EXPENSES

$475,000.00

BTLCF

$275,000.00

DWO

$121,465.00

IPMT

$46,750.00

PPMT

$85,000.00

TI=BTLCF-DWO-IPMT=

$106,785.00

T=TAX RATE*TI=

$42,714.00

ATCF=BTLCF-IPMT-PPMT-T= $100,536.00

PROBLEM 10.38

TAX RATE

40.00%

GI EXPENSES BTLCF

$500,000.00 $120,000.00 $380,000.00

DWO

$171,480.00

IPMT PPMT

$60,500.00 $0.00

TI=BTLCF-DWO-IPMT=

$148,020.00

T=TAX RATE*TI=

$59,208.00

ATCF=BTLCF-IPMT-PPMT-T= $260,292.00

PROBLEM 10.39 BASIS

$1,800,000.00

BORROWED

45.00%

INT RATE

12.50%

TAX RATE

40.00%

GI=BTLCF

DWO

$360,000.00

IPMT

$101,250.00

PPMT

$202,500.00

$328,000.00

TI=X-DWO-IPMT=

$328,000.00

X=DWO+IPMT+TI

$789,250.00

TI=X-DWO-IPMT=

$328,000.00

T=TAX RATE*TI=

$131,200.00

ATCF=X-IPMT-PPMT-T=

$354,300.00

PROBLEM 10.40 BASIS

$480,000.00

BORROWED

$275,000.00

INT RATE

12.00%

TAX RATE

40.00%

$300,000.00

EXPENSES

BTLCF

$300,000.00-Y

DWO

$68,592.00

IPMT

$33,000.00

PPMT

$0.00

$15,000.00

TI=GI-Y-DWO-IPMT=

$15,000.00

Y=GI-DWO-IPMT-TI

$183,408.00

TI=GI-Y-DWO-IPMT=

$15,000.00

T=TAX RATE*TI=

$6,000.00

ATCF=GI-Y-IPMT-PPMT-T=

$77,592.00

PROBLEM 10.41 a

LOAN METHOD 1 BASIS $850,000.00 LOAN PRINC $425,000.00 BTCF EST SALV $0.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $0.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$850,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00

PPMT -$425,000.00 $0.00 $0.00 $0.00 $0.00 $425,000.00 $0.00 $0.00 $0.00

IPMT

DWO

$46,750.00 $46,750.00 $46,750.00 $46,750.00 $46,750.00 $0.00 $0.00 $0.00

$121,465.00 $208,165.00 $148,665.00 $106,165.00 $75,905.00 $75,820.00 $75,905.00 $37,910.00 SUM DEPR $850,000.00 BOOK VALUE $0.00

LOAN METHOD 2 BASIS $850,000.00 LOAN PRINC $425,000.00 BTCF EST SALV $0.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $0.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$850,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00

PPMT -$425,000.00 $85,000.00 $85,000.00 $85,000.00 $85,000.00 $85,000.00 $0.00 $0.00 $0.00

IPMT

DWO

$46,750.00 $37,400.00 $28,050.00 $18,700.00 $9,350.00 $0.00 $0.00 $0.00

$121,465.00 $208,165.00 $148,665.00 $106,165.00 $75,905.00 $75,820.00 $75,905.00 $37,910.00 SUM DEPR $850,000.00 BOOK VALUE $0.00

LOAN METHOD 3 BASIS $850,000.00

LOAN PRINC

$425,000.00

BTCF

EST SALV RCVD SALV

$0.00 $0.00

LOAN PERIOD LOAN INT

5 11.00%

USEFUL LIFE PERIODS

EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$850,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00

PPMT -$425,000.00 $68,242.38 $75,749.04 $84,081.44 $93,330.40 $103,596.74 $0.00 $0.00 $0.00

IPMT

DWO

$46,750.00 $39,243.34 $30,910.94 $21,661.99 $11,395.64 $0.00 $0.00 $0.00

$121,465.00 $208,165.00 $148,665.00 $106,165.00 $75,905.00 $75,820.00 $75,905.00 $37,910.00 SUM DEPR $850,000.00 BOOK VALUE $0.00

LOAN METHOD 4 BASIS $850,000.00 LOAN PRINC $425,000.00 BTCF EST SALV $0.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $0.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$850,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00 $275,000.00

PPMT IPMT -$425,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $425,000.00 $291,149.72 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

DWO $121,465.00 $208,165.00 $148,665.00 $106,165.00 $75,905.00 $75,820.00 $75,905.00 $37,910.00 SUM DEPR $850,000.00 BOOK VALUE $0.00

$275,000.00 TAX RATE MARRAT 8 8 METHOD TI $106,785.00 $20,085.00 $79,585.00 $122,085.00 $152,345.00 $199,180.00 $199,095.00 $237,090.00

40.00% 10.00% 1

ATCF ATCF+ ATCFATCF MACRS(7) -$425,000.00 $0.00 $425,000.00 -$425,000.00 $42,714.00 $185,536.00 $185,536.00 $0.00 $0.00 14.29% $8,034.00 $220,216.00 $220,216.00 $0.00 $0.00 24.49% $31,834.00 $196,416.00 $196,416.00 $0.00 $0.00 17.49% $48,834.00 $179,416.00 $179,416.00 $0.00 $0.00 12.49% $60,938.00 -$257,688.00 $0.00 $257,688.00 -$257,688.00 8.93% $79,672.00 $195,328.00 $195,328.00 $0.00 $0.00 8.92% $79,638.00 $195,362.00 $195,362.00 $0.00 $0.00 8.93% $94,836.00 $180,164.00 $180,164.00 $0.00 $1,962,105.23 4.46% MARRAT = 10% PW AT = $330,332.60 FW AT = $708,097.26 AW AT = $61,918.87 IRRAT =

32.78%

ERRAT =

17.50%

$275,000.00 TAX RATE MARRAT 8 8 METHOD TI $106,785.00 $29,435.00 $98,285.00 $150,135.00 $189,745.00 $199,180.00 $199,095.00 $237,090.00

40.00% 10.00% 2

ATCF ATCF+ ATCFATCF MACRS(7) -$425,000.00 $0.00 $425,000.00 -$425,000.00 $42,714.00 $100,536.00 $100,536.00 $0.00 $0.00 14.29% $11,774.00 $140,826.00 $140,826.00 $0.00 $0.00 24.49% $39,314.00 $122,636.00 $122,636.00 $0.00 $0.00 17.49% $60,054.00 $111,246.00 $111,246.00 $0.00 $0.00 12.49% $75,898.00 $104,752.00 $104,752.00 $0.00 $0.00 8.93% $79,672.00 $195,328.00 $195,328.00 $0.00 $0.00 8.92% $79,638.00 $195,362.00 $195,362.00 $0.00 $0.00 8.93% $94,836.00 $180,164.00 $180,164.00 $0.00 $1,576,613.84 4.46% MARRAT = 10% PW AT = $310,501.99 FW AT = $665,588.59 AW AT = $58,201.74 IRRAT =

25.83%

ERRAT =

17.81%

$275,000.00 TAX RATE

40.00%

MARRAT

8 8

METHOD

$106,785.00 $27,591.66 $95,424.06 $147,173.01 $187,699.36 $199,180.00 $199,095.00 $237,090.00

10.00% 3

ATCF ATCF+ ATCFATCF MACRS(7) -$425,000.00 $0.00 $425,000.00 -$425,000.00 $42,714.00 $117,293.62 $117,293.62 $0.00 $0.00 14.29% $11,036.66 $148,970.95 $148,970.95 $0.00 $0.00 24.49% $38,169.62 $121,838.00 $121,838.00 $0.00 $0.00 17.49% $58,869.21 $101,138.41 $101,138.41 $0.00 $0.00 12.49% $75,079.74 $84,927.88 $84,927.88 $0.00 $0.00 8.93% $79,672.00 $195,328.00 $195,328.00 $0.00 $0.00 8.92% $79,638.00 $195,362.00 $195,362.00 $0.00 $0.00 8.93% $94,836.00 $180,164.00 $180,164.00 $0.00 $1,581,229.35 4.46% MARRAT = 10% PW AT = $312,655.16 FW AT = $670,204.11 AW AT =

$58,605.34

IRRAT =

26.46%

ERRAT =

17.85%

$275,000.00 TAX RATE MARRAT 8 8 METHOD TI

40.00% 10.00% 4

ATCF ATCF+ ATCFATCF MACRS(7) -$425,000.00 $0.00 $425,000.00 -$425,000.00 $153,535.00 $61,414.00 $213,586.00 $213,586.00 $0.00 $0.00 14.29% $66,835.00 $26,734.00 $248,266.00 $248,266.00 $0.00 $0.00 24.49% $126,335.00 $50,534.00 $224,466.00 $224,466.00 $0.00 $0.00 17.49% $168,835.00 $67,534.00 $207,466.00 $207,466.00 $0.00 $0.00 12.49% -$92,054.72 -$36,821.89 -$404,327.83 $0.00 $404,327.83 -$404,327.83 8.93% $199,180.00 $79,672.00 $195,328.00 $195,328.00 $0.00 $0.00 8.92% $199,095.00 $79,638.00 $195,362.00 $195,362.00 $0.00 $0.00 8.93% $237,090.00 $94,836.00 $180,164.00 $180,164.00 $0.00 $2,152,701.84 4.46% MARRAT = 10% PW AT = $328,195.53 FW AT = $703,516.26 AW AT =

$61,518.29

IRRAT =

35.75%

ERRAT =

17.11%

PROBLEM 10.42 a

LOAN METHOD 1 BASIS $1,200,000.00 LOAN PRINC $550,000.00 BTCF EST SALV $0.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $0.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,200,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00

PPMT -$550,000.00 $0.00 $0.00 $0.00 $0.00 $550,000.00 $0.00 $0.00 $0.00

IPMT

DWO

$60,500.00 $60,500.00 $60,500.00 $60,500.00 $60,500.00 $0.00 $0.00 $0.00

$171,480.00 $293,880.00 $209,880.00 $149,880.00 $107,160.00 $107,040.00 $107,160.00 $53,520.00 SUM DEPR $1,200,000.00 BOOK VALUE $0.00

LOAN METHOD 2 BASIS $1,200,000.00 LOAN PRINC $550,000.00 BTCF EST SALV $0.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $0.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,200,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00

PPMT -$550,000.00 $110,000.00 $110,000.00 $110,000.00 $110,000.00 $110,000.00 $0.00 $0.00 $0.00

IPMT

DWO

$60,500.00 $48,400.00 $36,300.00 $24,200.00 $12,100.00 $0.00 $0.00 $0.00

$171,480.00 $293,880.00 $209,880.00 $149,880.00 $107,160.00 $107,040.00 $107,160.00 $53,520.00 SUM DEPR $1,200,000.00 BOOK VALUE $0.00

LOAN METHOD 3 BASIS $1,200,000.00 LOAN PRINC $550,000.00 BTCF EST SALV $0.00 LOAN PERIOD 5 USEFUL LIFE

RCVD SALV

$0.00

LOAN INT

11.00%

PERIODS

EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,200,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00

PPMT -$550,000.00 $88,313.67 $98,028.17 $108,811.27 $120,780.51 $134,066.37 $0.00 $0.00 $0.00

IPMT

DWO

$60,500.00 $50,785.50 $40,002.40 $28,033.16 $14,747.30 $0.00 $0.00 $0.00

$171,480.00 $293,880.00 $209,880.00 $149,880.00 $107,160.00 $107,040.00 $107,160.00 $53,520.00 SUM DEPR $1,200,000.00 BOOK VALUE $0.00

LOAN METHOD 4 BASIS $1,200,000.00 LOAN PRINC $550,000.00 BTCF EST SALV $0.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $0.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,200,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00 $380,000.00

PPMT IPMT -$550,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $550,000.00 $376,781.99 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

DWO $171,480.00 $293,880.00 $209,880.00 $149,880.00 $107,160.00 $107,040.00 $107,160.00 $53,520.00 SUM DEPR $1,200,000.00 BOOK VALUE $0.00

$380,000.00 8 8

TAX RATE MARRAT

METHOD

40.00% 9.00% 1

ATCF ATCF+ ATCFATCF MACRS(7) -$650,000.00 $0.00 $650,000.00 -$650,000.00 $148,020.00 $59,208.00 $260,292.00 $260,292.00 $0.00 $0.00 14.29% $25,620.00 $10,248.00 $309,252.00 $309,252.00 $0.00 $0.00 24.49% $109,620.00 $43,848.00 $275,652.00 $275,652.00 $0.00 $0.00 17.49% $169,620.00 $67,848.00 $251,652.00 $251,652.00 $0.00 $0.00 12.49% $212,340.00 $84,936.00 -$315,436.00 $0.00 $315,436.00 -$315,436.00 8.93% $272,960.00 $109,184.00 $270,816.00 $270,816.00 $0.00 $0.00 8.92% $272,840.00 $109,136.00 $270,864.00 $270,864.00 $0.00 $0.00 8.93% $326,480.00 $130,592.00 $249,408.00 $249,408.00 $0.00 $2,640,228.88 4.46% MARRAT = 9% PW AT = $470,030.09 FW AT = $936,564.39 AW AT = $84,922.39 IRRAT =

29.39%

ERRAT =

16.11%

$380,000.00 8 8

TAX RATE MARRAT

METHOD

40.00% 9.00% 2

ATCF ATCF+ ATCFATCF MACRS(7) -$650,000.00 $0.00 $650,000.00 -$650,000.00 $148,020.00 $59,208.00 $150,292.00 $150,292.00 $0.00 $0.00 14.29% $37,720.00 $15,088.00 $206,512.00 $206,512.00 $0.00 $0.00 24.49% $133,820.00 $53,528.00 $180,172.00 $180,172.00 $0.00 $0.00 17.49% $205,920.00 $82,368.00 $163,432.00 $163,432.00 $0.00 $0.00 12.49% $260,740.00 $104,296.00 $153,604.00 $153,604.00 $0.00 $0.00 8.93% $272,960.00 $109,184.00 $270,816.00 $270,816.00 $0.00 $0.00 8.92% $272,840.00 $109,136.00 $270,864.00 $270,864.00 $0.00 $0.00 8.93% $326,480.00 $130,592.00 $249,408.00 $249,408.00 $0.00 $2,194,323.40 4.46% MARRAT = 9% PW AT = $451,256.92 FW AT = $899,157.68 AW AT = $81,530.56

$380,000.00 8

IRRAT =

24.04%

ERRAT =

16.43%

TAX RATE MARRAT

40.00% 9.00%

METHOD

ATCF ATCF+ ATCFATCF MACRS(7) -$650,000.00 $0.00 $650,000.00 -$650,000.00 $148,020.00 $59,208.00 $171,978.33 $171,978.33 $0.00 $0.00 14.29% $35,334.50 $14,133.80 $217,052.53 $217,052.53 $0.00 $0.00 24.49% $130,117.60 $52,047.04 $179,139.29 $179,139.29 $0.00 $0.00 17.49% $202,086.84 $80,834.74 $150,351.59 $150,351.59 $0.00 $0.00 12.49% $258,092.70 $103,237.08 $127,949.25 $127,949.25 $0.00 $0.00 8.93% $272,960.00 $109,184.00 $270,816.00 $270,816.00 $0.00 $0.00 8.92% $272,840.00 $109,136.00 $270,864.00 $270,864.00 $0.00 $0.00 8.93% $326,480.00 $130,592.00 $249,408.00 $249,408.00 $0.00 $2,198,367.72 4.46% MARRAT = 9% PW AT = $453,286.63 FW AT = $903,202.00 AW AT = $81,897.28 IRRAT =

24.54%

ERRAT =

16.45%

$380,000.00 8 8

TAX RATE MARRAT

METHOD

40.00% 9.00% 4

ATCF ATCF+ ATCFATCF MACRS(7) -$650,000.00 $0.00 $650,000.00 -$650,000.00 $208,520.00 $83,408.00 $296,592.00 $296,592.00 $0.00 $0.00 14.29% $86,120.00 $34,448.00 $345,552.00 $345,552.00 $0.00 $0.00 24.49% $170,120.00 $68,048.00 $311,952.00 $311,952.00 $0.00 $0.00 17.49% $230,120.00 $92,048.00 $287,952.00 $287,952.00 $0.00 $0.00 12.49% -$103,941.99 -$41,576.79 -$505,205.19 $0.00 $505,205.19 -$505,205.19 8.93% $272,960.00 $109,184.00 $270,816.00 $270,816.00 $0.00 $0.00 8.92% $272,840.00 $109,136.00 $270,864.00 $270,864.00 $0.00 $0.00 8.93% $326,480.00 $130,592.00 $249,408.00 $249,408.00 $0.00 $2,874,557.89 4.46% MARRAT = 9% PW AT = $464,294.97 FW AT = $925,136.80 AW AT = $83,886.20 IRRAT =

31.54%

ERRAT =

15.73%

PROBLEM 10.43 a

NET SAVINGS=

$428,632.84

LOAN METHOD 1 BASIS $1,800,000.00 LOAN PRINC $810,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 4 USEFUL LIFE RCVD SALV $250,000.00 LOAN INT 12.50% PERIODS EOY 0 1 2 3 4 5 6

BT&LCF -$1,800,000.00 $428,632.84 $428,632.84 $428,632.84 $428,632.84 $428,632.84 $678,632.84

PPMT IPMT -$810,000.00 $0.00 $101,250.00 $0.00 $101,250.00 $0.00 $101,250.00 $810,000.00 $101,250.00 $0.00 $0.00 $0.00 $0.00

DWO $360,000.00 $576,000.00 $345,600.00 $207,360.00 $207,360.00 $103,680.00 SUM DEPR $1,800,000.00 BOOK VALUE $0.00

NET SAVINGS=

$440,500.23

LOAN METHOD 2 BASIS $1,800,000.00 LOAN PRINC $810,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 4 USEFUL LIFE RCVD SALV $250,000.00 LOAN INT 12.50% PERIODS EOY 0 1 2 3 4 5 6

BT&LCF -$1,800,000.00 $440,500.23 $440,500.23 $440,500.23 $440,500.23 $440,500.23 $690,500.23

PPMT IPMT -$810,000.00 $202,500.00 $101,250.00 $202,500.00 $75,937.50 $202,500.00 $50,625.00 $202,500.00 $25,312.50 $0.00 $0.00 $0.00 $0.00

DWO $360,000.00 $576,000.00 $345,600.00 $207,360.00 $207,360.00 $103,680.00 SUM DEPR $1,800,000.00 BOOK VALUE $0.00

NET SAVINGS= LOAN METHOD 3

$439,301.61

BASIS EST SALV RCVD SALV EOY 0 1 2 3 4 5 6

$1,800,000.00 LOAN PRINC $810,000.00 BTCF $250,000.00 LOAN PERIOD 4 USEFUL LIFE $250,000.00 LOAN INT 12.50% PERIODS BT&LCF -$1,800,000.00 $439,301.61 $439,301.61 $439,301.61 $439,301.61 $439,301.61 $689,301.61

PPMT IPMT -$810,000.00 $168,243.41 $101,250.00 $189,273.83 $80,219.57 $212,933.06 $56,560.34 $239,549.70 $29,943.71 $0.00 $0.00 $0.00 $0.00

DWO $360,000.00 $576,000.00 $345,600.00 $207,360.00 $207,360.00 $103,680.00 SUM DEPR $1,800,000.00 BOOK VALUE $0.00

NET SAVINGS=

$430,283.83

LOAN METHOD 4 BASIS $1,800,000.00 LOAN PRINC $810,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 4 USEFUL LIFE RCVD SALV $250,000.00 LOAN INT 12.50% PERIODS EOY 0 1 2 3 4 5 6

BT&LCF -$1,800,000.00 $430,283.83 $430,283.83 $430,283.83 $430,283.83 $430,283.83 $680,283.83

PPMT IPMT -$810,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $810,000.00 $487,463.38 $0.00 $0.00 $0.00 $0.00

DWO $360,000.00 $576,000.00 $345,600.00 $207,360.00 $207,360.00 $103,680.00 SUM DEPR $1,800,000.00 BOOK VALUE $0.00

$428,632.84 GOAL SEEK CHANGED CELL 6 6 TI -$32,617.16 -$248,617.16 -$18,217.16 $120,022.84 $221,272.84 $574,952.84

-$20,749.77 -$211,437.27 $44,275.23 $207,827.73 $233,140.23 $586,820.23

METHOD

40.00% 11.00% 1

ATCF ATCF+ ATCFATCF MACRS(5) -$990,000.00 $0.00 $990,000.00 -$990,000.00 -$13,046.86 $340,429.70 $340,429.70 $0.00 $0.00 20.00% -$99,446.86 $426,829.70 $426,829.70 $0.00 $0.00 32.00% -$7,286.86 $334,669.70 $334,669.70 $0.00 $0.00 19.20% $48,009.14 -$530,626.30 $0.00 $530,626.30 -$530,626.30 11.52% $88,509.14 $340,123.70 $340,123.70 $0.00 $0.00 11.52% $229,981.14 $448,651.70 $448,651.70 $0.00 $2,505,495.07 5.76% MARRAT = 11% PW AT = $0.00 GOAL SEEK SET CELL FW AT =

$0.00

AW AT =

$0.00

IRRAT =

11.00%

ERRAT =

11.00%

$440,500.23 GOAL SEEK CHANGED CELL 6 6 TI

TAX RATE MARRAT

TAX RATE MARRAT METHOD

40.00% 11.00% 2

ATCF ATCF+ ATCFATCF MACRS(5) -$990,000.00 $0.00 $990,000.00 -$990,000.00 -$8,299.91 $145,050.14 $145,050.14 $0.00 $0.00 20.00% -$84,574.91 $246,637.64 $246,637.64 $0.00 $0.00 32.00% $17,710.09 $169,665.14 $169,665.14 $0.00 $0.00 19.20% $83,131.09 $129,556.64 $129,556.64 $0.00 $0.00 11.52% $93,256.09 $347,244.14 $347,244.14 $0.00 $0.00 11.52% $234,728.09 $455,772.14 $455,772.14 $0.00 $1,851,710.41 5.76% MARRAT = 11% PW AT = $0.00 GOAL SEEK SET CELL FW AT =

$0.00

AW AT =

$0.00

IRRAT =

11.00%

ERRAT =

11.00%

$439,301.61 GOAL SEEK CHANGED CELL 6 6 TI -$21,948.39 -$216,917.96 $37,141.27 $201,997.90 $231,941.61 $585,621.61

METHOD

40.00% 11.00% 3

ATCF ATCF+ ATCFATCF MACRS(5) -$990,000.00 $0.00 $990,000.00 -$990,000.00 -$8,779.35 $178,587.56 $178,587.56 $0.00 $0.00 20.00% -$86,767.18 $256,575.39 $256,575.39 $0.00 $0.00 32.00% $14,856.51 $154,951.70 $154,951.70 $0.00 $0.00 19.20% $80,799.16 $89,009.05 $89,009.05 $0.00 $0.00 11.52% $92,776.65 $346,524.97 $346,524.97 $0.00 $0.00 11.52% $234,248.65 $455,052.97 $455,052.97 $0.00 $1,851,710.41 5.76% MARRAT = 11% PW AT = $0.00 GOAL SEEK SET CELL FW AT =

$0.00

AW AT =

$0.00

IRRAT =

11.00%

ERRAT =

11.00%

$430,283.83 GOAL SEEK CHANGED CELL 6 6 TI

TAX RATE MARRAT

TAX RATE MARRAT METHOD

40.00% 11.00% 4

ATCF ATCF+ ATCFATCF MACRS(5) -$990,000.00 $0.00 $990,000.00 -$990,000.00 $70,283.83 $28,113.53 $402,170.30 $402,170.30 $0.00 $0.00 20.00% -$145,716.17 -$58,286.47 $488,570.30 $488,570.30 $0.00 $0.00 32.00% $84,683.83 $33,873.53 $396,410.30 $396,410.30 $0.00 $0.00 19.20% -$264,539.54 -$105,815.82 -$761,363.73 $0.00 $761,363.73 -$761,363.73 11.52% $222,923.83 $89,169.53 $341,114.30 $341,114.30 $0.00 $0.00 11.52% $576,603.83 $230,641.53 $449,642.30 $449,642.30 $0.00 $2,789,786.65 5.76% MARRAT = 11% PW AT = $0.00 GOAL SEEK SET CELL FW AT =

$0.00

AW AT =

$0.00

IRRAT =

11.00%

ERRAT =

11.00%

PROBLEM 10.44 a

O&M COST=

$300,000-BTCF= $220,209.06

LOAN METHOD 1 BASIS EST SALV RCVD SALV

$480,000.00 $0.00 $0.00

LOAN PRINC LOAN PERIOD LOAN INT

EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$480,000.00 $79,790.94 $79,790.94 $79,790.94 $79,790.94 $79,790.94 $79,790.94 $79,790.94 $79,790.94 $79,790.94 $79,790.94

PPMT -$275,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $275,000.00

$275,000.00 BTCF 10 USEFUL LIFE 12.00% PERIODS IPMT

DWO

$33,000.00 $33,000.00 $33,000.00 $33,000.00 $33,000.00 $33,000.00 $33,000.00 $33,000.00 $33,000.00 $33,000.00

$68,592.00 $117,552.00 $83,952.00 $59,952.00 $42,864.00 $42,816.00 $42,864.00 $21,408.00 $0.00 $0.00 SUM DEPR $480,000.00 BOOK VALUE $0.00

O&M COST=

$300,000-BTCF= $215,428.05

LOAN METHOD 1 BASIS EST SALV RCVD SALV

$480,000.00 $0.00 $0.00

LOAN PRINC LOAN PERIOD LOAN INT

EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$480,000.00 $84,571.95 $84,571.95 $84,571.95 $84,571.95 $84,571.95 $84,571.95 $84,571.95 $84,571.95 $84,571.95 $84,571.95

PPMT -$275,000.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00

$275,000.00 BTCF 10 USEFUL LIFE 12.00% PERIODS IPMT

DWO

$33,000.00 $29,700.00 $26,400.00 $23,100.00 $19,800.00 $16,500.00 $13,200.00 $9,900.00 $6,600.00 $3,300.00

$68,592.00 $117,552.00 $83,952.00 $59,952.00 $42,864.00 $42,816.00 $42,864.00 $21,408.00 $0.00 $0.00 SUM DEPR $480,000.00

BOOK VALUE $0.00

O&M COST=

$300,000-BTCF= $216,512.27

LOAN METHOD 1 BASIS EST SALV RCVD SALV

$480,000.00 $0.00 $0.00

LOAN PRINC LOAN PERIOD LOAN INT

EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$480,000.00 $83,487.73 $83,487.73 $83,487.73 $83,487.73 $83,487.73 $83,487.73 $83,487.73 $83,487.73 $83,487.73 $83,487.73

PPMT -$275,000.00 $15,670.65 $17,551.12 $19,657.26 $22,016.13 $24,658.06 $27,617.03 $30,931.07 $34,642.80 $38,799.94 $43,455.93

$275,000.00 BTCF 10 USEFUL LIFE 12.00% PERIODS IPMT

DWO

$33,000.00 $31,119.52 $29,013.39 $26,654.52 $24,012.58 $21,053.61 $17,739.57 $14,027.84 $9,870.70 $5,214.71

$68,592.00 $117,552.00 $83,952.00 $59,952.00 $42,864.00 $42,816.00 $42,864.00 $21,408.00 $0.00 $0.00 SUM DEPR $480,000.00 BOOK VALUE $0.00

O&M COST=

$300,000-BTCF

$216,872.68

LOAN METHOD 1 BASIS EST SALV RCVD SALV

$480,000.00 $0.00 $0.00

LOAN PRINC LOAN PERIOD LOAN INT

$275,000.00 BTCF 10 USEFUL LIFE 12.00% PERIODS

EOY 0 1 2 3 4 5 6 7 8 9

BT&LCF -$480,000.00 $83,127.32 $83,127.32 $83,127.32 $83,127.32 $83,127.32 $83,127.32 $83,127.32 $83,127.32 $83,127.32

PPMT -$275,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

IPMT $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

DWO $68,592.00 $117,552.00 $83,952.00 $59,952.00 $42,864.00 $42,816.00 $42,864.00 $21,408.00 $0.00

$83,127.32

$275,000.00 $579,108.26

$0.00 SUM DEPR $480,000.00 BOOK VALUE $0.00

$79,790.94 GOAL SEEK CHANGED CELL 10 10 TI -$21,801.06 -$70,761.06 -$37,161.06 -$13,161.06 $3,926.94 $3,974.94 $3,926.94 $25,382.94 $46,790.94 $46,790.94

-$17,020.05 -$62,680.05 -$25,780.05 $1,519.95 $21,907.95 $25,255.95 $28,507.95 $53,263.95 $77,971.95 $81,271.95

METHOD

40.00% 10.00% 1

ATCF ATCF+ ATCFATCF MACRS(7) -$205,000.00 $0.00 $205,000.00 -$205,000.00 -$8,720.42 $55,511.37 $55,511.37 $0.00 $0.00 14.29% -$28,304.42 $75,095.37 $75,095.37 $0.00 $0.00 24.49% -$14,864.42 $61,655.37 $61,655.37 $0.00 $0.00 17.49% -$5,264.42 $52,055.37 $52,055.37 $0.00 $0.00 12.49% $1,570.78 $45,220.17 $45,220.17 $0.00 $0.00 8.93% $1,589.98 $45,200.97 $45,200.97 $0.00 $0.00 8.92% $1,570.78 $45,220.17 $45,220.17 $0.00 $0.00 8.93% $10,153.18 $36,637.77 $36,637.77 $0.00 $0.00 4.46% $18,716.38 $28,074.57 $28,074.57 $0.00 $0.00 $18,716.38 -$246,925.43 $0.00 $246,925.43 $531,717.20 MARRAT = 10% PW AT = $0.00 GOAL SEEK SET CELL FW AT =

$0.00

AW AT =

$0.00

IRRAT =

10.00%

ERRAT =

10.00%

$84,571.95 GOAL SEEK CHANGED CELL 10 10 TI

TAX RATE MARRAT

TAX RATE MARRAT METHOD

40.00% 10.00% 2

ATCF ATCF+ ATCFATCF MACRS(7) -$205,000.00 $0.00 $205,000.00 -$205,000.00 -$6,808.02 $30,879.97 $30,879.97 $0.00 $0.00 14.29% -$25,072.02 $52,443.97 $52,443.97 $0.00 $0.00 24.49% -$10,312.02 $40,983.97 $40,983.97 $0.00 $0.00 17.49% $607.98 $33,363.97 $33,363.97 $0.00 $0.00 12.49% $8,763.18 $28,508.77 $28,508.77 $0.00 $0.00 8.93% $10,102.38 $30,469.57 $30,469.57 $0.00 $0.00 8.92% $11,403.18 $32,468.77 $32,468.77 $0.00 $0.00 8.93% $21,305.58 $25,866.37 $25,866.37 $0.00 $0.00 4.46% $31,188.78 $19,283.17 $19,283.17 $0.00 $0.00 $32,508.78 $21,263.17 $21,263.17 $0.00 $531,717.20 MARRAT = 10% PW AT = $0.00 GOAL SEEK SET CELL

FW AT =

$0.00

AW AT =

$0.00

IRRAT =

10.00%

ERRAT =

10.00%

$83,487.73 GOAL SEEK CHANGED CELL 10 10 TI -$18,104.27 -$65,183.79 -$29,477.65 -$3,118.78 $16,611.15 $19,618.12 $22,884.16 $48,051.89 $73,617.03 $78,273.02

$14,535.32 -$34,424.68 -$824.68 $23,175.32 $40,263.32 $40,311.32 $40,263.32 $61,719.32 $83,127.32

METHOD

40.00% 10.00% 3

ATCF ATCF+ ATCFATCF MACRS(7) -$205,000.00 $0.00 $205,000.00 -$205,000.00 -$7,241.71 $42,058.80 $42,058.80 $0.00 $0.00 14.29% -$26,073.52 $60,890.60 $60,890.60 $0.00 $0.00 24.49% -$11,791.06 $46,608.15 $46,608.15 $0.00 $0.00 17.49% -$1,247.51 $36,064.60 $36,064.60 $0.00 $0.00 12.49% $6,644.46 $28,172.63 $28,172.63 $0.00 $0.00 8.93% $7,847.25 $26,969.84 $26,969.84 $0.00 $0.00 8.92% $9,153.67 $25,663.42 $25,663.42 $0.00 $0.00 8.93% $19,220.76 $15,596.33 $15,596.33 $0.00 $0.00 4.46% $29,446.81 $5,370.28 $5,370.28 $0.00 $0.00 $31,309.21 $3,507.88 $3,507.88 $0.00 $531,717.20 MARRAT = 10% PW AT = $0.00 GOAL SEEK SET CELL FW AT =

$0.00

AW AT =

$0.00

IRRAT =

10.00%

ERRAT =

10.00%

$83,127.32 GOAL SEEK CHANGED CELL 10 10 TI

TAX RATE MARRAT

TAX RATE MARRAT METHOD

40.00% 10.00% 4

ATCF ATCF+ ATCFATCF MACRS(7) -$205,000.00 $0.00 $205,000.00 -$205,000.00 $5,814.13 $77,313.19 $77,313.19 $0.00 $0.00 14.29% -$13,769.87 $96,897.19 $96,897.19 $0.00 $0.00 24.49% -$329.87 $83,457.19 $83,457.19 $0.00 $0.00 17.49% $9,270.13 $73,857.19 $73,857.19 $0.00 $0.00 12.49% $16,105.33 $67,021.99 $67,021.99 $0.00 $0.00 8.93% $16,124.53 $67,002.79 $67,002.79 $0.00 $0.00 8.92% $16,105.33 $67,021.99 $67,021.99 $0.00 $0.00 8.93% $24,687.73 $58,439.59 $58,439.59 $0.00 $0.00 4.46% $33,250.93 $49,876.39 $49,876.39 $0.00 $0.00

-$495,980.94 -$198,392.37 -$572,588.56 $0.00 $572,588.56 $531,717.20 MARRAT = 10% PW AT = $0.00 GOAL SEEK SET CELL FW AT =

$0.00

AW AT =

$0.00

IRRAT =

10.00%

ERRAT =

10.00%

PROBLEM 10.45 a

SLN LOAN METHOD 1 BASIS $1,400,000.00 LOAN PRINC $600,000.00 BTCF EST SALV $200,000.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $200,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

PPMT -$600,000.00 $0.00 $0.00 $0.00 $0.00 $600,000.00 $0.00 $0.00 $0.00

IPMT

DWO

$66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $0.00 $0.00 $0.00

$150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 SUM DEPR $1,200,000.00 BOOK VALUE $200,000.00

SLN LOAN METHOD 2 BASIS $1,400,000.00 LOAN PRINC $600,000.00 BTCF EST SALV $200,000.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $200,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

PPMT -$600,000.00 $120,000.00 $120,000.00 $120,000.00 $120,000.00 $120,000.00 $0.00 $0.00 $0.00

IPMT

DWO

$66,000.00 $52,800.00 $39,600.00 $26,400.00 $13,200.00 $0.00 $0.00 $0.00

$150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 SUM DEPR $1,200,000.00 BOOK VALUE $200,000.00

SLN BASIS

LOAN METHOD 3 $1,400,000.00

LOAN PRINC

$600,000.00

BTCF

EST SALV RCVD SALV EOY 0 1 2 3 4 5 6 7 8

$200,000.00 $200,000.00 BT&LCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

LOAN PERIOD LOAN INT

5 11.00%

USEFUL LIFE PERIODS

PPMT -$600,000.00 $96,342.19 $106,939.83 $118,703.21 $131,760.56 $146,254.22 $0.00 $0.00 $0.00

IPMT

DWO

$66,000.00 $55,402.36 $43,638.98 $30,581.63 $16,087.96 $0.00 $0.00 $0.00

$150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 $150,000.00 SUM DEPR $1,200,000.00 BOOK VALUE $200,000.00

MACRS(5) LOAN METHOD 1 BASIS $1,400,000.00 LOAN PRINC $600,000.00 BTCF EST SALV $200,000.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $200,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

PPMT -$600,000.00 $0.00 $0.00 $0.00 $0.00 $600,000.00 $0.00 $0.00 $0.00

IPMT

DWO

$66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $0.00 $0.00 $0.00

$280,000.00 $448,000.00 $268,800.00 $161,280.00 $161,280.00 $80,640.00 $0.00 $0.00 SUM DEPR $1,400,000.00 BOOK VALUE $0.00

MACRS(5) LOAN METHOD 2 BASIS $1,400,000.00 LOAN PRINC $600,000.00 BTCF EST SALV $200,000.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $200,000.00 LOAN INT 11.00% PERIODS EOY

BT&LCF

PPMT

IPMT

DWO

0 1 2 3 4 5 6 7 8

-$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

-$600,000.00 $120,000.00 $120,000.00 $120,000.00 $120,000.00 $120,000.00 $0.00 $0.00 $0.00

$66,000.00 $52,800.00 $39,600.00 $26,400.00 $13,200.00 $0.00 $0.00 $0.00

$280,000.00 $448,000.00 $268,800.00 $161,280.00 $161,280.00 $80,640.00 $0.00 $0.00 SUM DEPR $1,400,000.00 BOOK VALUE $0.00

MACRS(5) LOAN METHOD 3 BASIS $1,400,000.00 LOAN PRINC $600,000.00 BTCF EST SALV $200,000.00 LOAN PERIOD 5 USEFUL LIFE RCVD SALV $200,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8

BT&LCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

PPMT -$600,000.00 $96,342.19 $106,939.83 $118,703.21 $131,760.56 $146,254.22 $0.00 $0.00 $0.00

IPMT

DWO

$66,000.00 $55,402.36 $43,638.98 $30,581.63 $16,087.96 $0.00 $0.00 $0.00

$280,000.00 $448,000.00 $268,800.00 $161,280.00 $161,280.00 $80,640.00 $0.00 $0.00 SUM DEPR $1,400,000.00 BOOK VALUE $0.00

$400,000.00 8 8

TAX RATE MARRAT

METHOD

40.00% 10.00% 1

ATCF ATCF+ ATCFATCF -$800,000.00 $0.00 $800,000.00 -$800,000.00 $184,000.00 $73,600.00 $260,400.00 $260,400.00 $0.00 $0.00 $184,000.00 $73,600.00 $260,400.00 $260,400.00 $0.00 $0.00 $184,000.00 $73,600.00 $260,400.00 $260,400.00 $0.00 $0.00 $184,000.00 $73,600.00 $260,400.00 $260,400.00 $0.00 $0.00 $184,000.00 $73,600.00 -$339,600.00 $0.00 $339,600.00 -$339,600.00 $250,000.00 $100,000.00 $300,000.00 $300,000.00 $0.00 $0.00 $250,000.00 $100,000.00 $300,000.00 $300,000.00 $0.00 $0.00 $250,000.00 $100,000.00 $500,000.00 $500,000.00 $0.00 $2,962,388.86 MARRAT = 10% PW AT = $371,111.39 FW AT = $795,510.21 AW AT = $69,562.61 IRRAT =

21.61%

ERRAT =

14.99%

$400,000.00 8 8

TAX RATE MARRAT

METHOD

40.00% 10.00% 2

ATCF ATCF+ ATCFATCF -$800,000.00 $0.00 $800,000.00 -$800,000.00 $184,000.00 $73,600.00 $140,400.00 $140,400.00 $0.00 $0.00 $197,200.00 $78,880.00 $148,320.00 $148,320.00 $0.00 $0.00 $210,400.00 $84,160.00 $156,240.00 $156,240.00 $0.00 $0.00 $223,600.00 $89,440.00 $164,160.00 $164,160.00 $0.00 $0.00 $236,800.00 $94,720.00 $172,080.00 $172,080.00 $0.00 $0.00 $250,000.00 $100,000.00 $300,000.00 $300,000.00 $0.00 $0.00 $250,000.00 $100,000.00 $300,000.00 $300,000.00 $0.00 $0.00 $250,000.00 $100,000.00 $500,000.00 $500,000.00 $0.00 $2,450,369.03 MARRAT = 10% PW AT = $343,115.24 FW AT = $735,497.98 AW AT = $64,314.90

$400,000.00

IRRAT =

18.61%

ERRAT =

15.02%

TAX RATE

40.00%

MARRAT

8 8

METHOD

10.00% 3

ATCF ATCF+ ATCFATCF -$800,000.00 $0.00 $800,000.00 -$800,000.00 $184,000.00 $73,600.00 $164,057.81 $164,057.81 $0.00 $0.00 $194,597.64 $77,839.06 $159,818.76 $159,818.76 $0.00 $0.00 $206,361.02 $82,544.41 $155,113.41 $155,113.41 $0.00 $0.00 $219,418.37 $87,767.35 $149,890.46 $149,890.46 $0.00 $0.00 $233,912.04 $93,564.81 $144,093.00 $144,093.00 $0.00 $0.00 $250,000.00 $100,000.00 $300,000.00 $300,000.00 $0.00 $0.00 $250,000.00 $100,000.00 $300,000.00 $300,000.00 $0.00 $0.00 $250,000.00 $100,000.00 $500,000.00 $500,000.00 $0.00 $2,456,885.05 MARRAT = 10% PW AT = $346,155.01 FW AT = $742,014.00 AW AT =

$64,884.69

IRRAT =

18.89%

ERRAT =

15.06%

$400,000.00 8 8

TAX RATE MARRAT

METHOD

40.00% 10.00% 1

ATCF ATCF+ ATCFATCF MACRS(5) -$800,000.00 $0.00 $800,000.00 -$800,000.00 $54,000.00 $21,600.00 $312,400.00 $312,400.00 $0.00 $0.00 20.00% -$114,000.00 -$45,600.00 $379,600.00 $379,600.00 $0.00 $0.00 32.00% $65,200.00 $26,080.00 $307,920.00 $307,920.00 $0.00 $0.00 19.20% $172,720.00 $69,088.00 $264,912.00 $264,912.00 $0.00 $0.00 11.52% $172,720.00 $69,088.00 -$335,088.00 $0.00 $335,088.00 -$335,088.00 11.52% $319,360.00 $127,744.00 $272,256.00 $272,256.00 $0.00 $0.00 5.76% $400,000.00 $160,000.00 $240,000.00 $240,000.00 $0.00 $0.00 $600,000.00 $240,000.00 $360,000.00 $360,000.00 $0.00 $3,118,459.44 MARRAT = 10% PW AT = $446,721.06 FW AT = $957,586.26 AW AT =

$83,735.19

IRRAT =

26.72%

ERRAT =

15.86%

$400,000.00 8 8

TAX RATE MARRAT METHOD

40.00% 10.00% 2

ATCF

ATCF+

ATCF-

ATCF

MACRS(5)

$54,000.00 $21,600.00 -$100,800.00 -$40,320.00 $91,600.00 $36,640.00 $212,320.00 $84,928.00 $225,520.00 $90,208.00 $319,360.00 $127,744.00 $400,000.00 $160,000.00 $600,000.00 $240,000.00 MARRAT =

-$800,000.00 $0.00 $800,000.00 -$800,000.00 $192,400.00 $192,400.00 $0.00 $0.00 $267,520.00 $267,520.00 $0.00 $0.00 $203,760.00 $203,760.00 $0.00 $0.00 $168,672.00 $168,672.00 $0.00 $0.00 $176,592.00 $176,592.00 $0.00 $0.00 $272,256.00 $272,256.00 $0.00 $0.00 $240,000.00 $240,000.00 $0.00 $0.00 $360,000.00 $360,000.00 $0.00 $2,612,445.07 10%

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

PW AT = $418,724.91 FW AT = $897,574.03 AW AT =

$78,487.48

IRRAT =

22.28%

ERRAT =

15.94%

$400,000.00 8 8

TAX RATE MARRAT

METHOD

40.00% 10.00% 3

ATCF ATCF+ ATCFATCF MACRS(5) -$800,000.00 $0.00 $800,000.00 -$800,000.00 $54,000.00 $21,600.00 $216,057.81 $216,057.81 $0.00 $0.00 20.00% -$103,402.36 -$41,360.94 $279,018.76 $279,018.76 $0.00 $0.00 32.00% $87,561.02 $35,024.41 $202,633.41 $202,633.41 $0.00 $0.00 19.20% $208,138.37 $83,255.35 $154,402.46 $154,402.46 $0.00 $0.00 11.52% $222,632.04 $89,052.81 $148,605.00 $148,605.00 $0.00 $0.00 11.52% $319,360.00 $127,744.00 $272,256.00 $272,256.00 $0.00 $0.00 5.76% $400,000.00 $160,000.00 $240,000.00 $240,000.00 $0.00 $0.00 $600,000.00 $240,000.00 $360,000.00 $360,000.00 $0.00 $2,618,961.10 MARRAT = 10% PW AT = $421,764.68 FW AT = $904,090.05 AW AT = $79,057.27 IRRAT =

22.69%

ERRAT =

15.98%

PROBLEM 10.46 a

SLN LOAN METHOD 1 BASIS $3,000,000.00 LOAN PRINC $1,500,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 8 USEFUL LIFE RCVD SALV $550,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF PPMT -$3,000,000.00 -$1,500,000.00 $500,000.00 $0.00 $512,000.00 $0.00 $524,288.00 $0.00 $536,870.91 $0.00 $549,755.81 $0.00 $562,949.95 $0.00 $576,460.75 $0.00 $590,295.81 $1,500,000.00 $604,462.91 $0.00 $1,168,970.02 $0.00

IPMT

DWO

$165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $0.00 $0.00

$91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 SUM DEPR $916,666.67 BOOK VALUE $2,083,333.33

SLN LOAN METHOD 2 BASIS $3,000,000.00 LOAN PRINC $1,500,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 8 USEFUL LIFE RCVD SALV $550,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF PPMT -$3,000,000.00 -$1,500,000.00 $500,000.00 $187,500.00 $512,000.00 $187,500.00 $524,288.00 $187,500.00 $536,870.91 $187,500.00 $549,755.81 $187,500.00 $562,949.95 $187,500.00 $576,460.75 $187,500.00 $590,295.81 $187,500.00 $604,462.91 $0.00 $1,168,970.02 $0.00

IPMT

DWO

$165,000.00 $144,375.00 $123,750.00 $103,125.00 $82,500.00 $61,875.00 $41,250.00 $20,625.00 $0.00 $0.00

$91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 SUM DEPR $916,666.67 BOOK VALUE $2,083,333.33

SLN LOAN METHOD 3 BASIS $3,000,000.00 LOAN PRINC $1,500,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 8 USEFUL LIFE RCVD SALV $550,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF PPMT -$3,000,000.00 -$1,500,000.00 $500,000.00 $126,481.58 $512,000.00 $140,394.56 $524,288.00 $155,837.96 $536,870.91 $172,980.13 $549,755.81 $192,007.95 $562,949.95 $213,128.82 $576,460.75 $236,572.99 $590,295.81 $262,596.02 $604,462.91 $0.00 $1,168,970.02 $0.00

IPMT

DWO

$165,000.00 $151,087.03 $135,643.62 $118,501.45 $99,473.64 $78,352.76 $54,908.59 $28,885.56 $0.00 $0.00

$91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 $91,666.67 SUM DEPR $916,666.67 BOOK VALUE $2,083,333.33

MACRS(20) LOAN METHOD 1 BASIS $3,000,000.00 LOAN PRINC $1,500,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 8 USEFUL LIFE RCVD SALV $550,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8 9 10

IPMT

DWO

$165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $165,000.00 $0.00 $0.00

$112,500.00 $216,570.00 $200,310.00 $185,310.00 $171,390.00 $158,550.00 $146,640.00 $135,660.00 $133,860.00 $66,915.00 SUM DEPR $1,527,705.00 BOOK VALUE $1,472,295.00

MACRS(20) LOAN METHOD 2 BASIS $3,000,000.00 LOAN PRINC $1,500,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 8 USEFUL LIFE RCVD SALV $550,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8 9 10

IPMT

DWO

$165,000.00 $144,375.00 $123,750.00 $103,125.00 $82,500.00 $61,875.00 $41,250.00 $20,625.00 $0.00 $0.00

$112,500.00 $216,570.00 $200,310.00 $185,310.00 $171,390.00 $158,550.00 $146,640.00 $135,660.00 $133,860.00 $66,915.00 SUM DEPR $1,527,705.00 BOOK VALUE $1,472,295.00

MACRS(20) LOAN METHOD 3 BASIS $3,000,000.00 LOAN PRINC $1,500,000.00 BTCF EST SALV $250,000.00 LOAN PERIOD 8 USEFUL LIFE RCVD SALV $550,000.00 LOAN INT 11.00% PERIODS EOY 0 1 2 3 4 5 6 7 8 9 10

IPMT

DWO

$165,000.00 $151,087.03 $135,643.62 $118,501.45 $99,473.64 $78,352.76 $54,908.59 $28,885.56 $0.00 $0.00

$112,500.00 $216,570.00 $200,310.00 $185,310.00 $171,390.00 $158,550.00 $146,640.00 $135,660.00 $133,860.00 $66,915.00 SUM DEPR $1,527,705.00 BOOK VALUE $1,472,295.00

$500,000.00 30 10

TAX RATE MARRAT

METHOD

$243,333.33 $97,333.33 $255,333.33 $102,133.33 $267,621.33 $107,048.53 $280,204.25 $112,081.70 $293,089.15 $117,235.66 $306,283.29 $122,513.31 $319,794.09 $127,917.63 $333,629.14 $133,451.66 $512,796.24 $205,118.50 -$1,006,029.98 -$402,411.99 MARRAT =

40.00% 9.00% 1 ATCF ATCF+ ATCFATCF -$1,500,000.00 $0.00 $1,500,000.00 -$1,500,000.00 $237,666.67 $237,666.67 $0.00 $0.00 $244,866.67 $244,866.67 $0.00 $0.00 $252,239.47 $252,239.47 $0.00 $0.00 $259,789.21 $259,789.21 $0.00 $0.00 $267,520.15 $267,520.15 $0.00 $0.00 $275,436.64 $275,436.64 $0.00 $0.00 $283,543.12 $283,543.12 $0.00 $0.00 -$1,208,155.85 $0.00 $1,208,155.85 -$1,208,155.85 $399,344.41 $399,344.41 $0.00 $0.00 $1,571,382.01 $1,571,382.01 $0.00 $5,075,173.14 9%

PW AT =

$37,475.30

FW AT =

$88,717.66

AW AT =

$5,839.40

IRRAT =

9.50%

ERRAT =

9.25%

$500,000.00 30 10

TAX RATE MARRAT

METHOD

$243,333.33 $97,333.33 $275,958.33 $110,383.33 $308,871.33 $123,548.53 $342,079.25 $136,831.70 $375,589.15 $150,235.66 $409,408.29 $163,763.31 $443,544.09 $177,417.63 $478,004.14 $191,201.66 $512,796.24 $205,118.50 -$1,006,029.98 -$402,411.99 MARRAT =

40.00% 9.00% 2 ATCF ATCF+ ATCFATCF -$1,500,000.00 $0.00 $1,500,000.00 -$1,500,000.00 $50,166.67 $50,166.67 $0.00 $0.00 $69,741.67 $69,741.67 $0.00 $0.00 $89,489.47 $89,489.47 $0.00 $0.00 $109,414.21 $109,414.21 $0.00 $0.00 $129,520.15 $129,520.15 $0.00 $0.00 $149,811.64 $149,811.64 $0.00 $0.00 $170,293.12 $170,293.12 $0.00 $0.00 $190,969.15 $190,969.15 $0.00 $0.00 $399,344.41 $399,344.41 $0.00 $0.00 $1,571,382.01 $1,571,382.01 $0.00 $3,459,856.69 9%

PW AT =

-$38,519.14

FW AT =

-$91,188.82

AW AT =

-$6,002.06

IRRAT =

8.64%

ERRAT =

8.72%

$500,000.00 30 10

TAX RATE MARRAT

METHOD

$243,333.33 $97,333.33 $269,246.31 $107,698.52 $296,977.71 $118,791.08 $326,702.80 $130,681.12 $358,615.51 $143,446.20 $392,930.53 $157,172.21 $429,885.49 $171,954.20 $469,743.58 $187,897.43 $512,796.24 $205,118.50 -$1,006,029.98 -$402,411.99 MARRAT =

40.00% 9.00% 3 ATCF ATCF+ ATCFATCF -$1,500,000.00 $0.00 $1,500,000.00 -$1,500,000.00 $111,185.09 $111,185.09 $0.00 $0.00 $112,819.90 $112,819.90 $0.00 $0.00 $114,015.34 $114,015.34 $0.00 $0.00 $114,708.21 $114,708.21 $0.00 $0.00 $114,828.03 $114,828.03 $0.00 $0.00 $114,296.16 $114,296.16 $0.00 $0.00 $113,024.97 $113,024.97 $0.00 $0.00 $110,916.80 $110,916.80 $0.00 $0.00 $399,344.41 $399,344.41 $0.00 $0.00 $1,571,382.01 $1,571,382.01 $0.00 $3,489,918.30 9%

PW AT =

-$25,820.80

FW AT =

-$61,127.21

AW AT =

-$4,023.40

IRRAT =

8.74%

ERRAT =

8.81%

$500,000.00 30 10

TAX RATE MARRAT

METHOD

$222,500.00 $89,000.00 $130,430.00 $52,172.00 $158,978.00 $63,591.20 $186,560.91 $74,624.36 $213,365.81 $85,346.33 $239,399.95 $95,759.98 $264,820.75 $105,928.30 $289,635.81 $115,854.32 $470,602.91 $188,241.16 -$370,239.98 -$148,095.99 MARRAT =

40.00% 9.00% 1 ATCF ATCF+ ATCFATCF MACRS(20) -$1,500,000.00 $0.00 $1,500,000.00 -$1,500,000.00 $246,000.00 $246,000.00 $0.00 $0.00 3.750% $294,828.00 $294,828.00 $0.00 $0.00 7.219% $295,696.80 $295,696.80 $0.00 $0.00 6.677% $297,246.55 $297,246.55 $0.00 $0.00 6.177% $299,409.49 $299,409.49 $0.00 $0.00 5.713% $302,189.97 $302,189.97 $0.00 $0.00 5.285% $305,532.45 $305,532.45 $0.00 $0.00 4.888% -$1,190,558.51 $0.00 $1,190,558.51 -$1,190,558.51 4.522% $416,221.75 $416,221.75 $0.00 $0.00 4.462% $1,317,066.01 $1,317,066.01 $0.00 $5,214,472.06 2.231% 9%

PW AT =

$105,148.18

FW AT =

$248,923.98

AW AT =

$16,384.20

IRRAT =

10.52%

ERRAT =

9.69%

$500,000.00 30 10

TAX RATE MARRAT

METHOD

$222,500.00 $89,000.00 $151,055.00 $60,422.00 $200,228.00 $80,091.20 $248,435.91 $99,374.36 $295,865.81 $118,346.33 $342,524.95 $137,009.98 $388,570.75 $155,428.30 $434,010.81 $173,604.32 $470,602.91 $188,241.16 -$370,239.98 -$148,095.99 MARRAT =

40.00% 9.00% 2 ATCF ATCF+ ATCFATCF MACRS(20) -$1,500,000.00 $0.00 $1,500,000.00 -$1,500,000.00 $58,500.00 $58,500.00 $0.00 $0.00 3.750% $119,703.00 $119,703.00 $0.00 $0.00 7.219% $132,946.80 $132,946.80 $0.00 $0.00 6.677% $146,871.55 $146,871.55 $0.00 $0.00 6.177% $161,409.49 $161,409.49 $0.00 $0.00 5.713% $176,564.97 $176,564.97 $0.00 $0.00 5.285% $192,282.45 $192,282.45 $0.00 $0.00 4.888% $208,566.49 $208,566.49 $0.00 $0.00 4.522% $416,221.75 $416,221.75 $0.00 $0.00 4.462% $1,317,066.01 $1,317,066.01 $0.00 $3,620,063.00 2.231% 9%

PW AT =

$29,153.73

FW AT =

$69,017.49

AW AT =

$4,542.74

IRRAT =

9.29%

ERRAT =

9.21%

$500,000.00 30 10

TAX RATE MARRAT

METHOD

$222,500.00 $89,000.00 $144,342.97 $57,737.19 $188,334.38 $75,333.75 $233,059.46 $93,223.78 $278,892.18 $111,556.87 $326,047.19 $130,418.88 $374,912.16 $149,964.86 $425,750.25 $170,300.10 $470,602.91 $188,241.16 -$370,239.98 -$148,095.99 MARRAT =

40.00% 9.00% 3 ATCF ATCF+ ATCFATCF MACRS(20) -$1,500,000.00 $0.00 $1,500,000.00 -$1,500,000.00 $119,518.42 $119,518.42 $0.00 $0.00 3.750% $162,781.23 $162,781.23 $0.00 $0.00 7.219% $157,472.67 $157,472.67 $0.00 $0.00 6.677% $152,165.55 $152,165.55 $0.00 $0.00 6.177% $146,717.36 $146,717.36 $0.00 $0.00 5.713% $141,049.50 $141,049.50 $0.00 $0.00 5.285% $135,014.31 $135,014.31 $0.00 $0.00 4.888% $128,514.13 $128,514.13 $0.00 $0.00 4.522% $416,221.75 $416,221.75 $0.00 $0.00 4.462% $1,317,066.01 $1,317,066.01 $0.00 $3,650,124.61 2.231% 9%

PW AT =

$41,852.08

FW AT =

$99,079.10

AW AT =

$6,521.40

IRRAT =

9.44%

ERRAT =

9.30%

PROBLEM 10.47 a

AS SHOWN

MARR=

12.00%

LOAN RATE=

7.00%

PROP CLASS=

MACRS(5)

TAX RATE=

36.00%

BASIS EST SALV RCVD SALV EOY 0 1 2 3 4

$180,000.00 LOAN PRINC $30,000.00 LOAN PERIOD $30,000.00 LOAN INT BT&LCF -$180,000.00 $40,000.00 $40,000.00 $40,000.00 $70,000.00

$70,000.00 6 7.00%

PPMT PRINC REMAIN -$70,000.00 $70,000.00 $9,785.71 $60,214.29 $10,470.71 $49,743.59 $11,203.65 $38,539.93 $38,539.93 $0.00 SUM LOAN $0.00

BTCF USEFUL LIFE PERIODS IPMT $4,900.00 $4,215.00 $3,482.05 $2,697.80

$40,000.00 4 4

TAX RATE MARRAT METHOD

36.00% 12.00% 3

DWO

BOOK VALUE TI T ATCF PWATCF ATCF+ $180,000.00 -$110,000.00 -$110,000.00 $0.00 $36,000.00 $144,000.00 -$900.00 -$324.00 $25,638.29 $22,891.33 $25,638.29 $57,600.00 $86,400.00 -$21,815.00 -$7,853.40 $33,167.69 $26,441.08 $33,167.69 $34,560.00 $51,840.00 $1,957.95 $704.86 $24,609.43 $17,516.51 $24,609.43 $10,368.00 $41,472.00 $15,462.20 $5,566.39 $23,195.88 $14,741.40 $23,195.88 MARRAT = SUM DEPR 12% PW AT = -$28,409.67 -$28,409.67 $138,528.00 BOOK VALUE

FW AT =

-$44,703.17

$41,472.00

AW AT =

-$9,353.44

IRRAT =

-1.28%

ERRAT =

3.94%

ERRAT =

ATCFATCF MACRS(5) $110,000.00 -$110,000.00 $0.00 $0.00 20.00% $0.00 $0.00 32.00% $0.00 $0.00 19.20% $0.00 $128,383.96 5.76%

PROBLEM 10.48 a

PROP CLASS=

MACRS(7)

MARR=

12.00%

SALV VAL=

$5,000.00

LOAN INT=

15.00%

AS SHOWN

NOTE DIFFERENT FORMAT AND NOTATION FOR PRACTICE

BASIS EST SALV RCVD SALV

$90,000.00 LOAN PRINC $5,000.00 LOAN PERIOD $5,000.00 LOAN INT

EOY 0 1 2 3

BT&LCF -$90,000.00 $35,000.00 $35,000.00 $40,000.00

$30,000.00 3 15.00%

PPMT PRINC REMAIN -$30,000.00 $30,000.00 $8,639.31 $21,360.69 $9,935.21 $11,425.49 $11,425.49 $0.00 SUM LOAN $0.00

BTCF USEFUL LIFE PERIODS IPMT $4,500.00 $3,204.10 $1,713.82

R PRACTICE

$35,000.00 10 3

TAX RATE MARRAT METHOD

42.00% 12.00% 3

DWO

BOOK VALUE TI T ATCF PWATCF ATCF+ ATCF$90,000.00 -$60,000.00 -$60,000.00 $0.00 $60,000.00 $12,861.00 $77,139.00 $17,639.00 $7,408.38 $14,452.31 $12,903.85 $14,452.31 $0.00 $22,041.00 $55,098.00 $9,754.90 $4,097.06 $17,763.63 $14,161.06 $17,763.63 $0.00 $7,870.50 $47,227.50 -$16,811.82 -$7,060.97 $33,921.66 $24,144.77 $33,921.66 $0.00 MARRAT = SUM DEPR 12% $42,772.50 BOOK VALUE $47,227.50

PW AT =

-$8,790.32

FW AT = -$12,349.77 AW AT =

-$3,659.84

IRRAT =

4.36%

ERRAT =

6.24%

ATCF MACRS(7) -$60,000.00 $0.00 14.290% $0.00 24.490% $71,945.91 8.745%

PROBLEM 10.49

THE MODIGLIANI-MILLER THEOREM (OF FRANCO MODIGLIANI, MERTON MILLER) FORMS THE BASIS FOR

THE BASIC THEOREM STATES THAT, IN THE ABSENCE OF TAXES, BANKRUPTCY COSTS, AND ASYMMET THE VALUE OF A FIRM IS UNAFFECTED BY HOW THAT FIRM IS FINANCED. IT DOES NOT MATTER IF THE BY ISSUING STOCK OR SELLING DEBT. IT DOES NOT MATTER WHAT THE FIRM'S DIVIDEND POLICY IS. MUCH MORE IS AVAILABLE AT THE WIKI SITE.

MILLER) FORMS THE BASIS FOR MODERN THINKING ON CAPITAL STRUCTURE.

KRUPTCY COSTS, AND ASYMMETRIC INFORMATION, AND IN AN EFFICIENT MARKET,

PROBLEM 10.50 a

ONLY PART a IS SHOWN. THESE WILL CHANGE SEVERAL TIMES PER YEAR

1,157,000/15,935

FOR THE THIRD COLUMN: LONG TERM DEBT / STOCKHOLDER EQUITY =

1,157,000/15,935,000=

7.26%

PROBLEM 10.51 a

AFTER-TAX AW= -$16,220.44 INV TAX CREDIT BASIS $70,000.00 EST SALV $3,000.00 RCVD SALV $3,000.00 EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

BTCF USEFUL PERIODS

-$18,000.00 16 16

TAX RATE MARRAT =

DWO

$6,650.00 $11,970.00 $9,576.00 $7,660.80 $6,131.30 $4,901.05 $4,355.75 $4,355.75 $4,362.40 $4,355.75 $2,181.20 $0.00 $0.00 $0.00 $0.00 $0.00 SUM DEPR

-$24,650.00 -$9,860.00 -$29,970.00 -$11,988.00 -$27,576.00 -$11,030.40 -$25,660.80 -$10,264.32 -$24,131.30 -$9,652.52 -$22,901.05 -$9,160.42 -$22,355.75 -$8,942.30 -$22,355.75 -$8,942.30 -$22,362.40 -$8,944.96 -$22,355.75 -$8,942.30 -$20,181.20 -$8,072.48 -$18,000.00 -$7,200.00 -$18,000.00 -$7,200.00 -$18,000.00 -$7,200.00 -$18,000.00 -$7,200.00 -$15,000.00 -$6,000.00 MARRAT =

$66,500.00

PW AT =

BOOK VALUE

FW AT =

$0.00

AW AT =

AFTER-TAX AW= -$16,076.18 SECTION 179 BASIS EST SALV RCVD SALV EOY 0 1 2 3 4 5 6 7 8 9

$70,000.00 $3,000.00 $3,000.00 BTCF SECTION 179 -$70,000.00 -$18,000.00 $70,000.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00

BTCF USEFUL PERIODS

-$18,000.00 16 16

DWO

$0.00 -$88,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00

10 11 12 13 14 15 16

-$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$18,000.00 -$15,000.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 SUM 179 $70,000.00

$0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$18,000.00 $0.00 -$15,000.00 SUM DEPR $0.00 BOOK VALUE $0.00

40.00% 9.00%

ITC $7,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

ATCF MACRS(10) -$70,000.00 -$1,140.00 10.00% -$6,012.00 18.00% -$6,969.60 14.40% -$7,735.68 11.52% -$8,347.48 9.22% -$8,839.58 7.37% -$9,057.70 6.55% -$9,057.70 6.55% -$9,055.04 6.56% -$9,057.70 6.55% -$9,927.52 3.28% -$10,800.00 -$10,800.00 -$10,800.00 -$10,800.00 -$9,000.00 9% -$134,833.39 -$535,329.79 -$16,220.44

TAX RATE MARRAT = SECTION 179 T -$35,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00

40.00% 9.00% $70,000.00 ATCF MACRS(10) -$70,000.00 $17,200.00 10.00% -$10,800.00 18.00% -$10,800.00 14.40% -$10,800.00 11.52% -$10,800.00 9.22% -$10,800.00 7.37% -$10,800.00 6.55% -$10,800.00 6.55% -$10,800.00 6.56%

-$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$7,200.00 -$6,000.00 MARRAT =

-$10,800.00 -$10,800.00 -$10,800.00 -$10,800.00 -$10,800.00 -$10,800.00 -$9,000.00 9%

PW AT = -$133,634.19 FW AT = -$530,568.61 AW AT =

-$16,076.18

6.55% 3.28%

PROBLEM 10.52 a

O&M COST=

INV TAX CREDIT BASIS $960,000.00 EST SALV $0.00 RCVD SALV $0.00 EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$960,000.00 $139,667.03 $139,667.03 $139,667.03 $139,667.03 $139,667.03 $139,667.03 $139,667.03 $139,667.03 $139,667.03 $139,667.03

$600,000-BTCF= $460,332.97

LOAN PRINC LOAN PERIOD LOAN INT PPMT -$550,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $550,000.00

$550,000.00 10 12.00%

BTCF USEFUL LIFE PERIODS

IPMT

DWO

$66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00

$130,324.80 $223,348.80 $159,508.80 $113,908.80 $81,441.60 $81,350.40 $81,441.60 $40,675.20 $0.00 $0.00 SUM DEPR $912,000.00 BOOK VALUE $0.00

O&M COST=

$600,000-BTCF= $442,250.38

BASIS EST SALV RCVD SALV

$960,000.00 $0.00 $0.00

LOAN PRINC LOAN PERIOD LOAN INT

EOY 0 1 2 3 4 5 6 7 8 9 10

BT&LCF -$960,000.00 $157,749.62 $157,749.62 $157,749.62 $157,749.62 $157,749.62 $157,749.62 $157,749.62 $157,749.62 $157,749.62 $157,749.62

PPMT -$550,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $550,000.00

$550,000.00 10 12.00%

BTCF USEFUL LIFE PERIODS

IPMT

SECTION 179

$66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00 $66,000.00

$90,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$139,667.03 10 10 TI -$56,657.77 -$149,681.77 -$85,841.77 -$40,241.77 -$7,774.57 -$7,683.37 -$7,774.57 $32,991.83 $73,667.03 $73,667.03

$157,749.62 10 10 DWO

GOAL SEEK CHANGED CELL

METHOD T

ITC

-$22,663.11 $96,000.00 -$59,872.71 $0.00 -$34,336.71 $0.00 -$16,096.71 $0.00 -$3,109.83 $0.00 -$3,073.35 $0.00 -$3,109.83 $0.00 $13,196.73 $0.00 $29,466.81 $0.00 $29,466.81 $0.00 MARRAT =

$0.00 GOAL SEEK SET CELL

FW AT =

$0.00

AW AT =

$0.00

IRRAT =

10.00%

ERRAT =

10.00%

TAX RATE MARRAT METHOD

PW AT =

SAVINGS/YR

ATCF ATCF+ ATCFATCF -$410,000.00 $0.00 $410,000.00 -$410,000.00 $192,330.14 $192,330.14 $0.00 $0.00 $133,539.74 $133,539.74 $0.00 $0.00 $108,003.74 $108,003.74 $0.00 $0.00 $89,763.74 $89,763.74 $0.00 $0.00 $76,776.86 $76,776.86 $0.00 $0.00 $76,740.38 $76,740.38 $0.00 $0.00 $76,776.86 $76,776.86 $0.00 $0.00 $60,470.30 $60,470.30 $0.00 $0.00 $44,200.22 $44,200.22 $0.00 $0.00 -$505,799.78 $0.00 $505,799.78 $1,063,434.41 10%

GOAL SEEK CHANGED CELL

40.00% 10.00% 1

PW AT =

$124,323.00 -$122,573.38 -$49,029.35 $213,063.00 -$121,313.38 -$48,525.35 $152,163.00 -$60,413.38 -$24,165.35 $108,663.00 -$16,913.38 -$6,765.35 $77,691.00 $14,058.62 $5,623.45 $77,604.00 $14,145.62 $5,658.25 $77,691.00 $14,058.62 $5,623.45 $38,802.00 $52,947.62 $21,179.05 $0.00 $91,749.62 $36,699.85 $0.00 $91,749.62 $36,699.85 MARRAT = SUM DEPR $870,000.00

TAX RATE MARRAT

40.00% 10.00% 1

SAVINGS SECTION 179

ATCF ATCF+ ATCFATCF -$410,000.00 $0.00 $410,000.00 -$410,000.00 $140,778.97 $140,778.97 $0.00 $0.00 $140,274.97 $140,274.97 $0.00 $0.00 $115,914.97 $115,914.97 $0.00 $0.00 $98,514.97 $98,514.97 $0.00 $0.00 $86,126.17 $86,126.17 $0.00 $0.00 $86,091.37 $86,091.37 $0.00 $0.00 $86,126.17 $86,126.17 $0.00 $0.00 $70,570.57 $70,570.57 $0.00 $0.00 $55,049.77 $55,049.77 $0.00 $0.00 -$494,950.23 $0.00 $494,950.23 $1,063,434.41 10% $0.00 GOAL SEEK SET CELL

BOOK VALUE

FW AT =

$0.00

AW AT =

$0.00

IRRAT =

10.00%

ERRAT =

10.00%

$600,000.00

MACRS(7) 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

$600,000.00 $90,000.00

MACRS(7) 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

Modified ACRS Rates - GDS MACRS CL ADR %

3-YR <=4 200%

5-YR 7-YR 10-YR 15-YR >4 to <10 >=10 to <16 .=16 to <20 >=20 to <25 200% 200% 200% 150%

20-YR >=25 150%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

33.33% 44.45% 14.81% 7.41%

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

5.00% 9.50% 8.55% 7.70% 6.93% 6.23% 5.90% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91% 2.95%

3.750% 7.219% 6.677% 6.177% 5.713% 5.285% 4.888% 4.522% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 2.231%

SUM

100.00% 100.00%

100.00%

100.000%

PROBLEM 11.1

CONSIDER A 4 YEAR OLD NOTEBOOK COMPUTER WITH A PENTIUM 4, 512 MEGS OF RAM, AND A 4 a

REASONS TO CONSIDER REPLACING 1 HARD DRIVE IS OF MARGINAL SIZE FOR TODAY'S FILES 2 MEMORY IS NOT ALWAYS SUFFICIENT 3 DISPLAYS ARE MUCH MORE CLEAR TODAY 4 WI-FI NOT BUILT IN 5 CANNOT BURN DVD 6 HAVING TO MAKE MINOR REPLACEMENTS (BATTERY, CHARGER, ETC.)

DELL NOTEBOOK COMPUTER ($2090) WITH 160 GIG HARD DRIVE 3 GIG SHARED DUAL CHANNEL MEMORY AT 667 MHZ HIGH RES SCREEN 1920x1200 GLOSSY WI-FI BUILT IN CD/DVD BURNER DELL NOTEBOOK COMPUTER ($1270) WITH 160 GIG HARD DRIVE 3 GIG SHARED DUAL CHANNEL MEMORY AT 667 MHZ WUXGA LCD DISPLAY WITH TRUE LIFE WI-FI BUILT IN CD/DVD BURNER THESE ARE PRELIMINARY LOOKS AT FEATURES. LARGE PRICE DIFFERENCE!

4, 512 MEGS OF RAM, AND A 40 GIG HARD DRIVE

PROBLEM 11.2 1

FUNCTIONAL OBSOLESCENCE A. A DISHWASHER THAT LASTED 22 YEARS, WEARING OUT SOME PARTS THAT WERE NO L B. A 1992 SATURN AUTOMOBILE WITH OVER 220,000 MILES (CHANGING OIL EVERY 3000 MI TO WEAR IN MANY PLACES AND CANNOT MEET ALL OF THE NEW ENVIRONME C. COAXIAL CABLE USED TO WIRE A HOUSE FROM A CENTRAL HUB - COAX DEGRADES AN

TECHNOLOGICAL OBSOLESCENCE A. A COUPLE OF PERSONAL COMPUTERS THAT STILL WORK WELL, BUT LACK IN SPEED, M AS WELL AS USB, FIREWIRE, AND CARD READER PORTS B. A TELEVISION THAT LACKS THE HIGH DEFINITION CAPABILITY C. COAXIAL CABLE USED TO WIRE A HOUSE FROM A CENTRAL HUB - NEWER CABLE HAS F EVEN WHEN THE OLD CABLE WAS NEW

ECONOMIC OBSOLESCENCE A. AN AIR CONDITIONER THAT STILL WORKS WELL, AND YET IS LESS THAN HALF AS EFFIC B. INCANDESCENT LIGHTING THAT IS OFTEN MORE COSTLY AND RELATIVELY DARK COMP EFFICIENT VARIETIES OF BULBS

SOME PARTS THAT WERE NO LONGER AVAILABLE FOR REPAIR CHANGING OIL EVERY 3000 MILES IS THE KEY) THAT IS STARTING

RAL HUB - COAX DEGRADES AND DEVELOPS LOSSES OVER TIME

K WELL, BUT LACK IN SPEED, MEMORY, HARD DRIVE CAPACITY,

RAL HUB - NEWER CABLE HAS FAR LESS LOSS THAN OLD CABLE,

T IS LESS THAN HALF AS EFFICIENT AS NEW AIR CONDITIONERS Y AND RELATIVELY DARK COMPARED TO NEW AND ECONOMICALLY

PROBLEM 11.3

REASONS WHY FAMILIES USE EQUIPMENT LONG AFTER IT WOULD BE ECONOMICALLY JUSTIFIED 1

REPLACING A COMPUTER IS SOMETIMES PUT OFF DUE TO THE HASSLE OF LEARNING A NEW OPE WANTING TO LET THE NEW OPERATING SYSTEM INCLUDE THE NUMEROUS FIXES NEEDED, TRAN RELOADING OF APPLICATIONS. (REASONS 2, 3, AND 9)

REPLACING A VERY INEFFICIENT HOME HEATER DUE TO THE NEED FOR A SUBSTANTIAL OUTLAY ONE TIME, ESPECIALLY IF MOVING TO A NEW HOME WITHIN A FEW YEARS IS ANTICIPATED. (REAS

REPLACING A TELEVISION AT A TIME WHEN THE HD PROTOCOL IS IN MANY FORMS, WITH NO ABS STANDARD. THIS IS A CASE OF "WAIT UNTIL NEXT YEAR AND THE TECHNOLOGY WILL BE EVEN M COSTS WILL BE LOWER." (REASONS 4 AND 8)

BE ECONOMICALLY JUSTIFIED TO REPLACE IT

SSLE OF LEARNING A NEW OPERATING SYSTEM, MEROUS FIXES NEEDED, TRANSFER OF DATA,

D FOR A SUBSTANTIAL OUTLAY OF MONEY ALL AT YEARS IS ANTICIPATED. (REASONS 2 AND 5)

IN MANY FORMS, WITH NO ABSOLUTE COMMON TECHNOLOGY WILL BE EVEN MORE PROVEN AND

PROBLEM 11.4 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING PAINTING MACHINE MARKET VALUE = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = REMAINING LIFE = MARR =

$40,000.00 $350,000.00 $0.00 10 20.00%

EUAC=350000=

$350,000.00

EOY CF EXISTING 0 $0.00 1 -$350,000.00 2 -$350,000.00 3 -$350,000.00 4 -$350,000.00 5 -$350,000.00 6 -$350,000.00 7 -$350,000.00 8 -$350,000.00 9 -$350,000.00 10 -$350,000.00 PW= -$1,467,365.23 EUAC= $350,000.00

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING PAINTING MACHINE MARKET VALUE = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = REMAINING LIFE = MARR =

$40,000.00 $350,000.00 $0.00 10 20.00%

EUAC=40000(A|P 20%,10)+350000= EUAC=40000(0.23852)+350000=

$359,540.80

EOY CF EXISTING 0 -$40,000.00

1 2 3 4 5 6 7 8 9 10

-$350,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$350,000.00

PW= -$1,507,365.23 EUAC= $359,540.91

REPLACE WITH NEW PAINTING MACHINE FIRST COST = ANNUAL O&M COST = SALVAGE VAL IN 10 YEARS = REMAINING LIFE = MARR =

$800,000.00 $120,000.00 $100,000.00 10 20.00%

EUAC=(800000-40000)(A|P 20%,10)+120000-100000(A|F 20%,10)= EUAC=(800000-40000)(0.23852)+120000-100000(0.03852)=

$297,423.20

RECOMMENDATION: REPLACE WITH NEW PAINTING MACHINE EOY CF NEW 0 -$760,000.00 1 -$120,000.00 2 -$120,000.00 3 -$120,000.00 4 -$120,000.00 5 -$120,000.00 6 -$120,000.00 7 -$120,000.00 8 -$120,000.00 9 -$120,000.00 10 -$20,000.00 PW= -$1,246,946.09 EUAC= $297,425.02 RECOMMENDATION: REPLACE WITH NEW PAINTING MACHINE EUAC DIFFERENCE =

$52,574.98

REPLACE WITH NEW PAINTING MACHINE FIRST COST = ANNUAL O&M COST = SALVAGE VAL IN 10 YEARS = REMAINING LIFE = MARR =

$800,000.00 $120,000.00 $100,000.00 10 20.00%

EUAC=800000(A|P 20%,10)+120000-100000(A|F 20%,10)= EUAC=800000(0.23852)+120000-100000(0.03852)=

$306,964.00

RECOMMENDATION: REPLACE WITH NEW PAINTING MACHINE EOY CF NEW 0 -$800,000.00

1 2 3 4 5 6 7 8 9 10

-$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$120,000.00 -$20,000.00

PW= -$1,286,946.09 EUAC= $306,965.93 RECOMMENDATION: REPLACE WITH NEW PAINTING MACHINE EUAC DIFFERENCE =

$52,574.98

PROBLEM 11.5 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING SPECIALTY CONCRETE MIXER MARKET VALUE = ANNUAL O&M COST = SALVAGE VALUE IN 8 YEARS = REMAINING LIFE = MARR =

$65,000.00 $105,000.00 $5,000.00 8 15.00%

EUAC=105000-5000(A|F 15%,8)= EUAC=105000-5000(0.07285)=

$104,635.75

RECOMMENDATION: KEEP EXISTING CONCRETE MIXER EOY CF EXISTING 0 $0.00 1 -$105,000.00 2 -$105,000.00 3 -$105,000.00 4 -$105,000.00 5 -$105,000.00 6 -$105,000.00 7 -$105,000.00 8 -$100,000.00 PW= -$469,534.25 EUAC= $104,635.75 RECOMMENDATION: KEEP THE EXISTING SPECIALTY MIXER EUAC DIFFERENCE =

$1,169.52

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING SPECIALTY CONCRETE MIXER MARKET VALUE = ANNUAL O&M COST = SALVAGE VALUE IN 8 YEARS = REMAINING LIFE = MARR =

$65,000.00 $105,000.00 $5,000.00 8 15.00%

EUAC=65000(A|P 15%,8)+105000-5000(A|F 15%,8)= EUAC=65000(0.22285)+105000-5000(0.07285)=

$119,121.00

RECOMMENDATION: KEEP EXISTING CONCRETE MIXER EOY CF EXISTING 0 -$65,000.00 1 -$105,000.00 2 -$105,000.00

3 4 5 6 7 8

-$105,000.00 -$105,000.00 -$105,000.00 -$105,000.00 -$105,000.00 -$100,000.00

PW= -$534,534.25 EUAC= $119,121.01 RECOMMENDATION: KEEP THE EXISTING SPECIALTY MIXER EUAC DIFFERENCE =

$1,169.52

REPLACE WITH NEW SPECIALTY CONCRETE MIXER FIRST COST = ANNUAL O&M COST = SALVAGE VALUE = REMAINING LIFE = MARR =

$375,000.00 $40,000.00 $45,000.00 8 15.00%

EUAC=(375000-65000)(A|P 15%,8)+40000-45000(A|F 15%,8)= EUAC=310000(0.22285)+40000-45000(0.07285)=

$105,805.25

EOY CF NEW 0 -$310,000.00 1 -$40,000.00 2 -$40,000.00 3 -$40,000.00 4 -$40,000.00 5 -$40,000.00 6 -$40,000.00 7 -$40,000.00 8 $5,000.00 PW= -$474,782.28 EUAC= $105,805.27

REPLACE WITH NEW SPECIALTY CONCRETE MIXER FIRST COST = ANNUAL O&M COST = SALVAGE VALUE = REMAINING LIFE = MARR =

$375,000.00 $40,000.00 $45,000.00 8 15.00%

EUAC=375000(A|P 15%,8)+40000-45000(A|F 15%,8)= EUAC=375000(0.22285)+40000-45000(0.07285)=

$120,290.50

EOY CF NEW 0 -$375,000.00 1 -$40,000.00 2 -$40,000.00

3 4 5 6 7 8

-$40,000.00 -$40,000.00 -$40,000.00 -$40,000.00 -$40,000.00 $5,000.00

PW= -$539,782.28 EUAC= $120,290.53

PROBLEM 11.6

INSIDER'S VIEWPOINT APPROACH MARKET VALUE = CASH COST ($108,000) MINUS COST WITH TRADE-IN ($91,000) = $17,000 MARKET VALUE = KEEP EXISTING EQUIPMENT, PLUS SUPPLEMENT IN YEARS 3, 4, 5 SALVAGE VALUE = O&M OF EXISTING EQPT YEARS 1-5 = LEASED SUPP HI-DEF EQPT ($ BEGINNING OF YRS 3, 4, 5) = LEASED SUPP HI-DEF EQPT O&M ($ END OF YEARS 3, 4, AND 5) = PLANNING HORIZON = MARR = EUAC=9000+30000(P|A 10%,3)(P|F 10%,1)(A|P 10%,5)+7000(P|A 10%,3)(P|F 10%,2)(A|P 10%,5)= EUAC=9000+30000(2.48685)(0.90909)(0.26380)+7000(2.48685)(0.82645)(0.26380)=

EOY 0 1 2 3 4 5 PW= EUAC=

OUTSIDER'S VIEWPOINT APPROACH MARKET VALUE = CASH COST ($108,000) MINUS COST WITH TRADE-IN ($91,000) = $17,000 MARKET VALUE = KEEP EXISTING EQUIPMENT, PLUS SUPPLEMENT IN YEARS 3, 4, 5 SALVAGE VALUE = O&M OF EXISTING EQPT YEARS 1-5 = LEASED SUPP HI-DEF EQPT ($ BEGINNING OF YRS 3, 4, 5) = LEASED SUPP HI-DEF EQPT O&M ($ END OF YEARS 3, 4, AND 5) = PLANNING HORIZON = MARR = EUAC=17000(A|P 10%,5)+9000+30000(P|A 10%,3)(P|F 10%,1)(A|P 10%,5)+7000(P|A 10%,3)(P|F 10%,2)(A|P 10%,5)= EUAC=17000(0.26380)+9000+30000(2.48685)(0.90909)(0.26380)+7000(2.48685)(0.82645)(0.26380)=

EOY 0 1 2 3 4 5 PW= EUAC=

$17,000.00 NEW TECHNOLOGY FOR DL $0.00 $9,000.00 $30,000.00 $7,000.00 5 10.00%

$30,686.98

FIRST COST = SALVAGE VALUE = O&M OF NEW TECHNOLOGY YEARS 1-5 =

$108,000.00 $20,000.00 $8,000.00

PLANNING HORIZON = MARR =

5 10.00%

EUAC=(108000-17000)(A|P 10%,5)+8000-20000(A|F 10%,5)= EUAC=(108000-17000)(0.26380)+8000-20000(0.16380)=

$28,729.80

RECOMMENDATION: INVEST IN NEW DL TECHNOLOGY CF EXISTING $0.00 -$9,000.00 -$39,000.00 -$46,000.00 -$46,000.00 -$16,000.00

EOY CF NEW 0 -$91,000.00 1 -$8,000.00 2 -$8,000.00 3 -$8,000.00 4 -$8,000.00 5 $12,000.00

-$116,327.06 $30,686.79

PW= -$108,907.87 EUAC= $28,729.62 RECOMMENDATION: INVEST IN NEW DL TECHNOLOGY EUAC DIFFERENCE =

$1,957.17

$17,000.00 NEW TECHNOLOGY FOR DL $0.00 $9,000.00 $30,000.00 $7,000.00 5 10.00%

0%,2)(A|P 10%,5)= $35,171.58

FIRST COST = SALVAGE VALUE = O&M OF NEW TECHNOLOGY YEARS 1-5 = PLANNING HORIZON = MARR = EUAC=108000(A|P 10%,5)+8000-20000(A|F 10%,5)= EUAC=108000(0.26380)+8000-20000(0.16380)= RECOMMENDATION: INVEST IN NEW DL TECHNOLOGY

$108,000.00 $20,000.00 $8,000.00 5 10.00%

$33,214.40

CF EXISTING -$17,000.00 -$9,000.00 -$39,000.00 -$46,000.00 -$46,000.00 -$16,000.00

EOY CF NEW 0 -$108,000.00 1 -$8,000.00 2 -$8,000.00 3 -$8,000.00 4 -$8,000.00 5 $12,000.00

-$133,327.06 $35,171.34

PW= -$125,907.87 EUAC= $33,214.18 RECOMMENDATION: INVEST IN NEW DL TECHNOLOGY EUAC DIFFERENCE =

$1,957.17

PROBLEM 11.7

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING SHREDDER MARKET VALUE = SALVAGE VALUE = O&M COST PER YEAR = PLANNING HORIZON = MARR = EUAC=100000-10000(A|F 15%,4)= EUAC=100000-10000(0.20027)=

EOY 0 1 2 3 4 PW= EUAC=

ANNUAL COST OF OPERATING WITHOUT ANY SHREDDER IS $190,000 OPERATING COST PER YEAR= PLANNING HORIZON = MARR = EUAC=-210000(A|P 15%,4)+190000= EUAC=-210000(0.35027)+190000=

EOY 0 1 2 3 4 PW= EUAC= RECOMMENDATION: STILL LEASE EQUIVALENT SHREDDER

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING SHREDDER MARKET VALUE = SALVAGE VALUE = O&M COST PER YEAR = PLANNING HORIZON = MARR = EUAC=200000(A|P 15%,4)+100000-10000(A|F 15%,4)= EUAC=200000(0.35027)+100000-10000(0.20027)=

EOY 0 1 2 3 4 PW= EUAC=

ANNUAL COST OF OPERATING WITHOUT ANY SHREDDER IS $190,000 OPERATING COST PER YEAR= PLANNING HORIZON = MARR = EUAC=190000= EUAC=190000=

EOY 0 1 2 3 4 PW= EUAC= RECOMMENDATION: LEASE EQUIVALENT SHREDDER

LEASE EQUIVALENT SHREDDER $210,000.00 $10,000.00 $100,000.00 4 15.00%

$97,997.30

COST PER DAY = COST PER HOUR OF ACTUAL USE = EXPECTED DAYS PER YEAR = EXPECTED HOURS OF USE PER YEAR = PLANNING HORIZON = MARR =

$200.00 $80.00 250 1500 4 15.00%

EUAC=-210000(A|P 15%,4)+200*250+80*1500= EUAC=-210000(0.35027)+200*250+80*1500=

$96,443.30

RECOMMENDATION: KEEP THE EXISTING SHREDDER CF EXISTING $0.00 -$100,000.00 -$100,000.00 -$100,000.00 -$90,000.00

EOY CF NEW 0 $210,000.00 1 -$170,000.00 2 -$170,000.00 3 -$170,000.00 4 -$170,000.00

-$279,780.30 $97,997.35

PW= -$275,346.32 EUAC= $96,444.28 RECOMMENDATION: LEASE EQUIVALENT SHREDDER EUAC DIFFERENCE =

$190,000.00 4 15.00%

$116,443.30

CF NO SHREDDER $210,000.00 -$190,000.00 -$190,000.00 -$190,000.00 -$190,000.00 -$332,445.89 $116,444.28

$1,553.07

LEASE EQUIVALENT SHREDDER $210,000.00 $10,000.00 $100,000.00 4 15.00%

$171,554.00

COST PER DAY = COST PER HOUR OF ACTUAL USE = EXPECTED DAYS PER YEAR = EXPECTED HOURS OF USE PER YEAR = PLANNING HORIZON = MARR =

$200.00 $80.00 250 1500 4 15.00%

EUAC=200*250+80*1500= EUAC=200*250+80*1500=

$170,000.00

RECOMMENDATION: LEASE EQUIVALENT SHREDDER CF EXISTING -$210,000.00 -$100,000.00 -$100,000.00 -$100,000.00 -$90,000.00

EOY CF NEW 0 $0.00 1 -$170,000.00 2 -$170,000.00 3 -$170,000.00 4 -$170,000.00

-$489,780.30 $171,553.07

PW= -$485,346.32 EUAC= $170,000.00 RECOMMENDATION: LEASE EQUIVALENT SHREDDER EUAC DIFFERENCE =

$190,000.00 4 15.00%

$190,000.00

CF NO SHREDDER $0.00 -$190,000.00 -$190,000.00 -$190,000.00 -$190,000.00 -$542,445.89 $190,000.00

$1,553.07

PROBLEM 11.8 KEEP EXISTING MATERIAL HANDLING SYSTEM TRADE-IN VALUE NOW IF NEW SYSTEM PURCHASED = ACTUAL MARKET VALUE NOW = SALVAGE VALUE IN 8 YEARS = ANNUAL O&M COST OF EXISTING SYSTEM = PLANNING HORIZON = MARR = EUAC=48000-6000(A|F 15%,8)= EUAC=48000-6000(0.07285)=

$55,000.00 $45,000.00 $6,000.00 $48,000.00 8 15.00%

$47,562.90

EOY CF EXISTING 0 $0.00 1 -$48,000.00 2 -$48,000.00 3 -$48,000.00 4 -$48,000.00 5 -$48,000.00 6 -$48,000.00 7 -$48,000.00 8 -$42,000.00 PW= -$213,430.02 EUAC= $47,562.90

TRADE IN EXISTING SYSTEM ON NEW MH SYSTEM FIRST COST IF EXISTING UNIT IS TRADED IN = ADJ BASIS DUE TO INFLATED TRADE-IN = SALVAGE VALUE = O&M OF NEW SYSTEM =

$175,000.00 $165,000.00 $50,000.00 $17,000.00

PLANNING HORIZON = MARR =

8 15.00%

EUAC=(165000-45000)(A|P 15%,8)+17000-50000(A|F 15%,8)= EUAC=(165000-45000)(0.22285)+17000-50000(0.07285)=

$40,099.50

EOY CF NEW 0 -$120,000.00 1 -$17,000.00 2 -$17,000.00 3 -$17,000.00 4 -$17,000.00 5 -$17,000.00 6 -$17,000.00 7 -$17,000.00 8 $33,000.00 PW= -$179,939.38 EUAC= $40,099.51 RECOMMENDATION: TRADE IN EXISTING SYSTEM ON NEW MH SYSTEM

SELL EXISTING SYSTEM AND LEASE NEW MH SYSTEM BEGINNING OF YEAR LEASE COST = ANNUAL O&M COST END OF YEAR =

PLANNING HORIZON = MARR = EUAC=31000(F|P 15%,1)+15000-45000(A|P15%,8)= EUAC=31000(1.15)+15000-45000(0.22285)=

$31,000.00 $15,000.00

8 15.00%

$40,621.75

EOY CF LEASE 0 $14,000.00 1 -$46,000.00 2 -$46,000.00 3 -$46,000.00 4 -$46,000.00 5 -$46,000.00 6 -$46,000.00 7 -$46,000.00 8 -$15,000.00 PW= -$182,282.83 EUAC= $40,621.75

PROBLEM 11.9 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING CRANE MARKET OR TRADE-IN VALUE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = MARR =

$40,000.00 $35,000.00 $0.00 5 20.00%

EUAC=35000= EUAC=35000=

$35,000.00

RECOMMENDATION: KEEP EXISTING CRANE EOY CF EXISTING 0 $0.00 1 -$35,000.00 2 -$35,000.00 3 -$35,000.00 4 -$35,000.00 5 -$35,000.00 PW= -$104,671.42 EUAC= $35,000.00 RECOMMENDATION: KEEP EXISTING CRANE EUAC DIFFERENCE = b

$2,390.88

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING CRANE MARKET OR TRADE-IN VALUE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = MARR =

$40,000.00 $35,000.00 $0.00 5 20.00%

EUAC=40000(A|P 20%,5)+35000= EUAC=40000(0.33438) +35000=

$48,375.20

RECOMMENDATION: KEEP EXISTING CRANE EOY CF EXISTING 0 -$40,000.00 1 -$35,000.00 2 -$35,000.00 3 -$35,000.00 4 -$35,000.00 5 -$35,000.00

PW= -$144,671.42 EUAC= $48,375.19 RECOMMENDATION: KEEP EXISTING CRANE EUAC DIFFERENCE=

$2,390.88

REPLACE WITH NEW CRANE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE AFTER 5 YEARS = PLANNING HORIZON = MARR =

$150,000.00 $8,000.00 $55,000.00 5 20.00%

EUAC=(150000-40000)(A|P 20%,5)+8000-55000(A|F 20%,5)= EUAC=(150000-40000)(0.33438)+8000-55000(0.13438)=

$37,390.90

EOY CF NEW 0 -$110,000.00 1 -$8,000.00 2 -$8,000.00 3 -$8,000.00 4 -$8,000.00 5 $47,000.00 PW= -$111,821.63 EUAC= $37,390.88

REPLACE WITH NEW CRANE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE AFTER 5 YEARS = PLANNING HORIZON = MARR =

$150,000.00 $8,000.00 $55,000.00 5 20.00%

EUAC=150000(A|P 20%,5)+8000-55000(A|F 20%,5)= EUAC=150000(0.33438)+8000-55000(0.13438)=

$50,766.10

EOY CF NEW 0 -$150,000.00 1 -$8,000.00 2 -$8,000.00 3 -$8,000.00 4 -$8,000.00 5 $47,000.00

PW= -$151,821.63 EUAC= $50,766.07

PROBLEM 11.10

INSIDER'S VIEWPOINT KEEP OLD TURRET LATHE AND CONTRACT OUT MARKET VALUE = ANNUAL CONTRACT COST = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = MARR =

$18,000.00 $13,000.00 $8,000.00 $3,000.00 8 15.00% EOY CF EXISTING 0 1 -$21,000.00 2 -$21,000.00 3 -$21,000.00 4 -$21,000.00 5 -$21,000.00 6 -$21,000.00 7 -$21,000.00 8 -$18,000.00

EUAC=8000+13000-3000(A|F 15%,8) EUAC=8000+13000-3000(0.07285)

$20,781.45

PW= EUAC=

-$93,253.05 $20,781.45

OUTSIDER'S VIEWPOINT ANALYSIS KEEP OLD TURRET LATHE AND CONTRACT OUT MARKET VALUE = ANNUAL CONTRACT COST = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = MARR =

$18,000.00 $13,000.00 $8,000.00 $3,000.00 8 15.00% EOY CF EXISTING 0 -$18,000.00 1 -$21,000.00 2 -$21,000.00 3 -$21,000.00 4 -$21,000.00

5 6 7 8 d

EUAC=18000(A|P 15%,8)+8000+13000-3000(A|F 15%,8) EUAC=18000(0.22285)+8000+13000-3000(0.07285)

-$21,000.00 -$21,000.00 -$21,000.00 -$18,000.00

$24,792.75

PW= -$111,253.05 EUAC= $24,792.75

REPLACE WITH NEW TURRET LATHE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE = $65,000*0.7^8

$65,000.00 $10,000.00 $3,747.12

PLANNING HORIZON = MARR =

8 15.00% EOY CF NEW 0 -$47,000.00 1 -$10,000.00 2 -$10,000.00 3 -$10,000.00 4 -$10,000.00 5 -$10,000.00 6 -$10,000.00 7 -$10,000.00 8 -$6,252.88

EUAC=(65000-18000)(A|P 15%,8)+10000-3747.12(A|F 15%,8)= EUAC=(65000-18000)(0.22285)+10000-3747.12(0.07285)=

$20,200.97

RECOMMENDATION: REPLACE WITH NEW TURRET LATHE PW= EUAC= RECOMMENDATION: REPLACE WITH NEW TURRET LATHE EUAC DIFFERENCE =

-$90,648.27 $20,200.98

$580.47

REPLACE WITH NEW TURRET LATHE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE = $65,000*0.7^8 PLANNING HORIZON = MARR =

$65,000.00 $10,000.00 $3,747.12 8 15.00% EOY CF NEW 0 -$65,000.00 1 -$10,000.00 2 -$10,000.00 3 -$10,000.00 4 -$10,000.00

5 6 7 8 EUAC=65000(A|P 15%,8)+10000-3747.12(A|F 15%,8)= EUAC=65000(0.22285)+10000-3747.12(0.07285)=

-$10,000.00 -$10,000.00 -$10,000.00 -$6,252.88

$24,212.27

RECOMMENDATION: REPLACE WITH NEW TURRET LATHE PW= -$108,648.27 EUAC= $24,212.28 RECOMMENDATION: REPLACE WITH NEW TURRET LATHE EUAC DIFFERENCE =

$580.47

PROBLEM 11.11

INSIDER'S VIEWPOINT APPROACH KEEP MULTI-AXIS NC MACHINE AND BUY MACHINE S MARKET VALUE OF EXISTING MACHINE = ANNUAL O&M COST = SALVAGE VALUE IN 5 YEARS= FIRST COST MACHINE S = ANNUAL O&M COST EXISTING = SALVAGE VALUE MACHINE S ($210,000*0.8^5= PLANNING HORIZON = MARR = EOY 0 1 2 3 4 5

EUAC=210000(A|P 20%,5)+50000+37000-68812.80(A|F 20%,5) EUAC=210000(0.33438)+87000-68812.80(0.13438) RECOMMENDATION: KEEP MULTI-AXIS MACHINE AND BUY MACHINE S PW= EUAC= RECOMMENDATION: KEEP MULTI-AXIS MACHINE AND BUY MACHINE S EUAC DIFFERENCE =

OUTSIDER'S VIEWPOINT APPROACH KEEP MULTI-AXIS NC MACHINE AND BUY MACHINE S MARKET VALUE OF EXISTING MACHINE = ANNUAL O&M COST = SALVAGE VALUE IN 5 YEARS= FIRST COST MACHINE S = ANNUAL O&M COST EXISTING = SALVAGE VALUE MACHINE S ($210,000*0.8^5= PLANNING HORIZON = MARR = EOY 0 1

2 3 4 5 d

EUAC=(210000+70000)(A|P 20%,5)+50000+37000-68812.80(A|F 20%,5) EUAC=(210000+70000)(0.33438)+87000-68812.80(0.13438) RECOMMENDATION: KEEP MULTI-AXIS MACHINE AND BUY MACHINE S PW= EUAC= RECOMMENDATION: KEEP MULTI-AXIS MACHINE AND BUY MACHINE S EUAC DIFFERENCE =

REPLACE MULTI-AXIS NC MACHINE WITH MACHINE L $70,000.00 $50,000.00 $0.00 $210,000.00 $37,000.00 $68,812.80 5 20.00%

CASH PRICE OF MACHINE L WITH NO TRADE IN ANNUAL O&M COST = SALVAGE VALUE ($450,000*0.8^5)=

PLANNING HORIZON = MARR =

CF EXISTING -$210,000.00 -$87,000.00 -$87,000.00 -$87,000.00 -$87,000.00 -$18,187.20

$147,972.74

$450,000.00 $74,000.00 $147,456.00

5 20.00% EOY CF NEW 0 -$380,000.00 1 -$74,000.00 2 -$74,000.00 3 -$74,000.00 4 -$74,000.00 5 $73,456.00

EUAC=(450000-70000)(A|P 20%,5)+74000-147456.00(A|F 20%,5)= EUAC=380000(0.33438)+74000-147456.00(0.13438)=

-$442,528.94 $147,972.69

$181,249.26

PW= -$542,046.04 EUAC= $181,249.19

$33,276.50

REPLACE MULTI-AXIS NC MACHINE WITH MACHINE L $70,000.00 $50,000.00 $0.00 $210,000.00 $37,000.00 $68,812.80 5 20.00% CF EXISTING -$280,000.00 -$87,000.00

CASH PRICE OF MACHINE L WITH NO TRADE IN ANNUAL O&M COST = SALVAGE VALUE ($450,000*0.8^5)=

PLANNING HORIZON = MARR =

$450,000.00 $74,000.00 $147,456.00

5 20.00% EOY CF NEW 0 -$450,000.00 1 -$74,000.00

-$87,000.00 -$87,000.00 -$87,000.00 -$18,187.20

$171,379.34

-$512,528.94 $171,379.27

$33,276.50

2 3 4 5 EUAC=450000(A|P 20%,5)+74000-147456.00(A|F 20%,5)= EUAC=450000(0.33438)+74000-147456.00(0.13438)=

-$74,000.00 -$74,000.00 -$74,000.00 $73,456.00

$204,655.86

PW= -$612,046.04 EUAC= $204,655.77

PROBLEM 11.12

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT MARKET VALUE OF EXISTING HVAC = NEXT YEAR'S OPERATING COST OF EXISTING HVAC = INCREMENTAL YEARLY OPERATING COST EXISTING = SALVAGE VALUE IN 10 YEARS EXISTING UNIT = FIRST COST ADDITIONAL UNIT = FIRST YEAR OPERATING COST ADDITIONAL UNIT= INCREMENTAL YEARLY OPERATING COST ADDITIONAL = SALVAGE VALUE ADDITIONAL IN 10 YEARS = PLANNING HORIZON = MARR = EOY 0 1 2 3 4 5 6 7 8 9 10

EUAC=18000(A|P 20%,10)+5050+350(A|G 20%,10)-3000(A|F 20%,10) EUAC=18000(0.23852)+4800+350(3.07386)-3000(0.03852) PW=EUAC*(P|A 20%,10) PW=EUAC(4.19247) RECOMMENDATION: KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT PW= EUAC= RECOMMENDATION: KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT PW DIFFERENCE =

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT MARKET VALUE OF EXISTING HVAC = NEXT YEAR'S OPERATING COST OF EXISTING HVAC =

INCREMENTAL YEARLY OPERATING COST EXISTING = SALVAGE VALUE IN 10 YEARS EXISTING UNIT = FIRST COST ADDITIONAL UNIT = FIRST YEAR OPERATING COST ADDITIONAL UNIT= INCREMENTAL YEARLY OPERATING COST ADDITIONAL = SALVAGE VALUE ADDITIONAL IN 10 YEARS = PLANNING HORIZON = MARR = EOY 0 1 2 3 4 5 6 7 8 9 10 EUAC=(18000+4000)(A|P 20%,10)+4800+350(A|G 20%,10)-3000(A|F 20%,10) EUAC=(18000+4000)(0.23852)+4800+350(3.07386)-3000(0.03852) PW=EUAC*(P|A 20%,10) PW=EUAC(4.19247) RECOMMENDATION: KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT d

PW= EUAC= RECOMMENDATION: KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT PW DIFFERENCE =

$7,000.00 $3,250.00 $250.00 $0.00 $18,000.00 $1,800.00 $100.00 $3,000.00 10 20.00% CF EXIST+ADDN -$18,000.00 -$5,050.00 -$5,400.00 -$5,750.00 -$6,100.00 -$6,450.00 -$6,800.00 -$7,150.00 -$7,500.00 -$7,850.00 -$5,200.00

$10,303.65 -$43,197.75

-$43,197.95 $10,303.69

$1,761.08

$7,000.00 $3,250.00

$250.00 $0.00 $18,000.00 $1,800.00 $100.00 $3,000.00 10 20.00% CF EXIST+ADDN -$25,000.00 -$5,050.00 -$5,400.00 -$5,750.00 -$6,100.00 -$6,450.00 -$6,800.00 -$7,150.00 -$7,500.00 -$7,850.00 -$5,200.00

$11,973.29 -$50,197.66

-$50,197.95 $11,973.35

$1,761.08

REPLACE EXISTING HVAC UNIT WITH NEW LARGER UNIT FIRST COST = FIRST YEAR OPERATING COST = INCREMENTAL YEARLY OPERATING COST = SALVAGE VALUE IN 10 YEARS =

$35,000.00 $3,700.00 $200.00 $7,000.00

PLANNING HORIZON = MARR =

10 20.00% EOY CF NEW 0 -$28,000.00 1 -$3,700.00 2 -$3,900.00 3 -$4,100.00 4 -$4,300.00 5 -$4,500.00 6 -$4,700.00 7 -$4,900.00 8 -$5,100.00 9 -$5,300.00 10 $1,500.00

EUAC=(35000-7000)(A|P 20%,10)+3700+200(A|G 20%,10)-7000(A|F 20%,10)= EUAC=(35000-7000)(0.23852)+3700+200(3.07386)-7000(0.03852)= PW=EUAC*(P|A 20%,10) PW=EUAC(4.19247)

$10,723.69 -$44,958.76

PW= -$44,959.02 EUAC= $10,723.75

REPLACE EXISTING HVAC UNIT WITH NEW LARGER UNIT FIRST COST = FIRST YEAR OPERATING COST =

$35,000.00 $3,700.00

INCREMENTAL YEARLY OPERATING COST = SALVAGE VALUE IN 10 YEARS =

PLANNING HORIZON = MARR =

$200.00 $7,000.00

10 20.00% EOY CF NEW 0 -$35,000.00 1 -$3,700.00 2 -$3,900.00 3 -$4,100.00 4 -$4,300.00 5 -$4,500.00 6 -$4,700.00 7 -$4,900.00 8 -$5,100.00 9 -$5,300.00 10 $1,500.00

EUAC=35000(A|P 20%,10)+3700+200(A|G 20%,10)-7000(A|F 20%,10)= EUAC=35000(0.23852)+3700+200(3.07386)-7000(0.03852)= PW=EUAC*(P|A 20%,10) PW=EUAC(4.19247)

$12,393.33 -$51,958.67

PW= -$51,959.02 EUAC= $12,393.41

PROBLEM 11.13

INSIDER'S VIEWPOINT APPROACH ALT A - KEEP EXISTING AUGER MARKET VALUE = SALVAGE VALUE = O&M COST YEARS 1-7 =

$12,000.00 $0.00 $13,000.00

PLANNING HORIZON = MARR =

7 15.00%

RECOMMENDATION: KEEP EXISTING AUGER EOY CF 0 $0.00 1 -$13,000.00 2 -$13,000.00 3 -$13,000.00 4 -$13,000.00 5 -$13,000.00 6 -$13,000.00 7 -$13,000.00 b

EUAC=13000 EUAC=13000

$13,000.00

RECOMMENDATION: KEEP EXISTING AUGER PW= -$54,085.46 EUAC= $13,000.00 RECOMMENDATION: KEEP EXISTING AUGER

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING AUGER MARKET VALUE =

$12,000.00

SALVAGE VALUE = O&M COST YEARS 1-7 =

$0.00 $13,000.00

PLANNING HORIZON = MARR =

7 15.00% EOY CF 0 -$12,000.00 1 -$13,000.00 2 -$13,000.00

3 -$13,000.00 4 -$13,000.00 5 -$13,000.00 6 -$13,000.00 7 -$13,000.00 d

EUAC=13000+12000(A|P 15%,7)= EUAC=13000+12000(0.24036)=

$15,884.32

RECOMMENDATION: KEEP EXISTING AUGER PW= -$66,085.46 EUAC= $15,884.32 RECOMMENDATION: KEEP EXISTING AUGER

ALT B - REPLACE EXISTING AUGER WITH NEW AUGER FIRST COST = TRADE-IN VALUE OF EXISTING AUGER = SALVAGE VALUE = O&M OF NEW AUGER YEARS 1-7 =

$54,000.00 $15,000.00 $14,000.00 $6,000.00

PLANNING HORIZON = MARR =

7 15.00%

EOY CF 0 -$39,000.00 1 -$6,000.00 2 -$6,000.00 3 -$6,000.00 4 -$6,000.00 5 -$6,000.00 6 -$6,000.00 7 $8,000.00 EUAC=(54000-15000)(A|P 15%,7)+6000-14000(A|F 15%,7)= EUAC=39000(0.24036)+6000-14000(0.09036)=

$14,109.00

PW= -$58,699.40 EUAC= $14,109.01

REPLACE EXISTING AUGER WITH NEW AUGER FIRST COST = TRADE-IN VALUE OF EXISTING AUGER = REDUCED FIRST COST SINCE TRADE-IN $3000 OVER MV SALVAGE VALUE = O&M OF NEW AUGER YEARS 1-7 = PLANNING HORIZON = MARR =

$54,000.00 $15,000.00 $51,000.00 $14,000.00 $6,000.00 7 15.00%

EOY CF 0 -$51,000.00 1 -$6,000.00 2 -$6,000.00

3 4 5 6 7 EUAC=51000(A|P 15%,7)+6000-14000(A|F 15%,7)= EUAC=51000(0.24036)+6000-14000(0.09036)=

-$6,000.00 -$6,000.00 -$6,000.00 -$6,000.00 $8,000.00

$16,993.32

PW= -$70,699.40 EUAC= $16,993.33

ALT C - REPLACE EXISTING AUGER WITH NEW "TREATED AUGER" FIRST COST = TRADE-IN VALUE OF EXISTING AUGER = SALVAGE VALUE = O&M OF NEW AUGER YEARS 1-7 = PLANNING HORIZON = MARR =

$68,000.00 $17,000.00 $18,000.00 $3,000.00 7 15.00%

EOY CF 0 -$51,000.00 1 -$3,000.00 2 -$3,000.00 3 -$3,000.00 4 -$3,000.00 5 -$3,000.00 6 -$3,000.00 7 $15,000.00 EUAC=(68000-17000)(A|P 15%,7)+3000-18000(A|F15%,7)= EUAC=51000(0.24036)+3000-18000(0.09036)=

$13,631.88

PW= -$56,714.39 EUAC= $13,631.89

REPLACE EXISTING AUGER WITH NEW TREATED AUGER FIRST COST = TRADE-IN VALUE OF EXISTING AUGER = REDUCED FIRST COST SINCE TRADE-IN $5000 OVER MV SALVAGE VALUE = O&M OF NEW AUGER YEARS 1-7 = PLANNING HORIZON = MARR =

$68,000.00 $17,000.00 $63,000.00 $18,000.00 $3,000.00 7 15.00% EOY CF 0 -$63,000.00 1 -$3,000.00 2 -$3,000.00

3 -$3,000.00 4 -$3,000.00 5 -$3,000.00 6 -$3,000.00 7 $15,000.00 EUAC=63000(A|P 15%,7)+3000-18000(A|F15%,7)= EUAC=63000(0.24036)+3000-18000(0.09036)=

$16,516.20

PW= -$68,714.39 EUAC= $16,516.22

ALT D - REPLACE EXISTING AUGER WITH COMPETITOR'S SERVICE BEGINNING OF YEAR LEASE COST = MARKET VALUE = ANNUAL O&M COST END OF YEAR =

PLANNING HORIZON = MARR =

$10,000.00 $12,000.00 $6,000.00

7 15.00%

EOY CF 0 $2,000.00 1 -$16,000.00 2 -$16,000.00 3 -$16,000.00 4 -$16,000.00 5 -$16,000.00 6 -$16,000.00 7 -$6,000.00 EUAC=-12000(A|P 15%,7)+10000(F|P15,1)+6000= EUAC=-12000(0.24036)+10000(1.15)+6000=

$14,615.68

PW= -$60,807.35 EUAC= $14,615.68

REPLACE EXISTING AUGER WITH COMPETITOR'S SERVICE BEGINNING OF YEAR LEASE COST = MARKET VALUE =

$10,000.00 $12,000.00

ANNUAL O&M COST END OF YEAR =

$6,000.00

PLANNING HORIZON = MARR =

7 15.00% EOY CF 0 -$10,000.00 1 -$16,000.00 2 -$16,000.00

3 -$16,000.00 4 -$16,000.00 5 -$16,000.00 6 -$16,000.00 7 -$6,000.00 EUAC=10000(F|P15,1)+6000= EUAC=10000(1.15)+6000=

$17,500.00

PW= -$72,807.35 EUAC= $17,500.00

PROBLEM 11.14 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING PAINTING MACHINE ORIGINAL PURCHASE PRICE = YEARS USED ALREADY = MARKET VALUE TODAY = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE = MACRS-GDS PROPERTY

$700,000.00 9 $40,000.00 $350,000.00 $0.00 10 12.00% 40.00% 7

EXISTING PAINTING MACHINE AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF DWO B TI $0.00 $0.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING PAINTING MACHINE ORIGINAL PURCHASE PRICE = YEARS USED ALREADY = MARKET VALUE TODAY = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE = MACRS-GDS PROPERTY

$700,000.00 9 $40,000.00 $350,000.00 $0.00 10 12.00% 40.00% 7

EXISTING PAINTING MACHINE AFTER-TAX ANALYSIS NOTE! BOOK VALUE OF EXISTING PAINTING MACHINE FOR TAX PURPOSES IS $0.00 SINCE IT IS F NOTE! TI ASSESSED IN YEAR 1 IF EXISTING PAINTING MACHINE WERE SOLD IS $40,000.00-$0.00 =

NOTE! IF THE EXISTING PAINTING MACHINE WERE SOLD, THERE WOULD BE AN ADDITIONAL TI O NOTE! BY PASSING UP THE "OPPORTUNITY" TO SELL FOR $40,000.00, THE OWNER PASSES UP THE "OPPORTUNITY" TO INCUR A GAIN OF $40,000.00 AND PAY A TAX OF $16,000.00 IN YEA EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF DWO B TI -$40,000.00 $0.00 -$350,000.00 $0.00 $0.00 -$390,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00

INSIDER'S VIEWPOINT APPROACH SECTION 1231 EXCHANGE KEEP EXISTING PAINTING MACHINE ORIGINAL PURCHASE PRICE = YEARS USED ALREADY = MARKET VALUE TODAY = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE = MACRS-GDS PROPERTY

$700,000.00 9 $40,000.00 $350,000.00 $0.00 10 12.00% 40.00% 7

EXISTING PAINTING MACHINE AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5 6 7

8 9 10

-$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00 -$350,000.00 $0.00 $0.00 -$350,000.00

REPLACE WITH NEW PAINTING MACHINE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE = MACRS-GDS PROPERTY NEW PAINTING MACHINE AFTER TAX ANALYSIS

NOTE! BOOK VALUE OF EXISTING PAINTING MACHINE FOR TA NOTE! TI FOR EXISTING PAINTING MACHINE IN YEAR 1 IS $40, NOTE! DEPRECIATION WRITEOFF OF NEW PAINTING MACHIN NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$120,000.00-$11 T

ATCF MACRS-GDS(7) $0.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% EUAC= $210,000.00

URPOSES IS $0.00 SINCE IT IS FULLY DEPRECIATED WERE SOLD IS $40,000.00-$0.00 = $40,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10

RECOMMENDATION: REPLACE WITH NEW PAINTING MACHINE EUAC DIFFERENCE = REPLACE WITH NEW PAINTING MACHINE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE = MACRS-GDS PROPERTY NEW PAINTING MACHINE AFTER TAX ANALYSIS

WOULD BE AN ADDITIONAL TI OF $40,000.00 WITH A RESULTANT TAX OF $16,000.00 0.00, THE OWNER PASSES PAY A TAX OF $16,000.00 IN YEAR 1 T

ATCF MACRS-GDS(7) -$40,000.00 0.000% -$156,000.00 -$194,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% -$140,000.00 -$210,000.00 0.000% EUAC= $214,551.02

EOY 0 1 2 3 4 5 6 7 8 9 10

RECOMMENDATION: REPLACE WITH NEW PAINTING MACHINE EUAC DIFFERENCE =

REPLACE WITH NEW PAINTING MACHINE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE IN 10 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE = MACRS-GDS PROPERTY

NEW PAINTING MACHINE AFTER TAX ANALYSIS NOTE! BOOK VALUE OF EXISTING PAINTING MACHINE FOR TA NOTE! TI FOR EXISTING PAINTING MACHINE IN YEAR 1 IS $40, NOTE! DEPRECIATION WRITEOFF OF NEW PAINTING MACHIN NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$120,000.00-$11 NOTE! INCOME TAX FOR TI OF EXISTING PAINTING MACHINE NOTE! SECTION 1031 DEFERRAL OF INCOME TAX FOR EXISTI

EOY 0 1 2 3 4 5 6 7

-$140,000.00 -$210,000.00 -$140,000.00 -$210,000.00 -$140,000.00 -$210,000.00 EUAC= $210,000.00

0.000% 0.000% 0.000%

8 9 10

RECOMMENDATION: REPLACE WITH NEW PAINTING MACHINE EUAC DIFFERENCE =

$800,000.00 $120,000.00 $100,000.00 10 12.00% 40.00% 7 TAX ANALYSIS

G PAINTING MACHINE FOR TAX PURPOSES IS $0 SINCE IT IS FULLY DEPRECIATED NG MACHINE IN YEAR 1 IS $40,000-$0=$40,000 F OF NEW PAINTING MACHINE IN YEAR 1 IS $800,000.00*0.1429=$114,320.00 IN YEAR 1 IS -$120,000.00-$114,320.00+$40,000-$0.00=-$194,320.00 BTCF DWO B TI T ATCF MACRS-GDS(7) -$760,000.00 $800,000.00 -$760,000.00 -$120,000.00 $114,320.00 $685,680.00 -$194,320.00 -$77,728.00 -$42,272.00 14.29% -$120,000.00 $195,920.00 $489,760.00 -$315,920.00 -$126,368.00 $6,368.00 24.49% -$120,000.00 $139,920.00 $349,840.00 -$259,920.00 -$103,968.00 -$16,032.00 17.49% -$120,000.00 $99,920.00 $249,920.00 -$219,920.00 -$87,968.00 -$32,032.00 12.49% -$120,000.00 $71,440.00 $178,480.00 -$191,440.00 -$76,576.00 -$43,424.00 8.93% -$120,000.00 $71,360.00 $107,120.00 -$191,360.00 -$76,544.00 -$43,456.00 8.92% -$120,000.00 $71,440.00 $35,680.00 -$191,440.00 -$76,576.00 -$43,424.00 8.93% -$120,000.00 $35,680.00 $0.00 -$155,680.00 -$62,272.00 -$57,728.00 4.46% -$120,000.00 $0.00 $0.00 -$120,000.00 -$48,000.00 -$72,000.00 0.000% -$20,000.00 $0.00 $0.00 -$20,000.00 -$8,000.00 -$12,000.00 0.000% EUAC= $167,051.17

WITH NEW PAINTING MACHINE $42,948.83

$800,000.00 $120,000.00 $100,000.00 10 12.00% 40.00% 7 TAX ANALYSIS

BTCF DWO B TI T ATCF MACRS-GDS(7) -$800,000.00 $800,000.00 -$800,000.00 -$120,000.00 $114,320.00 $685,680.00 -$234,320.00 -$93,728.00 -$26,272.00 14.29% -$120,000.00 $195,920.00 $489,760.00 -$315,920.00 -$126,368.00 $6,368.00 24.49% -$120,000.00 $139,920.00 $349,840.00 -$259,920.00 -$103,968.00 -$16,032.00 17.49% -$120,000.00 $99,920.00 $249,920.00 -$219,920.00 -$87,968.00 -$32,032.00 12.49% -$120,000.00 $71,440.00 $178,480.00 -$191,440.00 -$76,576.00 -$43,424.00 8.93% -$120,000.00 $71,360.00 $107,120.00 -$191,360.00 -$76,544.00 -$43,456.00 8.92% -$120,000.00 $71,440.00 $35,680.00 -$191,440.00 -$76,576.00 -$43,424.00 8.93% -$120,000.00 $35,680.00 $0.00 -$155,680.00 -$62,272.00 -$57,728.00 4.46% -$120,000.00 $0.00 $0.00 -$120,000.00 -$48,000.00 -$72,000.00 0.000% -$20,000.00 $0.00 $0.00 -$20,000.00 -$8,000.00 -$12,000.00 0.000% EUAC= $171,602.20

WITH NEW PAINTING MACHINE $42,948.83

$800,000.00 $120,000.00 $100,000.00 10 12.00% 40.00% 7

TAX ANALYSIS G PAINTING MACHINE FOR TAX PURPOSES IS $0 SINCE IT IS FULLY DEPRECIATED NG MACHINE IN YEAR 1 IS $40,000-$0=$40,000 F OF NEW PAINTING MACHINE IN YEAR 1 IS $800,000.00*0.1429=$114,320.00 IN YEAR 1 IS -$120,000.00-$114,320.00+$40,000-$0.00=-$194,320.00 XISTING PAINTING MACHINE SOLD IN YEAR 1 IS $40,000.00*0.40=$16,000.00 L OF INCOME TAX FOR EXISTING PAINTING MACHINE SOLD IN YEAR 1 IS $16,000.00

BTCF DWO B TI T -$760,000.00 $800,000.00 -$120,000.00 $114,320.00 $685,680.00 -$194,320.00 -$77,728.00 -$120,000.00 $195,920.00 $489,760.00 -$315,920.00 -$126,368.00 -$120,000.00 $139,920.00 $349,840.00 -$259,920.00 -$103,968.00 -$120,000.00 $99,920.00 $249,920.00 -$219,920.00 -$87,968.00 -$120,000.00 $71,440.00 $178,480.00 -$191,440.00 -$76,576.00 -$120,000.00 $71,360.00 $107,120.00 -$191,360.00 -$76,544.00 -$120,000.00 $71,440.00 $35,680.00 -$191,440.00 -$76,576.00

SECTION 1031 DEFERRAL $16,000.00

ATCF -$760,000.00 -$26,272.00 $6,368.00 -$16,032.00 -$32,032.00 -$43,424.00 -$43,456.00 -$43,424.00

-$120,000.00 -$120,000.00 -$20,000.00

$35,680.00 $0.00 $0.00

WITH NEW PAINTING MACHINE $45,477.17

$0.00 -$155,680.00 $0.00 -$120,000.00 $0.00 -$20,000.00

-$62,272.00 -$48,000.00 -$8,000.00 EUAC=

-$57,728.00 -$72,000.00 -$12,000.00 $164,522.83

MACRS-GDS(7) 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93%

4.46% 0.000% 0.000%

PROBLEM 11.15 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING SPECIALTY CONCRETE MIXER PURCHASE PRICE = YEARS USED ALREADY = MARKET VALUE TODAY = ANNUAL O&M COST = SALV VAL AFTER 8 YRS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$300,000.00 7 $65,000.00 $105,000.00 $5,000.00 8 9.00% 40.00%

EXISTING SPECIALTY CONCRETE MIXER AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5 6 7 8

BTCF DWO B TI T $0.00 $0.00 $0.00 $0.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$100,000.00 $0.00 $0.00 -$100,000.00 -$40,000.00 EUAC=

OUTSIDER'S VIEWPOINT APPROACH KEEP EXISTING SPECIALTY CONCRETE MIXER PURCHASE PRICE = YEARS USED ALREADY = MARKET VALUE TODAY = ANNUAL O&M COST = SALV VAL AFTER 8 YRS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$300,000.00 7 $65,000.00 $105,000.00 $5,000.00 8 9.00% 40.00%

EXISTING SPECIALTY CONCRETE MIXER AFTER-TAX ANALYSIS

NOTE! BOOK VALUE OF EXISTING SPECIALTY CONCRETE MIXER FOR TAX PURPOSES IS $0.00 SIN

NOTE! TI ASSESSED IN YEAR 1 IF EXISTING SPECIALTY CONCRETE MIXER WERE SOLD IS $65,000 NOTE! IF THE EXISTING PAINTING SPECIALTY CONCRETE MIXER WERE SOLD, THERE WOULD BE NOTE! BY PASSING UP THE "OPPORTUNITY" TO SELL FOR $65,000.00, THE OWNER PASSES UP THE "OPPORTUNITY" TO INCUR A GAIN OF $65,000.00 AND PAY A TAX OF $26,000.00 IN YEA

EOY 0 1 2 3 4 5 6 7 8

BTCF DWO B TI T -$65,000.00 $0.00 $0.00 $0.00 -$105,000.00 $0.00 $0.00 -$170,000.00 -$68,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$105,000.00 $0.00 $0.00 -$105,000.00 -$42,000.00 -$100,000.00 $0.00 $0.00 -$100,000.00 -$40,000.00 EUAC=

REPLACE WITH NEW SPECIALTY CONCRET FIRST COST = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

REPLACE WITH NEW SPECIALTY CONCRET

NOTE! BOOK VALUE OF EXISTING SPECIAL NOTE! TI FOR EXISTING SPECIALTY CONCR NOTE! DEPRECIATION WRITEOFF OF NEW NOTE! TOTAL TAXABLE INCOME IN YEAR 1 ATCF MACRS-GDS(5) $0.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$60,000.00 0.000% $62,727.98 SUM(1-8) = 0.000%

OR TAX PURPOSES IS $0.00 SINCE IT IS FULLY DEPRECIATED

EOY 0 1 2 3 4 5 6 7 8

RECOMMENDATION: REPLACE WITH NEW S EUAC DIFFERENCE =

REPLACE WITH NEW SPECIALTY CONCRET FIRST COST = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

MIXER WERE SOLD IS $65,000.00-$0.00 = $65,000.00 ERE SOLD, THERE WOULD BE AN ADDITIONAL TI OF $65,000.00 WITH A RESULTANT TAX OF $26,000.00 00, THE OWNER PASSES Y A TAX OF $26,000.00 IN YEAR 1

REPLACE WITH NEW SPECIALTY CONCRET ATCF MACRS-GDS(5) -$65,000.00 0.000% -$37,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$63,000.00 0.000% -$60,000.00 0.000% $70,162.15 SUM(1-8) = 0.000%

EOY 0 1 2 3 4 5 6 7 8

RECOMMENDATION: REPLACE WITH NEW S EUAC DIFFERENCE =

TH NEW SPECIALTY CONCRETE MIXER $375,000.00 $40,000.00 $45,000.00 8 9.00% 40.00%

TH NEW SPECIALTY CONCRETE MIXER AFTER-TAX ANALYSIS

VALUE OF EXISTING SPECIALTY CONCRETE MIXER FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY DEPRECIATED R EXISTING SPECIALTY CONCRETE MIXER IN YEAR 1 IS $65,000.00-$0.00=$65,000.00 ECIATION WRITEOFF OF NEW SPECIALTY CONCRETE MIXER IN YEAR 1 IS $375,000.00*0.2000=$75,000.00 L TAXABLE INCOME IN YEAR 1 IS -$40,000.00-$75,000.00+$65,000-$0.00=-$50,000.00 BTCF DWO B TI T ATCF MACRS-GDS(5) -$310,000.00 $375,000.00 $0.00 $0.00 -$310,000.00 -$40,000.00 $75,000.00 $300,000.00 -$50,000.00 -$20,000.00 -$20,000.00 20.00% -$40,000.00 $120,000.00 $180,000.00 -$160,000.00 -$64,000.00 $24,000.00 32.00% -$40,000.00 $72,000.00 $108,000.00 -$112,000.00 -$44,800.00 $4,800.00 19.20% -$40,000.00 $43,200.00 $64,800.00 -$83,200.00 -$33,280.00 -$6,720.00 11.52% -$40,000.00 $43,200.00 $21,600.00 -$83,200.00 -$33,280.00 -$6,720.00 11.52% -$40,000.00 $21,600.00 $0.00 -$61,600.00 -$24,640.00 -$15,360.00 5.76% -$40,000.00 $0.00 $0.00 -$40,000.00 -$16,000.00 -$24,000.00 0.00% $5,000.00 $0.00 $0.00 $5,000.00 $2,000.00 $3,000.00 0.00% EUAC= $60,408.82 0.00%

DATION: REPLACE WITH NEW SPECIALTY CONCRETE MIXER $2,319.16

TH NEW SPECIALTY CONCRETE MIXER $375,000.00 $40,000.00 $45,000.00 8 9.00% 40.00%

TH NEW SPECIALTY CONCRETE MIXER AFTER-TAX ANALYSIS BTCF DWO B TI T ATCF MACRS-GDS(5) -$375,000.00 $375,000.00 $0.00 $0.00 -$375,000.00 -$40,000.00 $75,000.00 $300,000.00 -$115,000.00 -$46,000.00 $6,000.00 20.00% -$40,000.00 $120,000.00 $180,000.00 -$160,000.00 -$64,000.00 $24,000.00 32.00% -$40,000.00 $72,000.00 $108,000.00 -$112,000.00 -$44,800.00 $4,800.00 19.20% -$40,000.00 $43,200.00 $64,800.00 -$83,200.00 -$33,280.00 -$6,720.00 11.52% -$40,000.00 $43,200.00 $21,600.00 -$83,200.00 -$33,280.00 -$6,720.00 11.52% -$40,000.00 $21,600.00 $0.00 -$61,600.00 -$24,640.00 -$15,360.00 5.76% -$40,000.00 $0.00 $0.00 -$40,000.00 -$16,000.00 -$24,000.00 0.00% $5,000.00 $0.00 $0.00 $5,000.00 $2,000.00 $3,000.00 0.00% EUAC= $67,842.99 0.00%

DATION: REPLACE WITH NEW SPECIALTY CONCRETE MIXER $2,319.16

FULLY DEPRECIATED

PROBLEM 11.16 a

KEEP EXISTING SHREDDER PURCHASE PRICE = YEARS USED ALREADY = MARKET VALUE TODAY = ANNUAL O&M COST = SALVAGE VALUE IN 4 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$800,000.00 6 $210,000.00 $100,000.00 $10,000.00 4 9.00% 40.00%

EXISTING SHREDDER AFTER-TAX ANALYSIS EOY 0 1 2 3 4

BTCF DWO B TI $0.00 $0.00 -$100,000.00 $0.00 $0.00 -$100,000.00 -$100,000.00 $0.00 $0.00 -$100,000.00 -$100,000.00 $0.00 $0.00 -$100,000.00 -$90,000.00 $0.00 $0.00 -$90,000.00

RECOMMENDATION: KEEP EXISTING SHREDDER

SELL EXISTING SHREDDER AND OPERATE WITHOUT ANY SHREDDER COST PER YEAR = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$190,000.00 4 9.00% 40.00%

SELL EXISTING SHREDDER AND OPERATE WITHOUT SHREDDER AFTER-TAX ANALYSIS NOTE! BOOK VALUE OF EXISTING SHREDDER FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY DE NOTE! TI FOR EXISTING SHREDDER IN YEAR 1 IS $210,000.00-$0.00=$210,000.00 NOTE! COSTS OF OPERATING WITHOUT SHREDDER ARE ALL EXPENSED AND NO DEPRECIATION NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$190,000.00+$210,000.00=$20,000.00 EOY 0 1 2 3 4

BTCF DWO B TI $210,000.00 $0.00 $0.00 -$190,000.00 $0.00 $0.00 $20,000.00 -$190,000.00 $0.00 $0.00 -$190,000.00 -$190,000.00 $0.00 $0.00 -$190,000.00 -$190,000.00 $0.00 $0.00 -$190,000.00

RECOMMENDATION: STILL KEEP EXISTING SHREDDER

SELL EXISTING SHREDDER AND LEASE EQUIVALENT SHREDDE COST PER DAY = COST PER HOUR OF ACTUAL USE = EXPECTED DAYS PER YEAR = EXPECTED HOURS OF USE PER YEAR = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

SELL EXISTING SHREDDER AND LEASE EQUIVALENT SHREDDE

NOTE! BOOK VALUE OF EXISTING SHREDDER FOR TAX PURPO NOTE! TI FOR EXISTING SHREDDER IN YEAR 1 IS $210,000.00-$ NOTE! LEASE COSTS ARE ALL EXPENSED AND NO DEPRECIAT NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$170,000.00+$210 T -$40,000.00 -$40,000.00 -$40,000.00 -$36,000.00 EUAC=

ATCF MACRS-GDS(5) $0.00 0.00% -$60,000.00 0.00% -$60,000.00 0.00% -$60,000.00 0.00% -$54,000.00 0.00% $58,687.99 SUM = 0.00%

ER AFTER-TAX ANALYSIS OSES IS $0.00 SINCE IT IS FULLY DEPRECIATED $0.00=$210,000.00 EXPENSED AND NO DEPRECIATION IS INVOLVED 10,000.00=$20,000.00 T ATCF $0.00 $210,000.00 $8,000.00 -$198,000.00 -$76,000.00 -$114,000.00 -$76,000.00 -$114,000.00 -$76,000.00 -$114,000.00 EUAC= $72,966.89

EOY 0 1 2 3 4

D LEASE EQUIVALENT SHREDDER $200.00 $80.00 250 1,500 $0.00 4 9.00% 40.00%

D LEASE EQUIVALENT SHREDDER AFTER-TAX ANALYSIS

NG SHREDDER FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY DEPRECIATED DER IN YEAR 1 IS $210,000.00-$0.00=$210,000.00 EXPENSED AND NO DEPRECIATION IS INVOLVED E IN YEAR 1 IS -$170,000.00+$210,000.00=$40,000.00 BTCF DWO B TI T ATCF $210,000.00 $0.00 $0.00 $0.00 $210,000.00 -$170,000.00 $0.00 $0.00 $40,000.00 $16,000.00 -$186,000.00 -$170,000.00 $0.00 $0.00 -$170,000.00 -$68,000.00 -$102,000.00 -$170,000.00 $0.00 $0.00 -$170,000.00 -$68,000.00 -$102,000.00 -$170,000.00 $0.00 $0.00 -$170,000.00 -$68,000.00 -$102,000.00 EUAC= $60,966.89

PROBLEM 11.17 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING MATERIAL HANDLING SYSTEM PURCHASE PRICE = TRADE-IN VALUE NOW IF NEW SYSTEM PURCHASED = ACTUAL MARKET VALUE NOW = YEARS USED ALREADY = ANNUAL O&M COST OF EXISTING SYSTEM = SALVAGE VALUE IN 8 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$130,000.00 $55,000.00 $45,000.00 7 $48,000.00 $6,000.00 8 9.00% 40.00%

KEEP EXISTING MATERIAL HANDLING SYSTEM AFTER TAX ANALYSIS EOY 0 1 2 3 4 5 6 7 8

BTCF $0.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$42,000.00

INSIDER'S VIEWPOINT APPROACH SECTION 1031 EXCHANGE KEEP EXISTING MATERIAL HANDLING SYSTEM PURCHASE PRICE = TRADE-IN VALUE NOW IF NEW SYSTEM PURCHASED = ACTUAL MARKET VALUE NOW = YEARS USED ALREADY = ANNUAL O&M COST OF EXISTING SYSTEM = SALVAGE VALUE IN 8 YEARS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$130,000.00 $55,000.00 $45,000.00 7 $48,000.00 $6,000.00 8 9.00% 40.00%

DWO $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

KEEP EXISTING MATERIAL HANDLING SYSTEM AFTER TAX ANALYSIS EOY 0 1 2 3 4 5 6 7 8

BTCF $0.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$48,000.00 -$42,000.00

DWO $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

TI T $0.00 $0.00 -$48,000.00 -$19,200.00 $0.00 -$48,000.00 -$19,200.00 $0.00 -$48,000.00 -$19,200.00 $0.00 -$48,000.00 -$19,200.00 $0.00 -$48,000.00 -$19,200.00 $0.00 -$48,000.00 -$19,200.00 $0.00 -$48,000.00 -$19,200.00 $0.00 -$42,000.00 -$16,800.00 EUAC=

ATCF MACRS-GDS(5) $0.00 0.00% -$28,800.00 0.00% -$28,800.00 0.00% -$28,800.00 0.00% -$28,800.00 0.00% -$28,800.00 0.00% -$28,800.00 0.00% -$28,800.00 0.00% -$25,200.00 0.00% $28,473.57 SUM = 0.00%

TRADE IN EXISTING SYSTEM ON NEW MH SYSTEM FIRST COST IF EXISTING UNIT IS TRADED IN = ADJ BASIS DUE TO INFLATED TRADE-IN = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$175,000.00 $165,000.00 $17,000.00 $50,000.00 8 9.00% 40.00%

TRADE IN EXISTING SYSTEM ON NEW MH SYSTEM AFTER TAX ANALYSIS NOTE! BOOK VALUE OF EXISTING MATERIAL HANDLING SYSTEM FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY D NOTE! TI FOR EXISTING MATERIAL HANDLING SYSTEM IN YEAR 1 IS $45,000.00-$0.00 = $45,000.00 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$17,000.00-$33,000.00+$45,000.00=-$5000.00 EOY 0 1 2 3 4 5 6 7 8

BTCF DWO B TI -$120,000.00 $165,000.00 $0.00 -$17,000.00 $33,000.00 $132,000.00 -$5,000.00 -$17,000.00 $52,800.00 $79,200.00 -$69,800.00 -$17,000.00 $31,680.00 $47,520.00 -$48,680.00 -$17,000.00 $19,008.00 $28,512.00 -$36,008.00 -$17,000.00 $19,008.00 $9,504.00 -$36,008.00 -$17,000.00 $9,504.00 $0.00 -$26,504.00 -$17,000.00 $0.00 $0.00 -$17,000.00 $33,000.00 $0.00 $0.00 $33,000.00

RECOMMEND: TRADE IN EXISTING SYSTEM ON NEW MH SYSTEM

$175,000.00 $165,000.00 $17,000.00 $50,000.00 8 9.00% 40.00%

TRADE IN EXISTING SYSTEM ON NEW MH SYSTEM AFTER TAX ANALYSIS

NOTE! BOOK VALUE OF EXISTING MATERIAL HANDLING SYSTEM FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY D NOTE! TI FOR EXISTING MATERIAL HANDLING SYSTEM IN YEAR 1 IS $45,000.00-$0.00 = $45,000.00 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$17,000.00-$33,000.00+$45,000.00=-$5000.00 NOTE! INCOME TAX FOR TI OF EXISTING MATERIAL HANDLING SYSTEM SOLD IN YEAR 1 IS $45,000.00*0.40=$18,000 NOTE! SECTION 1031 DEFERRAL OF INCOME TAX FOR EXISTING MATERIAL HANDLING SYSTEM SOLD IN YEAR 1 IS

EOY 0 1 2 3 4 5 6 7 8

RECOMMEND: TRADE IN EXISTING SYSTEM ON NEW MH SYSTEM

IS $0.00 SINCE IT IS FULLY DEPRECIATED

T ATCF MACRS-GDS(5) $0.00 -$120,000.00 -$2,000.00 -$15,000.00 20.00% -$27,920.00 $10,920.00 32.00% -$19,472.00 $2,472.00 19.20% -$14,403.20 -$2,596.80 11.52% -$14,403.20 -$2,596.80 11.52% -$10,601.60 -$6,398.40 5.76% -$6,800.00 -$10,200.00 $13,200.00 $19,800.00 EUAC= $22,701.16

STEM ON NEW MH SYSTEM

IS $0.00 SINCE IT IS FULLY DEPRECIATED

1 IS $45,000.00*0.40=$18,000.00 SYSTEM SOLD IN YEAR 1 IS $18,000.00

T $0.00 -$2,000.00 -$27,920.00 -$19,472.00 -$14,403.20 -$14,403.20 -$10,601.60 -$6,800.00 $13,200.00 EUAC=

SECTION 1031 DEFERRAL $18,000.00

STEM ON NEW MH SYSTEM

ATCF MACRS-GDS(5) -$120,000.00 $3,000.00 20.00% $10,920.00 32.00% $2,472.00 19.20% -$2,596.80 11.52% -$2,596.80 11.52% -$6,398.40 5.76% -$10,200.00 $19,800.00 $19,717.55

SELL EXISTING SYSTEM AND LEASE NEW MH SYSTEM BEGINNING OF YEAR LEASE COSTS = ANNUAL OPERATING COSTS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$31,000.00 $15,000.00 8 9.00% 40.00%

SELL EXISTING SYSTEM AND LEASE NEW MH SYSTEM AFTER TAX ANALYSIS NOTE! BOOK VALUE OF EXISTING MATERIAL HANDLING SYSTEM FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY D NOTE! TI FOR EXISTING MATERIAL HANDLING SYSTEM IN YEAR 1 IS $45,000.00-$0.00 = $45,000.00 NOTE! LEASE COSTS ARE ALL EXPENSED AND NO DEPRECIATION IS INVOLVED NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$46,000.00+$45,000.00=-$1000.00 EOY 0 1 2 3 4 5 6 7 8

BTCF DWO B TI T ATCF $14,000.00 $0.00 $0.00 $0.00 $14,000.00 -$46,000.00 $0.00 $0.00 -$1,000.00 -$400.00 -$45,600.00 -$46,000.00 $0.00 $0.00 -$46,000.00 -$18,400.00 -$27,600.00 -$46,000.00 $0.00 $0.00 -$46,000.00 -$18,400.00 -$27,600.00 -$46,000.00 $0.00 $0.00 -$46,000.00 -$18,400.00 -$27,600.00 -$46,000.00 $0.00 $0.00 -$46,000.00 -$18,400.00 -$27,600.00 -$46,000.00 $0.00 $0.00 -$46,000.00 -$18,400.00 -$27,600.00 -$46,000.00 $0.00 $0.00 -$46,000.00 -$18,400.00 -$27,600.00 -$15,000.00 $0.00 $0.00 -$15,000.00 -$6,000.00 -$9,000.00 EUAC= $26,367.63

SELL EXISTING SYSTEM AND LEASE NEW MH SYSTEM BEGINNING OF YEAR LEASE COSTS = ANNUAL OPERATING COSTS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$31,000.00 $15,000.00 8 9.00% 40.00%

EOY 0 1 2 3 4 5 6 7 8

0.00 SINCE IT IS FULLY DEPRECIATED

PROBLEM 11.18 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING CRANE PURCHASE PRICE = YEARS USED ALREADY = TRADE-IN VALUE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$130,000.00 6 $40,000.00 $35,000.00 $0.00 5 12.00% 40.00%

KEEP EXISTING CRANE AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5

BTCF DWO B TI $0.00 $0.00 $0.00 -$35,000.00 $0.00 $0.00 -$35,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00

RECOMMEND TO KEEP EXISTING CRANE EUAC DIFFERENCE = $739.95

OUTIDER'S VIEWPOINT APPROACH KEEP EXISTING CRANE PURCHASE PRICE = YEARS USED ALREADY = TRADE-IN VALUE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$130,000.00 6 $40,000.00 $35,000.00 $0.00 5 12.00% 40.00%

KEEP EXISTING CRANE AFTER-TAX ANALYSIS NOTE! BOOK VALUE OF EXISTING CRANE FOR TAX PURPOSES IS $0.00 NOTE! TI ASSESSED IN YEAR 1 IF EXISTING CRANE WERE SOLD IS $40,000.00-$0.00 = $40,000.00

NOTE! IF THE EXISTING CRANE WERE SOLD, THERE WOULD BE AN ADDITIONAL TI OF $40,000.00 NOTE! BY PASSING UP THE "OPPORTUNITY" TO SELL FOR $40,000.00, THE OWNER PASSES UP THE "OPPORTUNITY" TO INCUR A GAIN OF $40,000.00 AND PAY A TAX OF $16,000.00 IN YEA EOY 0 1 2 3 4 5

BTCF DWO B TI -$40,000.00 $0.00 $0.00 -$35,000.00 $0.00 $0.00 -$75,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00 -$35,000.00 $0.00 $0.00 -$35,000.00

RECOMMEND TO KEEP EXISTING CRANE EUAC DIFFERENCE = $739.95

INSIDER'S VIEWPOINT APPROACH SECTION 1231 EXCHANGE KEEP EXISTING CRANE PURCHASE PRICE = YEARS USED ALREADY = TRADE-IN VALUE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$130,000.00 6 $40,000.00 $35,000.00 $0.00 5 12.00% 40.00%

KEEP EXISTING CRANE AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5

SELL EXISTING CRANE AND PURCHASE NEW PURCHASE PRICE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

SELL EXISTING CRANE AND PURCHASE NEW NOTE! BOOK VALUE OF EXISTING CRANE FO NOTE! TI FOR EXISTING CRANE IN YEAR 1 IS NOTE! DEPRECIATION WRITEOFF OF NEW C NOTE! TOTAL DEPRECIATION WRITEOFF IN NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS NOTE! AT THE END OF 5 YEARS, THE NEW C NOTE! IN YEAR 5, BTCF INCLUDES O&M EXP NOTE! IN YEAR 5, DWO EQUALS $150,000.00 NOTE! IN YEAR 5, TI EQUALS $47,000.00-$864 T ATCF MACRS-GDS(5) $0.00 $0.00 5.76% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% EUAC= $21,000.00 SUM(1-5) = 0.00%

D IS $40,000.00-$0.00 = $40,000.00

EOY 0 1 2 3 4 5

SELL EXISTING CRANE AND PURCHASE NEW PURCHASE PRICE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

SELL EXISTING CRANE AND PURCHASE NEW

NOTE! DEPRECIATION WRITEOFF OF NEW C NOTE! TOTAL DEPRECIATION WRITEOFF IN NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS NOTE! AT THE END OF 5 YEARS, THE NEW C

E AN ADDITIONAL TI OF $40,000.00 WITH A RESULTANT TAX OF $16,000.00 000.00, THE OWNER PASSES ND PAY A TAX OF $16,000.00 IN YEAR 1 T ATCF MACRS-GDS(5) $0.00 -$40,000.00 5.76% -$30,000.00 -$5,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% EUAC= $28,133.39 SUM(1-5) = 0.00%

NOTE! IN YEAR 5, BTCF INCLUDES O&M EXP NOTE! IN YEAR 5, DWO EQUALS $150,000.00 NOTE! IN YEAR 5, TI EQUALS $47,000.00-$864 EOY 0 1 2 3 4 5

SELL EXISTING CRANE AND PURCHASE NEW PURCHASE PRICE = ANNUAL O&M COST = SALVAGE VALUE = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

SELL EXISTING CRANE AND PURCHASE NEW NOTE! BOOK VALUE OF EXISTING CRANE FO NOTE! TI FOR EXISTING CRANE IN YEAR 1 IS NOTE! DEPRECIATION WRITEOFF OF NEW C NOTE! TOTAL DEPRECIATION WRITEOFF IN NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS NOTE! AT THE END OF 5 YEARS, THE NEW C NOTE! IN YEAR 5, BTCF INCLUDES O&M EXP NOTE! IN YEAR 5, DWO EQUALS $150,000.00 NOTE! IN YEAR 5, TI EQUALS $47,000.00-$864 NOTE! INCOME TAX FOR TI OF EXISTING CR NOTE! SECTION 1031 DEFERRAL OF INCOME

T ATCF MACRS-GDS(5) $0.00 $0.00 5.76% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% -$14,000.00 -$21,000.00 0.00% EUAC= $21,000.00 SUM(1-5) = 0.00%

EOY 0 1 2 3 4 5

RECOMMEND TO SELL EXISTING CRANE AN EUAC DIFFERENCE =

NG CRANE AND PURCHASE NEW CRANE $150,000.00 $8,000.00 $55,000.00 5 12.00% 40.00%

NG CRANE AND PURCHASE NEW CRANE AFTER-TAX ANALYSIS VALUE OF EXISTING CRANE FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY DEPRECIATED R EXISTING CRANE IN YEAR 1 IS $40,000.00-$0.00=$40,000.00 ECIATION WRITEOFF OF NEW CRANE IN YEAR 1 IS $150,000.00*0.2000=$30,000.00 L DEPRECIATION WRITEOFF IN YEAR 1 IS $30,000.00+$0.00=$30,000.00 L TAXABLE INCOME IN YEAR 1 IS -$8,000.00-$30,000.00+$40,000-$0.00=$2000.00 HE END OF 5 YEARS, THE NEW CRANE IS NOT FULLY DEPRECIATED. IT HAS A BOOK VALUE OF $17,280.00 AR 5, BTCF INCLUDES O&M EXPENSES (-$8,000.00) AND SALVAGE VALUE OF NEW CRANE (+$55,000.00) OR $47,000.00 AR 5, DWO EQUALS $150,000.00*0.0576=$8640.00 AR 5, TI EQUALS $47,000.00-$8640.00-$17280.00=$21,080.00 BTCF DWO B TI T ATCF MACRS-GDS(5) -$110,000.00 $150,000.00 $0.00 $0.00 -$110,000.00 -$8,000.00 $30,000.00 $120,000.00 $2,000.00 $800.00 -$8,800.00 20.00% -$8,000.00 $48,000.00 $72,000.00 -$56,000.00 -$22,400.00 $14,400.00 32.00% -$8,000.00 $28,800.00 $43,200.00 -$36,800.00 -$14,720.00 $6,720.00 19.20% -$8,000.00 $17,280.00 $25,920.00 -$25,280.00 -$10,112.00 $2,112.00 11.52% $47,000.00 $8,640.00 $17,280.00 $21,080.00 $8,432.00 $38,568.00 5.76% EUAC= $21,739.95

NG CRANE AND PURCHASE NEW CRANE $150,000.00 $8,000.00 $55,000.00 5 12.00% 40.00%

NG CRANE AND PURCHASE NEW CRANE AFTER-TAX ANALYSIS

ECIATION WRITEOFF OF NEW CRANE IN YEAR 1 IS $150,000.00*0.2000=$30,000.00 L DEPRECIATION WRITEOFF IN YEAR 1 IS $30,000.00+$0.00=$30,000.00 L TAXABLE INCOME IN YEAR 1 IS -$8,000.00-$30,000.00=-$38,000.00 HE END OF 5 YEARS, THE NEW CRANE IS NOT FULLY DEPRECIATED. IT HAS A BOOK VALUE OF $17,280.00

AR 5, BTCF INCLUDES O&M EXPENSES (-$8,000.00) AND SALVAGE VALUE OF NEW CRANE (+$55,000.00) OR $47,000.00 AR 5, DWO EQUALS $150,000.00*0.0576=$8640.00 AR 5, TI EQUALS $47,000.00-$8640.00-$17280.00=$21,080.00 BTCF DWO B TI T ATCF MACRS-GDS(5) -$150,000.00 $150,000.00 $0.00 $0.00 -$150,000.00 -$8,000.00 $30,000.00 $120,000.00 -$38,000.00 -$15,200.00 $7,200.00 20.00% -$8,000.00 $48,000.00 $72,000.00 -$56,000.00 -$22,400.00 $14,400.00 32.00% -$8,000.00 $28,800.00 $43,200.00 -$36,800.00 -$14,720.00 $6,720.00 19.20% -$8,000.00 $17,280.00 $25,920.00 -$25,280.00 -$10,112.00 $2,112.00 11.52% $47,000.00 $8,640.00 $17,280.00 $21,080.00 $8,432.00 $38,568.00 5.76% EUAC= $28,873.34

NG CRANE AND PURCHASE NEW CRANE $150,000.00 $8,000.00 $55,000.00 5 12.00% 40.00%

NG CRANE AND PURCHASE NEW CRANE AFTER-TAX ANALYSIS VALUE OF EXISTING CRANE FOR TAX PURPOSES IS $0.00 SINCE IT IS FULLY DEPRECIATED R EXISTING CRANE IN YEAR 1 IS $40,000.00-$0.00=$40,000.00 ECIATION WRITEOFF OF NEW CRANE IN YEAR 1 IS $150,000.00*0.2000=$30,000.00 L DEPRECIATION WRITEOFF IN YEAR 1 IS $30,000.00+$0.00=$30,000.00 L TAXABLE INCOME IN YEAR 1 IS -$8,000.00-$30,000.00+$40,000-$0.00=$2000.00 HE END OF 5 YEARS, THE NEW CRANE IS NOT FULLY DEPRECIATED. IT HAS A BOOK VALUE OF $17,280.00 AR 5, BTCF INCLUDES O&M EXPENSES (-$8,000.00) AND SALVAGE VALUE OF NEW CRANE (+$55,000.00) OR $47,000.00 AR 5, DWO EQUALS $150,000.00*0.0576=$8640.00 AR 5, TI EQUALS $47,000.00-$8640.00-$17280.00=$21,080.00 ME TAX FOR TI OF EXISTING CRANE SOLD IN YEAR 1 IS $40,000.00*0.40=$16,000.00 ION 1031 DEFERRAL OF INCOME TAX FOR EXISTING CRANE SOLD IN YEAR 1 IS $16,000.00

BTCF DWO B TI T -$110,000.00 $150,000.00 $0.00 $0.00 -$8,000.00 $30,000.00 $120,000.00 $2,000.00 $800.00 -$8,000.00 $48,000.00 $72,000.00 -$56,000.00 -$22,400.00 -$8,000.00 $28,800.00 $43,200.00 -$36,800.00 -$14,720.00 -$8,000.00 $17,280.00 $25,920.00 -$25,280.00 -$10,112.00 $47,000.00 $8,640.00 $17,280.00 $21,080.00 $8,432.00 EUAC=

SECTION 1031 DEFERRAL $16,000.00

ATCF -$110,000.00 $7,200.00 $14,400.00 $6,720.00 $2,112.00 $38,568.00 $17,776.95

D TO SELL EXISTING CRANE AND PURCHASE NEW CRANE $3,223.05

$55,000.00) OR $47,000.00

OF $17,280.00 $55,000.00) OR $47,000.00

MACRS-GDS(5) 20.00% 32.00% 19.20% 11.52% 5.76%

PROBLEM 11.19

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING TURRET LATHE AND CONTRACT OUT PURCHASE PRICE = YEARS USED ALREADY = MARKET VALUE TODAY = DECREASE IN MV/YR = MINIMUM MARKET VALUE = ANNUAL CONTRACT COST = ANNUAL O&M COST = REMAINING LIFE = AFTER-TAX MARR = TAX RATE =

$96,000.00 5 $18,000.00 $3,000.00 $3,000.00 $13,000.00 $8,000.00 8 9.00% 40.00%

KEEP EXISTING TURRET LATHE AND CONTRACT OUT AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5 6 7 8

BTCF DWO B(EX) TI $0.00 $21,417.60 -$21,000.00 $8,563.20 $12,854.40 -$29,563.20 -$21,000.00 $8,572.80 $4,281.60 -$29,572.80 -$21,000.00 $4,281.60 $0.00 -$25,281.60 -$21,000.00 $0.00 $0.00 -$21,000.00 -$21,000.00 $0.00 $0.00 -$21,000.00 -$21,000.00 $0.00 $0.00 -$21,000.00 -$21,000.00 $0.00 $0.00 -$21,000.00 -$18,000.00 $0.00 $0.00 -$18,000.00

EUAC EXISTING TURRET LATHE AND CONTRACT OUT = $11,108.62 EUAC (REPLACE WITH NEW TURET LATHE) = $10,569.92 RECOMMENDATION: REPLACE WITH NEW TURRET LATHE (ALTHOUGH CLOSE)

REPLACE WITH NEW TURRET LATHE FIRST COST = ANNUAL O&M COST = SALVAGE VALUE = $65,000*0.7^8 REMAINING LIFE = AFTER-TAX MARR = TAX RATE =

$65,000.00 $10,000.00 $3,747.12 8 9.00% 40.00%

REPLACE WITH NEW TURRET LATHE AFTER-TAX ANALYSIS NOTE! DEPRECIATION WRITEOFF OF EXISTING TURRET LATHE NOTE! BOOK VALUE OF EXISTING TURRET LATHE AT END OF YE NOTE! TI FOR EXISTING TURRET LATHE IN YEAR 1 IS $18,000.00 NOTE! DEPRECIATION WRITEOFF OF NEW TURRET LATHE IN YE NOTE! TOTAL DEPRECIATION WRITEOFF IN YEAR 1 IS $4281.60+ NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$10,000.00-$13,570 ATCF MACRS-GDS(7) $0.00 8.93% -$11,825.28 -$9,174.72 8.92% -$11,829.12 -$9,170.88 8.93% -$10,112.64 -$10,887.36 4.46% -$8,400.00 -$12,600.00 0.000% -$8,400.00 -$12,600.00 0.000% -$8,400.00 -$12,600.00 0.000% -$8,400.00 -$12,600.00 0.000% -$7,200.00 -$10,800.00 0.000% EUAC= $11,108.62 SUM(1-8) = 22.31%

OUGH CLOSE)

EOY 0 1 2 3 4 5 6 7 8

BTCF -$47,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$10,000.00 -$6,252.88

E AFTER-TAX ANALYSIS F EXISTING TURRET LATHE IN YEAR 1 IS $96,000.00*0.0892/2=$4281.60 URRET LATHE AT END OF YEAR 1 FOR TAX PURPOSES IS $12,854.40+$4281.60=$21,417.60-$4281.60=$17,136.00 THE IN YEAR 1 IS $18,000.00-$17,136.00=$864.00 F NEW TURRET LATHE IN YEAR 1 IS $65,000.00*0.1429=$9288.50 EOFF IN YEAR 1 IS $4281.60+$9288.50=$13,570.10 YEAR 1 IS -$10,000.00-$13,570.10+$864.00=-$22,706.10 DWO

B(NEW) TI T ATCF MACRS-GDS(7) $65,000.00 $0.00 $0.00 -$47,000.00 $13,570.10 $55,711.50 -$22,706.10 -$9,082.44 -$917.56 14.29% $15,918.50 $39,793.00 -$25,918.50 -$10,367.40 $367.40 24.49% $11,368.50 $28,424.50 -$21,368.50 -$8,547.40 -$1,452.60 17.49% $8,118.50 $20,306.00 -$18,118.50 -$7,247.40 -$2,752.60 12.49% $5,804.50 $14,501.50 -$15,804.50 -$6,321.80 -$3,678.20 8.93% $5,798.00 $8,703.50 -$15,798.00 -$6,319.20 -$3,680.80 8.92% $5,804.50 $2,899.00 -$15,804.50 -$6,321.80 -$3,678.20 8.93% $2,899.00 $0.00 -$9,151.88 -$3,660.75 -$2,592.13 4.46% EUAC= $10,569.92

60=$17,136.00

PROBLEM 11.20 a

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING NC MACHINE AND SUPPLEMENT WITH MACHINE S EXISTING NC MACHINE ORIG PURCHASE PRICE = YEARS USED ALREADY = MV TODAY IF SOLD = SALV VALUE IN 5 YEARS = ANNUAL O&M COST = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

MACHINE S PURCHASE PRICE = SALVAGE VALUE ($210,000*0.8^5)= ANNUAL O&M COST =

$350,000.00 5 $70,000.00 $0.00 $50,000.00 5 12.00% 40.00%

KEEP EXISTING NC MACHINE AND SUPPLEMENT WITH MACHINE S AFTER-TAX ANALYSIS

NOTE! AT THE END OF 5 YEARS, MACHINE S IS NOT FULLY DEPRECIATED. IT HAS A BOOK VALUE NOTE! IN YEAR 5, BTCF INCLUDES O&M EXPENSES (-$87,000.00) AND SALVAGE VALUE OF MACHIN NOTE! IN YEAR 5, TI EQUALS -$87,000+(68,812.80-$56,227.50)=-$74,414.70

EOY 0 1 2 3 4 5

BTCF -$210,000.00 -$87,000.00 -$87,000.00 -$87,000.00 -$87,000.00 -$18,187.20

DWO(EX)

DWO(S)

$31,220.00 $31,255.00 $15,610.00 $0.00 $0.00

$30,009.00 $51,429.00 $36,729.00 $26,229.00 $9,376.50

RECOMMENDATION: KEEP MULTI-AXIS MACHINE AND BUY MACHINE S EUAC DIFFERENCE = $6,611.24

INSIDER'S VIEWPOINT APPROACH SECTION 1031 EXCHANGE KEEP EXISTING NC MACHINE AND SUPPLEMENT WITH MACHINE S EXISTING NC MACHINE ORIG PURCHASE PRICE = YEARS USED ALREADY = MV TODAY IF SOLD = SALV VALUE IN 5 YEARS = ANNUAL O&M COST = PLANNING HORIZON = AFTER-TAX MARR =

$350,000.00 5 $70,000.00 $0.00 $50,000.00 5 12.00%

MACHINE S PURCHASE PRICE = SALVAGE VALUE ($210,000*0.8^5)= ANNUAL O&M COST =

TAX RATE =

40.00%

KEEP EXISTING NC MACHINE AND SUPPLEMENT WITH MACHINE S AFTER-TAX ANALYSIS

EOY 0 1 2 3 4 5

BTCF -$210,000.00 -$87,000.00 -$87,000.00 -$87,000.00 -$87,000.00 -$18,187.20

DWO(EX)

DWO(S)

$31,220.00 $31,255.00 $15,610.00 $0.00 $0.00

RECOMMENDATION: KEEP MULTI-AXIS MACHINE AND BUY MACHINE S EUAC DIFFERENCE = $5,865.71

$30,009.00 $51,429.00 $36,729.00 $26,229.00 $9,376.50

$210,000*0.8^5)=

$210,000.00 $68,812.80 $37,000.00

R-TAX ANALYSIS

D. IT HAS A BOOK VALUE OF $56,227.50 LVAGE VALUE OF MACHINE S (+$68,812.80)

B(EX) B(S) TI $78,085.00 $210,000.00 $46,865.00 $179,991.00 -$118,220.00 $15,610.00 $128,562.00 -$118,255.00 $0.00 $91,833.00 -$102,610.00 $0.00 $65,604.00 -$87,000.00 $0.00 $56,227.50 -$74,414.70

$210,000*0.8^5)=

$210,000.00 $68,812.80 $37,000.00

EX S ATCF MACRS-GDS(7) MACRS-GDS(7) -$210,000.00 8.93% -$47,288.00 -$39,712.00 8.92% 14.29% -$47,302.00 -$39,698.00 8.93% 24.49% -$41,044.00 -$45,956.00 4.46% 17.49% -$34,800.00 -$52,200.00 0.00% 12.49% -$29,765.88 $11,578.68 0.00% 4.465% EUAC= $93,325.82 SUM(1-5) = 22.31% T

R-TAX ANALYSIS

D. IT HAS A BOOK VALUE OF $56,227.50 LVAGE VALUE OF MACHINE S (+$68,812.80)

B(EX) B(S) TI $78,085.00 $210,000.00 $46,865.00 $179,991.00 -$118,220.00 $15,610.00 $128,562.00 -$118,255.00 $0.00 $91,833.00 -$102,610.00 $0.00 $65,604.00 -$87,000.00 $0.00 $56,227.50 -$74,414.70

REPLACE WITH MACHINE L AND SELL EXISTING NC MACHINE ON THE OPEN MARKET FIRST COST = ANNUAL O&M COST = SALVAGE VALUE ($450,000*0.8^5)= PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$450,000.00 $74,000.00 $147,456.00 5 12.00% 40.00%

REPLACE WITH MACHINE L AND SELL EXISTING NC MACHINE ON THE OPEN MARKET AFTER-TAX ANALYS NOTE! DEPRECIATION WRITEOFF OF EXISTING MACHINE IN YEAR 1 IS $350,000.00*0.0892/2=$15,610.00 NOTE! BOOK VALUE OF EXISTING MACHINE AT END OF YEAR 1 FOR TAX PURPOSES IS $46,865.00+$15,61 NOTE! TI FOR EXISTING MACHINE IN YEAR 1 IS $70,000.00-$62,475.00=$7525.00 NOTE! DEPRECIATION WRITEOFF OF MACHINE L IN YEAR 1 IS $450,000.00*0.1429=$64,305.00 NOTE! TOTAL DEPRECIATION WRITEOFF IN YEAR 1 IS $15,610.00+$64,305.00=$79,915.00 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$74,000.00-$79,915.00+$7525.00=-$146,390.00 NOTE! AT THE END OF 5 YEARS, MACHINE L IS NOT FULLY DEPRECIATED. IT HAS A BOOK VALUE OF $12 NOTE! IN YEAR 5, BTCF INCLUDES O&M EXPENSES (-$74,000.00) AND SALVAGE VALUE OF MACHINE L (+$ NOTE! IN YEAR 5, DWO EQUALS $450,000.00*0.04465=$20,092.50 NOTE! IN YEAR 5, TI EQUALS -$74,000-$20,092.50.00+($147,456.00-$120,487.50)=-$67,124.00 EOY 0 1 2 3 4 5

BTCF DWO B(L) TI -$380,000.00 $450,000.00 $0.00 -$74,000.00 $79,915.00 $385,695.00 -$146,390.00 -$74,000.00 $110,205.00 $275,490.00 -$184,205.00 -$74,000.00 $78,705.00 $196,785.00 -$152,705.00 -$74,000.00 $56,205.00 $140,580.00 -$130,205.00 $73,456.00 $20,092.50 $120,487.50 -$67,124.00

REPLACE WITH MACHINE L AND SELL EXISTING NC MACHINE ON THE OPEN MARKET FIRST COST = ANNUAL O&M COST = SALVAGE VALUE ($450,000*0.8^5)= PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$450,000.00 $74,000.00 $147,456.00 5 12.00% 40.00%

REPLACE WITH MACHINE L AND SELL EXISTING NC MACHINE ON THE OPEN MARKET AFTER-TAX ANALYS

NOTE! DEPRECIATION WRITEOFF OF EXISTING MACHINE IN YEAR 1 IS $350,000.00*0.0892/2=$15,610.00 NOTE! BOOK VALUE OF EXISTING MACHINE AT END OF YEAR 1 FOR TAX PURPOSES IS $46,865.00+$15,61 NOTE! TI FOR EXISTING MACHINE IN YEAR 1 IS $70,000.00-$62,475.00=$7525.00 NOTE! DEPRECIATION WRITEOFF OF MACHINE L IN YEAR 1 IS $450,000.00*0.1429=$64,305.00 NOTE! TOTAL DEPRECIATION WRITEOFF IN YEAR 1 IS $15,610.00+$64,305.00=$79,915.00 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$74,000.00-$79,915.00+$7525.00=-$146,390.00 NOTE! AT THE END OF 5 YEARS, MACHINE L IS NOT FULLY DEPRECIATED. IT HAS A BOOK VALUE OF $12 NOTE! IN YEAR 5, BTCF INCLUDES O&M EXPENSES (-$74,000.00) AND SALVAGE VALUE OF MACHINE L (+$ NOTE! IN YEAR 5, DWO EQUALS $450,000.00*0.04465=$20,092.50 NOTE! IN YEAR 5, TI EQUALS -$74,000-$20,092.50.00+($147,456.00-$120,487.50)=-$67,124.00 NOTE! INCOME TAX FOR TI OF EXISTING MACHINE SOLD IN YEAR 1 IS $7525.00*0.40=$3010.00 NOTE! SECTION 1031 DEFERRAL OF INCOME TAX FOR EXISTING MACHINE SOLD IN YEAR 1 IS $3010.00, E NOTE! THE EUAC VALUES CHANGED FROM $99,937.07 TO $99,191.53, DOWN $745.54/YR, EXACTLY THE A

EOY 0 1 2 3 4 5

MARKET AFTER-TAX ANALYSIS 0.00*0.0892/2=$15,610.00 POSES IS $46,865.00+$15,610=$78,085.00-$15,610.00=$62,475.00

429=$64,305.00

=-$146,390.00 HAS A BOOK VALUE OF $120,487.50 E VALUE OF MACHINE L (+$147,456.00) OR $73,456.00

T ATCF MACRS-GDS(7) $0.00 -$380,000.00 -$58,556.00 -$15,444.00 14.29% -$73,682.00 -$318.00 24.49% -$61,082.00 -$12,918.00 17.49% -$52,082.00 -$21,918.00 12.49% -$26,849.60 $100,305.60 4.465% EUAC= $99,937.07

MARKET AFTER-TAX ANALYSIS

0.00*0.0892/2=$15,610.00 POSES IS $46,865.00+$15,610=$78,085.00-$15,610.00=$62,475.00

429=$64,305.00

=-$146,390.00 HAS A BOOK VALUE OF $120,487.50 E VALUE OF MACHINE L (+$147,456.00) OR $73,456.00

0*0.40=$3010.00 LD IN YEAR 1 IS $3010.00, EQUIVALENT TO $745.54 PER YEAR 745.54/YR, EXACTLY THE AMOUNT OF THE ANNUALIZED DEFERRAL

T $0.00 -$58,556.00 -$73,682.00 -$61,082.00 -$52,082.00 -$26,849.60

SECTION 1031 DEFERRAL $3,010.00

EUAC=

ATCF MACRS-GDS(7) -$380,000.00 -$12,434.00 14.29% -$318.00 24.49% -$12,918.00 17.49% -$21,918.00 12.49% $100,305.60 4.465% $99,191.53

PROBLEM 11.21

INSIDER'S VIEWPOINT APPROACH KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT EXISTING HVAC UNIT ORIG PURCHASE PRICE = YEARS USED ALREADY = MV TODAY IF SOLD = SALV VALUE IN 10 YRS = NEXT YEAR'S O&M = INCREASED O&M PER YR = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$25,000.00 5 $7,000.00 $0.00 $3,250.00 $250.00 10 12.00% 40.00%

ADDITIONAL UNIT PURCHASE PRICE = FIRST YEAR O&M COST = INCREASED O&M PER YR = SALVAGE VALUE IN 10 YRS =

KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF DWO(EX) DWO(ADD) -$18,000.00 -$5,050.00 $2,230.00 $2,572.20 -$5,400.00 $2,232.50 $4,408.20 -$5,750.00 $1,115.00 $3,148.20 -$6,100.00 $0.00 $2,248.20 -$6,450.00 $0.00 $1,607.40 -$6,800.00 $0.00 $1,605.60 -$7,150.00 $0.00 $1,607.40 -$7,500.00 $0.00 $802.80 -$7,850.00 $0.00 $0.00 -$5,200.00 $0.00 $0.00

B(EX) $5,577.50 $3,347.50 $1,115.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

PW(KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT) = PW(SELL EXISTING HVAC UNIT AND BUY REPLACEMENT UNIT) = RECOMMEND KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT

INSIDER'S VIEWPOINT APPROACH SECTION 1031 EXCHANGE KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT EXISTING HVAC UNIT ORIG PURCHASE PRICE = YEARS USED ALREADY =

$25,000.00 5

ADDITIONAL UNIT PURCHASE PRICE = FIRST YEAR O&M COST =

MV TODAY IF SOLD = SALV VALUE IN 10 YRS = NEXT YEAR'S O&M = INCREASED O&M PER YR = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$7,000.00 $0.00 $3,250.00 $250.00 10 12.00% 40.00%

INCREASED O&M PER YR = SALVAGE VALUE IN 10 YRS =

KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT AFTER-TAX ANALYSIS EOY 0 1 2 3 4 5 6 7 8 9 10

B(EX) $5,577.50 $3,347.50 $1,115.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

PW(KEEP EXISTING HVAC UNIT AND BUY ADDITIONAL UNIT) = PW(SELL EXISTING HVAC UNIT AND BUY REPLACEMENT UNIT) = RECOMMEND SELL EXISTING HVAC UNIT AND BUY REPLACEMENT UNIT

O&M COST = O&M PER YR = ALUE IN 10 YRS =

$18,000.00 $1,800.00 $100.00 $3,000.00

AX ANALYSIS B(AD) TI T $18,000.00 $15,427.80 -$9,852.20 -$3,940.88 $11,019.60 -$12,040.70 -$4,816.28 $7,871.40 -$10,013.20 -$4,005.28 $5,623.20 -$8,348.20 -$3,339.28 $4,015.80 -$8,057.40 -$3,222.96 $2,410.20 -$8,405.60 -$3,362.24 $802.80 -$8,757.40 -$3,502.96 $0.00 -$8,302.80 -$3,321.12 $0.00 -$7,850.00 -$3,140.00 $0.00 -$5,200.00 -$2,080.00 PW= EUAC=

-$32,065.30 -$32,306.53

O&M COST =

$18,000.00 $1,800.00

EX ADD ATCF MACRS-GDS(7) MACRS-GDS(7) -$18,000.00 8.93% -$1,109.12 8.92% 14.29% -$583.72 8.93% 24.49% -$1,744.72 4.46% 17.49% -$2,760.72 0.00% 12.49% -$3,227.04 0.00% 8.93% -$3,437.76 0.00% 8.92% -$3,647.04 0.00% 8.93% -$4,178.88 0.00% 4.46% -$4,710.00 0.00% 0.00% -$3,120.00 0.00% 0.00% -$32,065.30 $5,675.05 SUM(1-10) = 22.31%

O&M PER YR = ALUE IN 10 YRS =

$100.00 $3,000.00

-$32,065.30 -$31,400.28

SELL EXISTING HVAC UNIT AND BUY REPLACEMENT UNIT FIRST COST = FIRST YEAR O&M COST = INCREASED O&M PER YR = SALV VALUE IN 10 YRS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$35,000.00 $3,700.00 $200.00 $8,500.00 10 12.00% 40.00%

SELL EXISTING HVAC UNIT AND BUY REPLACEMENT UNIT AFTER-TAX ANALYSIS

NOTE! DEPRECIATION WRITEOFF OF EXISTING HVAC UNIT IN YEAR 1 IS $25,000.00*0.0892/2=$1115.00 NOTE! BOOK VALUE OF EXISTING HVAC UNIT AT END OF YEAR 1 FOR TAX PURPOSES IS $3347.50+$1115.00=$5577. NOTE! TI FOR EXISTING HVAC UNIT IN YEAR 1 IS $7000.00-$4462.50=$2537.50 NOTE! DEPRECIATION WRITEOFF OF REPLACEMENT HVAC UNIT IN YEAR 1 IS $35,000.00*0.1429=$5001.50 NOTE! TOTAL DEPRECIATION WRITEOFF IN YEAR 1 IS $1115.00+$5001.50=$6116.50 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$3700.00-$6116.50+$2537.50=-$7279.00 EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF DWO B(REPL) TI T ATCF -$28,000.00 $35,000.00 $0.00 $0.00 -$28,000.00 -$3,700.00 $6,116.50 $29,998.50 -$7,279.00 -$2,911.60 -$788.40 -$3,900.00 $8,571.50 $21,427.00 -$12,471.50 -$4,988.60 $1,088.60 -$4,100.00 $6,121.50 $15,305.50 -$10,221.50 -$4,088.60 -$11.40 -$4,300.00 $4,371.50 $10,934.00 -$8,671.50 -$3,468.60 -$831.40 -$4,500.00 $3,125.50 $7,808.50 -$7,625.50 -$3,050.20 -$1,449.80 -$4,700.00 $3,122.00 $4,686.50 -$7,822.00 -$3,128.80 -$1,571.20 -$4,900.00 $3,125.50 $1,561.00 -$8,025.50 -$3,210.20 -$1,689.80 -$5,100.00 $1,561.00 $0.00 -$6,661.00 -$2,664.40 -$2,435.60 -$5,300.00 $0.00 $0.00 -$5,300.00 -$2,120.00 -$3,180.00 $3,000.00 $0.00 $0.00 $3,000.00 $1,200.00 $1,800.00 PW= -$32,306.53 EUAC= $5,717.74

SELL EXISTING HVAC UNIT AND BUY REPLACEMENT UNIT FIRST COST = FIRST YEAR O&M COST = INCREASED O&M PER YR =

$35,000.00 $3,700.00 $200.00

SALV VALUE IN 10 YRS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$8,500.00 10 12.00% 40.00%

SELL EXISTING HVAC UNIT AND BUY REPLACEMENT UNIT AFTER-TAX ANALYSIS NOTE! DEPRECIATION WRITEOFF OF EXISTING HVAC UNIT IN YEAR 1 IS $25,000.00*0.0892/2=$1115.00 NOTE! BOOK VALUE OF EXISTING HVAC UNIT AT END OF YEAR 1 FOR TAX PURPOSES IS $3347.50+$1115.00=$5577. NOTE! TI FOR EXISTING HVAC UNIT IN YEAR 1 IS $7000.00-$4462.50=$2537.50 NOTE! DEPRECIATION WRITEOFF OF REPLACEMENT HVAC UNIT IN YEAR 1 IS $35,000.00*0.1429=$5001.50 NOTE! TOTAL DEPRECIATION WRITEOFF IN YEAR 1 IS $1115.00+$5001.50=$6116.50 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$3700.00-$6116.50+$2537.50=-$7279.00 NOTE! INCOME TAX FOR TI OF EXISTING HVAC UNIT SOLD IN YEAR 1 IS $2537.50*0.40=$1015.00 NOTE! SECTION 1031 DEFERRAL OF INCOME TAX FOR EXISTING HVAC UNIT SOLD IN YEAR 1 IS $1015.00, EQUIVALE NOTE! THE EUAC VALUES CHANGED FROM $5,717.74 TO $5,557.35, DOWN $160.39/YR, EXACTLY THE AMOUNT OF T

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF DWO B(REPL) TI T -$28,000.00 $35,000.00 $0.00 $0.00 -$3,700.00 $6,116.50 $29,998.50 -$7,279.00 -$2,911.60 -$3,900.00 $8,571.50 $21,427.00 -$12,471.50 -$4,988.60 -$4,100.00 $6,121.50 $15,305.50 -$10,221.50 -$4,088.60 -$4,300.00 $4,371.50 $10,934.00 -$8,671.50 -$3,468.60 -$4,500.00 $3,125.50 $7,808.50 -$7,625.50 -$3,050.20 -$4,700.00 $3,122.00 $4,686.50 -$7,822.00 -$3,128.80 -$4,900.00 $3,125.50 $1,561.00 -$8,025.50 -$3,210.20 -$5,100.00 $1,561.00 $0.00 -$6,661.00 -$2,664.40 -$5,300.00 $0.00 $0.00 -$5,300.00 -$2,120.00 $3,000.00 $0.00 $0.00 $3,000.00 $1,200.00 PW= EUAC=

SECTION 1031 DEFERRAL $1,015.00

92/2=$1115.00 S $3347.50+$1115.00=$5577.50-$1115.00=$4462.50

0*0.1429=$5001.50

MACRS-GDS(7) 14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

92/2=$1115.00 S $3347.50+$1115.00=$5577.50-$1115.00=$4462.50

0*0.1429=$5001.50

EAR 1 IS $1015.00, EQUIVALENT TO $160.39 PER YEAR EXACTLY THE AMOUNT OF THE ANNUALIZED DEFERRAL

ATCF MACRS-GDS(7) -$28,000.00 $226.60 14.29% $1,088.60 24.49% -$11.40 17.49% -$831.40 12.49% -$1,449.80 8.93% -$1,571.20 8.92% -$1,689.80 8.93% -$2,435.60 4.46% -$3,180.00 $1,800.00 -$31,400.28 $5,557.35

PROBLEM 11.22

INSIDER'S VIEWPOINT APPROACH ALT A - KEEP EXISTING DOWN-HOLE WELL AUGER EXISTING WELL AUGER ORIG PURCHASE PRICE = YEARS USED ALREADY = MV TODAY IF SOLD = TRADE-IN VAL NEW AUGER = TRADE-IN VAL "TREATED AUGER" = ANNUAL O&M COST = SALVAGE VALUE IN 7 YRS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$30,000.00 3 $12,000.00 TRUE MARKET VALUE - USED IN ALL ANALYSE $15,000.00 INFLATED TRADE-IN VALUE $17,000.00 INFLATED TRADE-IN VALUE $13,000.00 $0.00 7 9.00% 40.00%

KEEP EXISTING DOWN-HOLE WELL AUGER ANALYSIS EOY 0 1 2 3 4 5 6 7

BTCF DWO(EXIST) B(EXISTING) $0.00 $5,760.00 $8,640.00 -$13,000.00 $3,456.00 $5,184.00 -$13,000.00 $3,456.00 $1,728.00 -$13,000.00 $1,728.00 $0.00 -$13,000.00 $0.00 $0.00 -$13,000.00 $0.00 $0.00 -$13,000.00 $0.00 $0.00 -$13,000.00 $0.00 $0.00

EUAC(KEEP EXISTING DOWN-HOLE WELL AUGER)= EUAC(TRADE IN EXISTING AUGER FOR NEW AUGER)= EUAC(TRADE IN EXISTING AUGER FOR "TREATED AUGER")= EUAC(SELL EXISTING AUGER AND CONTRACT WITH COMPETITOR)= RECOMMENDATION: TRADE IN EXISTING AUGER FOR "TREATED AUGER"

ALT B - TRADE IN EXISTING AUGER FOR NEW AUGER

ALUE - USED IN ALL ANALYSES

FIRST COST = ADJ FIRST COST = $54,000-$3000 ANNUAL O&M COST = SALVAGE VALUE IN 7 YRS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

TRADE IN EXISTING AUGER FOR NEW AUGER AFTER

NOTE! DEPRECIATION WRITEOFF OF EXISTING AUGE NOTE! BOOK VALUE OF EXISTING AUGER AT END OF NOTE! TI FOR EXISTING AUGER IN YEAR 1 IS $12,000 NOTE! DEPRECIATION WRITEOFF OF NEW AUGER IN NOTE! TOTAL DEPRECIATION WRITEOFF IN YEAR 1 IS NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$6000. NOTE! TOTAL TAXABLE INCOME IN YEAR 7 IS $14,000

ATCF MACRS-GDS(5) $0.00 19.20% -$16,456.00 -$6,582.40 -$6,417.60 11.52% -$16,456.00 -$6,582.40 -$6,417.60 11.52% -$14,728.00 -$5,891.20 -$7,108.80 5.76% -$13,000.00 -$5,200.00 -$7,800.00 0.00% -$13,000.00 -$5,200.00 -$7,800.00 0.00% -$13,000.00 -$5,200.00 -$7,800.00 0.00% -$13,000.00 -$5,200.00 -$7,800.00 0.00% PW= -$36,291.50 EUAC= $7,210.78 SUM(1-7) = 28.80%

$7,210.78 $7,471.08 $7,039.25 $8,795.47

EOY 0 1 2 3 4 5 6 7

TING AUGER FOR NEW AUGER $54,000.00 $51,000.00 DUE TO INFLATED TRADE-IN VALUE - USE THIS FOR COST BASIS $6,000.00 $14,000.00 7 9.00% 40.00%

GER FOR NEW AUGER AFTER-TAX ANALYSIS

WRITEOFF OF EXISTING AUGER IN YEAR 1 IS $30,000.00*0.1152/2=$1728.00 F EXISTING AUGER AT END OF YEAR 1 FOR TAX PURPOSES IS $5,184.00+$1728.00=$8640.00-$1728.00=$6912.00 G AUGER IN YEAR 1 IS $12,000.00-$6912.00=$5088.00 WRITEOFF OF NEW AUGER IN YEAR 1 IS $51,000.00*0.2000=$10,200.00 ATION WRITEOFF IN YEAR 1 IS $1728.00+$10,200.00=$11,928.00 INCOME IN YEAR 1 IS -$6000.00-$11,928.00+$5088=-$12,840.00 INCOME IN YEAR 7 IS $14,000.00-$6,000.00=$8,000.00

BTCF DWO(NEW) DWO(EXIST) B(NEW) TI -$39,000.00 $51,000.00 $0.00 -$6,000.00 $10,200.00 $1,728.00 $40,800.00 -$12,840.00 -$6,000.00 $16,320.00 $24,480.00 -$22,320.00 -$6,000.00 $9,792.00 $14,688.00 -$15,792.00 -$6,000.00 $5,875.20 $8,812.80 -$11,875.20 -$6,000.00 $5,875.20 $2,937.60 -$11,875.20 -$6,000.00 $2,937.60 $0.00 -$8,937.60 $8,000.00 $0.00 $0.00 $8,000.00 TOTAL = $51,000.00

T ATCF MACRS-GDS(5) $0.00 -$39,000.00 -$5,136.00 -$864.00 20.00% -$8,928.00 $2,928.00 32.00% -$6,316.80 $316.80 19.20% -$4,750.08 -$1,249.92 11.52% -$4,750.08 -$1,249.92 11.52% -$3,575.04 -$2,424.96 5.76% $3,200.00 $4,800.00 0.00% PW= -$37,601.59 EUAC= $7,471.08

ALT C - TRADE IN EXISTING AUGER FOR "TREATED AUGER" FIRST COST = ADJ FIRST COST = $68,000-$5000 ANNUAL O&M COST = SALVAGE VALUE IN 7 YRS = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

$68,000.00 $63,000.00 DUE TO INFLATED TRADE-IN VALUE $3,000.00 $18,000.00 7 9.00% 40.00%

TRADE IN EXISTING AUGER FOR "TREATED AUGER" AFTER-TAX ANALYSIS

NOTE! DEPRECIATION WRITEOFF OF EXISTING AUGER IN YEAR 1 IS $30,000.00*0.1152/2=$1728.00 NOTE! BOOK VALUE OF EXISTING AUGER AT END OF YEAR 1 FOR TAX PURPOSES IS $5,184.00+$1728.00= NOTE! TI FOR EXISTING AUGER IN YEAR 1 IS $12,000.00-$6912.00=$5088.00 NOTE! DEPRECIATION WRITEOFF OF "TREATED AUGER" IN YEAR 1 IS $63,000.00*0.2000=$12,600.00 NOTE! TOTAL DEPRECIATION WRITEOFF IN YEAR 1 IS $1728.00+$12,600.00=$14,328.00 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$3000.00-$14,328.00+$5088.00=-$12,240.00 NOTE! TOTAL TAXABLE INCOME IN YEAR 7 IS $18,000.00-$3,000.00=$15,000.00

EOY 0 1 2 3 4 5 6 7

BTCF DWO(TRT) DWO(EXIST) B(TREATED) -$51,000.00 $63,000.00 -$3,000.00 $12,600.00 $1,728.00 $50,400.00 -$3,000.00 $20,160.00 $30,240.00 -$3,000.00 $12,096.00 $18,144.00 -$3,000.00 $7,257.60 $10,886.40 -$3,000.00 $7,257.60 $3,628.80 -$3,000.00 $3,628.80 $0.00 $15,000.00 $0.00 $0.00

ALT D - SELL EXISTING AUGER AND CONTRACT WITH BEGINNING OF YEAR RETAINER = END-OF-YEAR O&M = PLANNING HORIZON = AFTER-TAX MARR = TAX RATE =

00.00*0.1152/2=$1728.00 RPOSES IS $5,184.00+$1728.00=$8640.00-$1728.00=$6912.00

,000.00*0.2000=$12,600.00 0=$14,328.00 00=-$12,240.00

TI T ATCF MACRS-GDS(5) $0.00 $0.00 -$51,000.00 -$12,240.00 -$4,896.00 $1,896.00 20.00% -$23,160.00 -$9,264.00 $6,264.00 32.00% -$15,096.00 -$6,038.40 $3,038.40 19.20% -$10,257.60 -$4,103.04 $1,103.04 11.52% -$10,257.60 -$4,103.04 $1,103.04 11.52% -$6,628.80 -$2,651.52 -$348.48 5.76% $15,000.00 $6,000.00 $9,000.00 0.00% PW= -$35,428.22 EUAC= $7,039.25

SELL EXISTING AUGER AND CONTRACT WITH COMP

NOTE! DEPRECIATION WRITEOFF OF EXISTING AUGE NOTE! BOOK VALUE OF EXISTING AUGER AT END OF NOTE! TI FOR EXISTING AUGER IN YEAR 1 IS $12,000 NOTE! TOTAL TAXABLE INCOME IN YEAR 1 IS -$16,00

EOY 0 1 2 3 4 5 6 7

UGER AND CONTRACT WITH COMPETITOR $10,000.00 $6,000.00 7 9.00% 40.00%

AND CONTRACT WITH COMPETITOR AFTER-TAX ANALYSIS

RITEOFF OF EXISTING AUGER IN YEAR 1 IS $30,000.00*0.1152/2=$1728.00 EXISTING AUGER AT END OF YEAR 1 FOR TAX PURPOSES IS $5,184.00+$1728.00=$8640.00-$1728.00=$6912.00 AUGER IN YEAR 1 IS $12,000.00-$6912.00=$5088.00 NCOME IN YEAR 1 IS -$16,000.00-$1728.00+$5088.00=-$12,640.00

BTCF DWO(EXIST) B(CONTRACT) TI T ATCF $2,000.00 $0.00 $0.00 $0.00 $2,000.00 -$16,000.00 $1,728.00 $0.00 -$12,640.00 -$5,056.00 -$10,944.00 -$16,000.00 $0.00 $0.00 -$16,000.00 -$6,400.00 -$9,600.00 -$16,000.00 $0.00 $0.00 -$16,000.00 -$6,400.00 -$9,600.00 -$16,000.00 $0.00 $0.00 -$16,000.00 -$6,400.00 -$9,600.00 -$16,000.00 $0.00 $0.00 -$16,000.00 -$6,400.00 -$9,600.00 -$16,000.00 $0.00 $0.00 -$16,000.00 -$6,400.00 -$9,600.00 -$6,000.00 $0.00 $0.00 -$6,000.00 -$2,400.00 -$3,600.00 PW= -$44,267.17 EUAC= $8,795.47

00=$6912.00

PROBLEM 11.23 FIRST COST = MILES DRIVEN = O&M FIRST YEAR = O&M EACH ADDN YR = SALVAGE % DECLINE = MARR =

$28,000.00 15,000 MILES $0.505 PER MILE 10.00% 20.00% 9.00%

St LIFE CR O&M BTEUAO&MC BTEUAC 1 $22,400.00 $8,120.00 $7,575.00 $7,575.00 $15,695.00 2 $17,920.00 $7,342.97 $8,332.50 $7,937.44 $15,280.41 St(2) =28000*(1-20%)^2 CR(2) =PMT(9%,2,-28000,28000*(1-20%)^2) O&M(2) =15000*0.505*(1+10%)^(2-1) BTEUAO&MC(2) =PMT(9%,2,-NPV(9%,7575,8332.5)) BTEUAC(2) =7342.97+7937.44 3 $14,336.00 $6,688.27 $9,165.75 $8,312.14 $15,000.41 4 $11,468.80 $6,134.86 $10,082.33 $8,699.23 $14,834.08 5 $9,175.04 $5,665.51 $11,090.56 $9,098.80 $14,764.31 OPTIMUM 6 $7,340.03 $5,266.12 $12,199.61 $9,510.96 $14,777.08 7 $5,872.03 $4,925.10 $13,419.57 $9,935.79 $14,860.89 8 $4,697.62 $4,632.93 $14,761.53 $10,373.36 $15,006.29 9 $3,758.10 $4,381.75 $16,237.69 $10,823.73 $15,205.48

PROBLEM 11.24 FIRST COST = O&M FIRST YEAR = O&M EACH ADDN YR = SALVAGE % DECLINE = MARR =

$14,000.00 $3,500.00 $600.00 30% 15.00%

St LIFE CR 1 $9,800.00 $6,300.00 2 $6,860.00 $5,420.93 St(2) =14000*(1-30%)^2

O&M BTEUAO&MC BTEUAC $3,500.00 $3,500.00 $9,800.00 $4,100.00 $3,779.07 $9,200.00

CR(2)

3 4 5 6 7 8 9 10 11

$4,802.00 $3,361.40 $2,352.98 $1,647.09 $1,152.96 $807.07 $564.95 $395.47 $276.83

=PMT(15%,2,-14000,14000*(1-30%)^2) O&M(2) =3500+600*(2-1) BTEUAO&MC(2) =PMT(15%,2,-NPV(15%,3500,4100)) BTEUAC(2) =5420.93+3779.07 $4,748.81 $4,700.00 $4,044.28 $8,793.09 $4,230.54 $5,300.00 $4,295.75 $8,526.30 $3,827.43 $5,900.00 $4,533.69 $8,361.12 $3,511.16 $6,500.00 $4,758.31 $8,269.47 $3,260.86 $7,100.00 $4,969.91 $8,230.77 $3,061.11 $7,700.00 $5,168.80 $8,229.90 OPTIMUM $2,900.38 $8,300.00 $5,355.34 $8,255.72 $2,770.05 $8,900.00 $5,529.92 $8,299.97 $2,663.60 $9,500.00 $5,692.96 $8,356.56

PROBLEM 11.25 FIRST COST = O&M FIRST YEAR = O&M % INCREASE = SALVAGE % DECLINE = MARR =

$128,000.00 $10,000.00 25.00% 30.00% 15.00%

St LIFE CR 1 $89,600.00 $57,600.00 2 $62,720.00 $49,562.79 3 $43,904.00 $43,417.71 St(3) =128000*(1-30%)^3

O&M BTEUAO&MC BTEUAC $10,000.00 $10,000.00 $67,600.00 $12,500.00 $11,162.79 $60,725.58 $15,625.00 $12,447.80 $55,865.51

CR(3)

4 5 6 7 8 9 10 11

=PMT(15%,3,-128000,128000*(1-30%)^3) O&M(3) =10000*(1+25%)^(3-1) BTEUAO&MC(3) =PMT(15%,3,-NPV(15%,10000,12500,15625)) BTEUAC(3) =43417.71+12447.8 $30,732.80 $38,679.25 $19,531.25 $13,866.37 $52,545.62 $21,512.96 $34,993.68 $24,414.06 $15,430.76 $50,424.44 $15,059.07 $32,102.02 $30,517.58 $17,154.23 $49,256.25 $10,541.35 $29,813.61 $38,146.97 $19,051.14 $48,864.75 OPTIMUM $7,378.95 $27,987.25 $47,683.72 $21,137.03 $49,124.28 $5,165.26 $26,517.76 $59,604.64 $23,428.70 $49,946.46 $3,615.68 $25,326.18 $74,505.81 $25,944.35 $51,270.54 $2,530.98 $24,352.89 $93,132.26 $28,703.69 $53,056.58

PROBLEM 11.26 FIRST COST = O&M FIRST YEAR = O&M EACH ADDN YR = SALVAGE % DECLINE = MIN SALVAGE = MARR =

$70,000.00 $14,000.00 $1,000.00 20.00% $3,000.00 15.00%

St LIFE CR O&M BTEUAO&MC BTEUAC 1 $56,000.00 $24,500.00 $14,000.00 $14,000.00 $38,500.00 2 $44,800.00 $22,220.93 $15,000.00 $14,465.12 $36,686.05 3 $35,840.00 $20,337.29 $16,000.00 $14,907.13 $35,244.42 St(3) =MAX(70000*(1-20%)^3,3000) CR(3) =PMT(15%,3,-70000,35840) O&M(3) =14000+1000*(3-1) BTEUAO&MC(3) =PMT(15%,3,-NPV(15%,14000,15000,16000)) BTEUAC(3) =20337.29+14907.13 4 $28,672.00 $18,776.57 $17,000.00 $15,326.26 $34,102.82 5 $22,937.60 $17,480.09 $18,000.00 $15,722.81 $33,202.90 6 $18,350.08 $16,400.33 $19,000.00 $16,097.19 $32,497.52 7 $14,680.06 $15,498.73 $20,000.00 $16,449.85 $31,948.58 8 $11,744.05 $14,743.95 $21,000.00 $16,781.33 $31,525.28 9 $9,395.24 $14,110.47 $22,000.00 $17,092.23 $31,202.69 10 $7,516.19 $13,577.46 $23,000.00 $17,383.20 $30,960.65 11 $6,012.95 $13,127.88 $24,000.00 $17,654.94 $30,782.82 12 $4,810.36 $12,747.79 $25,000.00 $17,908.20 $30,655.99 13 $3,848.29 $12,425.71 $26,000.00 $18,143.76 $30,569.47 14 $3,078.63 $12,152.19 $27,000.00 $18,362.41 $30,514.60 15 $3,000.00 $11,908.14 $28,000.00 $18,564.96 $30,473.10 16 $3,000.00 $11,702.50 $29,000.00 $18,752.25 $30,454.74 17 $3,000.00 $11,529.58 $30,000.00 $18,925.09 $30,454.67 OPTIMUM 18 $3,000.00 $11,383.48 $31,000.00 $19,084.31 $30,467.79 19 $3,000.00 $11,259.54 $32,000.00 $19,230.73 $30,490.26 20 $3,000.00 $11,154.02 $33,000.00 $19,365.14 $30,519.16 21 $3,000.00 $11,063.93 $34,000.00 $19,488.32 $30,552.24

PROBLEM 11.27 FIRST COST = OP COST FIRST YEAR = OP COST INCR = MAINT COST FIRST YR = MAINT COST INCR = MARKET VAL YEAR 1 = MARKET VAL DECR = MARKET VAL MIN = MARR =

$400,000.00 $20,000.00 8.00% $8,000.00 35.00% $310,000.00 $40,000.00 $30,000.00 20.00%

St LIFE CR OP COST MAINT COST TOTAL O&M BTEUAO&MC BTEUAC 1 $310,000.00 $170,000.00 $20,000.00 $8,000.00 $28,000.00 $28,000.00 $198,000.00 2 $270,000.00 $139,090.91 $21,600.00 $10,800.00 $32,400.00 $30,000.00 $169,090.91 3 $230,000.00 $126,703.30 $23,328.00 $14,580.00 $37,908.00 $32,172.53 $158,875.82 St(3) =MAX(310000-40000*(3-1),30000) CR(3) =PMT(20%,3,-400000,MAX(310000-40000*(3-1),30000)) OP COST(3) =20000*(1+8%)^(3-1) MAINT COST(3) =8000*(1+35%)^(3-1) TOTAL O&M(3) =23328+14580 BTEUAO&MC(3) =PMT(20%,3,-NPV(20%,28000,32400,37908)) BTEUAC(3) =126703.3+32172.53 4 $190,000.00 $119,120.72 $25,194.24 $19,683.00 $44,877.24 $34,539.28 $153,659.99 5 $150,000.00 $113,594.93 $27,209.78 $26,572.05 $53,781.83 $37,125.09 $150,720.01 6 $110,000.00 $109,204.67 $29,386.56 $35,872.27 $65,258.83 $39,958.32 $149,162.98 7 $70,000.00 $105,549.90 $31,737.49 $48,427.56 $80,165.05 $43,071.28 $148,621.17 8 $30,000.00 $102,425.49 $34,276.49 $65,377.21 $99,653.69 $46,500.71 $148,926.19 9 $30,000.00 $97,789.40 $37,018.60 $88,259.23 $125,277.83 $50,288.27 $148,077.67 OPTIMUM 10 $30,000.00 $94,253.42 $39,980.09 $119,149.96 $159,130.05 $54,481.15 $148,734.57 11 $30,000.00 $91,508.40 $43,178.50 $160,852.45 $204,030.95 $59,132.72 $150,641.12 12 $30,000.00 $89,348.04 $46,632.78 $217,150.80 $263,783.58 $64,303.22 $153,651.25

PROBLEM 11.28 FIRST COST = O&M FIRST YEAR = O&M EACH ADDN YR = SALVAGE % DECLINE = MACRS-GDS PROPERTY = TAX RATE = AFTER-TAX MARR =

$14,000.00 $3,500.00 $600.00 30.00% 5 YEARS 40.00% 9.00%

LIFE

1 2 3 4 5 6 7 8 9 10

O&M

DWO1

DWO2

TI1

$9,800.00 -$3,500.00 $2,800.00 $2,800.00 -$6,300.00 $6,860.00 -$4,100.00 $4,480.00 $2,240.00 -$8,580.00 $4,802.00 -$4,700.00 $2,688.00 $1,344.00 -$7,388.00 $3,361.40 -$5,300.00 $1,612.80 $806.40 -$6,912.80 $2,352.98 -$5,900.00 $1,612.80 $806.40 -$7,512.80 $1,647.09 -$6,500.00 $806.40 $806.40 -$7,306.40 $1,152.96 -$7,100.00 $0.00 $0.00 -$7,100.00 $807.07 -$7,700.00 $0.00 $0.00 -$7,700.00 $564.95 -$8,300.00 $0.00 $0.00 -$8,300.00 $395.47 -$8,900.00 $0.00 $0.00 -$8,900.00

1 ASSUMES REPLACEMENT OCCURS IN A LATER YEAR 2 ASSUMES REPLACEMENT OCCURS IN CURRENT YEAR 3 DOES NOT INCLUDE SALVAGE VALUE OR REALIZED GAIN (LOSS) FRO 4 INCLUDES TAX ON REALIZED GAIN (LOSS)

COMPARE TO PROBLEM 11.24: AFTER-TAX ANALYSIS HAS LITTLE EF

TI2

T1,3

T2,3

ToRG2,4 ATEUAC

-$6,300.00 -$2,520.00 -$2,520.00 $11,200.00 $11,200.00 -$560.00 $5,880.00 -$6,340.00 -$3,432.00 -$2,536.00 $6,720.00 $8,960.00 -$840.00 $5,533.78 -$6,044.00 -$2,955.20 -$2,417.60 $4,032.00 $5,376.00 -$229.60 $5,269.41 -$6,106.40 -$2,765.12 -$2,442.56 $2,419.20 $3,225.60 $54.32 $5,089.98 -$6,706.40 -$3,005.12 -$2,682.56 $806.40 $1,612.80 $296.07 $4,976.97 -$7,306.40 -$2,922.56 -$2,922.56 $0.00 $0.00 $658.83 $4,910.86 -$7,100.00 -$2,840.00 -$2,840.00 $0.00 $0.00 $461.18 $4,882.01 OPTIMUM -$7,700.00 -$3,080.00 -$3,080.00 $0.00 $0.00 $322.83 $4,882.72 -$8,300.00 -$3,320.00 -$3,320.00 $0.00 $0.00 $225.98 $4,904.69 -$8,900.00 -$3,560.00 -$3,560.00 $0.00 $0.00 $158.19 $4,942.04

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

ATER YEAR RRENT YEAR REALIZED GAIN (LOSS) FROM REPLACEMENT

X ANALYSIS HAS LITTLE EFFECT ON OPTIMUM LIFE (8 VS 7); HOWEVER, EUAC IS SUBSTANTIALLY LESS

PROBLEM 11.29 FIRST COST = O&M FIRST YEAR = O&M % EACH ADDN YR = SALVAGE % DECLINE = MACRS-GDS PROPERTY = TAX RATE = AFTER-TAX MARR = LIFE 1 2 3 4 5 6 7 8 9 10

$128,000.00 $10,000.00 25.00% 30.00% 5 YEARS 40.00% 9.00% SV

O&M

DWO1

DWO2

$89,600.00 -$10,000.00 $25,600.00 $25,600.00 $62,720.00 -$12,500.00 $40,960.00 $20,480.00 $43,904.00 -$15,625.00 $24,576.00 $12,288.00 $30,732.80 -$19,531.25 $14,745.60 $7,372.80 $21,512.96 -$24,414.06 $14,745.60 $7,372.80 $15,059.07 -$30,517.58 $7,372.80 $7,372.80 $10,541.35 -$38,146.97 $0.00 $0.00 $7,378.95 -$47,683.72 $0.00 $0.00 $5,165.26 -$59,604.64 $0.00 $0.00 $3,615.68 -$74,505.81 $0.00 $0.00

1 ASSUMES REPLACEMENT OCCURS IN A LATER YEAR 2 ASSUMES REPLACEMENT OCCURS IN CURRENT YEAR 3 DOES NOT INCLUDE SALVAGE VALUE OR REALIZED GAIN (LOSS) FRO 4 INCLUDES TAX ON REALIZED GAIN (LOSS)

COMPARE TO PROBLEM 11.25: AFTER-TAX ANALYSIS HAS LITTLE EF

TI1

TI2

T1,3

T2,3

ToRG2,4

ATEUAC

-$35,600.00 -$35,600.00 -$14,240.00 -$14,240.00 $102,400.00 $102,400.00 -$5,120.00 $40,560.00 -$53,460.00 -$32,980.00 -$21,384.00 -$13,192.00 $61,440.00 $81,920.00 -$7,680.00 $36,537.42 -$40,201.00 -$27,913.00 -$16,080.40 -$11,165.20 $36,864.00 $49,152.00 -$2,099.20 $33,403.25 -$34,276.85 -$26,904.05 -$13,710.74 -$10,761.62 $22,118.40 $29,491.20 $496.64 $31,198.23 -$39,159.66 -$31,786.86 -$15,663.87 -$12,714.75 $7,372.80 $14,745.60 $2,706.94 $29,767.57 -$37,890.38 -$37,890.38 -$15,156.15 -$15,156.15 $0.00 $0.00 $6,023.63 $28,949.11 -$38,146.97 -$38,146.97 -$15,258.79 -$15,258.79 $0.00 $0.00 $4,216.54 $28,673.35 -$47,683.72 -$47,683.72 -$19,073.49 -$19,073.49 $0.00 $0.00 $2,951.58 $28,891.29 -$59,604.64 -$59,604.64 -$23,841.86 -$23,841.86 $0.00 $0.00 $2,066.10 $29,551.62 -$74,505.81 -$74,505.81 -$29,802.32 -$29,802.32 $0.00 $0.00 $1,446.27 $30,628.47

IN A LATER YEAR IN CURRENT YEAR E OR REALIZED GAIN (LOSS) FROM REPLACEMENT

ER-TAX ANALYSIS HAS LITTLE EFFECT ON OPTIMUM LIFE (7 VS 7); HOWEVER, EUAC IS SUBSTANTIALLY LESS

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76% OPTIMUM

TIALLY LESS

PROBLEM 11.30 FIRST COST = O&M FIRST YEAR = O&M EACH ADDN YR = SALVAGE % DECLINE = MIN SALVAGE = MACRS-GDS PROPERTY = TAX RATE = AFTER-TAX MARR =

$70,000.00 $14,000.00 $1,000.00 20.00% $3,000.00 10 YEARS 40.00% 9.00% O&M

DWO1

DWO2

TI1

LIFE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$56,000.00 -$14,000.00 $7,000.00 $7,000.00 -$21,000.00 $44,800.00 -$15,000.00 $12,600.00 $6,300.00 -$27,600.00 $35,840.00 -$16,000.00 $10,080.00 $5,040.00 -$26,080.00 $28,672.00 -$17,000.00 $8,064.00 $4,032.00 -$25,064.00 $22,937.60 -$18,000.00 $6,454.00 $3,227.00 -$24,454.00 $18,350.08 -$19,000.00 $5,159.00 $2,579.50 -$24,159.00 $14,680.06 -$20,000.00 $4,585.00 $2,292.50 -$24,585.00 $11,744.05 -$21,000.00 $4,585.00 $2,292.50 -$25,585.00 $9,395.24 -$22,000.00 $4,592.00 $2,296.00 -$26,592.00 $7,516.19 -$23,000.00 $4,585.00 $2,292.50 -$27,585.00 $6,012.95 -$24,000.00 $2,296.00 $2,296.00 -$26,296.00 $4,810.36 -$25,000.00 $0.00 $0.00 -$25,000.00 $3,848.29 -$26,000.00 $0.00 $0.00 -$26,000.00 $3,078.63 -$27,000.00 $0.00 $0.00 -$27,000.00 $3,000.00 -$28,000.00 $0.00 $0.00 -$28,000.00 $3,000.00 -$29,000.00 $0.00 $0.00 -$29,000.00 $3,000.00 -$30,000.00 $0.00 $0.00 -$30,000.00 $3,000.00 -$31,000.00 $0.00 $0.00 -$31,000.00 $3,000.00 -$32,000.00 $0.00 $0.00 -$32,000.00 $3,000.00 -$33,000.00 $0.00 $0.00 -$33,000.00

1 ASSUMES REPLACEMENT OCCURS IN A LATER YEAR 2 ASSUMES REPLACEMENT OCCURS IN CURRENT YEAR 3 DOES NOT INCLUDE SALVAGE VALUE OR REALIZED GAIN (LOSS) FRO 4 INCLUDES TAX ON REALIZED GAIN (LOSS)

COMPARE TO PROBLEM 11.26: AFTER-TAX ANALYSIS HAS LITTLE EF

TI2

T1,3

T2,3

ToRG2,4

ATEUAC

-$21,000.00 -$8,400.00 -$8,400.00 $63,000.00 $63,000.00 -$2,800.00 $23,100.00 -$21,300.00 -$11,040.00 -$8,520.00 $50,400.00 $56,700.00 -$4,760.00 $22,100.96 -$21,040.00 -$10,432.00 -$8,416.00 $40,320.00 $45,360.00 -$3,808.00 $21,218.93 -$21,032.00 -$10,025.60 -$8,412.80 $32,256.00 $36,288.00 -$3,046.40 $20,490.49 -$21,227.00 -$9,781.60 -$8,490.80 $25,802.00 $29,029.00 -$2,436.56 $19,898.93 -$21,579.50 -$9,663.60 -$8,631.80 $20,643.00 $23,222.50 -$1,948.97 $19,423.22 -$22,292.50 -$9,834.00 -$8,917.00 $16,058.00 $18,350.50 -$1,468.17 $19,044.20 -$23,292.50 -$10,234.00 -$9,317.00 $11,473.00 $13,765.50 -$808.58 $18,743.91 -$24,296.00 -$10,636.80 -$9,718.40 $6,881.00 $9,177.00 $87.30 $18,506.80 -$25,292.50 -$11,034.00 -$10,117.00 $2,296.00 $4,588.50 $1,171.08 $18,320.90 -$26,296.00 -$10,518.40 -$10,518.40 $0.00 $0.00 $2,405.18 $18,176.80 -$25,000.00 -$10,000.00 -$10,000.00 $0.00 $0.00 $1,924.15 $18,071.02 -$26,000.00 -$10,400.00 -$10,400.00 $0.00 $0.00 $1,539.32 $17,999.83 -$27,000.00 -$10,800.00 -$10,800.00 $0.00 $0.00 $1,231.45 $17,956.39 -$28,000.00 -$11,200.00 -$11,200.00 $0.00 $0.00 $1,200.00 $17,924.27 -$29,000.00 -$11,600.00 -$11,600.00 $0.00 $0.00 $1,200.00 $17,913.30 OPTIMUM -$30,000.00 -$12,000.00 -$12,000.00 $0.00 $0.00 $1,200.00 $17,920.02 -$31,000.00 -$12,400.00 -$12,400.00 $0.00 $0.00 $1,200.00 $17,940.41 -$32,000.00 -$12,800.00 -$12,800.00 $0.00 $0.00 $1,200.00 $17,971.30 -$33,000.00 -$13,200.00 -$13,200.00 $0.00 $0.00 $1,200.00 $18,010.21

ALIZED GAIN (LOSS) FROM REPLACEMENT

NALYSIS HAS LITTLE EFFECT ON OPTIMUM LIFE (17 VS 16); HOWEVER, EUAC IS SUBSTANTIALLY LESS

MACRS(10) 10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

PROBLEM 11.31 FIRST COST = OP COST FIRST YEAR = OP COST INCR = MAINT COST FIRST YR = MAINT COST INCR = MARKET VAL YEAR 1 = MARKET VAL DECR = MARKET VAL MIN = MACRS-GDS PROPERTY = TAX RATE = AFTER-TAX MARR =

$400,000.00 $20,000.00 8.00% $8,000.00 35.00% $310,000.00 $40,000.00 $30,000.00 5 YEARS 40.00% 12.00% O&M

DWO1

DWO2

LIFE

1 2 3 4 5 6 7 8 9 10 11 12

$310,000.00 -$28,000.00 $80,000.00 $80,000.00 $270,000.00 -$32,400.00 $128,000.00 $64,000.00 $230,000.00 -$37,908.00 $76,800.00 $38,400.00 $190,000.00 -$44,877.24 $46,080.00 $23,040.00 $150,000.00 -$53,781.83 $46,080.00 $23,040.00 $110,000.00 -$65,258.83 $23,040.00 $23,040.00 $70,000.00 -$80,165.05 $0.00 $0.00 $30,000.00 -$99,653.69 $0.00 $0.00 $30,000.00 -$125,277.83 $0.00 $0.00 $30,000.00 -$159,130.05 $0.00 $0.00 $30,000.00 -$204,030.95 $0.00 $0.00 $30,000.00 -$263,783.58 $0.00 $0.00

1 ASSUMES REPLACEMENT OCCURS IN A LATER YEAR 2 ASSUMES REPLACEMENT OCCURS IN CURRENT YEAR 3 DOES NOT INCLUDE SALVAGE VALUE OR REALIZED GAIN (LOSS) FRO 4 INCLUDES TAX ON REALIZED GAIN (LOSS)

COMPARE TO PROBLEM 11.27: AFTER-TAX ANALYSIS HAS LITTLE EF

TI1

TI2

T1,3

T2,3

ToRG2,4

ATEUAC

-$108,000.00 -$108,000.00 -$43,200.00 -$43,200.00 $320,000.00 $320,000.00 -$4,000.00 $118,800.00 -$160,400.00 -$96,400.00 -$64,160.00 -$38,560.00 $192,000.00 $256,000.00 $5,600.00 $101,026.42 -$114,708.00 -$76,308.00 -$45,883.20 -$30,523.20 $115,200.00 $153,600.00 $30,560.00 $93,432.29 -$90,957.24 -$67,917.24 -$36,382.90 -$27,166.90 $69,120.00 $92,160.00 $39,136.00 $89,160.49 -$99,861.83 -$76,821.83 -$39,944.73 -$30,728.73 $23,040.00 $46,080.00 $41,568.00 $86,658.68 -$88,298.83 -$88,298.83 -$35,319.53 -$35,319.53 $0.00 $0.00 $44,000.00 $85,229.57 -$80,165.05 -$80,165.05 -$32,066.02 -$32,066.02 $0.00 $0.00 $28,000.00 $84,713.11 -$99,653.69 -$99,653.69 -$39,861.48 -$39,861.48 $0.00 $0.00 $12,000.00 $85,048.01 -$125,277.83 -$125,277.83 -$50,111.13 -$50,111.13 $0.00 $0.00 $12,000.00 $84,525.44 -$159,130.05 -$159,130.05 -$63,652.02 -$63,652.02 $0.00 $0.00 $12,000.00 $85,272.65 -$204,030.95 -$204,030.95 -$81,612.38 -$81,612.38 $0.00 $0.00 $12,000.00 $87,175.66 -$263,783.58 -$263,783.58 -$105,513.43 -$105,513.43 $0.00 $0.00 $12,000.00 $90,211.09

A LATER YEAR CURRENT YEAR OR REALIZED GAIN (LOSS) FROM REPLACEMENT

TAX ANALYSIS HAS LITTLE EFFECT ON OPTIMUM LIFE (9 VS 9); HOWEVER, EUAC IS SUBSTANTIALLY LESS

MACRS(5) 20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

OPTIMUM

A 1 PROBLEM 12.1 2 3 4 5 6 7 8

B 1 2 3 4 5 6 7 8

SOME GOOD DEFINITIONS OF INFLATION ARE: PERSISTENT DECREASE IN THE PURCHASING POWER OF MONEY PERSISTENT INCREASE IN THE LEVEL OF PRICES WITHOUT INCREASING VALUE EROSION IN THE PURCHASING POWER OF MONEY SUSTAINED INCREASES IN THE PRICES OF GOODS AND SERVICES

A 1 PROBLEM 12.2 2 3 4 5 6 7 8 9 10

B 1 2 3 EXAMPLES OF GOODS OR SERVICES EXHIBITING INFLATION INCLUDE: 4 5 PRICE OF GASOLINE 6 COST OF HOUSING / REAL ESTATE (GEOGRAPHICALLY DEPENDENT - CAN ALSO DEFLATE) 7 PRICE OF COPPER 8 PRICE OF TEXTBOOKS 9 COST OF TUITION 10 COST PER HOUR OF MECHANIC WORK

A 1 PROBLEM 12.3 2 3 4 5 6 7 8 9 10

B 1 2 3 DEFLATION MAY BE EXPRESSED AS A NEGATIVE INFLATION 4 5 AN EXCELLENT EXAMPLE OF SOMETHING THAT HAS EXHIBITED DEFLATION IS 6 MOST ALL ELECTRONICS EQUIPMENT, INCLUDING TELEVISIONS, COMPUTERS, GAMES, PHONES 7 8 DEFLATION MAY BE EASIER TO SEE OVER THE LONG HAUL 9 FOR EXAMPLE, A REGULAR 19" COLOR TV COST ABOUT $450 IN 1969. 10 TODAY, ONE CAN BUY A BETTER REGULAR 19" COLOR (NO OTHER CHOICE!) TV EASILY FOR LESS THAN $150

C 1 2 3 4 5 6 7 8 9 SILY FOR LESS 10 THAN $150

A 1 PROBLEM 12.4 2

3 4

5 6 7 8 9

IN RECENT YEARS, WE HAVE SEEN THE PRICE OF REAL ESTATE (HOMES, APARTMENTS, OFFICES, AND LAND) INCREASE. THEN, BEGINNING IN 2006, THE SAME THINGS HAVE BEGUN TO DECREASE DRAMATICALLY IN PRICE. INTERESTINGLY, WE HAVE SEEN BOTH HAPPEN AT THE SAME TIME. FOR EXAMPLE, RECENT DEFLATION ON THE EAST AND WEST COASTS OF THE USA, WITH CONTINUED INFLATION IN THE MIDDLE OF THE COUNTRY.

ANOTHER EXAMPLE WOULD BE THE PRICE OF SOME VEHICLES INCLUDING SUVS, TRUCKS, AND LUXURY CARS THAT HAVE A HISTORY OF PRICE INCREASES THROUGH THE 2000'S UNTIL 2008. THEN, WITH THE ECONOMIC DOWNTURN, PRICES OF THE SAME VEHICLES HAVE FALLEN BY AS MUCH AS 30 PERCENT IN SOME CASES.

A 1 PROBLEM 12.5 2 3 4 5

B 1 2 3 THE CPI IS A MARKET BASKET RATE IN THAT IT IS BASED ON 80,000 PRICES THAT ARE RECORDED IN 4 87 URBAN AREAS. THE "MARKET BASKET" IS PURCHASED EACH MONTH AND REFLECTS WHAT 5 COUSUMERS PURCHASE FOR THEIR DAY TO DAY LIVING.

1 2 ARE RECORDED 3 IN 4 5

A 1 PROBLEM 12.6 2 3 4 5 6 7

B 1 2 3 4 5 6 7

THE CONSUMER PRICE INDEX (CPI) MEASURES PRICE CHANGES FROM THE PERSPECTIVE OF THE PURCHASE THE PRODUCERS PRICE INDEX (PPI) MEASURES PRICE CHANGES FROM THE PERSPECTIVE OF THE SELLER. THE PPI IS A FAMILY OF OVER 10,000 INDEXES PUBLISHED MONTHLY BY THE BLS, AND THERE IS AN INDEX FOR PRACTICALLY ANY BUSINESS.

C D 1 2 PECTIVE OF THE 3 PURCHASER. 4 PECTIVE OF THE 5 SELLER. 6 7

A 1 PROBLEM 12.7 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B 1 2 3 THE HIGHER EDUCATION PRICE INDEX (HEPI) MEASURES THE AVERAGE RELATIVE LEVEL IN THE PRICES OF 4 A FIXED MARKET BASKET OF GOODS AND SERVICES PURCHASED BY COLLEGES AND UNIVERSITIES, 5 EXCLUDING EXPENDITURES FOR RESEARCH. IT INCLUDES SALARIES, WAGES, AND FRINGE BENEFITS, 6 CONTRACTED SERVICES (DATA PROCESSING, COMMUNICATIONS, TRANSPORTATION, SUPPLIES, ETC.). 7 THERE ARE OVER 100 ITEMS PRICED IN THE HEPI. 8 9 THE HEPI IS SIMILAR TO THE CPI AND PPI; HOWEVER, THEY ARE FOCUSED ON CONSUMERS AND PRODUCER 10 RESPECTIVELY. THE HEPI IS FOCUSED STRICTLY ON HIGHER EDUCATION. 11 12 HEPI AND CPI ARE RELATED IN THAT THE CPI INCLUDES COLLEGE TUITION IN ONE OF ITS CATEGORIES. 13 THE CPI IS VIEWING THE COST OF HIGHER EDUCATION FROM THE VIEWPOINT OF THE STUDENT. THE 14 HEPI IS VIEWING THE COST OF HIGHER EDUCATION FROM THE PERSPECTIVE OF THE COLLEGE OR 15 UNIVERSITY.

C D 1 2 LEVEL IN THE3 PRICES OF 4 5 6 7 8 NSUMERS AND 9 PRODUCERS, 10 11 12 13 14 15

A 1 PROBLEM 12.8 2 3 4 5 6 7 8 9 10 11 12 13 14 15

B 1 2 3 THEY SHOULD NOT CONCLUDE THAT THE CPI IS IRRELEVANT TO THEM. THEY NEED TO REALIZE TWO 4 THINGS, IN PARTICULAR. FIRST, THE CPI DOES NOT "EXACTLY" DESCRIBE ANY INDIVIDUAL'S PURCHASING 5 HABITS. SECOND, THE ECONOMY TODAY IS VERY "CONNECTED" IN THAT PRICE FLUCTUATIONS IN CERTAIN 6 ITEMS A CONSUMER DOES NOT PURCHASE DO AFFECT PRICE FLUCTUATIONS IN THINGS THEY DO 7 PURCHASE. FOR EXAMPLE, LEATHER SHOES ARE AFFECTED BY THE PRICE OF ANIMALS FROM WHICH 8 THE LEATHER COMES. THE PRICE OF ANIMALS IS AFFECTED BY THE QUALITY OF THE ANIMALS AS 9 DETERMINED BY WHAT THEY ARE FED AND THE CARE THEY RECEIVE. FEED PRICES FOR THE ANIMALS 10 (INCLUDING PROCESSED FOODS OR NATURAL GRASS) ARE AFFECTED BY ENERGY USED IN PROCESSING 11 OF FEED OR FERTILIZER. THE PRICE OF ENERGY USED IS AFFECTED BY OIL AND GAS PRICES. AND SO ON. 12 13 THE BOTTOM LINE IS THAT THE CPI DOES A PRETTY GOOD JOB OF ESTIMATING OVERAL PRICE INCREASES 14 TO CONSUMERS, AND IT IS NOT IRRELEVANT SIMPLY BECAUSE ONE'S BUYING HABITS ARE NOT EXACTLY 15 REFLECTED BY THE MARKET BASKET.

C 1 2 3 4 LUCTUATIONS5 IN CERTAIN 6 7 8 9 10 11 12 13 14 15

A B C D E F G 1 PROBLEM 12.9 2 3 a YEAR 2006 2007 2008 2009 2010 4 INDEX 201.600 207.342 215.303 214.537 218.056 5 6 INFLATION RATE 2.85% 3.84% -0.36% 1.64% 7 8 b ((1+f)^4)-1 = ((INDEX2010 - INDEX2006)/INDEX2006) 9 (INDEX2010-INDEX2006)/INDEX2006= 8.16270% 10 11 ((1+f)^4)-1 = 8.16270% <--SOLVER TARGET CELL 12 13 f= 1.98103% <--SOLVER CHANGED CELL 14 15 OR 16 17 (F|P f%,4)-1= 8.16270% <--SOLVER TARGET CELL 18 19 f= 1.98103% <--SOLVER CHANGED CELL

A B C D E F G 1 PROBLEM 12.10 2 3 1 2 3 4 4 a MONTH JANUARY FEBRUARY MARCH APRIL 5 RATE % 2.215% 11.867% 7.629% 6 7 INDEX 278.404 284.571 318.341 342.627 8 9 b ((1+f)^3)-1 = ((INDEXAPRIL - INDEXJANUARY)/INDEXJANUARY) 10 (INDEXAPRIL-INDEXJANUARY)/INDEXJANUARY= 23.068223% 11 12 ((1+f)^3)-1 =23.06826% <--SOLVER TARGET CELL 13 14 f= 7.16394% <--SOLVER CHANGED CELL 15 16 OR 17 18 (F|P f%,3)-1= 23.06826% <--SOLVER TARGET CELL 19 20 f= 7.16394% <--SOLVER CHANGED CELL

A 1 PROBLEM 12.11 2 3 a 4 5 6 7 8 b 9 10 11 12 13 14 15 16 17 18 19

YEAR INDEX

2005 122.8

INCREASE RATE

2006 2007 127.2 135.2

2008 135.7

2009 146.2

3.58% 6.29%

0.37%

7.74%

((1+f)^4)-1 = ((INDEX2009 - INDEX2005)/INDEX2005) (INDEX2009-INDEX2005)/INDEX2005= 19.05537% ((1+f)^4)-1 = f=

19.05535% <--SOLVER TARGET CELL 4.45692% <--SOLVER CHANGED CELL

OR (F|P f%,4)-1= f=

19.05535% <--SOLVER TARGET CELL 4.45692% <--SOLVER CHANGED CELL

A 1 PROBLEM 12.12 2 3 a 4 5 6 7 8 b 9 10 11 12 13 14 15 16 17 18 19

YEAR RATE

2004

INDEX

$12.73

2005 2006 18.853% 15.995% $15.13

$17.55

2007 10.655% $19.42

((1+f)^5)-1 = ((INDEX2009 - INDEX2004)/INDEX2004) (INDEX2009-INDEX2004)/INDEX2004= 11.54770% ((1+f)^5)-1 = f=

11.54765% <--SOLVER TARGET CELL 2.20969% <--SOLVER CHANGED CELL

OR (F|P f%,5)-1= 11.54765% <--SOLVER TARGET CELL f=

2.20969% <--SOLVER CHANGED CELL

2008 2009 -16.220% -12.723% $16.27

$14.20

A 1 PROBLEM 12.13 2 3 4 5 6 7 8 9 10 11 12 13

COMBINED RATE= INFLATION RATE=

5.2000% 3.5000%

REAL INTEREST RATE= 1.6425% OR COMBINED RATE= INFLATION RATE=

5.2000% <--SOLVER TARGET CELL 3.5000%

REAL INTEREST RATE= 1.6425% <--SOLVER CHANGED CELL

A 1 PROBLEM 12.14 2 3 4 5 6 7 8 9 10 11 12 13

COMBINED RATE= INFLATION RATE=

6.2000% 4.0000%

REAL INTEREST RATE= 2.1154% OR COMBINED RATE INFLATION RATE

6.2001% <--SOLVER TARGET CELL 4.0000%

REAL INTEREST RATE

2.1155% <--SOLVER CHANGED CELL

A 1 PROBLEM 12.15 2 3 a 4 5 6 7 b 8 9 10 11 12 13 14 15 16 17

THE REASON FOR THE APPARENT DISCREPANCY IS THAT PRICES ON THE GOODS AND SER THEY ARE BUYING ARE INCREASING DUE TO INFLATION. THEREFORE, THEY ARE UNABLE TO BUY AS MUCH WITH THE SAME AMOUNT OF MONEY AS A YEAR BEFORE REAL INTEREST RATE= 10.0000% COMBINED RATE= 14.0000% INFLATION RATE=

3.6364%

OR REAL INTEREST RATE= 10.0000% COMBINED RATE= 14.0000% <--SOLVER TARGET CELL INFLATION RATE=

3.6364% <--SOLVER CHANGED CELL

E F 1 2 CY IS THAT PRICES 3 ON THE GOODS AND SERVICES 4 5 6 7 8 9 10 11 12 13 14 15 16 17

A B 1 PROBLEM 12.16 2 3 REAL INTEREST RATE 4 5 INFLATION RATE 6 7 COMBINED RATE

14.2000% 3.8000% 18.5396%

A B 1 PROBLEM 12.17 2 3 REAL INTEREST RATE 4 5 INFLATION RATE 6 7 COMBINED RATE

5.00%

6.00%

5.00% 0.00% 1.00% 2.00% 3.00% 4.00%

5.00% 6.05% 7.10% 8.15% 9.20% 10.25% 11.30%

1 2 3 4 5 6 7

7.00%

8.00%

9.00% 10.00% 15.00% 20.00% 50.00%

12.35% 13.40% 14.45% 15.50% 20.75% 26.00% 57.50%

A 1 PROBLEM 12.18 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

INTEREST EARNED = INFLATION RATE =

10.00% 4.00%

AMOUNT INVESTED =

$262,268.73 GOAL SEEK CHANGED CELL

INVESTED AT TIME = TIME HORIZON = TIME ZERO BUYING POWER =

5 20 $500,000.00

TIME ZERO BUYING POWER =

$500,000.00 GOAL SEEK SET CELL

OR USING INTEREST TABLES

$262,266.11 $500,000*(F|P 4%,20)*(P|F 10%,15)

E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

CHECK INVESTMENT AT TIME 5

$262,268.73 GOAL SEEK CHANGED CELL

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BUYING POWER $500,000.00 $520,000.00 $540,800.00 $562,432.00 $584,929.28 $608,326.45 $262,268.73 $632,659.51 $288,495.60 $657,965.89 $317,345.16 $684,284.53 $349,079.68 $711,655.91 $383,987.65 $740,122.14 $422,386.41 $769,727.03 $464,625.05 $800,516.11 $511,087.56 $832,536.75 $562,196.31 $865,838.22 $618,415.95 $900,471.75 $680,257.54 $936,490.62 $748,283.29 $973,950.25 $823,111.62 $1,012,908.26 $905,422.79 $1,053,424.59 $995,965.06 $1,095,561.57 $1,095,561.57 GOAL SEEK SET CELL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 L SEEK SET CELL 27

A 1 PROBLEM 12.19 2 3 4 5 6 7 8 9 10 11 12 13 14 15

TIME 0 LABOR REQS LABOR INCREASE RATE INFLATION RATE COMBINED RATE

$350,000.00 10.00% 4.00% 14.40%

EOY 0 1 2 3 4 5

a b THEN-CURRENT CONSTANT WORTH $350,000.00 $350,000.00 $400,400.00 $385,000.00 $458,057.60 $423,500.00 $524,017.89 $465,850.00 $599,476.47 $512,435.00 $685,801.08 $563,678.50

A 1 PROBLEM 12.20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

AMOUNT INVESTED COMBINED RATE INVESTMENT HORIZON INFLATION RATE BOAT COST AT INVESTMENT NAV SYSTEM AT INVESTMENT

$10,000.00 7.00% 10 3.70% $8,000.00 $4,000.00

INFLATING AT INFLATING AT

REAL RATE

BOAT COST AT HORIZON NAV SYSTEM AT HORIZON

$15,737.21 $3,268.29

AMOUNT EARNED TOTAL TO BUY BOAT AND NAV

$19,671.51 $19,005.50

AMOUNT LEFT OVER

3.18%

$666.01

E 1 2 3 4 5 6 7 7.00% 8 -2.00% 9 10 11 12 13 14 15 16 17 18

A 1 PROBLEM 12.21 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 16 b 17 18 19 20 21 22 23 24 c 25 26 d

REAL INTEREST RATE 10.68% INFLATION RATE 3.90% COMBINED INTEREST RATE 15.00% CURRENT EXPENSES $14,500.00 EOY 0 1 2 3 4 5

ACTUAL $ $15,065.50 $15,653.05 $16,263.52 $16,897.80 $17,556.82

EOY 0 1 2 3 4 5

REAL $ $14,500.00 $14,500.00 $14,500.00 $14,500.00 $14,500.00

$54,020.14

A B 1 PROBLEM 12.22 2 3 MATERIALS COST 4 INFLATION RATE 5 6 a MATERIALS COST 3 YEARS AGO 7 8 9 10 b MATERIALS COST IN 10 YEARS 11 12

$55,000.00 16.00% $35,236.17 FORMULA $35,236.17 EXCEL $242,628.93 FORMULA $242,628.93 EXCEL

A B 1 PROBLEM 12.23 2 3 REAL INTEREST RATE 4 INFLATION RATE 5 COMBINED INTEREST RATE 6 CURRENT STEEL COST 7 PERCENTAGE INCREASE IN ORDERS 8 9 a EOY 10 0 11 1 12 2 13 3 14 4 15 5 16 17 b EOY 18 0 19 1 20 2 21 3 22 4 23 5 24 25 c PW 26 27 d PW

16.00% 12.40% 30.38% $700,000.00 0.00% ACTUAL $ $786,800.00 $884,363.20 $994,024.24 $1,117,283.24 $1,255,826.36 REAL $ $700,000.00 $700,000.00 $700,000.00 $700,000.00 $700,000.00 $2,292,005.56 $2,292,005.56

A 1 PROBLEM 12.24 2 3 4 5 6 7 8 9 10 a 11 12 13 14 15 16 17 18 19 20 b 21 22 23 24 25 26 27 28 29 c 30 31 d

REAL INTEREST RATE INFLATION RATE COMBINED INTEREST RATE CURRENT STEEL COST PERCENTAGE INCREASE IN ORDERS

16.00% 12.40% 30.38% $700,000.00 20.00%

EOY 0 1 2 3 4 5

ACTUAL $ $944,160.00 $1,273,483.01 $1,717,673.88 $2,316,798.53 $3,124,897.86

EOY 0 1 2 3 4 5

REAL $ $840,000.00 $1,008,000.00 $1,209,600.00 $1,451,520.00 $1,741,824.00

$3,879,152.31

A 1 PROBLEM 12.25 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 16 17 18 19 20 b 21 22 c 23 24 25 26

COMBINED INTEREST RATE INFLATION RATE TIME HORIZON FINAL AMOUNT AMASSED

7.00% 4.00% 40 $2,000,000.00

AMOUNT INVESTED EACH YEAR

$10,018.20 USING INTEREST TABLES THIS IS =$2,000,000*(A|F 7%,40)

AMOUNT INVESTED EACH YEAR

$10,018.28 USING EXCEL'S PMT FUNCTION THIS IS =PMT(7%,40,,-2000000)

OR, CAN USE SOLVER TO DETERMINE THE AMOUNT INVESTED EACH YEAR AMOUNT INVESTED EACH YEAR FINAL AMOUNT AMASSED BUYING POWER BASE 40 YRS AGO

$10,018.28 <--SOLVER CHANGED CELL $2,000,000.00 <--SOLVER TARGET CELL $416,578.09

TV COST AT BEGINNING

$400.00

INFLATION RATE FOR TV

-3.00%

TV COST AT YEAR 40

$118.28

E 1 2 3 4 5 6 7 8 9 10 CEL'S PMT FUNCTION 11 THIS IS 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A B 1 PROBLEM 12.26 2 3 COMBINED INTEREST RATE 4 5 INFLATION RATE 6 7 TIME HORIZON 8 9 FINAL AMOUNT IN 1 JAN 2013 $ 10 11 a FINAL AMOUNT AMASSED 12 13 b $Z PER YEAR

8.00% 5.00% 40 $2,500,000.00 $17,599,971.78 $67,938.73

A 1 PROBLEM 12.27 2 3 4 5 6 7 8 9 10 11 12 13 14 15

REAL RETURN INFLATION COMBINED RETURN HORIZON

15.00% 7.00% 23.05% 4

EOY 0 1 2 3 4

$REAL $THEN-CURRENT -$8,000.00 -$8,000.00 $3,500.00 $3,745.00 $3,500.00 $4,007.15 $3,500.00 $4,287.65 $3,500.00 $4,587.79

$17,992.42

A B C D 1 PROBLEM 12.28 2 3 a PAYOUT TODAY $1,000,000.00 4 ALT ANNUAL PAYOUT $100,000.00 5 (NOTE BEGINNING OF YR) 6 PAYOUT HORIZON 20 7 REAL TVOM 3.50% 8 9 INFLATION RATE 4.00% 10 11 COMBINED RATE 7.64% 12 13 THEN-CURRENT 14 EOY LUMP SUM ANNUAL PAY 15 0 $1,000,000.00 $100,000.00 16 1 $100,000.00 17 2 $100,000.00 18 3 $100,000.00 19 4 $100,000.00 20 5 $100,000.00 21 6 $100,000.00 22 7 $100,000.00 23 8 $100,000.00 24 9 $100,000.00 25 10 $100,000.00 26 11 $100,000.00 27 12 $100,000.00 28 13 $100,000.00 29 14 $100,000.00 30 15 $100,000.00 31 16 $100,000.00 32 17 $100,000.00 33 18 $100,000.00 34 19 $100,000.00 35 20 $0.00 36 37 PW $1,000,000.00 $1,085,748.75 38 DEFERRING THE PAYMENTS IS SLIGHTLY BETTER ECONOMICALLY 39 40 41 b PAYOUT TODAY $1,000,000.00 42 ALT ANNUAL PAYOUT $100,000.00 43 (NOTE BEGINNING OF YR) 44 PAYOUT HORIZON 20 45 REAL TVOM 3.50% 46 47 INFLATION RATE 5.24% <--SOLVER CHANGED CELL 48 49 COMBINED RATE 8.92% 50 51 THEN-CURRENT

A 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

B EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

C LUMP SUM $1,000,000.00

D ANNUAL PAY $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $0.00

$1,000,000.00

I WOULD TAKE THE LUMP SUM - A BIRD IN THE HAND…INFLATION MIGHT GO UP; CONCERNS TAXES MAY BE EXCESSIVE WITH THE LUMP SUM VS YEARLY PAYMENTS, BUT MANY JUST PA GETTING IT OVER WITH. FOR THAT MATTER, IT WOULD TAKE A LOT HIGHER ANNUAL PAYOU ME TO CONSIDER TAKING THE ANNUAL PAYMENTS. THIS IS SUBJECTIVE - OTHERS WILL HA ANSWERS AND RATIONALE.

E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 CHANGED CELL 47 48 49 50 51

REAL ANNUAL PAY $100,000.00 $96,153.85 $92,455.62 $88,899.64 $85,480.42 $82,192.71 $79,031.45 $75,991.78 $73,069.02 $70,258.67 $67,556.42 $64,958.09 $62,459.70 $60,057.41 $57,747.51 $55,526.45 $53,390.82 $51,337.32 $49,362.81 $47,464.24 $0.00 $1,085,748.75

REAL

E F 52 ANNUAL PAY 53 $100,000.00 54 $95,024.21 55 $90,296.01 56 $85,803.07 57 $81,533.70 58 $77,476.75 59 $73,621.68 60 $69,958.42 61 $66,477.44 62 $63,169.66 63 $60,026.47 64 $57,039.68 65 $54,201.51 66 $51,504.56 67 $48,941.80 68 $46,506.56 69 $44,192.50 70 $41,993.57 71 $39,904.06 72 $37,918.52 73 $0.00 74 75 <--SOLVER TARGET CELL $1,000,000.00 76 77 …INFLATION78 MIGHT GO UP; CONCERNS ABOUT PAYMENTS; YEARLY PAYMENTS, 79 BUT MANY JUST PAY AND TAKE IT NOW, ULD TAKE A LOT 80 HIGHER ANNUAL PAYOUT (E.G., $140,000) TO GET THIS IS SUBJECTIVE 81 - OTHERS WILL HAVE DIFFERENT 82

A 1 PROBLEM 12.29 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

ENERGY COST RATE OF INCREASE

20.00%

DEVICE SAVINGS LAST YEAR

$1,000.00

LIFE OF DEVICE

COMBINED TVOM

12.00%

EOY

ENERGY SAVINGS

0 1 2 3 4 5 6 7 8 9 10

$1,200.00 $1,440.00 $1,728.00 $2,073.60 $2,488.32 $2,985.98 $3,583.18 $4,299.82 $5,159.78 $6,191.74

$14,903.60

A 1 PROBLEM 12.30 2 3 4 5 6 7 8 9 10 11 12 a 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 b 30 31 32 33 34 35 36 37 38 39 40 41 42 43

FIRST COST FIRST YEAR COST OF O&M YEARLY INCREASE IN O&M ACTUAL INCOME PER YEAR HORIZON INFLATION RATE REAL RETURN DESIRED COMBINED RETURN DESIRED EOY 0 1 2 3 4 5 6 7 8 9 10

$270,000.00 $40,000.00 11.00% $120,000.00 10 4.50% 3.60% 8.26% THEN-CURRENT INCOME $

THEN-CURRENT COST $ $270,000.00 $120,000.00 $40,000.00 $120,000.00 $44,400.00 $120,000.00 $49,284.00 $120,000.00 $54,705.24 $120,000.00 $60,722.82 $120,000.00 $67,402.33 $120,000.00 $74,816.58 $120,000.00 $83,046.41 $120,000.00 $92,181.51 $120,000.00 $102,321.48

EOY 0 1 2 3 4 5 6 7 8 9 10 PW

CONSTANT CONSTANT WORTH INCOME $ WORTH COST $ $270,000.00 $114,832.54 $38,277.51 $109,887.59 $40,658.41 $105,155.59 $43,187.40 $100,627.36 $45,873.70 $96,294.13 $48,727.09 $92,147.49 $51,757.96 $88,179.41 $54,977.35 $84,382.22 $58,397.00 $80,748.53 $62,029.35 $77,271.32 $65,887.63

E 1 2 3 4 5 6 7 8 9 10 11 12 THEN-CURRENT 13 $ 14 -$270,000.00 15 $80,000.00 16 $75,600.00 17 $70,716.00 18 $65,294.76 19 $59,277.18 20 $52,597.67 21 $45,183.42 22 $36,953.59 23 $27,818.49 24 $17,678.52 25 26 $111,292.23 27 28 29 CONSTANT 30 WORTH $ 31 -$270,000.00 32 $76,555.02 33 $69,229.18 34 $61,968.19 35 $54,753.66 36 $47,567.04 37 $40,389.53 38 $33,202.06 39 $25,985.22 40 $18,719.18 41 $11,383.69 42 43 $111,292.23

A 1 PROBLEM 12.31 2 3 4 5 6 7 8 9 10 11 a 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 b 40 41 42 43 44 45 46 47 48 49 50 51

INFLATION RATE COMBINED RATE FIRST DEPOSIT INCREASED RATE OF DEPOSIT AMOUNT OF FIRST WITHDRAWAL BIRTHDAY

DEPOSIT 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

PW FW

$12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $12,580.90 $0.00 $0.00 $0.00 $136,221.01 <--SOLVER TARGET CELL 1 $463,091.99

INFLATION RATE COMBINED RATE FIRST DEPOSIT INCREASED RATE OF DEPOSIT AMOUNT OF FIRST WITHDRAWAL BIRTHDAY

DEPOSIT 0 1 2 3

$5,748.43 $6,323.28 $6,955.61

A 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

B 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 PW FW

C $7,651.17 $8,416.28 $9,257.91 $10,183.70 $11,202.07 $12,322.28 $13,554.51 $14,909.96 $16,400.95 $18,041.05 $19,845.15 $21,829.67 $24,012.64 $26,413.90 $29,055.29 $0.00 $0.00 $0.00

$136,221.01 <--SOLVER TARGET CELL 2 $463,091.99

GRANDPARENTS NEED TO PUT UP $136,221.01 ON DATE OF BIRTH

E F 1 2 3 4.00% 4 6.00% 5 6 $12,580.90 <--SOLVER CHANGED CELL 1 7 8 0.00% 9 $100,000.00 10 11 WITHDRAWAL 12 13 $0.00 14 $0.00 15 $0.00 16 $0.00 17 $0.00 18 $0.00 19 $0.00 20 $0.00 21 $0.00 22 $0.00 23 $0.00 24 $0.00 25 $0.00 26 $0.00 27 $0.00 28 $0.00 29 $0.00 30 $100,000.00 31 $104,000.00 32 $108,160.00 33 $112,486.40 34 35 $136,221.01 36 $463,092.00 37 38 39 4.00% 40 6.00% 41 42 $5,748.43 <--SOLVER CHANGED CELL 2 43 44 10.00% 45 $100,000.00 46 47 WITHDRAWAL 48 49 $0.00 50 $0.00 51 $0.00

E 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $100,000.00 $104,000.00 $108,160.00 $112,486.40 $136,221.01 $463,092.00

A B C D E F 1 PROBLEM 12.32 2 3 INFLATION RATE 3.80% 4 COMBINED MARR 9.00% 5 REAL MARR 5.01% 6 AMOUNT BORROWED $160,000.00 7 LOAN INTEREST RATE 8.50% 8 LOAN PERIOD YEARS 5 9 10 INTEREST TOTAL $ OWED 11 REPAYMENT ACCRUED BEFORE YEARLY INTEREST 12 METHOD EOY DURING YR PAYMENT PAYMENT 13 a 1 0 14 1 $13,600.00 $173,600.00 $13,600.00 15 2 $13,600.00 $173,600.00 $13,600.00 16 3 $13,600.00 $173,600.00 $13,600.00 17 4 $13,600.00 $173,600.00 $13,600.00 18 5 $13,600.00 $173,600.00 $13,600.00 19 20 b 2 0 21 1 $13,600.00 $173,600.00 $13,600.00 22 2 $10,880.00 $138,880.00 $10,880.00 23 3 $8,160.00 $104,160.00 $8,160.00 24 4 $5,440.00 $69,440.00 $5,440.00 25 5 $2,720.00 $34,720.00 $2,720.00 26 27 c 3 0 28 1 $13,600.00 $173,600.00 $13,600.00 29 2 $11,304.79 $144,302.27 $11,304.79 30 3 $8,814.48 $112,514.22 $8,814.48 31 4 $6,112.49 $78,024.20 $6,112.49 32 5 $3,180.84 $40,602.52 $3,180.84 33 34 d 4 0 35 1 $13,600.00 $173,600.00 $0.00 36 2 $14,756.00 $188,356.00 $0.00 37 3 $16,010.26 $204,366.26 $0.00 38 4 $17,371.13 $221,737.39 $0.00 39 5 $18,847.68 $240,585.07 $80,585.07

G H I J 1 2 3 4 5 6 7 8 9 10 TOTAL $ OWED PW 11 PRINCIPAL TOTAL AFTER YEARLY CURRENT 12 PAYMENT PAYMENT PAYMENT $ 13 $160,000.00 14 $0.00 $13,600.00 $160,000.00 15 $0.00 $13,600.00 $160,000.00 16 $0.00 $13,600.00 $160,000.00 17 $0.00 $13,600.00 $160,000.00 18 $160,000.00 $173,600.00 $0.00 $156,888.28 19 20 $160,000.00 21 $32,000.00 $45,600.00 $128,000.00 22 $32,000.00 $42,880.00 $96,000.00 23 $32,000.00 $40,160.00 $64,000.00 24 $32,000.00 $37,440.00 $32,000.00 25 $32,000.00 $34,720.00 $0.00 $158,026.05 26 27 $160,000.00 28 $27,002.52 $40,602.52 $132,997.48 29 $29,297.73 $40,602.52 $103,699.75 30 $31,788.04 $40,602.52 $71,911.70 31 $34,490.03 $40,602.52 $37,421.68 32 $37,421.68 $40,602.52 $0.00 $157,929.64 33 34 $160,000.00 35 $0.00 $0.00 $173,600.00 36 $0.00 $0.00 $188,356.00 37 $0.00 $0.00 $204,366.26 38 $0.00 $0.00 $221,737.39 39 $160,000.00 $240,585.07 $0.00 $156,363.79

REAL TOTAL PAYMENT

PW REAL $

$13,102.12 $12,622.47 $12,160.37 $11,715.19 $144,066.48 $156,888.28

$43,930.64 $39,797.89 $35,908.86 $32,251.24 $28,813.30 $158,026.05

$39,116.11 $37,684.11 $36,304.54 $34,975.47 $33,695.06 $157,929.64

$0.00 $0.00 $0.00 $0.00 $199,655.79 $156,363.79

A B 1 PROBLEM 12.33 2 3 INFLATION RATE 4 COMBINED MARR 5 REAL MARR 6 AMOUNT BORROWED 7 LOAN INTEREST RATE 8 LOAN PERIOD YEARS 9 10 11 REPAYMENT 12 METHOD 13 a 1 14 15 16 17 18 19 20 b 2 21 22 23 24 25 26 27 c 3 28 29 30 31 32 33 34 d 4 35 36 37 38 39 40 41 42 LOAN INTEREST RATE 43 8.50% 44 45 5.00% 46 6.00% 47 7.00% 48 8.00% 49 9.00% 50 10.00% 51 11.00%

3.80% 9.00% 5.01% $160,000.00 8.50% 5

EOY 0 1 2 3 4 5

INTEREST TOTAL $ OWED ACCRUED BEFORE YEARLY INTEREST DURING YR PAYMENT PAYMENT $13,600.00 $13,600.00 $13,600.00 $13,600.00 $13,600.00

$173,600.00 $173,600.00 $173,600.00 $173,600.00 $173,600.00

$13,600.00 $13,600.00 $13,600.00 $13,600.00 $13,600.00

0 1 2 3 4 5

$13,600.00 $173,600.00 $10,880.00 $138,880.00 $8,160.00 $104,160.00 $5,440.00 $69,440.00 $2,720.00 $34,720.00

$13,600.00 $10,880.00 $8,160.00 $5,440.00 $2,720.00

0 1 2 3 4 5

$13,600.00 $173,600.00 $11,304.79 $144,302.27 $8,814.48 $112,514.22 $6,112.49 $78,024.20 $3,180.84 $40,602.52

$13,600.00 $11,304.79 $8,814.48 $6,112.49 $3,180.84

0 1 2 3 4 5

$13,600.00 $14,756.00 $16,010.26 $17,371.13 $18,847.68

$0.00 $0.00 $0.00 $0.00 $80,585.07

$173,600.00 $188,356.00 $204,366.26 $221,737.39 $240,585.07

PW METH 1 PW METH 2 PW METH 3 PW METH 4 $156,888.28 $158,026.05 $157,929.64 $156,363.79 $135,106.23 $141,329.67 $147,553.12 $153,776.56 $160,000.00 $166,223.44 $172,446.88

$144,208.37 $148,156.28 $152,104.19 $156,052.09 $160,000.00 $163,947.91 $167,895.81

$143,745.83 $147,742.27 $151,783.96 $155,870.12 $160,000.00 $164,172.83 $168,387.86

$132,719.27 $139,160.77 $145,849.98 $152,793.99 $160,000.00 $167,475.36 $175,227.55

A 52 53 54 55

B 12.00% 13.00% 14.00% 15.00%

C $178,670.33 $184,893.77 $191,117.21 $197,340.65

D $171,843.72 $175,791.63 $179,739.53 $183,687.44

E $172,644.34 $176,941.51 $181,278.63 $185,654.95

F $183,264.19 $191,593.03 $200,221.98 $209,159.07

REAL TOTAL PAYMENT

PW REAL $

$13,102.12 $12,622.47 $12,160.37 $11,715.19 $144,066.48 $156,888.28

$43,930.64 $39,797.89 $35,908.86 $32,251.24 $28,813.30 $158,026.05

$39,116.11 $37,684.11 $36,304.54 $34,975.47 $33,695.06 $157,929.64

$0.00 $0.00 $0.00 $0.00 $199,655.79 $156,363.79

52 53 54 55

G 2 2 2 2

A 1 PROBLEM 12.34 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

INFLATION RATE COMBINED MARR REAL MARR AMOUNT BORROWED LOAN INTEREST RATE LOAN PERIOD YEARS

3.90% 17.00% 12.61% $500,000.00 10.00% 4

REPAYMENT METHOD 1

INTEREST TOTAL $ OWED ACCRUED BEFORE YEARLY DURING YR PAYMENT

EOY 0 1 2 3 4

$50,000.00 $50,000.00 $50,000.00 $50,000.00

$550,000.00 $550,000.00 $550,000.00 $550,000.00

0 1 2 3 4

$50,000.00 $37,500.00 $25,000.00 $12,500.00

$550,000.00 $412,500.00 $275,000.00 $137,500.00

0 1 2 3 4

$50,000.00 $39,226.46 $27,375.57 $14,339.58

$550,000.00 $431,491.06 $301,131.22 $157,735.40

0 1 2 3 4

$50,000.00 $55,000.00 $60,500.00 $66,550.00

$550,000.00 $605,000.00 $665,500.00 $732,050.00

F G H I J 1 2 3 4 5 6 7 8 9 10 TOTAL $ OWED PW 11 INTEREST PRINCIPAL TOTAL AFTER YEARLY CURRENT 12 PAYMENT PAYMENT PAYMENT PAYMENT $ 13 $500,000.00 14 $50,000.00 $0.00 $50,000.00 $500,000.00 15 $50,000.00 $0.00 $50,000.00 $500,000.00 16 $50,000.00 $0.00 $50,000.00 $500,000.00 17 $50,000.00 $500,000.00 $550,000.00 $0.00 $403,986.77 18 19 $500,000.00 20 $50,000.00 $125,000.00 $175,000.00 $375,000.00 21 $37,500.00 $125,000.00 $162,500.00 $250,000.00 22 $25,000.00 $125,000.00 $150,000.00 $125,000.00 23 $12,500.00 $125,000.00 $137,500.00 $0.00 $435,313.57 24 25 $500,000.00 26 $50,000.00 $107,735.40 $157,735.40 $392,264.60 27 $39,226.46 $118,508.94 $157,735.40 $273,755.66 28 $27,375.57 $130,359.84 $157,735.40 $143,395.82 29 $14,339.58 $143,395.82 $157,735.40 $0.00 $432,705.28 30 31 $500,000.00 32 $0.00 $0.00 $0.00 $550,000.00 33 $0.00 $0.00 $0.00 $605,000.00 34 $0.00 $0.00 $0.00 $665,500.00 35 $232,050.00 $500,000.00 $732,050.00 $0.00 $390,658.52

REAL TOTAL PAYMENT

PW REAL $

$48,123.20 $46,316.84 $44,578.29 $471,954.90 $403,986.77

$168,431.18 $150,529.73 $133,734.86 $117,988.72 $435,313.57

$151,814.63 $146,116.10 $140,631.48 $135,352.72 $432,705.28

$0.00 $0.00 $0.00 $628,171.97 $390,658.52

A B C D E 1 PROBLEM 12.35 2 3 INFLATION RATE 3.90% 4 COMBINED MARR 17.00% 5 REAL MARR 12.61% 6 AMOUNT BORROWED $500,000.00 7 LOAN INTEREST RATE 10.00% 8 LOAN PERIOD YEARS 4 9 10 INTEREST TOTAL $ OWED 11 REPAYMENT ACCRUED BEFORE YEARLY 12 METHOD EOY DURING YR PAYMENT 13 a 1 0 14 1 $50,000.00 $550,000.00 15 2 $50,000.00 $550,000.00 16 3 $50,000.00 $550,000.00 17 4 $50,000.00 $550,000.00 18 19 b 2 0 20 1 $50,000.00 $550,000.00 21 2 $37,500.00 $412,500.00 22 3 $25,000.00 $275,000.00 23 4 $12,500.00 $137,500.00 24 25 c 3 0 26 1 $50,000.00 $550,000.00 27 2 $39,226.46 $431,491.06 28 3 $27,375.57 $301,131.22 29 4 $14,339.58 $157,735.40 30 31 d 4 0 32 1 $50,000.00 $550,000.00 33 2 $55,000.00 $605,000.00 34 3 $60,500.00 $665,500.00 35 4 $66,550.00 $732,050.00 36 37 38 LOAN INTEREST RATE PW METH 1 PW METH 2 39 10.00% $403,986.77 $435,313.57 40 41 7.00% $362,838.25 $407,590.81 42 8.00% $376,554.42 $416,831.73 43 9.00% $390,270.60 $426,072.65 44 10.00% $403,986.77 $435,313.57 45 11.00% $417,702.95 $444,554.49 46 12.00% $431,419.12 $453,795.40 47 13.00% $445,135.30 $463,036.32 48 14.00% $458,851.47 $472,277.24 49 15.00% $472,567.65 $481,518.16 50 16.00% $486,283.82 $490,759.08 51 17.00% $500,000.00 $500,000.00

A 52 53 54

C 18.00% 19.00% 20.00%

D $513,716.18 $527,432.35 $541,148.53

E $509,240.92 $518,481.84 $527,722.76

REAL TOTAL PAYMENT

PW REAL $

$48,123.20 $46,316.84 $44,578.29 $471,954.90 $403,986.77

$168,431.18 $150,529.73 $133,734.86 $117,988.72 $435,313.57

$151,814.63 $146,116.10 $140,631.48 $135,352.72 $432,705.28

$0.00 $0.00 $0.00 $628,171.97 $390,658.52

F G 52 $509,883.27 $517,314.42 53 $519,830.60 $535,074.68 54 $529,840.92 $553,288.37

H 2 2 2

A 1 PROBLEM 12.36 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

INFLATION RATE COMBINED MARR REAL MARR FIRST COST EOY 0 1 2 3 4

d3 IN REAL $=

REAL $

MACRS(3)

4.00% 10.00% 5.77% $10,000.00 THEN-CURRENT $

$3,333.00 $3,204.81 $4,445.00 $4,109.65 $1,481.00 $1,316.60 $741.00 $633.41

$1,316.60

33.33% 44.45% 14.81% 7.41% SUM 100.00%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

MODIFIED ACRS RATES - GDS MACRS CL ADR %

3-YR <=4 200%

5-YR 7-YR 10-YR >4 to <10 >=10 to <16 .=16 to <20 200% 200% 200%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

33.33% 44.45% 14.81% 7.41%

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

SUM

100.00% 100.00%

100.00%

G H 1 2 3 4 5 15-YR 20-YR 6 >=20 to <25 >=25 7 150% 150% 8 9 5.00% 3.750% 10 9.50% 7.219% 11 8.55% 6.677% 12 7.70% 6.177% 13 6.93% 5.713% 14 6.23% 5.285% 15 5.90% 4.888% 16 5.90% 4.522% 17 5.91% 4.462% 18 5.90% 4.461% 19 5.91% 4.462% 20 5.90% 4.461% 21 5.91% 4.462% 22 5.90% 4.461% 23 5.91% 4.462% 24 2.95% 4.461% 25 4.462% 26 4.461% 27 4.462% 28 4.461% 29 2.231% 30 31 100.00% 100.000%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BASIS EST SALV RCVD SALV

EOY 0 1 2 3 4 5 6 7 8 9 10

$500,000.00 REAL BTCF $124,166.67 INFL RATE= $50,000.00 BTCF INCR $0.00 TAX RATE MARRr= $50,000.00 USEFUL LIFE 10 PERIODS 10 MARRc= ACTUAL BTCF -$500,000.00 $129,133.34 $134,298.67 $139,670.62 $145,257.44 $151,067.74 $157,110.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

DWO

$100,000.00 $29,133.34 $160,000.00 -$25,701.33 $96,000.00 $43,670.62 $57,600.00 $87,657.44 $57,600.00 $93,467.74 $28,800.00 $128,310.45 $0.00 $163,394.87 $0.00 $169,930.66 $0.00 $176,727.89 $0.00 $257,809.22 SUM DEPR

4.00% 40.00% 10.00% 14.40%

ACTUAL ATCF -$500,000.00 $11,653.33 $117,480.00 -$10,280.53 $144,579.20 $17,468.25 $122,202.37 $35,062.98 $110,194.47 $37,387.10 $113,680.64 $51,324.18 $105,786.27 $65,357.95 $98,036.92 $67,972.26 $101,958.40 $70,691.16 $106,036.73 $103,123.69 $154,685.53 MARRc= 14.40% PW $T = $109,201.18

$500,000.00

BOOK VALUE

FW $T =

$419,264.00

$0.00

AW $T =

$21,263.15

IRRc=

19.99%

ERRc=

16.68%

IRRr=

15.38%

ERRr=

12.19%

1 2 3 4 5 6 7 8 MACRS(5) 9 10 20.00% 11 32.00% 12 19.20% 13 11.52% 14 11.52% 15 5.76% 16 17 18 19 20 21 22 23 24 25 26 27

ERRc= 16.68%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BASIS EST SALV RCVD SALV

EOY 0 1 2 3 4 5 6 7 8 9 10

$500,000.00 REAL BTCF $124,166.67 INFL RATE= $50,000.00 BTCF INCR $0.00 TAX RATE MARRr= $50,000.00 USEFUL LIFE 10 PERIODS 10 MARRc= REAL BTCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

REAL DWO

4.00% 40.00% 10.00% 14.40%

$448,767.27

REAL ATCF -$500,000.00 $11,205.13 $112,961.54 -$9,504.93 $133,671.60 $15,529.21 $108,637.46 $29,971.98 $94,194.69 $30,729.47 $93,437.20 $40,562.24 $83,604.43 $49,666.67 $74,500.00 $49,666.67 $74,500.00 $49,666.67 $74,500.00 $69,666.67 $104,500.00 MARRr= 10.00% PW $C = $109,201.18

BOOK VALUE

FW $C = $283,239.74

$0.00

$96,153.85 $28,012.82 $147,928.99 -$23,762.32 $85,343.65 $38,823.02 $49,236.72 $74,929.95 $47,343.00 $76,823.67 $22,761.06 $101,405.61 $0.00 $124,166.67 $0.00 $124,166.67 $0.00 $124,166.67 $0.00 $174,166.67 SUM DEPR

AW $C =

$17,771.99

IRRr =

15.38%

ERRr =

12.19%

IRRc =

19.99%

ERRc =

16.68%

1 2 3 4 5 6 7 8 MACRS(5) 9 10 20.00% 11 32.00% 12 19.20% 13 11.52% 14 11.52% 15 5.76% 16 17 18 19 20 SUM MACRS 21

100.00%

22 23 24 25 26 27

ERRr = 12.19%

1 2 3 4 5

A PROBLEM 12.37

6 7 8 9 10 11 12 13 14 15 16

BASIS EST SALV RCVD SALV

$9,000,000.00 $700,000.00 $700,000.00

EOY 0 1 2 3 4 5 6

ACTUAL BTCF -$9,000,000.00 $6,240,000.00 $5,408,000.00 $4,499,456.00 $3,509,575.68 $2,433,305.80 $2,151,042.33

REAL BTCF $6,000,000.00 BTCF INCR -$1,000,000.00 USEFUL LIFE 6

INFL RATE= TAX RATE MARRr=

PERIODS

MARRc=

DWO

$1,800,000.00 $2,880,000.00 $1,728,000.00 $1,036,800.00 $1,036,800.00 $518,400.00 SUM DEPR

$4,440,000.00 $1,776,000.00 $2,528,000.00 $1,011,200.00 $2,771,456.00 $1,108,582.40 $2,472,775.68 $989,110.27 $1,396,505.80 $558,602.32 $1,632,642.33 $653,056.93 MARRc=

$9,000,000.00

PW $T =

BOOK VALUE

FW $T =

$0.00

AW $T =

19 20

IRRc=

ERRc=

IRRr=

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

ERRr= a

AS SHOWN

PW$T =

$1,615,078.51

FW$T =

$5,516,780.68

AW$T =

$518,840.14

IRRc=

31.74%

ERRc=

26.14%

IRRr=

26.68%

ERRr=

21.29%

G 1 2 3 4 5

4.00% 40.00% 18.00%

6 22.72% 7 8 ACTUAL ATCF MACRS(5) 9 -$9,000,000.00 10 $4,464,000.00 20.00% 11 $4,396,800.00 32.00% 12 $3,390,873.60 19.20% 13 $2,520,465.41 11.52% 14 $1,874,703.48 11.52% 15 $1,497,985.40 5.76% 16 22.72% 17

$1,615,078.51

$5,516,780.68

$518,840.14

31.74%

26.14%

26.68%

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

21.29%

ERRc= 26.14%

1 2 3 4 5

A PROBLEM 12.38

BASIS $9,000,000.00 EST SALV $700,000.00 RCVD SALV $700,000.00

6 7 8 9 10 11 12 13 14 15 16

REAL BTCF $6,000,000.00 BTCF INCR -$1,000,000.00 USEFUL LIFE 6 PERIODS

EOY 0 1 2 3 4 5 6

INFL RATE= TAX RATE MARRr=

MARRc=

REAL BTCF REAL DWO -$9,000,000.00 $6,000,000.00 $1,730,769.23 $5,000,000.00 $2,662,721.89 $4,000,000.00 $1,536,185.71 $3,000,000.00 $886,260.99 $2,000,000.00 $852,174.02 $1,700,000.00 $409,699.05 SUM DEPR

$4,269,230.77 $1,707,692.31 $2,337,278.11 $934,911.24 $2,463,814.29 $985,525.72 $2,113,739.01 $845,495.61 $1,147,825.98 $459,130.39 $1,290,300.95 $516,120.38 MARRr=

$8,077,810.89

PW $C =

BOOK VALUE

FW $C =

$0.00

AW $C =

19 20

IRRr =

ERRr =

IRRc =

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

ERRc = a

AS SHOWN

PW $C =

$1,615,078.51

AW $C =

$461,767.31

FW $C =

$4,359,991.90

IRRr =

26.68%

ERRr =

21.29%

IRRc =

31.74%

ERRc =

26.14%

G 1 2 3 4 5

4.00% 40.00% 18.00%

6 22.72% 7 8 REAL ATCF MACRS(5) 9 -$9,000,000.00 10 $4,292,307.69 20.00% 11 $4,065,088.76 32.00% 12 $3,014,474.28 19.20% 13 $2,154,504.39 11.52% 14 $1,540,869.61 11.52% 15 $1,183,879.62 5.76% 16 18.00% SUM MACRS 17 $1,615,078.51

100.00%

18 $4,359,991.90 19

$461,767.31

26.68%

21.29%

31.74%

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

26.14%

ERRr = 21.29%

A 1 PROBLEM 12.39 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

BASIS EST SALV RCVD SALV

$190,000.00 $5,000.00 $5,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

ACTUAL BTCF -$190,000.00 $46,755.00 $48,578.45 $50,473.00 $52,441.45 $54,486.67 $56,611.65 $58,819.50 $61,113.46 $63,496.89 $65,973.27 $68,546.22 $79,132.81

REAL BTCF $45,000.00 INFL RATE= BTCF INCR $0.00 TAX RATE MARRr= USEFUL LIFE 12 MARRc= PERIODS 12 DWO

$27,151.00 $19,604.00 $46,531.00 $2,047.44 $33,231.00 $17,242.00 $23,731.00 $28,710.45 $16,967.00 $37,519.67 $16,948.00 $39,663.65 $16,967.00 $41,852.50 $8,474.00 $52,639.46 $0.00 $63,496.89 $0.00 $65,973.27 $0.00 $68,546.22 $0.00 $79,132.81 SUM DEPR

T $7,841.60 $818.98 $6,896.80 $11,484.18 $15,007.87 $15,865.46 $16,741.00 $21,055.79 $25,398.76 $26,389.31 $27,418.49 $31,653.12 MARRc=

$190,000.00

PW $T =

BOOK VALUE

FW $T =

$0.00

AW $T =

IRRc=

ERRc=

IRRr=

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

ERRr= a

AS SHOWN

PW $T =

$43,495.36

FW $T =

$216,043.77

AW $T =

$7,782.26

IRRc=

19.40%

ERRc=

16.27%

IRRr=

14.92%

ERRr=

11.91%

G 1 2 3 4 5

3.90% 40.00% 10.00%

6 14.29% 7 8 ACTUAL ATCF MACRS(7) 9 -$190,000.00 10 $38,913.40 14.29% 11 $47,759.47 24.49% 12 $43,576.20 17.49% 13 $40,957.27 12.49% 14 $39,478.80 8.93% 15 $40,746.19 8.92% 16 $42,078.50 8.93% 17 $40,057.68 4.46% 18 $38,098.13 19 $39,583.96 20 $41,127.73 21 $47,479.68 22 14.29% 23

$43,495.36

$216,043.77

$7,782.26

19.40%

16.27%

14.92%

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

11.91%

ERRc= 16.27%

A 1 PROBLEM 12.40 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

BASIS $190,000.00 EST SALV $5,000.00 RCVD SALV $5,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

REAL BTCF -$190,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $50,000.00

REAL BTCF $45,000.00 INFL RATE= BTCF INCR $0.00 TAX RATE MARRr= USEFUL LIFE 12 MARRc= PERIODS 12 REAL DWO

3.90% 40.00% 10.00% 14.29%

$165,931.43

REAL ATCF -$190,000.00 $7,547.26 $37,452.74 $758.65 $44,241.35 $6,148.95 $38,851.05 $9,854.57 $35,145.43 $12,394.85 $32,605.15 $12,611.29 $32,388.71 $12,807.74 $32,192.26 $15,504.12 $29,495.88 $18,000.00 $27,000.00 $18,000.00 $27,000.00 $18,000.00 $27,000.00 $20,000.00 $30,000.00 MARRr= 10.00% PW $C = $43,495.36

BOOK VALUE

FW $C = $136,507.08

$0.00

$26,131.86 $18,868.14 $43,103.38 $1,896.62 $29,627.62 $15,372.38 $20,363.57 $24,636.43 $14,012.88 $30,987.12 $13,471.79 $31,528.21 $12,980.64 $32,019.36 $6,239.71 $38,760.29 $0.00 $45,000.00 $0.00 $45,000.00 $0.00 $45,000.00 $0.00 $50,000.00 SUM DEPR

AW $C =

$6,383.52

IRRr =

14.92%

ERRr =

11.91%

IRRc =

19.40%

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

ERRc =

16.27%

AS SHOWN

PW $C =

$43,495.36

AW $C =

$6,383.52

FW $C =

$136,507.08

IRRr =

14.92%

ERRr =

11.91%

IRRc =

19.40%

ERRc =

16.27%

1 2 3 4 5 6 7 8 MACRS(7) 9 10 14.29% 11 24.49% 12 17.49% 13 12.49% 14 8.93% 15 8.92% 16 8.93% 17 4.46% 18 19 20 21 22 SUM MACRS 23

100.00%

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

ERRr =

11.91%

A 1 PROBLEM 12.41 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

BASIS $1,400,000.00 EST SALV $200,000.00 RCVD SALV $200,000.00

EOY 0 1 2 3 4 5 6 7 8

ACTUAL BTCF -$1,400,000.00 $416,800.00 $434,305.60 $452,546.44 $471,553.39 $491,358.63 $511,995.69 $533,499.51 $833,859.73

REAL BTCF $400,000.00 INFL RATE= BTCF INCR $0.00 TAX RATE MARRr= USEFUL LIFE 8 MARRc= PERIODS 8 DWO

$280,000.00 $136,800.00 $448,000.00 -$13,694.40 $268,800.00 $183,746.44 $161,280.00 $310,273.39 $161,280.00 $330,078.63 $80,640.00 $431,355.69 $0.00 $533,499.51 $0.00 $833,859.73 SUM DEPR

T $54,720.00 -$5,477.76 $73,498.57 $124,109.35 $132,031.45 $172,542.28 $213,399.80 $333,543.89 MARRc= PW $T =

$1,400,000.00

BOOK VALUE

FW $T =

$0.00

AW $T =

21 22

IRRc=

ERRc=

IRRr=

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

ERRr= a

AS SHOWN

PW $T =

$326,090.32

FW $T =

$971,451.55

AW $T =

$71,763.49

IRRc=

21.38%

ERRc=

17.66%

IRRr=

16.49%

ERRr=

12.92%

G 1 2 3 4 5

4.20% 40.00% 10.00%

6 14.62% 7 8 ACTUAL ATCF MACRS(5) 9 -$1,400,000.00 10 $362,080.00 20.00% 11 $439,783.36 32.00% 12 $379,047.86 19.20% 13 $347,444.03 11.52% 14 $359,327.18 11.52% 15 $339,453.41 5.76% 16 $320,099.71 17 $500,315.84 18 14.62% 19

$326,090.32

$971,451.55

$71,763.49

21.38%

17.66%

16.49%

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

12.92%

ERRc= 17.66%

A B 1 PROBLEM 12.42 2 3 BASIS 4 EST SALV 5 RCVD SALV 6 7 8 9 10 11 12 13 14 15 16 17 18

EOY 0 1 2 3 4 5 6 7 8

$1,400,000.00 $200,000.00 $200,000.00

REAL BTCF -$1,400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $400,000.00 $600,000.00

REAL BTCF $400,000.00 INFL RATE= BTCF INCR $0.00 TAX RATE MARRr= USEFUL LIFE 8 MARRc= PERIODS 8 REAL DWO

$268,714.01 $131,285.99 $412,612.69 -$12,612.69 $237,588.88 $162,411.12 $136,807.42 $263,192.58 $131,293.11 $268,706.89 $63,000.53 $336,999.47 $0.00 $400,000.00 $0.00 $600,000.00 SUM DEPR

4.20% 40.00% 10.00% 14.62%

$52,514.40 -$5,045.07 $64,964.45 $105,277.03 $107,482.76 $134,799.79 $160,000.00 $240,000.00 MARRr=

REAL ATCF -$1,400,000.00 $347,485.60 $405,045.07 $335,035.55 $294,722.97 $292,517.24 $265,200.21 $240,000.00 $360,000.00 10.00%

PW $C =

$326,090.32

$1,250,016.63

BOOK VALUE

FW $C =

$699,003.57

$0.00

AW $C =

$61,123.68

IRRr =

16.49%

ERRr =

12.92%

IRRc =

21.38%

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

ERRc =

17.66%

AS SHOWN

PW $C =

$326,090.32

AW $C =

$61,123.68

FW $C =

$699,003.57

IRRr =

16.49%

ERRr =

12.92%

IRRc =

21.38%

ERRc =

17.66%

1 2 3 4 5 6 7 8 MACRS(5) 9 10 20.00% 11 32.00% 12 19.20% 13 11.52% 14 11.52% 15 5.76% 16 17 18 SUM MACRS 19

100.00%

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

ERRr =

12.92%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BASIS EST SALV RCVD SALV

EOY 0 1 2 3 4 5 6 7 8 9 10

$500,000.00 ACTUAL BTCF $124,166.67 INFL RATE= $50,000.00 BTCF INCR $0.00 TAX RATE MARRr= $50,000.00 USEFUL LIFE 10 PERIODS 10 MARRc= ACTUAL BTCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

DWO

4.00% 40.00% 10.00% 14.40%

ACTUAL ATCF -$500,000.00 $9,666.67 $114,500.00 -$14,333.33 $138,500.00 $11,266.67 $112,900.00 $26,626.67 $97,540.00 $26,626.67 $97,540.00 $38,146.67 $86,020.00 $49,666.67 $74,500.00 $49,666.67 $74,500.00 $49,666.67 $74,500.00 $69,666.67 $104,500.00 MARRc= 14.40% PW $T = $30,288.04

$500,000.00

BOOK VALUE

FW $T =

$116,287.07

$0.00

AW $T =

$5,897.55

IRRc=

16.12%

ERRc=

15.07%

IRRr=

11.65%

ERRr=

10.65%

1 2 3 4 5 6 7 8 MACRS(5) 9 10 20.00% 11 32.00% 12 19.20% 13 11.52% 14 11.52% 15 5.76% 16 17 18 19 20 21 22 23 24 25 26 27

ERRc= 15.07%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BASIS EST SALV RCVD SALV

EOY 0 1 2 3 4 5 6 7 8 9 10

$500,000.00 ACTUAL BTCF $124,166.67 INFL RATE= $50,000.00 BTCF INCR $0.00 TAX RATE MARRr= $50,000.00 USEFUL LIFE 10 PERIODS 10 MARRc= REAL BTCF -$500,000.00 $119,391.03 $114,799.07 $110,383.72 $106,138.19 $102,055.95 $98,130.72 $94,356.46 $90,727.37 $87,237.86 $117,660.76

DWO

$96,153.85 $23,237.18 $147,928.99 -$33,129.93 $85,343.65 $25,040.07 $49,236.72 $56,901.47 $47,343.00 $54,712.95 $22,761.06 $75,369.66 $0.00 $94,356.46 $0.00 $90,727.37 $0.00 $87,237.86 $0.00 $117,660.76 SUM DEPR

4.00% 40.00% 10.00% 14.40%

REAL ATCF -$500,000.00 $9,294.87 $110,096.16 -$13,251.97 $128,051.04 $10,016.03 $100,367.69 $22,760.59 $83,377.60 $21,885.18 $80,170.77 $30,147.87 $67,982.86 $37,742.59 $56,613.88 $36,290.95 $54,436.42 $34,895.14 $52,342.71 $47,064.30 $70,596.46 MARRr= 10.00% PW $C = $30,288.04

$448,767.27

BOOK VALUE

FW $C =

$78,559.38

$0.00

AW $C =

$4,929.24

IRRr =

11.65%

ERRr =

10.65%

IRRc =

16.12%

ERRc =

15.07%

1 2 3 4 5 6 7 8 MACRS(5) 9 10 20.00% 11 32.00% 12 19.20% 13 11.52% 14 11.52% 15 5.76% 16 17 18 19 20 SUM MACRS 21

100.00%

22 23 24 25 26 27

ERRr = 10.65%

A 1 PROBLEM 12.43 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

BASIS $9,000,000.00 ACTUAL BTCF $6,000,000.00 EST SALV $700,000.00 BTCF INCR -$1,000,000.00 RCVD SALV $700,000.00 USEFUL LIFE 6

EOY 0 1 2 3 4 5 6

REAL BTCF -$9,000,000.00 $5,769,230.77 $4,622,781.07 $3,555,985.43 $2,564,412.57 $1,643,854.21 $1,343,534.69

INFL RATE= TAX RATE MARRr=

PERIODS

MARRc=

DWO

$1,730,769.23 $2,662,721.89 $1,536,185.71 $886,260.99 $852,174.02 $409,699.05 SUM DEPR

$4,038,461.54 $1,615,384.62 $1,960,059.17 $784,023.67 $2,019,799.73 $807,919.89 $1,678,151.59 $671,260.64 $791,680.19 $316,672.08 $933,835.64 $373,534.26 MARRr=

$8,077,810.89

PW $C =

BOOK VALUE

FW $C =

$0.00

AW $C =

19 20

IRRr =

ERRr =

IRRc =

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

ERRc = a

AS SHOWN

PW $C =

$865,610.93

FW $C =

$2,336,763.59

AW $C =

$247,486.93

IRRr =

22.82%

ERRr =

19.82%

IRRc =

27.73%

ERRc =

24.61%

G 1 2 3 4 5

4.00% 40.00% 18.00%

6 22.72% 7 8 REAL ATCF MACRS(5) 9 -$9,000,000.00 10 $4,153,846.15 20.00% 11 $3,838,757.40 32.00% 12 $2,748,065.54 19.20% 13 $1,893,151.94 11.52% 14 $1,327,182.14 11.52% 15 $970,000.44 5.76% 16 18.00% SUM MACRS 17

$865,610.93

100.00%

18 $2,336,763.59 19

$247,486.93

22.82%

19.82%

27.73%

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

24.61%

ERRr = 19.82%

A 1 PROBLEM 12.44 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

BASIS $9,000,000.00 ACTUAL BTCF $6,000,000.00 EST SALV $700,000.00 BTCF INCR -$1,000,000.00 RCVD SALV $700,000.00 USEFUL LIFE 6

EOY 0 1 2 3 4 5 6

ACTUAL BTCF -$9,000,000.00 $6,000,000.00 $5,000,000.00 $4,000,000.00 $3,000,000.00 $2,000,000.00 $1,700,000.00

INFL RATE= TAX RATE MARRr=

PERIODS

MARRc=

DWO

$1,800,000.00 $2,880,000.00 $1,728,000.00 $1,036,800.00 $1,036,800.00 $518,400.00 SUM DEPR

$4,200,000.00 $1,680,000.00 $2,120,000.00 $848,000.00 $2,272,000.00 $908,800.00 $1,963,200.00 $785,280.00 $963,200.00 $385,280.00 $1,181,600.00 $472,640.00 MARRc=

$9,000,000.00

PW $T =

BOOK VALUE

FW $T =

$0.00

AW $T =

19 20

IRRc=

ERRc=

IRRr=

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

ERRr= a

AS SHOWN

PW $T =

$865,610.93

AW $T =

$278,075.46

FW $T =

$2,956,751.41

IRRc=

27.73%

ERRc=

24.61%

IRRr=

22.82%

ERRr=

19.82%

G 1 2 3 4 5

4.00% 40.00% 18.00%

6 22.72% 7 8 ACTUAL ATCF MACRS(5) 9 -$9,000,000.00 10 $4,320,000.00 20.00% 11 $4,152,000.00 32.00% 12 $3,091,200.00 19.20% 13 $2,214,720.00 11.52% 14 $1,614,720.00 11.52% 15 $1,227,360.00 5.76% 16 22.72% 17

$865,610.93

$2,956,751.41

$278,075.46

27.73%

24.61%

22.82%

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

19.82%

ERRc= 24.61%

A 1 PROBLEM 12.45 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

BASIS $190,000.00 ACTUAL BTCF $45,000.00 INFL RATE= EST SALV $5,000.00 BTCF INCR $0.00 TAX RATE MARRr= RCVD SALV $5,000.00 USEFUL LIFE 12 MARRc= PERIODS 12 EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

REAL BTCF -$190,000.00 $43,186.18 $41,445.47 $39,774.92 $38,171.71 $36,633.12 $35,156.55 $33,739.49 $32,379.55 $31,074.42 $29,821.90 $28,619.87 $30,518.09

DWO

$26,056.62 $17,129.56 $42,855.54 -$1,410.07 $29,372.46 $10,402.47 $20,130.06 $18,041.65 $13,812.31 $22,820.81 $13,240.74 $21,915.81 $12,721.29 $21,018.20 $6,097.43 $26,282.12 $0.00 $31,074.42 $0.00 $29,821.90 $0.00 $28,619.87 $0.00 $30,518.09 SUM DEPR

4.20% 40.00% 10.00% 14.62%

REAL ATCF -$190,000.00 $6,851.82 $36,334.36 -$564.03 $42,009.50 $4,160.99 $35,613.94 $7,216.66 $30,955.05 $9,128.32 $27,504.80 $8,766.32 $26,390.22 $8,407.28 $25,332.21 $10,512.85 $21,866.70 $12,429.77 $18,644.65 $11,928.76 $17,893.14 $11,447.95 $17,171.92 $12,207.24 $18,310.86 MARRr= 10.00% PW $C = $7,483.92

$164,286.45

BOOK VALUE

FW $C =

$23,487.76

$0.00

AW $C =

$1,098.37

IRRr =

10.95%

ERRr =

10.35%

IRRc =

15.61%

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

ERRc =

14.99%

AS SHOWN

PW $C =

$7,483.92

FW $C =

$23,487.76

AW $C =

$1,098.37

IRRr =

10.95%

ERRr =

10.35%

IRRc =

15.61%

ERRc =

14.99%

1 2 3 4 5 6 7 8 MACRS(7) 9 10 14.29% 11 24.49% 12 17.49% 13 12.49% 14 8.93% 15 8.92% 16 8.93% 17 4.46% 18 19 20 21 22 SUM MACRS 23

100.00%

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

ERRr = 10.35%

A 1 PROBLEM 12.46 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

BASIS EST SALV RCVD SALV

$190,000.00 $5,000.00 $5,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

ACTUAL BTCF -$190,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $50,000.00

ACTUAL BTCF $45,000.00 INFL RATE= BTCF INCR $0.00 TAX RATE MARRr= USEFUL LIFE 12 MARRc= PERIODS 12 DWO

$27,151.00 $17,849.00 $46,531.00 -$1,531.00 $33,231.00 $11,769.00 $23,731.00 $21,269.00 $16,967.00 $28,033.00 $16,948.00 $28,052.00 $16,967.00 $28,033.00 $8,474.00 $36,526.00 $0.00 $45,000.00 $0.00 $45,000.00 $0.00 $45,000.00 $0.00 $50,000.00 SUM DEPR

T $7,139.60 -$612.40 $4,707.60 $8,507.60 $11,213.20 $11,220.80 $11,213.20 $14,610.40 $18,000.00 $18,000.00 $18,000.00 $20,000.00 MARRc=

$190,000.00

PW $T =

BOOK VALUE

FW $T =

$0.00

AW $T =

IRRc=

ERRc=

IRRr=

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

ERRr= a

AS SHOWN

PW $T =

$7,483.92

AW $T =

$1,358.31

FW $T =

$38,481.69

IRRc=

15.61%

ERRc=

14.99%

IRRr=

10.95%

ERRr=

10.35%

G 1 2 3 4 5

4.20% 40.00% 10.00%

6 14.62% 7 8 ACTUAL ATCF MACRS(7) 9 -$190,000.00 10 $37,860.40 14.29% 11 $45,612.40 24.49% 12 $40,292.40 17.49% 13 $36,492.40 12.49% 14 $33,786.80 8.93% 15 $33,779.20 8.92% 16 $33,786.80 8.93% 17 $30,389.60 4.46% 18 $27,000.00 19 $27,000.00 20 $27,000.00 21 $30,000.00 22 14.62% 23

$7,483.92

$38,481.69

$1,358.31

15.61%

14.99%

10.95%

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

10.35%

ERRc= 14.99%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

BASIS EST SALV

$500,000.00 LOAN PRINC $300,000.00 $50,000.00 LOAN PERIOD 10

REAL BTCF BTCF INCR

$124,166.67 $0.00

RCVD SALV

$50,000.00

LOAN INT

METHOD

EOY 0 1 2 3 4 5 6 7 8 9 10

$TBTLCF -$500,000.00 $129,133.34 $134,298.67 $139,670.62 $145,257.44 $151,067.74 $157,110.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

$TPPMT -$300,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $300,000.00

12.00% $TIPMT $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00

$TDWO

$100,000.00 -$6,866.66 $160,000.00 -$61,701.33 $96,000.00 $7,670.62 $57,600.00 $51,657.44 $57,600.00 $57,467.74 $28,800.00 $92,310.45 $0.00 $127,394.87 $0.00 $133,930.66 $0.00 $140,727.89 $0.00 $221,809.22 SUM DEPR

$500,000.00

BOOK VALUE

$0.00

23 24 25 26

$TTI

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

TAX RATE USEFUL LIFE PERIODS

40.00% INFL RATE= MARRr= 10 10 MARRc=

$TTax

4.00% 10.00% 14.40%

$TATCF $TATCF+ $TATCF$TATCF MACRS(5) -$200,000.00 $0.00 $200,000.00 -$200,000.00 -$2,746.67 $95,880.00 $95,880.00 $0.00 $0.00 20.00% -$24,680.53 $122,979.20 $122,979.20 $0.00 $0.00 32.00% $3,068.25 $100,602.37 $100,602.37 $0.00 $0.00 19.20% $20,662.98 $88,594.47 $88,594.47 $0.00 $0.00 11.52% $22,987.10 $92,080.64 $92,080.64 $0.00 $0.00 11.52% $36,924.18 $84,186.27 $84,186.27 $0.00 $0.00 5.76% $50,957.95 $76,436.92 $76,436.92 $0.00 $0.00 $53,572.26 $80,358.40 $80,358.40 $0.00 $0.00 $56,291.16 $84,436.73 $84,436.73 $0.00 $0.00 $88,723.69 -$166,914.47 $0.00 $166,914.47 $1,613,044.36 MARRc= 14.40% PW $T = $220,132.29

FW $T = $845,169.87

AW $T =

$42,863.15

IRRc=

47.70%

ERRc=

23.21%

IRRr=

42.02%

ERRr=

18.48%

A 1 PROBLEM 12.47 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BASIS EST SALV

$9,000,000.00 $700,000.00

RCVD SALV

$700,000.00

EOY 0 1 2 3 4 5 6

LOAN PRINC $4,000,000.00 LOAN PERIOD 6 LOAN INT

$TBTLCF $TPPMT -$9,000,000.00 -$4,000,000.00 $6,240,000.00 $0.00 $5,408,000.00 $0.00 $4,499,456.00 $0.00 $3,509,575.68 $0.00 $2,433,305.80 $0.00 $2,151,042.33 $4,000,000.00

REAL BTCF BTCF INCR

12.00%

METHOD

$TIPMT

$TDWO

$480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

$1,800,000.00 $2,880,000.00 $1,728,000.00 $1,036,800.00 $1,036,800.00 $518,400.00 SUM DEPR

$9,000,000.00

BOOK VALUE

$0.00

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

AS SHOWN

PW $T =

$3,547,544.14

FW $T =

$12,117,691.37

AW $T =

$1,139,640.14

IRRc=

65.45%

ERRc=

34.19%

IRRr=

59.09%

ERRr=

29.03%

G 1 2 3 4

$6,000,000.00 TAX RATE -$1,000,000.00 USEFUL LIFE

5 6 7 8 9 10 11 12 13 14 15

PERIODS

$TTI

$Ttax

$3,960,000.00 $1,584,000.00 $2,048,000.00 $819,200.00 $2,291,456.00 $916,582.40 $1,992,775.68 $797,110.27 $916,505.80 $366,602.32 $1,152,642.33 $461,056.93 MARRc=

PW $T =

40.00% 6

INFL RATE= MARRr=

4.00% 18.00%

MARRc=

22.72%

$TATCF $TATCF+ $TATCF$TATCF -$5,000,000.00 $0.00 $5,000,000.00 -$5,000,000.00 $4,176,000.00 $4,176,000.00 $0.00 $0.00 $4,108,800.00 $4,108,800.00 $0.00 $0.00 $3,102,873.60 $3,102,873.60 $0.00 $0.00 $2,232,465.41 $2,232,465.41 $0.00 $0.00 $1,586,703.48 $1,586,703.48 $0.00 $0.00 -$2,790,014.60 $0.00 $2,790,014.60 $29,196,677.42 22.72%

$3,547,544.14 FW $T = $12,117,691.37 AW $T = $1,139,640.14

IRRc=

65.45%

ERRc=

34.19%

IRRr=

59.09%

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

ERRr=

29.03%

ERRc=

34.19%

M 1 2 3 4 5 6 7 MACRS(5) 8 9 20.00% 10 32.00% 11 19.20% 12 11.52% 13 11.52% 14 5.76% 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

A 1 PROBLEM 12.48 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BASIS EST SALV

$9,000,000.00 LOAN PRINC $4,000,000.00 $700,000.00 LOAN PERIOD 6

REAL BTCF BTCF INCR

RCVD SALV

$700,000.00

12.00%

METHOD

$RIPMT

$RDWO

EOY 0 1 2 3 4 5 6

LOAN INT

$RBTLCF $RPPMT -$9,000,000.00 -$4,000,000.00 $6,000,000.00 $0.00 $5,000,000.00 $0.00 $4,000,000.00 $0.00 $3,000,000.00 $0.00 $2,000,000.00 $0.00 $1,700,000.00 $3,161,258.10

$461,538.46 $1,730,769.23 $443,786.98 $2,662,721.89 $426,718.25 $1,536,185.71 $410,306.01 $886,260.99 $394,525.01 $852,174.02 $379,350.97 $409,699.05 SUM DEPR

$8,077,810.89

BOOK VALUE

$0.00

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

AS SHOWN

PW $C =

$3,547,544.14

AW $C =

$1,014,278.80

FW $C =

$9,576,787.51

IRRr =

59.09%

ERRr =

29.03%

IRRc =

65.45%

ERRc =

34.19%

G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

$6,000,000.00 TAX RATE -$1,000,000.00 USEFUL LIFE 1

PERIODS

$RTI

$RTax

$3,807,692.31 $1,523,076.92 $1,893,491.12 $757,396.45 $2,037,096.04 $814,838.42 $1,703,433.00 $681,373.20 $753,300.96 $301,320.39 $910,949.98 $364,379.99 MARRr=

40.00% 6

INFL RATE= MARRr=

4.00% 18.00%

MARRc=

22.72%

$RATCF $RATCF+ $RATCF$RATCF -$5,000,000.00 $0.00 $5,000,000.00 -$5,000,000.00 $4,015,384.62 $4,015,384.62 $0.00 $0.00 $3,798,816.57 $3,798,816.57 $0.00 $0.00 $2,758,443.33 $2,758,443.33 $0.00 $0.00 $1,908,320.79 $1,908,320.79 $0.00 $0.00 $1,304,154.60 $1,304,154.60 $0.00 $0.00 -$2,204,989.07 $0.00 $2,204,989.07 $23,074,558.27 18.00%

PW $C = $3,547,544.14 FW $C = $9,576,787.51

AW $C = $1,014,278.80 IRRr = 59.09%

ERRr =

29.03%

IRRc =

65.45%

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

ERRc =

34.19%

ERRr =

29.03%

M 1 2 3 4 5 6 7 MACRS(5) 8 9 20.00% 10 32.00% 11 19.20% 12 11.52% 13 11.52% 14 5.76% 15 SUM 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

100.00%

A 1 PROBLEM 12.49 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS EST SALV

$190,000.00 LOAN PRINC $100,000.00 $5,000.00 LOAN PERIOD 6

REAL BTCF BTCF INCR

RCVD SALV

$5,000.00

LOAN INT

13.00%

METHOD

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

$TBTLCF -$190,000.00 $46,755.00 $48,578.45 $50,473.00 $52,441.45 $54,486.67 $56,611.65 $58,819.50 $61,113.46 $63,496.89 $65,973.27 $68,546.22 $79,132.81

$TPPMT -$100,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $100,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$TIPMT

$TDWO

$13,000.00 $13,000.00 $13,000.00 $13,000.00 $13,000.00 $13,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$27,151.00 $46,531.00 $33,231.00 $23,731.00 $16,967.00 $16,948.00 $16,967.00 $8,474.00 $0.00 $0.00 $0.00 $0.00 SUM DEPR

$190,000.00

BOOK VALUE

$0.00

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

AS SHOWN

PW $T =

$68,533.67

FW $T =

$340,410.35

AW $T =

$12,262.16

IRRc=

31.05%

ERRc=

19.25%

IRRr=

26.13%

ERRr=

14.77%

40.00% 12

INFL RATE= MARRr=

3.90% 10.00%

PERIODS

MARRc=

14.29%

$Ttax $2,641.60 -$4,381.02 $1,696.80 $6,284.18 $9,807.87 $10,665.46 $16,741.00 $21,055.79 $25,398.76 $26,389.31 $27,418.49 $31,653.12 MARRc=

$TATCF -$90,000.00 $31,113.40 $39,959.47 $35,776.20 $33,157.27 $31,678.80 -$67,053.81 $42,078.50 $40,057.68 $38,098.13 $39,583.96 $41,127.73 $47,479.68 14.29%

PW $T =

$68,533.67

FW $T = $340,410.35

AW $T =

$12,262.16

IRRc=

31.05%

ERRc=

19.25%

IRRr=

26.13%

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

ERRr=

14.77%

1 2 3 4

$45,000.00 TAX RATE $0.00 USEFUL LIFE

5 1 6 7 $TTI 8 9 $6,604.00 10 -$10,952.56 11 $4,242.00 12 $15,710.45 13 $24,519.67 14 $26,663.65 15 $41,852.50 16 $52,639.46 17 $63,496.89 18 $65,973.27 19 $68,546.22 20 $79,132.81 21

$TATCF+ $TATCF$TATCF MACRS(7) $0.00 $90,000.00 -$90,000.00 $31,113.40 $0.00 $0.00 14.29% $39,959.47 $0.00 $0.00 24.49% $35,776.20 $0.00 $0.00 17.49% $33,157.27 $0.00 $0.00 12.49% $31,678.80 $0.00 $0.00 8.93% $0.00 $67,053.81 -$67,053.81 8.92% $42,078.50 $0.00 $0.00 8.93% $40,057.68 $0.00 $0.00 4.46% $38,098.13 $0.00 $0.00 $39,583.96 $0.00 $0.00 $41,127.73 $0.00 $0.00 $47,479.68 $0.00 $936,887.19

A 1 PROBLEM 12.50 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

BASIS EST SALV RCVD SALV EOY 0 1 2 3 4 5 6 7 8 9 10 11 12

$190,000.00 LOAN PRINC $100,000.00 $5,000.00 LOAN PERIOD 6 $5,000.00 $RBTLCF -$190,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $50,000.00

LOAN INT $RPPMT -$100,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $79,488.94 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

13.00%

REAL BTCF BTCF INCR METHOD

$RIPMT

$RDWO

$12,512.03 $12,042.38 $11,590.35 $11,155.30 $10,736.57 $10,333.56 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$26,131.86 $43,103.38 $29,627.62 $20,363.57 $14,012.88 $13,471.79 $12,980.64 $6,239.71 $0.00 $0.00 $0.00 $0.00 SUM DEPR

$165,931.43

BOOK VALUE

$0.00

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

AS SHOWN

PW $C =

$68,533.67

AW $C =

$10,058.23

FW $C =

$215,088.00

IRRr =

26.13%

ERRr =

14.77%

IRRc =

31.05%

ERRc =

19.25%

G 1 2 3 4

$45,000.00 TAX RATE $0.00 USEFUL LIFE

5 1 6 7 $RTI 8 9 $6,356.11 10 -$10,145.75 11 $3,782.03 12 $13,481.14 13 $20,250.55 14 $21,194.65 15 $32,019.36 16 $38,760.29 17 $45,000.00 18 $45,000.00 19 $45,000.00 20 $50,000.00 21

PERIODS $RTax

40.00% INFL RATE= MARRr= 12 12 MARRc=

3.90% 10.00% 14.29%

$2,542.44 -$4,058.30 $1,512.81 $5,392.45 $8,100.22 $8,477.86 $12,807.74 $15,504.12 $18,000.00 $18,000.00 $18,000.00 $20,000.00 MARRr=

$RATCF -$90,000.00 $29,945.52 $37,015.92 $31,896.84 $28,452.25 $26,163.21 -$53,300.36 $32,192.26 $29,495.88 $27,000.00 $27,000.00 $27,000.00 $30,000.00 10.00%

$RATCF+ $RATCF$RATCF MACRS(7) $0.00 $90,000.00 -$90,000.00 $29,945.52 $0.00 $0.00 14.29% $37,015.92 $0.00 $0.00 24.49% $31,896.84 $0.00 $0.00 17.49% $28,452.25 $0.00 $0.00 12.49% $26,163.21 $0.00 $0.00 8.93% $0.00 $53,300.36 -$53,300.36 8.92% $32,192.26 $0.00 $0.00 8.93% $29,495.88 $0.00 $0.00 4.46% $27,000.00 $0.00 $0.00 $27,000.00 $0.00 $0.00 $27,000.00 $0.00 $0.00 $30,000.00 $0.00 $591,971.40 SUM

PW $C =

$68,533.67

100.00%

FW $C = $215,088.00

AW $C =

$10,058.23

IRRr =

26.13%

ERRr =

14.77%

IRRc =

31.05%

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

ERRc =

19.25%

A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

BASIS EST SALV

$500,000.00 LOAN PRINC $300,000.00 $50,000.00 LOAN PERIOD 10

REAL BTCF BTCF INCR

$124,166.67 $0.00

RCVD SALV

$50,000.00

LOAN INT

METHOD

EOY 0 1 2 3 4 5 6 7 8 9 10

$TBTLCF -$500,000.00 $129,133.34 $134,298.67 $139,670.62 $145,257.44 $151,067.74 $157,110.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

$TPPMT -$300,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $300,000.00

12.00% $TIPMT

$TDWO

$TTI

$36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00 $36,000.00

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00 SUM DEPR

-$6,866.66 -$61,701.33 $7,670.62 $51,657.44 $57,467.74 $92,310.45 $127,394.87 $133,930.66 $140,727.89 $221,809.22

$500,000.00

BOOK VALUE

$0.00

23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

BASIS EST SALV

$500,000.00 LOAN PRINC $300,000.00 $50,000.00 LOAN PERIOD 10

REAL BTCF BTCF INCR

$124,166.67 $0.00

RCVD SALV

$50,000.00

LOAN INT

METHOD

EOY 0 1 2 3 4 5 6 7 8 9 10

$TBTLCF -$500,000.00 $129,133.34 $134,298.67 $139,670.62 $145,257.44 $151,067.74 $157,110.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

$TPPMT -$300,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00

12.00% $TIPMT

$TDWO

$TTI

$36,000.00 $32,400.00 $28,800.00 $25,200.00 $21,600.00 $18,000.00 $14,400.00 $10,800.00 $7,200.00 $3,600.00

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00 SUM DEPR

-$6,866.66 -$58,101.33 $14,870.62 $62,457.44 $71,867.74 $110,310.45 $148,994.87 $159,130.66 $169,527.89 $254,209.22

$500,000.00

BOOK VALUE

$0.00

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

BASIS EST SALV

$500,000.00 LOAN PRINC $300,000.00 $50,000.00 LOAN PERIOD 10

REAL BTCF BTCF INCR

$124,166.67 $0.00

RCVD SALV

$50,000.00

LOAN INT

METHOD

EOY 0 1 2 3 4 5 6 7 8 9 10

$TBTLCF -$500,000.00 $129,133.34 $134,298.67 $139,670.62 $145,257.44 $151,067.74 $157,110.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

$TPPMT -$300,000.00 $17,095.25 $19,146.68 $21,444.28 $24,017.59 $26,899.71 $30,127.67 $33,742.99 $37,792.15 $42,327.21 $47,406.47

12.00% $TIPMT

$TDWO

$TTI

$36,000.00 $33,948.57 $31,650.97 $29,077.65 $26,195.54 $22,967.58 $19,352.26 $15,303.10 $10,768.04 $5,688.78

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00 SUM DEPR

-$6,866.66 -$59,649.90 $12,019.65 $58,579.79 $67,272.20 $105,342.87 $144,042.61 $154,627.56 $165,959.85 $252,120.44

$500,000.00

BOOK VALUE

$0.00

73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94

BASIS EST SALV

$500,000.00 LOAN PRINC $300,000.00 $50,000.00 LOAN PERIOD 10

REAL BTCF BTCF INCR

$124,166.67 $0.00

RCVD SALV

$50,000.00

12.00%

METHOD

EOY 0 1 2 3 4 5 6 7 8 9 10

$TBTLCF -$500,000.00 $129,133.34 $134,298.67 $139,670.62 $145,257.44 $151,067.74 $157,110.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

$TPPMT $TIPMT -$300,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $300,000.00 $631,754.46

$TDWO

LOAN INT

$TTI

F $500,000.00

BOOK VALUE

$0.00

98 99 100 101

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

TAX RATE USEFUL LIFE PERIODS

40.00% INFL RATE= MARRr= 10 10 MARRc=

4.00% 10.00% 14.40%

AW $T =

$42,863.15

IRRc=

47.70%

ERRc=

23.21%

IRRr=

42.02%

ERRr= 26 27 28 TAX RATE 29 USEFUL LIFE

18.48%

$TTax

30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

PERIODS

40.00% INFL RATE= MARRr= 10 10 MARRc=

$TTax

4.00% 10.00% 14.40%

$TATCF $TATCF+ $TATCF$TATCF MACRS(5) -$200,000.00 $0.00 $200,000.00 -$200,000.00 -$2,746.67 $65,880.00 $65,880.00 $0.00 $0.00 20.00% -$23,240.53 $95,139.20 $95,139.20 $0.00 $0.00 32.00% $5,948.25 $74,922.37 $74,922.37 $0.00 $0.00 19.20% $24,982.98 $65,074.47 $65,074.47 $0.00 $0.00 11.52% $28,747.10 $70,720.64 $70,720.64 $0.00 $0.00 11.52% $44,124.18 $64,986.27 $64,986.27 $0.00 $0.00 5.76% $59,597.95 $59,396.92 $59,396.92 $0.00 $0.00 $63,652.26 $65,478.40 $65,478.40 $0.00 $0.00 $67,811.16 $71,716.73 $71,716.73 $0.00 $0.00 $101,683.69 $122,525.53 $122,525.53 $0.00 $1,467,276.40 MARRc= 14.40% PW $T = $182,165.68

FW $T = $699,401.91

AW $T =

$35,470.47

H IRRc=

I 35.34%

ERRc=

22.05%

IRRr=

30.13%

ERRr= 51 52 53 TAX RATE 54 USEFUL LIFE

17.36%

55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70

PERIODS

40.00% INFL RATE= MARRr= 10 MARR 10 c=

4.00% 10.00% 14.40%

$TTax

$TATCF $TATCF+ $TATCF$TATCF MACRS(5) -$200,000.00 $0.00 $200,000.00 -$200,000.00 -$2,746.67 $78,784.75 $78,784.75 $0.00 $0.00 20.00% -$23,859.96 $105,063.38 $105,063.38 $0.00 $0.00 32.00% $4,807.86 $81,767.51 $81,767.51 $0.00 $0.00 19.20% $23,431.91 $68,730.28 $68,730.28 $0.00 $0.00 11.52% $26,908.88 $71,063.61 $71,063.61 $0.00 $0.00 11.52% $42,137.15 $61,878.05 $61,878.05 $0.00 $0.00 5.76% $57,617.04 $52,682.57 $52,682.57 $0.00 $0.00 $61,851.02 $54,984.39 $54,984.39 $0.00 $0.00 $66,383.94 $57,248.70 $57,248.70 $0.00 $0.00 $100,848.18 $103,865.79 $103,865.79 $0.00 $1,501,798.95 MARRc= 14% PW $T = $191,157.40

FW $T = $733,924.46

AW $T =

$37,221.30

IRRc=

38.58%

ERRc=

22.34%

IRRr=

33.25%

ERRr= 76 77 78 TAX RATE 79 USEFUL LIFE

17.63%

80 81 82 83 84 85 86 87 88 89 90 91 92 93 94

PERIODS $TTax

40.00% INFL RATE= MARRr= 10 10 MARRc=

$TATCF -$200,000.00 $11,653.33 $117,480.00 -$10,280.53 $144,579.20 $17,468.25 $122,202.37 $35,062.98 $110,194.47 $37,387.10 $113,680.64 $51,324.18 $105,786.27 $65,357.95 $98,036.92 $67,972.26 $101,958.40 $70,691.16 $106,036.73 -$149,578.10 -$524,367.15 MARRc= 14.40%

4.00% 10.00% 14.40%

$TATCF+ $TATCF$TATCF MACRS(5) $0.00 $200,000.00 -$200,000.00 $117,480.00 $0.00 $0.00 20.00% $144,579.20 $0.00 $0.00 32.00% $122,202.37 $0.00 $0.00 19.20% $110,194.47 $0.00 $0.00 11.52% $113,680.64 $0.00 $0.00 11.52% $105,786.27 $0.00 $0.00 5.76% $98,036.92 $0.00 $0.00 $101,958.40 $0.00 $0.00 $106,036.73 $0.00 $0.00 $0.00 $524,367.15 $1,659,897.55

H I PW $T = $232,335.64

FW $T = $892,023.06

AW $T =

$45,239.33

IRRc=

58.76%

ERRc=

23.57%

100

IRRr=

52.66%

101

ERRr=

18.82%

1 2 3 4

A PROBLEM 12.51

BASIS EST SALV

5 6 7 8 9 10 11 12 13 14 15 16 17

$1,400,000.00 LOAN PRINC $200,000.00 LOAN PERIOD

RCVD SALV

$200,000.00

LOAN INT

EOY 0 1 2 3 4 5 6 7 8

$TBTLCF -$1,400,000.00 $416,800.00 $434,305.60 $452,546.44 $471,553.39 $491,358.63 $511,995.69 $533,499.51 $833,859.73

$TPPMT -$800,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $800,000.00

$800,000.00 8

REAL BTCF BTCF INCR

12.00%

METHOD

$TIPMT $96,000.00 $96,000.00 $96,000.00 $96,000.00 $96,000.00 $96,000.00 $96,000.00 $96,000.00

$TDWO $280,000.00 $448,000.00 $268,800.00 $161,280.00 $161,280.00 $80,640.00 $0.00 $0.00 SUM DEPR

$1,400,000.00

BOOK VALUE

$0.00

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

BASIS EST SALV

$1,400,000.00 LOAN PRINC $200,000.00 LOAN PERIOD

RCVD SALV

$200,000.00

LOAN INT

EOY 0 1 2 3 4 5 6 7 8

$TBTLCF -$1,400,000.00 $416,800.00 $434,305.60 $452,546.44 $471,553.39 $491,358.63 $511,995.69 $533,499.51 $833,859.73

$TPPMT -$800,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00

$800,000.00 8

REAL BTCF BTCF INCR

12.00%

METHOD

$TIPMT $96,000.00 $84,000.00 $72,000.00 $60,000.00 $48,000.00 $36,000.00 $24,000.00 $12,000.00

$TDWO $280,000.00 $448,000.00 $268,800.00 $161,280.00 $161,280.00 $80,640.00 $0.00 $0.00 SUM DEPR

$1,400,000.00

BOOK VALUE

$0.00

44 45 46

47 48 49 50

BASIS EST SALV

51 52 53 54 55 56 57 58 59 60 61 62 63

$1,400,000.00 LOAN PRINC $200,000.00 LOAN PERIOD

RCVD SALV

$200,000.00

LOAN INT

EOY 0 1 2 3 4 5 6 7 8

$TBTLCF -$1,400,000.00 $416,800.00 $434,305.60 $452,546.44 $471,553.39 $491,358.63 $511,995.69 $533,499.51 $833,859.73

$TPPMT -$800,000.00 $65,042.27 $72,847.35 $81,589.03 $91,379.71 $102,345.28 $114,626.71 $128,381.91 $143,787.74

$800,000.00 8

REAL BTCF BTCF INCR

12.00%

METHOD

$TIPMT $96,000.00 $88,194.93 $79,453.25 $69,662.56 $58,697.00 $46,415.56 $32,660.36 $17,254.53

$TDWO $280,000.00 $448,000.00 $268,800.00 $161,280.00 $161,280.00 $80,640.00 $0.00 $0.00 SUM DEPR

$1,400,000.00

BOOK VALUE

$0.00

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86

BASIS EST SALV

$1,400,000.00 LOAN PRINC $200,000.00 LOAN PERIOD

RCVD SALV

$200,000.00

EOY 0 1 2 3 4 5 6 7 8

$TBTLCF -$1,400,000.00 $416,800.00 $434,305.60 $452,546.44 $471,553.39 $491,358.63 $511,995.69 $533,499.51 $833,859.73

$800,000.00 8

REAL BTCF BTCF INCR

12.00%

METHOD

$TPPMT $TIPMT -$800,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $800,000.00 $1,180,770.54

$TDWO

LOAN INT

$280,000.00 $448,000.00 $268,800.00 $161,280.00 $161,280.00 $80,640.00 $0.00 $0.00 SUM DEPR

$1,400,000.00

BOOK VALUE

$0.00

90 91 92

A 93 94 95

METHOD 4 IS THE PREFERRED METHOD DUE TO ITS HIGHER PW

G 1 2 3 4

$400,000.00 TAX RATE $0.00 USEFUL LIFE

5 1 6 7 $TTI 8 9 $40,800.00 10 -$109,694.40 11 $87,746.44 12 $214,273.39 13 $234,078.63 14 $335,355.69 15 $437,499.51 16 $737,859.73 17 18

PERIODS $TTax

40.00% INFL RATE= MARRr= 8 8 MARRc=

$16,320.00 -$43,877.76 $35,098.57 $85,709.35 $93,631.45 $134,142.28 $174,999.80 $295,143.89 MARRc=

$TATCF -$600,000.00 $304,480.00 $382,183.36 $321,447.86 $289,844.03 $301,727.18 $281,853.41 $262,499.71 -$357,284.16 14.62%

PW $T =

$595,819.70

FW $T = $1,774,998.90

AW $T =

$131,123.49

IRRc=

49.07%

ERRc=

24.94%

IRRr=

43.07%

24 25 26 27

ERRr=

19.90%

28 29 30 31 32 33 34 35 36 37 38 39 40

$400,000.00 TAX RATE $0.00 USEFUL LIFE 2

PERIODS

$TATCF+ $0.00 $304,480.00 $382,183.36 $321,447.86 $289,844.03 $301,727.18 $281,853.41 $262,499.71 $0.00

40.00% INFL RATE= MARRr= 8 MARR 8 c=

$TTI

$TTax

$40,800.00 -$97,694.40 $111,746.44 $250,273.39 $282,078.63 $395,355.69 $509,499.51 $821,859.73

$16,320.00 -$39,077.76 $44,698.57 $100,109.35 $112,831.45 $158,142.28 $203,799.80 $328,743.89 MARRc=

$TATCF -$600,000.00 $204,480.00 $289,383.36 $235,847.86 $211,444.03 $230,527.18 $217,853.41 $205,699.71 $393,115.84 14.62%

PW $T =

$501,492.71

42 43

FW $T = $1,493,990.56 AW $T = $110,364.72

IRRc=

36.28%

ERRc=

23.66%

IRRr=

30.79%

$TATCF+ $0.00 $204,480.00 $289,383.36 $235,847.86 $211,444.03 $230,527.18 $217,853.41 $205,699.71 $393,115.84

4.20% 10.00% 14.62% $TATCF$TATCF MACRS(5) $600,000.00 -$600,000.00 $0.00 $0.00 20.00% $0.00 $0.00 32.00% $0.00 $0.00 19.20% $0.00 $0.00 11.52% $0.00 $0.00 11.52% $0.00 $0.00 5.76% $0.00 $0.00 $357,284.16 $3,562,451.30

G 47 48 49 50

H ERRr=

$400,000.00 TAX RATE $0.00 USEFUL LIFE

51 3 52 53 $TTI 54 55 $40,800.00 56 -$101,889.33 57 $104,293.19 58 $240,610.82 59 $271,381.63 60 $384,940.13 61 $500,839.15 62 $816,605.20 63

PERIODS $TTax $16,320.00 -$40,755.73 $41,717.28 $96,244.33 $108,552.65 $153,976.05 $200,335.66 $326,642.08 MARRc=

I 18.68%

40.00% INFL RATE= MARRr= 8 8 MARRc= $TATCF -$600,000.00 $239,437.73 $314,019.06 $249,786.89 $214,266.78 $221,763.70 $196,977.37 $172,121.58 $346,175.38 15%

$TATCF+ $0.00 $239,437.73 $314,019.06 $249,786.89 $214,266.78 $221,763.70 $196,977.37 $172,121.58 $346,175.38

PW $T =

64 66

$519,323.56 FW $T = $1,547,110.23 AW $T = $114,288.80

IRRc=

38.78%

ERRc=

23.91%

IRRr=

33.18%

70 71 72 73

ERRr=

18.92%

$400,000.00 TAX RATE $0.00 USEFUL LIFE

74 4 75 76 $TTI 77 78 $136,800.00 79 -$13,694.40 80 $183,746.44 81 $310,273.39 82 $330,078.63 83 $431,355.69 84 $533,499.51 85 -$346,910.81 86 87

PERIODS $TTax

40.00% INFL RATE= MARRr= 8 8 MARRc=

$54,720.00 -$5,477.76 $73,498.57 $124,109.35 $132,031.45 $172,542.28 $213,399.80 -$138,764.32 MARRc=

$TATCF -$600,000.00 $362,080.00 $439,783.36 $379,047.86 $347,444.03 $359,327.18 $339,453.41 $320,099.71 -$1,008,146.49 14.62%

PW $T =

$619,739.83

FW $T = $1,846,259.08

AW $T =

$136,387.65

IRRc=

58.31%

ERRc=

25.25%

IRRr=

51.93%

4.20% 10.00% 14.62%

$TATCF+ $TATCF$TATCF MACRS(5) $0.00 $600,000.00 -$600,000.00 $362,080.00 $0.00 $0.00 20.00% $439,783.36 $0.00 $0.00 32.00% $379,047.86 $0.00 $0.00 19.20% $347,444.03 $0.00 $0.00 11.52% $359,327.18 $0.00 $0.00 11.52% $339,453.41 $0.00 $0.00 5.76% $320,099.71 $0.00 $0.00 $0.00 $1,008,146.49 $3,633,711.47

G 93 94 95

H ERRr=

I 20.20%

1 2 3 4

A PROBLEM 12.52

BASIS EST SALV

$9,000,000.00 LOAN PRINC $4,000,000.00 $700,000.00 LOAN PERIOD 6

REAL BTCF BTCF INCR

RCVD SALV

$700,000.00

12.00%

METHOD

$TIPMT

$TDWO

$480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00 $480,000.00

$1,800,000.00 $2,880,000.00 $1,728,000.00 $1,036,800.00 $1,036,800.00 $518,400.00 SUM DEPR

5 6 7 8 9 10 11 12 13 14 15

EOY 0 1 2 3 4 5 6

LOAN INT

$TBTLCF $TPPMT -$9,000,000.00 -$4,000,000.00 $6,240,000.00 $0.00 $5,408,000.00 $0.00 $4,499,456.00 $0.00 $3,509,575.68 $0.00 $2,433,305.80 $0.00 $2,151,042.33 $4,000,000.00

$9,000,000.00

BOOK VALUE

$0.00

19 20 21 22 23 24 25

26 27 28 29 30 31 32 33 34 35 36

BASIS EST SALV

$9,000,000.00 LOAN PRINC $4,000,000.00 $700,000.00 LOAN PERIOD 6

REAL BTCF BTCF INCR

RCVD SALV

$700,000.00

12.00%

METHOD

$TIPMT

$TDWO

$480,000.00 $400,000.00 $320,000.00 $240,000.00 $160,000.00 $80,000.00

$1,800,000.00 $2,880,000.00 $1,728,000.00 $1,036,800.00 $1,036,800.00 $518,400.00 SUM DEPR

EOY 0 1 2 3 4 5 6

LOAN INT

$TBTLCF $TPPMT -$9,000,000.00 -$4,000,000.00 $6,240,000.00 $666,666.67 $5,408,000.00 $666,666.67 $4,499,456.00 $666,666.67 $3,509,575.68 $666,666.67 $2,433,305.80 $666,666.67 $2,151,042.33 $666,666.67

$9,000,000.00

BOOK VALUE

$0.00

40 41 42 43 44 45 46

BASIS EST SALV

$9,000,000.00 LOAN PRINC $4,000,000.00 $700,000.00 LOAN PERIOD 6

REAL BTCF BTCF INCR

A 47 48 49 50 51 52 53 54 55 56 57

B RCVD SALV EOY 0 1 2 3 4 5 6

C $700,000.00

D LOAN INT

$TBTLCF $TPPMT -$9,000,000.00 -$4,000,000.00 $6,240,000.00 $492,902.87 $5,408,000.00 $552,051.22 $4,499,456.00 $618,297.36 $3,509,575.68 $692,493.05 $2,433,305.80 $775,592.21 $2,151,042.33 $868,663.28

E 12.00%

F METHOD

$TIPMT

$TDWO

$480,000.00 $420,851.66 $354,605.51 $280,409.83 $197,310.66 $104,239.59

$1,800,000.00 $2,880,000.00 $1,728,000.00 $1,036,800.00 $1,036,800.00 $518,400.00 SUM DEPR

$9,000,000.00

BOOK VALUE

$0.00

61 62 63 64 65 66 67

68 69 70 71 72 73 74 75 76 77 78

BASIS EST SALV

$9,000,000.00 LOAN PRINC $4,000,000.00 $700,000.00 LOAN PERIOD 6

REAL BTCF BTCF INCR

RCVD SALV

$700,000.00

METHOD

EOY 0 1 2 3 4 5 6

LOAN INT

12.00%

$TBTLCF $TPPMT $TIPMT -$9,000,000.00 -$4,000,000.00 $6,240,000.00 $0.00 $0.00 $5,408,000.00 $0.00 $0.00 $4,499,456.00 $0.00 $0.00 $3,509,575.68 $0.00 $0.00 $2,433,305.80 $0.00 $0.00 $2,151,042.33 $4,000,000.00 $3,895,290.74

$TDWO $1,800,000.00 $2,880,000.00 $1,728,000.00 $1,036,800.00 $1,036,800.00 $518,400.00 SUM DEPR

$9,000,000.00

BOOK VALUE

$0.00

82 83 84 85 86 87

PREFERRED METHOD IS METHOD 4

G 1 2 3 4

$6,000,000.00 TAX RATE -$1,000,000.00 USEFUL LIFE

5 6 7 8 9 10 11 12 13 14 15

PERIODS

$TTI

$TTax

$3,960,000.00 $1,584,000.00 $2,048,000.00 $819,200.00 $2,291,456.00 $916,582.40 $1,992,775.68 $797,110.27 $916,505.80 $366,602.32 $1,152,642.33 $461,056.93 MARRc=

PW $T =

40.00% 6

INFL RATE= MARRr=

4.00% 18.00%

MARRc=

22.72%

$3,547,544.14 FW $T = $12,117,691.37 AW $T = $1,139,640.14

IRRc=

65.45%

ERRc=

34.19%

IRRr=

59.09%

ERRr=

29.03%

22 23 24 $6,000,000.00 TAX RATE 25 -$1,000,000.00 USEFUL LIFE 26 27 28 29 30 31 32 33 34 35 36

PERIODS

$TTI

$TTax

$3,960,000.00 $1,584,000.00 $2,128,000.00 $851,200.00 $2,451,456.00 $980,582.40 $2,232,775.68 $893,110.27 $1,236,505.80 $494,602.32 $1,552,642.33 $621,056.93 MARRc=

PW $T =

40.00% 6

INFL RATE= MARRr=

4.00% 18.00%

MARRc=

22.72%

$TATCF $TATCF+ $TATCF$TATCF -$5,000,000.00 $0.00 $5,000,000.00 -$5,000,000.00 $3,509,333.33 $3,509,333.33 $0.00 $0.00 $3,490,133.33 $3,490,133.33 $0.00 $0.00 $2,532,206.93 $2,532,206.93 $0.00 $0.00 $1,709,798.74 $1,709,798.74 $0.00 $0.00 $1,112,036.82 $1,112,036.82 $0.00 $0.00 $783,318.73 $783,318.73 $0.00 $27,086,854.44 22.72% $2,929,877.79

FW $T = $10,007,868.38

AW $T =

$941,216.29

IRRc=

52.96%

ERRc=

32.53%

IRRr=

47.08%

ERRr= 43 44 45 $6,000,000.00 TAX RATE 46 -$1,000,000.00 USEFUL LIFE

27.43% 40.00% 6

INFL RATE= MARRr=

4.00% 18.00%

G 3

H PERIODS

$TTI

$TTax

47 48 49 50 51 52 53 54 55 56 57

$3,960,000.00 $1,584,000.00 $2,107,148.34 $842,859.34 $2,416,850.49 $966,740.20 $2,192,365.85 $876,946.34 $1,199,195.15 $479,678.06 $1,528,402.74 $611,361.10 MARRc=

PW $T =

I 6

J MARRc=

60 61

IRRc=

54.95%

ERRc=

32.78%

IRRr=

48.99%

ERRr=

27.67%

64 65 66 $6,000,000.00 TAX RATE 67 -$1,000,000.00 USEFUL LIFE

68 4 PERIODS 69 70 $TTI $TTax 71 72 $4,440,000.00 $1,776,000.00 73 $2,528,000.00 $1,011,200.00 74 $2,771,456.00 $1,108,582.40 75 $2,472,775.68 $989,110.27 76 $1,396,505.80 $558,602.32 77 -$2,262,648.41 -$905,059.36 MARRc= 78 PW $T = 79

40.00% 6

INFL RATE= MARRr=

4.00% 18.00%

MARRc=

22.72%

$TATCF $TATCF+ $TATCF$TATCF -$5,000,000.00 $0.00 $5,000,000.00 -$5,000,000.00 $4,464,000.00 $4,464,000.00 $0.00 $0.00 $4,396,800.00 $4,396,800.00 $0.00 $0.00 $3,390,873.60 $3,390,873.60 $0.00 $0.00 $2,520,465.41 $2,520,465.41 $0.00 $0.00 $1,874,703.48 $1,874,703.48 $0.00 $0.00 -$4,839,189.05 $0.00 $4,839,189.05 $29,921,781.13 22.72%

$3,759,823.63 FW $T = $12,842,795.08 AW $T = $1,207,834.43

IRRc=

71.45%

ERRc=

34.74%

IRRr=

64.86%

85 86 87

ERRr=

29.56%

$TATCF $TATCF+ $TATCF$TATCF -$5,000,000.00 $0.00 $5,000,000.00 -$5,000,000.00 $3,683,097.13 $3,683,097.13 $0.00 $0.00 $3,592,237.79 $3,592,237.79 $0.00 $0.00 $2,559,812.93 $2,559,812.93 $0.00 $0.00 $1,659,726.46 $1,659,726.46 $0.00 $0.00 $980,724.87 $980,724.87 $0.00 $0.00 $566,778.36 $566,778.36 $0.00 $27,400,017.33 22.72%

$3,021,558.55 FW $T = $10,321,031.27 AW $T = $970,668.52

K 22.72%

M 1 2 3 4 5 6 7 MACRS(5) 8 9 20.00% 10 32.00% 11 19.20% 12 11.52% 13 11.52% 14 5.76% 15 16 17 18 19 20 21 22 23 24 25 26 27 28 MACRS(5) 29 30 20.00% 31 32.00% 32 19.20% 33 11.52% 34 11.52% 35 5.76% 36 37 38 39 40 41 42 43 44 45 46

M 47 48 49 MACRS(5) 50 51 20.00% 52 32.00% 53 19.20% 54 11.52% 55 11.52% 56 5.76% 57 58 59 60 61 62 63 64 65 66 67 68 69 70 MACRS(5) 71 72 20.00% 73 32.00% 74 19.20% 75 11.52% 76 11.52% 77 5.76% 78 79 80 81 82 83 84 85 86 87

PROBLEM 13.1 MUTLIPLE CORRECT ANSWERS ARE POSSIBLE FOR THIS QUESTION DEPENDING UPON THE ASSUMPTION A STUDENT MAKES ABOUT THE PROJECT OR COMPANY MAKING THE EVALUATION. THE ANSWER BELOW REPRESENTS A RELATIVELY GENERIC RESPONSE THAT IS APPROPRIATE ACROSS A BROAD RANGE OF PROJECTS AND COMPANIES. RANKED FROM LEAST UNCERTAIN TO MOST UNCERTAIN FIRST COST - SINCE FIRST COST IS A t=0 VALUE (A "TODAY" COST) IT IS FREQUENTLY KNOWN WITH THE MOST CERTAINTY. OPERATING AND MAINTENCE COSTS - IF THE PROJECT BEING EVALUATED IS SIMILAR TO OTHERS WITHIN THE COMPANY OR WITHIN THE INDUSTRY, THEN DOCUMENTED HISTORIES OF OPERATING AND MAINTENANCE COSTS FOR SIMILAR ASSETS MAY BE READILY AVAILABLE FROM COMPANY HISTORICAL RECORDS, INDUSTRY CONSORTIUMS, AND/OR VENDORS. PLANNING HORIZON - PLANNING HORIZON MAY BE A COMPANY SET VALUE. IF SO THEN PLANNING HORIZON WOULD MOVE TO THE TOP OF THIS LIST AND BE THE LEAST UNCERTAIN. IF THE HORIZON IS BASED ON THE PROJECT LIFE OF THIS ASSET, THEN THE ARGUMENT MADE UNDER "OPERATING AND MAINTENANCE" IS ALSO RELEVANT HERE. IF NONE OF THESE SITUATION APPLY THEN THE PLANNING HORIZON IS SUBJECT TO THE UNCERTAINTY OF THE LIFE OF THIS ASSET AS WELL AS THE LIVES OF THE OTHER ALTERNATIVES BEING CONSIDERED. MARR - IF MARR IS A COMPANY SET VALUE THEN MARR WOULD ALSO MOVE TO THE TOP OF THIS LIST AND BE LEAST UNCERTAIN. IF MARR IS BASED ON COST OF CAPITAL, THEN THE UNCERTAINTY OF MARR IS DIRECTLY RELATED TO THE CERTAINTY WITH WHICH THE COST OF THE VARIOUS COMPONENTS AND THE MIX (PERCENTAGE FROM EACH SOURCE) IS KNOWN. IF MARR IS BASED ON COST OF CAPITAL PLUS CONSIDERATION OF OTHER ISSUES (RISK, ETC.) THEN CONSIDERABLE UNCERTAINTY MAY EXIST IN THE DETERMINATION OF MARR. SALVAGE VALUE - SALVAGE VALUE IS A SINGLE VALUE (FREQUENTLY SMALL RELATIVE TO THE OTHER COSTS AND THUS LESS IMPORTANT WITH RESPECT TO ECONOMIC JUSTIFICATION) AND IS LOCATED THE FARTHEST OUT IN TIME. FOR THESE REASONS IT IS USUALLY THE MOST UNCERTAIN.

ONENTS AND

RESPECT TO

PROBLEM 13.2 a b c

(3) (1) (2)

PROBLEM 13.3 FOR BREAKEVEN, PW OF REVENUE = PW OF COSTS LET X BE THE NUMBER OF UNITS SOLD ANNUALLY PW OF REVENUE = $10.25(X)(P|A 12%,7) PW OF COSTS = $10,000 + $3,500(P|A 12%,7) FOR BREAKEVEN $10.25(X)(P|A 12%,7) = $100,000 + $3,500(P|A 12%,7) $10.25(X)(4.56376) = $100,000 + $3,500(4.56376) X= 2479.2 ROUNDING UP RESULTS IN 2,480 UNITS

PROBLEM 13.3 ORIGINAL PROBLEM BREAKEVEN VALUE IS 2,480 UNITS a

FALSE FOR BREAKEVEN $10.25(X)(P|A 12%,7) = $200,000 + $3,500(P|A 12%,7) $10.25(X)(4.56376) = $200,000 + $3,500(4.56376) X= 4616.9 ROUNDING UP RESULTS IN 4,617 UNITS 4,617 IS NOT EQUAL TO (2,480)(2)

TRUE FOR BREAKEVEN $20.50(X)(P|A 12%,7) = $100,000 + $3,500(P|A 12%,7) $20.50(X)(4.56376) = $100,000 + $3,500(4.56376) X= 1239.6 ROUNDING UP RESULTS IN 1,240 UNITS 1,240 IS EQUAL TO (2,480)(0.5)

FALSE FOR BREAKEVEN $10.25(X)(P|A 12%,7) = $100,000 + $7,000(P|A 12%,7) $10.25(X)(4.56376) = $100,000 + $7,000(4.56376) X= 2820.7 ROUNDING UP RESULTS IN 2,821 UNITS 2,821 IS NOT EQUAL TO (2,480)(2)

PROBLEM 13.5 a

TO BE EQUAL ECONOMICALLY, THE PW OF THE COSTS OF THE TWO ALTERNATIVES MUST BE EQUAL PW OF COST OF FLOW LINE PW = $15,000 + (6.00)(X)(P|A 8%,5) PW OF COST OF MANUFACTURING CELL PW = $10,000 + (7.00)(X)(P|A 8%,5) EQUATING THE PW VALUES AND SOLVING FOR X $15,000 + (6.00)(X)(P|A 8%,5) = $10,000 + (7.00)(X)(P|A 8%,5) $15,000 + (6.00)(X)(3.99271) = $10,000 + (7.00)(X)(3.99271) X= 1252.3 ROUNDING UP RESULTS IN 1,253 UNITS

AT A PRODUCTION RATE OF 300 RAILS THE PW OF EACH IS AS FOLLOWS PW OF COST OF FLOW LINE PW = $15,000 + (6.00)(X)(P|A 8%,5) PW = $15,000 + (6.00)(300)(3.99271) PW = $22,186.88 PW OF COST OF MANUFACTURING CELL PW = $10,000 + (7.00)(X)(P|A 8%,5) PW = $10,000 + (7.00)(300)(3.99271) PW = $18,384.69 THE MANUFACTURING CELL IS PREFERRED AT A PRODUCTION RATE OF 300 RAILS TOTAL ANNUAL COST OF THE MANUFACTURING CELL IS VARIABLE COST = (7.00)(300) = $2,100 CAPITAL RECOVERY COST = $10,000(A|P 8%,5) = $10,000(0.25046) = $2,504.60 TOTAL ANNUAL COST = $2,100 + $2,504.60 = $4,604.60

PROBLEM 13.6 a

TO BE EQUALLY ATTRACTIVE, THE PW OF INCOME FROM PLAN 1 AND PLAN 2 MUST BE EQUAL PW OF REVENUE FROM PLAN 1 PW = $50,000 PW OF REVENUE FROM PLAN 2 PW = ($2,000 + ($1.00)(X))(P|A 10%,10) SET THE PW VALUES EQUAL AND SOLVING FOR X $50,000 = ($2,000 + ($1.00)(X))(P|A 10%,10) $50,000 = ($2,000 + ($1.00)(X))(6.14457) X= 6137.3 ROUNDING TO NEAREST INTEGER RESULTS IN 6,137

IF FEWER THAN 6,137 UNITS ARE SCHEDULED THEN THE PLAN WITH THE HIGHEST PW WILL BE PREFERRED. FOR EXAMPLE IF 1,000 UNITS ARE SCHEDULED: PW OF PLAN 1 = $50,000 PW OF PLAN 2 = ($2,000 + ($1.00)(1,000))(6.14457) = $18,433.71 PLAN 1 WILL BE PREFERRED FOR ANY NUMBER OF UNITS BELOW 6,137

PROBLEM 13.7 a

TO DETERMINE THE BREAKEVEN NUMBER OF DAYS, THE PW OF THE COSTS OF THE TWO OPTIONS MUST BE EQUAL PW OF COST OF PURCHASE PW = $40,000 + ($2,400 + ($60(X)))(P|A 7%,6) PW OF COST OF HIRE PW = ($150)(X)(P|A 7%,6) SETTING THE PW VALUES EQUAL AND SOLVING FOR X $40,000 + ($2,400 + ($60(X)))(P|A 7%,6) = ($150)(X)(P|A 7%,6) $40,000 + ($2,400 + ($60(X)))(4.76654) = ($150)(X)(4.76654) X= 119.9 ROUNDING UP RESULTS IN 120 DAYS

IF X = 180 DAYS, THE PW VALUES ARE AS FOLLOWS PW OF PURCHASE PW = $40,000 + ($2,400 + ($60(180)))(P|A 7%,6) PW = $40,000 + ($2,400 + ($60($180)))(4.76654) PW = $102,918.33 PW OF HIRE PW = ($150)(180)(P|A 7%,6) PW = ($150)(180)(4.76654) PW = $128,696.58 WHEN OPERATING FOR 180 DAYS, PURCHASING IS PREFERRED ANNUAL SAVINGS WILL BE THE ANNUALIZED DIFFERENCE IN PW VALUES SAVINGS = ($128,696.58 - $102,918.33)(A|P 7%,6) SAVINGS = ($128,696.58 - $102,918.33)(0.20980) SAVINGS = $5,408.28

PROBLEM 13.8 a

LET X BE THE NUMBER OF UNITS PRODUCED AND SOLD PROFIT = ($1.00)(X) - ($192,000 + ($0.376)(X)) OPERATING AT 64% OF CAPACITY IS (650,000)(0.64) OR 416,000 UNITS/YR PROFIT = ($1.00)(X) - ($192,000 + ($0.376)(X)) PROFIT = ($1.00)(416,000) - ($192,000 + ($0.376)(416,000)) PROFIT = $67,584.00

FOR BREAKEVEN, REVENUE = COST ($1.00)(X) = $192,000 + ($0.376)(X) X= 307692.3 ROUNDING TO THE NEAREST INTEGER RESULTS IN 307,692 UNITS

OPERATING AT 80% OF CAPACITY IS (650,000)(0.80) OR 520,000 UNITS/YR PROFIT = ($1.00)(X) - ($192,000 + ($0.376)(X)) PROFIT = ($1.00)(520,000) - ($192,000 + ($0.376)(520,000)) PROFIT = $132,480.00

PROBLEM 13.9 SOLUTION USING FACTOR TABLES LET X BE THE NUMBER OF YEARS THE SAVINGS WILL BE REALIZED. BREAKEVEN WILL OCCUR WHEN THE PW OF THE INCREMENTAL SAVINGS EQUALS THE INCREMENTAL COST. $1,500 = $300(P|A 10%,n) 5.00 = (P|A 10%,n) THE LOWEST VALUE OF n SUCH THAT THE (P|A 10%,n) FACTOR EQUALS OR EXCEEDS 5.00 WILL RESULT IN JUSTIFYING THE INCREMENTAL INVESTMENT. SEARCHING THE 10% INTEREST TABLE YIELDS A VALUE OF n=8 AS THE LOWEST VALUE OF n SUCH THAT (P|A 10%,n) EXCEEDS 5.00. THE SAVINGS MUST BE REALIZED FOR AT LEAST 8 YEARS TO JUSTIFY THE INCREMENTAL INVESTMENT IN THE HYBRID ENGINE. SOLUTION USING EXCEL'S NPER FUNCTION =NPER(10%,-300,1500) 7.27 YEARS THE SAVINGS MUST BE REALIZED FOR AT LEAST 8 YEARS TO JUSTIFY THE INCREMENTAL INVESTMENT IN THE HYBRID ENGINE. NOTE: THERE ARE LIKELY ADDITIONAL "GREEN" CONSIDERATIONS IN THIS DECISION BEYOND THE ACTUAL FUEL SAVINGS.

PROBLEM 13.10 a

FOR BREAKEVEN, THE TOTAL COST OF BRASS AND THE TOTAL COST OF STEEL MUST BE EQUAL. TOTAL COST IS THE SUM OF PURCHASE COST PLUS MACHINING COST. LET L BE THE LENGTH OF THE ROD COST OF BRASS COST = ($0.022)(L) + ($0.0054 + ($0.006)(L)) = $0.0054 + ($0.028)(L) COST OF STEEL COST = ($0.007)(L) + ($0.0072 + ($0.010)(L)) = $0.0072 + ($0.017)(L) FOR BREAKEVEN $0.0054 + ($0.028)(L) = $0.0072 + ($0.017)(L) L= 0.1636 BREAKEVEN OCURRS AT 0.1636 INCHES BRASS IS PREFERRED BELOW 0.1636 INCHES STEEL IS PREFERRED ABOVE 0.1636 INCHES

SINCE THE RANGE OF NEED IS FROM 0.25 TO 4 INCHES ACCORDING TO THE PROBLEM STATEMENT AND THIS ENTIRE RANGE FALLS ABOVE THE BREAKEVEN, THE STEEL RODS ARE PREFERRED.

PROBLEM 13.11 a

LET H BE THE NUMBER OF HOURS THE GENERATOR IS OPERATED COST OF GENERATOR 1 COST = $4,000 + ($7.00)(H) COST OF GENERATOR 2 COST = $8,000 + ($5.50)(H) FOR BREAKEVEN, THE COSTS OF THE TWO GENERATORS MUST BE EQUAL $4,000 + ($7.00)(H) = $8,000 + ($5.50)(H) SOLVING FOR H H= 2666.7 HOURS CONVERTING TO HOURS PER SHIFT HOURS PER SHIFT = 2666.7/((3)(250)) = 3.56 HOURS/SHIFT

FOR 2.5 HOURS PER SHIFT; H = (2.5)(3)(250) = 1,875 COST OF GENERATOR 1 = $4,000 + ($7.00)(1,875) = $17,125.00 COST OF GENERATOR 2 = $8,000 + ($5.50)(1,875) = $18,312.50 GENERATOR 1 IS PREFERRED FOR 2.5 HOURS/SHIFT USE AT AN ANNUAL COST OF $17,125.00

FOR 5.5 HOURS PER SHIFT; H = (5.5)(3)(250) = 4,125 COST OF GENERATOR 1 = $4,000 + ($7.00)(4,125) = $32,875 COST OF GENERATOR 2 = $8,000 + ($5.50)(4,125) = $30,687.50 GENERATOR 2 IS PREFERRED FOR 5.5 HOURS/SHIFT USE AT AN ANNUAL COST OF $30,687.50

PROBLEM 13.12 THE FOLLOWING SOLUTION USES TVOM FACTORS. THE SOLUTION SHOWN BELOW IT USES EXCEL'S SOLVER AND IS THE ANSWER SHOWN IN THE BACK OF THE BOOK IN THE EVEN NUMBERED ANSWER SECTION. LET X BE THE ANNUAL FUEL SAVINGS CAPITAL RECOVERY COSTS = $20,000(A|P 12%,10) - ($20,000)(0.20)(A|F 12%,10) CAPITAL RECOVERY = $20,000(0.17698) - ($20,000)(0.20)(0.05698) = $3,311.68 UNIFORM O&M COSTS = $1,500 + $100(A|G, 12%,10) UNIFORM O&M COSTS = $1,500 + $100(3.58465) = $1,858.47 MINIMUM ACCEPTABLE SAVINGS = SUM OF ANNUAL COSTS MINIMUM ACCEPTABLE SAVINGS = $3,311.68 + $1,858.47 = $5,170.15 SOLUTION USING SOLVER EOY 0 1 2 3 4 5 6 7 8 9 10

CAPITAL -$20,000.00

NET CF -$20,000.00 -$1,500.00 $5,170.21 $3,670.21 -$1,600.00 $5,170.21 $3,570.21 -$1,700.00 $5,170.21 $3,470.21 -$1,800.00 $5,170.21 $3,370.21 -$1,900.00 $5,170.21 $3,270.21 -$2,000.00 $5,170.21 $3,170.21 -$2,100.00 $5,170.21 $3,070.21 -$2,200.00 $5,170.21 $2,970.21 -$2,300.00 $5,170.21 $2,870.21 $4,000.00 -$2,400.00 $5,170.21 $6,770.21

TO USE SOLVER SET TARGET CELL EQUAL TO: VALUE OF: BY CHANGING CELLS:

O&M

$5,170.21 SAVINGS

H31 0.00 E17

12.00% (P|F i%,n) 1.00000 0.89286 0.79719 0.71178 0.63552 0.56743 0.50663 0.45235 0.40388 0.36061 0.32197

PW OF CF -$20,000.00 $3,276.97 $2,846.15 $2,470.03 $2,141.83 $1,855.61 $1,606.13 $1,388.81 $1,199.62 $1,035.03 $2,179.83

PW ->

$0.00

PRESENT WORTH ZERO ANNUAL SAVINGS

MINIMUM ACCEPTABLE SAVINGS = $5,170.21

PROBLEM 13.13 LET X BE THE NUMBER OF DAYS SNOW REMOVAL IS REQUIRED PW OF COST OF CONTRACTING PW = ($400)(X)(P|A 12%,6) PW OF COST OF PURCHASING PW = $25,000 + $5,000(P|A 12%,6) FOR BREAKEVEN THE COST OF CONTRACTING AND THE PW OF COST OF PURCHASING MUST BE EQUAL ($400)(X)(P|A 12%,6) = $25,000 + $5,000(P|A 12%,6) ($400)(X)(4.11141) = $25,000 + $5,000(4.11141) X= 27.7 ROUNDING UP RESULTS IN 28 DAYS SNOW REMOVAL MUST BE REQUIRED FOR AT LEAST 28 DAYS TO JUSTIFY THE PURCHASE OF THE MACHINE.

PROBLEM 13.14 THE FOLLOWING SOLUTION USES TVOM FACTORS. THE SOLUTION SHOWN BELOW IT USES EXCEL'S SOLVER AND IS THE ANSWER SHOWN IN THE BACK OF THE BOOK IN THE EVEN NUMBERED ANSWER SECTION. LET X BE THE NUMBER OF HOLES PER YEAR PW OF COST OF MANUAL PW = (X/1.5)($11.20)(P|A 8%,8) PW OF COST OF THE POWER-DRIVEN DIGGER PW = $8,000 - $1,000(P|F 8%,8) + $8,000(0.15)(P|A 8%,8) + (X/25)($40.00)(P|A 8%,8) FOR BREAKEVNE THE PW OF COST OF MANUAL MUST EQUAL THE PW OF COST OF THE POWER-DRIVEN DIGGER (X/1.5)($11.20)(P|A 8%,8) = $8,000 - $1,000(P|F 8%,8) + $8,000(0.15)(P|A 8%,8) + (X/25)($40.00)(P|A 8%,8) (X/1.5)($11.20)(5.74664) = $8,000 - $1,000(0.54027) + $8,000(0.15)(5.74664) + (X/25)($40.00)(5.74664) X= 423.96 ROUNDING UP RESULTS IN 424 HOLES PER YEAR 424 HOLES PER YEAR ARE REQUIRED TO JUSTIFY THE PURCHASE OF THE POWER-DRIVEN DIGGER. SOLUTION USING SOLVER

EOY 0 1 2 3 4 5 6 7 8

CAPITAL -$8,000.00

$1,000.00

TO USE SOLVER SET TARGET CELL EQUAL TO: VALUE OF: BY CHANGING CELLS:

425.8 <- HOLES/YR 17.03 283.88 <- # OF DAYS MAINTAIN OPERATE MANUAL NET INCR CF -$8,000.00 -$1,200.00 -$681.30 -$3,179.40 $1,298.10 -$1,200.00 -$681.30 -$3,179.40 $1,298.10 -$1,200.00 -$681.30 -$3,179.40 $1,298.10 -$1,200.00 -$681.30 -$3,179.40 $1,298.10 -$1,200.00 -$681.30 -$3,179.40 $1,298.10 -$1,200.00 -$681.30 -$3,179.40 $1,298.10 -$1,200.00 -$681.30 -$3,179.40 $1,298.10 -$1,200.00 -$681.30 -$3,179.40 $2,298.10

I40 0.00 E27

PRESENT WORTH ZERO # OF HOLES

MINIMUM NUMBER OF HOLES = 425.8; ROUNDED T0 426 HOLES PER YEAR

SHOWN IN THE

0.00)(P|A 8%,8)

8.00% (P|F i%,n) PW OF CF 1.00000 -$8,000.00 0.92593 $1,201.95 0.85734 $1,112.91 0.79383 $1,030.48 0.73503 $954.14 0.68058 $883.47 0.63017 $818.03 0.58349 $757.43 0.54027 $1,241.59 PW ->

$0.00

PROBLEM 13.15 a

COST PER BATCH IF PURCHASED COST = 1,000($4.00) = $4,000 COST IF MANUFACTURED COST = $1,500 + (120)($10.00) + (120)($7.50) = $3,600 THE ITEM SHOULD BE MANUFACTURED.

LET X BE THE OVERHEAD RATE PER DIRECT LABOR HOUR. BREAK EVEN OCURRS WHEN THE PURCHASE COST EQUALS THE COST OF MANUFACTURE. 1,000($4.00) = $1,500 + (120)($10.00) + (120)(X) X= $10.83 BREAKEVEN OCCURS AT AN OVERHEAD RATE OF $10.83. BELOW BREAKEVEN THE PART SHOULD BE MANUFACTURED, ABOVE IT SHOULD BE PURCHASED.

PROBLEM 13.16 a

50% OF CAPACITY EQUALS 500,000 CASTINGS PER YEAR PROFIT = (500,000)(15.00) - ($3,500,000 + (500,000)(9.00)) PROFIT = -$500,000.00 AT 50% OF CAPACITY, THE PLANT IS OPERATING AT A $500,000 ANNUAL LOSS.

LET X EQUAL THE PROPORTION OF CAPACITY BREAKEVEN OCCURS WHEN PROFIT = 0 0 = (1,000,000)(X)(15.00) - ($3,500,000 + (1,000,000)(X)($9.00) X= 0.5833 OPERATING AT 58.33% OF CAPACITY IS REQUIRED FOR BREAKEVEN

PROBLEM 13.17 LET X BE THE NUMBER OF UNITS SOLD PER DAY PW OF REVENUE = (365)(X)($35.00)(P|A MARR,10) PW OF COST = $5,000,000 - ($5,000,000)(0.25)(P|F MARR,10) + ($45,000)(P|A MARR,10) FOR BREAKEVEN, THE PW OF REVENUE MUST EQUAL THE PW OF COST (365)(X)($35.00)(P|A MARR,10) = $5,000,000 - ($5,000,000)(0.25)(P|F MARR,10) + ($45,000)(P|A MARR,10) a

FOR MARR = 5% (365)(X)($35.00)(P|A 5%,10) = $5,000,000 - ($5,000,000)(0.25)(P|F 5%,10) + ($45,000)(P|A 5%,10) (365)(X)($35.00)(7.72173) = $5,000,000 - ($5,000,000)(0.25)(0.61391) + ($45,000)(7.72173) X= 46.43 ROUNDING TO THE NEAREST INTEGER RESULTS IN 47 UNITS PER DAY

FOR MARR = 10% (365)(X)($35.00)(P|A 10%,10) = $5,000,000 - ($5,000,000)(0.25)(P|F 10%,10) + ($45,000)(P|A 10%,10) (365)(X)($35.00)(6.14457) = $5,000,000 - ($5,000,000)(0.25)(0.38554) + ($45,000)(6.14457) X= 61.08 ROUNDING TO THE NEAREST INTEGER RESULTS IN 61 UNITS PER DAY

FOR MARR = 15% (365)(X)($35.00)(P|A 15%,10) = $5,000,000 - ($5,000,000)(0.25)(P|F 15%,10) + ($45,000)(P|A 15%,10) (365)(X)($35.00)(5.01877) = $5,000,000 - ($5,000,000)(0.25)(0.24718) + ($45,000)(5.01877) X= 76.69 ROUNDING TO THE NEAREST INTEGER RESULTS IN 77 UNITS PER DAY

PROBLEM 13.18 a

70% PRODUCTION EQUALS (0.7)(300,000) OR 210,000 PALLETS PER YEAR REVENUE = (210,000)($18.25) = $3,832,500 COST = $550,000 + (210,000)($15.75) = $3,857,500 PROFIT = $3,832,500 - $3,857,500 = -$25,000 AT 70% PRODUCTION THE PLANT REALIZES A $25,000 ANNUAL LOSS

LET X EQUAL THE NUMBER OF PALLETS PER YEAR AT BREAKEVEN, REVENUE EQUALS COST (X)($18.25) = $550,000 + (X)($15.75) X= 220,000 BREAKEVEN AT 220,000 PALLETS PER YEAR

90% PRODUCTION EQUALS (0.9)(300,000) OR 270,000 PALLETS PER YEAR REVENUE = (270,000)($18.25) = $4,927,500 COST = $550,000 + (270,000)($15.75) = $4,802,500 PROFIT = $4,927,500 - $4,802,500 = $125,000 AT 90% PRODUCTION THE PLANT REALIZES A $125,000 ANNUAL PROFIT

THE NEW FIXED COSTS EQUALS (1-0.40)($550,000) OR $330,000 LET X EQUAL THE NUMBER OF PALLETS PER YEAR AT BREAKEVEN, REVENUE EQUALS COST (X)($18.25) = $330,000 + (X)($15.75) X= 132,000 BREAKEVEN AT 132,000 PALLETS PER YEAR

PROBLEM 13.19 THE INSTRUCTOR MAY WANT TO SUGGEST THAT A GRAPH OF THE COST CURVES IS HELPFUL IN VISUALIZING THE SOLUTION TO THIS PROBLEM. SINCE THE COST FUNCTIONS ARE LINEAR, ONLY TWO POINTS WOULD BE NEEDED TO DEFINE THE CURVES. THE TABLE BELOW USES 7 POINTS FOR ILLUSTRATIVE PURPOSES ONLY.

VOLUME 0 25 50 75 100 125 150

COST CT1 $300.00 $525.00 $750.00 $975.00 $1,200.00 $1,425.00 $1,650.00

COST CT2 $750.00 $825.00 $900.00 $975.00 $1,050.00 $1,125.00 $1,200.00

COST CT3 $500.00 $625.00 $750.00 $875.00 $1,000.00 $1,125.00 $1,250.00

ORDER COST BY CUTTING TOOL COST PER ORDER

$1,800.00 $1,600.00 $1,400.00 $1,200.00 $1,000.00 $800.00 $600.00 $400.00 $200.00 $0.00

CT1 CT2 CT3

100

150

200

ORDER SIZE

FROM THE GRAPH IT BECOMES APPARENT THAT FOR SMALL ORDERS CT1 IS PREFERRED; FOR MEDIUM SIZE ORDERS CT3 IS PREFERRED; AND FOR LARGE ORDERS CT2 IS PREFERRED. TO DETERMINE THE BREAK POINTS IN PREFERRABILITY, TWO BREAKEVEN VALUES MUST BE DETERMINED; THE BREAKEVEN BETWEEN CT1 & CT3 AND THE BREAKEVEN BETWEEN CT2 & CT3 BREAKEVEN FOR CT1 & CT3 $300 + ($9.00)(X) = $500 + ($5.00)(X) X= 50.0 THE BREAKEVEN OCCURS AT AN ORDER SIZE OF 50 UNITS BREAKEVEN FOR CT2 & CT3 $750 + ($3.00)(X) = $500 + ($5.00)(X) X= 125.0

THE BREAKEVEN OCCURS AT AN ORDER SIZE OF 125 UNITS THE GUIDELINES FOR CUTTING TOOL PREFERRABILITY CAN BE SUMMARIZED: FOR AN ORDER SIZE UP TO 50 UNITS, PREFER CUTTING TOOL CT1 FOR AN ORDER SIZE GREATER THAN 50 UNITS AND UP TO 125 UNITS, PREFER CT3 FOR AN ORDER SIZE GREATER THEN 125 UNITS, PREFER CT2 b

FOR AN ORDER OF SIZE 75, CUTTING TOOL CT3 IS PREFERRED ORDER COST = $500 + (75)(5.00) = $875.00

& CT3 AND THE

SUMMARIZED:

NITS, PREFER CT3

PROBLEM 13.20 a

AW = -$30,000(A|P 12%,7) + $7,000(A|F 12%,7) + $13,000 AW = -$30,000(0.21912) + $7,000(0.09912) + $13,000 AW = $7,120.24 SINCE AW > 0, THE INVESTMENT IN THE MODERNIZING IS ATTRACTIVE

FOR THE REQUESTED SENSITIVITY ANALYSIS, THE FIRST COST AND SALVAGE VALUE REMAIN UNCHANGED, ONLY THE ANNUAL SAVINGS CHANGE. % CHANGE -80.00% -60.00% -40.00% -20.00% 0.00% 20.00% 40.00%

AW 1ST COST AW SALVAGE SAVINGS -$6,573.60 $693.84 $2,600.00 -$6,573.60 $693.84 $5,200.00 -$6,573.60 $693.84 $7,800.00 -$6,573.60 $693.84 $10,400.00 -$6,573.60 $693.84 $13,000.00 -$6,573.60 $693.84 $15,600.00 -$6,573.60 $693.84 $18,200.00

AW -$3,279.76 -$679.76 $1,920.24 $4,520.24 $7,120.24 $9,720.24 $12,320.24

THE 0.00% IS INCLUDED IN THE TABLE AS CONFIRMATION OF THE RESULT IN PART a c

A REVERSAL IN THE DECISION REGARDING THE ATTRACTIVENESS OF THE MODERNIZATION WOULD OCCUR WHEN AW = 0. LET X BE THE PROPORTION CHANGE IN ANNUAL SAVINGS THIS CAN BE DETERMINED BY SOLVING THE FOLLOWING EQUATION FOR X 0 = -$30,000(0.21912) + $7,000(0.09912) + $13,000(1+X) X= -0.548 THE ATTRACTIVENESS DECISION WILL REVERSE IF THE ANNUAL SAVINGS ARE REDUCED BY 54.8% (I.E., THE CHANGE IS -54.8%)

PROBLEM 13.21 a

IF A SINGLE EQUATION IS USED, THEN THE EQUATION MUST REPRESENT THE DIFFERENCE IN A MEASURE OF WORTH CALCULATED FOR BOTH CHOICES. IF TWO EQUATIONS ARE USED, THEN A MEASURE OF WORTH EQUATION FOR EACH CHOICE CAN BE WRITTEN AND THE RESULTS COMPARED. SINCE THE PROBLEM IS STATED AS "THE EQUATION", A SINGLE EQUATION APPROACH WILL BE USED HERE. NO SPECIFIC MEASURE OF WORTH IS SPECIFIED SO STUDENTS MAY CHOOSE FROM AMONG SEVERAL MEASURES. A PW MEASURE WILL BE USED HERE. SINCE LIFE IS GIVEN AS THE SENSITIVITY VARIABLE, THE PW EQUATIONS WILL BE WRITTEN USING THE VARIABLE N FOR LIFE. PW OF COST FOR STORAGE FACILITY PW = $213,000 + $3,200(P|A 15%,N) PW OF COST FOR HOLDING TANK PW = ($90,000 + $45,000) + $8,500(P|A 15%,N) THE DIFFERENCE EQUATION WILL BE WRITTEN AS DIFF = STORAGE FACILITY - HOLDING TANK IF THIS DIFFERENCE IS POSITIVE, THE HOLDING TANK IS PREFERRED IF THIS DIFFERENCE IS NEGATIVE, THE STORAGE FACILITY IS PREFERRED DIFF = ($213,000 + $3,200(P|A 15%,N)) - (($90,000+$45,000)+$8,500(P|A 15%,N)) DIFF = ($78,000 - $5,300(P|A 15%,N))

LIFE 15 16 17 18 19 20 21 22 23 24 25

(P|A 15%,LIFE) 5.84737 5.95423 6.04716 6.12797 6.19823 6.25933 6.31246 6.35866 6.39884 6.43377 6.46415

DIFF $47,008.94 $46,442.56 $45,950.05 $45,521.78 $45,149.37 $44,825.54 $44,543.95 $44,299.09 $44,086.16 $43,901.01 $43,740.01

PREFERRED HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK HOLDING TANK

ALTHOUGH THE PROBLEM STATEMENT DOES NOT ASK FOR A CONCLUSION FOR THE ANALYSIS OF PART b. THE TABLE ABOVE INDICATES THAT SENSITIVITY TO EXPECTED LIFE IS NOT A CONCERN IN THE RANGE OF 15 TO 25. IN ALL CASES THE HOLDING TANK IS PREFERRED.

PROBLEM 13.22 THE EQUATIONS BELOW CAN BE USED TO DETERMINE THE AW FOR EACH OF THE REQUESTED SENSITIVITIES. THE VARIABLE "DELTA" IS USED TO EXPRESS THE PROPORTION CHANGE IN THE PARAMETER OF INTEREST. INITIAL INVESTMENT AW = -$80,000(A|P 12%,7)(1+DELTA) + $15,000 + $2,500(A|F 12%,7) ANNUAL REVENUE AW = -$80,000(A|P 12%,7) + $15,000(1+DELTA) + $2,500(A|F 12%,7) SALVAGE VALUE AW = -$80,000(A|P 12%,7) + $15,000 + $2,500(A|F 12%,7)(1+DELTA) IN THE ANALYSIS REQUESTED BY THE PROBLEM STATEMENT, THE VALUES OF MARR (12%) AND LIFE (7 YEARS) ARE NOT VARIED. THEREFORE, THE TVOM FACTOR VALUES DO NOT CHANGE (A|P 12%,7) = 0.21912 (A|F 12%,7) = 0.09912 IN EACH COLUMN OF THE TABLE THE VALUES OF AW ARE PRESENTED WITH THE IDENTIFIED PARAMETER (IN THE COLUMN HEADING) MULTIPLIED BY (1+DELTA)

DELTA -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

AW FOR DELTA AW FOR DELTA INITIAL INVESTMENT ANNUAL REVENUE $6,483.00 -$9,781.80 $4,730.04 -$8,281.80 $2,977.08 -$6,781.80 $1,224.12 -$5,281.80 -$528.84 -$3,781.80 -$2,281.80 -$2,281.80 -$4,034.76 -$781.80 -$5,787.72 $718.20 -$7,540.68 $2,218.20 -$9,293.64 $3,718.20 -$11,046.60 $5,218.20

AW FOR DELTA SALVAGE VALUE -$2,405.70 -$2,380.92 -$2,356.14 -$2,331.36 -$2,306.58 -$2,281.80 -$2,257.02 -$2,232.24 -$2,207.46 -$2,182.68 -$2,157.90

NOTE: FOR VALIDATION, STUDENTS SHOULD NOTICE THAT THE DELTA=0 ROW SHOWS THE SAME VALUE FOR EACH SENSITIVITY COLUMN.

SENSITIVITY GRAPH $10,000

ANNUAL WORTH

$5,000

-60%

$0 -40%

-20% -$5,000

20%

40%

60%

INIT INV ANN REV

ANNUAL WORTH

-$5,000

ANN REV SALVAGE

-$10,000 -$15,000 PERCENT CHANGE IN PARAMETER

NOTE: ALTHOUGH ANALYSIS OF THIS GRAPH IS NOT REQUESTED IN THE PROBLEM STATEMENT, IT CAN BE SEEN THAT THIS PROJECT IS NOT ATTRACTIVE UNLESS AN ENHANCEMENT OF REVENUE OR A REDUCTION IN INITIAL COST IS ACHIEVED. NO CHANGE IN THE SALVAGE VALUE (WITHIN THE RANGE +/- 50%) WILL LEAD TO THE PROJECT BECOMING ATTRACTIVE.

PROBLEM 13.23 THE EQUATIONS BELOW CAN BE USED TO DETERMINE THE AW FOR EACH OF THE REQUESTED SENSITIVITIES. THE VARIABLE "DELTA" IS USED TO EXPRESS THE PROPORTION CHANGE IN THE PARAMETER OF INTEREST INITIAL INVESTMENT AW = -$120,000(A|P 3%,4)(1+DELTA) + $25,000 + $35,000(A|F 3%,4) ANNUAL REVENUE AW = -$120,000(A|P 3%,4) + $25,000(1+DELTA) + $35,000(A|F 3%,4) SALVAGE VALUE AW = -$120,000(A|P 3%,4) + $25,000 + $35,000(A|F 3%,4)(1+DELTA) IN THE ANALYSIS REQUESTED BY THE PROBLEM STATEMENT, THE VALUES OF MARR (3%) AND LIFE (4 YEARS) ARE NOT VARIED. THEREFORE, THE TVOM FACTOR VALUES DO NOT CHANGE (A|P 3%,4) = 0.26903 (A|F 3%,4) = 0.23903 IN EACH COLUMN OF THE TABLE THE VALUES OF AW ARE PRESENTED WITH THE IDENTIFIED PARAMETER (IN THE COLUMN HEADING) MULTIPLIED BY (1+DELTA)

DELTA -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

AW FOR DELTA AW FOR DELTA INITIAL INVESTMENT ANNUAL REVENUE $7,539.17 -$3,917.55 $5,924.99 -$2,667.55 $4,310.81 -$1,417.55 $2,696.63 -$167.55 $1,082.45 $1,082.45 -$531.73 $2,332.45 -$2,145.91 $3,582.45 -$3,760.09 $4,832.45 -$5,374.27 $6,082.45

AW FOR DELTA SALVAGE VALUE -$590.76 -$172.46 $245.85 $664.15 $1,082.45 $1,500.75 $1,919.06 $2,337.36 $2,755.66

NOTE: FOR VALIDATION, STUDENTS SHOULD NOTICE THAT THE DELTA=0 ROW SHOWS THE SAME VALUE FOR EACH SENSITIVITY COLUMN.

SENSITIVITY GRAPH $10,000

ANNUAL WORTH

$8,000

-30%

$6,000 $4,000 $2,000 -20%

$0 -10% -$2,000 0% -$4,000

INIT INV

ANN REV 10%

20%

30%

SALVAGE

ANNUAL WORTH

SALVAGE -$4,000 -$6,000 -$8,000 PERCENT CHANGE IN PARAMETER

THE ANALYSIS IS MOST SENSITIVE TO CHANGES IN INITIAL INVESTMENT SINCE THIS LINE HAS THE STEEPEST (LARGEST ABSOLUTE VALUE) SLOPE. THE ANALYSIS IS LEAST SENSITIVE TO CHANGES SALVAGE VALUE SINCE THIS LINE HAS THE FLATEST (SMALLEST ABSOLUTE VALUE) SLOPE.

PROBLEM 13.24 THE EQUATIONS BELOW CAN BE USED TO DETERMINE THE AW FOR EACH OF THE REQUESTED SENSITIVITIES. THE VARIABLE "DELTA" IS USED TO EXPRESS THE PROPORTION CHANGE IN THE PARAMETER OF INTEREST INITIAL INVESTMENT AW = -$800,000(A|P 20%,10)(1+DELTA) + $330,000 + $130,000(A|F 20%,10) ANNUAL REVENUE AW = -$800,000(A|P 20%,10) + $330,000(1+DELTA) + $130,000(A|F 20%,10) SALVAGE VALUE AW = -$800,000(A|P 20%,10) + $330,000 + $130,000(A|F 20%,10)(1+DELTA) IN THE ANALYSIS REQUESTED BY THE PROBLEM STATEMENT, THE VALUES OF MARR (20%) AND LIFE (10 YEARS) ARE NOT VARIED. THEREFORE, THE TVOM FACTOR VALUES DO NOT CHANGE (A|P 20%,10) = 0.23852 (A|F 20%,10) = 0.03852 IN EACH COLUMN OF THE TABLE THE VALUES OF AW ARE PRESENTED WITH THE IDENTIFIED PARAMETER (IN THE COLUMN HEADING) MULTIPLIED BY (1+DELTA)

DELTA -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

AW FOR DELTA AW FOR DELTA INITIAL INVESTMENT ANNUAL REVENUE $182,354.80 $78,191.60 $172,814.00 $94,691.60 $163,273.20 $111,191.60 $153,732.40 $127,691.60 $144,191.60 $144,191.60 $134,650.80 $160,691.60 $125,110.00 $177,191.60 $115,569.20 $193,691.60 $106,028.40 $210,191.60

AW FOR DELTA SALVAGE VALUE $143,190.08 $143,440.46 $143,690.84 $143,941.22 $144,191.60 $144,441.98 $144,692.36 $144,942.74 $145,193.12

NOTE: FOR VALIDATION, STUDENTS SHOULD NOTICE THAT THE DELTA=0 ROW SHOWS THE SAME VALUE FOR EACH SENSITIVITY COLUMN.

SENSITIVITY GRAPH ANNUAL WORTH

$250,000 $200,000 $150,000 $100,000 $50,000

INIT INV ANN REV SALVAGE

$50,000

SALVAGE

$0 -30%

-20%

-10%

10%

20%

30%

PERCENT CHANGE IN PARAMETER

THE ANALYSIS IS MOST SENSITIVE TO CHANGES IN ANNUAL REVENUE SINCE THIS LINE HAS THE STEEPEST (LARGEST ABSOLUTE VALUE) SLOPE. THE ANALYSIS IS LEAST SENSITIVE TO CHANGES SALVAGE VALUE SINCE THIS LINE HAS THE FLATEST (SMALLEST ABSOLUTE VALUE) SLOPE.

PROBLEM 13.25 AW = -$120,000(A|P 3%,4) + $35,000(A|F 3%,4) + $25,000 AW = -$120,000(0.26903) + $35,000(0.23903) + $25,000 AW = -$32,283.60 + $8,366.05 + $25,000.00 FOR THE PROJECT TO BE ATTRACTIVE, AW MUST BE GREATER THAN OR EQUAL TO ZERO. SO, -$32,283.60 + $8,366.05 + $25,000.00 >= 0 LET X DENOTE THE PROPORTION ERROR IN ANNUAL REVENUE LET Y DENOTE THE PROPORTION ERROR IN SALVAGE VALUE THE AW SENSITIVITY EQUATION BECOMES -$32,283.60 + $8,366.05(1+Y) + $25,000.00(1+X) >= 0 WHICH SIMPLIFIES TO Y >= -0.129 - 2.988(X) SINCE THIS IS A LINEAR FUNCTION, WE CAN DETERMINE THE LINE FOR THE PLOT WITH TWO POINTS. X -0.20 0.20

Y 0.469 -0.727

SENSITIVITY GRAPH SALVAGE VALUE ERROR

30.00% 20% ERROR REGION

20.00% UNFAVORABLE REGION

-25%

-20%

-15%

-10%

10.00%

FAVORABLE REGION

0.00% -5% 0% -10.00%

10%

-20.00% -30.00% ANNUAL REVENUE ERROR

15%

20%

25%

PROBLEM 13.26 AW = -$80,000(A|P 12%,7) + $2,500(A|F 12%,7) + $15,000 AW = -$80,000(0.21912) + $2,500(0.09912) + $15,000 AW = -$17,529.60 + $247.80 + $15,000.00 FOR THE PROJECT TO BE ATTRACTIVE, AW MUST BE GREATER THAN OR EQUAL TO ZERO. SO, -$17,529.60 + $247.80 + $15,000.00 >= 0 LET X DENOTE THE PROPORTION ERROR IN ANNUAL REVENUE LET Y DENOTE THE PROPORTION ERROR IN SALVAGE VALUE THE AW SENSITIVITY EQUATION BECOMES -$17,529.60 + $247.80(1+Y) + $15,000.00(1+X) >= 0 WHICH SIMPLIFIES TO Y >= 9.2 - 60.5(X) SINCE THIS IS A LINEAR FUNCTION, WE CAN DETERMINE THE LINE FOR THE PLOT WITH TWO POINTS. X -0.20 0.20

Y 21.300 -2.900

SENSITIVITY GRAPH 20%

SALVAGE VALUE ERROR

15% ERROR REGION

15% 10% 5%

-20%

-15%

-10%

0% -5% -5% 0%

UNFAVORABLE REGION

10%

FAVORABLE REGION

15%

20%

25%

-10% -15% -20% ANNUAL REVENUE ERROR

NOTE: THE NEAR VERTICAL LINE INDICATES THAT THE PROJECT IS ESSENTIALLY INSENSITIVE TO CHANGES IN SALVAGE VALUE. NOTE: WITHIN THE RANGE OF UNCERTAINTY FOR THE PARAMETERS, IT IS ALMOST ASSURED THAT THE PROJECT IS UNATTRACTIVE. ONLY IN THE CORNER REPRESENTED BY +15% ERROR IN BOTH PARAMETERS IS A SMALL REGION WHERE THE PROJECT BECOMES ATTRACTIVE. THIS ANALYSIS LIKELY LEADS TO A DECISION TO REJECT THE PROJECT.

PROBLEM 13.27 a

THERE WILL BE TWENTY-SEVEN AW VALUES. THE TABLE BELOW LISTS THE PARAMETER COMBINATION FOR EACH AW NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

INITIAL INVESTMENT $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00

RECEIPTS $1,750.00 $1,750.00 $1,750.00 $1,750.00 $1,750.00 $1,750.00 $1,750.00 $1,750.00 $1,750.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $3,250.00 $3,250.00 $3,250.00 $3,250.00 $3,250.00 $3,250.00 $3,250.00 $3,250.00 $3,250.00

LIFE 8 8 8 10 10 10 12 12 12 8 8 8 10 10 10 12 12 12 8 8 8 10 10 10 12 12 12

SALVAGE $250.00 $500.00 $750.00 $250.00 $500.00 $750.00 $250.00 $500.00 $750.00 $250.00 $500.00 $750.00 $250.00 $500.00 $750.00 $250.00 $500.00 $750.00 $250.00 $500.00 $750.00 $250.00 $500.00 $750.00 $250.00 $500.00 $750.00

MARR 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00%

THE SOLUTIONS BELOW USE EXCEL'S PMT FUNCTION TO CALCULATE THE AW FOR EACH COMBINATION. AW = RECEIPTS-PMT(MARR,LIFE,-INVESMENT,SALVAGE) NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

LIFE 8 8 8 10 10 10 12 12 12 8 8 8 10 10 10 12 12 12 8 8 8 10 10 10 12 12 12

MARR 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00% 15.00%

AW -$1,574.54 -$1,556.33 -$1,538.11 -$1,226.47 -$1,214.15 -$1,201.84 -$1,008.59 -$999.97 -$991.35 -$824.54 -$806.33 -$788.11 -$476.47 -$464.15 -$451.84 -$258.59 -$249.97 -$241.35 -$74.54 -$56.33 -$38.11 $273.53 $285.85 $298.16 $491.41 $500.03 $508.65

PROBLEM 13.28 THE ANALYSIS BELOW IS BASED ON A PW MEASURE OF WORTH. OTHER MEASURES COULD BE USED SINCE THE PROBLEM STATEMENT DOES NOT SPECIFY THE MEASURE TO BE USED. a

PESSIMISTIC ESTIMATES PW = -$10,500,000 + ($1,500,000 - $350,000)(P|A 20%,15) PW = -$10,500,000 + ($1,500,000 - $350,000)(4.67547) PW = -$5,123,209.50 USING PESSIMISTIC ESTIMATES, THE MOTEL IS NOT ATTRACTIVE.

MOST LIKELY ESTIMATES PW = -$8,875,000 + ($2,500,000 - $175,000)(P|A 20%,15) PW = -$8,875,000 + ($2,500,000 - $175,000)(4.67547) PW = $1,995,467.75 USING MOST LIKELY ESTIMATES, THE MOTEL IS ATTRACTIVE.

OPTIMISTIC ESTIMATES PW = -$6,000,000 + ($3,500,000 - $150,000)(P|A 20%,15) PW = -$6,000,000 + ($3,500,000 - $150,000)(4.67547) PW = $9,662,824.50 USING OPTIMISTIC ESTIMATES, THE MOTEL IS ATTRACTIVE.

EXPECTED VALUE ESTIMATES INITIAL COST = ($10,500,000 + (4)($8,875,000) + $6,000,000) / 6 = $8,666,667 OPERATING COST = ($350,000 + (4)($175,000) + $150,000) / 6 = $200,000 REVENUE = ($1,500,000 + (4)($2,500,000) + $3,500,000) / 6 = $2,500,000 PW = -$8,666,667 + ($2,500,000 - $200,000)(P|A 20%,15) PW = -$8,666,667+ ($2,500,000 - $200,000)(4.67547) PW = $2,086,914.00 USING EXPECTED VALUE ESTIMATES, THE MOTEL IS ATTRACTIVE.

PROBLEM 13.27 a

THERE WILL BE TWENTY-SEVEN PW VALUES. THE TABLE BELOW LISTS THE PARAMETER COMBINATION FOR EACH AW NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

INITIAL COST -$10,500,000.00 -$10,500,000.00 -$10,500,000.00 -$10,500,000.00 -$10,500,000.00 -$10,500,000.00 -$10,500,000.00 -$10,500,000.00 -$10,500,000.00 -$8,875,000.00 -$8,875,000.00 -$8,875,000.00 -$8,875,000.00 -$8,875,000.00 -$8,875,000.00 -$8,875,000.00 -$8,875,000.00 -$8,875,000.00 -$6,000,000.00 -$6,000,000.00 -$6,000,000.00 -$6,000,000.00 -$6,000,000.00 -$6,000,000.00 -$6,000,000.00 -$6,000,000.00 -$6,000,000.00

OPERATING -$350,000.00 -$350,000.00 -$350,000.00 -$175,000.00 -$175,000.00 -$175,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$175,000.00 -$175,000.00 -$175,000.00 -$150,000.00 -$150,000.00 -$150,000.00 -$350,000.00 -$350,000.00 -$350,000.00 -$175,000.00 -$175,000.00 -$175,000.00 -$150,000.00 -$150,000.00 -$150,000.00

REVENUE $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00 $1,500,000.00 $2,500,000.00 $3,500,000.00

PW = INITIAL INVESTMENT + (REVENUE - OPERATING)(P|A 20%,15) THE (P|A 20%,15) REMAINS CONSTANT FOR EACH CASE AT 4.67547 PW = INITIAL INVESTMENT + (REVENUE - OPERATING)(4.67547) NUMBER 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

PW -$5,123,209.50 -$447,739.50 $4,227,730.50 -$4,305,002.25 $370,467.75 $5,045,937.75 -$4,188,115.50 $487,354.50 $5,162,824.50 -$3,498,209.50 $1,177,260.50 $5,852,730.50 -$2,680,002.25 $1,995,467.75 $6,670,937.75 -$2,563,115.50 $2,112,354.50 $6,787,824.50 -$623,209.50 $4,052,260.50 $8,727,730.50 $194,997.75 $4,870,467.75 $9,545,937.75 $311,884.50 $4,987,354.50 $9,662,824.50

PROBLEM 13.30 a

ASSUMPTION OF INDEPENDENCE EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED.

EOY 0 1 2 3 4 5 6 7 8 9 10

CF -$400,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000

VAR OF CF 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000

10.00% (P|F i%,n) E(PW OF CF) 1.00000 -$400,000.00 0.90909 $72,727.27 0.82645 $66,115.70 0.75131 $60,105.18 0.68301 $54,641.08 0.62092 $49,673.71 0.56447 $45,157.91 0.51316 $41,052.65 0.46651 $37,320.59 0.42410 $33,927.81 0.38554 $30,843.46 SUMS ->

$91,565.37 SQ. ROOT ->

VAR(PW OF CF) 0.00 20,661,157.02 17,075,336.38 14,111,848.25 11,662,684.51 9,638,582.24 7,965,770.44 6,583,281.36 5,440,728.39 4,496,469.75 3,716,090.70 101,351,949.04 10,067.37

EXPECTED VALUE OF PW = $91,565 STANDARD DEVIATION OF PW = $10,067 b

ASSUMPTION OF PERFECT CORRELATION EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. STANDARD DEVIATION OF PW IS THE SUM OF THE STANDARD DEVIATIONS OF THE CASH FLOW TIMES THE DISCOUNT FACTORS.

EOY 0 1 2 3 4 5 6 7 8 9 10

CF -$400,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000 $80,000

VAR OF CF 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000

EXPECTED VALUE OF PW = $91,565 STANDARD DEVIATION OF PW = $30,723

$91,565.37

SD(PW OF CF) 0.00 4,545.45 4,132.23 3,756.57 3,415.07 3,104.61 2,822.37 2,565.79 2,332.54 2,120.49 1,927.72 $30,722.84

S OF THE CASH

PROBLEM 13.31 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED. PRIOR TO DETERMINING THE MEAN AND STANDARD DEVIATION OF PW, THE MEAN AND VARIANCE OF THE ANNUAL CONTRACT REMOVAL SERVICE MUST BE DETERMINED. # OF DAYS 20 40 60 80 100

COST PROBABILITY EXPECTED COST $10,000.00 0.15 $1,500.00 $20,000.00 0.15 $3,000.00 $30,000.00 0.35 $10,500.00 $40,000.00 0.30 $12,000.00 $50,000.00 0.05 $2,500.00 MEAN -> $29,500.00

EXPECTED ANNUAL COST OF CONTRACTING = $29,500 VARIANCE OF ANNUAL COST OF CONTRACTING = 995,00,000 - (29,500^2) = 124,750,000

NOW, DETERMINE THE MEAN AND STANDARD DEVIATION OF PW OF SAVINGS. SINCE THE NUMB SNOW DAYS PER YEAR IS INDEPENDENT (PROBLEM STATEMENT), THE SAVINGS EACH YEAR AR

EOY 0 1 2 3 4 5 6 7 8 9 10

E[CONTRACT] VAR[CONTRACT] $0 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000 $29,500 124,750,000

MACHINE $40,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000 $14,000

EXPECTED VALUE OF PW = $55,241.00 STANDARD DEVIATION OF PW = $22,488.80 b

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW OF SAVINGS>VALUE) = NORMSDIST((E(PW) - VALUE) / SD(PW)) PROB(PW>0) = NORMSDIST((55,241.00 - 0) / 22,488.80)

PROB(PW>0) =

0.993

THE PROBABILITY OF POSITIVE SAVINGS FROM PURCHASING THE SNOW BLOWER IS 0.993 OR 99.3%. c

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3 4 5 6 7 8 9 10

CF PURCHASE -40000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000

CF CONTRACT 0 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500

ESTIMATE OF MEAN = $55,240.79 ESTIMATE OF STANDARD DEVIATION = $22,302.26 PROBABILITY OF PW OF SAVINGS > 0 = 0.991 OR 99.1%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3 4 5 6 7 8 9 10

CF PURCHASE -40000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000 -14000

CF CONTRACT 0 #NAME? =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500 =-RiskDiscrete({20,40,60,80,100},{0.15,0.15,0.35,0.30,0.05})*500

ESTIMATE OF MEAN = $55,337.90 ESTIMATE OF STANDARD DEVIATION = $22,317.03 PROBABILITY OF PW OF SAVINGS > 0 = 0.992 OR 99.2%

AND LATIN HYPERCUBE ER DUE TO THE RIBUTIONS. SSION OF EXAMPLES

D CASH FLOWS. ASH FLOWS TIMES

VIATION OF PW, THE MEAN SERVICE MUST BE DETERMINED. EXP. SQUARE COST 15,000,000.00 60,000,000.00 315,000,000.00 480,000,000.00 125,000,000.00 995,000,000.00

0,000 - (29,500^2) = 124,750,000

ON OF PW OF SAVINGS. SINCE THE NUMBER OF ATEMENT), THE SAVINGS EACH YEAR ARE INDEPENDENT. 10.00% E[SAVINGS] (P|F i%,n) -$40,000 1.00000 $15,500 0.90909 $15,500 0.82645 $15,500 0.75131 $15,500 0.68301 $15,500 0.62092 $15,500 0.56447 $15,500 0.51316 $15,500 0.46651 $15,500 0.42410 $15,500 0.38554

PW OF SAVINGS -$40,000 $14,091 $12,810 $11,645 $10,587 $9,624 $8,749 $7,954 $7,231 $6,574 $5,976

VAR OF PW OF SAVINGS 103,099,173.55 85,205,928.56 70,418,122.77 58,196,795.68 48,096,525.36 39,749,194.51 32,850,573.97 27,149,234.69 22,437,384.04 18,543,292.60

SUMS ->

$55,241 SQ. ROOT ->

505,746,225.73 22,488.80

E THE PROBABILITY OF

VALUE) / SD(PW))

ASING THE SNOW

IONS NECESSARY

HYPERCUBE, SEED=987654321

CONTRACT 0 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500

SAVINGS =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =CONTRACT-PURCHASE =RiskOutput("PW(10%)")+NPV(10%,EOY1:EOY10)+EOY0

IONS NECESSARY CARLO, SEED=987654321

CONTRACT 0 #NAME? 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500 0,100},{0.15,0.15,0.35,0.30,0.05})*500

PROBLEM 13.32 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED.

EOY 0 1 2 3 4 5

E[CF] -$19,700,000 $1,200,000 $3,600,000 $6,000,000 $9,600,000 $11,000,000

SD[CF] 120,000 240,000 650,000 750,000 1,080,000

VAR[CF] 14,400,000,000 57,600,000,000 422,500,000,000 562,500,000,000 1,166,400,000,000

EXPECTED VALUE OF PW = -$1,031,532 STANDARD DEVIATION OF PW = $835,870 b

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3 4 5

CF -19700000 =RiskNormal(1200000,120000) =RiskNormal(3600000,240000) =RiskNormal(6000000,650000) =RiskNormal(9600000,750000) =RiskNormal(11000000,1080000) =RiskOutput("NPV(15%)")+NPV(0.15,EOY1:EOY5)+EOY0

ESTIMATE OF MEAN = -$1,031,539 ESTIMATE OF STANDARD DEVIATION = $828,138 PROBABILITY OF PW > 0 = 0.107 0R 10.7%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3 4 5

ESTIMATE OF MEAN = -$,1032,209 ESTIMATE OF STANDARD DEVIATION = $827,269 PROBABILITY OF PW > 0 = 0.107 OR 10.7%

AND LATIN HYPERCUBE DIFFER DUE TO THE RIBUTIONS. SSION OF EXAMPLES

D CASH FLOWS. ASH FLOWS TIMES

15.00% (P|F i%,n) 1.00000 0.86957 0.75614 0.65752 0.57175 0.49718 SUMS ->

E THE PROBABILITY OF

VALUE) / SD(PW))

IONS NECESSARY

HYPERCUBE, SEED=987654321

PW OF VAR OF PW SAVINGS OF SAVINGS -$19,700,000 $1,043,478 10,888,468,809 $2,722,117 32,932,986,946 $3,945,097 182,658,409,273 $5,488,831 183,882,247,788 $5,468,944 288,316,241,221 -$1,031,532 SQ. ROOT ->

698,678,354,037 835,870

PROBLEM 13.33 a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED.

EOY 0 1 2 3 4 5 6 7 8

CF -$22,500 $6,250 $6,250 $6,250 $6,250 $6,250 $6,250 $6,250 $6,250

15.00% (P|F i%,n) 1.00000 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690

PW OF CF -$22,500.00 $5,434.78 $4,725.90 $4,109.48 $3,573.46 $3,107.35 $2,702.05 $2,349.61 $2,043.14

PW OF LIFE

-$4,656.39 -$1,549.03 $1,153.02 $3,502.62 $5,545.76

PROBABILITY THAT PW > 0 IS THE SUM OF THE PROBABILITIES FOR LIVES WITH PW > 0 = 0.45 + 0.15 + 0.05 = 0.65 OR 65%

PROBABILITY THAT PW > 1,000 IS THE SUM OF THE PROBABILITIES FOR LIVES WITH PW > 1,000 = 0.45 + 0.15 + 0.05 = 0.65 OR 65%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 LIFE EOY 0 1 2 3 4 5 6 7 8

=RiskDiscrete({4,5,6,7,8},{0.1,0.25,0.45,0.15,0.05}) CF -22500 6250 6250 6250 6250 6250 6250 6250 6250

CF|LIFE =C32 =C33 =C34 =C35 =C36 =IF(B37<=C$29,C37,0) =IF(B38<=C$29,C38,0) =IF(B39<=C$29,C39,0) =IF(B40<=C$29,C40,0) =RiskOutput("PW(LIFE)")+NPV(15%,EOY1:EOY8)+EOY0

PROBABILITY OF PW > 0 = 0.65 OR 65%

PROB OF LIFE

0.10 0.25 0.45 0.15 0.05

IVES WITH PW > 0

OR LIVES WITH PW > 1,000

SEED=987654321

EOY8)+EOY0

PROBLEM 13.34 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

CASH FLOWS ARE EXPRESSED AS COSTS (I.E., POSITIVE VALUES REPRESENT COST NOT REVEN ALTERNATIVE A WILL BE PREFERRED IF PW(COSTS A) < PW(COSTS B) OR IF PW(COSTS A-B) < 0 VARIANCE = (STANDARD DEVIATION)^2 SALVAGE VALUE IS TREATED AS A NEGATIVE CASH FLOWS SINCE CASH FLOWS ARE EXPRESSE AS COSTS. EXPECTED VALUE OF A DIFFERENCE IS THE DIFFERENCE OF THE EXPECTED VALUES. VARIANCE OF A DIFFERENCE IS THE SUM OF VARIANCES. EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED,

EOY 0 1 2 3 4 5 6 7 8

E[CF A] $13,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $3,000

VAR[CF A]

E[CF B]

0 250,000 250,000 250,000 250,000 250,000 250,000 250,000 890,000

$0 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500 $7,500

VAR[CF B] 0 562,500 562,500 562,500 562,500 562,500 562,500 562,500 562,500

E[A-B] $13,000 -$2,500 -$2,500 -$2,500 -$2,500 -$2,500 -$2,500 -$2,500 -$4,500

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW OF A-B<VALUE) = 1 - NORMSDIST((E(PW A-B) - VALUE) / SD(PW A-B)) PROB(PW OF A-B<0) = 1 - NORMSDIST((1,128 - 0) / 1522.68) PROB(PW A-B<0) = 0.229 THE PROBABILITY THAT A IS THE PREFERRED ALTERNATIVE IS 0.229 OR 22.9%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2

ALT A =13000 =RiskNormal(5000,500) =RiskNormal(5000,500)

B =RiskNormal(7500,750) =RiskNormal(7500,750)

3 4 5 6 7 8

=RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500)-RiskNormal(2000,800)

=RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750)

THE PROBABILITY THAT A IS THE PREFERRED ALTERNATIVE IS 0.234 OR 23.4%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3 4 5 6 7 8

ALT A =13000 =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500) =RiskNormal(5000,500)-RiskNormal(2000,800)

B =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750) =RiskNormal(7500,750)

THE PROBABILITY THAT A IS THE PREFERRED ALTERNATIVE IS 0.232 OR 23.2%

RESENT COST NOT REVENUE) OR IF PW(COSTS A-B) < 0

SH FLOWS ARE EXPRESSED

ECTED VALUES.

VAR[A-B] 0 812,500 812,500 812,500 812,500 812,500 812,500 812,500 1,452,500

15.00% (P|F i%,n) 1.00000 0.86957 0.75614 0.65752 0.57175 0.49718 0.43233 0.37594 0.32690 SUMS ->

E[PW A-B] VAR[PW A-B] $13,000 0 -$2,174 614,367 -$1,890 464,550 -$1,644 351,266 -$1,429 265,608 -$1,243 200,838 -$1,081 151,862 -$940 114,830 -$1,471 155,221 $1,128 SQ. ROOT ->

2,318,540 1,523

EED=987654321 B

RiskNormal(7500,750) RiskNormal(7500,750)

A-B =C46-D46 =C47-D47 =C48-D48

RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750)

RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750) RiskNormal(7500,750)

=C49-D49 =C50-D50 =C51-D51 =C52-D52 =C53-D53 =C54-D54 =RiskOutput("PW(COST A-B)")+NPV(0.15,EOY1:EOY8)+EOY0

A-B =C46-D46 =C47-D47 =C48-D48 =C49-D49 =C50-D50 =C51-D51 =C52-D52 =C53-D53 =C54-D54 =RiskOutput("PW(COST A-B)")+NPV(0.15,EOY1:EOY8)+EOY0

PROBLEM 13.35 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED. EXPECTED VALUE OF A UNIFORMLY DISTRIBUTED RANDOM VARIABLE = (MIN + MAX)/2 EXPECTED VALUE = ($60,000 + $70,000)/2 = $65,000 VARIANCE OF A UNIFORMLY DISTRIBUTED RANDOM VARIABLE = ((MAX - MIN)^2)/12 VARIANCE = (($70,000 - $60,000)^2)/12 = 8,333,333

EOY 0 1 2 3 4 5 6

E[CF] -$263,000 $65,000 $65,000 $65,000 $65,000 $65,000 $65,000

VAR[CF] 0 8,333,333 8,333,333 8,333,333 8,333,333 8,333,333 8,333,333

12.00% (P|F i%,n) E[PW OF CF] 1.00000 -$263,000 0.89286 $58,036 0.79719 $51,818 0.71178 $46,266 0.63552 $41,309 0.56743 $36,883 0.50663 $32,931 SUMS ->

$4,241 SQ. ROOT ->

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW>VALUE) = NORMSDIST((E(PW) - VALUE) / SD(PW)) PROB(PW>0) = NORMSDIST((4241 - 0) / 4934) PROB(PW>0) = 0.805 THE PROBABILITY THAT PW IS GREATER THAN ZERO IS 0.805 OR 80.5%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3 4 5 6

CF -263000 =RiskUniform(60000,70000) =RiskUniform(60000,70000) =RiskUniform(60000,70000) =RiskUniform(60000,70000) =RiskUniform(60000,70000) =RiskUniform(60000,70000) =RiskOutput("NPV(12)")+NPV(0.12,EOY1:EOY6)+EOY0

THE PROBABILITY THAT PW > 0 IS 0.796 OR 79.6%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3 4 5 6

THE PROBABILITY THAT PW > 0 IS 0.797 OR 79.7%

AND LATIN HYPERCUBE FFER DUE TO THE

SION OF EXAMPLES

CASH FLOWS. SH FLOWS TIMES

OM VARIABLE = (MIN + MAX)/2

IABLE = ((MAX - MIN)^2)/12

VAR[PW OF CF] 0 6,643,282 5,295,984 4,221,926 3,365,693 2,683,110 2,138,959 24,348,954 4,934 THE PROBABILITY OF

0.805 OR 80.5%

ONS NECESSARY

YPERCUBE, SEED=987654321

PROBLEM 13.36 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED.

EOY 0 1 2 3 4 5 6 7 8 9 10

E[CF] -$10,000 $1,800 $1,800 $1,800 $1,800 $1,800 $1,800 $1,800 $1,800 $1,800 $1,800

VAR[CF] 1,000,000 40,000 40,000 40,000 40,000 40,000 40,000 40,000 40,000 40,000 40,000

12.00% (P|F i%,n) E[PW OF CF] 1.00000 -$10,000 0.89286 $1,607 0.79719 $1,435 0.71178 $1,281 0.63552 $1,144 0.56743 $1,021 0.50663 $912 0.45235 $814 0.40388 $727 0.36061 $649 0.32197 $580 SUMS ->

$170 SQ. ROOT ->

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW>VALUE) = NORMSDIST((E(PW) - VALUE) / SD(PW)) PROB(PW<0) = 1 - NORMSDIST((170 - 0) / 1068) PROB(PW<0) = 0.437 THE PROBABILITY THAT PW IS LESS THAN ZERO IS 0.437 OR 43.7%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3 4 5 6 7 8

9 10

=RiskNormal(1800,200) =RiskNormal(1800,200) =RiskOutput("NPV(12)")+NPV(0.12,EOY1:EOY10)+EOY0

THE PROBABILITY THAT PW < 0 IS 0.440 OR 44.0%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3 4 5 6 7 8 9 10

CF =RiskNormal(-10000,1000) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskNormal(1800,200) =RiskOutput("NPV(12)")+NPV(0.12,EOY1:EOY10)+EOY0

THE PROBABILITY THAT PW < 0 IS 0.437 OR 43.7%

AND LATIN HYPERCUBE FFER DUE TO THE

SION OF EXAMPLES

CASH FLOWS. SH FLOWS TIMES

VAR[PW OF CF] 1,000,000 31,888 25,421 20,265 16,155 12,879 10,267 8,185 6,525 5,202 4,147 1,140,933 1,068 THE PROBABILITY OF

ONS NECESSARY

YPERCUBE, SEED=987654321

PROBLEM 13.37 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED. THE EXPECTED VALUES AND VARIANCES FOR EACH YEAR'S RETURNS ARE SHOWN BELOW EXPECTED CASH FLOW = SUM OF (OUTCOME * PROBABILITY) VARIANCE OF CASH FLOW = E[CF^2] - E[CF]^2 EOY 1 2 3

E[CF] $2,080 $2,500 $3,200

VAR[CF] 117,600 250,000 210,000

EOY 0 1 2 3

E[CF] -$5,000 $2,080 $2,500 $3,200

VAR[CF] 0 117,600 250,000 210,000

15.00% (P|F i%,n) E[PW OF CF] 1.00000 -$5,000 0.86957 $1,809 0.75614 $1,890 0.65752 $2,104 SUMS ->

$803 SQ. ROOT ->

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW>VALUE) = NORMSDIST((E(PW) - VALUE) / SD(PW)) PROB(PW<0) = 1 - NORMSDIST((803 - 0) / 568) PROB(PW<0) = 0.079 THE PROBABILITY THAT PW IS LESS THAN ZERO IS 0.079 OR 7.9%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3

CF -5000 =RiskDiscrete({2500,1800},{0.4,0.6}) =RiskDiscrete({3000,2000},{0.5,0.5}) =RiskDiscrete({3500,2500},{0.7,0.3}) =RiskOutput("NPV(15%)")+NPV(15%,EOY1:EOY3)+EOY0

THE PROBABILITY THAT PW < 0 IS 0.087 OR 8.7%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3

CF -5000 =RiskDiscrete({2500,1800},{0.4,0.6}) =RiskDiscrete({3000,2000},{0.5,0.5}) =RiskDiscrete({3500,2500},{0.7,0.3}) =RiskOutput("NPV(15%)")+NPV(15%,EOY1:EOY3)+EOY0

THE PROBABILITY THAT PW < 0 IS 0.086 OR 8.6%

AND LATIN HYPERCUBE FFER DUE TO THE

SION OF EXAMPLES

CASH FLOWS. SH FLOWS TIMES

R'S RETURNS ARE SHOWN BELOW

VAR[PW OF CF] 0 88,922 142,938 90,789 322,650 568 THE PROBABILITY OF

ONS NECESSARY

YPERCUBE, SEED=987654321

PROBLEM 13.38 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED.

EOY 0 1 2

E[CF] -$800,000 $1,000,000 $1,000,000

VAR[CF] 62,500,000,000 202,500,000,000 360,000,000,000

15.00% (P|F i%,n) E[PW OF CF] 1.00000 -$800,000 0.86957 $869,565 0.75614 $756,144 SUMS ->

$825,709 SQ. ROOT ->

MEAN OF PW = $825,709 STANDARD DEVIATION OF PW = $649,192 b

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW>VALUE) = NORMSDIST((E(PW) - VALUE) / SD(PW)) PROB(PW<0) = 1 - NORMSDIST((825709 - 0) / 649192) PROB(PW<0) = 0.102 THE PROBABILITY THAT PW IS LESS THAN ZERO IS 0.102 OR 10.2%

PROB(PW>1,000,000) = NORMSDIST((825709 - 1000000) / 649192) PROB(PW>1000000) = 0.394 THE PROBABILITY THAT PW IS GREATER THAN $1,000,000 IS 0.394 OR 39.4%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2

=RiskNormal(-800000,250000) =RiskNormal(1000000,450000) =RiskNormal(1000000,600000) =RiskOutput("NPV(15)")+NPV(0.15,EOY1:EOY2)+EOY0

THE PROBABILITY THAT PW < 0 IS 0.101 OR 10.1%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY EOY 0 1 2

CF =RiskNormal(-800000,250000) =RiskNormal(1000000,450000) =RiskNormal(1000000,600000) =RiskOutput("NPV(15)")+NPV(0.15,EOY1:EOY2)+EOY0

THE PROBABILITY THAT PW < 0 IS 0.104 OR 10.4%

ATIN HYPERCUBE DUE TO THE

OF EXAMPLES

LOWS TIMES

VAR[PW OF CF] 62,500,000,000 153,119,092,628 205,831,168,413 421,450,261,041 649,192

PROBABILITY OF

0.394 OR 39.4%

NECESSARY

CUBE, SEED=987654321

PROBLEM 13.39 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED.

EOY 0 1 2 3 4 5

E[CF] -$32,000 $4,000 $8,000 $12,000 $12,000 $12,000

VAR[CF] 1,000,000 4,000,000 9,000,000 25,000,000 36,000,000 49,000,000

18.00% (P|F i%,n) E[PW OF CF] 1.00000 -$32,000 0.84746 $3,390 0.71818 $5,745 0.60863 $7,304 0.51579 $6,189 0.43711 $5,245 SUMS ->

-$4,126 SQ. ROOT ->

MEAN OF PW = -$4,126 STANDARD DEVIATION OF PW = $6,059 b

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW>VALUE) = NORMSDIST((E(PW) - VALUE) / SD(PW)) PROB(PW<0) = 1 - NORMSDIST((-4126 - 0) / 6059) PROB(PW<0) = 0.752 THE PROBABILITY THAT PW IS LESS THAN ZERO IS 0.752 OR 75.2%

PROB(PW>5,000) = NORMSDIST((-4126 - 5000) / 6059) PROB(PW>1000000) = 0.066 THE PROBABILITY THAT PW IS GREATER THAN $5,000 IS 0.066 OR 6.6%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3 4 5

CF =RiskNormal(-32000,1000) =RiskNormal(4000,2000) =RiskNormal(8000,3000) =RiskNormal(12000,5000) =RiskNormal(12000,6000) =RiskNormal(12000,7000) =RiskOutput("NPV(18)")+NPV(0.18,EOY1:EOY5)+EOY0

THE PROBABILITY THAT PW > $5,000 IS 0.064 OR 6.4%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3 4 5

CF =RiskNormal(-32000,1000) =RiskNormal(4000,2000) =RiskNormal(8000,3000) =RiskNormal(12000,5000) =RiskNormal(12000,6000) =RiskNormal(12000,7000) =RiskOutput("NPV(18)")+NPV(0.18,EOY1:EOY5)+EOY0

THE PROBABILITY THAT PW > $5,000 IS 0.064 OR 6.4%

ATIN HYPERCUBE DUE TO THE

OF EXAMPLES

LOWS TIMES

VAR[PW OF CF] 1,000,000 2,872,738 4,642,100 9,260,788 9,577,374 9,362,159 36,715,159 6,059

PROBABILITY OF

NECESSARY

CUBE, SEED=987654321

PROBLEM 13.40 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED VALUE OF A DIFFERENCE (REVENUE - EXPENSE) IS THE DIFFERENCE OF EXPECTED VARIANCE OF A DIFFERENCE (REVENUE - EXPENSE) IS THE SUM OF VARIANCES. EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCE OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED.

EOY 0 1 2 3

E[REV]

VAR[REV]

$0 $24,000 $24,000 $24,000

0 16,000,000 16,000,000 16,000,000

E[COST] $5,000 $20,000 $20,000 $20,000

VAR[COST] 0 9,000,000 9,000,000 9,000,000

E[CF] -$5,000 $4,000 $4,000 $4,000

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW OF CF<VALUE) = 1 - NORMSDIST((E(PW CF) - VALUE) / SD(PW CF)) PROB(PW OF CF<0) = 1 - NORMSDIST((3426 - 0) / 6147) PROB(PW A-B<0) = 0.289 THE PROBABILITY THAT THE IMPROVEMENT RESULTS IN A LOSS IS 0.289 OR 28.9%

EXCEL'S NORMSDIST FUNCTION IS USED TO DETERMINE THE PROBABILITY OF THE PW EXCEED A VALUE OF INTEREST. PROB(PW OF CF>VALUE) = NORMSDIST((E(PW CF) - VALUE) / SD(PW CF)) PROB(PW OF CF>$10,000) = 1 - NORMSDIST((3426 - 10000) / 6147) PROB(PW CF>$10,000) = 0.142

THE PROBABILITY THAT THE IMPROVEMENT RESULTS IN A PW GREATER THAN $10,000 IS 0.14.2

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3

REV =RiskNormal(24000,4000) =RiskNormal(24000,4000) =RiskNormal(24000,4000)

EXP 6000 =RiskNormal(20000,3000) =RiskNormal(20000,3000) =RiskNormal(20000,3000)

CF =REV-EXP =REV-EXP =REV-EXP =REV-EXP

=RiskOutput("PW(CF)")+NPV(

THE PROBABILITY THAT THE PW IS GREATER THAN $10,000 IS 0.141 OR 14.1%

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, MONTE CARLO, SEED=987654321 EOY 0 1 2 3

REV =RiskNormal(24000,4000) =RiskNormal(24000,4000) =RiskNormal(24000,4000)

EXP 6000 =RiskNormal(20000,3000) =RiskNormal(20000,3000) =RiskNormal(20000,3000)

CF =REV-EXP =REV-EXP =REV-EXP =REV-EXP =RiskOutput("PW(CF)")+NPV(

THE PROBABILITY THAT THE PW IS GREATER THAN $10,000 IS 0.141 OR 14.1%

FFERENCE OF EXPECTED VALUES.

VAR[CF] 0 25,000,000 25,000,000 25,000,000

20.00% (P|F i%,n) 1.00000 0.83333 0.69444 0.57870 SUMS ->

289 OR 28.9%

TER THAN $10,000 IS 0.14.2 OR 14.2%

EED=987654321

E[PW CF] -$5,000 $3,333 $2,778 $2,315

VAR[PW CF]

$3,426 SQ. ROOT ->

37,789,888 6,147

0 17,361,111 12,056,327 8,372,449

PROBLEM 13.41 a

THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATION SIMULATION PARAMETERS: 10,000 ITERATIONS, LATIN HYPERCUBE, SEED=987654321 EOY 0 1 2 3 4 5 6 7 8 9 10

ALT 1 =RiskNormal(-750000,15000) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500)+RiskNormal(125000,2500) =RiskOutput("PW(ALT1)")+NPV(0.12,EOY1:EOY10)+EOY0

E[PW ALT1] = -$285,987 SD[PW ALT1] = $15,279

E[PW ALT1] = -$285,991 SD[PW ALT1] = $152,809

PROBABILITY THAT ALTERNATIVE 1 IS PREFERRED OVER ALTERNATIVE 2 IS P[PW(ALT1) - PW(ALT2)] > 0 THIS CAN BE ACCOMPLISHED BY ADDING THE FOLLOWING COLUMN TO THE CALCULATIONS ABOVE EOY 0 1 2 3 4 5 6 7 8 9 10

ALT =RiskNormal(-750000,15000) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500) =RiskNormal(75000,1500)+RiskNormal(125000,2500) =RiskOutput("PW(ALT1-ALT2")+NPV(0.12,EOY1:EOY10)+EOY0

THE PROBABILITY THAT ALTERNATIVE 1 IS PREFERRED OVER ALTERNATIVE 2 IS 0.502 OR 50.2%

ED=987654321 ALT2 =RiskNormal(-750000,150000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000) =RiskNormal(75000,15000)+RiskNormal(125000,25000) =RiskOutput("PW(ALT2)")+NPV(0.12,EOY1:EOY10)+EOY0

=RiskOutput("PW(CF)")+NPV(0.20,EOY1:EOY

PROBLEM 13.42 NOTE: FOR PROBLEMS SHOWING BOTH MONTE CARLO AND LATIN HYPERCUBE SIMULATION RESULTS, THE RESULTS WILL LIKELY TO DIFFER DUE TO THE DIFFERENCES IN THE SAMPLING FROM THE INPUT DISTRIBUTIONS. THESE DIFFERENCES ARE HIGHLIGHTED IN THE DISCUSSION OF EXAMPLES 13.20 AND 13.21 IN THE TEXT. a

EXPECTED PW IS THE DISCOUNTED SUM OF EXPECTED CASH FLOWS. VARIANCE OF PW IS THE SUM OF THE VARIANCES OF CASH FLOWS TIMES THE DISCOUNT FACTORS SQUARED. PRIOR TO DETERMINING THE MEAN OF PW, THE MEAN OF THE ANNUAL RETURN MUST BE DETERMINED. RETURN $500.00 $2,000.00 $4,500.00 $6,000.00 $9,000.00

PROBABILITY 0.05 0.15 0.25 0.35 0.20 MEAN ->

E[RETURN] $25.00 $300.00 $1,125.00 $2,100.00 $1,800.00 $5,350.00

EXPECTED ANNUAL RETURN = $5,350 NOW, DETERMINE THE EXPECTED PW.

EOY 0 1 2 3 4 5 6

E[RETURN] -$19,000 $5,350 $5,350 $5,350 $5,350 $5,350 $5,350

20.00% (P|F i%,n) 1.00000 0.83333 0.69444 0.57870 0.48225 0.40188 0.33490

PW(CF) -$19,000 $4,458 $3,715 $3,096 $2,580 $2,150 $1,792 -$1,209

EXPECTED VALUE OF PW = -$1,209 ALTERNATE SOLUTION USING E[RETURN] AND FACTOR TALBES PW = -$19,000 + $5,350(P|A 20%,6) PW = -$19,000 + $5,350(3.32551) PW = -$1,208.52 THE FOLLOWING TABLE SHOWS THE DATA AND FUNCTIONS NECESSARY TO RUN THE @RISK SIMULATIONS IN PARTS b, c, d, AND e SIMULATION PARAMETER USED IN ALL PARTS: SEED=987654321 EOY 0

ALT 1 -19000

1 2 3 4 5 6

=RiskDiscrete({500,2000,4500,6000,9000},{0.05,0.15,0.25,0.35,0.2}) =RiskDiscrete({500,2000,4500,6000,9000},{0.05,0.15,0.25,0.35,0.2}) =RiskDiscrete({500,2000,4500,6000,9000},{0.05,0.15,0.25,0.35,0.2}) =RiskDiscrete({500,2000,4500,6000,9000},{0.05,0.15,0.25,0.35,0.2}) =RiskDiscrete({500,2000,4500,6000,9000},{0.05,0.15,0.25,0.35,0.2}) =RiskDiscrete({500,2000,4500,6000,9000},{0.05,0.15,0.25,0.35,0.2}) =RiskOutput("PW(20%)")+NPV(20%,C42:C47)+C41

ADDITIONAL SIMULATION PARAMETERS: 25 ITERATIONS, LATIN HYPERCUBE

EXPECTED PW = -$1,273.56 PROBABILITY PW < 0 = 0.560 c

ADDITIONAL SIMULATION PARAMETERS: 100,000 ITERATIONS, LATIN HYPERCUBE

EXPECTED PW = -$1,208.52 PROBABILITY PW < 0 = 0.631

ADDITIONAL SIMULATION PARAMETERS: 25 ITERATIONS, MONTE CARLO

EXPECTED PW = -$1,304.40 PROBABILITY PW < 0 = 0.640

ADDITIONAL SIMULATION PARAMETERS: 100,000 ITERATIONS, MONTE CARLO

EXPECTED PW = -$1,211.07 PROBABILITY PW < 0 = 0.632

NOTE: ALTHOUGH IT IS NOT PART OF THE PROBLEM STATEMENT, STUDENTS SHOULD NOTE HO CLOSER THE SIMULATION ESTIMATES FROM THE LONGER RUN LENGTHS ARE TO THE ANALYTIC SOLUTION AS APPOSED TO THE SHORTER RUN LENGTHS. NOTE: STUDENTS SHOULD ALSO NOTE THE IMPACT THAT THE NUMBER OF ITERATIONS HAS ON THE DISTRIBUTION OF PW VALUES.

PROBLEM 13.43 a 0.4

PREFER PW=$3,500

LIGHT

$2,375

LEASE 0.6

HEAVY

$4,250

DECISION 0.4

PW=$3,600

$3,000

BUY 0.6

LIGHT

HEAVY

$4,000

DECISION CALCULATONS

LEASE LEASE

LIGHT HEAVY TOTAL

BUY

LIGHT HEAVY TOTAL

PROB 0.4 0.6

EUAC $2,375 $4,250

0.4 0.6

$3,000 $4,000

SINCE E(LEASE) < E(BUY), LEASE IS PREFERRED

E(EUAC) $950 $2,550 $3,500 <- E(LEASE) $1,200 $2,400 $3,600 <- E(BUY)

PROBLEM 13.44 a

PREFER PW=$312

0.25

OUTCOME 1

PW = -$9,000+$3,500(P|A 20%,6) $2,639

0.40

OUTCOME 2

PW = -$9,000+$3,000(P|A 20%,6) $977

0.25

OUTCOME 3

PW = -$9,000+$2,300(P|A 20%,6) -$1,351

0.10

OUTCOME 4

PW = -$9,000+$1,500(P|A 20%,6) -$4,012

BUY

DECISION

PW=$0

DON'T BUY

PROB 0.25 0.40 0.25 0.10

PW $2,639 $977 -$1,351 -$4,012

1.00

DECISION CALCULATONS BUY OUTCOME #1 OUTCOME #2 OUTCOME #3 OUTCOME #4 TOTAL DON'T BUY

E(PW) $659.75 $390.80 -$337.75 -$401.20 $311.60 <- E(BUY) $0.00 <- E(DON'T BUY)

SINCE E(BUY) > E(DON'T BUY), BUYING THE COMPRESSOR IS PREFERRED

PROBLEM 13.45 a 0.25

PW=$28,050

FULL

0.60

STRONG

AVERAGE

PW = $78,000

PW = $28,000

DECISION 0.15

0.25

PREFER PW=$30,450

PARTIAL

0.60

0.15

0.25

PW=$0

NONE

0.60

0.15

WEAK

STRONG

AVERAGE

WEAK

STRONG

AVERAGE

WEAK

PW = -$55,000

PW = $51,000

PW = $32,000

PW = -$10,000

PW = $0

DECISION CALCULATONS FULL STRONG AVERAGE WEAK TOTAL PARTIAL STRONG AVERAGE

PROB 0.25 0.60 0.15

PW $78,000 $28,000 -$55,000

E(PW) $19,500.00 $16,800.00 -$8,250.00 $28,050.00 <- E(FULL)

PROB 0.25 0.60

PW $51,000 $32,000

E(PW) $12,750.00 $19,200.00

WEAK TOTAL NONE STRONG AVERAGE WEAK TOTAL

0.15

-$10,000

-$1,500.00 $30,450.00 <- E(FULL)

PROB 0.25 0.60 0.15

E(PW) $0.00 $0.00 $0.00 $0.00 <- E(FULL)

$0 $0 $0

SINCE E(PARTIAL) IS HIGHEST, PARTIAL IMPLEMENTATION IS PREFERRED

PROBLEM 13.46 a PREFER PW=-$223K

AUTOMATIC

PW = -$100,000 - $20,000(P|A 10%,10) PW = -$222,891.34

DECISION PW=-$237K PW=-$232K

MANUAL

PW = -$40,000 - $28,000(P|A PW =

MANAUL PREFER PW=-$232K

SEMI AUTOMATIC

PW = -$40,000 - $28,000(P|A PW =

DECISION CALCULATONS FOR PW ARE SHOWN AT THE END OF EACH BRANCH PW(AUTOMATIC) = -$222,891 PW(MANUAL+MANUAL) = -$236,885 PW(MANUAL+SEMIAUTOMATIC) = -$232,177 AUTOMATIC HAS THE HIGHEST PW AND IS THEREFORE PREFERRED.

PW = -$40,000 - $28,000(P|A 10%,5) + (-$40,000 - $28,000(P|A 10%,5))(P|F 10%,5) -$236,884.73

PW = -$40,000 - $28,000(P|A 10%,5) + (-$80,000 - $22,000(P|A 10%,5) + $40,000(P|F 10%,5))(P|F 10%,5) -$232,177.17

ACH BRANCH

PROBLEM 13.47 a 0.50

PW=$58,000

STOCK

0.30

HIGH

MEDIUM

DECISION 0.20

PW=$0.00

PREFER PW=$73,190

DON'T STOCK

LOW

PW = $0

0.61

POPULARITY UP DECISION

0.39

POPULARITY DOWN DECISION

SURVEY

DETERMINATION OF POSTERIOR PROBABILITIES

GIVEN SURVEY SHOWS POPULARITY WILL GO UP POPULARITY HIGH MEDIUM LOW

P(POP) 0.50 0.30 0.20

P(UP|POP) 0.90 0.40 0.20 SUM ->

JOINT P 0.45 0.12 0.04 0.61

GIVEN SURVEY SHOWS POPULARITY WILL GO DOWN POPULARITY HIGH MEDIUM LOW

P(POP) 0.50 0.30 0.20

P(DWN|POP) 0.10 0.60 0.80 SUM ->

P(POP) 0.738 0.197 0.066

PW(POP) $200,000 -$40,000 -$150,000 SUM ->

JOINT P 0.05 0.18 0.16 0.39

DECISION ANALYSIS POPULARITY UP DECISION STOCK POPULARITY HIGH MEDIUM LOW

E[PW] $147,600 -$7,880 -$9,900 $129,820

DON'T STOCK PW = $0 IF SURVEY SHOWS POPULARITY IS UP, STOCK IS PREFERRED POPULARITY DOWN DECISION STOCK POPULARITY HIGH MEDIUM LOW

P(POP) 0.128 0.462 0.410

PW(POP) $200,000 -$40,000 -$150,000 SUM ->

E[PW] $25,600 -$18,480 -$61,500 -$54,380

DON'T STOCK PW = $0 IF SURVEY SHOWS POPULARITY IS DOWN, DON'T STOCK IS PREFERRED

PRIMARY DECISION STOCK

POPULARITY UP DOWN LOW

P(POP) 0.500 0.300 0.200

PW(POP) $200,000 -$40,000 -$150,000 SUM ->

E[PW] $100,000 -$12,000 -$30,000 $58,000

PW(POP) $129,820 $0

E[PW]

DON'T STOCK PW = $0 SURVEY POPULARITY UP DOWN SURVEY FEE

P(POP) 0.610 0.390

SUM ->

$79,190 $0 -$6,000 $73,190

PW = $200,000

PW = -$40,000

PW = -$150,000

0.738

PREFER PW=$129,820

STOCK

0.197

0.066

PW=$0

DON'T STOCK

STOCK

0.462

0.410

PREFER PW=$0

DON'T STOCK

MEDIUM

LOW

PW = $200,000

PW = -$40,000

PW = -$150,000

PW = $0

0.128

PW=-$54,380

HIGH

PW = $0

HIGH

MEDIUM

LOW

PW = $200,000

PW = -$40,000

PW = -$150,000

P(POP|UP) 0.738 0.197 0.066

P(POP|DWN) 0.128 0.462 0.410

<- E(STOCK)

K IS PREFERRED

<- E(STOCK)

<- E(SURVEY)

PROBLEM 13.48 a 0.60

PREFER PW=$10.30

0.10

HIGH

MEDIUM

PW = $15

PW = $10

DECISION 0.30

0.30

PW=$10.00

0.50

0.20

0.4

PW=$9.90

LOW

HIGH

MEDIUM

LOW

NO OPTION

PW = $1

PW = $20

PW = $10

PW = -$5

PW = $12

PREFER PW=$8.50 0.6

OPTION DECISION

PW=$8.00 b

DECISION ANALYSIS OPTION DECISION OPTION 1, PW = (0.5)($7) + (0.5)($10) PW = $8.50 OPTION 2, PW = 8.00 PREFER OPTION 1

PRIMARY DECISION - A BRANCH PW = $15(0.6) + $10(0.1) + $1(0.3) PW = $10.30 PRIMARY DECISION - B BRANCH PW = $20(0.3) + $10(0.5) - $5(0.2) PW = $10.00 PRIMARY DECISION - C BRANCH PW = $12(0.4) + $8.50(0.6) PW = $9.90 PRIMARY DECISION: PREFER A

0.5

HIGH

PW = $7

OPTION 1

0.5

OPTION 2

PW = $8

LOW

PW = $10

MODIFIED ACRS RATES - GDS MACRS CL ADR %

3-YR <=4 200%

5-YR 7-YR 10-YR 15-YR >4 to <10 >=10 to <16 .=16 to <20 >=20 to <25 200% 200% 200% 150%

20-YR >=25 150%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

33.33% 44.45% 14.81% 7.41%

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

14.29% 24.49% 17.49% 12.49% 8.93% 8.92% 8.93% 4.46%

10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28%

5.00% 9.50% 8.55% 7.70% 6.93% 6.23% 5.90% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91% 5.90% 5.91% 2.95%

3.750% 7.219% 6.677% 6.177% 5.713% 5.285% 4.888% 4.522% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 2.231%

SUM

100.00% 100.00%

100.00%

100.000%

PROBLEM 14.1 PROJECT: WIDENING OF TWO SEPARATE MILES OF STREETS IN STILLWATER, OK MAIN THRUST: COMPLETELY REMOVE, WIDEN, IMPROVE ACCESS TO, AND REPAVE STREETS GOING FROM 2- TO 4-LANE. BENEFITS TO: LOCAL RESIDENTS DUE TO EASIER ACCESS, SHORTER TRANSIT TIMES, SAFER CONDITIONS, IMPROVED HOME VALUES LOCAL RESIDENTS MAY ALSO HAVE SOME NEGATIVE BENEFITS DUE TO LOSS OF YARD AND RELOCATION OF UTILITIES. OTHER RESIDENTS OF STILLWATER WHO NOW USE THOSE STREETS AS "CUTTHROUGHS" DUE TO THEIR EASE OF USE PRIVATE AND PUBLIC SERVICE PROVIDERS SUCH AS DELIVERY PEOPLE, REFUSE PERSONNEL, ETC. PAYERS: STATE OF OKLAHOMA INITIALLY FUNDED MOST OF THE IMPROVEMENT CITY OF STILLWATER PAID SOME INITIALLY AND WILL MAINTAIN IN FUTURE ULTIMATELY, TAXPAYERS ARE THE SOURCE OF THE MONEY FEE OR CHARGE: NO FEES OR CHARGES (UNLIKE ACCESS FEES FOR PUBLIC LAKE USE, TURNPIKE CHARGES, ETC.) PLANNING HORIZON: UNKNOWN BEST GUESS IS 30 YEARS

PROBLEM 14.2

THE PHU MY COMPLEX IN VIETNAM HAS 5 GASFIRED ELECTRICAL GENERATION PLANTS; THESE ARE MORE RELIABLE THAN HYDROELECTRIC PLANTS DUE TO DROUGHTS. GROUPS INVOLVED INCLUDE IDA, THE MULTILATERAL INVESTMENT GUARANTEE AGENCY (MIGA), FRENCH AND SINGAPOREAN INVESTORS, PM3, AND THE VIETNAMESE GOVT. THE LOCATION IS ABOUT 45 MILES SE OF HCMC, THE OLD SAIGON.

RESULTS INCLUDE INCREASED ELECTRICITY AND MORE STEADY POWER, EMPLOYMENT GENERATION, TAX REVENUES, AND SOCIETAL HELP TO LE LOI SCHOOL WITH BOOKS, COMPUTERS, BATHROOMS, SCHOLARSHIPS, AND HEALTH CHECKS, PLUS ADDITIONAL TRAINING AND JOBS TO SOME ENGINEERS.

HERE ARE MORE PARTICIPANTS.

PROBLEM 14.3 ONE SET

ANOTHER SET

PROBLEM 14.4 a

MONUMENT MEMORIALIZING A PARTICULARLY UNFORTUNATE EVENT BENEFIT: HONOR THOSE THAT WERE LOST, IF ANY. REMINDER TO FAMILY, FRIENDS, AND KINDRED SPIRITS WHO WANT A PLACE TO GRIEVE OR PLACE REMEMBRANCES DISBENEFIT: SEEN BY SOME AS A WASTE OF TAXPAYER MONEY AND A CONSTANT AND COSTLY REMINDER OF SOMETHING BAD

A PUBLIC LIBRARY BENEFIT: HELPFUL TO A WIDE RANGE OF USERS OF ALL AGES, PROVIDING ARCHIVAL MATERIALS, SEARCH EXPERTISE, ELECTRONIC RESEARCH CAPABILITIES, MEETING ROOMS, ETC. DISBENEFIT: MAY NOT BE SUITABLE FOR THE NEEDS OF MANY CITIZENS WHO HELPED PAY FOR IT, CONSIDERING RESOURCES, LOCATION, TRANSPORTATION, ETC.

A WEB SITE GIVING INFORMATION ON A REGION'S PUBLIC RECREATION AND EDUCATION ACTIVITIES BENEFIT: USEFUL TO MANY WHO TAKE ADVANTAGE OF CITY HAPPENINGS THAT ARE EDUCATIONAL, RECREATIONAL, PROMOTIONAL; THIS INCLUDES LOCALS AND VISITORS DISBENEFIT: MAY NOT BE SUITED TO THE INTERESTS AND NEEDS OF MANY; LIKELY ONLY A SMALL MINORITY OF USERS; OFTEN NOT WELL MAINTAINED

A PUBLIC PARK WITH PLAYGROUND BENEFIT: KIDS OF ALL AGES GO FOR FUN, PICNICS, RIDES, EXERCISE, GROUP ACTIVITIES DISBENEFIT: OFTEN NOT SAFE FOR CHILDREN ALONE; REQUIRES UPKEEP AND MAINTENANCE; MAY ATTRACT WRONG ELEMENT

RENOVATION OF PUBLIC ACCESS AREAS AT PUBLIC RECREATIONAL LAKE BENEFIT: MUCH EASIER TO LAUNCH ALL WATERCRAFT SAFELY; USABLE DURING MORE OF THE YEAR; IMPROVED PARKING DISBENEFIT: HIGHER AND / OR NEW USER CHARGE PUT IN PLACE; MORE USERS PLACES MORE TRAFFIC ON LAKE

PROBLEM 14.5 A NEW ELECTRICAL DISTRIBUTION SYSTEM ….. BENEFIT: MORE RELIABLE POWER AVAILABILITY DISBENEFIT: UNSIGHTLY AND, AT TIMES, ELECTRICALLY NOISY (STATIC DUE TO ARCING) MONETARY COSTS: COST TO CONSTRUCT, INCLUDING STATION ITSELF, RIGHT-OF-WAY; TRANSMISSION LINES; MAINTENANCE ANNEXATION OF AN ADJOINING SEMI-RURAL AREA IN THE CITY BENEFIT: PROVISION OF CITY SERVICES TO NEW AREA DISBENEFIT: SOME DO NOT WANT TO JOIN THE CITY, MEET CITY CODES, AND ANSWER TO A NEW LEVEL OF BUREAUCRACY MONETARY COSTS: COST TO PURCHASE WATER, ELECTRICAL, SEWER SYSTEMS BY THE CITY; COST TO MAINTAIN OR PROVIDE SERVICES REPLACEMENT OF OLD SCHOOL BUSES BENEFIT: SAFER AND MORE RELIABLE FOR KIDS AND DRIVERS DISBENEFIT: HAVING TO FOREGO OTHER SCHOOL NEEDS SUCH AS ACADEMIC SUPPLIES MONETARY COSTS: COST TO PURCHASE, RETRAIN DRIVERS, UPDATE MAINTENANCE FACILITIES RENOVATION OF REST STOPS ….. BENEFIT: PLACE TO USE THE RESTROOM, HAVE A PICNIC, WAKE UP, REDUCE FATIGUE, EXERCISE PET DISBENEFIT: MAY REQUIRE TAKING OF LAND TO BUILD; CHANGING STOPPING AND SHOPPING PATTERNS OF DRIVERS MONETARY COSTS: COST TO DESIGN, PURCHASE LAND, CONSTRUCT, PROVIDE UTILITIES, MAINTAIN NEW STADIUM / COLISEUM FOR SPORTING EVENTS BENEFIT: ENJOYED BY MANY FANS; ATTRACTS VISITORS; ATTRACTS TEAMS, PLAYERS, ETC.; AURA OF BEING A "MODERN" CITY DISBENEFIT: TRAFFIC SNARLS; MAY ATTRACT WRONG ELEMENT; CRIME MONETARY COSTS: COST TO DESIGN, PURCHASE LAND, CONSTRUCT, PROVIDE UTILITIES, MAINTAIN

PROBLEM 14.6 PROPOSAL #1 BENEFITS $K/YR COSTS $K/YEAR $1,800 $1,470

PROPOSAL #2 BENEFITS $K/YR $1,260 ELIMINATE IMMEDIATELY B<C

INCREMENT ΔB ΔC ΔB/ΔC #2 IS OUT

B-C

$330

B-C

PROPOSAL #3 BENEFITS $K/YR COSTS $K/YEAR $1,590 $1,050

COSTS $K/YEAR $1,300

INCREMENT ΔB ΔC ΔB/ΔC

-$40

#1-#3 $210 $420 0.50 #3 BEATS #1 #3 WINS B-C

$540 #3 WINS

PROPOSAL #4 BENEFITS $K/YR $2,000

INCREMENT ΔB ΔC ΔB/ΔC

B-C

PROPOSAL #5 BENEFITS $K/YR COSTS $K/YEAR $1,550 $1,160

COSTS $K/YEAR $1,800

#4-#3 $410 $750 0.55 #3 BEATS #4

$200

INCREMENT ΔB ΔC ΔB/ΔC

#5-#3 -$40 $110 -0.36 #3 BEATS #5

B-C

$390

PROBLEM 14.7 FIRST COST $25,000.00 SALVAGE VALUE $5,000.00 SERVICE LIFE 10 ANNUAL MAINT COST $500.00 ANNUAL BENEFIT $7,000.00 INTEREST RATE 6.00% EOY 0 1 2 3 4 5 6 7 8 9 10

BENEFIT

PW B/C

$51,520.61 $25,888.07 1.99 DESIRABLE PROJECT

$7,000.00 $7,000.00 $7,000.00 $7,000.00 $7,000.00 $7,000.00 $7,000.00 $7,000.00 $7,000.00 $7,000.00

COST $25,000.00 $500.00 $500.00 $500.00 $500.00 $500.00 $500.00 $500.00 $500.00 $500.00 -$4,500.00

PROBLEM 14.8 INTEREST VISITORS 1ST YEAR INCR IN VISITORS BENEFIT PER VISIT EOY 0 1 2 3 4 5 6 7 8 9 10

7.00% FIRST COST 100,000 ANN COST 30,000 SALVAGE $0.80 VISITORS

BEN/VISIT

100,000 130,000 160,000 190,000 220,000 250,000 280,000 310,000 340,000 370,000

$0.80 $0.80 $0.80 $0.80 $0.80 $0.80 $0.80 $0.80 $0.80 $0.80 PW B/C B-C

$325,000.00 $80,000.00 $60,000.00

BENEFIT $80,000.00 $104,000.00 $128,000.00 $152,000.00 $176,000.00 $200,000.00 $224,000.00 $248,000.00 $272,000.00 $296,000.00

COST $325,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $20,000.00

$1,227,059.76 $856,385.57 1.432835645 YES, SUPPORT $370,674.20 YES, SUPPORT

PROBLEM 14.9 ANNUAL BENEFIT PER MAN= COST TO REMOVE STONE= NUMBER OF STONES= NUMBER OF MEN= LIFE SPAN= INTEREST RATE= MANAGEMENT CHARGE PAID PER PERSON= a

INDIVIDUAL ANALYSIS WORKING ALONE EOY BENEFIT COST 0 $100.00 1 $6.00 $0.00 2 $6.00 $0.00 3 $6.00 $0.00 4 $6.00 $0.00 5 $6.00 $0.00 6 $6.00 $0.00 7 $6.00 $0.00 8 $6.00 $0.00 9 $6.00 $0.00 10 $6.00 $0.00 PW B/C

$53.90 0.54

$100.00

INDIVIDUAL ANALYSIS WORKING COLLECTIVELY EOY BENEFIT 0 1 $6.00 2 $6.00 3 $6.00 4 $6.00 5 $6.00 6 $6.00 7 $6.00 8 $6.00 9 $6.00 10 $6.00

COST $10.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

PW B/C

$10.00

$53.90 5.39

INDIVIDUAL ANALYSIS WORKING COLLECTIVELY PLUS MANAGER EOY BENEFIT COST 0 $26.95 1 $6.00 $0.00 2 $6.00 $0.00 3 $6.00 $0.00

6 1 100 10 10 2.00% $16.95

GOAL SEEK CHANGED CELL

4 5 6 7 8 9 10

$6.00 $6.00 $6.00 $6.00 $6.00 $6.00 $6.00

PW B/C

$53.90 2.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $26.95 GOAL SEEK SET CELL

USED GOAL SEEK TO SET B/C= TOTAL MANAGEMENT CHARGE =

2.00 10*$16.95=

$169.50

PROBLEM 14.10 a

INTEREST PLANNING HORIZON INITIAL RENOVATION COST INITIAL NEW EQUIPMENT COST INITIAL E-ACCESS COST SALVAGE % MAINTENANCE/YR E-VOLUME RENEWAL/YR ADDITIONAL VISITS FIRST YR INCREMENTAL VISITS/YR INCREMENTAL BENEFIT/VISIT

8.00% 10 $33,000.00 $21,000.00 $17,500.00 30.00% $3,500.00 $4,000.00 2,500 500 $2.00

EOY 0 1 2 3 4 5 6 7 8 9 10

INCR VISITS

INCR BENEFITS $5,000.00 $6,000.00 $7,000.00 $8,000.00 $9,000.00 $10,000.00 $11,000.00 $12,000.00 $13,000.00 $14,000.00

COSTS $71,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 -$2,400.00

$59,527.24

$117,239.99

B-C

-$57,712.76 DO NOT APPROVE

EOY 0 1 2 3 4 5 6 7 8 9

2,500 3,000 3,500 4,000 4,500 5,000 5,500 6,000 6,500 7,000

8.00% 10 $33,000.00 $21,000.00 $17,500.00 30.00% $3,500.00 $4,000.00 2500 500 $3.94 <--SOLVER CHANGED CELL

INCR VISITS 2500 3000 3500 4000 4500 5000 5500 6000 6500

INCR BENEFITS $9,847.59 $11,817.11 $13,786.63 $15,756.15 $17,725.67 $19,695.18 $21,664.70 $23,634.22 $25,603.74

COSTS $71,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00 $7,500.00

10 PW= B-C=

7000

$27,573.26

-$2,400.00

$117,239.99

$0.00 <--SOLVER TARGET CELL MINIMUM BENEFIT/VISIT=

$3.94

GET CELL

PROBLEM 14.11 INITIAL COST PHYS FACIL NEW SPECIES FIRST YEAR ANNUAL COST PERCENT INCREASE EACH YR SALVAGE % FACIL SALVAGE VALUE FACIL INTEREST PLANNING HORIZON

$1,800,000.00 $310,000.00 $145,000.00 3.00% 40.00% $720,000.00 7.00% 20

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

COST $2,110,000.00 $145,000.00 $149,350.00 $153,830.50 $158,445.42 $163,198.78 $168,094.74 $173,137.58 $178,331.71 $183,681.66 $189,192.11 $194,867.88 $200,713.91 $206,735.33 $212,937.39 $219,325.51 $225,905.28 $232,682.43 $239,662.91 $246,852.79 -$465,741.62

PW AW

$3,857,029.51 $364,076.30

ATTENDEES/YR NEEDED BENEFIT/ATTENDEE

1,500,000 $0.2427

PROBLEM 14.12 OVERNIGHT BENEFITS PER FAMILY= NUMBER OF NIGHTS PER FAMILY= NUMBER OF FAMILIES PER SEASON=

$12.00 8 250

BENEFITS PER DAY FOR DAY-USERS= NUMBER OF DAY USERS PER SEASON=

$4.00 2,200

TOTAL BENEFITS PER YEAR=

$32,800.00

ANNUAL COST OF FACILITY=

$30,000.00

B/C=

1.09

B-C=

$2,800.00

PROBLEM 14.13 DN A B C BENEFITS $0.00 $200,000.00 $300,000.00 $400,000.00 DISBENEFITS $0.00 $37,000.00 $69,000.00 $102,000.00 NET BENEFITS $0.00 $163,000.00 $231,000.00 $298,000.00 COSTS SAVINGS NET COSTS

$0.00 $150,000.00 $234,000.00 $312,000.00 $0.00 $15,000.00 $31,000.00 $42,000.00 $0.00 $135,000.00 $203,000.00 $270,000.00

B/C

1.21

1.14

1.10

INCREMENT ΔB/ΔC

A-DN 1.21

B-A 1.00

C-B 1.00

B-C

$0.00

$28,000.00

A, B, AND C ARE EQUALLY DESIRABLE

$28,000.00 A, B, AND C ARE EQUALLY DESIRABLE

PROBLEM 14.14 INTEREST RATE PLAN HORIZON SALVAGE % ROUTE A FIRST COST SALVAGE ANNUAL COST BENEFITS

7.00% 15 50.00% ROUTE B FIRST COST SALVAGE ANNUAL COST BENEFITS

$4,000,000.00 $2,000,000.00 $210,000.00 $500,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

NET BENEFITS

PW B-C

$4,553,957.00 -$633,812.90

$500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00 $500,000.00

NET COST $4,000,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 $210,000.00 -$1,790,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

$5,187,769.90

PW B-C

ROUTE C FIRST COST SALVAGE ANNUAL COST BENEFITS

$6,000,000.00 $3,000,000.00 $180,000.00 $850,000.00

NET BENEFITS

$9,000,000.00 $4,500,000.00 $260,000.00 $1,000,000.00

NET COST $6,000,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 $180,000.00 -$2,820,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

NET BENEFITS

$7,741,726.90 $6,552,086.46 $1,189,640.44 CONSTRUCT B

PW B-C

$9,107,914.01 -$629,136.55

$850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00 $850,000.00

$1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00 $1,000,000.00

NET COST $9,000,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 $260,000.00 -$4,240,000.00 $9,737,050.55

PROBLEM 14.15

BENEFITS DISBENEFITS COSTS SAVINGS

OPTION 1 OPTION 2 OPTION 3 $400,000 $550,000 $575,000 $78,000 $125,000 $180,000 $235,000 $390,000 $480,000 $25,000 $65,000 $90,000

NET BENEFITS NET COSTS B/C

$322,000 $210,000 1.53

$425,000 $325,000 1.31

$395,000 $390,000 1.01

CANNOT TELL FROM B/C WHICH IS BEST b

INCREMENT ΔB ΔC ΔB/ΔC

OPT 2-OPT 1 OPT 3-OPT 1 $103,000 $73,000 $115,000 $180,000 0.90 0.41

SELECT OPTION 1 SINCE ΔB/ΔC <1 FOR OPTIONS 2 AND 3 c

B-C

$112,000

$100,000

$5,000

SELECT OPTION 1 d BENEFITS DISBENEFITS COSTS SAVINGS

OPTION 1 OPTION 2 $400,000 $550,000 $78,000 $125,000 $235,000 $378,000 <--SOLVER CHANGED CELL $25,000 $65,000

NET BENEFITS NET COSTS B/C

$322,000 $210,000 1.53

INCREMENT ΔB ΔC ΔB/ΔC B-C

$425,000 $313,000 1.36 OPT 2-OPT 1 $103,000 $103,000 1.00 <--SOLVER TARGET CELL

$112,000

$112,000 $378,000 COSTS OPTION 2

PROBLEM 14.16 MARR STUDY PERIOD INITIAL COST SALVAGE % ANNUAL COST USER COST

7.00% 20 N $2,400,000.00 20.00% $155,000.00 $625,000.00

N (NORTH) EOY

COST

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$2,400,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 $155,000.00 -$325,000.00

$625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00

$3,918,031.09

$6,621,258.90

PW a

INCREMENT ΔBENEFIT PW ΔCOST PW ΔB/ΔC SA IS WINNER

B-C

-$10,539,289.99

SA IS WINNER c

MARR STUDY PERIOD

0.00% 20

SA SB $4,200,000.00 $5,200,000.00 20.00% 20.00% $88,000.00 $125,000.00 $410,000.00 $310,000.00

USER COST (DISBENEFIT)

SA (SOUTH A) EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

INITIAL COST SALVAGE % ANNUAL COST USER COST

N $2,400,000.00 20.00% $155,000.00 $625,000.00

N (NORTH) EOY

COST

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

SA SB $4,200,000.00 $5,200,000.00 20.00% 20.00% $88,000.00 $125,000.00 $410,000.00 $310,000.00

USER COST (DISBENEFIT) $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00 $625,000.00

$5,020,000.00 $12,500,000.00 INCREMENT ΔBENEFIT PW ΔCOST PW ΔB/ΔC

B-C

SB IS WINNER

-$17,520,000.00

SA (SOUTH A) EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

COST $4,200,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 $88,000.00 -$752,000.00

USER COST (DISBENEFIT) $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00 $410,000.00

SB (SOUTH B) EOY

COST

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$5,200,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 $125,000.00 -$915,000.00

USER COST (DISBENEFIT) $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00 $310,000.00

$4,915,201.29 $4,343,545.84

$6,255,496.02 $3,284,144.42

SA-N $2,277,713.06 $997,170.20 2.28 SA WINS

SB-SA $1,059,401.42 $1,340,294.73 0.79 SA WINS

-$9,258,747.13 SA WINS

-$9,539,640.43

SB (SOUTH B) EOY

COST

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$5,120,000.00 $8,200,000.00

$6,660,000.00 $6,200,000.00

SA-N $4,300,000.00 $100,000.00 43.00 SA WINS

SB-SA $2,000,000.00 $1,540,000.00 1.30 SB WINS

-$13,320,000.00

-$12,860,000.00 SB WINS

PROBLEM 14.17

FIRST COST SALVAGE MAINTENANCE COST BENEFITS (RELATIVE TO EAST) SERVICE LIFE INTEREST RATE

EAST $3,500,000.00 $0.00 $120,000.00 $0.00

WEST $5,000,000.00 $0.00 $90,000.00 $220,000.00

20 7.00% EOY

INCREMENT FOR WEST-EAST BENEFITS

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00 $220,000.00

$2,330,683.13

SEE ABOVE

INCREMENT ΔB/ΔC B-C

WEST-EAST 1.97 $1,148,503.56

INCREMENTAL WEST OVER EAST $1,500,000.00 $0.00 -$30,000.00 $220,000.00

COSTS $1,500,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 -$30,000.00 $1,182,179.57

WEST PREFERRED

PROBLEM 14.18 VEHICLES AFFECTED PER DAY PRIVATE VEHICLES PER DAY COMMERCIAL VEHICLES PER DAY DAYS PER YEAR EXTRA START-STOPS PER VEHICLE PER DAY COST OF START-STOP PER VEHICLE EXTRA WAITING PER VEHICLE PER DAY COST OF WAITING PER HOUR - PRIVATE COST OF WAITING PER HOUR - COMMERCIAL PERCENTAGE OF AFFECTED VEHICLES PERCENTAGE REDUCTION IN START-STOPS AND WAITING

12,000 9,000 3,000 300 3 $0.03 2 $18.00 $45.00 10.00% 90.00%

BENEFITS DUE TO START-STOP REDUCTION PER YEAR BENEFITS DUE TO WAITING REDUCTION PER YEAR

$29,160.00 $267,300.00

TOTAL BENEFITS PER YEAR INTEREST RATE PLANNING HORIZON

$296,460.00 7.00% 10

ALLOWABLE INITIAL COST OF PROJECT

$2,082,210.98

MINUTES

PROBLEM 14.19 INTEREST PLANNING HORIZON

7.00% 20

FUEL

YEAR #1

COAL (TONS) FUEL OIL (BARRELS) LOW-SULPHUR FUEL OIL (BARRELS) NATURAL GAS (CUBIC FEET) COAL EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a.

PRESENT WORTH ANNUAL WORTH

BETWEEN WHICH ΔB ΔC ΔB/ΔC

B-C

770,000 3,005,000

GRADIENT EACH YEAR THEREAFTER 38,500 150,250

$41.00 $71.00

2,800,000

140,000

$102.00

16,800,000,000

840,000,000

$0.0080

USAGE

DISBENEFIT

COST

770,000 808,500 847,000 885,500 924,000 962,500 1,001,000 1,039,500 1,078,000 1,116,500 1,155,000 1,193,500 1,232,000 1,270,500 1,309,000 1,347,500 1,386,000 1,424,500 1,463,000 1,501,500

$107,669,100.00 $113,052,555.00 $118,436,010.00 $123,819,465.00 $129,202,920.00 $134,586,375.00 $139,969,830.00 $145,353,285.00 $150,736,740.00 $156,120,195.00 $161,503,650.00 $166,887,105.00 $172,270,560.00 $177,654,015.00 $183,037,470.00 $188,420,925.00 $193,804,380.00 $199,187,835.00 $204,571,290.00 $209,954,745.00

$48,818,000.00 $51,258,900.00 $53,699,800.00 $56,140,700.00 $58,581,600.00 $61,022,500.00 $63,463,400.00 $65,904,300.00 $68,345,200.00 $70,786,100.00 $73,227,000.00 $75,667,900.00 $78,108,800.00 $80,549,700.00 $82,990,600.00 $85,431,500.00 $87,872,400.00 $90,313,300.00 $92,754,200.00 $95,195,100.00

$1,557,914,514.98 $147,056,109.13

$706,370,451.62 $66,676,373.59

-$2,264,284,966.59

COST

TRANSPORTATION AND STORAGE $22.40 $4.20

HEALTH

CROPS

UNCLEANLINESS

$27.86 $2.25

$70.05 $5.70

$41.92 $3.45

$4.20

$0.69

$1.68

$1.02

$0.0005

$0.0000002

$0.0000004

USAGE

DISBENEFIT

COST

3,005,000 3,155,250 3,305,500 3,455,750 3,606,000 3,756,250 3,906,500 4,056,750 4,207,000 4,357,250 4,507,500 4,657,750 4,808,000 4,958,250 5,108,500 5,258,750 5,409,000 5,559,250 5,709,500 5,859,750

$34,257,000.00 $35,969,850.00 $37,682,700.00 $39,395,550.00 $41,108,400.00 $42,821,250.00 $44,534,100.00 $46,246,950.00 $47,959,800.00 $49,672,650.00 $51,385,500.00 $53,098,350.00 $54,811,200.00 $56,524,050.00 $58,236,900.00 $59,949,750.00 $61,662,600.00 $63,375,450.00 $65,088,300.00 $66,801,150.00

$225,976,000.00 $237,274,800.00 $248,573,600.00 $259,872,400.00 $271,171,200.00 $282,470,000.00 $293,768,800.00 $305,067,600.00 $316,366,400.00 $327,665,200.00 $338,964,000.00 $350,262,800.00 $361,561,600.00 $372,860,400.00 $384,159,200.00 $395,458,000.00 $406,756,800.00 $418,055,600.00 $429,354,400.00 $440,653,200.00

$495,680,539.17 $46,788,736.33

$3,269,752,328.54 $308,641,488.75

FUEL OIL EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

FUEL OIL -COAL $100,267,372.80 $241,965,115.16 0.414 COAL WINS -$3,765,432,867.70

LS FUEL OIL EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

USAGE

DISBENEFIT

COST

2,800,000 2,940,000 3,080,000 3,220,000 3,360,000 3,500,000 3,640,000 3,780,000 3,920,000 4,060,000 4,200,000 4,340,000 4,480,000 4,620,000 4,760,000 4,900,000 5,040,000 5,180,000 5,320,000 5,460,000

$9,492,000.00 $9,966,600.00 $10,441,200.00 $10,915,800.00 $11,390,400.00 $11,865,000.00 $12,339,600.00 $12,814,200.00 $13,288,800.00 $13,763,400.00 $14,238,000.00 $14,712,600.00 $15,187,200.00 $15,661,800.00 $16,136,400.00 $16,611,000.00 $17,085,600.00 $17,560,200.00 $18,034,800.00 $18,509,400.00

$297,360,000.00 $312,228,000.00 $327,096,000.00 $341,964,000.00 $356,832,000.00 $371,700,000.00 $386,568,000.00 $401,436,000.00 $416,304,000.00 $431,172,000.00 $446,040,000.00 $460,908,000.00 $475,776,000.00 $490,644,000.00 $505,512,000.00 $520,380,000.00 $535,248,000.00 $550,116,000.00 $564,984,000.00 $579,852,000.00

$137,344,183.02 $12,964,319.27

$4,302,640,777.84 $406,138,851.44

LS FUEL OIL-COAL $134,091,789.86 $339,462,477.86 0.395 COAL WINS -$4,439,984,960.86

NATURAL GAS EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

USAGE

DISBENEFIT

COST

16,800,000,000 17,640,000,000 18,480,000,000 19,320,000,000 20,160,000,000 21,000,000,000 21,840,000,000 22,680,000,000 23,520,000,000 24,360,000,000 25,200,000,000 26,040,000,000 26,880,000,000 27,720,000,000 28,560,000,000 29,400,000,000 30,240,000,000 31,080,000,000 31,920,000,000 32,760,000,000

$16,800.00 $17,640.00 $18,480.00 $19,320.00 $20,160.00 $21,000.00 $21,840.00 $22,680.00 $23,520.00 $24,360.00 $25,200.00 $26,040.00 $26,880.00 $27,720.00 $28,560.00 $29,400.00 $30,240.00 $31,080.00 $31,920.00 $32,760.00

$142,800,000.00 $149,940,000.00 $157,080,000.00 $164,220,000.00 $171,360,000.00 $178,500,000.00 $185,640,000.00 $192,780,000.00 $199,920,000.00 $207,060,000.00 $214,200,000.00 $221,340,000.00 $228,480,000.00 $235,620,000.00 $242,760,000.00 $249,900,000.00 $257,040,000.00 $264,180,000.00 $271,320,000.00 $278,460,000.00

$243,087.05 $22,945.70

$2,066,239,921.56 $195,038,431.48

NAT GAS-COAL $147,033,163.43 $128,362,057.90 1.145 NATURAL GAS WINS -$2,066,483,008.61 NATURAL GAS WINS

PROBLEM 14.20 INTEREST STUDY PERIOD

7.00% 20 EXISTING STEEL CONCRETE BRIDGE BRIDGE INITIAL COST $0.00 $300,000.00 MAINT/YEAR $12,000.00 $2,500.00 BEAM REPL @0 $115,000.00 $0.00 RESURFACING @0 $30,000.00 $0.00 RESURFACING @10 $30,000.00 $0.00 RESURFACING @15 $0.00 $30,000.00 SALVAGE $0.00 $200,000.00

EXISTING STEEL BRIDGE

COST

CONCRETE BRIDGE

COST

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$145,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $42,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00 $12,000.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$300,000.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 $32,500.00 $2,500.00 $2,500.00 $2,500.00 $2,500.00 -$197,500.00

PW AW

$287,378.65 $27,126.51

$285,674.62 $26,965.66

STEEL BRIDGE STEEL BRIDGE IS A SUNK COST. THERE IS NO RELEVANCE OF THE "YEARLY COST OF BRIDGE" C MAINTENANCE CALCULATION DOES NOT CONSIDER TIME VALUE OF MONEY (TVM) ALSO, THERE IS AN EXTRA $30,000 IN THERE AS IF RESURFACING WOULD OCCUR IN YEAR 20. EVEN IF THE INTEREST RATE WERE 0.0%, THE TIMING HAS PROBLEMS. THE REPLACEMENT OF BEAMS DUE TO RUST IS NOT CONSIDERED. CONCRETE BRIDGE

THE COST OF THE BRIDGE IS BEING PRORATED OVER 60 YEARS, WELL BEYOND THE PLANNING THERE IS NO TVM IN THE ANALYSIS. ANNUAL MAINTENANCE IS FINE; HOWEVER THERE IS ONLY ONE RESURFACING DURING THE PLA NO SALVAGE VALUE (RESIDUAL WORTH) WAS CONSIDERED.

UNFORTUNATELY, THIS IS PRETTY TYPICAL OF HOW MANY LAY PERSONS DO AN ECONOMIC AN b

A PROPER ANALYSIS IS SHOWN ABOVE. NOTE THAT THE TWO OPTIONS ARE ESSENTIALLY EQU THE CONCRETE BRIDGE IS SLIGHTLY BETTER

PROBLEM 14.21 a

THE FIRST (B/C=2.72) B/C RATIO TAKES A "LOCAL" POINT OF VIEW AND DETERMINES THE B/C RATIO WITHOUT CO OF EITHER (1) ALL SOURCES OF MONEY, AND (2) BENEFITS OR COSTS OF THE RURAL WATER ADDITION.

THE SECOND (B/C=2.37) B/C RATIO STILL TAKES A "LOCAL" POINT OF VIEW AND DETERMINES THE B/C RATIO WITH CONSIDERATION OF (1) ALL SOURCES OF MONEY, AND (2) BENEFITS OF THE RURAL WATER ADDITION, IF ANY. A BETTER B/C RATIO WOULD BE B/C=($4,250,000 + $450,000)/($5,750,000+$260,000)=0.78 THIS EXPLICITLY ACCOUNTS FOR THE FACT THAT TAXPAYERS ARE FUNDING THE FEDERAL CONTRIBUTION AND CONSIDERS THE COST AND BENEFITS OF THE SMALL RURAL WATER SYSTEM.

/C RATIO WITHOUT CONSIDERATION

PROBLEM 14.22 a

INTEREST RATE=

0.00%

END OF YEAR 0 1 2 3

A B C -$10,000.00 -$15,000.00 -$18,000.00 $5,000.00 $7,000.00 $8,000.00 $5,000.00 $7,000.00 $8,000.00 $5,000.00 $7,000.00 $8,000.00

PWB PWC

$15,000.00 $21,000.00 $24,000.00 $10,000.00 $15,000.00 $18,000.00

INCR CONSIDERED ΔB ΔC ΔB/ΔC WINNER

A-DN $15,000.00 $10,000.00 1.50 A

B-A $6,000.00 $5,000.00 1.20 B

C-B $3,000.00 $3,000.00 1.00 B OR C

EITHER B OR C IS PREFERRED

INTEREST RATE=

7.00%

END OF YEAR 0 1 2 3

A B C -$10,000.00 -$15,000.00 -$18,000.00 $5,000.00 $7,000.00 $8,000.00 $5,000.00 $7,000.00 $8,000.00 $5,000.00 $7,000.00 $8,000.00

PWB PWC

$13,121.58 $18,370.21 $20,994.53 $10,000.00 $15,000.00 $18,000.00

INCR CONSIDERED ΔB ΔC ΔB/ΔC WINNER

A-DN $13,121.58 $10,000.00 1.31 A

B-A $5,248.63 $5,000.00 1.05 B

C-B $2,624.32 $3,000.00 0.87 B

B IS PREFERRED

INTEREST RATE=

14.00%

END OF YEAR 0 1 2 3

A B C -$10,000.00 -$15,000.00 -$18,000.00 $5,000.00 $7,000.00 $8,000.00 $5,000.00 $7,000.00 $8,000.00 $5,000.00 $7,000.00 $8,000.00

PWB PWC

$11,608.16 $16,251.42 $18,573.06 $10,000.00 $15,000.00 $18,000.00

INCR CONSIDERED ΔB

A-DN $11,608.16

B-A $4,643.26

C-B $2,321.63

ΔC ΔB/ΔC WINNER A IS PREFERRED

$10,000.00 1.16 A

$5,000.00 0.93 A

$3,000.00 0.77 A

PROBLEM 14.23 PROJECT EDUCATION HEALTH WELFARE

PW BENEFITS $1,200,000.00 $280,000.00 $300,000.00

PW COSTS $1,000,000.00 $200,000.00 $150,000.00

Δ(EDUCATION-HEALTH) Δ(HEALTH-WELFARE) Δ(EDUCATION-WELFARE)

INCREMENTAL PW BENEFITS ∆B $920,000.00 -$20,000.00 $900,000.00

INCREMENTAL PW COSTS ∆C $800,000.00 $50,000.00 $850,000.00

THE Δ(HEALTH-WELFARE) INCREMENTAL ANALYSIS IS NOT NEEDED BECAUSE IT IS OBVIOUS THE INCREMENTAL BENEFIT IS NEGATIVE, WHILE THE INCREMENTAL COST IS POSITIVE. a

EDUCATION PROJECT

ΔB/ΔC

EDUCATION-HEALTH HEALTH-WELFARE 1.15 -0.40 EDUCATION>HEALTH WELFARE>HEALTH EDUCATION PREFERRED! MUST DO INCREMENTAL ANALYSIS AS SHOWN HERE

B-C

EDUCATION $200,000.00 EDUCATION PREFERRED!

HEALTH $80,000.00

B/C RATIO 1.20 1.40 2.00

∆B/∆C 1.15 -0.40 1.06

DED BECAUSE IT IS OBVIOUS ENTAL COST IS POSITIVE.

EDUCATION-WELFARE 1.06 EDUCATION>WELFARE

AS SHOWN HERE WELFARE $150,000.00

PROBLEM 14.24 a

USE 7% SINCE THAT IS WHAT THE CITIZENS EARN ON THEIR MONEY ON AVERAGE. ALSO, THIS IS THE FIGURE RECOMMENDED BY OMB CIRCULAR NO. A-94, REVISED.

MAXIMUM AMOUNT CITY CAN AFFORD=

$5,677,027.20

INITIAL INVESTMENT SALVAGE VALUE USEFUL LIFE ANNUAL OPERATING COST % OF INV ANNUAL OPERATING COST (EOY) ANNUAL CONTRACTOR SAVINGS (BOY) ANNUAL BENEFITS TO PUBLIC (EOY) INTEREST RATE

$5,677,027.20 GOAL SEEK CHANGED CELL $0.00 25 5.00% $283,851.36 $300,000.00 $450,000.00 7.00%

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 PRESENT WORTH B/C RATIO B-C

BENEFITS $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00

COST $5,377,027.20 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 -$16,148.64 $283,851.36

$5,244,112.43 $5,244,112.43 1.00 $0.00 GOAL SEEK SET CELL

THE MAXIMUM AMOUNT THE CITY CAN AFFORD TO PAY IS $5,677,027.20 DETERMINED USING GOAL SEEK TO GIVE B-C = 0.0 (RESULTING IN B/C = 1.0).

******************************************************************************************* FOR FUN, THE ANALYSIS WAS REPEATED USING AN INTERST RATE OF 0%. NOTE THE MUCH LARGER INITIAL INVESTMENT OF $8,333,333.33.

INITIAL INVESTMENT SALVAGE VALUE USEFUL LIFE ANNUAL OPERATING COST % OF INV ANNUAL OPERATING COST (EOY) ANNUAL CONTRACTOR SAVINGS (BOY) ANNUAL BENEFITS TO PUBLIC (EOY) INTEREST RATE

$8,333,333.33 $0.00 25 5.00% $416,666.67 $300,000.00 $450,000.00 0.00%

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

BENEFITS

PRESENT WORTH B/C RATIO B-C

$450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00 $450,000.00

COST $8,033,333.33 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $116,666.67 $416,666.67

$11,250,000.00 $11,250,000.00 1.00 $0.00

PROBLEM 14.25 a

INTEREST PLANNING HORIZON BUDGET GIVEN FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

17.00% TRY DIFFERENT VALUES OF INTEREST - 17.0% DELETED E 10 $243,000.00 $100,800.00 $9,180.00 $49,000.00 $44,100.00

EOY 0 1 2 3 4 5 6 7 8 9 10

PROJECT 1 COSTS BENEFITS $100,800.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 -$39,820.00 $44,100.00

EOY 0 1 2 3 4 5 6 7 8 9 10

$133,372.15 $205,444.42

B-C FIRST COST

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

$72,072.27 $100,800.00

SUM BUDGET GIVEN PROJECTS SELECTED

$183,600.00 $243,000.00 1, 2 AT 17.0%

INTEREST PLANNING HORIZON BUDGET GIVEN

6.00% 10 $243,000.00

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

$100,800.00 $9,180.00 $49,000.00 $44,100.00

EOY 0 1 2 3 4 5

PROJECT 1 COSTS BENEFITS $100,800.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00 $9,180.00 $44,100.00

B-C FIRST COST

TOTAL COST $183,600.00

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

EOY 0 1 2 3 4 5

6 7 8 9 10

$9,180.00 $9,180.00 $9,180.00 $9,180.00 -$39,820.00

$44,100.00 $44,100.00 $44,100.00 $44,100.00 $44,100.00

6 7 8 9 10

$141,004.26 $324,579.84

B-C

$183,575.58

B-C

THE APPROACH OF PART a DOES NOT GUARANTEE AN OPTIMUM SOLUTION, EVEN THOUGH SOM THE FOLLOWING COMPLETE ENUMERATION OF THE PROBLEM SHOWS THAT PROJECTS 1, 2, AN THE APPROACH OF PART a ELIMINATED PROJECT 8 ON THE BASIS OF B-C<$0 BEFORE IT GOT TO HAD A B-C VALUE > 0 AT 6% AND COULD FIT WITHIN THE FIRST COST TOTAL CONSTRAINT. USING COMPLETE ENUMERATION TO SEE ALL POSSIBILITIES: B-C $183,575.58 $68,882.30 $81,439.30 FIRST COST $100,800.00 $82,800.00 $126,000.00 1 2 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

$62,354.56 $117,000.00 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1

84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1

188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

NTEREST - 17.0% DELETED ENOUGH PROJECTS TO LEAVE ONLY 1 AND 2, THEREBY BEING FEASIBLE.

$82,800.00 $4,600.00 $24,500.00 $23,350.00

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

$126,000.00 $7,650.00 $36,700.00 $33,050.00

PROJECT 2 COSTS BENEFITS $82,800.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 -$19,900.00 $23,350.00

EOY 0 1 2 3 4 5 6 7 8 9 10

PROJECT 3 COSTS BENEFITS $126,000.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 -$29,050.00 $33,050.00

$99,132.66 $108,778.39

$154,003.35 $153,966.85

$9,645.73 $82,800.00

B-C FIRST COST

-$36.50 $0.00

B-C AT 17.0%= $81,718.00

$82,800.00 $4,600.00 $24,500.00 $23,350.00 PROJECT 2 COSTS BENEFITS $82,800.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00 $4,600.00 $23,350.00

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

EOY 0 1 2 3 4 5

$126,000.00 $7,650.00 $36,700.00 $33,050.00 PROJECT 3 COSTS BENEFITS $126,000.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00 $7,650.00 $33,050.00

$4,600.00 $4,600.00 $4,600.00 $4,600.00 -$19,900.00

$23,350.00 $23,350.00 $23,350.00 $23,350.00 $23,350.00

6 7 8 9 10

$7,650.00 $7,650.00 $7,650.00 $7,650.00 -$29,050.00

$33,050.00 $33,050.00 $33,050.00 $33,050.00 $33,050.00

$102,975.73 $171,858.03

$161,811.58 $243,250.88

$68,882.30

B-C

$81,439.30

OLUTION, EVEN THOUGH SOME TEXTS USE IT AS AN OPTIMIZATION PROCEDURE. OWS THAT PROJECTS 1, 2, AND 8 GIVE THE LARGEST FEASIBLE B-C. OF B-C<$0 BEFORE IT GOT TO 17.0%, EVEN THOUGH THIS SMALL FIRST COST ST TOTAL CONSTRAINT.

$34,554.51 $17,179.55 $15,322.27 $91,800.00 $104,400.00 $77,400.00 5 6 7 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

$25,600.98 $57,200.00 8

TOTAL B-C

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

$0.00 $25,600.98 $15,322.27 $40,923.25 $17,179.55 $42,780.53 $32,501.82 $58,102.80 $34,554.51 $60,155.49 $49,876.78 $75,477.76 $51,734.06 $77,335.04 $67,056.33 $92,657.31 $62,354.56 $87,955.54 $77,676.82 $103,277.80 $79,534.10 $105,135.08 $94,856.37 $120,457.35 $96,909.07 $122,510.05 $112,231.34 $137,832.32 $114,088.62 $139,689.60 $129,410.89 $155,011.87

TOTAL FEASIBLE FIRST COST B-C MAXIMUM $278,058.87 $0.00 $57,200.00 $77,400.00 $134,600.00 $104,400.00 $161,600.00 $181,800.00 $239,000.00 $91,800.00 $149,000.00 $169,200.00 $226,400.00 $196,200.00 $253,400.00 $273,600.00 $330,800.00 $117,000.00 $174,200.00 $194,400.00 $251,600.00 $221,400.00 $278,600.00 $298,800.00 $356,000.00 $208,800.00 $266,000.00 $286,200.00 $343,400.00 $313,200.00 $370,400.00 $390,600.00 $447,800.00

$0.00 $25,600.98 $15,322.27 $40,923.25 $17,179.55 $42,780.53 $32,501.82 $58,102.80 $34,554.51 $60,155.49 $49,876.78 $75,477.76 $51,734.06 $0.00 $0.00 $0.00 $62,354.56 $87,955.54 $77,676.82 $0.00 $79,534.10 $0.00 $0.00 $0.00 $96,909.07 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

$81,439.30 $107,040.28 $96,761.57 $122,362.55 $98,618.85 $124,219.83 $113,941.12 $139,542.09 $115,993.81 $141,594.79 $131,316.08 $156,917.06 $133,173.36 $158,774.34 $148,495.63 $174,096.61 $143,793.86 $169,394.83 $159,116.12 $184,717.10 $160,973.40 $186,574.38 $176,295.67 $201,896.65 $178,348.37 $203,949.35 $193,670.64 $219,271.62 $195,527.92 $221,128.90 $210,850.19 $236,451.17 $68,882.30 $94,483.28 $84,204.57 $109,805.55 $86,061.85 $111,662.83 $101,384.12 $126,985.10 $103,436.82 $129,037.80 $118,759.09 $144,360.07 $120,616.37 $146,217.35 $135,938.64 $161,539.61 $131,236.86 $156,837.84 $146,559.13 $172,160.11

$126,000.00 $183,200.00 $203,400.00 $260,600.00 $230,400.00 $287,600.00 $307,800.00 $365,000.00 $217,800.00 $275,000.00 $295,200.00 $352,400.00 $322,200.00 $379,400.00 $399,600.00 $456,800.00 $243,000.00 $300,200.00 $320,400.00 $377,600.00 $347,400.00 $404,600.00 $424,800.00 $482,000.00 $334,800.00 $392,000.00 $412,200.00 $469,400.00 $439,200.00 $496,400.00 $516,600.00 $573,800.00 $82,800.00 $140,000.00 $160,200.00 $217,400.00 $187,200.00 $244,400.00 $264,600.00 $321,800.00 $174,600.00 $231,800.00 $252,000.00 $309,200.00 $279,000.00 $336,200.00 $356,400.00 $413,600.00 $199,800.00 $257,000.00 $277,200.00 $334,400.00

$81,439.30 $107,040.28 $96,761.57 $0.00 $98,618.85 $0.00 $0.00 $0.00 $115,993.81 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $143,793.86 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $68,882.30 $94,483.28 $84,204.57 $109,805.55 $86,061.85 $0.00 $0.00 $0.00 $103,436.82 $129,037.80 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $131,236.86 $0.00 $0.00 $0.00

0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

$148,416.41 $174,017.39 $163,738.68 $189,339.66 $165,791.38 $191,392.35 $181,113.64 $206,714.62 $182,970.92 $208,571.90 $198,293.19 $223,894.17 $150,321.60 $175,922.58 $165,643.87 $191,244.85 $167,501.15 $193,102.13 $182,823.42 $208,424.40 $184,876.12 $210,477.10 $200,198.39 $225,799.37 $202,055.67 $227,656.65 $217,377.93 $242,978.91 $212,676.16 $238,277.14 $227,998.43 $253,599.41 $229,855.71 $255,456.69 $245,177.98 $270,778.96 $247,230.67 $272,831.65 $262,552.94 $288,153.92 $264,410.22 $290,011.20 $279,732.49 $305,333.47 $183,575.58 $209,176.56 $198,897.85 $224,498.83 $200,755.13 $226,356.11 $216,077.40 $241,678.38

$304,200.00 $361,400.00 $381,600.00 $438,800.00 $291,600.00 $348,800.00 $369,000.00 $426,200.00 $396,000.00 $453,200.00 $473,400.00 $530,600.00 $208,800.00 $266,000.00 $286,200.00 $343,400.00 $313,200.00 $370,400.00 $390,600.00 $447,800.00 $300,600.00 $357,800.00 $378,000.00 $435,200.00 $405,000.00 $462,200.00 $482,400.00 $539,600.00 $325,800.00 $383,000.00 $403,200.00 $460,400.00 $430,200.00 $487,400.00 $507,600.00 $564,800.00 $417,600.00 $474,800.00 $495,000.00 $552,200.00 $522,000.00 $579,200.00 $599,400.00 $656,600.00 $100,800.00 $158,000.00 $178,200.00 $235,400.00 $205,200.00 $262,400.00 $282,600.00 $339,800.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $150,321.60 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $183,575.58 $209,176.56 $198,897.85 $224,498.83 $200,755.13 $0.00 $0.00 $0.00

1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

$218,130.10 $243,731.08 $233,452.37 $259,053.35 $235,309.65 $260,910.63 $250,631.91 $276,232.89 $245,930.14 $271,531.12 $261,252.41 $286,853.39 $263,109.69 $288,710.67 $278,431.96 $304,032.94 $280,484.65 $306,085.63 $295,806.92 $321,407.90 $297,664.20 $323,265.18 $312,986.47 $338,587.45 $265,014.88 $290,615.86 $280,337.15 $305,938.13 $282,194.43 $307,795.41 $297,516.70 $323,117.68 $299,569.40 $325,170.38 $314,891.67 $340,492.65 $316,748.95 $342,349.93 $332,071.21 $357,672.19 $327,369.44 $352,970.42 $342,691.71 $368,292.69 $344,548.99 $370,149.97 $359,871.26 $385,472.23 $361,923.95 $387,524.93 $377,246.22 $402,847.20

$192,600.00 $249,800.00 $270,000.00 $327,200.00 $297,000.00 $354,200.00 $374,400.00 $431,600.00 $217,800.00 $275,000.00 $295,200.00 $352,400.00 $322,200.00 $379,400.00 $399,600.00 $456,800.00 $309,600.00 $366,800.00 $387,000.00 $444,200.00 $414,000.00 $471,200.00 $491,400.00 $548,600.00 $226,800.00 $284,000.00 $304,200.00 $361,400.00 $331,200.00 $388,400.00 $408,600.00 $465,800.00 $318,600.00 $375,800.00 $396,000.00 $453,200.00 $423,000.00 $480,200.00 $500,400.00 $557,600.00 $343,800.00 $401,000.00 $421,200.00 $478,400.00 $448,200.00 $505,400.00 $525,600.00 $582,800.00 $435,600.00 $492,800.00 $513,000.00 $570,200.00

$218,130.10 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $245,930.14 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $265,014.88 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

$379,103.50 $404,704.48 $394,425.77 $420,026.75 $252,457.89 $278,058.87 $267,780.16 $293,381.14 $269,637.44 $295,238.42 $284,959.70 $310,560.68 $287,012.40 $312,613.38 $302,334.67 $327,935.65 $304,191.95 $329,792.93 $319,514.22 $345,115.20 $314,812.44 $340,413.42 $330,134.71 $355,735.69 $331,991.99 $357,592.97 $347,314.26 $372,915.24 $349,366.96 $374,967.94 $364,689.23 $390,290.21 $366,546.51 $392,147.49 $381,868.78 $407,469.75 $333,897.19 $359,498.17 $349,219.46 $374,820.43 $351,076.74 $376,677.72 $366,399.00 $391,999.98 $368,451.70 $394,052.68 $383,773.97 $409,374.95 $385,631.25 $411,232.23 $400,953.52 $426,554.50

$540,000.00 $597,200.00 $617,400.00 $674,600.00 $183,600.00 $240,800.00 $261,000.00 $318,200.00 $288,000.00 $345,200.00 $365,400.00 $422,600.00 $275,400.00 $332,600.00 $352,800.00 $410,000.00 $379,800.00 $437,000.00 $457,200.00 $514,400.00 $300,600.00 $357,800.00 $378,000.00 $435,200.00 $405,000.00 $462,200.00 $482,400.00 $539,600.00 $392,400.00 $449,600.00 $469,800.00 $527,000.00 $496,800.00 $554,000.00 $574,200.00 $631,400.00 $309,600.00 $366,800.00 $387,000.00 $444,200.00 $414,000.00 $471,200.00 $491,400.00 $548,600.00 $401,400.00 $458,600.00 $478,800.00 $536,000.00 $505,800.00 $563,000.00 $583,200.00 $640,400.00

$0.00 $0.00 $0.00 $0.00 $252,457.89 $278,058.87 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1

0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1

0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1

0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

$396,251.74 $421,852.72 $411,574.01 $437,174.99 $413,431.29 $439,032.27 $428,753.56 $454,354.54 $430,806.26 $456,407.24 $446,128.53 $471,729.51 $447,985.81 $473,586.79 $463,308.07 $488,909.05

$426,600.00 $483,800.00 $504,000.00 $561,200.00 $531,000.00 $588,200.00 $608,400.00 $665,600.00 $518,400.00 $575,600.00 $595,800.00 $653,000.00 $622,800.00 $680,000.00 $700,200.00 $757,400.00

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

FIRST COST $117,000.00 O&M / YR $4,900.00 SALVAGE(10) $44,400.00 BENEFITS/YR $25,900.00

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

$91,800.00 $12,850.00 $49,000.00 $26,300.00

EOY 0 1 2 3 4 5 6 7 8 9 10

PROJECT 4 COSTS BENEFITS $117,000.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 -$39,500.00 $25,900.00

EOY 0 1 2 3 4 5 6 7 8 9 10

PROJECT 5 COSTS BENEFITS $91,800.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 -$36,150.00 $26,300.00

$130,590.30 $120,657.83

$141,469.22 $122,521.28

B-C FIRST COST

-$9,932.46 $0.00

FIRST COST $117,000.00 O&M / YR $4,900.00 SALVAGE(10) $44,400.00 BENEFITS/YR $25,900.00

EOY 0 1 2 3 4 5

PROJECT 4 COSTS BENEFITS $117,000.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00 $4,900.00 $25,900.00

B-C FIRST COST

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

EOY 0 1 2 3 4 5

-$18,947.95 $0.00

$91,800.00 $12,850.00 $49,000.00 $26,300.00 PROJECT 5 COSTS BENEFITS $91,800.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00 $12,850.00 $26,300.00

6 7 8 9 10

$4,900.00 $4,900.00 $4,900.00 $4,900.00 -$39,500.00

$25,900.00 $25,900.00 $25,900.00 $25,900.00 $25,900.00

6 7 8 9 10

$12,850.00 $12,850.00 $12,850.00 $12,850.00 -$36,150.00

$128,271.70 $190,626.25

$159,015.77 $193,570.29

B-C

$62,354.56

B-C

$34,554.51

PROJ 1, 2, 8

$26,300.00 $26,300.00 $26,300.00 $26,300.00 $26,300.00

FIRST COST $104,400.00 O&M / YR $1,840.00 SALVAGE(10) $24,500.00 BENEFITS/YR $16,500.00

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

$77,400.00 $15,600.00 $9,200.00 $27,500.00

EOY 0 1 2 3 4 5 6 7 8 9 10

PROJECT 6 COSTS BENEFITS $104,400.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 -$22,660.00 $16,500.00

EOY 0 1 2 3 4 5 6 7 8 9 10

PROJECT 7 COSTS $77,400.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00 $6,400.00

$107,874.91

$76,866.96

$148,160.27

-$31,007.95 $0.00

B-C FIRST COST

FIRST COST $104,400.00 O&M / YR $1,840.00 SALVAGE(10) $24,500.00 BENEFITS/YR $16,500.00

EOY 0 1 2 3 4 5

PROJECT 6 COSTS BENEFITS $104,400.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00 $1,840.00 $16,500.00

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

$77,400.00 $15,600.00 $9,200.00 $27,500.00

EOY 0 1 2 3 4 5

PROJECT 7 COSTS $77,400.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00 $15,600.00

6 7 8 9 10

$1,840.00 $1,840.00 $1,840.00 $1,840.00 -$22,660.00

$16,500.00 $16,500.00 $16,500.00 $16,500.00 $16,500.00

6 7 8 9 10

$15,600.00 $15,600.00 $15,600.00 $15,600.00 $6,400.00

$104,261.89

$121,441.44

$187,080.13

$17,179.55

B-C

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

BENEFITS $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00

EOY 0 1 2 3 4 5 6 7 8 9 10

$128,111.60

-$20,048.67 $0.00

B-C FIRST COST

FIRST COST O&M / YR SALVAGE(10) BENEFITS/YR

BENEFITS $27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00

EOY 0 1 2 3 4 5

$57,200.00 $6,550.00 $0.00 $17,800.00 PROJECT 8 COSTS BENEFITS $57,200.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $87,713.85

$82,923.14 -$4,790.71 $0.00

$57,200.00 $6,550.00 $0.00 $17,800.00 PROJECT 8 COSTS BENEFITS $57,200.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00 $6,550.00 $17,800.00

$27,500.00 $27,500.00 $27,500.00 $27,500.00 $27,500.00

6 7 8 9 10

$6,550.00 $6,550.00 $6,550.00 $6,550.00 $6,550.00

$17,800.00 $17,800.00 $17,800.00 $17,800.00 $17,800.00

$202,402.39

$105,408.57 $131,009.55

$15,322.27

B-C

$25,600.98

PROBLEM 14.26 a

INTEREST RATE PLANNING HORIZON

7.00% 20 PROJECT 1 FIRST COST SALVAGE VALUE ANNUAL OP COST ANNUAL BENEFIT

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BENEFIT $208,000.00 $208,000.00 $208,000.00 $208,000.00 $208,000.00 $208,000.00 $208,000.00 $208,000.00 $208,000.00 $208,000.00

PW B PW C PW B-C

INTEREST RATE PLANNING HORIZON

$770,000.00 $0.00 $80,000.00 $208,000.00

COST $770,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00

$1,460,904.96 $1,331,886.52 $129,018.44 PROJECT 1 IS LEAST DESIRABLE

7.00% 20 PROJECT 1 FIRST COST SALVAGE VALUE ANNUAL OP COST ANNUAL BENEFIT

$770,000.00 $0.00 $80,000.00 $245,918.42

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

BENEFIT $245,918.42 $245,918.42 $245,918.42 $245,918.42 $245,918.42 $245,918.42 $245,918.42 $245,918.42 $245,918.42 $245,918.42

PW B PW C PW B-C

COST $770,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00

$1,727,228.09 $1,331,886.52 $395,341.57 ANNUAL BENEFIT MUST EQUAL $245,918.42

PROJECT 2 FIRST COST SALVAGE VALUE ANNUAL OP COST ANNUAL BENEFIT

BENEFIT $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00

PW B PW C PW B-C

GOAL SEEK CHANGED VALUE

PROJECT 2 FIRST COST SALVAGE VALUE ANNUAL OP COST ANNUAL BENEFIT

$770,000.00 $0.00 $80,000.00 $195,000.00

COST $770,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00

$1,776,043.23 $1,498,633.12 $277,410.11

$770,000.00 $0.00 $80,000.00 $195,000.00

BENEFIT $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00 $195,000.00

GOAL SEEK SET CELL

PW B PW C PW B-C

COST $770,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00

$1,776,043.23 $1,498,633.12 $277,410.11

PROJECT 3 FIRST COST SALVAGE VALUE ANNUAL OP COST ANNUAL BENEFIT

BENEFIT $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 $190,000.00 PW B PW C PW B-C

PROJECT 3 FIRST COST SALVAGE VALUE ANNUAL OP COST ANNUAL BENEFIT

$770,000.00 $0.00 $80,000.00 $190,000.00

COST $770,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $2,012,862.71 $1,617,521.14 $395,341.57 PROJECT 3 IS MOST DESIRABLE

$770,000.00 $0.00 $80,000.00 $190,000.00

PROBLEM 14.27 INTEREST RATE

7.00%

ANALYSIS SHOULD BE AS FOLLOWS: (1) BASEBALL AND SOCCER FIRST COST SALVAGE VALUE @ USEFUL LIFE ANNUAL BENEFITS TO PUBLIC USEFUL LIFE

$120,000.00 $15,000.00 $50,000.00 5

AE(1) BASEBALL AND SOCCER

$23,341.48

(2) CITIZEN GARDEN PLOTS FIRST COST SALVAGE VALUE @ USEFUL LIFE ANNUAL BENEFITS TO PUBLIC USEFUL LIFE

$70,000.00 $20,000.00 $45,000.00 3

AE(2) CITIZEN GARDEN PLOTS

$24,547.42

$64,420.18 $15,711.48

AE (1) AS PRESENTED - CORRECT FOR 5 YEAR PLANNING HORIZON

AE (2) AS PRESENTED - WRONG NEED TO TAKE TO PRESENT AND THEN SPREAD OVER 5 YEAR HORIZON PRESENT WORTH AE (2) AS CORRECTED - CORRECT FOR 5 YEAR PLANNING HORIZON SHOULD SELECT (1) BASEBALL AND SOCCER

PROBLEM 14.28 INITIAL COST MAINT COST / YEAR

NO. OF PERSONS PERCENTAGE PERCENTAGE PERCENTAGE TOT NET BENEFIT / YR PW OF B PW OF C B/C B-C

$1,800,000.00 PLANNING HORIZON $200,000.00 INTEREST RATE

90,000 40.00% BENEFIT PER VISIT 45.00% BENEFIT PER VISIT 15.00% BENEFIT PER VISIT TOTAL BENEFITS PER YEAR $384,750.00

30 6.00%

$3.00 $4.50 $7.00 $384,750.00

$5,296,018.79 $4,552,966.23 1.16 ACCEPTABLE $743,052.56 ACCEPTABLE

90,000 40.00% BENEFIT PER VISIT 45.00% BENEFIT PER VISIT 15.00% BENEFIT PER VISIT TOTAL BENEFITS PER YEAR $60,750.00 $836,213.49 $1,579,762.70 0.53 NOT ACCEPTABLE -$743,549.21 NOT ACCEPTABLE

$3.00 $4.50 $7.00 $276,750.00

COST / DISBENEFIT PER VISIT COST / DISBENEFIT PER VISIT COST / DISBENEFIT PER VISIT TOTAL COST / DISBENEFIT PER YEAR

WILL NOT VISIT! COST / DISBENEFIT PER VISIT COST / DISBENEFIT PER VISIT COST / DISBENEFIT PER VISIT TOTAL COST / DISBENEFIT PER YEAR

$0.00 $0.00 $0.00 $0.00

$4.00 WILL NOT VISIT! $4.00 $4.00 $216,000.00

PROBLEM 14.29 INTEREST STUDY PERIOD

7.00% 20

INITIAL COST PHYS FACIL NEW SPECIES FIRST YEAR ANNUAL COST PERCENT INCREASE EACH YR SALVAGE % FACIL SALVAGE VALUE FACIL PLANNING HORIZON

$1,800,000.00 $310,000.00 $145,000.00 3.00% 40.00% $720,000.00 20

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

PW AW

$3,857,029.51 $364,076.30

ATTENDEES/YR NEEDED BENEFIT/ATTENDEE

1,500,000 $0.2427

THE FLAW IN REASONING IS THAT SINCE THE AVERAGE BENEFIT MUST BE $0.2427, SOME PERSO WITH FEWER THAN 1,500,000 VISITORS TO THE NEW AREA, IF ONLY $0.25 IS CHARGED, THE NEW ALTERNATIVES MAY BE TO CHARGE A HIGHER, AND STILL NOMINAL, FEE. OR, THE ZOO MAY SEE

PROBLEM 14.30

FIRST, DETERMINE ANNUAL COST OF RENOVATION INITIAL COST PHYS FACIL NEW SPECIES FIRST YEAR ANNUAL COST PERCENT INCREASE EACH YR SALVAGE % FACIL SALVAGE VALUE FACIL INTEREST PLANNING HORIZON

$1,800,000.00 $310,000.00 $145,000.00 SEE COLUMN TO RIGHT FOR PW AND AW 3.00% SEE COLUMN TO RIGHT FOR PW AND AW 40.00% $720,000.00 7.00% 20

PW COST= AW COST=

$3,857,029.51 $364,076.30 PER YEAR

TOTAL VISITS/YEAR PERCENT PERCENT PERCENT PERCENT

1,500,000 2.00% BENEFIT/VISIT PERCEIVED 8.00% BENEFIT/VISIT PERCEIVED 20.00% BENEFIT/VISIT PERCEIVED 70.00% BENEFIT/VISIT PERCEIVED

$3.00 $2.00 $1.00 $0.00

100.00% a

FEE= PERCENT PERCENT PERCENT PERCENT

$0.50 2.00% BENEFIT/VISIT PERCEIVED 8.00% BENEFIT/VISIT PERCEIVED 20.00% BENEFIT/VISIT PERCEIVED 70.00% BENEFIT/VISIT PERCEIVED

$3.00 $2.00 $1.00 $0.00

100.00%

FEE= PERCENT PERCENT PERCENT PERCENT

$1.50 2.00% BENEFIT/VISIT PERCEIVED 8.00% BENEFIT/VISIT PERCEIVED 20.00% BENEFIT/VISIT PERCEIVED 70.00% BENEFIT/VISIT PERCEIVED

$3.00 $2.00 $1.00 $0.00

100.00%

FEE= PERCENT PERCENT PERCENT PERCENT

$2.50 2.00% BENEFIT/VISIT PERCEIVED 8.00% BENEFIT/VISIT PERCEIVED 20.00% BENEFIT/VISIT PERCEIVED 70.00% BENEFIT/VISIT PERCEIVED 100.00%

$3.00 $2.00 $1.00 $0.00

FEE= PERCENT PERCENT PERCENT PERCENT

$5.00 2.00% BENEFIT/VISIT PERCEIVED 8.00% BENEFIT/VISIT PERCEIVED 20.00% BENEFIT/VISIT PERCEIVED 70.00% BENEFIT/VISIT PERCEIVED

$3.00 $2.00 $1.00 $0.00

100.00%

NOTE! EVEN THOUGH THERE IS A VERY LARGE PERCEIVED BENEFIT ($630,000) TO THE ZOO PAT WHEN FEES ARE CHARGED AND COSTS SUBTRACTED FROM THE FEE REVENUE, ALL SCENARIO END UP BEING NEGATIVE FROM A MONETARY STANDPOINT.

T FOR PW AND AW T FOR PW AND AW

TOTAL BENEFIT TOTAL BENEFIT TOTAL BENEFIT TOTAL BENEFIT

$90,000.00 $240,000.00 $300,000.00 $0.00 $630,000.00

EOY

ANNUAL COST

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$145,000.00 $149,350.00 $153,830.50 $158,445.42 $163,198.78 $168,094.74 $173,137.58 $178,331.71 $183,681.66 $189,192.11 $194,867.88 $200,713.91 $206,735.33 $212,937.39 $219,325.51 $225,905.28 $232,682.43 $239,662.91 $246,852.79 $254,258.38

TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED

PW= $1,933,091.19 $15,000.00 AW= $182,470.13 $60,000.00 $150,000.00 $0.00 NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT

REVENUE INCREASE= ANNUAL COST= NET FINANCIAL GAIN =

$225,000.00 $364,076.30 -$139,076.30

TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED

$45,000.00 $180,000.00 $0.00 NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT $0.00 NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT

REVENUE INCREASE= ANNUAL COST= NET FINANCIAL GAIN =

$225,000.00 $364,076.30 -$139,076.30

TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED

$75,000.00 $0.00 $0.00 $0.00

REVENUE INCREASE=

$75,000.00

NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT

ANNUAL COST= NET FINANCIAL GAIN =

$364,076.30 -$289,076.30

TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED TOTAL FEE RECEIVED

$0.00 $0.00 $0.00 $0.00

REVENUE INCREASE= ANNUAL COST= NET FINANCIAL GAIN =

$0.00 $364,076.30 -$364,076.30

$630,000) TO THE ZOO PATRONS, REVENUE, ALL SCENARIOS

NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT NO VISIT - CHARGE EXCEEDS PERCEIVED BENEFIT

EIVED BENEFIT

EIVED BENEFIT EIVED BENEFIT

EIVED BENEFIT EIVED BENEFIT EIVED BENEFIT

EIVED BENEFIT EIVED BENEFIT EIVED BENEFIT EIVED BENEFIT

PROBLEM 14.31 PROPOSED USER CHARGE TO CAMPING FAMILIES/DAY PROPOSED USER CHARGE TO DAY USERS/DAY

$15.00 $3.00

PERCENTAGE OF CAMPING FAMILIES OVERNIGHT BENEFITS PERCEIVED PER FAMILY NUMBER OF NIGHTS PER FAMILY NUMBER OF PAYING FAMILIES PER SEASON

30.00% $7.00 8 0

8 250

60.00% $15.00 8 150

BENEFITS REALIZED BY FAMILIES DISBENEFITS REALIZED BY FAMILIES NET BENEFITS REALIZED BY FAMILES

$0.00 $18,000.00 $0.00 $18,000.00 $0.00 $0.00

PERCENTAGE OF DAY USERS BENEFITS PER DAY FOR DAY-USERS NUMBER OF DAY USERS PER SEASON

40.00% $3.00 880

BENEFITS REALIZED BY DAY USERS DISBENEFITS REALIZED BY DAY USERS NET BENEFITS REALIZED BY DAY USERS TOTAL NET BENEFITS PER YEAR TOTAL COSTS PER YEAR TOTAL USER FEE INCOME PER YEAR NET COSTS PER YEAR a

B/C=

1.93

B-C=

$2,240.00

2,200 $0.00 $0.00 $0.00

$2,640.00 $2,640.00 $0.00 $4,640.00

$30,000.00 $27,600.00 $2,400.00

10.00% $25.00 8 25

175 SUM

$5,000.00 $23,000.00 SUM $3,000.00 $21,000.00 SUM $2,000.00 $2,000.00 SUM

60.00% $5.00 1320

2,200 SUM

$6,600.00 $3,960.00 $2,640.00

$9,240.00 SUM $6,600.00 SUM $2,640.00 SUM

PROBLEM 14.32 a

THE ANALYSIS IS WRONG. WHILE THE DISBENEFIT IS INDEED SUBTRACTED FROM THE BENEFIT LINE IN THE ANALYSIS, THERE IS STILL THE ASSUMPTION THAT THE NUMBER OF VISITORS WILL NOT BE IMPACTED. REMEMBER, IF THE PERCEIVED BENEFIT IS LESS THAN THE COST OF ADMISSION, THE VISIT WILL NOT TAKE PLACE AND THERE WILL BE NO INCOME FROM THOSE NON-VISITS!

THE CORRECTED B/C ANALYSIS FOLLOWS: PROPOSED ADMISSION CHARGE ANNUALIZED COST OF CENTER

VISITORS BENEFITS/VISIT DISBENEFITS/VISIT (COST/VISIT) NET BENEFITS/VISIT PAYING VISITORS NET BENEFITS TO VISITORS/YEAR INCOME TO CENTER/YEAR ANNUALIZED COST OF CENTER

NET BENEFITS TO VISITORS/YEAR NET COST OF CENTER/YEAR B/C RATIO=

$5.75 $250,000.00

6,000 $7.00 $5.75 $1.25 6,000

9,000 $10.00 $5.75 $4.25 9,000

SUM 41,000

12,000 $3.00 $5.75 -$2.75 0

14,000 $5.00 $5.75 -$0.75 0

$0.00 $0.00

$0.00 $7,500.00 $38,250.00 $45,750.00 $0.00 $34,500.00 $51,750.00 $86,250.00 $250,000.00

15,000

$45,750.00 $163,750.00 0.28

PROBLEM 14.33 a

THE ANALYSIS IS WRONG. THE "DISBENEFIT" OF $106,000 IS NOT A DISBENEFIT AT ALL. IT IS SIMPLY THE LOST REVENUE DUE TO THE LOSS OF 26,000 VISITORS. TO SUBTRACT THESE AS A "DISBENEFIT" IS WRONG AND, IN A SENSE, DOUBLE COUNTING SINCE THE LOSS OF INCOME TO THE CENTER IS ALREADY REFLECTED IN THE DENOMINATOR.

THE CORRECTED B/C ANALYSIS FOLLOWS: PROPOSED ADMISSION CHARGE ANNUALIZED COST OF CENTER

VISITORS BENEFITS/VISIT DISBENEFITS/VISIT (COST/VISIT) NET BENEFITS/VISIT PAYING VISITORS NET BENEFITS TO VISITORS/YEAR INCOME TO CENTER/YEAR ANNUALIZED COST OF CENTER

NET BENEFITS TO VISITORS/YEAR NET COST OF CENTER/YEAR B/C RATIO=

$5.75 $250,000.00

6,000 $7.00 $5.75 $1.25 6,000

9,000 $10.00 $5.75 $4.25 9,000

SUM 41,000

12,000 $3.00 $5.75 -$2.75 0

14,000 $5.00 $5.75 -$0.75 0

$0.00 $0.00

$0.00 $7,500.00 $38,250.00 $45,750.00 $0.00 $34,500.00 $51,750.00 $86,250.00 $250,000.00

15,000

$45,750.00 $163,750.00 0.28

PROBLEM 14.34 a

PROPOSED ADMISSION CHARGE ANNUALIZED COST OF CENTER

VISITORS BENEFITS/VISIT DISBENEFITS/VISIT (COST/VISIT) NET BENEFITS/VISIT PAYING VISITORS NET BENEFITS TO VISITORS/YEAR INCOME TO CENTER/YEAR ANNUALIZED COST OF CENTER

NET BENEFITS TO VISITORS/YEAR NET COST OF CENTER/YEAR B/C RATIO= PROPOSED ADMISSION CHARGE TO MAXIMIZE INCOME TO CENTER/YEAR= INCOME TO CENTER/YEAR=

PROPOSED ADMISSION CHARGE ANNUALIZED COST OF CENTER

VISITORS BENEFITS/VISIT DISBENEFITS/VISIT (COST/VISIT) NET BENEFITS/VISIT PAYING VISITORS NET BENEFITS TO VISITORS/YEAR INCOME TO CENTER/YEAR ANNUALIZED COST OF CENTER

NET BENEFITS TO VISITORS/YEAR NET COST OF CENTER/YEAR B/C RATIO= PROPOSED ADMISSION CHARGE TO MAXIMIZE B/C RATIO= B/C RATIO=

NO FEASIBLE SOLUTION - CANNOT GET B/C > 1.0 WITH A CHARGE > 0.0

$7.00 <--SOLVER CHANGED CELL $250,000.00

12,000 $3.00 $7.00 -$4.00 0 $0.00 $0.00

14,000 5 7 -2 0

6,000 $7.00 $7.00 $0.00 6,000

9,000 $10.00 $7.00 $3.00 9,000

SUM 41,000

15,000

0 $0.00 $27,000.00 $27,000.00 0 $42,000.00 $63,000.00 $105,000.00 <--SOLVER TARGET CELL $250,000.00

$27,000.00 $145,000.00 0.19 $7.00 $105,000.00

$0.00 <--SOLVER CHANGED CELL $250,000.00

12,000 $3.00 $0.00 $3.00 12,000 $36,000.00 $0.00

14,000 5 0 5 14000

6,000 $7.00 $0.00 $7.00 6,000

9,000 $10.00 $0.00 $10.00 9,000

SUM 41,000

41,000

70000 $42,000.00 $90,000.00 $238,000.00 0 $0.00 $0.00 $0.00 $250,000.00

$238,000.00 $250,000.00 0.95 $0.00 $0.95

<--SOLVER TARGET CELL

PROBLEM 14.35

INTEREST RATE PROJECT LIFE

5.00% 50

ALTERNATIVES

INITIAL COST: ANNUAL OPERATING AND MAINTENANCE COSTS FLOOD CONTROL SAVINGS TO REGION IRRIGATION BENEFITS TO REGION RECREATION BENEFITS TO REGION

$0 $0 $0 $0 $0

A PW BENEFITS PW COSTS B/C B-C

A $2,000,000 $200,000 $250,000 $350,000 $100,000

$0.00 $12,779,147.82 $0.00 $5,651,185.09 NA 2.26 $0.00 $7,127,962.73

INCREMENT BETWEEN WHICH TWO ALTERNATIVES INCREMENTAL PW BENEFITS INCREMENTAL PW COSTS ΔB/ΔC CONCLUSION

A-DN $12,779,147.82 $5,651,185.09 2.26 PREFER A LARGEST B/C RATIO IS FOR A LARGEST ∆B/∆C RATIO IS FOR C BEST ALTERNATIVE BASED ON B-C IS C

INTEREST RATE PROJECT LIFE

8.00% 50

ALTERNATIVES

INITIAL COST: ANNUAL OPERATING AND MAINTENANCE COSTS FLOOD CONTROL SAVINGS TO REGION IRRIGATION BENEFITS TO REGION RECREATION BENEFITS TO REGION

$0 $0 $0 $0 $0

$2,000,000 $200,000 $250,000 $350,000 $100,000

$0.00 $0.00 NA $0.00

$8,563,439.25 $4,446,696.93 1.93 $4,116,742.32

A PW BENEFITS PW COSTS B/C B-C

INCREMENT BETWEEN WHICH TWO ALTERNATIVES

A-DN

INCREMENTAL PW BENEFITS INCREMENTAL PW COSTS ΔB/ΔC CONCLUSION

$8,563,439.25 $4,446,696.93 1.93 PREFER A LARGEST B/C RATIO IS FOR A LARGEST ∆B/∆C RATIO IS FOR B BEST ALTERNATIVE BASED ON B-C IS B

SEE ABOVE FOR ∆B/∆C RATIO ANALYSIS IT AGREES WITH THE B-C ANALYSIS

$4,500,000 $280,000 $350,000 $450,000 $200,000

$9,000,000 $450,000 $500,000 $600,000 $350,000

$18,255,925.46 $26,471,091.92 $9,611,659.13 $17,215,166.46 1.90 1.54 $8,644,266.33 $9,255,925.46 PREFER C B-A $5,476,777.64 $3,960,474.04 1.38 PREFER B

C-B $8,215,166.46 $7,603,507.33 1.08 PREFER C

/C RATIO IS FOR A B/∆C RATIO IS FOR C RNATIVE BASED ON B-C IS C

$4,500,000 $280,000 $350,000 $450,000 $200,000

$9,000,000 $450,000 $500,000 $600,000 $350,000

$12,233,484.64 $17,738,552.73 $7,925,375.70 $14,505,068.09 1.54 1.22 $4,308,108.94 $3,233,484.64 PREFER B B-A

C-B

$3,670,045.39 $3,478,678.77 1.06 PREFER B

/C RATIO IS FOR A B/∆C RATIO IS FOR B RNATIVE BASED ON B-C IS B

$5,505,068.09 $6,579,692.39 0.84 PREFER B

PROBLEM 14.36

INTEREST PLANNING HORIZON

8.00% 50

TOTAL INVESTMENT $47,000,000.00 $24,275,000.00 $3,300,000.00 $4,200,000.00 $800,000.00

OP AND MAINT COST/YEAR % OF TOT INV FOR O&M COST 5.00% $3,978,750.00

ANNUAL INCOME FROM CUSTOMERS $9,500,000.00

$79,575,000.00

$3,978,750.00

$9,500,000.00

$12,030,872.91

NET COSTS>$0 DOES NOT BREAK EVEN

TOTAL INVESTMENT $47,000,000.00 $24,275,000.00 $3,300,000.00 $4,200,000.00 $800,000.00

OP AND MAINT COST % OF TOT INV FOR O&M COST 5.00%

ANNUAL INCOME FROM CUSTOMERS

$79,575,000.00

$3,978,750.00

$9,500,000.00

PW OF COSTS=

PW NET COSTS

$12,030,872.91

PW NET BENEFITS

$50,793,428.24

B/C

4.22

PROJECT IS FAVORABLE

B-C

$38,762,555.32

PROJECT IS FAVORABLE

ANNUAL BENEFITS $1,252,000.00 $525,000.00 $11,875,000.00 -$9,500,000.00

$4,152,000.00

BENEFIT BENEFIT BENEFIT DISBENEFIT

PROBLEM 14.37 CATEGORY AMOUNT/YEAR BENEFITS $2,350,000.00 DISBENEFITS $1,640,000.00 $710,000.00 NET BENEFITS COSTS $1,800,000.00 SAVINGS $1,450,000.00 $350,000.00 NET COSTS a

B/C=

2.03

B-C=

$360,000.00

B/C(ERROR)=

1.10

B-C(ERROR)=

$360,000.00

CATEGORY AMOUNT/YEAR BENEFITS $1,990,000.00 <--SOLVER CHANGED CELL DISBENEFITS $1,640,000.00 $350,000.00 NET BENEFITS COSTS $1,800,000.00 SAVINGS $1,450,000.00 $350,000.00 NET COSTS a

B/C=

1.00

B-C=

$0.00

B/C(ERROR)=

1.00

B-C(ERROR)=

$0.00

<--SOLVER TARGET CELL

NOTE THAT B/C AND B-C ARE STILL CONSISTENT WHEN DISBENEFITS ARE TREATED AS COSTS AND SAVINGS ARE TREATED AS BENEFITS, MISTAKENLY. B/C DOES CHANGE VALUE, HOWEVER, WHILE B-C DOES NOT f g

B/C=

1.00

B-C IS EASIER TO EXPLAIN THAN B/C BECAUSE IT IS EQUAL TO BENEFITS - DISBENEFITS - COSTS + SAVINGS, NO MATTER HOW THEY ARE PAIRED OFF, THEY RESULT IN THE SAME VALUE OF B-C AS SEEN ABOVE. THE SAME IS NOT TRUE OF THE B/C RATIO.

PROBLEM 14.38 INCOME TAX TAX RATE DEBT INTEREST RATE ON DEBT BOOK VALUE DEPRECIATION RATE TCBIT

$9,000,000.00 40.00% $80,000,000.00 7.00% $190,000,000.00 6.677% $56,000,000.00

INTEREST ON DEBT

$5,600,000.00

DEPRECIATION CHARGE

$12,686,300.00

ANNUAL EXPENSE

$37,713,700.00

RETURN TO OWNERS

$13,500,000.00

REVENUE REQUIREMENT

$78,500,000.00

PROBLEM 14.39 INCOME TAX TAX RATE DEBT INTEREST RATE ON DEBT BOOK VALUE DEPRECIATION RATE TCBIT

$6,000,000.00 40.00% $75,000,000.00 10.00% $150,000,000.00 7.219% $39,000,000.00

INTEREST ON DEBT

$7,500,000.00

DEPRECIATION CHARGE

$10,828,500.00

ANNUAL EXPENSE

$20,671,500.00

RETURN TO OWNERS

$9,000,000.00

REVENUE REQUIREMENT

$54,000,000.00

PROBLEM 14.40 INCOME TAX TAX RATE DEBT INTEREST ON DEBT FINANCIAL DEPRECIATION INITIAL INVESTMENT MACRS(20) PERCENTAGE TCBIT

$5,500,000.00 40.00% $70,000,000.00 10.00% $8,000,000.00 $200,000,000.00 5.285% $37,000,000.00

NOTE! THIS IS A BIT TRICKY SINCE FINANCIAL DEPRECIATION AND TAX DEPRECIATION ARE DIFF SEE FIGURE 14.7 AND EQN 14.9. NOTE THAT DEPRECIATION IN FIGURE 14.7 IS FINANCIAL, NOT TAX, DEPRECIATION. a

INTEREST ON DEBT

$7,000,000.00

FINANCIAL DEPRECIATION CHARGE

$8,000,000.00

TAX DEPRECIATION CHARGE

$10,570,000.00

ANNUAL EXPENSE

$22,000,000.00

RETURN TO OWNERS

$10,820,000.00

REVENUE REQUIREMENT

$53,320,000.00

IAL DEPRECIATION AND TAX DEPRECIATION ARE DIFFERENT. IS FINANCIAL, NOT TAX, DEPRECIATION.

SEE EQN 14.9 REMEMBER, RETURN TO OWNERS IS ie*(1-c)*Bhatt-1

PROBLEM 14.41 INCOME TAX TAX RATE DEBT INTEREST ON DEBT FINANCIAL DEPRECIATION INITIAL INVESTMENT MACRS(20) PERCENTAGE TCBIT

$7,112,000.00 40.00% $100,000,000.00 9.00% $10,000,000.00 $250,000,000.00 4.888% $52,000,000.00

NOTE! THIS IS A BIT TRICKY SINCE FINANCIAL DEPRECIATION AND TAX DEPRECIATION ARE DIFF SEE FIGURE 14.7 AND EQN 14.9. NOTE THAT DEPRECIATION IN FIGURE 14.7 IS FINANCIAL, NOT TAX, DEPRECIATION. a

INTEREST ON DEBT

$9,000,000.00

FINANCIAL DEPRECIATION CHARGE

$10,000,000.00

TAX DEPRECIATION CHARGE

$12,220,000.00

ANNUAL EXPENSE

$33,000,000.00

RETURN TO OWNERS

$12,888,000.00

REVENUE REQUIREMENT

$72,000,000.00

IAL DEPRECIATION AND TAX DEPRECIATION ARE DIFFERENT. IS FINANCIAL, NOT TAX, DEPRECIATION.

SEE EQN 14.9 REMEMBER, RETURN TO OWNERS IS ie*(1-c)*Bhatt-1

PROBLEM 14.42 TAX RATE UNRECOVERED INVESTMENT PERCENT DEBT FINANCING INTEREST RATE ON DEBT ANNUAL EXPENSE DEPRECIATION WRITEOFF FIXED CHARGES

40.00% $40,000,000.00 30.00% 6.00% $2,500,000.00 $3,800,000.00 $8,800,000.00

SOME USEFUL CALCULATIONS: DEBT INTEREST ON DEBT FINANCING

$12,000,000.00 $720,000.00

TAXABLE INCOME

$4,280,000.00

INCOME TAX PAID

$1,712,000.00

EQUITY EARNINGS

$2,568,000.00

AMOUNT OF EQUITY FINANCING

$28,000,000.00

PERCENT RETURN ON EQUITY

REVENUE REQUIREMENT

$11,300,000.00

AFTER-TAX CASH FLOW

$6,368,000.00

9.17%

PROBLEM 14.43 TAX RATE UNRECOVERED INVESTMENT PERCENT DEBT FINANCING INTEREST RATE ON DEBT ANNUAL EXPENSE DEPRECIATION WRITEOFF FIXED CHARGES

40.00% $85,000,000.00 45.00% 8.00% $6,000,000.00 $7,800,000.00 $18,500,000.00

SOME USEFUL CALCULATIONS: DEBT INTEREST ON DEBT FINANCING

$38,250,000.00 $3,060,000.00

TAXABLE INCOME

$7,640,000.00

INCOME TAX PAID

$3,056,000.00

EQUITY EARNINGS

$4,584,000.00

AMOUNT OF EQUITY FINANCING

$46,750,000.00

PERCENT RETURN ON EQUITY

REVENUE REQUIREMENT

$24,500,000.00

AFTER-TAX CASH FLOW

$12,384,000.00

9.81%

PROBLEM 14.44 PERCENTAGE DEBT=

35.00%

EOY

UNRECOV BOOK INVEST

BOOK DEPR

UNRECOV TAX INVEST

TAX DEPR

DEBT RETURN

0 1 2 3 4 5

$90,000.00 $86,625.00 $80,127.90 $74,118.60 $68,559.30 $63,417.60

$3,375.00 $6,497.10 $6,009.30 $5,559.30 $5,141.70

$90,000.00 $86,625.00 $80,127.90 $74,118.60 $68,559.30 $63,417.60

$3,375.00 $6,497.10 $6,009.30 $5,559.30 $5,141.70

$1,890.00 $1,819.13 $1,682.69 $1,556.49 $1,439.75

AMOUNT OF INVESTMENT

$90,000.00

MACRS RECOVERY PERIOD

20 YEARS SINCE $3,375/$90,000 = 0.0375

COST OF BORROWED CAPITAL

6.00%

SINCE $1,890/(.35*$90,000) = 0.06

REVENUE REQUIREMENT YR 1

$31,965

SINCE RR = $15,000+$3,375+$1,890+$4,680+$7,020

EQUITY RETURN

INCOME TAX

ANNUAL EXPENSES

$7,020.00 $6,756.75 $6,249.98 $5,781.25 $5,347.63

$4,680.00 $4,504.50 $4,166.65 $3,854.17 $3,565.08

$15,000.00 $15,000.00 $15,000.00 $15,000.00 $15,000.00

3,375+$1,890+$4,680+$7,020

PROBLEM 14.45 a

PWRR(3)=

$41,439.40

ie=

16.4462%

PWRR=

$312,050.95

ie=

(WACC-(1-itr)*c*id)/(1-c)

SEE BELOW FOR DETAILS ALL ACTUAL VALUES P

INITIAL INVESTMENT

F C1

SALVAGE VALUE

YR 1 ANN EXPENSE

$9,000

ΔCt

INCREMENT ANN EXP DEBT RATIO COST OF DEBT

$0 48.00% 8.50%

RETURN ON EQUITY TAX RATE PROJECT BOOK LIFE

16.4462% 40.00% 25

c id ie itr n END OF YEAR t A 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

$170,000

SL BOOK UNRECOVERED TAX DEPRECIATION INVESTMENT DEPRECIATION dt B̂t d̂ t B C D $170,000.00 $6,800.00 $163,200.00 $6,375.00 $6,800.00 $156,400.00 $12,272.30 $6,800.00 $149,600.00 $11,350.90 $6,800.00 $142,800.00 $10,500.90 $6,800.00 $136,000.00 $9,712.10 $6,800.00 $129,200.00 $8,984.50 $6,800.00 $122,400.00 $8,309.60 $6,800.00 $115,600.00 $7,687.40 $6,800.00 $108,800.00 $7,585.40 $6,800.00 $102,000.00 $7,583.70 $6,800.00 $95,200.00 $7,585.40 $6,800.00 $88,400.00 $7,583.70 $6,800.00 $81,600.00 $7,585.40 $6,800.00 $74,800.00 $7,583.70 $6,800.00 $68,000.00 $7,585.40 $6,800.00 $61,200.00 $7,583.70 $6,800.00 $54,400.00 $7,585.40 $6,800.00 $47,600.00 $7,583.70 $6,800.00 $40,800.00 $7,585.40 $6,800.00 $34,000.00 $7,583.70 $6,800.00 $27,200.00 $3,792.70 $6,800.00 $20,400.00 $0.00 $6,800.00 $13,600.00 $0.00

<--SOLVER CHANGED CELL

EQUITY RETURN E $14,538.40 $13,956.86 $13,375.33 $12,793.79 $12,212.26 $11,630.72 $11,049.18 $10,467.65 $9,886.11 $9,304.58 $8,723.04 $8,141.50 $7,559.97 $6,978.43 $6,396.90 $5,815.36 $5,233.82 $4,652.29 $4,070.75 $3,489.22 $2,907.68 $2,326.14 $1,744.61

24 25

$6,800.00 $6,800.00

$6,800.00 $0.00

$0.00 $0.00

$1,163.07 $581.54

EXTRA ANALYSIS NOT REQUIRED BY PROBLEM. SEE SECTION 14.12 END OF YEAR t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

CAPITAL EXPENDITURE P

GROSS INCOME GIt

ANNUAL EXPENSES Ct

TAX DEPRECIATION dt

-$170,000.00

$0.00

$37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01 $37,053.01

$9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00 $9,000.00

$6,375.00 $12,272.30 $11,350.90 $10,500.90 $9,712.10 $8,984.50 $8,309.60 $7,687.40 $7,585.40 $7,583.70 $7,585.40 $7,583.70 $7,585.40 $7,583.70 $7,585.40 $7,583.70 $7,585.40 $7,583.70 $7,585.40 $7,583.70 $3,792.70 $0.00 $0.00 $0.00 $0.00

OR CAN BE SOLVED USING "SOLVER" AS SHOWN BELOW

NEEDED TO SHOW EQUIVALENCY BETWEEN REVENUE REQUIREMENTS AND ATCF METHODS GI1

YR 1 GROSS INCOME

$37,053.01

ΔGIt

INCREMENT ANN INC

$0.00

AFTER TAX RATE SUMMARY (CALCULATED VALUES)

OLVER CHANGED CELL AFTER-TAX COST OF DEBT RETURN ON EQUITY (ALREADY AFTER TAX) OVERALL AFTER-TAX COST OF CAPITAL

5.10% 16.45% 11.00% <--SOLVER TARGET CELL

DEBT PAYMENT

INCOME TAX Tt

ANNUAL EXPENSE Ct

REVENUE REQUIREMENT B+E+F+G+H

PW RR @ WACC

MACRS RATE %

$6,936.00 $6,658.56 $6,381.12 $6,103.68 $5,826.24 $5,548.80 $5,271.36 $4,993.92 $4,716.48 $4,439.04 $4,161.60 $3,884.16 $3,606.72 $3,329.28 $3,051.84 $2,774.40 $2,496.96 $2,219.52 $1,942.08 $1,664.64 $1,387.20 $1,109.76 $832.32

$9,975.60 $5,656.38 $5,882.95 $6,061.93 $6,200.10 $6,297.48 $6,359.72 $6,386.83 $6,067.14 $5,680.58 $5,291.76 $4,905.20 $4,516.38 $4,129.82 $3,741.00 $3,354.44 $2,965.62 $2,579.06 $2,190.23 $1,803.68 $3,943.32 $6,084.10 $5,696.41

$47,250.00 $42,071.80 $41,439.40 $40,759.40 $40,038.60 $39,277.00 $38,480.27 $37,648.40 $36,469.73 $35,224.20 $33,976.40 $32,730.87 $31,483.07 $30,237.53 $28,989.73 $27,744.20 $26,496.40 $25,250.87 $24,003.07 $22,757.53 $24,038.20 $25,320.00 $24,073.33

$42,567.57 $34,146.42 $30,300.13 $26,849.48 $23,760.96 $20,999.09 $18,534.34 $16,336.64 $14,256.92 $12,405.42 $10,780.14 $9,355.82 $8,107.34 $7,014.95 $6,058.98 $5,224.02 $4,494.65 $3,858.89 $3,304.69 $2,822.71 $2,686.08 $2,548.93 $2,183.27

3.750% 7.219% 6.677% 6.177% 5.713% 5.285% 4.888% 4.522% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 4.462% 4.461% 2.231%

YEAR t A

GROSS Income GIt

0 1 $37,053.01 2 $37,053.01 3 $37,053.01 4 $37,053.01 5 $37,053.01 6 $37,053.01 7 $37,053.01 8 $37,053.01 9 $37,053.01 10 $37,053.01 11 $37,053.01 12 $37,053.01 13 $37,053.01 14 $37,053.01 15 $37,053.01 16 $37,053.01 17 $37,053.01 18 $37,053.01 19 $37,053.01 20 $37,053.01 21 $37,053.01 22 $37,053.01 23 $37,053.01

$554.88 $277.44

$5,308.71 $4,921.02

LOAN DEBT PRINCIPLE PAYMENT LIt PAYMENT -$81,600.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00 $3,264.00

$9,000.00 $9,000.00 PWRR ARR CAPRR

$22,826.67 $1,865.05 $21,580.00 $1,588.46 $312,050.95 $312,050.95 $37,053.01 $37,053.01 $2,836,826.84 $2,836,826.84

TAXABLE INCOME Tit

INCOME TAX Tt

GIt-Ct-dt-LIt

itr*TIt

$14,742.01 $9,122.15 $10,320.99 $11,448.43 $12,514.67 $13,519.71 $14,472.05 $15,371.69 $15,751.13 $16,030.27 $16,306.01 $16,585.15 $16,860.89 $17,140.03 $17,415.77 $17,694.91 $17,970.65 $18,249.79 $18,525.53 $18,804.67 $22,873.11 $26,943.25 $27,220.69 $27,498.13 $27,775.57

$5,896.80 $3,648.86 $4,128.40 $4,579.37 $5,005.87 $5,407.88 $5,788.82 $6,148.68 $6,300.45 $6,412.11 $6,522.40 $6,634.06 $6,744.36 $6,856.01 $6,966.31 $7,077.96 $7,188.26 $7,299.92 $7,410.21 $7,521.87 $9,149.24 $10,777.30 $10,888.28 $10,999.25 $11,110.23

ATCF ATCFt

24 $37,053.01 25 $37,053.01

PWATCF EVAL AT ie

-$88,400.00 -$88,400.00 $11,956.21 $10,267.58 $14,481.59 $10,679.87 $14,279.49 $9,043.52 $14,105.96 $7,671.88 $13,956.90 $6,518.73 $13,832.33 $5,548.10 $13,728.83 $4,728.87 $13,646.41 $4,036.62 $13,772.08 $3,498.43 $13,937.86 $3,040.50 $14,105.01 $2,642.39 $14,270.79 $2,295.86 $14,437.93 $1,994.70 $14,603.72 $1,732.65 $14,770.86 $1,504.97 $14,936.65 $1,306.93 $15,103.79 $1,134.90 $15,269.57 $985.31 $15,436.72 $855.42 $15,602.50 $742.49 $14,252.57 $582.46 $12,901.95 $452.80 $13,068.41 $393.86 $13,234.88 $342.54 $13,401.34 $297.87 PWATCF(ie)= -$6,100.75

VER TARGET CELL

GROSS INCRev Reqs GIt-RRt

AFTER-TAX GIt-RRt

PW PW(GIt-RRt)

(1-t)*(GIt-RRt)

Eval at ie

-$10,196.99 -$5,018.79 -$4,386.39 -$3,706.39 -$2,985.59 -$2,223.99 -$1,427.26 -$595.39 $583.28 $1,828.81 $3,076.61 $4,322.14 $5,569.94 $6,815.48 $8,063.28 $9,308.81 $10,556.61 $11,802.14 $13,049.94 $14,295.48 $13,014.81 $11,733.01 $12,979.68

-$6,118.19 -$3,011.27 -$2,631.83 -$2,223.83 -$1,791.35 -$1,334.39 -$856.35 -$357.23 $349.97 $1,097.29 $1,845.97 $2,593.29 $3,341.97 $4,089.29 $4,837.97 $5,585.29 $6,333.97 $7,081.29 $7,829.97 $8,577.29 $7,808.89 $7,039.81 $7,787.81

-$5,254.10 -$2,220.75 -$1,666.80 -$1,209.49 -$836.67 -$535.22 -$294.97 -$105.67 $88.90 $239.37 $345.82 $417.20 $461.72 $485.17 $492.93 $488.70 $475.94 $456.94 $433.89 $408.18 $319.13 $247.06 $234.71

$14,226.34 $15,473.01

$8,535.81 $9,283.81 PWGI-RR(ie)=

$220.92 $206.35 -$6,100.75

PROBLEM 14.46 RR(1)=

$329,394.00

RR(2)=

$236,892.50

RR(3)=

$356,343.00

RR(4)=

$360,145.50

SEE BELOW FOR DETAILS ALL ACTUAL VALUES P F % C1

INITIAL INVESTMENT SALVAGE VALUE ANN EXP PERCENT ANNUAL EXPENSE

$780,000 $0 5.00% $39,000

ΔCt

INCREMENT ANN EXP DEBT RATIO COST OF DEBT

$0 45.00% 11.00%

AFTER TAX RATE SUMMAR

RETURN ON EQUITY TAX RATE PROJECT BOOK LIFE

14.00% 40.00% 4

AFTER-TAX COST OF DEB RETURN ON EQUITY (ALR OVERALL AFTER-TAX COS

c id ie itr n

END OF SL BOOK UNRECOVERED TAX EQUITY DEBT YEAR DEPRECIATION INVESTMENT DEPRECIATION RETURN PAYMENT dt t d̂ t B̂t A B C D E F 0 $780,000.00 1 $195,000.00 $585,000.00 $259,974.00 $60,060.00 $38,610.00 2 $195,000.00 $390,000.00 $346,710.00 $45,045.00 $28,957.50 3 $195,000.00 $195,000.00 $115,518.00 $30,030.00 $19,305.00 4 $195,000.00 $0.00 $57,798.00 $15,015.00 $9,652.50 SUM

$780,000.00

SUM

$780,000.00

AFTER TAX RATE SUMMARY (CALCULATED VALUES) AFTER-TAX COST OF DEBT RETURN ON EQUITY (ALREADY AFTER TAX) OVERALL AFTER-TAX COST OF CAPITAL INCOME TAX Tt G

ANNUAL REVENUE EXPENSE REQUIREMENT Ct B+E+F+G+H H I

-$3,276.00 $39,000.00 -$71,110.00 $39,000.00 $73,008.00 $39,000.00 $101,478.00 $39,000.00

6.60% 14.00% 10.67% PW RR @ WACC

MACRS RATE %

$329,394.00 $297,636.22 $236,892.50 $193,415.60 $356,343.00 $262,892.69 $360,145.50 $240,081.31 PWRR $994,025.81 ARR $122,141.82 CAPRR $9,316,080.67

33.33% 44.45% 14.81% 7.41%

PROBLEM 14.47 a

RR(1)=

$45,120.71

RR(2)=

$37,353.81

RR(3)=

$45,293.57

RR(4)=

$49,990.67

RR(5)=

$49,823.76

RR(6)=

$53,304.86

RR(7)=

$56,785.95

AWRR(ie)=

$47,327.32

SEE BELOW FOR DETAILS

ALL ACTUAL VALUES P

INITIAL INVESTMENT

F C1

SALVAGE VALUE YR 1 ANN EXPENSE

$20,000

ΔCt

INCREMENT ANN EXP DEBT RATIO COST OF DEBT

$2,000 45.00% 9.00%

RETURN ON EQUITY TAX RATE PROJECT BOOK LIFE

13.00% 40.00% 7

c id ie itr n END OF YEAR t A 0 1 2 3 4 5 6 7

END OF

$95,000 $0

SL BOOK UNRECOVERED TAX DEPRECIATION INVESTMENT DEPRECIATION dt B̂t d̂ t B C D $95,000.00 $13,571.43 $81,428.57 $19,000.00 $13,571.43 $67,857.14 $30,400.00 $13,571.43 $54,285.71 $18,240.00 $13,571.43 $40,714.29 $10,944.00 $13,571.43 $27,142.86 $10,944.00 $13,571.43 $13,571.43 $5,472.00 $13,571.43 $0.00 $0.00

CAPITAL

GROSS

ANNUAL

EQUITY RETURN E $6,792.50 $5,822.14 $4,851.79 $3,881.43 $2,911.07 $1,940.71 $970.36

TAX

YEAR t 0 1 2 3 4 5 6 7

EXPENDITURE P

INCOME GIt

EXPENSES Ct

DEPRECIATION dt

-$95,000.00

$0.00

$50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00

$20,000.00 $22,000.00 $24,000.00 $26,000.00 $28,000.00 $30,000.00 $32,000.00

$19,000.00 $30,400.00 $18,240.00 $10,944.00 $10,944.00 $5,472.00 $0.00

NEEDED TO SHOW EQUIVALENCY BETWEEN REVENUE REQUIREMENTS AND ATCF METHODS GI1

YR 1 GROSS INCOME

$50,000.00

ΔGIt

INCREMENT ANN INC

$0.00

AFTER TAX RATE SUMMARY (CALCULATED VALUES) AFTER-TAX COST OF DEBT RETURN ON EQUITY (ALREADY AFTER TAX) OVERALL AFTER-TAX COST OF CAPITAL

5.40% 13.00% 9.58%

DEBT PAYMENT

INCOME TAX Tt

ANNUAL EXPENSE Ct

REVENUE REQUIREMENT B+E+F+G+H

PW RR @ WACC

MACRS RATE %

$3,847.50 $3,297.86 $2,748.21 $2,198.57 $1,648.93 $1,099.29 $549.64

$909.29 -$7,337.62 $122.14 $4,339.24 $3,692.33 $6,693.43 $9,694.52

$20,000.00 $22,000.00 $24,000.00 $26,000.00 $28,000.00 $30,000.00 $32,000.00 PWRR AWRR CAPRR

$45,120.71 $37,353.81 $45,293.57 $49,990.67 $49,823.76 $53,304.86 $56,785.95 $233,630.31 $47,327.32 $2,438,729.79

$41,176.05 $31,108.02 $34,422.52 $34,670.79 $31,534.07 $30,787.82 $29,931.04 $233,630.31 $47,327.32 $2,438,729.79

LOAN

DEBT

TAXABLE

INCOME

20.00% 32.00% 19.20% 11.52% 11.52% 5.76%

YEAR t A 0 1 2 3 4 5 6 7

PRINCIPLE PAYMENT -$42,750.00 $6,107.14 $6,107.14 $6,107.14 $6,107.14 $6,107.14 $6,107.14 $6,107.14

PAYMENT LIt

$3,847.50 $3,297.86 $2,748.21 $2,198.57 $1,648.93 $1,099.29 $549.64

INCOME Tit

TAX Tt

GIt-Ct-dt-LIt

itr*TIt

$7,152.50 -$5,697.86 $5,011.79 $10,857.43 $9,407.07 $13,428.71 $17,450.36

$2,861.00 -$2,279.14 $2,004.71 $4,342.97 $3,762.83 $5,371.49 $6,980.14

ATCF ATCFt -$52,250.00 $17,184.36 $20,874.14 $15,139.93 $11,351.31 $10,481.10 $7,422.09 $4,363.07 PWATCF(ie)=

PWATCF EVAL AT ie

-$52,250.00 $15,207.40 $16,347.52 $10,492.73 $6,961.97 $5,688.72 $3,564.97 $1,854.57 $7,867.87 MATCHES PWGI-RR(ie) ABOV

GROSS INCOME GIt

GROSS INCREV REQS GIt-RRt

$50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00 $50,000.00

$4,879.29 $12,646.19 $4,706.43 $9.33 $176.24 -$3,304.86 -$6,785.95

AFTER-TAX GIt-RRt

PW PW(GIt-RRt)

(1-t)*(Gt-RRt)

EVAL AT ie

$2,927.57 $7,587.71 $2,823.86 $5.60 $105.74 -$1,982.91 -$4,071.57 PWGI-RR(ie)=

$2,590.77 $5,942.29 $1,957.07 $3.43 $57.39 -$952.43 -$1,730.66 $7,867.87 MATCHES PWATCF(ie) BELOW

A 1 INVESTMENT OPPORTUNITY 2 INITIAL INVESTMENT 3 ANNUAL RETURN 4 SALVAGE VALUE 5 PRESENT WORTH 6 INTERNAL RATE OF RETURN 7 VALUE OF x 8 PORTFOLIO INVESTMENT 9 PORTFOLIO PRESENT WORTH 10 MARR 11 INVESTMENT PERIOD 12 13 REALIZED INITIAL INVESTMENT 14 REALIZED ANNUAL RETURN 15 REALIZED SALVAGE VALUE 16 17 PORTFOLIO IRR

B C D E F G 1 2 3 4 5 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24 25.00% 20.00% 23.13% 22.50% 20.36% 0 0 1 1 0 $0.00 $0.00 $40,000.00 $50,000.00 $0.00 $90,000.00 $0.00 $0.00 $9,212.88 $10,111.69 $0.00 $19,324.57 18% CAP CONSTRAINT $100,000.00 10 $0.00 $0.00 $0.00 22.78%

$0.00 $40,000.00 $50,000.00 $0.00 $9,250.00 $11,250.00 $0.00 $40,000.00 $50,000.00

$0.00 $0.00 $0.00

$90,000.00 $20,500.00 $90,000.00

1 2 3 4 5 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24 25.00% 20.00% 23.13% 22.50% 20.36% 1 1 0 1 0 $15,000.00 $25,000.00 $0.00 $50,000.00 $0.00 $90,000.00 $4,718.79 $2,247.04 $0.00 $10,111.69 $0.00 $17,077.53 18% CAP CONSTRAINT $100,000.00 10 $15,000.00 $25,000.00 $3,750.00 $5,000.00 $15,000.00 $25,000.00 22.22%

$0.00 $50,000.00 $0.00 $11,250.00 $0.00 $50,000.00

$0.00 $0.00 $0.00

$90,000.00 $20,000.00 $90,000.00

A 1 INVESTMENT OPPORTUNITY 2 INITIAL INVESTMENT 3 ANNUAL RETURN 4 SALVAGE VALUE 5 PRESENT WORTH 6 INTERNAL RATE OF RETURN 7 VALUE OF x 8 PORTFOLIO INVESTMENT 9 PORTFOLIO PRESENT WORTH 10 MARR 11 INVESTMENT PERIOD 12 MUTUALLY EXCLUSIVE CONSTRAINT 13 14 REALIZED INITIAL INVESTMENT 15 REALIZED ANNUAL RETURN 16 REALIZED SALVAGE VALUE 17 18 PORTFOLIO IRR

1 2 3 4 5 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24 25.00% 20.00% 23.13% 22.50% 20.36% 1 1 1 0 0 $15,000.00 $25,000.00 $40,000.00 $0.00 $0.00 $80,000.00 $4,718.79 $2,247.04 $9,212.88 $0.00 $0.00 $16,178.71 18% CAP CONSTRAINT $100,000.00 10 1 $15,000.00 $25,000.00 $40,000.00 $3,750.00 $5,000.00 $9,250.00 $15,000.00 $25,000.00 $40,000.00 22.50%

$0.00 $0.00 $0.00

$80,000.00 $18,000.00 $80,000.00

A 1 EOY 2 0 3 1 4 2 5 3 6 4 7 5 8 PW 9 VALUE OF X 10 P'FOLIO INV 11 P'FOLIO PW 12 MARR 13 INV PERIOD 14 MUTUALLY EXCLUSIVE CONSTRAINT 15 EITHER/OR CONTINGENCY CONSTRAINT

CF(1) CF(2) CF(3) CF(4) CF(5) CF(6) CF(P'FOLIO) -$15,000.00 -$18,000.00 -$20,000.00 -$25,000.00 -$30,000.00 -$40,000.00 -$100,000.00 $4,500.00 $3,000.00 $4,000.00 $6,500.00 $6,000.00 $15,000.00 $30,000.00 $4,500.00 $4,500.00 $5,000.00 $6,500.00 $9,000.00 $15,000.00 $31,000.00 $4,500.00 $6,000.00 $6,000.00 $6,500.00 $12,000.00 $25,000.00 $42,000.00 $4,500.00 $7,500.00 $7,000.00 $6,500.00 $15,000.00 $0.00 $18,000.00 $4,500.00 $9,000.00 $8,000.00 $12,500.00 $0.00 $0.00 $25,000.00 $2,058.54 $3,665.06 $2,024.95 $3,365.64 $2,153.54 $4,815.93 $12,265.06 1 0 1 1 0 1 4 $15,000.00 $0.00 $20,000.00 $25,000.00 $0.00 $40,000.00 $100,000.00 $2,058.54 $0.00 $2,024.95 $3,365.64 $0.00 $4,815.93 $12,265.06 10.00% CAPITAL LIMIT $100,000.00 5 P'FOLIO IRR 14.94% 1 =B9+C9 2 =D9+E9

A 1 EOY 2 0 3 1 4 2 5 3 6 4 7 5 8 PW 9 VALUE OF X 10 P'FOLIO INV 11 P'FOLIO PW 12 MARR 13 INV PERIOD 14 MUTUALLY EXCLUSIVE CONSTRAINT 15 EITHER/OR CONTINGENCY CONSTRAINT

CF(1) CF(2) CF(3) CF(4) CF(5) CF(6) CF(P'FOLIO) -$15,000.00 -$18,000.00 -$20,000.00 -$25,000.00 -$30,000.00 -$40,000.00 -$83,000.00 $4,500.00 $3,000.00 $4,000.00 $6,500.00 $6,000.00 $15,000.00 $24,500.00 $4,500.00 $4,500.00 $5,000.00 $6,500.00 $9,000.00 $15,000.00 $26,000.00 $4,500.00 $6,000.00 $6,000.00 $6,500.00 $12,000.00 $25,000.00 $37,500.00 $4,500.00 $7,500.00 $7,000.00 $6,500.00 $15,000.00 $0.00 $14,000.00 $4,500.00 $9,000.00 $8,000.00 $12,500.00 $0.00 $0.00 $21,500.00 $2,058.54 $3,665.06 $2,024.95 $3,365.64 $2,153.54 $4,815.93 $11,846.63 0 1 0 1 0 1 3 $0.00 $18,000.00 $0.00 $25,000.00 $0.00 $40,000.00 $83,000.00 $0.00 $3,665.06 $0.00 $3,365.64 $0.00 $4,815.93 $11,846.63 10.00% CAPITAL LIMIT $100,000.00 5 P'FOLIO IRR 15.70% 1 =B9+C9 1 =D9+E9

A 1 EOY 2 0 3 1 4 2 5 3 6 4 7 5 8 PW 9 VALUE OF X 10 P'FOLIO INV 11 P'FOLIO PW 12 MARR 13 INV PERIOD 14 MUTUALLY EXCLUSIVE CONSTRAINT 15 EITHER/OR CONTINGENCY CONSTRAINT

CF(1) CF(2) CF(3) CF(4) CF(5) CF(6) CF(P'FOLIO) -$15,000.00 -$18,000.00 -$20,000.00 -$22,000.00 -$35,000.00 -$40,000.00 -$75,000.00 $4,500.00 $10,000.00 $4,000.00 $6,500.00 $6,000.00 $10,000.00 $25,000.00 $4,500.00 $7,500.00 $5,000.00 $6,000.00 $6,900.00 $10,000.00 $23,000.00 $4,500.00 $5,000.00 $6,000.00 $5,500.00 $7,935.00 $10,000.00 $21,000.00 $4,500.00 $2,500.00 $7,000.00 $5,000.00 $9,125.25 $10,000.00 $19,000.00 $4,500.00 $5,000.00 $8,000.00 $8,500.00 $15,494.04 $15,000.00 $26,000.00 $2,058.54 $5,857.97 $2,024.95 $1,692.90 -$2,028.04 $1,012.47 $11,634.36 1 1 1 1 0 0 4 $15,000.00 $18,000.00 $20,000.00 $22,000.00 $0.00 $0.00 $75,000.00 $2,058.54 $5,857.97 $2,024.95 $1,692.90 $0.00 $0.00 $11,634.36 10.00% CAPITAL LIMIT $100,000.00 5 P'FOLIO IRR 15.98% 2 =B9+C9 2 =D9+E9

1 ECONOMICALLY VIABLE INVESTMENTS SORTED BY IRR 2 INVESTMENT OPPORTUNITY 1 3 3 INITIAL INVESTMENT $15,000.00 $40,000.00 4 ANNUAL RETURN $3,750.00 $9,250.00 5 SALVAGE VALUE $15,000.00 $40,000.00 6 PRESENT WORTH $4,718.79 $9,212.88 7 INTERNAL RATE OF RETURN 25.00% 23.13% 8 VALUE OF x 1 1 9 PORTFOLIO INVESTMENT $15,000.00 $40,000.00 10 PORTFOLIO PRESENT WORTH $4,718.79 $9,212.88 11 MARR 18% 12 INVESTMENT PERIOD 10 13 14 REALIZED INITIAL INVESTMENT $15,000.00 $40,000.00 15 REALIZED ANNUAL RETURN $3,750.00 $9,250.00 16 REALIZED SALVAGE VALUE $15,000.00 $40,000.00 17 18 PORTFOLIO IRR 23.13%

4 5 2 $50,000.00 $70,000.00 $25,000.00 $11,250.00 $14,250.00 $5,000.00 $50,000.00 $70,000.00 $25,000.00 $10,111.69 $7,415.24 $2,247.04 22.50% 20.36% 20.00% 0.9 0 0 $45,000.00 $0.00 $0.00 $100,000.00 $9,100.52 $0.00 $0.00 $23,032.19 CAP CONSTRAINT $100,000.00

$45,000.00 $10,125.00 $45,000.00

$0.00 $0.00 $0.00

$0.00 $100,000.00 $0.00 $23,125.00 $0.00 $100,000.00

1 2 3 4 5 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24 25.00% 20.00% 23.13% 22.50% 20.36% 1 0 1 0.9 0 $15,000.00 $0.00 $40,000.00 $45,000.00 $0.00 $100,000.00 $4,718.79 $0.00 $9,212.88 $9,100.52 $0.00 $23,032.19 18% CAP CONSTRAINT $100,000.00 10 $15,000.00 $3,750.00 $15,000.00 23.13%

$0.00 $40,000.00 $45,000.00 $0.00 $9,250.00 $10,125.00 $0.00 $40,000.00 $45,000.00

$0.00 $100,000.00 $0.00 $23,125.00 $0.00 $100,000.00

1 2 3 4 5 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00 $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00 $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24 25.00% 20.00% 23.13% 22.50% 20.36% 1 0 1 0 0.642857143 $15,000.00 $0.00 $40,000.00 $0.00 $45,000.00 $100,000.00 $4,718.79 $0.00 $9,212.88 $0.00 $4,766.94 $18,698.61 18% CAP CONSTRAINT $100,000.00 10 $15,000.00 $3,750.00 $15,000.00

$0.00 $40,000.00 $0.00 $9,250.00 $0.00 $40,000.00

22.16% 1 B7+C7 1 D7+E7 1

$0.00 $0.00 $0.00

$45,000.00 $100,000.00 $9,160.71 $22,160.71 $45,000.00 $100,000.00

1 PROBLEM 15.1 2 3 TRUE 4 5 PW AND AW AND FW ARE ALL CONSISTENT MEASURES

1 PROBLEM 15.2 2 3 a OPTIMUM PORTFOLIO 4 5 b PRESENT WORTH 6 7 c PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RETURN 14 SALVAGE VALUE 15 PRESENT WORTH 16 INTERNAL RATE OF RETURN 17 VALUE OF x 18 PORTFOLIO INVESTMENT 19 PORTFOLIO PRESENT WORTH 20 MARR 21 INVESTMENT PERIOD 22 23 REALIZED INITIAL INVESTMENT 24 REALIZED ANNUAL RETURN 25 REALIZED SALVAGE VALUE 26 27 PORTFOLIO IRR 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

2, 4, 5 $43,617.79 16.94%

1 $75,000.00 $10,800.00 $75,000.00 $6,488.60 14.40% 0 $0.00 $0.00 12% 5 $0.00 $0.00 $0.00 16.94%

2 3 4 5 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $12,000.00 $7,500.00 $13,750.00 $15,750.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $15,140.06 $5,407.16 $14,959.82 $13,517.91 18.46% 15.00% 17.19% 15.75% 1 0 1 1 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00 $15,140.06 $0.00 $14,959.82 $13,517.91 $43,617.79 CAP CONSTRAINT $250,000.00

$65,000.00 $12,000.00 $65,000.00

$0.00 $80,000.00 $0.00 $13,750.00 $0.00 $80,000.00

$100,000.00 $245,000.00 $15,750.00 $41,500.00 $100,000.00 $245,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO

PRESENT WORTH

$43,617.79

PORTFOLIO IRR

16.94%

2, 4, 5

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $75,000.00 $10,800.00 $75,000.00 $6,488.60 14.40% 0 $0.00 $0.00 12% 5

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT

$65,000.00 $12,000.00 $65,000.00

16.94% 1 C58+F58

$0.00 $80,000.00 $0.00 $13,750.00 $0.00 $80,000.00

$100,000.00 $245,000.00 $15,750.00 $41,500.00 $100,000.00 $245,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

g CAP CONSTRAINT $200,000.00 $250,000.00 $300,000.00 h

MARR

9.60% 12.00% 14.40%

PORTFOLIO PW 2, 3, 4 $33,507.05 2, 4, 5 $43,617.79 2, 3, 4, 5 $49,000.00 2, 4, 5 2, 4, 5 2, 4, 5

$68,860.59 $43,617.79 $21,150.07

***

SEE BELOW FOR ONE SETUP *** INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $75,000.00 $10,800.00 $75,000.00 $0.00 14.40% 0 $0.00 $0.00 14.40% 5

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

16.94%

2 3 4 5 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $12,000.00 $7,500.00 $13,750.00 $15,750.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $8,976.88 $1,020.10 $7,582.74 $4,590.45 18.46% 15.00% 17.19% 15.75% 1 0 1 1 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00 $8,976.88 $0.00 $7,582.74 $4,590.45 $21,150.07 CAP CONSTRAINT $250,000.00

$65,000.00 $12,000.00 $65,000.00

$0.00 $80,000.00 $0.00 $13,750.00 $0.00 $80,000.00

$100,000.00 $245,000.00 $15,750.00 $41,500.00 $100,000.00 $245,000.00

1 PROBLEM 15.3 2 3 a OPTIMUM PORTFOLIO 4 5 PRESENT WORTH 6 7 PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RETURN 14 SALVAGE VALUE 15 PRESENT WORTH 16 INTERNAL RATE OF RETURN 17 VALUE OF x 18 PORTFOLIO INVESTMENT 19 PORTFOLIO PRESENT WORTH 20 MARR 21 INVESTMENT PERIOD 22 23 REALIZED INITIAL INVESTMENT 24 REALIZED ANNUAL RETURN 25 REALIZED SALVAGE VALUE 26 27 PORTFOLIO IRR 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

2, 4, 5 $567,672.40 27.50%

1 $350,000.00 $90,000.00 $350,000.00 $141,918.10 25.71% 0 $0.00 $0.00 15% 6 $0.00 $0.00 $0.00 27.50%

2 3 4 5 $300,000.00 $250,000.00 $500,000.00 $400,000.00 $85,000.00 $75,000.00 $130,000.00 $115,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00 $151,379.31 $141,918.10 $208,146.55 $208,146.55 28.33% 30.00% 26.00% 28.75% 1 0 1 1 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00 $151,379.31 $0.00 $208,146.55 $208,146.55 $567,672.40 CAP CONSTRAINT $1,250,000.00

$300,000.00 $85,000.00 $300,000.00

$0.00 $500,000.00 $0.00 $130,000.00 $0.00 $500,000.00

$400,000.00 $1,200,000.00 $115,000.00 $330,000.00 $400,000.00 $1,200,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO

PRESENT WORTH

$558,211.20

PORTFOLIO IRR

27.83%

3, 4, 5

1 $350,000.00 $90,000.00 $350,000.00 $141,918.10 25.71% 0 $0.00 $0.00 15% 6

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT

2 $300,000.00 $85,000.00 $300,000.00 $151,379.31 28.33% 0 $0.00 $0.00

3 $250,000.00 $75,000.00 $250,000.00 $141,918.10 30.00% 1 $250,000.00 $141,918.10

4 5 $500,000.00 $400,000.00 $130,000.00 $115,000.00 $500,000.00 $400,000.00 $208,146.55 $208,146.55 26.00% 28.75% 1 1 3 $500,000.00 $400,000.00 $1,150,000.00 $208,146.55 $208,146.55 $558,211.20 CAP CONSTRAINT $1,250,000.00

$0.00 $250,000.00 $500,000.00 $0.00 $75,000.00 $130,000.00 $0.00 $250,000.00 $500,000.00

27.83% 1 C58+D58+F58

$400,000.00 $1,150,000.00 $115,000.00 $320,000.00 $400,000.00 $1,150,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

g CAP CONSTRAINT $1,000,000.00 $1,250,000.00 $1,500,000.00

PORTFOLIO 2, 3, 5 2, 4, 5 2, 3, 4, 5

PW $501,443.96 $567,672.40 $709,590.51

2, 4, 5 2, 4, 5 2, 4, 5

$764,721.76 $567,672.40 $398,726.69

h MARR

12.00% 15.00% 18.00%

***

1 $350,000.00 $90,000.00 $350,000.00 $94,435.27 25.71% 0 $0.00 $0.00 18% 6

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

27.50%

2 3 4 5 $300,000.00 $250,000.00 $500,000.00 $400,000.00 $85,000.00 $75,000.00 $130,000.00 $115,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00 $108,425.68 $104,928.08 $139,904.10 $150,396.91 28.33% 30.00% 26.00% 28.75% 1 0 1 1 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00 $108,425.68 $0.00 $139,904.10 $150,396.91 $398,726.69 CAP CONSTRAINT $1,250,000.00

$300,000.00 $85,000.00 $300,000.00

$0.00 $500,000.00 $0.00 $130,000.00 $0.00 $500,000.00

$400,000.00 $1,200,000.00 $115,000.00 $330,000.00 $400,000.00 $1,200,000.00

1 PROBLEM 15.4 2 3 a OPTIMUM PORTFOLIO 4 5 b PRESENT WORTH 6 7 c PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RETURN 14 SALVAGE VALUE 15 PRESENT WORTH 16 INTERNAL RATE OF RETURN 17 VALUE OF x 18 PORTFOLIO INVESTMENT 19 PORTFOLIO PRESENT WORTH 20 MARR 21 INVESTMENT PERIOD 22 23 REALIZED INITIAL INVESTMENT 24 REALIZED ANNUAL RETURN 25 REALIZED SALVAGE VALUE 26 27 PORTFOLIO IRR 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

1, 2, 3, 4 $113,550.45 24.60%

1 $25,000.00 $7,500.00 $25,000.00 $16,221.49 30.00% 1 $25,000.00 $16,221.49 12% 5

2 $40,000.00 $12,000.00 $40,000.00 $25,954.39 30.00% 1 $40,000.00 $25,954.39

3 4 5 $85,000.00 $100,000.00 $65,000.00 $20,000.00 $22,000.00 $17,000.00 $85,000.00 $100,000.00 $65,000.00 $35,326.81 $36,047.76 $33,163.94 23.53% 22.00% 26.15% 1 1 0 $85,000.00 $100,000.00 $0.00 $250,000.00 $35,326.81 $36,047.76 $0.00 $113,550.45 CAP CONSTRAINT $250,000.00

$25,000.00 $7,500.00 $25,000.00

$40,000.00 $12,000.00 $40,000.00

$85,000.00 $100,000.00 $20,000.00 $22,000.00 $85,000.00 $100,000.00

24.60%

$0.00 $250,000.00 $0.00 $61,500.00 $0.00 $250,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO

PRESENT WORTH

$111,387.58

PORTFOLIO IRR

25.43%

1, 2, 4, 5

1 $25,000.00 $7,500.00 $25,000.00 $16,221.49 30.00% 1 $25,000.00 $16,221.49 12% 5

2 $40,000.00 $12,000.00 $40,000.00 $25,954.39 30.00% 1 $40,000.00 $25,954.39

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$25,000.00 $7,500.00 $25,000.00

$40,000.00 $12,000.00 $40,000.00

P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT CONTINGENCY CONSTRAINT

25.43% 1 E58+F58 2 C58+D58

3 4 5 $85,000.00 $100,000.00 $65,000.00 $20,000.00 $22,000.00 $17,000.00 $85,000.00 $100,000.00 $65,000.00 $35,326.81 $36,047.76 $33,163.94 23.53% 22.00% 26.15% 0 1 1 $0.00 $100,000.00 $65,000.00 $230,000.00 $0.00 $36,047.76 $33,163.94 $111,387.58 CAP CONSTRAINT $250,000.00

$0.00 $100,000.00 $0.00 $22,000.00 $0.00 $100,000.00

$65,000.00 $230,000.00 $17,000.00 $58,500.00 $65,000.00 $230,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

g CAP CONSTRAINT $200,000.00 $250,000.00 $300,000.00 h

MARR

9.60% 12.00% 14.40%

PORTFOLIO PW 2, 3, 5 $94,445.14 1, 2, 3, 4 $113,550.45 2, 3, 4, 5 $130,492.90 1, 2, 3, 4 1, 2, 3, 4 1, 2, 3, 5

$143,619.14 $113,550.45 $86,844.50

***

1 $25,000.00 $7,500.00 $25,000.00 $13,261.30 30.00% 1 $25,000.00 $13,261.30 14.40% 5

2 $40,000.00 $12,000.00 $40,000.00 $21,218.08 30.00% 1 $40,000.00 $21,218.08

3 4 5 $85,000.00 $100,000.00 $65,000.00 $20,000.00 $22,000.00 $17,000.00 $85,000.00 $100,000.00 $65,000.00 $26,386.58 $25,842.53 $25,978.54 23.53% 22.00% 26.15% 1 0 1 $85,000.00 $0.00 $65,000.00 $215,000.00 $26,386.58 $0.00 $25,978.54 $86,844.50 CAP CONSTRAINT $250,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$25,000.00 $7,500.00 $25,000.00

$40,000.00 $12,000.00 $40,000.00

$85,000.00 $20,000.00 $85,000.00

P'FOLIO IRR

26.28%

$0.00 $0.00 $0.00

$65,000.00 $215,000.00 $17,000.00 $56,500.00 $65,000.00 $215,000.00

1 PROBLEM 15.5 2 3 a OPTIMUM PORTFOLIO 4 5 b PRESENT WORTH 6 7 c PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RETURN 14 SALVAGE VALUE 15 PRESENT WORTH 16 INTERNAL RATE OF RETURN 17 VALUE OF x 18 PORTFOLIO INVESTMENT 19 PORTFOLIO PRESENT WORTH 20 MARR 21 INVESTMENT PERIOD 22 23 REALIZED INITIAL INVESTMENT 24 REALIZED ANNUAL RETURN 25 REALIZED SALVAGE VALUE 26 27 PORTFOLIO IRR 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

2, 5 $56,590.58 15.76%

1 2 3 4 5 $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $24,000.00 $22,000.00 $15,000.00 $25,000.00 $30,000.00 $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $27,382.54 $29,208.04 $13,691.27 $26,469.79 $27,382.54 16.00% 16.92% 15.00% 15.63% 15.00% 0 1 0 0 1 $0.00 $130,000.00 $0.00 $0.00 $200,000.00 $330,000.00 $0.00 $29,208.04 $0.00 $0.00 $27,382.54 $56,590.58 12% CAP CONSTRAINT $350,000.00 7 $0.00 $130,000.00 $0.00 $22,000.00 $0.00 $130,000.00 15.76%

$0.00 $0.00 $0.00

$0.00 $200,000.00 $330,000.00 $0.00 $30,000.00 $52,000.00 $0.00 $200,000.00 $330,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO

PRESENT WORTH

$56,590.58

PORTFOLIO IRR

16.43%

1, 2

1 2 3 4 5 $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $24,000.00 $22,000.00 $15,000.00 $25,000.00 $30,000.00 $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $27,382.54 $29,208.04 $13,691.27 $26,469.79 $27,382.54 16.00% 16.92% 15.00% 15.63% 15.00% 1 1 0 0 0 $150,000.00 $130,000.00 $0.00 $0.00 $0.00 $280,000.00 $27,382.54 $29,208.04 $0.00 $0.00 $0.00 $56,590.58 12% CAP CONSTRAINT $350,000.00 7

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $130,000.00 $24,000.00 $22,000.00 $150,000.00 $130,000.00

P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT

16.43% 1 D58+G58

$0.00 $0.00 $0.00

$0.00 $280,000.00 $0.00 $46,000.00 $0.00 $280,000.00

85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

CAP CONSTRAINT

$280,000.00 $350,000.00 $420,000.00

PORTFOLIO 1, 2 2, 5 1, 2, 3

PW $46,000.00 $56,590.58 $70,281.85

MARR

9.60% 12.00% 14.40%

1, 5 2, 5 1, 2

$100,637.36 $56,590.58 $24,062.77

***

1 2 3 4 5 $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $24,000.00 $22,000.00 $15,000.00 $25,000.00 $30,000.00 $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $10,167.37 $13,895.40 $2,541.84 $8,303.35 $5,083.68 16.00% 16.92% 15.00% 15.63% 15.00% 1 1 0 0 0 $150,000.00 $130,000.00 $0.00 $0.00 $0.00 $280,000.00 $10,167.37 $13,895.40 $0.00 $0.00 $0.00 $24,062.77 14.40% CAP CONSTRAINT $350,000.00 7

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $130,000.00 $24,000.00 $22,000.00 $150,000.00 $130,000.00

P'FOLIO IRR

16.43%

$0.00 $0.00 $0.00

$280,000.00 $46,000.00 $280,000.00

A 1 PROBLEM 15.6 2 3 a 4 5 b 6 7 c 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

OPTIMUM PORTFOLIO

1, 3, 4

PRESENT WORTH

$90,978.88

PORTFOLIO IRR

12.00%

1 2 3 4 5 $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $50,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00 $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $37,907.87 $22,744.72 $18,953.93 $34,117.08 $18,953.93 12.50% 12.00% 12.50% 11.50% 11.00% 1 0 1 1 0 $400,000.00 $0.00 $200,000.00 $600,000.00 $0.00 $1,200,000.00 $37,907.87 $0.00 $18,953.93 $34,117.08 $0.00 $90,978.88 10% CAP CONSTRAINT $1,250,000.00 5

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$400,000.00 $50,000.00 $400,000.00

PORTFOLIO IRR

12.00%

$0.00 $200,000.00 $600,000.00 $0.00 $25,000.00 $69,000.00 $0.00 $200,000.00 $600,000.00

$0.00 $1,200,000.00 $0.00 $144,000.00 $0.00 $1,200,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO

PRESENT WORTH

$79,606.52

PORTFOLIO IRR

12.33%

1, 2, 3

1 2 3 4 5 $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $50,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00 $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $37,907.87 $22,744.72 $18,953.93 $34,117.08 $18,953.93 12.50% 12.00% 12.50% 11.50% 11.00% 1 1 1 0 0 $400,000.00 $300,000.00 $200,000.00 $0.00 $0.00 $900,000.00 $37,907.87 $22,744.72 $18,953.93 $0.00 $0.00 $79,606.52 10% CAP CONSTRAINT $1,250,000.00 5

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$400,000.00 $300,000.00 $200,000.00 $50,000.00 $36,000.00 $25,000.00 $400,000.00 $300,000.00 $200,000.00

P'FOLIO IRR

12.33%

$0.00 $0.00 $0.00

$900,000.00 $111,000.00 $900,000.00

A 85 86 g 87 88 89 90 h 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

CAP CONSTRAINT $1,000,000.00 $1,250,000.00 $1,500,000.00 MARR

8.00% 10.00% 12.00%

PORTFOLIO PW 1, 2, 3 $79,606.52 1, 3, 4 $90,978.88 1, 2, 3, 4 $113,723.60 1, 3, 4 1, 3, 4 1, 3

$191,650.08 $90,978.88 $10,814.33

***

1 2 3 4 5 $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $50,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00 $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $7,209.55 $0.00 $3,604.78 -$10,814.33 -$18,023.88 12.50% 12.00% 12.50% 11.50% 11.00% 1 0 1 0 0 $400,000.00 $0.00 $200,000.00 $0.00 $0.00 $600,000.00 $7,209.55 $0.00 $3,604.78 $0.00 $0.00 $10,814.33 12% CAP CONSTRAINT $1,250,000.00 5

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$400,000.00 $50,000.00 $400,000.00

P'FOLIO IRR

12.50%

$0.00 $200,000.00 $0.00 $25,000.00 $0.00 $200,000.00

$0.00 $0.00 $0.00

$600,000.00 $75,000.00 $600,000.00

1 PROBLEM 15.7 2 3 a OPTIMUM PORTFOLIO 4 5 b PRESENT WORTH 6 7 c PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RETURN 14 SALVAGE VALUE 15 PRESENT WORTH 16 INTERNAL RATE OF RETURN 17 VALUE OF x 18 PORTFOLIO INVESTMENT 19 PORTFOLIO PRESENT WORTH 20 MARR 21 INVESTMENT PERIOD 22 23 REALIZED INITIAL INVESTMENT 24 REALIZED ANNUAL RETURN 25 REALIZED SALVAGE VALUE 26 27 PORTFOLIO IRR 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

2, 4, 5 $20,604.13 12.77%

1 $45,000.00 $4,000.00 $45,000.00 -$1,584.93 8.89% 0 $0.00 $0.00 10% 4 $0.00 $0.00 $0.00 12.77%

2 3 4 5 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $3,169.87 $1,584.93 $6,339.73 $11,094.53 11.67% 10.59% 12.00% 14.67% 1 0 1 1 $60,000.00 $0.00 $100,000.00 $75,000.00 $235,000.00 $3,169.87 $0.00 $6,339.73 $11,094.53 $20,604.13 CAP CONSTRAINT $250,000.00

$60,000.00 $7,000.00 $60,000.00

$0.00 $100,000.00 $0.00 $12,000.00 $0.00 $100,000.00

$75,000.00 $235,000.00 $11,000.00 $30,000.00 $75,000.00 $235,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO

PRESENT WORTH

$15,849.33

PORTFOLIO IRR

12.27%

2, 3, 5

1 $45,000.00 $4,000.00 $45,000.00 -$1,584.93 8.89% 0 $0.00 $0.00 10% 4

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR MUTUAL EXCLUSIVITH CONSTRAINT

2 3 4 5 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $3,169.87 $1,584.93 $6,339.73 $11,094.53 11.67% 10.59% 12.00% 14.67% 1 1 0 1 $60,000.00 $85,000.00 $0.00 $75,000.00 $220,000.00 $3,169.87 $1,584.93 $0.00 $11,094.53 $15,849.33 CAP CONSTRAINT $250,000.00

$60,000.00 $85,000.00 $7,000.00 $9,000.00 $60,000.00 $85,000.00

12.27% 1 F58+G58

$0.00 $0.00 $0.00

$75,000.00 $220,000.00 $11,000.00 $27,000.00 $75,000.00 $220,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113

CAP CONSTRAINT $200,000.00 $250,000.00 $300,000.00

MARR

8.00% 10.00% 12.00%

PORTFOLIO PW 4, 5 $17,434.26 2, 4, 5 $20,604.13 2, 4, 5 $20,604.13 2, 4, 5 2, 4, 5 4, 5

$37,095.82 $20,604.13 $6,074.70

***

1 $45,000.00 $4,000.00 $45,000.00 -$4,252.29 8.89% 0 $0.00 $0.00 12% 4

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

13.14%

2 3 4 5 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00 -$607.47 -$3,644.82 $0.00 $6,074.70 11.67% 10.59% 12.00% 14.67% 0 0 1 1 $0.00 $0.00 $100,000.00 $75,000.00 $175,000.00 $0.00 $0.00 $0.00 $6,074.70 $6,074.70 CAP CONSTRAINT $250,000.00

$0.00 $0.00 $0.00

$0.00 $100,000.00 $0.00 $12,000.00 $0.00 $100,000.00

$75,000.00 $175,000.00 $11,000.00 $23,000.00 $75,000.00 $175,000.00

1 PROBLEM 15.8 2 3 a OPTIMUM PORTFOLIO 4 5 b PRESENT WORTH 6 7 c PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RECEIPTS 14 ANNUAL DISBURSEMENTS 15 ANNUAL RETURN 16 SALVAGE VALUE 17 PRESENT WORTH 18 INTERNAL RATE OF RETURN 19 VALUE OF x 20 PORTFOLIO INVESTMENT 21 PORTFOLIO PRESENT WORTH 22 MARR 23 INVESTMENT PERIOD 24 25 REALIZED INITIAL INVESTMENT 26 REALIZED ANNUAL RETURN 27 REALIZED SALVAGE VALUE 28 29 PORTFOLIO IRR 30 31 32 33 34 35 36 37 38 39 40 41 42

2 $400,000.00 $230,000.00 $130,000.00 $100,000.00 $50,000.00 $233,733.88 21.94% 1 $400,000.00 $233,733.88

3 $450,000.00 $245,000.00 $140,000.00 $105,000.00 $60,000.00 $218,312.14 19.99% 0 $0.00 $0.00

2, 4 $530,720.51 21.99%

1 $300,000.00 $205,000.00 $125,000.00 $80,000.00 $50,000.00 $210,842.53 24.04% 0 $0.00 $0.00 10% 10

$0.00 $400,000.00 $0.00 $100,000.00 $0.00 $50,000.00 21.99%

4 5 $500,000.00 $600,000.00 $260,000.00 $290,000.00 $135,000.00 $150,000.00 $125,000.00 $140,000.00 $75,000.00 $75,000.00 $296,986.63 $289,155.14 22.04% 19.96% 1 0 $500,000.00 $0.00 $900,000.00 $296,986.63 $0.00 $530,720.51 CAP CONSTRAINT $1,000,000.00

$0.00 $500,000.00 $0.00 $125,000.00 $0.00 $75,000.00

$0.00 $0.00 $0.00

$900,000.00 $225,000.00 $125,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

2 $400,000.00 $230,000.00 $130,000.00 $100,000.00 $50,000.00 $233,733.88 21.94% 1 $400,000.00 $233,733.88

3 $450,000.00 $245,000.00 $140,000.00 $105,000.00 $60,000.00 $218,312.14 19.99% 0 $0.00 $0.00

$0.00 $400,000.00 $0.00 $100,000.00 $0.00 $50,000.00

$0.00 $0.00 $0.00

OPTIMUM PORTFOLIO

PRESENT WORTH

$522,889.02

PORTFOLIO IRR

20.75%

2, 5

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RECEIPTS ANNUAL DISBURSEMENTS ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT

1 $300,000.00 $205,000.00 $125,000.00 $80,000.00 $50,000.00 $210,842.53 24.04% 0 $0.00 $0.00 10% 10

20.75% 1 D62+F62

4 5 $500,000.00 $600,000.00 $260,000.00 $290,000.00 $135,000.00 $150,000.00 $125,000.00 $140,000.00 $75,000.00 $75,000.00 $296,986.63 $289,155.14 22.04% 19.96% 0 1 2 $0.00 $600,000.00 $1,000,000.00 $0.00 $289,155.14 $522,889.02 CAP CONSTRAINT $1,000,000.00

$0.00 $0.00 $0.00

$600,000.00 $1,000,000.00 $140,000.00 $240,000.00 $75,000.00 $125,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119

CAP CONSTRAINT

$800,000.00 $1,000,000.00 $1,200,000.00

MARR

8.00% 10.00% 12.00%

PORTFOLIO PW 1, 4 $507,829.17 2, 4 $530,720.51 1, 2, 4 $741,563.04 2, 5 2, 4 2, 4

$668,318.72 $530,720.51 $411,546.84

2 $400,000.00 $230,000.00 $130,000.00 $100,000.00 $50,000.00 $181,120.96 21.94% 1 $400,000.00 $181,120.96

3 $450,000.00 $245,000.00 $140,000.00 $105,000.00 $60,000.00 $162,591.81 19.99% 0 $0.00 $0.00

***

SEE BELOW FOR ONE SETUP *** INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RECEIPTS ANNUAL DISBURSEMENTS ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE P'FOLIO IRR

1 $300,000.00 $205,000.00 $125,000.00 $80,000.00 $50,000.00 $168,116.50 24.04% 0 $0.00 $0.00 12% 10

$0.00 $400,000.00 $0.00 $100,000.00 $0.00 $50,000.00 21.99%

4 5 $500,000.00 $600,000.00 $260,000.00 $290,000.00 $135,000.00 $150,000.00 $125,000.00 $140,000.00 $75,000.00 $75,000.00 $230,425.87 $215,179.22 22.04% 19.96% 1 0 $500,000.00 $0.00 $900,000.00 $230,425.87 $0.00 $411,546.84 CAP CONSTRAINT $1,000,000.00

$0.00 $500,000.00 $0.00 $125,000.00 $0.00 $75,000.00

$0.00 $0.00 $0.00

$900,000.00 $225,000.00 $125,000.00

A 1 PROBLEM 15.9 2 3 a 4 5 b 6 7 c 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

OPTIMUM PORTFOLIO PRESENT WORTH PORTFOLIO IRR

1, 4, 6, 7, 9, 10 $1,025,054.50 18.68%

1 $150,000.00 $35,000.00 $25,000.00 $74,698.43 20.15% 1 $150,000.00 $74,698.43 10% 10

2 $200,000.00 $38,000.00 $50,000.00 $52,770.71 15.37% 0 $0.00 $0.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$0.00 $0.00 $0.00

PORTFOLIO IRR

18.68%

3 $225,000.00 $45,000.00 $22,500.00 $60,180.24 15.72% 0 $0.00 $0.00

4 5 $275,000.00 $350,000.00 $60,000.00 $75,000.00 $27,500.00 $55,000.00 $104,276.47 $132,047.41 17.99% 17.81% 1 0 $275,000.00 $0.00 $104,276.47 $0.00

$0.00 $275,000.00 $0.00 $60,000.00 $0.00 $27,500.00

$0.00 $0.00 $0.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO

PRESENT WORTH

PORTFOLIO IRR

3 $225,000.00 $45,000.00 $22,500.00 $60,180.24 15.72% 0 $0.00 $0.00

4 $275,000.00 $60,000.00 $27,500.00 $104,276.47 17.99% 1 $275,000.00 $104,276.47

5 $350,000.00 $75,000.00 $55,000.00 $132,047.41 17.81% 1 $350,000.00 $132,047.41

1, 2, 4, 5, 6, 7, 9 $1,012,885.99 18.72%

1 $150,000.00 $35,000.00 $25,000.00 $74,698.43 20.15% 1 $150,000.00 $74,698.43 10% 10

2 $200,000.00 $38,000.00 $50,000.00 $52,770.71 15.37% 1 $200,000.00 $52,770.71

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$200,000.00 $38,000.00 $50,000.00

P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT CONTINGENCY CONSTRAINT

18.72% 1 C58+E58 2 D58+G58

$0.00 $275,000.00 $350,000.00 $0.00 $60,000.00 $75,000.00 $0.00 $27,500.00 $55,000.00

A 85 86 87 88 g 89 90 91 92 h 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

CAP CONSTRAINT

$2,000,000.00 $2,500,000.00 $3,000,000.00

PORTFOLIO 1, 5, 6, 7, 9 1, 4, 6, 7, 9, 10 1, 2, 4, 5, 6, 7, 9, 10

PW $855,838.81 $1,025,054.50 $1,209,872.63

MARR

8.00% 10.00% 12.00%

1, 4, 6, 7, 9, 10 1, 4, 6, 7, 9, 10 1, 4, 6, 7, 9, 10

$1,358,690.23 $1,025,054.50 $734,817.79

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $150,000.00 $35,000.00 $25,000.00 $55,807.14 20.15% 1 $150,000.00 $55,807.14 12% 10

2 $200,000.00 $38,000.00 $50,000.00 $30,807.14 15.37% 0 $0.00 $0.00

3 $225,000.00 $45,000.00 $22,500.00 $36,504.43 15.72% 0 $0.00 $0.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$0.00 $0.00 $0.00

P'FOLIO IRR

18.68%

***

SEE BELOW FOR ONE SETUP *** 4 5 $275,000.00 $350,000.00 $60,000.00 $75,000.00 $27,500.00 $55,000.00 $72,867.65 $91,475.26 17.99% 17.81% 1 0 $275,000.00 $0.00 $72,867.65 $0.00

$275,000.00 $60,000.00 $27,500.00

$0.00 $0.00 $0.00

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

6 $400,000.00 $95,000.00 $75,000.00 $212,649.62 20.73% 1 $400,000.00 $212,649.62

7 8 9 10 $475,000.00 $500,000.00 $550,000.00 $600,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 $220,179.55 $60,842.53 $216,263.80 $196,986.63 19.65% 12.56% 18.18% 16.91% 1 0 1 1 $475,000.00 $0.00 $550,000.00 $600,000.00 $2,450,000.00 $220,179.55 $0.00 $216,263.80 $196,986.63 $1,025,054.50 CAP CONSTRAINT $2,500,000.00

$400,000.00 $475,000.00 $95,000.00 $110,000.00 $75,000.00 $50,000.00

$0.00 $550,000.00 $0.00 $120,000.00 $0.00 $75,000.00

$600,000.00 $2,450,000.00 $125,000.00 $545,000.00 $75,000.00 $327,500.00

H 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

6 $400,000.00 $95,000.00 $75,000.00 $212,649.62 20.73% 1 $400,000.00 $212,649.62

7 8 9 10 $475,000.00 $500,000.00 $550,000.00 $600,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 $220,179.55 $60,842.53 $216,263.80 $196,986.63 19.65% 12.56% 18.18% 16.91% 1 0 1 0 7 $475,000.00 $0.00 $550,000.00 $0.00 $2,400,000.00 $220,179.55 $0.00 $216,263.80 $0.00 $1,012,885.99 CAP CONSTRAINT $2,500,000.00

$400,000.00 $475,000.00 $95,000.00 $110,000.00 $75,000.00 $50,000.00

$0.00 $550,000.00 $0.00 $120,000.00 $0.00 $75,000.00

$0.00 $2,400,000.00 $0.00 $533,000.00 $0.00 $357,500.00

H 85 86 87 88 89 90 91 92 93 94 95 96 97 98 6 99 $400,000.00 100 $95,000.00 101 $75,000.00 102 $160,919.18 103 20.73% 104 1 105 $400,000.00 106 $160,919.18 107 108 109 110 $400,000.00 111 $95,000.00 112 $75,000.00 113 114

7 8 9 10 $475,000.00 $500,000.00 $550,000.00 $600,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 $162,623.19 $12,466.28 $152,174.76 $130,425.87 19.65% 12.56% 18.18% 16.91% 1 0 1 1 $475,000.00 $0.00 $550,000.00 $600,000.00 $2,450,000.00 $162,623.19 $0.00 $152,174.76 $130,425.87 $734,817.79 CAP CONSTRAINT $2,500,000.00

$475,000.00 $110,000.00 $50,000.00

$0.00 $0.00 $0.00

$550,000.00 $600,000.00 $2,450,000.00 $120,000.00 $125,000.00 $545,000.00 $75,000.00 $75,000.00 $327,500.00

1 PROBLEM 15.10 2 3 a OPTIMUM PORTFOLIO 4 5 b PRESENT WORTH 6 7 c PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RETURN 14 SALVAGE VALUE 15 PRESENT WORTH 16 INTERNAL RATE OF RETURN 17 VALUE OF x 18 PORTFOLIO INVESTMENT 19 PORTFOLIO PRESENT WORTH 20 MARR 21 INVESTMENT PERIOD 22 23 REALIZED INITIAL INVESTMENT 24 REALIZED ANNUAL RETURN 25 REALIZED SALVAGE VALUE 26 27 PORTFOLIO IRR 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

2, 4, 5, 6 $9,950.82 11.42%

1 $25,000.00 $2,600.00 $25,000.00 $379.08 10.40% 0 $0.00 $0.00 10% 5

2 $35,000.00 $3,750.00 $35,000.00 $947.70 10.71% 1 $35,000.00 $947.70

3 $30,000.00 $3,050.00 $30,000.00 $189.54 10.17% 0 $0.00 $0.00

4 5 $40,000.00 $60,000.00 $4,775.00 $6,750.00 $40,000.00 $60,000.00 $2,937.86 $2,843.09 11.94% 11.25% 1 1 $40,000.00 $60,000.00 $2,937.86 $2,843.09 CAP CONSTRAINT

6 $50,000.00 $5,850.00 $50,000.00 $3,222.17 11.70% 1 $50,000.00 $3,222.17

$0.00 $0.00 $0.00

$35,000.00 $3,750.00 $35,000.00

$0.00 $0.00 $0.00

$40,000.00 $60,000.00 $4,775.00 $6,750.00 $40,000.00 $60,000.00

$50,000.00 $5,850.00 $50,000.00

11.42%

$185,000.00 $9,950.82 $200,000.00

$185,000.00 $21,125.00 $185,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

OPTIMUM PORTFOLIO PRESENT WORTH PORTFOLIO IRR

1, 2, 3, 4, 6 $7,676.34 11.13%

OPTIMUM PORTFOLIO PRESENT WORTH PORTFOLIO IRR

2, 4, 5, 6 $9,950.82 11.42%

OPTIMUM PORTFOLIO PRESENT WORTH PORTFOLIO IRR

2, 4, 5, 6 $9,950.82 11.42%

OPTIMUM PORTFOLIO PRESENT WORTH PORTFOLIO IRR

1, 2, 4, 6 $7,486.80 11.32%

1 $25,000.00 $2,600.00 $25,000.00 $379.08 10.40% 1 $25,000.00 $379.08 10% 5

2 $35,000.00 $3,750.00 $35,000.00 $947.70 10.71% 1 $35,000.00 $947.70

3 $30,000.00 $3,050.00 $30,000.00 $189.54 10.17% 0 $0.00 $0.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$25,000.00 $2,600.00 $25,000.00

$35,000.00 $3,750.00 $35,000.00

$0.00 $0.00 $0.00

P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT

11.32% 1 F68+G68

4 5 $40,000.00 $60,000.00 $4,775.00 $6,750.00 $40,000.00 $60,000.00 $2,937.86 $2,843.09 11.94% 11.25% 1 0 $40,000.00 $0.00 $2,937.86 $0.00 CAP CONSTRAINT

6 $50,000.00 $5,850.00 $50,000.00 $3,222.17 11.70% 1 $50,000.00 $3,222.17

$40,000.00 $4,775.00 $40,000.00

$50,000.00 $5,850.00 $50,000.00

$0.00 $0.00 $0.00

4 $150,000.00 $7,486.80 $200,000.00

$150,000.00 $16,975.00 $150,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164

CAP CONSTRAINT

MARR

PORTFOLIO $160,000.00 4, 5, 6 $200,000.00 2, 4, 5, 6 $240,000.00 1, 2, 3, 4, 5, 6 8.00% 10.00% 12.00%

PW $9,003.12 $9,950.82 $10,519.43

2, 4, 5, 6 2, 4, 5, 6 NONE

$25,253.89 $9,950.82 $0.00

***

1 $25,000.00 $2,600.00 $25,000.00 -$1,441.91 10.40% 0 $0.00 $0.00 12% 5

2 $35,000.00 $3,750.00 $35,000.00 -$1,622.15 10.71% 0 $0.00 $0.00

3 $30,000.00 $3,050.00 $30,000.00 -$1,982.63 10.17% 0 $0.00 $0.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

#NUM!

4 5 $40,000.00 $60,000.00 $4,775.00 $6,750.00 $40,000.00 $60,000.00 -$90.12 -$1,622.15 11.94% 11.25% 0 0 $0.00 $0.00 $0.00 $0.00 CAP CONSTRAINT

$0.00 $0.00 $0.00

6 $50,000.00 $5,850.00 $50,000.00 -$540.72 11.70% 0 $0.00 $0.00

$0.00 $0.00 $200,000.00

$0.00 $0.00 $0.00

THIS TABLE IS NOT AN ERROR - THE LAST ANALYSIS HAD NO PORTFOLIO

$0.00 $0.00 $0.00

1 PROBLEM 15.11 2 3 a OPTIMUM PORTFOLIO 1, 2, 4 4 5 b PRESENT WORTH $555,534.60 6 7 c PORTFOLIO IRR 27.73% 8 9 SEE BELOW FOR DETAILS 10 11 OVERALL 12 EOY CF(1) CF(2) CF(3) CF(4) P'FOLIO CF 13 0 -$50,000 -$125,000 -$200,000 -$250,000 -$425,000 14 1 -$100,000 -$75,000 $50,000 $75,000 -$100,000 15 2 $50,000 $70,000 $50,000 $75,000 $195,000 16 3 $50,000 $70,000 $50,000 $75,000 $195,000 17 4 $50,000 $70,000 $50,000 $75,000 $195,000 18 5 $50,000 $70,000 $75,000 $75,000 $195,000 19 6 $50,000 $70,000 $75,000 $85,000 $205,000 20 7 $50,000 $70,000 $75,000 $85,000 $205,000 21 8 $50,000 $70,000 $75,000 $85,000 $205,000 22 9 $50,000 $70,000 $75,000 $85,000 $205,000 23 10 $75,000 $100,000 $75,000 $100,000 $275,000 24 PRESENT WORTH $130,503 $184,868 $181,596 $240,163 $555,535 25 INTERNAL RATE OF RETURN 27.59% 26.85% 26.28% 28.51% 27.73% 26 VALUE OF x 1 1 0 1 27 PORTFOLIO INVESTMENT YR 0 $50,000.00 $125,000.00 $0.00 $250,000.00 $425,000.00 28 PORTFOLIO INVESTMENT YR 1 $100,000.00 $75,000.00 $0.00 $0.00 $175,000.00 29 PORTFOLIO PRESENT WORTH $130,503.30 $184,867.81 $0.00 $240,163.49 $555,534.60 30 MARR 10% CAP CONSTRAINT YR 0 $500,000.00 31 INVESTMENT PERIOD 10 CAP CONSTRAINT YR 1 $175,000.00 32 33 PORTFOLIO IRR 27.73% 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 d PORTFOLIO PW 53 CAP CONSTRAINT $400,000.00 1, 2, 3 $496,967.01 54 $500,000.00 1, 2, 4 $555,534.60 55 $600,000.00 2, 3, 4 $606,627.20 56

A 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

C MARR

8.00% 10.00% 12.00%

1, 2, 4 1, 2, 4 1, 2, 4

$669,914.98 $555,534.60 $456,393.23

***

SEE BELOW FOR ONE SETUP *** EOY 0 1 2 3 4 5 6 7 8 9 10 PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT YR 0 PORTFOLIO INVESTMENT YR 1 PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD P'FOLIO IRR

CF(1) CF(2) CF(3) CF(4) P'FOLIO CF -$50,000 -$125,000 -$200,000 -$250,000 -$425,000 -$100,000 -$75,000 $50,000 $75,000 -$100,000 $50,000 $70,000 $50,000 $75,000 $195,000 $50,000 $70,000 $50,000 $75,000 $195,000 $50,000 $70,000 $50,000 $75,000 $195,000 $50,000 $70,000 $75,000 $75,000 $195,000 $50,000 $70,000 $75,000 $85,000 $205,000 $50,000 $70,000 $75,000 $85,000 $205,000 $50,000 $70,000 $75,000 $85,000 $205,000 $50,000 $70,000 $75,000 $85,000 $205,000 $75,000 $100,000 $75,000 $100,000 $275,000 $106,632 $150,711 $147,833 $199,051 $456,393 27.59% 26.85% 26.28% 28.51% 27.73% 1 1 0 1 $50,000.00 $125,000.00 $0.00 $250,000.00 $425,000.00 $100,000.00 $75,000.00 $0.00 $0.00 $175,000.00 $106,631.91 $150,710.52 $0.00 $199,050.79 $456,393.23 12% CAP CONSTRAINT YR 0 $500,000.00 10 CAP CONSTRAINT YR 1 $175,000.00 27.73%

1 PROBLEM 15.12 2 3 a OPTIMUM ALTERNATIVE 4 5 PRESENT WORTH 6 7 PORTFOLIO IRR 8 9 SEE BELOW FOR DETAILS 10 11 INVESTMENT OPPORTUNITY 12 INITIAL INVESTMENT 13 ANNUAL RETURN 14 SALVAGE VALUE 15 PRESENT WORTH 16 INTERNAL RATE OF RETURN 17 NOTES 18 CURRENT BEST 19 20 MARR 21 INVESTMENT PERIOD 22 23 VALUE OF X 24 PRESENT WORTH OF PORTFOLIO 25 ALTERNATIVE 4 IS SELECTED 26 27 28 29 b OPTIMUM ALTERNATIVE 30 31 PRESENT WORTH 32 33 PORTFOLIO IRR 34 35 SEE BELOW FOR DETAILS 36 37 INVESTMENT OPPORTUNITY 38 INITIAL INVESTMENT 39 ANNUAL RETURN 40 SALVAGE VALUE 41 PRESENT WORTH 42 INTERNAL RATE OF RETURN 43 44 MARR 45 INVESTMENT PERIOD 46 47 VALUE OF X 48 PRESENT WORTH OF PORTFOLIO 49 50 MUTUAL EXCLUSIVITY CONSTRAINT 51 52 53 54 55 56

4 $3,722.84 13.55%

1 3 3-1 $40,000.00 $60,000.00 $20,000.00 $5,200.00 $7,500.00 $2,300.00 $40,000.00 $60,000.00 $20,000.00 $960.73 $720.55 -$240.18 13.00% 12.50% 11.50% >MARR <MARR 1 1 12% 3 0 $0.00

0 $0.00

4 $3,722.84 13.55%

1 2 3 $40,000.00 $80,000.00 $60,000.00 $5,200.00 $10,050.00 $7,500.00 $40,000.00 $80,000.00 $60,000.00 $960.73 $1,080.82 $720.55 13.00% 12.56% 12.50% 12% 3 0 $0.00

0 $0.00

1 C47+D47+E47+F47+G47+H47

A 57 58 59 60 61 62 63 64 65 66 67

1 2 3 4 5 6 7 8 9 10 11 2 2-1 4 4-2 6 6-4 5 5-4 12 $80,000.00 $40,000.00 $100,000.00 $20,000.00 $120,000.00 $20,000.00 $150,000.00 $50,000.00 13 $10,050.00 $4,850.00 $13,550.00 $3,500.00 $15,700.00 $2,150.00 $18,700.00 $5,150.00 14 $80,000.00 $40,000.00 $100,000.00 $20,000.00 $120,000.00 $20,000.00 $150,000.00 $50,000.00 15 $1,080.82 $120.09 $3,722.84 $2,642.01 $3,122.38 -$600.46 $1,681.28 -$2,041.56 16 12.56% 12.13% 13.55% 17.50% 13.08% 10.75% 12.47% 10.30% 17 >MARR >MARR <MARR <MARR 18 2 4 4 4 19 ALTERNATIVE 4 IS SELECTED 20 21 22 23 0 0 1 0 0 SUM OF X 1 24 $0.00 $3,722.84 $0.00 SUM OF PW $3,722.84 25 26 27 28 29 30 31 32 33 34 35 36 37 4 5 6 SUM 38 $100,000.00 $150,000.00 $120,000.00 $100,000.00 39 $13,550.00 $18,700.00 $15,700.00 $13,550.00 40 $100,000.00 $150,000.00 $120,000.00 $100,000.00 41 $3,722.84 $1,681.28 $3,122.38 $3,722.84 42 13.55% 12.47% 13.08% 13.55% 43 44 45 46 47 1 0 0 48 $3,722.84 $0.00 $0.00 49 47+F47+G47+H47 50 51 52 53 54 55 56

A 1 PROBLEM 15.13 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 b 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

OPTIMUM ALTERNATIVE

PRESENT WORTH

$2,653.55

PORTFOLIO IRR

11.00%

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN NOTES CURRENT BEST

1 3 3-1 2 $20,000.00 $30,000.00 $10,000.00 $40,000.00 $2,100.00 $3,050.00 $950.00 $4,400.00 $20,000.00 $30,000.00 $10,000.00 $40,000.00 $379.08 $189.54 -$189.54 $1,516.31 10.50% 10.17% 9.50% 11.00% >MARR <MARR 1 1

MARR INVESTMENT PERIOD

10% 5

VALUE OF X PRESENT WORTH OF PORTFOLIO ALTERNATIVE 4 IS SELECTED

0 $0.00

OPTIMUM ALTERNATIVE

0 $0.00

PRESENT WORTH

$2,653.55

PORTFOLIO IRR

11.00%

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN

1 2 3 4 $20,000.00 $40,000.00 $30,000.00 $50,000.00 $2,100.00 $4,400.00 $3,050.00 $5,700.00 $20,000.00 $40,000.00 $30,000.00 $50,000.00 $379.08 $1,516.31 $189.54 $2,653.55 10.50% 11.00% 10.17% 11.40%

MARR INVESTMENT PERIOD

10% 5

VALUE OF X PRESENT WORTH OF PORTFOLIO

0 $0.00

MUTUAL EXCLUSIVITY CONSTRAINTS

0 $0.00

1 $2,653.55

1 C46+D46+E46+F46+G46+H46

A 57 58 59 60 61 62 63 64 65 66

G 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

2-1 4 4-2 6 6-4 5 5-4 $20,000.00 $50,000.00 $10,000.00 $60,000.00 $10,000.00 $75,000.00 $25,000.00 $2,300.00 $5,700.00 $1,300.00 $6,650.00 $950.00 $8,200.00 $2,500.00 $20,000.00 $50,000.00 $10,000.00 $60,000.00 $10,000.00 $75,000.00 $25,000.00 $1,137.24 $2,653.55 $1,137.24 $2,464.01 -$189.54 $2,653.55 $0.00 11.50% 11.40% 13.00% 11.08% 9.50% 10.93% 10.00% >MARR >MARR <MARR <MARR =MARR 2 4 4 4 (OR 5) ALTERNATIVE 4 IS SELECTED

1 $2,653.55

0 $0.00

5 6 $75,000.00 $60,000.00 $8,200.00 $6,650.00 $75,000.00 $60,000.00 $2,653.55 $2,464.01 10.93% 11.08%

0 $0.00

$2,653.55

0 $0.00

SUM OF X SUM PW

1 $2,653.55

A 1 PROBLEM 15.14 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 b 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56

OPTIMUM ALTERNATIVE

PRESENT WORTH

$3,222.17

PORTFOLIO IRR

11.70%

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN NOTES CURRENT BEST

1 3 $25,000.00 $30,000.00 $2,600.00 $3,050.00 $25,000.00 $30,000.00 $379.08 $189.54 10.40% 10.17% >MARR 1

MARR INVESTMENT PERIOD

10% 5

VALUE OF X PRESENT WORTH OF PORTFOLIO

0 $0.00

OPTIMUM ALTERNATIVE

3-1 2 $5,000.00 $35,000.00 $450.00 $3,750.00 $5,000.00 $35,000.00 -$189.54 $947.70 9.00% 10.71% <MARR 1

COULD BE ANY NUMBER OF YEARS 0 $0.00

0 $0.00

PRESENT WORTH

$3,222.17

PORTFOLIO IRR

11.70%

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN MARR INVESTMENT PERIOD VALUE OF X PRESENT WORTH OF PORTFOLIO MUTUAL EXCLUSIVITY CONSTRAINT

1 2 3 4 $25,000.00 $35,000.00 $30,000.00 $40,000.00 $2,600.00 $3,750.00 $3,050.00 $4,775.00 $25,000.00 $35,000.00 $30,000.00 $40,000.00 $379.08 $947.70 $189.54 $2,937.86 10.40% 10.71% 10.17% 11.94% 10% 5 COULD BE ANY NUMBER OF YEARS 0 $0.00

0 $0.00

1 C45+D45+E45+F45+G45+H45

A 57 58 59 60 61 62 63 64 65

1 2 3 4 5 6 7 8 9 10 11 2-1 12 $10,000.00 13 $1,150.00 14 $10,000.00 15 $568.62 16 11.50% 17 >MARR 18 2 19 20 R OF YEARS 21 22 23 0 24 25 26 27 28 29 30 31 32 33 34 35 5 36 $60,000.00 37 $6,750.00 38 $60,000.00 39 $2,843.09 40 11.25% 41 42 R OF YEARS 43 44 45 0 46 $0.00 47 48 49 50 51 52 53 54 55 56

4 $40,000.00 $4,775.00 $40,000.00 $2,937.86 11.94%

0 $0.00

4-2 6 6-4 5 5-6 $5,000.00 $50,000.00 $10,000.00 $60,000.00 $10,000.00 $1,025.00 $5,850.00 $1,075.00 $6,750.00 $900.00 $5,000.00 $50,000.00 $10,000.00 $60,000.00 $10,000.00 $1,990.16 $3,222.17 $284.31 $2,843.09 -$379.08 20.50% 11.70% 10.75% 11.25% 9.00% >MARR >MARR <MARR 4 6 6 ALTERNATIVE 6 IS SELECTED

1 $3,222.17

6 $50,000.00 $5,850.00 $50,000.00 $3,222.17 11.70%

1 $3,222.17 SUM PW

$3,222.17

0 $0.00

SUM OF X SUM PW

1 $3,222.17

1 PROBLEM 15.15 2 3 a I21 (H11) NOTE! CELL LETTERS AND NUMBERS DO NOT CORRESPOND TO THE 4 PICTURE IN THE TEXT BECAUSE OF FORMATTING IN THIS SOLUTION. 5 b C19:H19 (B9:G9) 6 IT IS THE SAME PROBLEM, HOWEVER. 7 c C19:H19 = BINARY (B9:G9 = BINARY) 8 I20<= I22 (H10<=H12) 9 10 SEE BELOW FOR DETAILS 11 12 LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM 13 INVESTMENT OPPORTUNITY 1 2 3 4 5 6 14 INITIAL INVESTMENT $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00 15 ANNUAL RETURN $2,600.00 $5,025.00 $3,750.00 $6,775.00 $9,350.00 $7,850.00 16 SALVAGE VALUE $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00 17 PRESENT WORTH $1,130.04 $1,271.30 $847.53 $4,378.92 $1,977.58 $3,672.64 18 INTERNAL RATE OF RETURN 13.00% 12.56% 12.50% 13.55% 12.47% 13.08% 19 VALUE OF x 1 1 0 1 0 1 20 PORTFOLIO INVESTMENT $20,000.00 $40,000.00 $0.00 $50,000.00 $0.00 $60,000.00 21 PORTFOLIO PRESENT WORTH $1,130.04 $1,271.30 $0.00 $4,378.92 $0.00 $3,672.64 22 MARR 12% CAP CONSTRAINT 23 INVESTMENT PERIOD 10 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 ` 41 42 d SET UP CELL C58 AS THE SUM OF X1+X2

$170,000.00 $10,452.91 $175,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

REQUIRE CELL C58 TO BE <=1 SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD MUTUAL EXCLUSIVITY CONSTRAINT

1 2 3 $20,000.00 $40,000.00 $30,000.00 $2,600.00 $5,025.00 $3,750.00 $20,000.00 $40,000.00 $30,000.00 $1,130.04 $1,271.30 $847.53 13.00% 12.56% 12.50% 1 0 1 $20,000.00 $0.00 $30,000.00 $1,130.04 $0.00 $847.53 12% 10 1 C53+D53

4 5 6 $50,000.00 $75,000.00 $60,000.00 $6,775.00 $9,350.00 $7,850.00 $50,000.00 $75,000.00 $60,000.00 $4,378.92 $1,977.58 $3,672.64 13.55% 12.47% 13.08% 1 0 1 $50,000.00 $0.00 $60,000.00 $4,378.92 $0.00 $3,672.64 CAP CONSTRAINT

SET X2<=X3 AS A CONSTRAINT THAT IS THE D89<=E89 CONSTRAINT LISTED SEE BELOW FOR DETAILS LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM INVESTMENT OPPORTUNITY 1 2 3 4 5 6 INITIAL INVESTMENT $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00

$160,000.00 $10,029.15 $175,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

B ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

C $2,600.00 $20,000.00 $1,130.04 13.00% 1 $20,000.00 $1,130.04 12% 10

$5,025.00 $3,750.00 $40,000.00 $30,000.00 $1,271.30 $847.53 12.56% 12.50% 0 1 $0.00 $30,000.00 $0.00 $847.53

$6,775.00 $9,350.00 $7,850.00 $50,000.00 $75,000.00 $60,000.00 $4,378.92 $1,977.58 $3,672.64 13.55% 12.47% 13.08% 1 0 1 $50,000.00 $0.00 $60,000.00 $4,378.92 $0.00 $3,672.64 CAP CONSTRAINT

$160,000.00 $10,029.15 $175,000.00

LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM INVESTMENT OPPORTUNITY 1 2 3 4 5 6 INITIAL INVESTMENT $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00 ANNUAL RETURN $2,600.00 $5,025.00 $3,750.00 $6,775.00 $9,350.00 $7,850.00 SALVAGE VALUE $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00 PRESENT WORTH $1,130.04 $1,271.30 $847.53 $4,378.92 $1,977.58 $3,672.64 INTERNAL RATE OF RETURN 13.00% 12.56% 12.50% 13.55% 12.47% 13.08% VALUE OF x 1 1 0 1 0 1 PORTFOLIO INVESTMENT $20,000.00 $40,000.00 $0.00 $50,000.00 $0.00 $60,000.00

4 $170,000.00

SET SUM OF X'S TO <=4 AND SUM OF X'S >=3 THAT IS THE I125<=4 AND I25>=3 SEE BELOW FOR DETAILS

A 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146

B PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

C $1,130.04 12% 10

D $1,271.30

E $0.00

F $4,378.92

$0.00 $3,672.64 CAP CONSTRAINT

I $10,452.91 $175,000.00

1 PROBLEM 15.16 2 3 a I21 (H11) NOTE! CELL LETTERS AND NUMBERS DO NOT CORRESPOND TO THE 4 PICTURE IN THE TEXT BECAUSE OF FORMATTING IN THIS SOLUTION. 5 b C19:H19 (B9:G9) 6 IT IS THE SAME PROBLEM, HOWEVER. 7 c C19:H19 = BINARY (B9:G9 = BINARY) 8 I20<=I22 (H10<=H12) 9 10 SEE BELOW FOR DETAILS 11 12 LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM 13 INVESTMENT OPPORTUNITY 1 2 3 4 5 6 14 INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 15 ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00 16 SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 17 PRESENT WORTH $379.08 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17 18 INTERNAL RATE OF RETURN 10.40% 10.71% 10.17% 11.94% 11.25% 11.70% 19 VALUE OF x 1 0 0 1 1 1 20 PORTFOLIO INVESTMENT $25,000.00 $0.00 $0.00 $40,000.00 $60,000.00 $50,000.00 21 PORTFOLIO PRESENT WORTH $379.08 $0.00 $0.00 $2,937.86 $2,843.09 $3,222.17 22 MARR 10% CAP CONSTRAINT 23 INVESTMENT PERIOD 5 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 d DETERMINE X4+X5 40 THEN, SET X4+X5<=1 41 THIS IS THE C57<=1 CONSTRAINT 42

$175,000.00 $9,382.20 $180,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

1 2 $25,000.00 $35,000.00 $2,600.00 $3,750.00 $25,000.00 $35,000.00 $379.08 $947.70 10.40% 10.71% 1 1 $25,000.00 $35,000.00 $379.08 $947.70 10% 5 1 F51+G51

3 $30,000.00 $3,050.00 $30,000.00 $189.54 10.17% 1 $30,000.00 $189.54

4 $40,000.00 $4,775.00 $40,000.00 $2,937.86 11.94% 1 $40,000.00 $2,937.86

5 6 $60,000.00 $50,000.00 $6,750.00 $5,850.00 $60,000.00 $50,000.00 $2,843.09 $3,222.17 11.25% 11.70% 0 1 $0.00 $50,000.00 $0.00 $3,222.17 CAP CONSTRAINT

$180,000.00 $7,676.34 $180,000.00

1 $25,000.00 $2,600.00 $25,000.00 $379.08 10.40% 1 $25,000.00

3 $30,000.00 $3,050.00 $30,000.00 $189.54 10.17% 0 $0.00

4 $40,000.00 $4,775.00 $40,000.00 $2,937.86 11.94% 1 $40,000.00

5 6 $60,000.00 $50,000.00 $6,750.00 $5,850.00 $60,000.00 $50,000.00 $2,843.09 $3,222.17 11.25% 11.70% 1 1 $60,000.00 $50,000.00

$175,000.00

SET THE CONSTRAINT X6<=X5 THIS IS THE H83<=G83 CONSTRAINT SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT

2 $35,000.00 $3,750.00 $35,000.00 $947.70 10.71% 0 $0.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

B PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

$379.08 10% 5

$0.00

$2,937.86

$2,843.09 $3,222.17 CAP CONSTRAINT

$9,382.20 $180,000.00

1 $25,000.00 $2,600.00 $25,000.00 $379.08 10.40% 0 $0.00 $0.00 10% 5

2 $35,000.00 $3,750.00 $35,000.00 $947.70 10.71% 0 $0.00 $0.00

3 $30,000.00 $3,050.00 $30,000.00 $189.54 10.17% 0 $0.00 $0.00

4 $40,000.00 $4,775.00 $40,000.00 $2,937.86 11.94% 1 $40,000.00 $2,937.86

5 6 $60,000.00 $50,000.00 $6,750.00 $5,850.00 $60,000.00 $50,000.00 $2,843.09 $3,222.17 11.25% 11.70% 1 1 $60,000.00 $50,000.00 $2,843.09 $3,222.17 CAP CONSTRAINT

3 $150,000.00 $9,003.12 $180,000.00

DETERMINE THE SUM OF THE X'S SET THIS SUM = 3 THIS IS THE I115=3 CONSTRAINT SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

A 127 128 129 130 131 132 133 134 135 136

1 PROBLEM 15.17 2 3 FALSE 4 5 A COUNTEREXAMPLE TO THIS IS SHOWN IN THE TEXT

1 PROBLEM 15.18 2 3 TRUE 4 5

THIS IS BECAUSE WE ARE MAKING MULTIPLE INVESTMENTS AND EACH CAN BE ANY PERCENTAGE FROM 0% TO 100%

1 PROBLEM 15.19 2 3 a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR 4 OPTIMAL PORTFOLIO 2 4 5 6 PERCENT 100% 100% 7 8 TOTAL PW $44,158.51 9 10 TOTAL INVESTMENT $250,000.00 11 12 SEE BELOW FOR DETAILS 13 14 INVESTMENT OPPORTUNITY 1 2 15 INITIAL INVESTMENT $75,000.00 $65,000.00 16 ANNUAL RETURN $10,800.00 $12,000.00 17 SALVAGE VALUE $75,000.00 $65,000.00 18 PRESENT WORTH $6,488.60 $15,140.06 19 INTERNAL RATE OF RETURN 14.40% 18.46% 20 VALUE OF x 0 1 21 PORTFOLIO INVESTMENT $0.00 $65,000.00 22 PORTFOLIO PRESENT WORTH $0.00 $15,140.06 23 MARR 12% 24 INVESTMENT PERIOD 5 25 26 REALIZED INITIAL INVESTMENT $0.00 $65,000.00 27 REALIZED ANNUAL RETURN $0.00 $12,000.00 28 REALIZED SALVAGE VALUE $0.00 $65,000.00 29 30 P'FOLIO IRR 16.90% 31 32 b PORTFOLIO 33 CAP CONSTRAINT $200,000.00 2, 4, 5(55.00%) 34 $250,000.00 2, 4, 5, 3(10.00%) 35 $300,000.00 2, 4, 5, 3, 1(6.67%) 36 37 c MARR 9.60% 2, 4, 5, 3(10.00%) 38 12.00% 2, 4, 5, 3(10.00%) 39 14.40% 2, 4, 5, 3(10.00%) 40 41 SEE BELOW FOR ONE SETUP *** 42

100%

10%

3 $50,000.00 $7,500.00 $50,000.00 $5,407.16 15.00% 0.1 $5,000.00 $540.72

4 5 $80,000.00 $100,000.00 $13,750.00 $15,750.00 $80,000.00 $100,000.00 $14,959.82 $13,517.91 17.19% 15.75% 1 1 $80,000.00 $100,000.00 $250,000.00 $14,959.82 $13,517.91 $44,158.51 CAP CONSTRAINT $250,000.00

$5,000.00 $80,000.00 $100,000.00 $250,000.00 $750.00 $13,750.00 $15,750.00 $42,250.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00

PW $37,534.73 $44,158.51 $49,457.53 $69,894.65 $44,158.51 $21,252.08

***

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $75,000.00 $10,800.00 $75,000.00 $6,488.60 14.40% 0 $0.00 $0.00 12.00% 5

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

2 3 4 5 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $12,000.00 $7,500.00 $13,750.00 $15,750.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $15,140.06 $5,407.16 $14,959.82 $13,517.91 18.46% 15.00% 17.19% 15.75% 1 0.1 1 1.000 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00 $15,140.06 $540.72 $14,959.82 $13,517.91 $44,158.51 CAP CONSTRAINT $250,000.00

$65,000.00 $12,000.00 $65,000.00

$5,000.00 $80,000.00 $100,000.00 $250,000.00 $750.00 $13,750.00 $15,750.00 $42,250.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00

P'FOLIO IRR

16.90%

OPTIMAL PORTFOLIO

PERCENT

100%

10%

TOTAL PW

$44,158.51

TOTAL INVESTMENT

$250,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120

1 $75,000.00 $10,800.00 $75,000.00 $6,488.60 14.40% 0 $0.00 $0.00 12.00% 5

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

16.90%

2 3 4 5 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $12,000.00 $7,500.00 $13,750.00 $15,750.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00 $15,140.06 $5,407.16 $14,959.82 $13,517.91 18.46% 15.00% 17.19% 15.75% 1 0.1 1 1 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00 $15,140.06 $540.72 $14,959.82 $13,517.91 $44,158.51 CAP CONSTRAINT $250,000.00

$65,000.00 $12,000.00 $65,000.00

$5,000.00 $80,000.00 $100,000.00 $250,000.00 $750.00 $13,750.00 $15,750.00 $42,250.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00

1 PROBLEM 15.20 2 3 a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR 4 OPTIMAL PORTFOLIO 3 5 5 6 PERCENT 100% 100% 7 8 TOTAL PW $626,331.89 9 10 TOTAL INVESTMENT $1,250,000.00 11 12 SEE BELOW FOR DETAILS 13 14 INVESTMENT OPPORTUNITY 1 2 15 INITIAL INVESTMENT $350,000.00 $300,000.00 16 ANNUAL RETURN $90,000.00 $85,000.00 17 SALVAGE VALUE $350,000.00 $300,000.00 18 PRESENT WORTH $141,918.10 $151,379.31 19 INTERNAL RATE OF RETURN 25.71% 28.33% 20 VALUE OF x 0 1 21 PORTFOLIO INVESTMENT $0.00 $300,000.00 22 PORTFOLIO PRESENT WORTH $0.00 $151,379.31 23 MARR 15% 24 INVESTMENT PERIOD 6 25 26 REALIZED INITIAL INVESTMENT $0.00 $300,000.00 27 REALIZED ANNUAL RETURN $0.00 $85,000.00 28 REALIZED SALVAGE VALUE $0.00 $300,000.00 29 30 P'FOLIO IRR 28.24% 31 32 33 b PORTFOLIO 34 CAP CONSTRAINT $1,000,000.00 3, 5, 2, 4(10%) 35 $1,250,000.00 3, 5, 2, 4(60%) 36 $1,500,000.00 3, 5, 2, 4, 1(14.29%) 37 38 c MARR 12.00% 3, 5, 2, 4(60%) 39 15.00% 3, 5, 2, 4(60%) 40 18.00% 3, 5, 2, 4(60%) 41 42 SEE BELOW FOR ONE SETUP ***

100%

60%

3 $250,000.00 $75,000.00 $250,000.00 $141,918.10 30.00% 1 $250,000.00 $141,918.10

4 5 $500,000.00 $400,000.00 $130,000.00 $115,000.00 $500,000.00 $400,000.00 $208,146.55 $208,146.55 26.00% 28.75% 0.6 1 $300,000.00 $400,000.00 $1,250,000.00 $124,887.93 $208,146.55 $626,331.89 CAP CONSTRAINT $1,250,000.00

$250,000.00 $300,000.00 $400,000.00 $1,250,000.00 $75,000.00 $78,000.00 $115,000.00 $353,000.00 $250,000.00 $300,000.00 $400,000.00 $1,250,000.00

PW $522,258.61 $626,331.89 $729,864.52 $834,615.69 $626,331.89 $447,693.13

***

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $350,000.00 $90,000.00 $350,000.00 $141,918.10 25.71% 0 $0.00 $0.00 15% 6

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

2 $300,000.00 $85,000.00 $300,000.00 $151,379.31 28.33% 1 $300,000.00 $151,379.31

E 3 $250,000.00 $75,000.00 $250,000.00 $141,918.10 30.00% 1 $250,000.00 $141,918.10

$300,000.00 $250,000.00 $300,000.00 $400,000.00 $1,250,000.00 $85,000.00 $75,000.00 $78,000.00 $115,000.00 $353,000.00 $300,000.00 $250,000.00 $300,000.00 $400,000.00 $1,250,000.00

P'FOLIO IRR

28.24%

OPTIMAL PORTFOLIO

PERCENT

100%

60%

TOTAL PW

$626,331.89

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122

B TOTAL INVESTMENT

$1,250,000.00

1 $350,000.00 $90,000.00 $350,000.00 $141,918.10 25.71% 0 $0.00 $0.00 15% 6

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

28.24%

2 $300,000.00 $85,000.00 $300,000.00 $151,379.31 28.33% 1 $300,000.00 $151,379.31

3 $250,000.00 $75,000.00 $250,000.00 $141,918.10 30.00% 1 $250,000.00 $141,918.10

$300,000.00 $250,000.00 $300,000.00 $400,000.00 $1,250,000.00 $85,000.00 $75,000.00 $78,000.00 $115,000.00 $353,000.00 $300,000.00 $250,000.00 $300,000.00 $400,000.00 $1,250,000.00

1 PROBLEM 15.21 2 3 a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR 4 OPTIMAL PORTFOLIO 1 2 5 5 6 PERCENT 100% 100% 100% 7 8 TOTAL PW $123,283.35 9 10 TOTAL INVESTMENT $250,000.00 11 12 SEE BELOW FOR DETAILS 13 14 INVESTMENT OPPORTUNITY 1 2 3 15 INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 16 ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 17 SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 18 PRESENT WORTH $16,221.49 $25,954.39 $35,326.81 19 INTERNAL RATE OF RETURN 30.00% 30.00% 23.53% 20 VALUE OF x 1 1 1 21 PORTFOLIO INVESTMENT $25,000.00 $40,000.00 $85,000.00 22 PORTFOLIO PRESENT WORTH $16,221.49 $25,954.39 $35,326.81 23 MARR 12% 24 INVESTMENT PERIOD 5 25 26 REALIZED INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 27 REALIZED ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 28 REALIZED SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 29 30 P'FOLIO IRR 25.68% 31 32 33 34 35 36 37 38 b PORTFOLIO PW 39 CAP CONSTRAINT $200,000.00 1, 2, 5, 3(82.36% $104,432.49 40 $250,000.00 1, 2, 5, 3, 4(35%) $123,283.35 41 $300,000.00 1, 2, 5, 3, 4(85%) $141,307.23 42

100%

35%

4 $100,000.00 $22,000.00 $100,000.00 $36,047.76 22.00% 0.35 $35,000.00 $12,616.72

5 $65,000.00 $17,000.00 $65,000.00 $33,163.94 26.15% 1 $65,000.00 $250,000.00 $33,163.94 $123,283.35 CAP CONSTRAINT $250,000.00

$35,000.00 $7,700.00 $35,000.00

$65,000.00 $250,000.00 $17,000.00 $64,200.00 $65,000.00 $250,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

C MARR

9.60% 12.00% 14.40%

1, 2, 5, 3, 4(35%) 1, 2, 5, 3, 4(35%) 1, 2, 5, 3, 4(35%)

$153,959.71 $123,283.35 $95,889.39

***

SEE BELOW FOR ONE SETUP ***

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $25,000.00 $7,500.00 $25,000.00 $13,261.30 30.00% 1 $25,000.00 $13,261.30 14.40% 5

2 $40,000.00 $12,000.00 $40,000.00 $21,218.08 30.00% 1 $40,000.00 $21,218.08

3 $85,000.00 $20,000.00 $85,000.00 $26,386.58 23.53% 1 $85,000.00 $26,386.58

4 $100,000.00 $22,000.00 $100,000.00 $25,842.53 22.00% 0.35 $35,000.00 $9,044.89

5 $65,000.00 $17,000.00 $65,000.00 $25,978.54 26.15% 1 $65,000.00 $250,000.00 $25,978.54 $95,889.39 CAP CONSTRAINT $250,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$25,000.00 $7,500.00 $25,000.00

$40,000.00 $12,000.00 $40,000.00

$85,000.00 $20,000.00 $85,000.00

$35,000.00 $7,700.00 $35,000.00

$65,000.00 $250,000.00 $17,000.00 $64,200.00 $65,000.00 $250,000.00

P'FOLIO IRR

25.68%

OPTIMAL PORTFOLIO

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

PERCENT

100%

TOTAL PW

$113,550.45

TOTAL INVESTMENT

$250,000.00

1 $25,000.00 $7,500.00 $25,000.00 $16,221.49 30.00% 1 $25,000.00 $16,221.49 12% 5

2 $40,000.00 $12,000.00 $40,000.00 $25,954.39 30.00% 1 $40,000.00 $25,954.39

3 $85,000.00 $20,000.00 $85,000.00 $35,326.81 23.53% 1 $85,000.00 $35,326.81

4 $100,000.00 $22,000.00 $100,000.00 $36,047.76 22.00% 1 $100,000.00 $36,047.76

5 $65,000.00 $17,000.00 $65,000.00 $33,163.94 26.15% 0 $0.00 $250,000.00 $0.00 $113,550.45 CAP CONSTRAINT $250,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$25,000.00 $7,500.00 $25,000.00

$40,000.00 $12,000.00 $40,000.00

$85,000.00 $20,000.00 $85,000.00

$100,000.00 $22,000.00 $100,000.00

$0.00 $250,000.00 $0.00 $61,500.00 $0.00 $250,000.00

P'FOLIO IRR

24.60%

A 1 PROBLEM 15.22 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 b 35 36 37 38 c 39 40 41 42

LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR OPTIMAL PORTFOLIO 2 1 PERCENT

100%

TOTAL PW

$68,171.11

TOTAL INVESTMENT

$350,000.00

100%

4 43.75%

1 $150,000.00 $24,000.00 $150,000.00 $27,382.54 16.00% 1 $150,000.00 $27,382.54 12% 7

2 3 4 5 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $22,000.00 $15,000.00 $25,000.00 $30,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $29,208.04 $13,691.27 $26,469.79 $27,382.54 16.92% 15.00% 15.63% 15.00% 1 0 0.4375 0 $130,000.00 $0.00 $70,000.00 $0.00 $350,000.00 $29,208.04 $0.00 $11,580.53 $0.00 $68,171.11 CAP CONSTRAINT $350,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $24,000.00 $150,000.00

$130,000.00 $22,000.00 $130,000.00

$0.00 $0.00 $0.00

PORTFOLIO CAP CONSTRAINT $280,000.00 2, 1 $350,000.00 2, 1, 4(43.75%) $420,000.00 2, 1, 4(87.5%)

PW $56,590.58 $68,171.11 $79,751.65

P'FOLIO IRR

$70,000.00 $10,937.50 $70,000.00

16.27%

MARR

SEE BELOW FOR ONE SETUP ***

9.60% 2, 1, 4(43.75%) 12.00% 2, 1, 4(43.75%) 14.40% 2, 1, 4(43.75%)

$115,128.65 $68,171.11 $27,695.48

***

$0.00 $350,000.00 $0.00 $56,937.50 $0.00 $350,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $150,000.00 $24,000.00 $150,000.00 $27,382.54 16.00% 1 $150,000.00 $27,382.54 12.00% 7

2 3 4 5 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $22,000.00 $15,000.00 $25,000.00 $30,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $29,208.04 $13,691.27 $26,469.79 $27,382.54 16.92% 15.00% 15.63% 15.00% 1 0 0 0 $130,000.00 $0.00 $0.00 $0.00 $280,000.00 $29,208.04 $0.00 $0.00 $0.00 $56,590.58 CAP CONSTRAINT $280,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $24,000.00 $150,000.00

$130,000.00 $22,000.00 $130,000.00

$0.00 $0.00 $0.00

P'FOLIO IRR

16.43%

OPTIMAL PORTFOLIO

PERCENT

100%

40%

TOTAL PW

$66,630.85

$0.00 $0.00 $0.00

$0.00 $280,000.00 $0.00 $46,000.00 $0.00 $280,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122

B TOTAL INVESTMENT

$350,000.00

1 $150,000.00 $24,000.00 $150,000.00 $27,382.54 16.00% 0.4 $60,000.00 $10,953.02 12% 7

2 3 4 5 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $22,000.00 $15,000.00 $25,000.00 $30,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00 $29,208.04 $13,691.27 $26,469.79 $27,382.54 16.92% 15.00% 15.63% 15.00% 1 0 1 0 $130,000.00 $0.00 $160,000.00 $0.00 $350,000.00 $29,208.04 $0.00 $26,469.79 $0.00 $66,630.85 CAP CONSTRAINT $350,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$60,000.00 $9,600.00 $60,000.00

$130,000.00 $22,000.00 $130,000.00

P'FOLIO IRR

16.17%

$0.00 $160,000.00 $0.00 $25,000.00 $0.00 $160,000.00

$0.00 $350,000.00 $0.00 $56,600.00 $0.00 $350,000.00

1 PROBLEM 15.23 2 3 a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR 4 OPTIMAL PORTFOLIO 1 3 5 6 PERCENT 100% 100% 7 8 TOTAL PW $99,508.15 9 10 TOTAL INVESTMENT $1,250,000.00 11 12 SEE BELOW FOR DETAILS 13 14 INVESTMENT OPPORTUNITY 1 2 15 INITIAL INVESTMENT $400,000.00 $300,000.00 16 ANNUAL RETURN $50,000.00 $36,000.00 17 SALVAGE VALUE $400,000.00 $300,000.00 18 PRESENT WORTH $37,907.87 $22,744.72 19 INTERNAL RATE OF RETURN 12.50% 12.00% 20 VALUE OF x 1 1 21 PORTFOLIO INVESTMENT $400,000.00 $300,000.00 22 PORTFOLIO PRESENT WORTH $37,907.87 $22,744.72 23 MARR 10% 24 INVESTMENT PERIOD 5 25 26 REALIZED INITIAL INVESTMENT $400,000.00 $300,000.00 27 REALIZED ANNUAL RETURN $50,000.00 $36,000.00 28 REALIZED SALVAGE VALUE $400,000.00 $300,000.00 29 30 P'FOLIO IRR 12.10% 31 32 LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR 33 ALTERNATIVE 34 PERCENT 35 TOTAL PW 36 TOTAL INVESTMENT 37 38 39 b PORTFOLIO 40 CAP CONSTRAINT $1,000,000.00 1, 3, 2, 4(16.67%) 41 $1,250,000.00 1, 3, 2, 4(58.33%) 42 $1,500,000.00 1, 3, 2, 4

100.00%

58.33%

3 4 5 $200,000.00 $600,000.00 $500,000.00 $25,000.00 $69,000.00 $55,000.00 $200,000.00 $600,000.00 $500,000.00 $18,953.93 $34,117.08 $18,953.93 12.50% 11.50% 11.00% 1 0.583333333 0 $200,000.00 $350,000.00 $0.00 $1,250,000.00 $18,953.93 $19,901.63 $0.00 $99,508.15 CAP CONSTRAINT $1,250,000.00

$200,000.00 $25,000.00 $200,000.00

PW $85,292.70 $99,508.15 $113,723.60

$350,000.00 $40,250.00 $350,000.00

$0.00 $1,250,000.00 $0.00 $151,250.00 $0.00 $1,250,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

C MARR

8.00% 1, 3, 2, 4(58.33%) 10.00% 1, 3, 2, 4(58.33%) 12.00% 1, 3, 2

$204,626.39 *** $99,508.15 $10,814.33 NOTE! INVESTMENTS 4 AND 5 HAVE IRR<MARR=12% THIS PRECLUDES THEIR INCLUSION

1 $400,000.00 $50,000.00 $400,000.00 $71,868.78 12.50% 1 $400,000.00 $71,868.78 8.00% 5

2 3 4 5 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $47,912.52 $35,934.39 $83,846.91 $59,890.65 12.00% 12.50% 11.50% 11.00% 1 1 0.583333333 0 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00 $47,912.52 $35,934.39 $48,910.70 $0.00 $204,626.39 CAP CONSTRAINT $1,250,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$400,000.00 $50,000.00 $400,000.00

$300,000.00 $200,000.00 $36,000.00 $25,000.00 $300,000.00 $200,000.00

P'FOLIO IRR

12.10%

$350,000.00 $40,250.00 $350,000.00

$0.00 $1,250,000.00 $0.00 $151,250.00 $0.00 $1,250,000.00

A 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124

PERCENT

100%

58.33%

TOTAL PW

$99,508.15

OPTIMAL PORTFOLIO

TOTAL INVESTMENT

$1,250,000.00

SEE BELOW FOR DETAILS

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $400,000.00 $50,000.00 $400,000.00 $37,907.87 12.50% 1 $400,000.00 $37,907.87 10% 5

2 3 4 5 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00 $22,744.72 $18,953.93 $34,117.08 $18,953.93 12.00% 12.50% 11.50% 11.00% 1 1 0.583333333 0 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00 $22,744.72 $18,953.93 $19,901.63 $0.00 $99,508.15 CAP CONSTRAINT $1,250,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$400,000.00 $50,000.00 $400,000.00

$300,000.00 $200,000.00 $36,000.00 $25,000.00 $300,000.00 $200,000.00

P'FOLIO IRR

12.10%

$350,000.00 $40,250.00 $350,000.00

$0.00 $1,250,000.00 $0.00 $151,250.00 $0.00 $1,250,000.00

A 125 126 127 128 129

A 1 PROBLEM 15.24 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 b 34 35 36 37 38 c 39

LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR OPTIMAL PORTFOLIO 5 4

PERCENT

100%

TOTAL PW

$20,883.82

TOTAL INVESTMENT

$250,000.00

100%

100.00%

17.65%

1 $45,000.00 $4,000.00 $45,000.00 -$1,584.93 8.89% 0 $0.00 $0.00 10% 4

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

2 3 4 5 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $3,169.87 $1,584.93 $6,339.73 $11,094.53 11.67% 10.59% 12.00% 14.67% 1 0.176470588 1 1 $60,000.00 $15,000.00 $100,000.00 $75,000.00 $250,000.00 $3,169.87 $279.69 $6,339.73 $11,094.53 $20,883.82 CAP CONSTRAINT $250,000.00

$60,000.00 $7,000.00 $60,000.00

$15,000.00 $100,000.00 $75,000.00 $250,000.00 $1,588.24 $12,000.00 $11,000.00 $31,588.24 $15,000.00 $100,000.00 $75,000.00 $250,000.00

12.64%

PORTFOLIO CAP CONSTRAINT $200,000.00 5, 4, 2(41.67%) $250,000.00 5, 4, 2, 3(17.65%) $300,000.00 5, 4, 2, 3(76.47%) MARR

8.00% 5, 4, 2, 3(17.65%) 10.00% 5, 4, 2, 3(17.65%)

PW $18,775.04 $20,883.82 $21,816.13

***

$31,588.24 $20,883.82 NOTE! INVESTMENT 1 HAS IRR<MARR=10%

A 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

12.00%

$6,074.70 NOTE! INVESTMENTS 1, 2, AND 3 HAVE IRR<MARR=12% THIS PRECLUDES THEIR INCLUSION

SEE BELOW FOR ONE SETUP ***

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $45,000.00 $4,000.00 $45,000.00 -$1,584.93 8.89% 0 $0.00 $0.00 10% 4

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

12.29%

OPTIMAL PORTFOLIO

2 3 4 5 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $3,169.87 $1,584.93 $6,339.73 $11,094.53 11.67% 10.59% 12.00% 14.67% 1 0.764705882 1 1 $60,000.00 $65,000.00 $100,000.00 $75,000.00 $300,000.00 $3,169.87 $1,212.01 $6,339.73 $11,094.53 $21,816.13 CAP CONSTRAINT $300,000.00

$60,000.00 $7,000.00 $60,000.00

$65,000.00 $100,000.00 $75,000.00 $300,000.00 $6,882.35 $12,000.00 $11,000.00 $36,882.35 $65,000.00 $100,000.00 $75,000.00 $300,000.00

A 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121

PERCENT

100%

TOTAL PW

$20,883.82

TOTAL INVESTMENT

$250,000.00

17.65%

1 $45,000.00 $4,000.00 $45,000.00 -$1,584.93 8.89% 0 $0.00 $0.00 10% 4

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$0.00 $0.00 $0.00

P'FOLIO IRR

12.64%

2 3 4 5 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00 $3,169.87 $1,584.93 $6,339.73 $11,094.53 11.67% 10.59% 12.00% 14.67% 1 0.176470588 1 1 $60,000.00 $15,000.00 $100,000.00 $75,000.00 $250,000.00 $3,169.87 $279.69 $6,339.73 $11,094.53 $20,883.82 CAP CONSTRAINT $250,000.00

$60,000.00 $7,000.00 $60,000.00

$15,000.00 $100,000.00 $75,000.00 $250,000.00 $1,588.24 $12,000.00 $11,000.00 $31,588.24 $15,000.00 $100,000.00 $75,000.00 $250,000.00

A 122

1 PROBLEM 15.25 2 3 a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR 4 OPTIMAL PORTFOLIO 1 4 2 5 6 PERCENT 100% 100% 50.00% 7 8 TOTAL PW $624,696.11 9 10 TOTAL INVESTMENT $1,000,000.00 11 12 SEE BELOW FOR DETAILS 13 14 INVESTMENT OPPORTUNITY 1 2 3 15 INITIAL INVESTMENT $300,000.00 $400,000.00 $450,000.00 16 ANNUAL RECEIPTS $205,000.00 $230,000.00 $245,000.00 17 ANNUAL DISBURSEMENTS $125,000.00 $130,000.00 $140,000.00 18 ANNUAL RETURN $80,000.00 $100,000.00 $105,000.00 19 SALVAGE VALUE $50,000.00 $50,000.00 $60,000.00 20 PRESENT WORTH $210,842.53 $233,733.88 $218,312.14 21 INTERNAL RATE OF RETURN 24.04% 21.94% 19.99% 22 VALUE OF x 1 0.5 0 23 PORTFOLIO INVESTMENT $300,000.00 $200,000.00 $0.00 24 PORTFOLIO PRESENT WORTH $210,842.53 $116,866.94 $0.00 25 MARR 10% 26 INVESTMENT PERIOD 10 27 28 REALIZED INITIAL INVESTMENT $300,000.00 $200,000.00 $0.00 29 REALIZED ANNUAL RETURN $80,000.00 $50,000.00 $0.00 30 REALIZED SALVAGE VALUE $50,000.00 $25,000.00 $0.00 31 32 P'FOLIO IRR 22.62% 33 34 35 b PORTFOLIO PW 36 CAP CONSTRAINT $800,000.00 1, 4 $507,829.17 37 $1,000,000.00 1, 4, 2(50%) $624,696.11 38 $1,200,000.00 1, 4, 2 $741,563.04 39 40 c MARR 8.00% 1, 4, 2(50%) $780,549.78 41 10.00% 1, 4, 2(50%) $624,696.11 42 12.00% 1, 4, 2(50%) $489,102.86

4 5 $500,000.00 $600,000.00 $260,000.00 $290,000.00 $135,000.00 $150,000.00 $125,000.00 $140,000.00 $75,000.00 $75,000.00 $296,986.63 $289,155.14 22.04% 19.96% 1 0 $500,000.00 $0.00 $1,000,000.00 $296,986.63 $0.00 $624,696.11 CAP CONSTRAINT $1,000,000.00

$500,000.00 $125,000.00 $75,000.00

***

$0.00 $1,000,000.00 $0.00 $255,000.00 $0.00 $150,000.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RECEIPTS ANNUAL DISBURSEMENTS ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $300,000.00 $205,000.00 $125,000.00 $80,000.00 $50,000.00 $210,842.53 24.04% 1 $300,000.00 $210,842.53 10% 10

2 $400,000.00 $230,000.00 $130,000.00 $100,000.00 $50,000.00 $233,733.88 21.94% 0.5 $200,000.00 $116,866.94

3 $450,000.00 $245,000.00 $140,000.00 $105,000.00 $60,000.00 $218,312.14 19.99% 0 $0.00 $0.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$300,000.00 $200,000.00 $80,000.00 $50,000.00 $50,000.00 $25,000.00

SEE BELOW FOR ONE SETUP ***

P'FOLIO IRR

22.62%

OPTIMAL PORTFOLIO

4 5 $500,000.00 $600,000.00 $260,000.00 $290,000.00 $135,000.00 $150,000.00 $125,000.00 $140,000.00 $75,000.00 $75,000.00 $296,986.63 $289,155.14 22.04% 19.96% 1 0 $500,000.00 $0.00 $1,000,000.00 $296,986.63 $0.00 $624,696.11 CAP CONSTRAINT $1,000,000.00

$0.00 $500,000.00 $0.00 $125,000.00 $0.00 $75,000.00

$0.00 $1,000,000.00 $0.00 $255,000.00 $0.00 $150,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

PERCENT

100%

50%

TOTAL PW

$624,696.11

2 $400,000.00 $230,000.00 $130,000.00 $100,000.00 $50,000.00 $233,733.88 21.94% 0.5 1 $200,000.00 $116,866.94

3 $450,000.00 $245,000.00 $140,000.00 $105,000.00 $60,000.00 $218,312.14 19.99% 0 0 $0.00 $0.00

TOTAL INVESTMENT

$1,000,000.00

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RECEIPTS ANNUAL DISBURSEMENTS ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x VALUE IF X ROUNDED UP PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $300,000.00 $205,000.00 $125,000.00 $80,000.00 $50,000.00 $210,842.53 24.04% 1 1 $300,000.00 $210,842.53 10% 10

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$300,000.00 $200,000.00 $80,000.00 $50,000.00 $50,000.00 $25,000.00

P'FOLIO IRR

22.62%

4 5 $500,000.00 $600,000.00 $260,000.00 $290,000.00 $135,000.00 $150,000.00 $125,000.00 $140,000.00 $75,000.00 $75,000.00 $296,986.63 $289,155.14 22.04% 19.96% 1 0 1 0 3 $500,000.00 $0.00 $1,000,000.00 $296,986.63 $0.00 $624,696.11 CAP CONSTRAINT $1,000,000.00

$0.00 $500,000.00 $0.00 $125,000.00 $0.00 $75,000.00

$0.00 $1,000,000.00 $0.00 $255,000.00 $0.00 $150,000.00

A 127 128 129

A 1 PROBLEM 15.26 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 b 33 34 35 36 37 c 38 39 40 41 42

LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR OPTIMAL PORTFOLIO 6 PERCENT

100%

TOTAL PW

$1,058,608.60

TOTAL INVESTMENT

$2,500,000.00

100%

100.00%

100%

1 $150,000.00 $35,000.00 $25,000.00 $74,698.43 20.15% 1 $150,000.00 $74,698.43 10% 10

2 $200,000.00 $38,000.00 $50,000.00 $52,770.71 15.37% 0 $0.00 $0.00

3 $225,000.00 $45,000.00 $22,500.00 $60,180.24 15.72% 0 $0.00 $0.00

4 $275,000.00 $60,000.00 $27,500.00 $104,276.47 17.99% 1 $275,000.00 $104,276.47

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$0.00 $0.00 $0.00

$275,000.00 $60,000.00 $27,500.00

PORTFOLIO 6, 1, 7, 9, 4, 5(42.86%) 6, 1, 7, 9, 4, 5, 10(50%) 6, 1, 7, 9, 4, 5, 10, 3(88.89%)

PW $884,659.61 $1,058,608.60 $1,210,595.46

6, 1, 7, 9, 4, 5, 10(50%) 6, 1, 7, 9, 4, 5, 10(50%) 6, 1, 7, 9, 4, 5, 10(50%)

$1,400,672.13 $1,058,608.60 $761,080.10

P'FOLIO IRR

18.77%

CAP CONSTRAINT $2,000,000.00 $2,500,000.00 $3,000,000.00 MARR

SEE BELOW FOR ONE SETUP ***

8.00% 10.00% 12.00%

***

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $150,000.00 $35,000.00 $25,000.00 $74,698.43 20.15% 1 $150,000.00 $74,698.43 10% 10

2 $200,000.00 $38,000.00 $50,000.00 $52,770.71 15.37% 0 $0.00 $0.00

3 $225,000.00 $45,000.00 $22,500.00 $60,180.24 15.72% 0 $0.00 $0.00

4 $275,000.00 $60,000.00 $27,500.00 $104,276.47 17.99% 1 $275,000.00 $104,276.47

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$0.00 $0.00 $0.00

$275,000.00 $60,000.00 $27,500.00

P'FOLIO IRR

19.14%

OPTIMAL PORTFOLIO

PERCENT

100%

TOTAL PW

$1,043,918.42

TOTAL INVESTMENT

$2,500,000.00

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

SEE BELOW FOR DETAILS

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $150,000.00 $35,000.00 $25,000.00 $74,698.43 20.15% 1 $150,000.00 $74,698.43 10% 10

2 $200,000.00 $38,000.00 $50,000.00 $52,770.71 15.37% 0 $0.00 $0.00

3 $225,000.00 $45,000.00 $22,500.00 $60,180.24 15.72% 0 $0.00 $0.00

4 $275,000.00 $60,000.00 $27,500.00 $104,276.47 17.99% 1 $275,000.00 $104,276.47

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$0.00 $0.00 $0.00

$275,000.00 $60,000.00 $27,500.00

P'FOLIO IRR

18.67%

OPTIMAL PORTFOLIO

PERCENT

100%

TOTAL PW

$1,058,608.60

A 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

B TOTAL INVESTMENT

$2,500,000.00

SEE BELOW FOR DETAILS

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $150,000.00 $35,000.00 $25,000.00 $74,698.43 20.15% 1 $150,000.00 $74,698.43 10% 10

2 $200,000.00 $38,000.00 $50,000.00 $52,770.71 15.37% 0 $0.00 $0.00

3 $225,000.00 $45,000.00 $22,500.00 $60,180.24 15.72% 0 $0.00 $0.00

4 $275,000.00 $60,000.00 $27,500.00 $104,276.47 17.99% 1 $275,000.00 $104,276.47

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$0.00 $0.00 $0.00

$275,000.00 $60,000.00 $27,500.00

P'FOLIO IRR

18.77%

OPTIMAL PORTFOLIO

A 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210

PERCENT

100%

TOTAL PW

$1,028,578.56

TOTAL INVESTMENT

$2,500,000.00

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x VALUE OF X ROUNDED UP PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $150,000.00 $35,000.00 $25,000.00 $74,698.43 20.15% 1 1 $150,000.00 $74,698.43 10% 10

2 $200,000.00 $38,000.00 $50,000.00 $52,770.71 15.37% 1 1 $200,000.00 $52,770.71

3 $225,000.00 $45,000.00 $22,500.00 $60,180.24 15.72% 0 0 $0.00 $0.00

4 $275,000.00 $60,000.00 $27,500.00 $104,276.47 17.99% 1 1 $275,000.00 $104,276.47

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$150,000.00 $35,000.00 $25,000.00

$200,000.00 $38,000.00 $50,000.00

$0.00 $0.00 $0.00

$275,000.00 $60,000.00 $27,500.00

P'FOLIO IRR MUTUAL EXCLUSIVITY CONSTRAINT CONTINGENCY CONSTRAINT

18.52% 1 C183+E183+G183 1 D184+G184

A 211 212 213 214

NOTE! '$M$185 <= $M$187 IS NOT SHOWN IN THE SCREEN CAPTURE

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

100%

100.00%

50%

5 $350,000.00 $75,000.00 $55,000.00 $132,047.41 17.81% 1 $350,000.00 $132,047.41

6 $400,000.00 $95,000.00 $75,000.00 $212,649.62 20.73% 1 $400,000.00 $212,649.62

7 8 9 10 $475,000.00 $500,000.00 $550,000.00 $600,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 $220,179.55 $60,842.53 $216,263.80 $196,986.63 19.65% 12.56% 18.18% 16.91% 1 0 1 0.5 $475,000.00 $0.00 $550,000.00 $300,000.00 $2,500,000.00 $220,179.55 $0.00 $216,263.80 $98,493.32 $1,058,608.60 CAP CONSTRAINT $2,500,000.00

$350,000.00 $400,000.00 $475,000.00 $75,000.00 $95,000.00 $110,000.00 $55,000.00 $75,000.00 $50,000.00

$0.00 $550,000.00 $300,000.00 $2,500,000.00 $0.00 $120,000.00 $62,500.00 $557,500.00 $0.00 $75,000.00 $37,500.00 $345,000.00

43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

5 $350,000.00 $75,000.00 $55,000.00 $132,047.41 17.81% 0.428571429 $150,000.00 $56,591.75

6 $400,000.00 $95,000.00 $75,000.00 $212,649.62 20.73% 1 $400,000.00 $212,649.62

7 8 9 10 $475,000.00 $500,000.00 $550,000.00 $600,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 $220,179.55 $60,842.53 $216,263.80 $196,986.63 19.65% 12.56% 18.18% 16.91% 1 0 1 0 $475,000.00 $0.00 $550,000.00 $0.00 $2,000,000.00 $220,179.55 $0.00 $216,263.80 $0.00 $884,659.61 CAP CONSTRAINT $2,000,000.00

$150,000.00 $400,000.00 $475,000.00 $32,142.86 $95,000.00 $110,000.00 $23,571.43 $75,000.00 $50,000.00

100%

14.29%

$0.00 $550,000.00 $0.00 $120,000.00 $0.00 $75,000.00

$0.00 $2,000,000.00 $0.00 $452,142.86 $0.00 $276,071.43

85 86 87 88 5 6 7 8 9 10 89 $350,000.00 $400,000.00 $475,000.00 $500,000.00 $550,000.00 $600,000.00 90 $75,000.00 $95,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 91 $55,000.00 $75,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 92 $132,047.41 $212,649.62 $220,179.55 $60,842.53 $216,263.80 $196,986.63 93 17.81% 20.73% 19.65% 12.56% 18.18% 16.91% 94 0.142857143 1 1 0 1 1 95 $50,000.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $600,000.00 $2,500,000.00 96 $18,863.92 $212,649.62 $220,179.55 $0.00 $216,263.80 $196,986.63 $1,043,918.42 97 CAP CONSTRAINT $2,500,000.00 98 99 100 $50,000.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $600,000.00 $2,500,000.00 101 $10,714.29 $95,000.00 $110,000.00 $0.00 $120,000.00 $125,000.00 $555,714.29 102 $7,857.14 $75,000.00 $50,000.00 $0.00 $75,000.00 $75,000.00 $335,357.14 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 4 5 10 123 124 100% 100% 50.00% 125 126

127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168

5 $350,000.00 $75,000.00 $55,000.00 $132,047.41 17.81% 1 $350,000.00 $132,047.41

6 $400,000.00 $95,000.00 $75,000.00 $212,649.62 20.73% 1 $400,000.00 $212,649.62

7 8 9 10 $475,000.00 $500,000.00 $550,000.00 $600,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 $220,179.55 $60,842.53 $216,263.80 $196,986.63 19.65% 12.56% 18.18% 16.91% 1 0 1 0.5 $475,000.00 $0.00 $550,000.00 $300,000.00 $2,500,000.00 $220,179.55 $0.00 $216,263.80 $98,493.32 $1,058,608.60 CAP CONSTRAINT $2,500,000.00

$350,000.00 $400,000.00 $475,000.00 $75,000.00 $95,000.00 $110,000.00 $55,000.00 $75,000.00 $50,000.00

$0.00 $550,000.00 $300,000.00 $2,500,000.00 $0.00 $120,000.00 $62,500.00 $557,500.00 $0.00 $75,000.00 $37,500.00 $345,000.00

169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210

100%

75.00%

5 $350,000.00 $75,000.00 $55,000.00 $132,047.41 17.81% 0 0 $0.00 $0.00

6 $400,000.00 $95,000.00 $75,000.00 $212,649.62 20.73% 1 1 $400,000.00 $212,649.62

7 8 9 10 $475,000.00 $500,000.00 $550,000.00 $600,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00 $220,179.55 $60,842.53 $216,263.80 $196,986.63 19.65% 12.56% 18.18% 16.91% 1 0 1 0.75 1 0 1 1 7 $475,000.00 $0.00 $550,000.00 $450,000.00 $2,500,000.00 $220,179.55 $0.00 $216,263.80 $147,739.98 $1,028,578.56 CAP CONSTRAINT $2,500,000.00

$0.00 $400,000.00 $475,000.00 $0.00 $95,000.00 $110,000.00 $0.00 $75,000.00 $50,000.00

$0.00 $550,000.00 $450,000.00 $2,500,000.00 $0.00 $120,000.00 $93,750.00 $551,750.00 $0.00 $75,000.00 $56,250.00 $358,750.00

1 PROBLEM 15.27 2 3 a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR 4 OPTIMAL PORTFOLIO 4 6 5 5 6 PERCENT 100% 100% 100% 7 8 TOTAL PW $10,178.26 9 10 TOTAL INVESTMENT $200,000.00 11 12 SEE BELOW FOR DETAILS 13 14 INVESTMENT OPPORTUNITY 1 2 3 15 INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 16 ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 17 SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 18 PRESENT WORTH $379.08 $947.70 $189.54 19 INTERNAL RATE OF RETURN 10.40% 10.71% 10.17% 20 VALUE OF x 0.6 1 0 21 PORTFOLIO INVESTMENT $15,000.00 $35,000.00 $0.00 22 PORTFOLIO PRESENT WORTH $227.45 $947.70 $0.00 23 MARR 10% 24 INVESTMENT PERIOD 5 25 26 REALIZED INITIAL INVESTMENT $15,000.00 $35,000.00 $0.00 27 REALIZED ANNUAL RETURN $1,560.00 $3,750.00 $0.00 28 REALIZED SALVAGE VALUE $15,000.00 $35,000.00 $0.00 29 30 P'FOLIO IRR 11.34% 31 32 33 b PORTFOLIO PW 34 CAP CONSTRAINT $160,000.00 4, 6, 5, 2(28.57%) $9,273.89 35 $200,000.00 4, 6, 5, 2, 1(60%) $10,178.26 36 $240,000.00 4, 6, 5, 2, 1, 3 $10,519.43 37 38 c MARR 8.00% 4, 6, 5, 2, 1(60%) $26,691.27 39 10.00% 4, 6, 5, 2, 1(60%) $10,178.26 12.00%

None

$0.00

100%

60%

4 5 6 $40,000.00 $60,000.00 $50,000.00 $4,775.00 $6,750.00 $5,850.00 $40,000.00 $60,000.00 $50,000.00 $2,937.86 $2,843.09 $3,222.17 11.94% 11.25% 11.70% 1 1 1 $40,000.00 $60,000.00 $50,000.00 $200,000.00 $2,937.86 $2,843.09 $3,222.17 $10,178.26 CAP CONSTRAINT $200,000.00

$40,000.00 $4,775.00 $40,000.00

$60,000.00 $50,000.00 $200,000.00 $6,750.00 $5,850.00 $22,685.00 $60,000.00 $50,000.00 $200,000.00

***

NOTE! INVESTMENTS 1, 2, 3, 4, AND 5 HAVE IRR<MARR=12%

A 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

THIS PRECLUDES THEIR INCLUSION SEE BELOW FOR ONE SETUP ***

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $25,000.00 $2,600.00 $25,000.00 $379.08 10.40% 1 $25,000.00 $379.08 10% 5

2 3 4 5 6 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17 10.71% 10.17% 11.94% 11.25% 11.70% 1 1 1 1 1 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $240,000.00 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17 $10,519.43 CAP CONSTRAINT $240,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$25,000.00 $2,600.00 $25,000.00

$35,000.00 $30,000.00 $40,000.00 $3,750.00 $3,050.00 $4,775.00 $35,000.00 $30,000.00 $40,000.00

$60,000.00 $50,000.00 $240,000.00 $6,750.00 $5,850.00 $26,775.00 $60,000.00 $50,000.00 $240,000.00

P'FOLIO IRR

11.16%

OPTIMAL PORTFOLIO

100%

83%

100%

PERCENT

A 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124

TOTAL PW

$9,856.05

TOTAL INVESTMENT

$200,000.00

SEE BELOW FOR DETAILS

INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $25,000.00 $2,600.00 $25,000.00 $379.08 10.40% 1 $25,000.00 $379.08 10% 5

2 3 4 5 6 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17 10.71% 10.17% 11.94% 11.25% 11.70% 1 0 1 0.83333333 1 $35,000.00 $0.00 $40,000.00 $50,000.00 $50,000.00 $200,000.00 $947.70 $0.00 $2,937.86 $2,369.24 $3,222.17 $9,856.05 CAP CONSTRAINT $200,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$25,000.00 $2,600.00 $25,000.00

$35,000.00 $3,750.00 $35,000.00

$0.00 $40,000.00 $0.00 $4,775.00 $0.00 $40,000.00

P'FOLIO IRR

11.30%

OPTIMAL PORTFOLIO

$50,000.00 $50,000.00 $200,000.00 $5,625.00 $5,850.00 $22,600.00 $50,000.00 $50,000.00 $200,000.00

A 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166

PERCENT

100%

50%

TOTAL PW

$10,140.35

TOTAL INVESTMENT

$197,500.00

SEE BELOW FOR DETAILS INVESTMENT OPPORTUNITY INITIAL INVESTMENT ANNUAL RETURN SALVAGE VALUE PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x VALUE OF 4x PORTFOLIO INVESTMENT PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD

1 $25,000.00 $2,600.00 $25,000.00 $379.08 10.40% 0.5 2 $12,500.00 $189.54 10% 5

2 3 4 5 6 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17 10.71% 10.17% 11.94% 11.25% 11.70% 1 0 1 1 1 4 0 4 4 4 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $197,500.00 $947.70 $0.00 $2,937.86 $2,843.09 $3,222.17 $10,140.35 CAP CONSTRAINT $200,000.00

REALIZED INITIAL INVESTMENT REALIZED ANNUAL RETURN REALIZED SALVAGE VALUE

$12,500.00 $1,300.00 $12,500.00

$35,000.00 $3,750.00 $35,000.00

P'FOLIO IRR

11.35%

$0.00 $40,000.00 $0.00 $4,775.00 $0.00 $40,000.00

$60,000.00 $50,000.00 $197,500.00 $6,750.00 $5,850.00 $22,425.00 $60,000.00 $50,000.00 $197,500.00

A 167 168

A 1 PROBLEM 15.28 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 b 39 40 41 42

LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR OPTIMAL PORTFOLIO 4 1

100%

37.5%

PERCENT

100%

TOTAL PW

$623,633.06

TOTAL INVESTMENT

$500,000.00 $175,000.00

100%

YEAR 0 YEAR 1

SEE BELOW FOR DETAILS

EOY 0 1 2 3 4 5 6 7 8 9 10 PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT YR 0 PORTFOLIO INVESTMENT YR 1 PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD P'FOLIO IRR

OVERALL CF(1) CF(2) CF(3) CF(4) P'FOLIO CF -$50,000 -$125,000 -$200,000 -$250,000 -$500,000 -$100,000 -$75,000 $50,000 $75,000 -$81,250 $50,000 $70,000 $50,000 $75,000 $213,750 $50,000 $70,000 $50,000 $75,000 $213,750 $50,000 $70,000 $50,000 $75,000 $213,750 $50,000 $70,000 $75,000 $75,000 $223,125 $50,000 $70,000 $75,000 $85,000 $233,125 $50,000 $70,000 $75,000 $85,000 $233,125 $50,000 $70,000 $75,000 $85,000 $233,125 $50,000 $70,000 $75,000 $85,000 $233,125 $75,000 $100,000 $75,000 $100,000 $303,125 $130,503 $184,868 $181,596 $240,163 $623,633 27.59% 26.85% 26.28% 28.51% 27.55% 1 1 0.375 1 $50,000.00 $125,000.00 $75,000.00 $250,000.00 $500,000.00 $100,000.00 $75,000.00 $0.00 $0.00 $175,000.00 $130,503.30 $184,867.81 $68,098.46 $240,163.49 $623,633.06 10% CAP CONSTRAINT YR 0 $500,000.00 10 CAP CONSTRAINT YR 1 $175,000.00 27.55%

CAP CONSTRAINT

PORTFOLIO $400,000.00 1, 2, 4(90%) $500,000.00 4, 1, 2, 3(37.5%) $600,000.00 4, 1, 2, 3(87.5%)

PW $531,518.25 $623,633.06 $714,431.01

***

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

C MARR

8.00% 4, 1, 2, 3(37.5%) 10.00% 4, 1, 2, 3(37.5%) 12.00% 4, 1, 2, 3(37.5%)

$752,584.83 $623,633.06 $511,830.60

SEE BELOW FOR ONE SETUP ***

EOY 0 1 2 3 4 5 6 7 8 9 10 PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT YR 0 PORTFOLIO INVESTMENT YR 1 PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD P'FOLIO IRR

OVERALL CF(1) CF(2) CF(3) CF(4) P'FOLIO CF -$50,000.00 -$125,000.00 -$200,000.00 -$250,000.00 -$600,000.00 -$100,000.00 -$75,000.00 $50,000.00 $75,000.00 -$56,250.00 $50,000.00 $70,000.00 $50,000.00 $75,000.00 $238,750.00 $50,000.00 $70,000.00 $50,000.00 $75,000.00 $238,750.00 $50,000.00 $70,000.00 $50,000.00 $75,000.00 $238,750.00 $50,000.00 $70,000.00 $75,000.00 $75,000.00 $260,625.00 $50,000.00 $70,000.00 $75,000.00 $85,000.00 $270,625.00 $50,000.00 $70,000.00 $75,000.00 $85,000.00 $270,625.00 $50,000.00 $70,000.00 $75,000.00 $85,000.00 $270,625.00 $50,000.00 $70,000.00 $75,000.00 $85,000.00 $270,625.00 $75,000.00 $100,000.00 $75,000.00 $100,000.00 $340,625.00 $130,503.30 $184,867.81 $181,595.90 $240,163.49 $714,431.01 27.59% 26.85% 26.28% 28.51% 27.38% 1.00 1.00 0.875 1.00 $50,000.00 $125,000.00 $175,000.00 $250,000.00 $600,000.00 $100,000.00 $75,000.00 $0.00 $0.00 $175,000.00 $130,503.30 $184,867.81 $158,896.41 $240,163.49 $714,431.01 10% CAP CONSTRAINT YR 0 $600,000.00 10 CAP CONSTRAINT YR 1 $175,000.00 27.38%

A 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

PERCENT

100%

50%

TOTAL PW

$581,080.90

TOTAL INVESTMENT

$500,000.00 $125,000.00

OPTIMAL PORTFOLIO

YEAR 0 YEAR 1

SEE BELOW FOR DETAILS

EOY 0 1 2 3 4 5 6 7 8 9 10 PRESENT WORTH INTERNAL RATE OF RETURN VALUE OF x PORTFOLIO INVESTMENT YR 0 PORTFOLIO INVESTMENT YR 1 PORTFOLIO PRESENT WORTH MARR INVESTMENT PERIOD P'FOLIO IRR

OVERALL CF(1) CF(2) CF(3) CF(4) P'FOLIO CF -$50,000 -$125,000 -$200,000 -$250,000 -$500,000 -$100,000 -$75,000 $50,000 $75,000 -$25,000 $50,000 $70,000 $50,000 $75,000 $195,000 $50,000 $70,000 $50,000 $75,000 $195,000 $50,000 $70,000 $50,000 $75,000 $195,000 $50,000 $70,000 $75,000 $75,000 $207,500 $50,000 $70,000 $75,000 $85,000 $217,500 $50,000 $70,000 $75,000 $85,000 $217,500 $50,000 $70,000 $75,000 $85,000 $217,500 $50,000 $70,000 $75,000 $85,000 $217,500 $75,000 $100,000 $75,000 $100,000 $275,000 $130,503 $184,868 $181,596 $240,163 $581,081 27.59% 26.85% 26.28% 28.51% 27.50% 0.50 1.00 0.50 1.00 $25,000.00 $125,000.00 $100,000.00 $250,000.00 $500,000.00 $50,000.00 $75,000.00 $0.00 $0.00 $125,000.00 $65,251.65 $184,867.81 $90,797.95 $240,163.49 $581,080.90 10% CAP CONSTRAINT YR 0 $500,000.00 10 CAP CONSTRAINT YR 1 $125,000.00 27.50%

A 127 128 129 130 131 132 133 134 135 136 137 138

PROBLEM 16.1 MANY RESPONSES ARE POSSIBLE FOR THIS QUESTION DEPENDING UPON THE SCENARIO ASSUMED (OR STATED) BY THE STUDENTS. AMONG THE ISSUES THAT SHOULD BE CONSIDERED ARE THE FOLLOWING. a

ADDITIONAL ASSUMPTIONS/DATA INCLUDE: (1) DEPRECIATION SCHEDULE (2) VALUE OF MARR (3) COSTS AND REVENUES ASSOCIATED WITH THE USE OF THE 25% EXCESS CAPACITY (4) PLANNING HORIZON (5) SALVAGE VALUE AT THE END OF THE PLANNING HORIZON (6) ANY RELEVANT TAX CONSIDERATIONS (7) IS DEBT FINANCING REQUIRED FOR THE PURCHASE

SOURCES: (1) MACRS CLASSIFICATION TAXONOMY AND DEPRECIATION SCHEDULE (2) COMPANY RECORDS AND/OR POLICY IN ADDITION TO CONSIDERATIONS FROM CHAPTER 4 (3) COMPANY RECORDS (4) CONSIDERATIONS FROM CHAPTER 4 (5) MACHINE MANUFACTURER, PAST EXPERIENCE, MARKET ANALYSIS (6) COMPANY POLICIES AND PRACTICES (7) COMPANY POLICIES, PRACTICES, AND FINANCIAL POSITION

THE FOLLOWING ASSUMPTIONS ARE MADE IN DETERMINING THE SOLUTION BELOW: (1) MACRS 5-YEAR PROPERTY (2) MARR = 20% (3) ADDITIONAL CAPACITY IS ASSUMED TO GENERATE COSTS AND REVENUES SIMILAR TO 163H (4) 4 YEAR PLANNING HORIZON (LENGTH OF THE CONTRACT) IS ASSUMED (5) A SALVAGE VALUE 10% HIGHER THAN THE STATED 5-YEAR SALVAGE IS ASSUMED (6) A MARGINAL TAX RATE OF 40% IS ASSUMED (7) NO DEBT FINANCING IS ASSUMED

EOY 0 1 2 3 4

REVENUE $0.00 $68,750.00 $68,750.00 $68,750.00 $68,750.00

PRODUCTION COSTS $46,875.00 $46,875.00 $46,875.00 $46,875.00

CAPITAL DEPRECIATION COSTS EXPENSE -$50,000.00 $10,000.00 $16,000.00 $9,600.00 $27,500.00 $5,760.00

CALCULATIONS: REVENUE = ($22.00)(2,500)(1.25) PRODUCTION COSTS = ($15.00)(2,500)(1.25) DEPRECIATION EXPENSE IS BASED ON $50,000 INVESTMENT AND MACRS 5-YEAR PROPERTY DEP MARGINAL TAXES = (REVENUE - PRODUCTION COSTS - DEPRECIATION EXPENSE) * 0.40 ATCF = (CAPITAL COSTS + REVENUE - PRODUCTION COSTS - TAXES) BASED ON THE ANALYSIS, THE TURRET LATHE IS ATTRACTIVE AND SHOULD BE PURCHASED.

NDING UPON

E 25% EXCESS CAPACITY

SIDERATIONS FROM CHAPTER 4

HE SOLUTION BELOW:

AND REVENUES SIMILAR TO 163H S ASSUMED SALVAGE IS ASSUMED

40.00% MARGINAL TAXES

ATCF -$50,000.00 $4,750.00 $17,125.00 $2,350.00 $19,525.00 $4,910.00 $16,965.00 $6,446.00 $42,929.00

20.00% (P|F 10%,n) 1.00000 0.83333 0.69444 0.57870 0.48225

ND MACRS 5-YEAR PROPERTY DEPRECIATION CIATION EXPENSE) * 0.40

AND SHOULD BE PURCHASED.

PW OF CF -$50,000.00 $14,270.83 $13,559.03 $9,817.71 $20,702.64 $8,350.21 <- PW

PROBLEM 16.2 a b c d e f g h i j k l m

(2) (3) (11) (13) (6) (12) (4) (7) (9) (10) (8) (1) (5)

PROBLEM 16.3 a

ANNUAL PROFIT/LOSS = $700,000 - $300,000 - (1,000,000)(0.70)($0.50) ANNUAL PROFIT/LOSS = $50,000.00

HERE, AN ASSUMPTION IS MADE THAT REVENUE IS A LINEAR FUNCTION OF VOLUME BASED ON THE INFORMATION PROVIDED IN THE PROBLEM THE REVENUE IS $1.00/UNIT FOR BREAK EVEN REVENUE = COSTS ($1.00)(X) = $300,000 + ($0.50)(X) $0.50(X) = $300,000 X = 600,000 UNITS OR 60% OF CAPACITY

AT 90% CAPACITY, 900,000 UNITS ARE PRODUCED ANNUAL PROFIT/LOSS = 900,000($1.00) - $300,000 - (900,000)($0.50) ANNUAL PROFIT/LOSS = $150,000.00

ANNUAL PROFIT/LOSS = 1,000,000(X)($1.00) - $300,000 - (1,000,000)(X)($0.50) WHERE X IS PROPORT $90,000 = 1,000,000(X)($1.00) - $300,000 - (1,000,000)(X)($0.50) $390,000 = $500,000(X) X = 0.78 OR 78% OF CAPACITY

.50) WHERE X IS PROPORTION OF CAPACITY

PROBLEM 16.4 METHOD 1: COST = $1,000 + $20.00(X) METHOD 2: COST = $400 + $100.00(X) BREAKEVEN $1,000 + $20.00X = $400 + $100.00X $80.00X = $600.00 X = 7.5 UNITS FOR X = 7.5; BREAK EVEN FOR X < 7.5; METHOD II IS PREFERRED (LOWER COST) FOR X > 7.5; METHOD I IS PREFERRED (LOWER COST)

UNITS 0 1 2 3 4 5 6 7 8 9 10

COST OF COST OF METHOD I METHOD II COST COST $1,000.00 $400.00 $1,020.00 $500.00 $1,040.00 $600.00 $1,060.00 $700.00 $1,080.00 $800.00 $1,100.00 $900.00 $1,120.00 $1,000.00 $1,140.00 $1,100.00 $1,160.00 $1,200.00 $1,180.00 $1,300.00 $1,200.00 $1,400.00

PROBLEM 16.5 IMPACT OF ROONEY COST = (CURRENT FIXED COST + CHANGE) + (PRODUCTION VOLUME)(CURRENT VARIABLE COST COST = (CURRENT FIXED COST + $20,000) + (8,000)($20.00 + (-$5.60)) COST = CURRENT FIXED COST + $135,200 IMPACT OF BLAIR COST = (CURRENT FIXED COST + CHANGE) + (PRODUCTION VOLUME)(CURRENT VARIABLE COST COST = (CURRENT FIXED COST + $5,000) + (8,000)($20.00 + (-$4.00)) COST = CURRENT FIXED COST + $133,000 BLAIR IS PREFERRED DUE TO A SMALLER COST INCREASE

RRENT VARIABLE COST + CHANGE)

PROBLEM 16.6 a

PROFIT = 500N - (0.04N^3 - 700N + 50,000) PROFIT = 500N - 0.04N^3 + 700N - 50,000

TAKING THE DERIVATIVE OF PROFIT WITH RESPECT TO VOLUME dPROFIT/dN = 500 - 0.12N^2 + 700 dPROFIT/dN = 1,200 - 0.12N^2 SETTING EQUAL TO ZERO AND SOLVING FOR N N^2 = 1200/0.12 = 10,000 N = 100 UNITS (N COULD ALSO BE -100 BUT THIS INTERPRETATION IS NOT MEANINGFUL IN THE PR b

PROFIT = 500N - 0.04N^3 + 700N - 50,000 PROFIT = 500(100) - 0.04*100^3 + 700(100) - 50,000 PROFIT = $50,000 - 440,000 + $70,000 - $50,000 = $30,000

FIXED COST = CONSTANT IN THE COST EQUATION FIXED COST = $50,000

IS NOT MEANINGFUL IN THE PROBLEM STATEMENT

PROBLEM 16.7 a

$600.00 THE COST AT ZERO PRODUCTION VOLUME

VARIABLE COST = TOTAL COST - FIXED COST = $1,800 - $600 = $1,200

COST PER UNIT = TOTAL COST / NUMBER OF UNITS = $1,600/400 = $4.00 PER UNIT

THE VARIABLE COST SLOPE BETWEEN 0 UNITS AND 200 UNITS IS $3.00 PER UNIT = ($1200-$600)/20 THEREFORE, THE INCREMENTAL COST OF PRODUCING THE 100TH UNIT IS $3.00

THE VARIABLE COST SLOPE BETWEEN 400 UNITS AND 600 UNITS IS $1.00 PER UNIT = ($1800-$1600 THEREFORE, THE INCREMENTAL COST OF PRODUCING THE 500TH UNIT IS $1.00

FIXED COST PER UNIT FOR 1,000 WIDGETS = $600/1,000 = $0.60/UNIT

AN ASSUMPTION IS REQUIRED REGARDING THE BEHAVIOR OF VARIABLE COSTS FOR PRODUCTION QUANTITIES GREATER THAN 600 (THE LAST TABLED VALUE). LACKING OTHER INFORMATION, THE VARIABLE COST OF THE PREVIOUS RANGE IS A LOGICAL ASSUMPTION. THEREFORE, VARIABLE COST PER UNIT AT 1,000 IS $1.00, THE SAME AS PART (e).

3.00 PER UNIT = ($1200-$600)/200

S $1.00 PER UNIT = ($1800-$1600)/200

PROBLEM 16.8 a

PROFIT = 15N - (3,500,000 + 9N) AT 50% CAPACITY, N=500,000 PROFIT = 15*(500,000) - (3,500,000 + 9*500,000) PROFIT = 7,500,000 - (3,500,000 + 4,500,000) = -$500,000 ($500,000 LOSS)

FOR BREAKEVEN 15N = 3,500,000 + 9N 6N = 3,500,000 N = 583,333.33; ROUNDED TO 583,333 TOOLS

AT A PRODUCTION LEVEL OF 583,333 TOTAL COST = 3,500,000 + 9*(583,333) TOTAL COST = 8,749,997 COST/TOOL = 8,749,997 / 583,333 = $15.00/TOOL

PROBLEM 16.9 a

RECALL MARGINAL COST IS DEFINED AS THE COST OF ADDING THE NEXT FLOOR. FOR EXAMPLE, MC(2) = COST(3) - COST(2) OTHER REFERENCES MAY DEFINE MC(2) = COST(2) - COST(1) CARE SHOULD BE TAKEN WHEN DEALING WITH MARGINAL COST TO REVIEW THE DEFINITION BEI BUILDING (SQ-FT) 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000 10,000,000

FLOORS 1 2 3 4 5 6 7 8 9 10 11 12

AREA PER FLOOR 10,000,000 5,000,000 3,333,333 2,500,000 2,000,000 1,666,667 1,428,571 1,250,000 1,111,111 1,000,000 909,091 833,333

TOTAL COST $2,820,000,000.00 $1,840,000,000.00 $1,526,666,666.67 $1,380,000,000.00 $1,300,000,000.00 $1,253,333,333.33 $1,225,714,285.71 $1,210,000,000.00 $1,202,222,222.22 $1,200,000,000.00 $1,201,818,181.82 $1,206,666,666.67

OPTIMAL NUMBER OF FLOORS IS 10 SINCE IT HAS THE LOWEST TOTAL COST

OPTIMAL NUMBER OF FLOORS IS 10 SINCE THE MARGINAL COST AT 10 IS THE FIRST ONE TO TUR IN OTHER WORDS, ADDING THE 11TH FLOOR INCREASES TOTAL COST

ASSUMING X IS CONTINUOUS, THE OPTIMAL WILL OCCUR WHERE dTC/dX EQUALS ZERO dTC/dX = (200 + 80X +2X2)A d/dX = 0 SINCE A = 10,000,000 / X dTC/dX = (200 + 80X +2X2) (10,000,000/X) d/dX = 0 (2,000,000,000 X-1 + 800,000,000 + 20,000,000X) d/dX = 0 -2,000,000,000 X-2 + 20,000,000 = 0 -2,000,000,000 + 20,000,000 X2 = 0 20,000,000 X2 = 2,000,000,000 X2 = 100 X = 10

NEXT FLOOR.

REVIEW THE DEFINITION BEING APPLIED. AVERAGE COST PER FLOOR $2,820,000,000.00 $920,000,000.00 $508,888,888.89 $345,000,000.00 $260,000,000.00 $208,888,888.89 $175,102,040.82 $151,250,000.00 $133,580,246.91 $120,000,000.00 $109,256,198.35 $100,555,555.56

MARGINAL COST -$980,000,000.00 -$313,333,333.33 -$146,666,666.67 -$80,000,000.00 -$46,666,666.67 -$27,619,047.62 -$15,714,285.71 -$7,777,777.78 -$2,222,222.22 $1,818,181.82 $4,848,484.85 N/A

10 IS THE FIRST ONE TO TURN POSITIVE

C/dX EQUALS ZERO

PROBLEM 16.10

ORDER SIZE 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

TOTAL TOTAL TOTAL M1 COST M2 COST M3 COST $300 $750 $500 $390 $780 $550 $480 $810 $600 $570 $840 $650 $660 $870 $700 $750 $900 $750 $840 $930 $800 $930 $960 $850 $1,020 $990 $900 $1,110 $1,020 $950 $1,200 $1,050 $1,000 $1,290 $1,080 $1,050 $1,380 $1,110 $1,100 $1,470 $1,140 $1,150 $1,560 $1,170 $1,200 $1,650 $1,200 $1,250 $1,740 $1,230 $1,300 $1,830 $1,260 $1,350 $1,920 $1,290 $1,400 $2,010 $1,320 $1,450 $2,100 $1,350 $1,500

$2,500 $2,000 $1,500

Cost

$1,000 $500 $0 0

BREAK EVEN FOR M1 AND M3 300 + 9X = 500 + 5X X = 50 BREAKEVEN FOR M3 AND M2 500 + 5X = 750 + 3X X = 125

FOR AN ORDER OF SIZE 75, M3 IS PREFERRED

FOR AN ORDER OF SIZE 160, M2 IS PREFERRED, THEN M3, THEN M1 COST ON M2: $750 + (160)($3) = $1,230 COST ON M3: $500 + (160)($5) = $1,300 COST ON M1: $300 + (160)($9) = $1,740 DIFFERENTIAL BETWEEN PREFERRED AND 2ND = $1,300 - $1,230 = $70 DIFFERENTIAL BETWEEN PREFERRED AND 3RD = $1,740 - $1,230 = $510

Order Cost versus Order Size by Machine

100

125

150

175

Order Size M1 COST

M2 COST

M3 COST

200

PROBLEM 16.11 FOR EACH PRODUCTION QUANTITY, FOUR OPTIONS ARE EXAMINED: R = PRODUCE ALL UNITS ON PROCESS R R+T = PRODUCE 4,000 UNITS ON PROCESS R, REMAINING UNITS ON PROCESS T T = PRODUCE ALL UNITS ON PROCESS T T+R = PRODUCE 5,000 UNITS ON PROCESS T, REMAINING UNITS ON PROCESS R

IN THE FOLLOWING R1 REPRESENTS THE PRODUCTION IN PROCESS R UP TO THE VARIABLE CO R2 REPRESENTS THE PRODUCTION IN PROCESS R LESS GREATER THAN THE VAR T1 REPRESENTS THE PRODUCTION IN PROCESS T LESS THAN THE VARIABLE COS T2 REPRESENTS THE PRODUCTION IN PROCESS R GREATER THAN THE VARIABLE a

PRODUCTION QUANTITY = 5,500

OPTION R R+T T T+R

FIXED COST

QUANTITY X1 $170,000.00 4,000 $170,000.00 4,000 $170,000.00 0 $170,000.00 500

$8.00 VARIABLE COST QUANTITY X1 X2 $32,000.00 1,500 $32,000.00 0 $0.00 0 $4,000.00 0

$17.00 VARIABLE COST X2 $25,500.00 $0.00 $0.00 $0.00

DECISION: PRODUCE 4,000 UNITS ON PROCESS R AND 1,500 UNITS ON PROCESS T b

TOTAL COST FOR 5,500 UNITS = $215,500 AVERAGE COST PER UNIT = $215,500 / 5,500 = $39.18

PRODUCTION QUANTITY = 9,500

OPTION R R+T T T+R

FIXED COST

QUANTITY R1 $170,000.00 4,000 $170,000.00 4,000 $170,000.00 0 $170,000.00 4,000

$8.00 VARIABLE COST QUANTITY R1 R2 $32,000.00 5,500 $32,000.00 0 $0.00 0 $32,000.00 500

$17.00 VARIABLE COST R2 $93,500.00 $0.00 $0.00 $8,500.00

TWO OTHER OPTIONS ARE VIABLE FOR THIS PRODUCTION QUANTITY. THEY ARE EXAMINED BE R+T+R T+R+T

$170,000.00 $170,000.00

4,000 4,000

$32,000.00 $32,000.00

DECISION: PRODUCE 9,500 UNITS ON PROCESS T TOTAL COST FOR 9,500 UNITS = $237,500 AVERAGE COST PER UNIT = $237,500 / 9,500 = $25.00

500 0

$8,500.00 $0.00

UP TO THE VARIABLE COST RATE CHANGE (4,000 UNITS) GREATER THAN THE VARIABLE COST RATE CHANGE HAN THE VARIABLE COST RATE CHANGE (5,000 UNITS) TER THAN THE VARIABLE COST RATE CHANGE

QUANTITY Y1 0 1,500 5,000 5,000

$9.00 VARIABLE COST QUANTITY Y2 Y1 $0.00 0 $13,500.00 0 $45,000.00 500 $45,000.00 0

$5.00 VARIABLE COST Y2 $0.00 $0.00 $2,500.00 $0.00

QUANTITY T1 0 5,000 5,000 5,000

$9.00 VARIABLE COST QUANTITY T2 T1 $0.00 0 $45,000.00 500 $45,000.00 4,500 $45,000.00 0

$5.00 VARIABLE COST T2 $0.00 $2,500.00 $22,500.00 $0.00

$295,500.00 $249,500.00 $237,500.00 $255,500.00

$0.00 $2,500.00

$255,500.00 $249,500.00

TOTAL COST $227,500.00 $215,500.00 $217,500.00 $219,000.00

TOTAL COST

THEY ARE EXAMINED BELOW 5,000 5,000

$45,000.00 $45,000.00

0 500

PROBLEM 16.12 a

AVERAGE COST = TOTAL COST / UNITS PRODUCED = (FIXED COSTS + VARIABLE COSTS) / UNITS SUBSTITUTING KNOWN VALUES $800 = (FIXED COSTS + ($500)(600)) / 600 FIXED COSTS = $180,000

AVERAGE COST = TOTAL COST / UNITS PRODUCED = (FIXED COSTS + VARIABLE COSTS) / UNITS SUBSTITUTING KNOWN VALUES $710 = ($180,000 + ($500)(700)+(RATE)(300)) / 1,000 RATE = $600 PER TON FOR TONS OVER 700 WEIGHTED AVERAGE RATE = $530 PER TON ACROSS ALL 1,000 TONS

PROBLEM 16.13 a

THERE ARE MANY POSSIBLE RESPONSES TO THIS QUESTION. LISTED BELOW ARE THREE EXAM OF A GOOGLE SEARCH ON THE PHRASE "COST ESTIMATING" WWW.SCEAONLINE.NET WWW.COSTESTIMATING.COM HTTP://PMBOOK.CE.CMU.EDU/05_COST_ESTIMATION.HTML

WEB PAGE FOR THE SOCIET WEB PAGE FOR INDUSTRIAL WEB PAGE FOR THE COST E PROJECT MANAGEMENT F

THE THIRD REFERENCE HTTP://PMBOOK.CE.CMU.EDU/05_COST_ESTIMATION.HTML CONTAINS D ALTHOUGH ITS SCOPE IS RATHER TIGHTLY FOCUSED ON FACILITIES CONSTRUCTION, IT CONTA CAN BE GENERALIZED INTO OTHER AREAS.

THE WEB SITE INCLUDES A COMPLETE TEXT CHAPTER PRESENTING CONCEPTS, TECHNIQUES, FOR CONSTRUCTION PROJECTS. THE CHAPTER INCLUDES MANY ILLUSTRATIONS AS WELL AS R THE END. THE CHAPTER IS PART OF A TEXT ON PROJECT MANAGEMENT FOR CONSTRUCTION.

PROBLEM 16.14 a b c d e f

$63.63 $0.279 WEIGHT COST COST = $63.63 + ($0.279)(600) = $231.03 98.24% OF THE CHANGE IN COST CAN BE EXPLAINED BY CHANGE IN WEIGHT

PROBLEM 16.15 a

(1) CONSTRUCTION COSTS PUBLISHED IN PUBLIC RECORDS FOR OTHER BUILDINGS IN NEW YOR AREAS ALONG THE NORTHEASTERN SEABOARD). (2) COMPANY RECORDS

(1) CONSTRUCTION COSTS PUBLISHED IN PUBLIC RECORDS FOR OTHER RURAL BRIDGES IN OK ANOTHER SOURCE MIGHT BE INDUSTRY DATABASES OR HANDBOOKS. (2) COMPANY RECORDS

(1) VENDOR DATA AND/OR QUOTATIONS (2) PAST EXPERIENCE IS LESS LIKELY TO BE VALUABLE IN THIS INSTANCE; THE VENDOR DATA W RELIABLE SOURCE.

(1) SALARY DATABASES, PROFESSIONAL ADS FOR SIMILAR POSITIONS, PROFESSIONAL ASSOCIA (2) PAST EXPERIENCE IS LESS LIKELY TO BE VALUABLE IN THIS INSTANCE; THE SOURCES ABOV RELIABLE SOURCES.

PROBLEM 16.16

WEEK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

CIRCUIT BOARD ASSEMBLY SUPPORT COST $66,402 $56,943 $60,337 $50,096 $64,241 $60,846 $43,119 $63,412 $59,283 $60,070 $53,345 $65,027 $58,220 $65,406 $35,268 $46,394 $71,877 $61,903 $50,009 $49,327 $44,703 $45,582 $43,818 $62,122 $52,403

DIRECT LABOR HOURS 7,619 7,678 7,816 7,659 7,646 7,765 7,685 7,962 7,793 7,732 7,771 7,842 7,940 7,750 7,954 7,768 7,764 7,635 7,849 7,869 7,576 7,557 7,569 7,672 7,653

NUMBER OF BOARDS COMPLETED 2,983 2,830 2,413 2,221 2,701 2,656 2,495 2,128 2,127 2,127 2,338 2,685 2,602 2,029 2,136 2,046 2,786 2,822 2,178 2,244 2,195 2,370 2,016 2,515 2,942

AVERAGE CYCLE TIME 186.44 139.14 151.13 138.30 158.63 148.71 105.85 174.02 155.30 162.20 142.97 176.08 150.19 194.06 100.51 137.47 197.44 164.69 141.95 123.37 128.25 106.16 131.41 154.88 140.07

REGRESSION STATISTICS 5.9604 9466.87 16.0724 124429.43 0.0059 9308.51 0.1375 23 11916588.78 1992910151.86

Support Cost

Labor Hours versus Support Cost $80,000 $70,000 $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0

7,500

y = 5.9604x + 9466.9 R² = 0.0059 7,550

7,600

7,650

7,700

7,750

7,800

7,850

7,900

7,950

8,000

Labor Hours

REGRESSION STATISTICS 13.9454 21810.74 5.4443 13296.02 0.2220 8235.25 6.5613 23 444980845.73 1559845894.91

Support Cost

Boards Completed versus Support Cost $80,000 $60,000 $40,000 $20,000 $0 1,800

y = 13.945x + 21811 R² = 0.222 2,000

2,200

2,400

2,600

2,800

3,000

3,200

Boards Completed

REGRESSION STATISTICS 330.4829 6572.77 28.4855 4286.13 0.8541 3566.63 134.6018 23 1712247575.47 292579165.17

Support Cost

Average Cycle Time versus Support Cost $80,000 $70,000 $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0

80.00

y = 330.48x + 6572.8 R² = 0.8541 100.00

120.00

140.00

160.00

180.00

Average Cycle Time

AVERAGE CYCLE TIME IS THE PREFERRED DRIVER SINCE IT HAS THE HIGHEST VALUE OF R^2

THE PERCENTAGE OF CHANGE IN COST EXPLAINED BY CHANGES IN AVERAGE CYCLE TIME IS 85.41%

200.00

220.00

PROBLEM 16.17 a b c d e f g

$94,227 = $283,727 - ($36,000+(b)+$30,000+$18,500+$15,000+$10,000+$8,000) $72,000 = $80,000 - $8,000 $40,000 = $36,000 + $4,000 $6,000 = $51,000 - ($20,000+$25,000) $32,727 = (f) - $200,000 $232,727 = (g) - $51,000 $283,727 = TOTAL ASSETS (BALANCING TOTAL)

PROBLEM 16.18 a

ASSETS: CASH, ACCOUNTS RECEIVABLE, RAW MATERIALS INVENTORY, WIP INVENTORY, FINISH LAND, BUILDING, EQUIPMENT LIABILITIES: NOTES PAYABLE, ACCOUNTS PAYABLE, DIVIDENDS PAYABLE NET WORTH: COMMON STOCK, RETAINED EARNINGS

TOTAL ASSETS = $469,000 TOTAL LIABILITIES = $51,000 RETAINED EARNINGS = TOTAL ASSETS - TOTAL LIABILITIES - STOCK RETAINED EARNINGS = $469,000 - $51,000 - $100,000 = $318,000

ORY, WIP INVENTORY, FINISHED GOODS INVENTORY,

PROBLEM 16.19 a

SCOTT COMPANY BALANCE SHEET AS OF DECEMBER 31, 2006 ASSETS CASH ACCOUNTS RECEIVABLE FINISHED GOODS RAW MATERIAL BUILDINGS (NET) EQUIPMENT (NET) LAND TOTAL ASSETS

$40,000 $80,000 $30,000 $40,000 $205,000 $180,000 $115,000 $690,000

ASSETS = LIABILITIES + NET WORTH $690,000 = $540,000 + $150,000 $690,000 = $690,000

COTT COMPANY ALANCE SHEET DECEMBER 31, 2006 LIABILITIES ACCOUNTS PAYABLE DIVIDENDS PAYABLE NOTES PAYABLE TAXES PAYABLE MORTGAGE TOTAL LIABILITIES

$50,000 $20,000 $60,000 $20,000 $390,000 $540,000

NET WORTH STOCKHOLDER'S EQUITY TOTAL NET WORTH TOTAL LIABILITIES AND NET WORTH

$150,000 $150,000 $690,000

PROBLEM 16.20 SCOTT COMPANY INCOME STATEMENT YEAR ENDED DECEMBER 31, 2006 SALES COST OF GOODS SOLD RAW MATERIAL DIRECT LABOR FACTORY OVERHEAD GROSS PROFIT OTHER EXPENSES ADMINISTRATIVE INTEREST DEPRECIATION INCOME BEFORE TAXES INCOME TAXES NET INCOME

$400,000 $90,000 $70,000 $35,000 $205,000 $30,000 $40,000 $30,000 $105,000 $20,000 $85,000

PROBLEM 16.21 a

ACCURATE TAX SERVICE INCOME STATEMENT YEAR ENDED APRIL 30, 2007 REVENUE EXPENSES SALARIES ADVERTISING RENT AUTOMOBILE OFFICE SUPPLIES NET INCOME

$115,100 $12,500 $900 $6,000 $1,300 $7,500 $86,900 ACCURATE TAX SERVICE BALANCE SHEET AS OF APRIL 30, 2007

ASSETS CASH ACCOUNTS RECIEVABLE OFFICE FURNITURE AND FIXTURES OFFICE MACHINES AND EQUIPMENT AUTOMOBILE TOTAL ASSETS

$62,500 $3,700 $11,300 $15,000 $9,500 $102,000

NOTE: BETTY SMITH CAPITAL BALANCE = $32,000 - $18,600 + $86,900 = $100,300

RATE TAX SERVICE ALANCE SHEET OF APRIL 30, 2007 LIABILITIES ACCOUNTS PAYABLE

$1,700

NET WORTH BETTY SMITH, CAPITAL

$100,300

TOTAL LIABILITIES AND NET WORTH

$18,600 + $86,900 = $100,300

$102,000

PROBLEM 16.22 a

JANCO COMPANY BALANCE SHEET ASSETS CASH ACCOUNTS RECEIVABLE INVENTORY PREPAID RENT PROPERTY, PLANT & EQUIPMENT TOTAL ASSETS

$22,950 $21,000 $14,400 $1,050 $15,300 $74,700

JANCO COMPANY INCOME STATEMENT REVENUE COST OF GOODS SOLD GROSS PROFIT OTHER EXPENSES ADVERTISING DEPRECIATION RENT WAGES NET INCOME

$27,000 $15,000 $12,000 $600 $300 $2,100 $7,500 $1,500

NCO COMPANY ALANCE SHEET LIABILITIES ACCOUNTS PAYABLE NOTES PAYABLE WAGES PAYABLE TOTAL LIABILITIES

$12,000 $6,000 $1,200 $19,200

NET WORTH COMMON STOCK RETAINED EARNINGS TOTAL NET WORTH TOTAL LIABILITIES AND NET WORTH

$54,000 $1,500 $55,500 $74,700

PROBLEM 16.23 a

INVENTORY = TOTAL ASSETS - (ACCOUNTS RECEIVABLE+CASH+OTHER ASSETS+PROPERTY,PLA INVENTORY = $378,045 - ($8,739+$92,827+$30,350+$103,684) INVENTORY = $142,445 TOTAL NET WORTH = COMMON STOCK+CAPITAL IN EXCESS+RETAINED EARNINGS TOTAL NET WORTH =$402+$187,506+$35,097 TOTAL NET WORTH = $223,005 TOTAL LIABILITIES AND NET WORTH = TOTAL ASSETS TOTAL LIABILITIES AND NET WORTH = $378,045 TOTAL LIABILITIES = TOTAL LIABILITIES AND NET WORTH - TOTAL NET WORTH TOTAL LIABILITIES =$378,045 - $223,005 TOTAL LIABILITIES = $155,040

ACCOUNTS PAYABLE = TOTAL LIABILITIES - (LONG TERM LIABILITIES+NOTES PAYABLE+OTHER L ACCOUNTS PAYABLE = $155,040 - ($9,474+$11,195+$57,786) ACCOUNTS PAYABLE = $76,585 b

PACKERS COMPANY BALANCE SHEET ASSETS CASH ACCOUNTS RECEIVABLE INVENTORY PROPERTY, PLANT & EQUIPMENT OTHER ASSETS TOTAL ASSETS

$92,827 $8,739 $142,445 $103,684 $30,350 $378,045

VABLE+CASH+OTHER ASSETS+PROPERTY,PLANT & EQUIPMENT)

N EXCESS+RETAINED EARNINGS

WORTH - TOTAL NET WORTH

TERM LIABILITIES+NOTES PAYABLE+OTHER LIABILITIES)

CKERS COMPANY ALANCE SHEET LIABILITIES ACCOUNTS PAYABLE NOTES PAYABLE LONG TERM LIABILITIES OTHER LIABILITIES TOTAL LIABILITIES

$76,585 $11,195 $9,474 $57,786 $155,040

NET WORTH COMMON STOCK CAPITAL IN EXCESS OF PAR RETAINED EARNINGS TOTAL NET WORTH TOTAL LIABILITIES AND NET WORTH

$402 $187,506 $35,097 $223,005 $378,045

PROBLEM 16.24 a

NET INCOME = (0.09)($27,000,000,000) = $2,430,000,000

TOTAL REVENUES = NET INCOME / $0.04 = $2,430,000,000 / $0.04 = $60,750,000,000

AVERAGE STOCKHOLDER'S EQUITY = NET INCOME / 0.19 = $2,430,000,000 / 0.19 = $12,789,473,684

GALLONS SOLD = NET INCOME / $0.035 = $2,430,000,000 / $0.035 = $69,428,571,429

PROBLEM 16.25 a

RETURN ON ASSETS EMPLOYED = NET INCOME / AVERAGE TOTAL ASSETS RETURN ON ASSETS EMPLOYED = $564,259 / ((0.5)($4,428,941+$3,513,693)) RETURN ON ASSETS EMPLOYED = 14.21%

RETURN ON OWNER'S EQUITY = NET INCOME / AVERAGE OWNER'S EQUITY RETURN ON OWNER'S EQUITY = $564,259 / ((0.5)($2,228,506+$2,090,262)) RETURN ON OWNER'S EQUITY = 26.13%

CURRENT RATIO = CURRENT ASSETS / CURRENT LIABILITIES CURRENT RATIO = $1,529,788 / $1,935,620 CURRENT RATIO = 0.790

ACID TEST RATIO = (CASH + ACCOUNTS RECEIVABLE + SHORT TERM INVESTMENTS) / CURRENT ACID TEST RATIO = ($312,606 + $224,271 + $141,038) / $1,935,620 ACID TEST RATIO = 0.350

ACCOUNTS RECEIVABLE TURNOVER = NET SALES / AVERAGE ACCOUNTS RECEIVABLE ACCOUNTS RECEIVABLE TURNOVER = $7,786,942 / ((0.5)($224,271+$190,762)) ACCOUNTS RECEIVABLE TURNOVER = 37.52

INVENTORY TURNOVER = COST OF GOODS SOLD / AVERAGE INVENTORY INVENTORY TURNOVER = $3,178,791 / ((0.5)($636,222+$546,299) INVENTORY TURNOVER = 5.38

DEBT TO EQUITY RATIO = TOTAL LIABILITIES / TOTAL CAPITAL WORTH DEBT TO EQUITY RATIO = $2,200,435 / $2,228,506 DEBT TO EQUITY RATIO = 0.987

OPERATING INCOME TO TOTAL ASSETS = NET OPERATING INCOME / TOTAL ASSETS OPERATING INCOME TO TOTAL ASSETS = $893,952 / $4,428,941 OPERATING INCOME TO TOTAL ASSETS = 0.202

EBIT = NET INCOME + INCOME TAXES + INTEREST EXPENSE EBIT = $564,259 + $324,770 + (-$12,291) EBIT = $876,738

EBITDA = NET INCOME + INCOME TAXES + INTEREST EXPENSE + (DEPRECIATION + AMORTIZATIO EBITDA = $564,259 + $324,770 + (-$12,291) + ($387,211) EBITDA = $1,263,949

PROBLEM 16.26 a

MANY SITES PROVIDE VALUABLE INFORMATION, AMONG THEM ARE: WWW.INVESTOPEDIA.COM WWW.FOOL.COM WWW.BUSINESS.COM

WWW.INVESTOPEDIA.COM

WWW.INVESTOPEDIA.COM HAS A WELL ORGANIZED AND EASY TO NAVIGATE TUTORIAL ON FINA

THERE ARE MANY INCLUDING CASH CONVERSION CYCLE, RETURN ON CAPITAL EMPLOYED, INT CASH FLOW TO DEBT RATIO, FIXED ASSET TURNOVER, PRICE TO SALES RATIO.

PROBLEM 16.27 a

MATERIAL COST FOR A LOT OF 10,000 UNITS 2 UNITS PER SHEET OF ALUMINUM WITH A COST PER SQUARE FOOT OF $3.50 SHEETS ARE 4' X 4' MATERIAL = (10,000/2)(4)(4)($3.50) = $280,000 OVERHEAD COST FOR A LOT OF 10,000 UNITS OVERHEAD = $304,000

LABOR COST FOR A LOT OF 10,000 UNITS LABOR = ($20.00)(3.0/60)(10,000)+($18.20)(1.0/60)(10,000)+($17.20)(2.0/60)(10,000)+($16.00)(5.0/60)(10 LABOR = $33,300 TOTAL COST = MATERIAL + OVERHEAD + LABOR TOTAL COST = $280,000 + $304,000 + $33,300 TOTAL COST = $617,300 b

COST PER PIECE = TOTAL COST / NUMBER OF PIECES COST PER PIECE = $617,300 / 10,000 COST PER PIECE = $61.73

DEPARTMENT CUTTING STAMPING

FLOOR SPACE 1,300 1,600

% OF TOTAL FLOOR SPACE 17.11% 21.05%

OVERHEAD DISTRIBUTED $52,000.00 $64,000.00

TRIMMING

1,200

15.79%

$48,000.00

ASSEMBLE

2,000

26.32%

$80,000.00

PACKAGE TOTALS

1,500 7,600

19.74% 100.00%

$60,000.00 $304,000.00

PROBLEM 16.28 CATEGORY RAW MATERIAL DEPT A LABOR DEPT B LABOR DEPT A OVHD DEPT B OVHD TOTAL PROFIT BID

COST $750.00 $375.00 $750.00 $375.00 $1,000.00 $3,250.00 $812.50 $4,062.50

CALCULATION GIVEN ($15.00/HR)(25 HRS) ($15.00/HR)(50 HRS) (25 HRS)($13,500/900 HRS) (50 HRS)($27,000/1,350 HRS) SUM 25% OF TOTAL COST TOTAL COST + PROFIT

PROBLEM 16.29 a

OVERHEAD APPLICATION RATE = $437.50 / 35 HRS = $12.50 / HR PREVIOUS PERIOD OVERHEAD COSTS = (OVHD RATE)(LABOR HOURS) PREVIOUS PERIOD OVERHEAD COSTS = ($12.50/HR)(1,000 HRS) = $12,500

OVERHEAD APPLICATION RATE = $12,500 / ((1,000 HRS)($10/HR)) = $1.25 / LABOR $ OVERHEAD APPLIED TO JOB = ($1.25/LABOR $)(35 HRS)($10/HR) = $437.50

NOTE: THE SAME ALLOCATED OVHD DOLLARS AS THOSE ALLOCATION PER LABOR HOUR IS EXP SINCE THE LABOR RATE ($10/HR) WAS THE SAME IN BOTH PERIODS

PER LABOR HOUR IS EXPECTED

PROBLEM 16.30 a

CATEGORY RAW MATERIAL LABOR OVERHEAD TOTAL COST PER UNIT

COST $1,500.00 $1,200.00 $900.00 $3,600.00 $3.60

CALCULATION GIVEN ($10.00/HR)(120 HRS) ($7.50/HR)(120 HRS) TOTAL COST / 1,000 UNITS

MAKING THE UNIT AT $3.60/UNIT IS PREFERRED TO BUYING AT $4.00/UNIT b

BREAKEVEN VALUE FOR OVERHEAD RATE PURCHASE COST = MAKE COST ($4.00/UNIT)(1,000 UNITS) = $1,500 + $1,200 + (120 HRS)(RATE) RATE = ($4,000 - $1,500 - $1,200) / 120 HRS RATE = $10.83 MAKE IS PREFERRED FOR OVERHEAD RATES UP TO $10.83 / HR BUY IS PREFERRED FOR OVERHEAD RATES ABOVE $10.83 / HR

PROBLEM 16.31 a

EVA IN YEAR 8 = NET OPERATING PROFIT AFTER TAXES - CAPITAL CHARGE = $208,440 - $9,600 =

CAPITAL CHARGE IN YEAR 9 = (COST OF CAPITAL)(CAPITAL) = (0.1)($57,600) = $5,760

CHARGE = $208,440 - $9,600 = $198,840

PROBLEM 16.32 a

EVA IN YEAR 5 = NET OPERATING PROFIT AFTER TAXES - CAPITAL CHARGE = $201,758 - $12,384 =

CAPITAL CHARGE IN YEAR 6 = (COST OF CAPITAL)(CAPITAL) = (0.1)($74,304) = $7,430.40

CHARGE = $201,758 - $12,384 = $189,374

PROBLEM 16.33

EVA IN YEAR 3 = (REVENUE - EXPENSES - DEPRECIATION)(1 - TAX RATE) - (MARR)(CAPITAL EMPL EVA IN YEAR 3 = ($20,000 - $3,000 - ($60,000)(0.1481))(1 - 0.30) - ((0.10)($60,000-($60,000)(0.3333+0.44 EVA IN YEAR 3 = $4,346.60

) - (MARR)(CAPITAL EMPLOYED, EOY 2)

PROBLEM 16.34 LIVE WIRE ELECTRONICS INCOME STATEMENT MONTH ENDED JUNE 30 SALES COST OF GOODS SOLD GROSS PROFIT OTHER EXPENSES ADVERTISING ADMINISTRATIVE TAXES NET INCOME

$500,000 $170,000 $330,000 $25,000 $75,000 $70,000 $160,000

PROBLEM 16.35

EVA IN YEAR 3 = (REVENUE - EXPENSES - DEPRECIATION)(1 - TAX RATE) - (MARR)(CAPITAL EMPL EVA IN YEAR 3 = ($25,000 - $1,500 - ($50,000)(0.1481))(1 - 0.40) - ((0.10)($50,000-($50,000)(0.3333+0.44 EVA IN YEAR 3 = $8,546.00

7405

PROBLEM 16.36 a

OVERHEAD RATE AS A PERCENT OF DIRECT LABOR COST = $4,800 / $11,200 = 0.4286 = 42.86%

OVERHEAD RATE AS A PERCENT OF PRIME COST = $4,800 / ($11,200+$3,000) = 0.3380 = 33.80%

OVERHEAD RATE PER DIRECT LABOR HOUR = $4,800 / 2,800 HRS = $1.7143 / HR

OVHD CHARGE = RATE * HOURS = ($1.7143/HR)(125 HRS) = $214.29

/ $11,200 = 0.4286 = 42.86%

0+$3,000) = 0.3380 = 33.80%

PROBLEM 16.37 a

MANY SITES PROVIDE VALUABLE INFORMATION, AMONG THEM ARE: HTTP://EN.WIKIPEDIA.ORG/WIKI/ACTIVITY-BASED_COSTING HTTP://WWW.DIRECTIVES.DOE.GOV/PDFS/DOE/DOETEXT/NEWORD/430/G4301-1CHP24.PDF HTTP://WWW.ASAFM.ARMY.MIL/CEAC/CM-ABC/TRNG/BASIC-ABC.PPT HTTP://WWW.CIMAGLOBAL.COM/CPS/RDE/XBCR/LIVE/ABM_TECHRPT_0401.PDF

HTTP://WWW.ASAFM.ARMY.MIL/CEAC/CM-ABC/TRNG/BASIC-ABC.PPT

HTTP://WWW.ASAFM.ARMY.MIL/CEAC/CM-ABC/TRNG/BASIC-ABC.PPT IS A DOWNLOADABLE POWE DEPARTMENT OF THE ARMY. IT IS INTRODUCTORY BUT PROVIDES A GOOD OVERVIEW OF BASI

PROBLEM 16.38 a

MANY SITES PROVIDE VALUABLE INFORMATION, AMONG THEM ARE: WWW.INVESTOPEDIA.COM WWW.VALUEBASEDMANAGEMENT.NET WWW.VALUATIONRESOURCES.COM,

WWW.INVESTOPEDIA.COM

INVESTOPEDIA.COM HAS A WELL ORGANIZED AND EASY TO NAVIGATE TUTORIAL ON ECONOMIC

PROBLEM 16.39 a

TRADITIONAL ALLOCATION BASED ON DIRECT LABOR HOURS OVERHEAD ALLOCATED TO UPPER = ($2,500,000)(25,000/(25,000+28,000)) OVERHEAD ALLOCATED TO UPPER = $1,179,245 CATEGORY MATERIAL LABOR OVERHEAD TOTAL NUMBER OF UNITS COST PER UNIT

COST $1,500,000 $1,000,000 $1,179,245 $3,679,245 10,000 $367.92

ACTIVITY BASED COSTING CATEGORY REWORK MATERIAL HANDLING CATEGORY MATERIAL LABOR

COST $1,800,000

DRIVER UNITS 46,500

COST PER UNIT $38.71

$700,000

60,000

$11.67

COST $1,500,000.00 $1,000,000.00

OVERHEAD REWORK

$1,645,161.29 (42,500 HOURS)(38.71/HR)

MATL HANDLING TOTAL NUMBER OF UNITS COST PER UNIT

$233,333.33 (20,000 MOVES)($11.67/MOVE) $4,378,494.62 10,000 $437.85

PROBLEM 16.40 a

TRADITIONAL ALLOCATION BASED ON DIRECT LABOR HOURS OVERHEAD ALLOCATED TO LOWER = ($2,500,000)(28,000/(25,000+28,000)) OVERHEAD ALLOCATED TO LOWER = $1,320,755 CATEGORY MATERIAL LABOR OVERHEAD TOTAL NUMBER OF UNITS COST PER UNIT

COST $2,000,000 $700,000 $1,320,755 $4,020,755.00 20,000 $201.04

ACTIVITY BASED COSTING CATEGORY REWORK MATERIAL HANDLING CATEGORY MATERIAL LABOR OVERHEAD REWORK MATL HANDLING TOTAL NUMBER OF UNITS COST PER UNIT

COST $1,800,000 $700,000

DRIVER UNITS 46500 60000

COST PER UNIT $38.71 $11.67

COST $2,000,000.00 $700,000.00 $154,838.71 (4,000 HOURS)(38.71/HR) $466,666.67 (40,000 MOVES)($11.67/MOVE) $3,321,505.38 20,000 $166.08

PROBLEM 16.41 a

TRADITIONAL ALLOCATION BASED ON NUMBER OF UNITS PRODUCED OVERHEAD ALLOCATED TO PRETTY SAFE = ($750,000)(3,000/(3,000+2,000)) OVERHEAD ALLOCATED TO PRETTY SAFE = $450,000 CATEGORY MATERIAL LABOR OVERHEAD TOTAL NUMBER OF UNITS COST PER UNIT

COST $350,000 $100,000 $450,000 $900,000 3,000 $300.00

ACTIVITY BASED COSTING CATEGORY PRODUCTION ENGINEERING CATEGORY MATERIAL LABOR

COST $500,000

DRIVER UNITS 5,000

COST PER UNIT $100.00

$250,000

5,000

$50.00

COST $350,000.00 $100,000.00

OVERHEAD PRODUCTION

$100,000.00 (1,000 HOURS)($100/HR)

ENGINEERING

$100,000.00 (2,000 HOURS)($50/HR) $650,000.00 3,000 $216.67

TOTAL NUMBER OF UNITS COST PER UNIT

PROBLEM 16.42 a

TRADITIONAL ALLOCATION BASED ON NUMBER OF UNITS PRODUCED OVERHEAD ALLOCATED TO VIRTUALLY IMPENETRABLE = ($750,000)(2,000/(3,000+2,000)) OVERHEAD ALLOCATED TO VIRTUALLY IMPENETRABLE = CATEGORY MATERIAL LABOR OVERHEAD TOTAL NUMBER OF UNITS COST PER UNIT

COST $150,000 $200,000 $300,000 $650,000 2,000 $325.00

ACTIVITY BASED COSTING CATEGORY PRODUCTION ENGINEERING

COST $500,000 $250,000

CATEGORY MATERIAL LABOR OVERHEAD PRODUCTION ENGINEERING

COST $150,000.00 $200,000.00

TOTAL NUMBER OF UNITS COST PER UNIT

DRIVER UNITS 5,000 5,000

$400,000.00 (4,000 HOURS)($100/HR) $150,000.00 (3,000 HOURS)($50/HR) $900,000.00 2,000 $450.00

NITS PRODUCED

E = ($750,000)(2,000/(3,000+2,000)) $300,000

COST PER UNIT $100.00 $50.00

HOURS)($100/HR) HOURS)($50/HR)

FE-type Sample Questions for PEEA 6e Chapter 1 Chapter 1

1. The fact that one should not add or subtract money unless it occurs at the same point in time is an illustration of what concept? (a) time value of money (b) marginal return (c) economy of scale (d) Pareto principle Answer: (a)

2. If a set of investment alternatives contains all possible choices that can be made, then the set is said to be which of the following? (a) coherent (b) collectively exhaustive (c) independent (d) mutually exclusive Answer: (b)

3. Which of the following examples does not illustrate a cash flow approach? (a) a payroll manager writes a check to pay a shop worker (b) a neighbor pays $0.25 to buy a glass of lemonade at a lemonade stand (c) a hungry teenager pays for snacks with a debit card (d) a building contractor buys lumber on account at a local lumber yard Answer: (d) 4. The “discounting” in a discounted cash flow approach requires the use of which of the following? (a) an interest rate (b) the economic value added (c) the gross margin (d) the incremental cost Answer: (a)

5. Risks and returns are generally ______________ correlated. (a) inversely (b) negatively (c) not (d) positively Answer: (d) 6. Assuming zero incremental costs for the “do nothing” alternative is generally (a) appropriate (b) risky (c) optimistic (d) realistic Answer: (b) 7. Answering “what if” questions with respect to an economic analysis is an example of which step in the Systematic Economic Analysis Technique? (a) identifying the investment alternatives (b) defining the planning horizon (c) comparing the alternatives (d) performing supplementary analysis Answer: (d) 8. Which of the following is useful in making a final selection when multiple criteria exist? (a) four discounted cash flow rules (b) seven step systematic analysis technique (c) ten principles of engineering economic analysis (d) weighted factor comparison method Answer: (d)

9. Time value of money calculations may not be required in an economic evaluation for all of the following reasons except (a) annual cash flows are proportional to the first year cash flow (b) inflation is absent (c) no investment of capital is required (d) no differences in the cash flows of the alternatives after the first year Answer: (b) 10. If a student’s time value of money rate is 30 percent, then the student would be indifferent between $100 today and how much in one year? (a) $30 (b) $100 (c) $103 (d) $130 Answer: (d)

11. A bottled mango juice drink must contain at least 17.0% mango juice for proper taste. The drink is created by blending unprocessed juice from two orchards. RightRipe Orchard sells unprocessed mango juice that is 12.5% mango juice and 87.5% base liquids. PureBlend Orchard sells unprocessed juice that is 20.0% mango juice and 80.0% base. What percentage of unprocessed juice from each orchard is required to exactly meet the 17.0% specification? (a) 40% RightRipe; 60% PureBlend (b) 50% RightRipe; 50% PureBlend (c) 60% RightRipe; 50% PureBlend (d) Can not be determined from the information given Answer: (a)

12. A printed circuit board is produced by passing through a sequence of three steps. The scrap rates for steps one through three are 5%, 3%, and 3%, respectively. If 10,000 good parts are needed, the number that should be started at step one is closest to which of the following? (a) 11,100 (b) 11,140 (c) 11,190 (d) 11,240 Answer: (c)

13. Reconsider the preceding problem assuming that the sequence can be rearranged such that the processing step with the 5% scrap rate occurs last rather than first. Using this redesigned sequence, the number of parts that should be started will (a) Increase (b) Decrease (c) Be unchanged (d) Cannot be determined from the information given Answer: (c)

FE-type Sample Questions for PEEA 6e Chapter 2 Chapter 2

1. A deposit of $3,000 is made in a savings account that pays 7.5% interest compounded annually. How much money will be available to the depositor at the end of 16 years? (a) $8,877 (b) $10,258 (c) $9,542 (d) $943 Answer: (c) 2. The plan was to leave $5,000 on deposit in a savings account for 15 years at 6.5% interest compounded annually. It became necessary to withdraw $1,500 at the end of the 5th year. How much will be on deposit at the end of the 15 year period? (a) $11,359 (b) $9,359 (c) $12,043 (d) $10,043 Answer: (d) 3. A child receives $100,000 as a gift which is deposited in a 6% bank account compounded semiannually. If $5,000 is withdrawn at the end of each half year, how long will the money last? (a) 21.0 years (b) 15.5 years (c) 25.0 years (d) 18.0 years Answer: (b)

4. Your company seeks to take over Good Deal Company. Your company’s offer for Good Deal is for $3,000,000 in cash upon signing the agreement followed by 10 annual payments of $300,000 starting one year later. The time value of money is 10%. What is the present worth your company’s offer? (a) $3,000,000 (b) $2,281,830 (c) $4,843,380 (d) $5,281,830 Answer: (c)

5. If you want to triple your money at an interest rate of 6% per year compounded annually, for how many years would you have to leave the money in the account? (a) 12 years (b) 19 years (c) 32 years (d) cannot be determined without knowing the amount invested. Answer: (b)

6. Let F be the accumulated sum, P the principal invested, i the annual compound interest rate, and n the number of years. Which of the following correctly relates these quantities? (a) F = P (1 + in) (b) F = P (1 + i)n (c) F = P (1 + n)i (d) F = P (1 + ni)n-1 Answer: (b) 7. The maintenance costs of a car increase by $200 each year. This cash flow pattern is best described by which of the following? (a) gradient series (b) geometric series (c) infinite series (d) uniform series Answer: (a)

8. If you invest $5,000 three years from now, how much will be in the account fifteen years from now if i = 10% compounded annually. (a) $8,053 (b) $15,692 (c) $20,886 (d) $27,800 Answer: (b) 9. The president of a growing engineering firm wishes to give each of 20 employees a holiday bonus. How much needs to be deposited each month for a year at a 12% nominal rate, compounded monthly, so that each employee will receive a $2,500 bonus? (a) $2,070 (b) $3,840 (c) $3,940 (d) $4,170 Answer: (c)

10. What is the annual interest rate if a simple interest loan of $10,000 for four years charges a total of $2,800 interest? The loan is repaid with a single payment at the end of year four. (a) 7.0% (b) 28.0% (c) i such that 12,800 = 10,000 (F|P,i,4) (d) cannot be determined from the information given Answer: (a)

11. What is the effective annual interest rate if the nominal annual interest rate is 24% per year compounded monthly? (a) 2.00% (b) 24.00% (c) 26.82% (d) 27.12% Answer: (c)

12. Under what circumstances are the effective annual interest rate and the period interest rate equal? (a) Never true (b) If the number of compounding periods per year is one (c) If the number of compounding periods per year is infinite (d) Always true Answer: (b)

13. Consider the following cash flow diagram. What is the value of X if the present worth of the diagram is $400 and the interest rate is 15% compounded annually? 200 X

(a) $246 (b) $165 (c) $200 (d) $146 Answer: (b)

14. A young engineer calculated that monthly payments of $A are required to pay off a $5,000 loan for n years at i% interest, compounded annually. If the engineer decides to borrow $10,000 instead with the same n and i%, her monthly payments will be $2A. (a) TRUE (b) FALSE (c) Can not be determined without knowing the value of n and i (d) Can not be determined without knowing the value of n or i Answer: (a)

FE-type Sample Questions for PEEA 6e Chapter 3 Chapter 3 1. When repaying a loan using Method 1 (interest each period; principal only at end), what can be said about the payments? (a) The interest payments will decrease by a constant amount each period. (b) The interest payments will increase by a constant amount each period. (c) The interest payments will either increase or decrease, but not necessarily by a constant amount each period. (d) The interest payments will remain constant from period to period. Answer (d) 2. When repaying a loan using Method 3 (equal end-of-period payments), which of the following is true? (a) Interest payments will increase and principal payments will decrease from period to period. (b) Interest payments will decrease and principal payments will increase from period to period. (c) Interest payments and principal payments will both increase from period to period. (d) Interest payments and principal payments will both decrease from period to period. Answer (b) 3. When repaying a loan using the four methods presented in chapter 3 (assuming no taxes and no inflation), what can be said about the borrower’s preferred payment method? (a) Since Method 3 is most commonly used, it is the preferred method. (b) Method 2 is preferred if the borrower’s TVOM < lender’s interest rate and Method 4 is preferred otherwise. (c) Method 4 is preferred if the borrower’s TVOM < lender’s interest rate and Method 2 is preferred otherwise. (d) Methods 1 and 3 are equally advantageous to the borrower. Abswer (b) 4. A house is to be purchased for $180,000 with a 10% down payment, thereby financing $162,000 with a home loan and mortgage. There are no “points” or other closing charges associated with the loan. A conventional 30 year loan is used at 7.5%, resulting in monthly payments of $1132.73. The interest portion of the first monthly payment will be what? (a) $1012.50 (b) $682.73

(c) $120.23 (d) Answer cannot be determined without more information. Answer (a) 5. A house is to be purchased for $270,000 with a 5% down payment, thereby financing $256,500 with a home loan and mortgage. There are 2 “points” assessed and there are additional closing charges of $3500 at the time of closing, with both “points” and additional charges being included in the loan. A conventional 30 year loan is used at 7.5%, resulting in monthly payments of $1853.83. Which of the following statements is false? (a) The loan will be figured on a total of $265,130 borrowed. (b) There can (unfortunately) be multiple methods of computing the APR (annual percentage rate) on such a loan, yielding (usually slightly) different answers. (c) The effective interest rate will exceed 7.5%. (d) The APR will be less than 7.5%. Answer (d) 6. You want to purchase a house and you have done a thorough job of identifying many different local and Web-based financing plans. Various plans have different up-front charges, and you intend to roll all such charges into the loan, thereby paying no loan-related charges out of your pocket at time of closing. Your best estimate is that you will be in the house for only 5 years, at which time you will sell it and move on. Right now, you want to determine the most economically advantageous financing plan. Your approach should be to calculate which of the following for each financing alternative? (a) Determine all payments you will make over the 5 years, including the loan “payoff” at the end of the 5 years, and determine the PW using your TVOM; select the largest (least negative) PW. (b) Determine all payments you will make over the 5 years, including the loan “payoff” at the end of the 5 years, and determine the PW using the loan rate of interest; select the largest (least negative) PW. (c) Determine the PW at your TVOM of the estimated market value of the house after 5 years, less all monthly payments you will make over the 5 years; select the largest PW. (d) Determine the PW at your loan rate of interest of the estimated market value of the house after 5 years, less all monthly payments you will make over the 5 years; select the largest PW. Answer (a) 7. Consider a 7/1 ARM loan, starting at 5.0% with potential up-or-down yearly increments of 1.0% in the rate. Why is such an ARM loan potentially economically dangerous?

(a) Actually, many people have financed their house with an ARM and such loans are not considered potentially economically dangerous. (b) The loan interest rate can increase without limit over the life of the loan. (c) The loan interest rate for the example mentioned can start at 5% and increase to as much as 12% after 7 years, effectively doubling (+/-) the monthly payment. (d) The economic risk of an ARM loan is neutralized because it is just as likely that the interest rate for the example mentioned could go down each year by the maximum amount. Answer (c) 8. One of your financing options is a balloon loan on a $200,000 30 year mortgage with monthly payments and an interest rate of 7.5% per year. Which of the following statements is correct? (a) Monthly payments are $1500 and balloon payment is $200,000 after 30 years. (b) Monthly payments are $1500 and balloon payment is more than $200,000 after 30 years. (c) Monthly payments are $1250 and balloon payment is $200,000 only after 30 years. (d) Monthly payments are $1250 and balloon payment is $200,000 at any time the loan is paid off. Answer (d) 9. You borrow $5000 at 10% per year and will pay off the loan in 3 equal annual payments starting one year after the loan is made. The end-of-year payments are $2010.57. Which of the following is true for your payment at the end of year 2? (a) Interest is $500.00 and principal is $1510.57. (b) Interest is $450.00 and principal is $1560.57. (c) Interest is $348.94 and principal is $1661.63. (d) Interest is $182.78 and principal is $1827.79. Answer (c) 10. You borrow $10,000 at 15% per year and will pay off the loan in 3 equal annual payments with the first occurring at the end of the 4th year after the loan is made. The three equal annual payments will be $4379.77. Which of the following is true for your first payment at the end of year 4? (a) Interest = $4379.77; principal = $0.00. (b) Interest = $2281.31; principal = $2098.46. (c) Interest = $1500.00; principal = $2879.77. (d) Interest = $0.00; principal = $4379.77 Answer (a)

11. You are looking ahead to retirement and desire to invest 7% of your salary in investments earning 6%. You expect your salary to increase at 5% per year throughout your working life of 35 years. If you are now earning $50,000 and you will make your first investment at the end of this year, which of the following is the correct estimate of the future value of your investments at retirement? (a) F=$3500(F|P 6%,35)+$175(A|G 6%,35)(F|A 6%,35) (b) F=$3500(F|A1 6%,5%,35) (c) F=$3500(F|A1 5%,6%,35) (d) F=$3500(P|A1 6%,5%,35)(A|P 6%,35) Answer (b) 12. What series of equal annual payments is equivalent to a series of decreasing payments as follows: $5000, $4000, $3000, $2000, $1000 if the interest rate is 10% per year? (a) $3000 (b) $3000(1+0.1) = $3300 (c) [$5000(F|P 10%,4)+$4000(F|P 10%,3)+$3000(F|P 10%,2)+$2000(F|P 10%,1)+1000]/5 (d) $5000(A|P 10%,5)-$1000(A|G 10%,5) Answer (d) 13. You purchase a $10,000 bond with a bond rate of 6% per year payable semiannually for 2 years. You pay $9600 for the bond. Which statement is correct? (a) Semiannual cash flows will be -$9600, $300, $300, $300, $9900 and the bond will earn more than 10% (b) Semiannual cash flows will be -$9600, $300, $300, $300, $9900 and the bond will earn less than 10% (c) Semiannual cash flows will be -$9600, $300, $300, $300, $10,300 and the bond will earn more than 10% (d) Semiannual cash flows will be -$9600, $300, $300, $300, $10,300 and the bond will earn less than 10% 14. Consider a cash flow and interest profile as shown: Year 0 Year 1 Year 2 Year 3 Cash Flow at End of Year -$1000 $3000 $2000 $1000 Interest Rate During Year NA 6% 8% 10% The worth at the end of Year 3 of these cash flows is: (a) $5000.00 (b) $5504.72 (c) $5994.56 (d) $5440.00 Answer (b)

FE-type Sample Questions for PEEA 6e Chapter 4 Chapter 4

1. When using the "shortest life" planning horizon, what issue should you explicitly consider for alternatives whose cash flow profiles extend longer than the "shortest life." (a) determination of salvage values for truncated cash flows (b) the validity of the assumption that cash flow profiles are repetitive (c) both (a) and (b) (d) neither (a) nor (b) Answer: (a)

2. Given the following information about sources of capital, what is the appropriate weighted average cost of capital to use in determining MARR? Source Loans Bonds Retained Earnings

Before Tax Cost 10.0% 15.0% ---

After Tax Cost 6.6% 9.9% 12.0%

Proportion of Total Funds 0.20 0.50 0.30

(a) 9.87% (b) 10.55% (c) 12.42% (d) 13.10% Answer: (a)

3. When using the "longest life" planning horizon, what issue(s) might you have to consider for alternatives whose cash flow profiles are shorter than the "longest life"? (a) determination of salvage values for any truncated cash flows (b) the validity of the assumption that cash flow profiles are repetitive (c) both (a) and (b) (d) neither (a) nor (b) Answer: (c)

4. Kooche Company plans to invest $1,000,000 in projects next year. $700,000 will be provided through debt capital with a before tax cost of 7.3%. The remaining $300,000 will be provided through equity capital at a cost of 6.5%. Kooche’s corporate tax rate is 40%. What is the weighted average cost of capital? (a) 5.02% (b) 6.50% (c) 7.06% (d) 13.80% Answer: (a)

5. Three alternatives are being considered. Alternative A has a useful life of 3 years; Alternative B, 5 years; and Alternative C, 6 years. Using the longest life approach, what is the planning horizon? (a) 6 years (b) 14 years (c) 18 years (d) 30 years Answer: (a)

6. Three alternatives are being considered. Alternative A has a useful life of 5 years; Alternative B, 6 years; and Alternative C, 8 years. Using the least common multiple approach, what is the planning horizon? (a) 30 years (b) 48 years (c) 120 years (d) 240 years Answer: (c)

7. Three alternatives are being considered. Alternative A has a useful life of 6 years; Alternative B, 2 years; and Alternative C, 3 years. What is the difference (in years) between the planning horizons determined by the longest life approach and the least common multiple approach? (a) 0 years (b) 6 years (c) 12 years (d) 30 years Answer: (a)

8. Which of the following best represents the relationship between the weighted average cost of capital (WACC) and the minimum attractive rate of return (MARR)? (a) WACC and MARR are unrelated (b) WACC is a lower bound for MARR (c) WACC is an upper bound for MARR (d) MARR <= WACC Answer: (b)

9. Which of the following is true about the minimum attractive rate of return (MARR) used in judging the economic value of projects? (a) MARR has no bearing on engineering projects (b) MARR is the same for all companies (c) MARR is usually much smaller than the interest rate used in discounted cash flow analysis (d) the value of MARR is usually determined by management based on many factors Answer: (d)

10. The after tax cost of capital for a loan is less than the effective interest rate on the loan for the following reason? (a) discounting (b) inflation (c) MARR (d) tax deductions Answer: (d) 11. The “weights” in the weighted average cost of capital (WACC) approach are usually determined based on which of the following? (a) 1/n where n is the number of sources (b) negotiations with fund providers (c) proportion of funds obtained from each source (d) the ratio of the after tax cost for each source Answer: (c)

12. Within the context of engineering economy, beta (β) symbolizes which of the following? (a) The corporate tax rate (b) The price of a company’s preferred stock (c) The ratio of common stock price to preferred stock price (d) The volatility of a stock relative to the overall market Answer: (d)

13. When calculating the weighted average cost of capital, the costs of which of the following types of capital include a (1-T) multiplier, where T is the effective tax rate? (a) Debt capital (b) Equity capital (c) Both (a) and (b) (d) Neither (a) nor (b) Answer: (a)

FE-type Sample Questions for PEEA 6e Chapter 5 Chapter 5

1. When using present worth to evaluate the attractiveness of a single alternative, what value is the calculated PW compared to in determining if an investment is attractive? (a) 0.0 (b) MARR (c) 1.0 (d) WACC Answer: (a)

2. A natural gas well is projected to produce $200,000 in profit during its first year of operation, $190,000 the second year, $180,000 the third year, and so on continuing this pattern. If the well is expected to produce for a total of 10 years, and the effective annual interest rate is 8%, which of the following most closely represents the present worth of the well? (a) $1,770,000 (b) $1,508,000 (c) $1,253,000 (d) $1,082,000 Answer: (d)

3. The present worth of a multi-year investment with all positive cash flows (incomes) other than the initial investment is PW = $10,000 at MARR = i%. If MARR changes to (i+1)%, the present worth will be (a) less than $10,000 (b) equal to $10,000 (c) greater than $10,000 (d) cannot determine without the cash flow profile and a value for i

Answer: (a)

4. Consider the following cash flow diagram. Which of the following expressions is not a valid expression for the present worth?

$100 + -

$150 2

$200

$250

10%/yr

(a) P = 100(P|A,10,6) + 50(P|G,10,3) + 150(P|A,10,3)(P|F,10,3) (b) P = 100(P|A,10,3) + 50(P|G,10,3) + 250(P|A,10,3)(P|F,10,3) (c) P = 250(P|A,10,6) - 50(P|G,10,3) (d) P = 100(P|A,10,4) + 50(P|G,10,4) + 250(P|A,10,2)(P|F,10,4) Answer: (c)

5. Ivan the industrial engineer is working a homework problem for Engineering Economy. He needs to calculate the PW at 12% of a cash flow series with $1,000 at t = 3, $1,500 at t = 4 and $2,000 at t = 5. If Ivan uses the equation: P = 1000(P/A,12,3) + 500(P/G,12,3), where is the P now located? (a) t = 4 (b) t = 2 (c) t = 1 (d) t = 0 Answer: (b)

6. The owner of a cemetery plans to offer a perpetual care service for grave sites. The owner estimates that it will cost $120 per year to maintain a grave site. If the interest rate is 8%, what one-time fee should the owner charge for the perpetual care service? (a) $96 (b) $120 (c) $1,500 (d) $12,000 Answer: (c)

7. Consider a palletizer at a bottling plant that has a first cost of $150,000, operating and maintenance costs of $17,500 per year, and an estimated net salvage value of $25,000 at the end of thirty years. Assume an interest rate of 8%. What is the present equivalent cost of the investment if the planning horizon is thirty years? (a) $335,000 (b) $344,500 (c) $360,000 (d) $395,500 Answer: (b)

8. The heat loss through the windows of a home is estimated to cost the homeowner $412 per year in wasted energy. Thermal windows will reduce heat loss by 93% and can be installed for $1,232. The windows will have no salvage value at the end of their estimated life of eight years. Determine the net present equivalent value of the windows if the interest rate is 10%. (a) $412 (b) $812 (c) $1,044 (d) $1,834 Answer (b)

9. An inline filter has an estimated life of nine years. By adding a purifier to the filter, savings of $300 in annual operating costs can be obtained. Interest on capital is 8%. Compute the maximum expenditure justifiable for the purifier. (a) $24 (b) $33 (c) $300 (d) $1,875 Answer: (d)

10. The city council has approved the building of a new bridge over Running Water Creek. The bridge will cost $17,000 for initial construction and have an annual maintenance cost of $1,000. The council plans to withdraw money from the city's Bridges & Highways account to open a special account to cover the initial construction and to fund a perpetuity to cover the maintenance costs forever. How much money must be withdrawn from the Bridges & Highways account if the city can expect to earn 5% on the special account? (a) $1,000 (b) $17,000 (c) $18,000 (d) $37,000 Answer (d)

11. Two projects, A and B, are analyzed using ranking present worth analysis with MARR at i%. It is found that PW(A) > PW(B). If MARR is changed to (i+1)%, what will be the relationship between PW(A) and PW(B)? (a) PW(A) > PW(B) (b) PW(A) = PW(B) (c) PW(A) < PW(B) (d) can not be determined without the cash flow profiles Answer: (d)

FE-type Sample Questions for PEEA 6e Chapter 6 Chapter 6

1. Moving money forward in time while accounting for the time value of money is referred to by what term? (a) weighted average cost of capital (b) minimum attractive rate of return (c) discounting (d) compounding Answer: (d)

2. When using future worth to evaluate the attractiveness of a single alternative, what value is the calculated FW compared to in determining if an investment is attractive? (a) 0.0 (b) 1.0 (c) MARR (d) WACC Answer: (a)

3. If you invest $3,000 three years from now, how much will be in the account fifteen years from now if i = 8% compounded annually. (a) $3,500 (b) $7,555 (c) $9,415 (d) $9,516 Answer: (b)

4. Consider a palletizer at a bottling plant that has a first cost of $150,000, operating and maintenance costs of $17,500 per year, and an estimated net salvage value of $25,000 at the end of thirty years. Assume an interest rate of 8%. What is the future equivalent cost of the investment if the planning horizon is thirty years? (a) $3,371,000 (b) $3,517,000 (c) $3,623,000 (d) $3,980,000 Answer: (b)

5. $5,000 is deposited in an account that pays 6% interest. Two years from today, another $5,000 is deposited. Five years from today $10,000 is withdrawn from the account. How much money is in the account six years from today? (a) $0 (b) $2,646 (c) $2,805 (d) $3,056 Answer: (c)

6. Scott wants to accumulate $2,500 over a period of 7 years so that a cash payment can be made for a new roof on his summer cottage. To have this amount when it is needed, he will make annual deposits at the end of each year into a savings account that earns 8% annual interest per year. How much must each annual deposit be? (a) $244 (b) $259 (c) $280 (d) $357 Answer: (c)

7. Which of the following expressions will correctly determine the future worth of the following general cash flow series at time 7?

10%

(a) W(F|A,10,3)(F|P,10,4) - W(F|P,10,3) + W(F|A,10,3) (b) W(F|A,10,3)(F|P,10,3) - W(F|P,10,3) + W(F|A,10,3) (c) W(F|A,10,7) - W(F|P,10,4) (d) none of the above Answer: (a)

8. A piece of machinery costs $20,000 and has an estimated life of eight years and a scrap value of $2,000. What uniform annual amount must be set aside at the end of each of the eight years for replacement if the interest rate is 4%? (a) $1,953 (b) $2,174 (c) $2,250 (d) $2,492 Answer: (a)

9. How much money would be accumulated in 5 years with an initial deposit of $10,000, if the account earned interest at 12% per year for the first 3 years and at 15% per year for the last 2 years? (a) $17,623 (b) $18,580 (c) $18,836 (d) $19,078 Answer: (b)

10. A deposit of $800 is planned for the end of each year into an account paying 8%/yr compounded annually. The deposits were not made for the 10th and 11th years. All other deposits were made as planned. What amount of money will be in the account after the deposit at the end of 25th year. (a) $55.397 (b) $55,397 (c) $59,537 (d) $53,597 Answer: (d)

11. Consider the time value of money factors (F|P, i, n) and (F|P, i/12, n*12). Assume i > 0 and n > 0. What can be said about the value of these factors? (a) These factors are always equal (b) These factors are never equal (c) Cannot determine without knowing either i or n (d) Cannot determine without knowing both i and n Answer: (b)

12. The present worth of an alternative is zero. What do we know about the value of the future worth? (a) FW < 0 (b) FW = 0 (c) FW > 0 (d) Cannot be determined without cash flows Answer: (b)

13. On the day your daughter is born, you deposit $1,000 in a college savings account that earns 8% compounded annually. On each of her birthdays thereafter, up to and including her 18th birthday, you deposit an additional $1,000. How much money is in the college account the day after her 18th birthday? (a) $37,450 (b) $38,950 (c) $41,450 (d) $46,800 Answer: (c)

FE-type Sample Questions for PEEA 6e Chapter 7 Chapter 7

1. Consider a palletizer at a bottling plant that has a first cost of $150,000, operating and maintenance costs of $17,500 per year, and an estimated net salvage value of $25,000 at the end of thirty years. Assume an interest rate of 8%. What is the annual equivalent cost of the investment if the planning horizon is thirty years? (a) $29,760 (b) $31,050 (c) $31,980 (d) $35,130 Answer: (b)

2. When using annual worth to evaluate the attractiveness of a single alternative, what value is the calculated AW compared to in determining if an investment is attractive? (a) PW (b) FW (c) 0.0 (d) MARR Answer: (c)

3. The annual worth of an alternative is zero. Which of the following is (are) also true? I. II.

PW = 0 FW = 0

(a) I (b) II (c) Both I and II (d) Neither I nor II Answer: (c)

4. The overhead costs in a highly automated factory are expected to increase at an annual compound rate of 10% for the next 7 years. The overhead cost at the end of the first year is $200,000. What is the annual worth of the overhead costs for the seven-year period? The time value of money rate is 8%/yr. (a) $263,250 (b) $231,520 (c) $200,000 (d) $187,020 Answer: (a)

5. The operating and maintenance expenses for a mining machine are expected to be $11,000 in the first year, and increase by $800 per year during the 15 year life of the machine. What uniform series of payments would cover these expenses over the life of the machine? Interest is 10%/yr compounded annually. (a) $11,000 (b) $4,223 (c) $13,423 (d) $15,223 Answer: (d)

6. A successful alumnus gives State University $2 million to establish an endowed scholarship fund. If the university can invest at 5%/yr and gives $100,000 in scholarships each year, for how many years will the endowment last? (a) 37 years (b) 20 years (c) forever (d) cannot be determined Answer: (c)

7. Consider the cash flow profile given in the table below. What is the annual worth of these costs? End of Year 0 1 2 3 4 5

Cost $1,000 $100 $200 $300 $400 $300

(a) $418 (b) $436 (c) $502 (d) $536 Answer: (c)

8. A grinding machine has a first cost of $24,000 with an expected useful life of 13 years. Salvage value at the end of its useful life is estimated to be $8,000. Annual maintenance expenses are $350. What is the equivalent uniform annual cost of the grinding machine? (a) $2,370 (b) $2,665 (c) $2,980 (d) $3,010 Answer: (d)

9. Reconsider the grinding machine from the previous question. What is the capital recovery cost of the grinding machine? (a) $2,020 (b) $2,665 (c) $2,980 (d) $3,010 Answer: (b)

10. What is the equivalent uniform annual cost of the following cash flow profile? Assume an interest rate of 15%

End of Year 0 1 2 3 (a) $45,130 (b) $53,125 (c) $62,100 (d) $79,050 Answer: (d)

Cost $50,000 $100,000 $25,000 $37,500

FE-type Sample Questions for PEEA 6e Chapter 8 Chapter 8

1. Using an incremental internal rate of return (IRR) analysis the decision to replace the "current best" by the "challenger" is based on what decision rule (a) the internal rate of return of the increment is greater than the external rate of return (b) the internal rate of return of the increment is greater than the internal rate of return of the previous increment (c) the internal rate of return of the increment is greater than zero (d) the internal rate of return of the increment is greater than MARR Answer: (c)

2. A company is considering two alternatives, one of which must be implemented. Of the two projects, A has the higher maintenance cost, but B has the higher investment cost. The appropriate (and properly calculated) incremental IRR is 17.6%. Which alternative is preferred if the Minimum Attractive Rate of Return is 20%. (a) A (b) B (c) the company is indifferent between A and B (d) can not be determined from the information given Answer: (a)

3. Consider the calculation of an external rate of return (ERR). The positive cash flows in the cash flow profile are moved forward to t = n using what value of i in the (F|P,i,n-t) factors? (a) 0 (b) the unknown value of ERR (i') (c) MARR (d) IRR Answer: (c)

4. If the internal rate of return (IRR) of a well behaved investment alternative is equal to MARR, which of the following statements about the other measures of worth for this alternative must be true? I. II.

PW = 0 AW = 0

(a) I only (b) II only (c) Neither I nor II (d) Both I and II Answer: (d)

5. An investment is guaranteed to have a unique value of IRR if which of the following is true. (a) alternating positive and negative cash flows (b) an initial negative cash flow followed by all positive cash flows (c) a unique value for ERR (d) a positive PW at MARR Answer: (b)

6. Consider the IRR and ERR measures of worth. If we define a "root" to mean a value for the measure that results in PW = 0, then which of the following statements is true. (a) IRR can have multiple roots and ERR can have multiple roots (b) IRR has only a single root but ERR can have multiple roots (c) ERR has only a single root but IRR can have multiple roots (d) IRR has only a single root and ERR has only a single root Answer: (c)

7. When conducting an incremental analysis, what step must always be taken immediately prior to beginning the pair wise comparisons. (a) order the alternatives from highest to lowest initial investment (b) order the alternatives from lowest to highest present worth (c) order the alternatives from lowest to highest internal rate of return (d) order the alternatives from lowest to highest initial investment Answer: (d)

Present Worth

The next two questions are based on the following "present worth versus interest rate" graph for a well behaved investment.

Interest Rate

8. If the interest rate at B is 20%, then which of the following best describes the analysis of the investment? (a) the IRR of the investment is less than 20% (b) the IRR of the investment is equal to 20% (c) the IRR of the investment is greater than 20% (d) none of the above are true Answer: (c)

9. The IRR of this investment is located at which point? (a) A (b) C (c) D (d) E Answer: (d)

10. If the IRR of Alternative A is 18%, the IRR of Alternative B is 16%, and MARR is 12%, which of the following is correct. (a) alternative B is preferred over alternative A. (b) alternative A is preferred over alternative B. (c) not enough information is given to determine which alternative is preferred. (d) neither alternative A nor alternative B is acceptable. Answer: (c)

11. Consider the following cash flow diagram. What is the value of X if the internal rate of return is 15%?

$400

(a) $246 (b) $255 (c) $281 (d) $290 Answer: (a)

12. What is the internal rate of return of the following cash flow diagram?

$30

$31

$15 $30

(a) 20.0% (b) 18.2% (c) 17.5% (d) 15.0% Answer: (d)

13. A snow cone machine at an ice cream shop costs $15,000. The machine is expected to generate profits of $2,500 each year of its 10 year useful life. At the end of the 10 years the machine will have a salvage value of zero. Within what interest rate range does the IRR fall? (a) Less than 10% (b) 10% to 12% (c) 12% to 14% (d) Greater than 14% Answer: (b)

FE-type Sample Questions for PEEA 6e Chapter 9 Chapter 9

1. A lumber company purchases and installs a wood chipper for $200,000. The chipper is classified as MACRS 7-year property. The chipper’s useful life is 10 years. The estimated salvage value at the end of 10 years is $25,000. Using MACRS depreciation, compute the first year depreciation. $17,500.00 $20,000.00 $25,007.50 $28,580.00 Answer: (d)

2. A lumber company purchases and installs a wood chipper for $200,000. The chipper is classified as MACRS 7-year property. The chipper’s useful life is 10 years. The estimated salvage value at the end of 10 years is $25,000. Using Straight Line depreciation, compute the first year depreciation. (a) $28,571.43 (b) $20,000.00 (c) $17,500.00 (d) $25,000.00 Answer: (c)

3. The concept similar to depreciation that is applied to natural resources is called what? (a) Depletion (b) Declining Balance (c) Amortization (d) MACRS Answer: (a)

4. An x-ray machine at a dental office is MACRS 5-year property. The x-ray machine costs $6,000 and has an expected useful life of 8 years. The salvage value at the end of 8 years is expected to be $500. Assuming MACRS depreciation, what is the book value at the end of the third year? (a) $1,584 (b) $1,728 (c) $3,916 (d) $4,272 Answer: (b) 5. Which of the following is not a requirement for an asset to be depreciable? (a) It must have a life longer than 1 year (b) It must have a basis (initial purchase plus installation cost) greater than $1,000 (c) It must be held with the intent to produce income (d) It must wear out or get used up Answer: (b)

6. MACRS-GDS deductions are a combination of which other methods of depreciation? (a) Sum of Years Digits and Straight Line (b) Sum of Years Digits and Declining Balance (c) Double Declining Balance and 150% Declining Balance (d) Double Declining Balance and Straight Line Answer: (d)

7. Production equipment used in the bottling of soft drinks (MACRS-GDS, 10 year property) is purchased and installed for $630,000. What is the depreciation deduction in the 4th year under MACRS-GDS? (a) $90,720 (b) $78,687 (c) $72,576 (d) $48,510 Answer: (c)

8. Which of the following is (are) required to calculate MACRS-GDS depreciation deductions? I. II. III. IV.

Property Class Salvage Value First Cost Annual Maintenance Costs

(a) I and III only (b) II and III only (c) I, II, and III (d) I, II, III, and IV Answer: (a)

9. The depreciation deduction for year 11 of a 15-year property with a 20-year class life is $4,000. If the salvage value of the asset is estimated to be $5,000 and MACRS-GDS is used to calculate the depreciation deduction for year 11, what was the initial cost of the asset? (a) $42,105 (b) $67,682 (c) $72,682 (d) $80,000 Answer: (b) 10. The depreciation deduction for year 11 of an asset with a 20-year useful life is $4,000. If the salvage value of the asset was estimated to be zero and straight line depreciation was used to calculate the depreciation deduction for year 11, what was the initial cost of the asset? (a) $42,105 (b) $67,682 (c) $72,682 (d) $80,000 Answer: (d)

11. Which of the following is not true about depreciation? (a) depreciation is not a cash flow (b) to be depreciable, an asset must have a life longer than one year (c) a 5-year property will generate a regular MACRS-GDS depreciation deductions in six fiscal years. (d) for MACRS-GDS an estimate of the salvage values is required Answer: (d)

12. The depreciation allowance for a $100,000 MACRS-GDS asset was $8,550 after its third year. What was the depreciation allowance after its second year? (a) $8,550 (b) $9,500 (c) $18,000 (d) Cannot be determined with the information given Answer: (b)

FE-type Sample Questions for PEEA 6e Chapter 10 Chapter 10

1. The correctly calculated taxes due on a corporate taxable income of $13,000,000 are closest to which of the following? (Table 10.1 or similar is required for this question.) (a) $3,400,000 (b) $4,420,000 (c) $4,450,000 (d) $4,550,000 Answer: (c)

2. When a business calculates taxable income from gross income, which of the following is true? (a) depreciation, interest, and principal are all subtracted (b) depreciation and interest are subtracted, principal is not (c) depreciation is subtracted, interest and principal are not (d) interest and principal are subtracted, depreciation is not Answer: (b)

3. Consider the following data extracted from an After Tax Cash Flow calculation. Before Tax Cash Flow = 22,500 Loan Principal Payment = 5,926 Loan Interest Payment = 2,400 MACRS Depreciation Deduction = 16,665 Which of the following is closest to the Taxable Income? (a) -$2,491 (b) -$91 (c) $3,435 (d) $14,174 Answer: (c)

4. Consider the following data extracted from an After Tax Cash Flow calculation. Before Tax Cash Flow = 22,500 Loan Principal Payment = 7,434 Loan Interest Payment = 892 MACRS Depreciation Deduction = 7,405 Taxes Due = 5,397 Which of the following is closest to the After Tax Cash Flow? (a) $1,372 (b) $8,777 (c) $8,806 (d) $16,211 Answer: (b)

5. The marginal tax rate on a corporate income of $87,000 is closest to which of the following? (Table 10.1 or similar is required for this question.) (a) 15.0% (b) 20.5% (c) 25.0% (d) 34.0% Answer: (d)

6. The average tax rate on a corporate income of $87,000 is closest to which of the following? (Table 10.1 or similar is required for this question.) (a) 15.0% (b) 20.5% (c) 25.0% (d) 34.0% Answer: (b)

7. When considering the use of debt capital to finance a project, the upper limit for the interest rate on an attractive loan can be determined by which of the following? (a) MARR (b) MARR * (1 + tax rate) (c) MARR / (1 – tax rate) (d) MARR * (1 – tax rate) Answer: (c)

8. Consider the following data for 20x6 from an after tax cash flow analysis. What is the after tax cash flow for 20x6? before tax cash flow = $23,000 loan principal payment = $3,203 loan interest payment = $3,877 depreciation deduction = $12,490 taxable income = $6,633 taxes due = $2,255 (a) $20,744 (b) $13,665 (c) $3,430 (d) $1,175 Answer: (b)

9. Consider the following data for 2007 from an after-tax cash flow analysis. What is the taxable income for 2007? before tax cash flow = $23,000 loan principal payment = $3,203 loan interest payment = $3,877 depreciation deduction = $12,490 taxes due = $2,255 after tax cash flow = $21,530 (a) $40,000 (b) $35,540 (c) $6,633 (d) $28,460 Answer: (c)

10. Consider the following data for 20x4 from an after tax cash flow analysis. What is the loan interest payment for 20x4? before tax cash flow = $20,000 loan principal payment = $4,018 depreciation deduction = $8,920 taxable income = $8,018 taxes due = $2,726 after tax cash flow = $10,194 (a) $1,274 (b) $3,062 (c) $7,062 (d) $11,080 Answer: (b)

FE-type Sample Questions for PEEA 6e Chapter 11 Chapter 11

1. A company owns a 6-year old gear hobber that has a book value of $60,000. The present market value of the hobber is $80,000. A new gear hobber can be purchased for $450,000. Using an insider's point of view, what is the net first cost of purchasing the new gear hobber? (a) $310,000 (b) $370,000 (c) $390,000 (d) $450,000 Answer: (b)

2. A company owns a 6-year old gear hobber that has a book value of $60,000. The present market value of the hobber is $80,000. A new gear hobber can be purchased for $450,000. Using an outsider’s point of view, what is the net first cost of purchasing the new gear hobber? (a) $310,000 (b) $370,000 (c) $390,000 (d) $450,000 Answer: (d)

3. In evaluating a piece of equipment for its optimal replacement interval, the following table of equivalent uniform annual costs is obtained. What is the optimal replacement interval for the equipment? n 1 2 3 4 (a) 1 year (b) 2 years (c) 3 years (d) 4 years Answer: (b)

EUAC(n) 1582.00 1550.00 1575.00 1580.00

4. A radiology clinic is considering buying a new $700,000 x-ray machine which will have no salvage value after installation since the cost of removal will be approximately equal to its sales value. Maintenance is estimated at $24,000 per year as long as the machine is owned. After ten years the x-ray source will be depleted and the machine must be scrapped. Which of the following represents the most economic life of this x-ray machine? (a) one year since it will have no salvage after installation (b) five years since the maintenance costs are constant (c) ten years because maintenance costs don't increase (d) cannot be determined from the information given Answer: (c)

5. Which of the following is not an approach to replacement analysis? (a) cash flow approach (b) insider viewpoint (c) outsider viewpoint (d) supply chain approach Answer: (d)

6. The most common approach to determining the planning horizon for replacement analysis is which of the following? (a) Shortest life (b) Median Life (c) Longest life (d) Least Common Multiple Answer: (a)

7. A company owns a 5-year old turret lathe that has a book value of $20,000. The present market value of the lathe is $16,000. A new turret lathe can be purchased for $45,000. Using a before tax analysis and an outsider's point of view, what is the first cost of keeping the old lathe? (a) $29,000 (b) $45,000 (c) $20,000 (d) $16,000 Answer: (d)

8. A company owns a 5-year old turret lathe that has a book value of $20,000. The present market value of the lathe is $16,000. A new turret lathe can be purchased for $45,000. Using a before tax analysis and an insider’s point of view, what is the first cost of the new lathe? (a) $29,000 (b) $45,000 (c) $25,000 (d) $16,000 Answer: (a)

9. What two cost categories form the trade off that leads to an optimal replacement interval? (a) Direct costs and indirect costs (b) Insider costs and outsider costs (c) Operating & maintenance costs and capital recovery costs (d) Sunk costs and opportunity costs Answer: (c)

10. Increasing the magnitude of the initial investment tends to ____________ the optimum replacement interval. (a) Decrease (b) Increase (c) Reverse (d) Not affect Answer: (b)

FE-type Sample Questions for PEEA 6e Chapter 12 Chapter 12

1. Logan is conducting an economic evaluation under inflation using the thencurrent approach. If the inflation rate is j and the real time value of money rate is d, which of the following is the interest rate he should use for discounting the cash flows? (a) j (b) d (c) j + d (d) j + d + dj Answer: (d) 2. Mike’s Veneer Shop owns a vacuum press that requires annual maintenance. Mike has a contract to cover the maintenance expenses for the next five years. The contract calls for an annual payment of $600 with adjustment each year for inflation. Inflation is expected to hold constant at 6%/yr over this period. The then-current cash flow pattern for this expense is best described by which of the following? (a) uniform series (b) gradient series (c) geometric series (d) continuous series Answer (c) 3. Mike’s Veneer Shop owns a vacuum press that requires annual maintenance. Mike has a contract to cover the maintenance expenses for the next five years. The contract calls for an annual payment of $600 with adjustment each year for inflation. Inflation is expected to hold constant at 6%/yr over this period. The constant dollar cash flow pattern for this expense is best described by which of the following? (a) uniform series (b) gradient series (c) geometric series (d) continuous series Answer (a)

4. An economist has predicted that there will be a 7% per year inflation of prices during the next ten years. If this prediction proves to be correct, an item that presently sells for $10 would sell for what price in ten years? (a) $ 5.08 (b) $10.70 (c) $17.00 (d) $19.67 Answer: (d)

5. If the real discount rate is 7% and the inflation rate is 10%, which of the following interest rates will be used to find the present worth of a series of cash flows that are in then-current dollars? (a) 10.0% (b) 17.7% (c) 7.0% (d) 10.7% Answer: (b) 6. If the real discount rate is 7% and the inflation rate is 10%, which of the following interest rates will be used to find the present worth of a series of cash flows that are in constant-worth dollars? (a) 10.0% (b) 17.7% (c) 7.0% (d) 10.7% Answer: (c)

7. When done correctly, what is the relationship between the present worth of an alternative calculated using a then-current approach and the present worth of the alternative calculated using a constant-worth approach? (a) they are equal (b) then-current PW is higher because it uses inflated dollars (c) constant worth PW is higher because is uses a lower discount rate (d) cannot be determined without knowing the cash flows and inflation rate Answer: (a)

8. A government agency has reported the quarterly inflation rates shown below for the previous four quarters. What was the effective annual inflation rate? Quarter 1 2 3 4

Quarterly Inflation Rate 3% 2% 4% 2%

(a) 2.00% (b) 2.75% (c) 11.00% (d) 11.45% Answer: (d)

9. As reported by the Bureau of Labor Statistics, the CPI for 2005 was 585.0 (using a Base Year of 1967 = 100). The CPI for 2006 was 603.9. Based on this data, what was the inflation rate for 2006? (a) 3.23% (b) 5.85% (c) 6.04% (d) 18.9% Answer: (a)

10. Ten years ago Jennifer bought an investment property for $100,000. Over the ten year period inflation as held consistently at 3% annually. If Jennifer expects a 13%/yr real rate of return, what would she sell the property for today? (a) $116,000 (b) $134,400 (c) $339,500 (d) $456,200 Answer: (d)

FE-type Sample Questions for PEEA 6e Chapter 13 Chapter 13

1. If total cost for producing widgets can be represented by TC = 8,000 + 0.75*X, where X is the number of widgets produced and total revenue can be represented by TR = 4.00*x, what is the breakeven value for number of widgets produced? (a) 1,684 (b) 2,000 (c) 2,462 (d) 3,763 Answer: (c)

The next five questions refer to the following sensitivity graph

-30

-20

-10

3500 3000 2500 2000 1500 1000 500 0 -500 0 -1000 -1500

Percent Change Annual Revenue

Initial Investment

Salvage Value

2. The analysis is most sensitive to changes in which component? (a) Annual Revenue (b) Initial Investment (c) Salvage Value (d) Cannot be determined from the information given Answer: (a)

3. The analysis is least sensitive to changes in which component? (a) Annual Revenue (b) Initial Investment (c) Salvage Value (d) Cannot be determined from the information given Answer: (c)

4. What is the numeric value of the present worth of the original project (i.e., no changes)? (a) -10 (b) 20 (c) 1,000 (d) Cannot be determined from the information given Answer: (c)

5. What percentage change in initial investment would cause the project to become unattractive? (a) -10 (b) 20 (c) 1000 (d) Cannot be determined from the information given Answer: (b) 6. If a line for “annual expenses” was to be added to the graph what slope would you expect the line to have? (a) Positive slope (line rises as it goes left to right (b) Negative slope (line falls as it goes left to right) (c) Zero slope (horizontal line) (d) Infinite slope (vertical line) Answer: (b)

7. Which of the following is not a method typically used for supplementary analysis of engineering economy problems (a) break-even analysis (b) depreciation analysis (c) risk analysis (d) sensitivity analysis Answer: (b)

8. The probability of weather related crop damage during the growing season in a typical year is given by the following table. If the interest rate is 8%, what is the expected present worth of crop damage over the next five years. Value of Crop Damage $0 $100,000 $200,000 $300,000

Probability 60% 25% 13% 2%

(a) $57,000 (b) $167,000 (c) $240,000 (d) $285,000 Answer: (c)

9. Gooey Bites sells snack packs for $3 per pack. Variable expenses involved in producing snack packs are estimated to be $1 per pack and fixed costs for operating the production line are estimated to be $14,000. How many snack packs must Gooey Bites sell to break even? (a) 14,000 (b) 3,500 (c) 4,667 (d) 7,000 Answer: (d)

10. Reconsider the previous problem. After making changes to the production line, Gooey Bites made a profit $36,000 by selling 20,000 snack packs. Variable costs were modified by the line changes but fixed costs were unaffected. What is the new variable cost per pack? (a) 0.33 (b) 0.50 (c) 1.00 (d) 1.50 Answer: (b)

FE-type Sample Questions for PEEA 6e Chapter 14 Chapter 14

1. When using the benefit cost ratio measure of worth, what benchmark is the calculated ratio compared to in determining if an individual investment is attractive? (a) 0.0 (b) MARR (c) 1.0 (d) IRR Answer: (c)

2. Consider a situation in which you do not know the timing or amounts of individual cash flows. However you do know the discounted and summed values of the revenues, Rt*(P|F,MARR,t), and the discounted and summed values of the expenses, Ct*(P|F,MARR,t). Which of the following measures of worth can you calculate? I. II.

PW B/C ratio

(a) I only (b) II only (c) Both I and II (d) Neither I nor II Answer: (c)

3. Elm City is considering a replacement for its police radio. The benefits and costs of the replacement are shown below. What is the benefit cost ratio of the replacement if the effective annual interest rate is 8%? Purchase Cost: $7,000 Annual Savings: $1,500 Life: 15 years (a) 3.21 (b) 1.83 (c) 1.76 (d) 1.34 Answer: (b)

4. A library shelving system has a first cost of $20,000 and a useful life of 10 years. The annual maintenance is expected to be $2,500. The annual benefits to the library staff are expected to be $9,000. If the effective annual interest rate is 10%, what is the benefit cost ratio of the shelving system? (a) 1.51 (b) 2.24 (c) 1.73 (d) 1.56 Answer: (d)

5. The two most common forms of benefit cost analysis are: (a) B/C and B-C (b) B/C and B*C (c) B+C and B-C (d) B-C and B*C Answer: (a)

6. Which of the following would be least likely to use public sector economic analysis? (a) A Library Board (b) A Public Housing Authority (c) A Travel Agency (d) A Veteran’s Hospital Answer: (c)

7. Which of the following are typical characteristics of public sector projects? I. II. III.

Large first costs Benefits that may be hard to quantify Benefits that are realized quickly

(a) I and III only (b) I and II only (c) II and III only (d) I, II, and III Answer: (b)

8. An integrated public-private partnership to deliver public projects is known by which of the following acronyms? (a) EOQ (b) DCF (c) IRR (d) BOT Answer: (d)

9. An approach to justifying public sector projects that minimizes revenues while still allowing a business to earn a fair return for its shareholders is (a) Revenue Requirements (b) Revenue Effectivity (c) Cost Plus Pricing (d) Activity Based Costing Answer: (a)

10. When using a benefit cost analysis to evaluate multiple alternatives, which of the following approaches is acceptable? (a) Ranking approach only (b) Incremental approach only (c) Either Incremental or Ranking (d) Neither Incremental nor Ranking Answer: (b)

FE-type Sample Questions for PEEA 6e Chapter 15 Chapter 15

1. Sarah is considering two investment proposals. Proposal A is to purchase a new computer. Proposal B is to purchase a new printer. She will not buy the printer unless she buys the computer. The relationship between Proposals A and B is best described by which of the following. (a) B and A are mutually exclusive (b) B is contingent on A (c) A is contingent on B (d) not enough information is given to determine a relationship Answer: (b)

2. Consider a capital rationing formulation where the binary variables X1 and X2 are used to represent the acceptance (Xi = 1) or rejection (Xi = 0) of each alternative. A mutual exclusivity constraint between the two alternatives can be represented by which of the following? (a) X1 + X2 <= 1 (b) X2 <= X1 (c) X1 + X2 >= 1 (d) X1 <= X2 Answer: (a)

3. Consider a capital rationing formulation where the binary variables X1 and X2 are used to represent the acceptance (Xi = 1) or rejection (Xi = 0) of each alternative. The requirement that X2 is contingent upon X1 can be represented by which of the following? (a) X1 + X2 <= 1 (b) X2 <= X1 (c) X1 + X2 >= 1 (d) X1 <= X2 Answer: (b)

4. Consider a capital rationing formulation where the binary variables X1 and X2 are used to represent the acceptance (Xi = 1) or rejection (Xi = 0) of each alternative. The requirement that the null alternative is not feasible can be represented by which of the following? (a) X1 + X2 <= 1 (b) X2 <= X1 (c) X1 + X2 >= 1 (d) X1 <= X2 Answer: (c)

5. Sebastian is about to compare a set of mutually exclusive and indivisible alternatives using a ranking approach. Which of the following is not an appropriate measure of worth? (a) present worth (b) future worth (c) annual worth (d) internal rate of return Answer: (d)

6. If six investment proposals are under consideration, how many investment combinations must be evaluated if a complete enumeration approach is being used? (a) 6 (b) 2*6 = 12 (c) 62 = 36 (d) 26 = 64 Answer: (d)

7. Which of the following is not an approach which can be used to perform a capital rationing economic analysis? (a) Box-Jenkins algorithm (b) Excel SOLVER (c) Exhaustive enumeration (d) Lori-Savage formulation Answer: (a)

8. To determine an optimal portfolio of investments when the available choices are divisible, the investment choices should first be ranked in increasing order based on which of the following? (a) FW (b) Initial investment (c) IRR (d) PW Answer: (c)

9. Consider the following binary linear programming formulation of a capital rationing problem. Max s.t.

1,200 x1 + 600 x2 + 950 x3 + 1,650 x4 15,000 x1 + 20,000 x2 + 25,000 x3 + 30,000 x4 <= 70,000 x1 + x2 <= 1 x4 <= x3 x1, x2, x3, x4 = (0,1)

The first cost of project x3 is (a) 70,000 (b) 25,000 (c) 950 (d) x4 Answer: (b)

10. Consider the following binary linear programming formulation a capital rationing problem. Max s.t.

1,200 x1 + 600 x2 + 950 x3 + 1,650 x4 15,000 x1 + 20,000 x2 + 25,000 x3 + 30,000 x4 <= 70,000 x1 + x2 <= 1 x4 <= x3 x1, x2, x3, x4 = (0,1)

Projects x3 and x4 are (a) mutually exclusive (b) x3 is contingent on x4 (c) x4 is contingent on x3 (d) not related

Answer: (c)

11. Consider the following binary linear programming formulation a capital rationing problem. Max s.t.

1,200 x1 + 600 x2 + 950 x3 + 1,650 x4 15,000 x1 + 20,000 x2 + 25,000 x3 + 30,000 x4 <= 70,000 x1 + x2 <= 1 x4 <= x3 x1, x2, x3, x4 = (0,1)

The capital budget limit is (a) $90,000 (b) $70,000 (c) $30,000 (d) $4,400 Answer: (b)

FE-type Sample Questions for PEEA 6e Chapter 16 Chapter 16

1. On a balance sheet, a corporations economic obligations to non-owners is (are) called: (a) owners’ equity (b) liabilities (c) assets (d) retained earnings Answer: (b)

2. The information below has been extracted from the books of the Shelley Company. Which of the following represents Shelley’s current ratio? Current assets: Cash $86 Accounts receivable 130 Inventory 140

Current liabilities: Accts payable $78 Wages payable 68 Taxes payable 28

Total

$356

$174

(a) 0.76 (b) 1.48 (c) 2.05 (d) 2.51 Answer: (c)

3. The fundamental equation used within an accounting balance sheet is (a) Net Profit = Gross Profit - Expenses - Taxes (b) Assets + Liabilities = Net Worth (c) Assets + Liabilities + Net Worth = 0 (d) Assets = Liabilities + Net Worth Answer: (d)

4. Marginal cost is: (a) any cost occurring after "time now" (b) the ratio of total cost to total quantity of output (c) the market value of an asset at the end of its life less its disposal costs (d) the incremental cost of producing one more unit of output Answer: (d)

5. The three major categories that comprise cost of goods manufactured are: (a) Material, labor, overhead (b) Average, marginal, instantaneous (c) Past, present, future (d) Initial, operating, salvage Answer: (a)

6. The total cost equation for producing X widgets is given by TC = $1,000 + 46*X. The average cost per widget for producing 500 widgets is closest to which of the following? (a) $1,000 (b) $6 (c) $8 (d) $4,000 Answer: (c)

7. The total cost equation for producing X widgets is given by TC = $1,000 + $6*X. The variable cost per widget is closest to which of the following? (a) $1,000 (b) $6 (c) $8 (d) $4,000 Answer: (b)

8. The total cost equation for producing X widgets is given by TC = $1,000 + $6*X. The marginal cost per widget at a production level of 300 units is closest to which of the following? (a) $2,800 (b) $6 (c) $8 (d) $4,000 Answer: (b)

9. Fixed cost is: (a) any cost that does not vary with the quantity of output (b) the ratio of total cost to total quantity of output (c) the market value of an asset at the end of its life less its disposal costs (d) the incremental cost of producing one more unit of output Answer: (a)

10. When an organization considers its work-in-process, how should it be classified on a balance sheet? (a) Asset (b) Liability (c) Net worth (d) Expense Answer: (a)

Collection of Pit Stop Answer Sheets

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #1—Checking Your Pulse • True or False: If someone offers you the choice of receiving $1,000 today versus receiving $1,000 a year from today, you should take the money today if your time value of money is greater than zero. TRUE • True or False: A strength of the weighted factor comparison technique is its scientific foundation and its elimination of subjectivity from decision making. FALSE • True or False: If your time value of money is 10% annually, then you will be indifferent between receiving $1,000 today and receiving $1,100 one year from today. TRUE • True or False: Based on the principles of engineering economic analysis, you should bet on the horse with the lowest odds to win, because risk and returns tend to be positively correlated. FALSE (odds are established so that “the house” wins in the long run) • True or False: Every economic decision should be based on the time value of money. FALSE White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #2 — Hang On! 1. True or False: If money is worth 5% compounded annually to you, then you should prefer to receive $2,750 today than to receive $3,500 five years from today. True PV(5%,5,,-3500) = $2,742.34 < $2,750.00 2. True or False: If money is worth 7% compounded annually to you, then you should prefer to receive $1,000,000 thirty years from now than to receive $200,000 today. False $1,000,000.00 < FV(7%,30,,-200000) = $1,522,451.01 3. True or False: If money is worth 6% compounded annually to you, then you should prefer to receive $1750 per year for 5 years than to receive $1,000 per year for 10 years, assuming the first receipt occurs one year from today in both cases. True PV(6%,5,-1750) = $7,371.64 > PV(6%,10,-1000) = $7,360.09 4. True or False: If money is worth 7% compounded annually to you, then you would prefer to receive $2,200 each year for 5 years than to receive $4,000 the first year, $3,000 the second year, $2,000 the third year, $1,000 the fourth year, and $0 the fifth year. True PV(7%,5,-2200) = $9,020.43 > NPV(7%,4000,3000,2000,1000) = $8,754.12 5. True or False: If money has a time value of 8% compounded annually, you should prefer to receive a uniform series of ten $1,000 cash flows over the interval [1,10] to receiving a uniform series of ten $1,260 cash flows over the interval [4,13]. False PV(8%,10,-1000) = $6,710.08 < PV(8%,3,,PV(8%,10,1260)) = $6,711.62 White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #3— Checking Your Vital Signs 1. True or False: If you can earn 8% on your investments and you can borrow money at an annual compound rate of 6%, then (of the four repayment methods described in the chapter) you would prefer to repay the loan with equal monthly payments. FALSE (prefer Method 4) 2. True or False: In purchasing a house, the points and other closing costs you pay are included in the stated interest rate for a 30-year conventional loan. FALSE (closing costs and points are “extra” costs)

3. True or False: The annual percentage rate is the same as the effective annual interest rate. FALSE (as shown in the examples) 4. True or False: When repaying a loan with equal monthly payments, the amount of interest and the amount of principal in a loan payment remain proportionally the same over the loan period. FALSE (as shown in the examples) 5. True or False: If you purchase a $1000, 8% semiannual bond for $1000 and sell it after 5 years for $1000, then your effective annual yield on the bond is 8%. FALSE (effective annual yield > 8%) White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #4—Take a Deep Breath 1. 2. 3. 4. 5.

6. 7. 8.

9. 10.

True or False: When dealing with multiple alternatives having unequal lives, the planning horizon equals the least common multiple of lives. False, depends on the situation; planning horizon might be specified by company True or False: The MARR should be at least as great as the firm’s weighted cost of capital and should reflect the opportunity cost for money. True True or False: Among the various sources of capital, U.S. large cap equities have a lower cost of capital than do U.S. small cap equities. True True or False: The most common method of valuing the cost of equity capital is to divide the annual dividend by the average market value of a share of stock. False (this is argumentative; lots of methods are used) True or False: The cost of debt capital needs to reflect the tax deductibility of costs of debt. True True or False: The Eastman hurdle rate calculator can be used for any company and under any conditions that are specifically targeted by the calculator. False (it was based on Eastman’s global experiences) True or False: A company’s beta can be used to accurately forecast its stock price during the coming year. False True or False: Historical beta values are not impacted by rare events that might adversely affect a firm’s stock price. False True or False: The Federal Reserve Bank’s prime lending rate should be used for the riskfree rate in the capital asset pricing model. False True or False: When using the Eastman hurdle rate calculator, if venture capital is being sought, the hurdle rate obtained will not be affected by ownership, plant site, or technology profiles. True White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #5— Open Road Ahead! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

True or False: Present worth analysis is the most popular DCF measure of economic worth. TRUE True or False: Unless non-monetary considerations dictate otherwise, choose the mutually exclusive investment alternative that has the greatest present worth, regardless of the lives of the alternatives. FALSE True or False: When using present worth analysis to evaluate the economic viability of mutually exclusive alternatives, use a common period of time in the comparison. TRUE True or False: If PW > 0 and MARR = 20%, then DPBP < 5 years. FALSE (knowing PW > 0 only indicates DPBP < n, the planning horizon) True or False: DPBP > PBP. TRUE True or False: If CW > 0, then PW > 0. TRUE True or False: If PW(A) > PW(B), then CW(A) > CW(B), DPBP(A) < DPBP(B), and PBP(A) < PBP(B). FALSE (rank ordering of PW, FW, AW, CW does not indicate ranking ordering of PBP or DPBP) True or False: PW, FW, AW, CW, and B/C are ranking methods; therefore, the alternative having the greatest PW, FW, AW, CW, or B/C should be recommended. FALSE (B/C is an incremental method, not a ranking method) True or False: Either ranking or incremental analysis can be used with all four “worth” methods (PW, FW, AW, and CW). TRUE True or False: The “do nothing” alternative always has negligible incremental costs and revenues. FALSE White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #6—It’s Time to Put the Peddle to the Metal! 1. 2.

3. 4. 5. 6.

True or False: Future worth analysis is the most popular DCF measure of economic worth. FALSE (PW is most popular DCF measure) True or False: Unless non-monetary considerations dictate otherwise, choose the mutually exclusive investment alternative that has the greatest future worth, regardless of the lives of the alternatives. FALSE (need to use a common planning horizon unless “one shot” investment) True or False: If FW > 0 when the MARR = 20%, then DPBP < 5 years. FALSE (knowing FW > 0 means DPBP < planning horizon) True or False: If FW < 0, then PW < 0. TRUE True or False: If FW(A) > FW(B), then DPBP(A) < DPBP(B), and PBP(A) < PBP(B). FALSE (rank ordering of FW does not indicate rank ordering of PBP and DPBP) True or False: When using future worth analysis with mutually exclusive alternatives having unequal lives, use a planning horizon equal to the least common multiple of lives. FALSE (it is situation and circumstance dependent, e.g., “one shot” investments, planning horizon specified by the company, planning horizon specified by the situation, such as the expiration date on a contract)

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #7—No Time to Coast 1. 2.

3. 4. 5. 6. 7. 8. 9. 10.

True or False: Annual worth analysis is the most popular DCF measure of economic worth. FALSE (PW is the most popular DCF measure) True or False: Unless non-monetary considerations dictate otherwise, choose the mutually exclusive investment alternative that has the greatest annual worth over the planning horizon. TRUE True or False: The capital recovery cost is the uniform annual cost of the investment less the uniform annual worth of the salvage value. TRUE True or False: If AW > 0, then PW > 0, and FW > 0. TRUE True or False: If AW(A) > AW(B), then PW(A) > PW(B). TRUE True or False: If AW (A) < AW(B), then AW(B-A) > 0. TRUE True or False: If AW(A) > AW(B), then CW(A) > CW(B) and DPBP(A) < DPBP(B). FALSE (rank ordering of AW and CW does not imply rank ordering of DPBP) True or False: AW can be applied as either a ranking method or as an incremental method. TRUE True or False: To compute capital recovery cost using Excel, enter =PMT(i%,n,-P,F) in any cell in a spreadsheet. TRUE True or False: When using annual worth analysis with mutually exclusive alternatives having unequal lives, always use a planning horizon equal to the least common multiple of lives. FALSE (depends on situation and circumstance -- see answers in previous chapters)

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #8—Halfway Home! Miles to Go! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

True or False: For personal investment decision making, rates of return are used more frequently than present worth. TRUE True or False: Unless non-monetary considerations dictate otherwise, you should choose the mutually exclusive investment alternative having the greatest rate of return over the planning horizon. FALSE (IRR and ERR are incremental methods, not ranking methods) True or False: If ERR > MARR, then IRR > ERR > MARR. TRUE True or False: If PW > 0, then IRR > MARR. TRUE True or False: If ERR > MARR, then MIRR > MARR. FALSE (depending on the finance rate, MIRR value can vary significantly from IRR and ERR value) True or False: If IRR(A) > IRR(B), then ERR(A) > ERR(B). FALSE (the rank order of IRR does not guarantee the rank order of ERR) True or False: If PW(A) > PW(B), then FW(A) > FW(B), AW(A) > AW(B), CW(A) > CW(B), and IRR(A) > IRR(B). FALSE (rank order of ranking methods does not assure the rank order of incremental methods) True or False: Multiple roots can exist when using IRR and MIRR methods. FALSE (multiple roots can exist when using IRR, but not MIRR or ERR) True or False: Excel’s IRR worksheet function signals if multiple roots exist for a cash flow series. FALSE True or False: Of all the equivalent DCF methods, the one that is the most difficult to use is the external rate of return method because of its requirement of a reinvestment rate for recovered capital. FALSE (a reinvestment rate is needed with all DCF methods; the ERR method is easier to use than IRR, particularly when there is a single negative-valued cash flow and it occurs at EOY = 0)

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #9—Avoid the Pot Holes 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

True or False: Straight-line depreciation is the most popular depreciation method used in financial reporting. True True or False: The Modified Accelerated Cost Recovery System is the most popular depreciation method used in computing corporate income tax liabilities. True True or False: Based on maximizing the present worth of depreciation allowances, MACRS is preferred to SLN for recovery periods greater than 5 years. True True or False: Accelerated depreciation plans were adopted after World War II to stimulate capital investment. True True or False: Engineers seldom have an opportunity to influence the recovery period for expenditures. False (choosing technologies to use determines the recovery period) True or False: MACRS is equivalent to DDB, switching to SLN, with a mid-year convention. True True or False: The most popular variation of MACRS is MACRS-ADS. False (MACRS-GDS is more commonly used, due to the number of investments in personal property versus real property) True or False: Sum-of-Years’-Digits depreciation is a popular depreciation method and is most often used to compute income tax liabilities. False True or False: When given a choice of depreciation methods to use, choose the one that maximizes the present worth of book value. False (maximizes the present worth of depreciation charges, which minimizes book value) True or False: Sinking fund depreciation is the only depreciation method described in the book that is based on the time value of money. True

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #10—It’s Been A Taxing Experience 1. 2. 3. 4. 5.

6. 7. 8. 9. 10.

True or False: If an investment cannot be justified economically using a before-tax analysis, it cannot be justified using an after-tax analysis. False True or False: After-tax present worth will be greater when using MACRS than it will be when using SLN. True True or False: The faster an asset is depreciated, the greater will be its after-tax present worth. True True or False: If money can be borrowed for 20% compounded annually and the marginal income tax rate is 40%, then it will be profitable to borrow the investment capital if your after-tax MARR is greater than 12%. True True or False: If the same amount of money is invested in something that can be expensed as in something that must be depreciated (and both provide the same annual returns) then, to maximize after-tax present worth, you should choose the investment that can be depreciated. False True or False: If investment capital is borrowed, the income tax rate equals 40%, the aftertax MARR is 12%, and the loan rate is 15%, then it is best to repay the loan using Method 1. True True or False: If investment capital is borrowed, the income tax rate equals 40%, the aftertax MARR is 12%, and the loan rate is 10%, then it is best to repay the loan using Method 4. True True or False: If investment capital is borrowed, the income tax rate equals 40%, the aftertax MARR is 9%, and the loan rate is 18%, then it is best to repay the loan using Method 2. True True or False: The investment tax credit is not in force, currently. True True or False: Section 179 Expense Reduction is not in force, currently. False White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #11—Pick Up the Pace! Don’t Get Replaced! 1.

3. 4. 5. 6. 7. 8.

9. 10.

True or False: In performing engineering economic analyses of replacement alternatives, it is best to perform before-tax analyses, since incorporating income tax considerations in the analysis is difficult, due to the treatment of trade-in values not equaling book values. False (after-tax analyses can result in recommendations that are different from those obtained when using before-tax analyses) True or False: The two approaches used in performing replacement analyses are the cash flow approach and the insider approach. False (these are the same approaches) True or False: In determining the optimum replacement interval, it is necessary to assume negligible salvage values. False (salvage values can be included) True or False: Before-tax replacement analyses and after-tax replacement analyses seldom yield the same recommendation. False (argumentative, depends on data) True or False: Section 1031 exchanges of property can be performed for any real or personal property. False (must satisfy the “like kind” test, plus other IRS conditions) True or False: If the optimum replacement interval for an over-the-road tractor is 4 years and the initial cost of the tractor is increased by 20% then the optimum replacement interval for the next tractor might be less than 4 years. False True or False: If the optimum replacement interval for an over-the-road tractor is 4 years and the salvage value for used tractors is suddenly cut in half, then the optimum replacement interval for the next tractor might be greater than 4 years. True True or False: If the optimum replacement interval for an over-the-road tractor is 4 years and the ATMARR is increased from 9% to 12%, then the optimum replacement interval for the next tractor might be less than 4 years. False True or False: If the optimum replacement interval for an over-the-road tractor is 4 years and the rate of increase in O&M costs doubles, then the optimum replacement interval for the next tractor might be less than 4 years. True True or False: Section 1031 Property Exchanges are no longer permitted by the U.S. Internal Revenue Service. False White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #12—Check Your Tires for Proper Inflation! 1. 2. 3. 4. 5. 6. 7.

8. 9. 10.

True or False: Inflation decreases the purchasing power of money. TRUE True or False: The most commonly used measure of inflation is the relative change in the Consumer Price Index. TRUE True or False: The Consumer Price Index typically increases faster than the Higher Education Price Index. FALSE True or False: In performing engineering economic analyses in inflationary conditions, the after-tax present worth will always be less than it would be if inflation were negligible. FALSE True or False: The two approaches used in considering inflation are the constant dollar and the thencurrent dollar approaches. TRUE True or False: If the real minimum attractive rate of return is 8%, inflation is 4%, and the tax rate is 40%, then money should not be borrowed if the interest rate on the loan is greater than 18%. FALSE True or False: if the real minimum attractive rate of return is 8%, inflation is 4%, the tax rate is 40%, and money can be borrowed at 16% annual compound interest, then the loan should be repaid using Method 4, i.e., don’t pay anything until the end of the loan period. FALSE True or False: If the real minimum attractive rate of return is 8%, inflation is 4%, the tax rate is 40%, and money can be borrowed at 12% annual compound interest, then the loan should be repaid using Method 1, i.e., pay interest annually and pay principal at the end of the loan period. FALSE True or False: If the combined minimum attractive rate of return is 12% and inflation is 4%, then the real minimum attractive rate of return is approximately 7.7%. TRUE True or False: When investing in capital equipment, inflation reduces the after-tax present worth because depreciation does not increase with inflation. TRUE

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #13—Don’t Be Superstitious. Take Some Risks! 1. 2. 3. 4. 5. 6.

9. 10.

True or False: In the absence of perfect information accurate investment decisions cannot be made. FALSE (depends on the sensitivity of the problem parameters) True or False: Break-even analysis is a brand new concept, nothing like it has been presented previously in the book. FALSE True or False: Sensitivity analysis is a technique used by psychologists to gauge a person’s reaction to criticism. FALSE (psychologists might use it for this purpose; engineers use it to determine the impact of changes in values of parameters) True or False: Risk analyses are performed when complete uncertainty exists and no reasonable estimates can be made regarding the probability of occurrence of parameter values. FALSE True or False: Monte Carlo simulation is used in casinos, but has no application other than in roulette and other gambling establishments. FALSE True or False: If the cost of producing one unit of product is uniformly distributed with a mean of 25¢ and a standard deviation of 10¢, then the cost of producing, independently, 1000 units of product will be distributed uniformly with a mean of $250 and a standard deviation of $100. FALSE (normally distributed with a standard deviation of $3.162) True or False: If the cost to produce one unit of product is normally distributed with a mean cost of 25¢ and a standard deviation of 10¢, then there will be a 0.999 probability of it costing less than $260 to produce 1000 units of product when the units are produced independently. TRUE (=NORMSDIST((260-(1000*0.25))/SQRT((0.1^2)*1000))=0.9992173) True or False: if the cost to produce one unit of product is normally distributed with a mean cost of 25¢ and a standard deviation of 10¢, then there will be a 0.841 probability of it costing less than $260 to produce 1000 units if the costs of producing units of product are perfectly correlated. TRUE (=NORMSDIST((260-(1000*0.25))/SQRT(0.1*1000))=0.8413447) True or False: If X and Y are independent random variables with expected values and variances of E(X), E(Y), V(X), and V(Y), respectively, then the expected value of the product of X and Y is equal to E(X)E(Y) and the variance of the product of X and Y is equal to V(X)V(Y). FALSE (V(XY) = V(X)V(Y) + V(X)[E(Y)]2 + V(Y)[E(X)]2 True or False: @RISK simulation is limited to Latin Hypercube sampling. False (includes Monte Carlo sampling)

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #14 – Same Thing; Different Look 1. True or False: Benefit-cost analysis is primarily used by regulated utilities. False. It is used in the public sector. Revenue Requirements analysis is used by regulated utilities. 2. True or False: Build-Operate-Transfer (BOT) makes use of a public-private partnership. True, in order to utilize the strengths of both public and private sectors. 3. True or False: Benefits and disbenefits must be converted to monetary values to use benefit-cost analysis. True. Then, the PW or AW values are used in the benefit-cost analyses. 4. True or False: OMB’s Circular No. A-94, Revised is the definitive document for benefitcost analysis. True in the United States of America.

5. True or False: The seven step SEAT is only applicable to public sector evaluation after extensive modification. False. SEAT is applicable as-is, and explanation is facilitated by only minor modification to some wording.

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #14 – Same Thing; Different Look 6. True or False: The B/C ratio is directly applicable to evaluation of one or many alternatives. False. The B/C ratio is applicable to evaluation of one alternative, but multiple alternatives require incremental B/C analysis. 7. True or False: The B-C evaluation is directly applicable to evaluation of one or many alternatives. True. B-C analysis is very robust. Unfortunately, the B/C ratio is more often used. 8. True or False: Some in the public sector recommend using an interest rate of 0% on any money from outside sources. True, unfortunately. This can lead to acceptance of projects that should never see the light of day. 9. True or False: The Revenue Requirements method is not economically equivalent to the industrial ATCF approach. False. While it follows a different analysis format, both methods are completely equivalent .

10. True or False: The Revenue Requirements method determines the income that exactly “pays” for costs, depreciation, interest on borrowed money, taxes, and a desirable return to owners. True. This is known as the minimum revenue requirement. White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #15—The Finish Line Is In Sight! 1. 2. 3. 4. 5.

True or False: When several independent, indivisible investments are available, form the investment portfolio so that the present worth of the portfolio is maximized. True True or False: If independent, indivisible investments 3 and 4 are mutually exclusive, then x3 + x4 < 1 is added as a constraint to the BLP formulation. True True or False: If indivisible investment 2 is contingent on indivisible investment 1 being funded, then x2 - x1 < 0 is added as a constraint to the BLP formulation. True True or False: When multiple independent, divisible investments are available, form the investment portfolio so that the internal rate of return is maximized. False True or False: When multiple independent divisible investments are available, choose investments to add to the portfolio on the basis of their IRR and move from the largest to the smallest IRR until the capacity limit is reached. True

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #16 – Is Accounting a Foreign Language? 1. True or False: When conducting an economic analysis, an engineer should consider costs from one and only one cost viewpoint. False, all viewpoints should be considered. 2. True or False: The cost of foregoing an opportunity to earn interest, or a return, on investment funds is referred to as a sunk cost. False, the cost of foregoing an opportunity is the opportunity cost. 3. True or False: Prime cost is the sum of direct material cost and direct labor cost. True 4. True or False: If the cost function for producing x units is TC(x) = 700+0.6x and the revenue function is TR(x) = 2.0x; then the breakeven value is 500 units? True 5. True or False: The average cost function for Question 4 is given by AC(x) = 500 + 1.4x? False, the average cost function is AC(x)=700/x + 0.6 6. True or False: The tradeoff being considered when determining the level of detail of an estimate is the cost of making the estimate versus the cost of errors resulting from an inaccurate estimate. True

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

Pit Stop #16 – Is Accounting a Foreign Language? 7. True or False: An income statement shows the assets, liabilities, and net worth of a firm at a point in time. False, an income statement shows revenues, expenses, and resulting profit over a period of time. 8. True or False: The fundamental equation of accounting states that assets = liabilities + net worth. True 9. True or False: EBIT can also be referred to as operating earnings. True

10. True or False: In cost accounting, the acronym ABC refers to a Pareto analysis of costs where A items are most important, C items are least important, and B items are somewhere between. False, in cost accounting, ABC is the acronym for Activity Based Costing. 11. True or False: EVA is a management tool that focuses manager’s attention on adding value for the shareholders. True

White, Case, & Pratt: Principles of Engineering Economic Analysis, 6th edition

WEIGHTED FACTOR COMPARISON FORM Company: Description of investment:

Prepared by:

Factor

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Totals

100

A Sc

B Sc

C Sc

Date:

D Sc

E Sc

WEIGHTED FACTOR COMPARISON FORM Company: Ajax Manufacturing Company Prepared by: JAW Date: 4/1/09 Description of investment: order picking equipment for Chicago distribution center A B C D Rt Sc Rt Sc Rt Sc Rt Sc 30 10 300 8 240 7.2 216 40 8 320 10 400 5 200 20 3 60 10 200 7 140 10 8 80 5 50 10 100

Factor

1. Present worth 2. Product quality 3. Fill time, customer order 4. Supplier reputation 5. 6. 7. 8. 9. 10. Totals

100

760

890

656

E Sc

End of Year (EOY) A B B-A 0 -$100,000 -$100,000 $0 1 $10,000 $50,000 $40,000 2 $20,000 $40,000 $20,000 3 $30,000 $30,000 $0 4 $40,000 $20,000 -$20,000 5 $50,000 $10,000 -$40,000

Month

Unpaid Balance at the Beginning of the Month

Monthly Interest

Payment

Unpaid Balance at the End of the Month

1 2 3 4 5 6 7 8 9 10 11 12

$6,000.00 $5,500.00 $5,000.00 $4,500.00 $4,000.00 $3,500.00 $3,000.00 $2,500.00 $2,000.00 $1,500.00 $1,000.00 $500.00

$30.00 $27.50 $25.00 $22.50 $20.00 $17.50 $15.00 $12.50 $10.00 $7.50 $5.00 $2.50

$530.00 $527.50 $525.00 $522.50 $520.00 $517.50 $515.00 $512.50 $510.00 $507.50 $505.00 $502.50

$5,500.00 $5,000.00 $4,500.00 $4,000.00 $3,500.00 $3,000.00 $2,500.00 $2,000.00 $1,500.00 $1,000.00 $500.00 $0.00

Year 1 2 3 4 5

Unpaid Balance at the Beginning of the Year $10,000.00 $11,000.00 $12,100.00 $13,310.00 $14,641.00

Annual Interest

Payment

$1,000.00 $0.00 $1,100.00 $0.00 $1,210.00 $0.00 $1,331.00 $0.00 $1,464.10 $16,105.10

Unpaid Balance at the End of the Year $11,000.00 $12,100.00 $13,310.00 $14,641.00 $0.00

Table 2.5 Present Worth and Future Worth Calculations for Example 2.12 End of Year Cash Flow Present Future (P |F 10%,n) PV(10%,n,,-CF) (F |P 10%,5-n) FV(10%,5-n,,-CF) (n) (CF) Worth Worth 0 -$100,000 1.0000 -$100,000.00 -$100,000.00 1.6105 -$161,050.00 -$161,051.00 1 $50,000 0.9091 $45,455.00 $45,454.55 1.4641 $73,205.00 $73,205.00 2 $40,000 0.8264 $33,056.00 $33,057.85 1.3310 $53,240.00 $53,240.00 3 $30,000 0.7513 $22,539.00 $22,539.44 1.2100 $36,300.00 $36,300.00 4 $40,000 0.6830 $27,320.00 $27,320.54 1.1000 $44,000.00 $44,000.00 5 $50,000 0.6209 $31,045.00 $31,046.07 1.0000 $50,000.00 $50,000.00 SUM $59,415.00 $59,418.45 $95,695.00 $95,694.00

End of Year Cash Flow (n) (CF) 0 -$100,000 1 $50,000 2 $40,000 3 $30,000 4 $40,000 5 $50,000 P= $59,418.45 F= $95,694.00 End of Year Cash Flow (n) (CF) 0 $0 1 $3,000 2 $0 3 -$3,000 4 $2,000 5 $0 6 $4,000 7 $0 8 $2,000 P= $5,970.19

$9,515.57

To Find Given

Factor

Symbol

(1 + i)-n

(P|F i%,n )

(1 + i)n

(F|P i%,n )

(1 + i)n - 1

(P|A i%,n )

i(1 + i)n i(1 + i)n

(A|P i%,n )

(1 + i)n - 1

(1 + i)n - 1 i

i (1 + i)n - 1

A 1 ,j

1 - (1 + j )n (1 + i )-n i-j

(P|A 1 i%,j%,n )

A 1 ,j

i-j 1 - (1 + j )n (1 + i )-n

(F|A 1 i%,j%,n )

[1 - (1 + ni )(1 + i )-n ] i2 (1 + i)n - (1 + ni ) i [(1 + i )n - 1]

(F|A i%,n )

(A|F i%,n )

(P|G i%,n )

(A|G i%,n )

for i ≠ j

Name Single payment, present worth factor Single payment, compound amount factor Uniform series, present worth factor

Uniform series, capital recovery factor

Uniform series, compound amount factor

Uniform series, sinking fund factor

Gradient series, present worth factor

Gradient series, uniform series factor

Geometric series, present worth factor

Geometric series, future worth factor

Table 2.7 Summary of Selected Excel Worksheet Financial Functions To Find Given Worksheet Function Cell Entry =PV(i%,n,,-F ) P i, n, F PV i, n, A =PV(i%,n,-A ) P PV i, n, F, A =PV(i%,n,-A,-F ) P PV i, A , A , …, A =NPV(i%,A 1 ,A 2 ,…,A n ) P NPV 1 2 n =FV(i%,n,,-P ) F i, n, P FV i, n, A =FV(i%,n,-A ) F FV =FV(i%,n,-A,-P ) F i, n, P, A FV =PMT(i%,n,-P ) A i, n, P PMT =PMT(i%,n,,-F ) A i, n, F PMT =PMT(i%,n,-P,-F ) A i, n, P, F PMT =RATE(n,A,-P ) i n, P,A RATE =RATE(n,,-P,F ) i n, P,F RATE =RATE(n,A,-F ) i n, A, F RATE =RATE(n,A,-P,F ) i n, P, A, F RATE =NPER(i%,A,-P ) n i, P,A NPER =NPER(i%,,-P,F ) n i, P,F NPER =NPER(i%,-A,,F ) n i, A, F NPER =NPER(i%,A,-P,F ) n i, P, A, F NPER =EFFECT(r%,m ) i eff r, m EFFECT

Variable and Limit n→∞ i→0 n→∞ i→0 n→∞ i→0 n→∞ i→0 n→∞ i→0 n→∞ i→0

Result F→∞ F→P P→0 P→F A → Pi A → P/n P → A/i P → nA F→∞ F → nA A→ 0 A → F/n

Cash Flow Table End of Year (EOY) CF(A) CF(B) CF(B-A) 0 -$100,000 -$100,000 $0 1 $10,000 $50,000 $40,000 2 $20,000 $40,000 $20,000 3 $30,000 $30,000 $0 4 $40,000 $20,000 -$20,000 5 $50,000 $10,000 -$40,000

Cash Flow

CFD for Alternative A

CFD for Alternative B - Alternative A $40,000

Cash Flow

EOY

CFD for Alternative B $40,000 $20,000 $0 -$20,000 -$40,000 -$60,000 -$80,000 -$100,000

$40,000 $20,000 $0 -$20,000 -$40,000 -$60,000 -$80,000 -$100,000

$20,000 $0 -$20,000

-$40,000

EOY

$16,105.10

=FV(10%,5,,-10000)

$16,105.10

=FV(0.1,5,,-10000)

-$16,105.10

=FV(10%,5,,10000)

-$16,105.10

=FV(0.1,5,,10000)

(F|P i %,n ) n Excel's FV Function 2% 34.99911185231 1.99985437960 =FV(A2,B2,,-1) 3% 23.44819333654 1.99990666057 =FV(A3,B3,,-1) 4% 17.67238866717 1.99995301273 =FV(A4,B4,,-1) 6% 11.89466421507 1.99988383488 =FV(A5,B5,,-1) 8% 9.00760138602 2.00017440810 =FV(A6,B6,,-1) 12% 6.11628834874 2.00000747394 =FV(A7,B7,,-1)

i% 2% 3% 4% 6% 8% 12%

(F|P i %,n ) n Excel's FV Function 35.00278878391 2.000000000109640 =FV(A2,B2,,-1) 23.44976171081 1.999999376922840 =FV(A3,B3,,-1) 17.67298990119 2.000000173831020 =FV(A4,B4,,-1) 11.89566104644 2.000000000058340 =FV(A5,B5,,-1) 9.00646833967 1.999999999641560 =FV(A6,B6,,-1) 6.11625537418 1.999999999994970 =FV(A7,B7,,-1)

35.00278878115 23.44977225044 17.67298768513 11.89566104594 9.00646834200 6.11625537420

2.000000000000000 2.000000000000000 2.000000000000000 2.000000000000000 2.000000000000000 2.000000000000000

35.00278878115 23.44977225044 17.67298768513 11.89566104594 9.00646834200 6.11625537420

$8,227.02

=PV(5%,4,,-10000)

$8,227.02

=PV(0.05,4,,-10000)

-$8,227.02

=PV(5%,4,,10000)

-$8,227.02

=PV(0.05,4,,10000)

End of Year (n) 0 1 2 3 4 5 P= F=

Cash Flow (CF) -$100,000 $50,000 $40,000 $30,000 $40,000 $50,000 $59,418.45 $95,694.00

=NPV(10%,C5:C9)+C4 =FV(10%,5,,-C10)

End of Year Cash Flow (n) (CF) 0 $0 1 $300 2 $0 3 -$300 4 $200 5 $0 6 $400 7 $0 8 $200 P= $597.02 F= $951.56

=NPV(6%,C15:C22) =FV(10%,5,,-C23)

End of Year (n) 0 1 2 3 4 5 P= A= F=

Cash Flow (CF) $0 $3,000 $4,000 $5,000 $6,000 $7,000 $19,350.56 $4,846.47 $28,432.31

=NPV(8%,C4:C8) =PMT(8%,5,-C9) =FV(8%,5,-C10)

End of Cash Flow Year (n) (CF) 0 $0 1 $800 2 $700 3 $600 4 $500 5 $400 P= $2,456.93 F= $3,610.03

=NPV(8%,C4:C8) =FV(8%,5,,-C9)

End of Year (n) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 P=

Cash Flow (CF) $0 $1,000 $1,080 $1,166 $1,260 $1,360 $1,469 $1,587 $1,714 $1,851 $1,999 $2,159 $2,332 $2,518 $2,720 $2,937 $12,030.40

=C14*1.08

=NPV(10%,C4:C18)

End of Year (n) 0 1 2 3 4 5 6 7 8 9 10 P= F=

Cash Flow (CF) $0 $500 $550 $605 $666 $732 $805 $886 $974 $1,072 $1,179 $5,035.12 $10,870.44

=C14*1.1

=NPV(8%,C4:C18) =FV(8%,10,,-C9)

End of Year (n) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 P=

Cash Flow (CF) -$100,000 $25,000 $22,500 $20,250 $18,225 $16,403 $14,762 $13,286 $11,957 $10,762 $9,686 $8,717 $7,845 $7,061 $6,355 $5,719 $5,147 $4,633 $4,169 $3,752 $3,377 $12,204.15

=C14*0.9

=NPV(12%,C4:C23)+C3

Payment Plan

End of Year

0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5

C Interest Accrued During Year

D Total Money Owed Before Yearly Payment

Interest Payment

Principal Payment

Total Payment

$1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00

$11,500.00 $11,500.00 $11,500.00 $11,500.00 $11,500.00

$1,500.00 $0.00 $1,500.00 $1,500.00 $0.00 $1,500.00 $1,500.00 $0.00 $1,500.00 $1,500.00 $0.00 $1,500.00 $1,500.00 $10,000.00 $11,500.00

$1,500.00 $1,200.00 $900.00 $600.00 $300.00

$11,500.00 $9,200.00 $6,900.00 $4,600.00 $2,300.00

$1,500.00 $1,200.00 $900.00 $600.00 $300.00

$2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

$3,500.00 $3,200.00 $2,900.00 $2,600.00 $2,300.00

$1,500.00 $1,277.53 $1,021.68 $727.46 $389.11

$11,500.00 $9,794.37 $7,832.90 $5,577.20 $2,983.16

$1,500.00 $1,277.53 $1,021.68 $727.46 $389.11

$1,483.16 $1,705.63 $1,961.47 $2,255.69 $2,594.05

$2,983.16 $2,983.16 $2,983.16 $2,983.16 $2,983.16

$1,500.00 $1,725.00 $1,983.75 $2,281.31 $2,623.51

$11,500.00 $0.00 $0.00 $0.00 $13,225.00 $0.00 $0.00 $0.00 $15,208.75 $0.00 $0.00 $0.00 $17,490.06 $0.00 $0.00 $0.00 $20,113.57 $10,113.57 $10,000.00 $20,113.57

H Total Money Owed After Yearly Payment $10,000.00 $10,000.00 $10,000.00 $10,000.00 $10,000.00 $0.00 $10,000.00 $8,000.00 $6,000.00 $4,000.00 $2,000.00 $0.00 $10,000.00 $8,516.84 $6,811.22 $4,849.74 $2,594.05 $0.00 $10,000.00 $11,500.00 $13,225.00 $15,208.75 $17,490.06 $0.00

Lender's Interest Rate = 10% End of Plan 1 Plan 2 Plan 3 Plan 4 Year Payment Payment Payment Payment $10,000.00 $10,000.00 $10,000.00 $10,000.00 0 1 -$1,000.00 -$3,000.00 -$2,637.97 $0.00 2 -$1,000.00 -$2,800.00 -$2,637.97 $0.00 3 -$1,000.00 -$2,600.00 -$2,637.97 $0.00 4 -$1,000.00 -$2,400.00 -$2,637.97 $0.00 5 -$11,000.00 -$2,200.00 -$2,637.97 -$16,105.10 PW(15%) $1,676.08 $1,098.56 $1,157.10 $1,992.92 Lender's Interest Rate = 15% End of Plan 1 Plan 2 Plan 3 Plan 4 Year Payment Payment Payment Payment $10,000.00 $10,000.00 $10,000.00 $10,000.00 0 1 -$1,500.00 -$3,500.00 -$2,983.16 $0.00 2 -$1,500.00 -$3,200.00 -$2,983.16 $0.00 3 -$1,500.00 -$2,900.00 -$2,983.16 $0.00 4 -$1,500.00 -$2,600.00 -$2,983.16 $0.00 5 -$11,500.00 -$2,300.00 -$2,983.16 -$20,113.57 PW(15%) $0.00 $0.00 $0.00 $0.00 Lender's Interest Rate = 20% End of Plan 1 Plan 2 Plan 3 Plan 4 Year Payment Payment Payment Payment $10,000.00 $10,000.00 $10,000.00 $10,000.00 0 1 -$2,000.00 -$4,000.00 -$3,343.80 $0.00 2 -$2,000.00 -$3,600.00 -$3,343.80 $0.00 3 -$2,000.00 -$3,200.00 -$3,343.80 $0.00 4 -$2,000.00 -$2,800.00 -$3,343.80 $0.00 5 -$12,000.00 -$2,400.00 -$3,343.80 -$24,883.20 PW(15%) -$1,676.08 -$1,098.56 -$1,208.93 -$2,371.35

Year

2 3 4 5 6 7 8 9 10 11 12 13 14

1 2 3 4 5 >5

Nominal Size of Annual Monthly Interest Rate Payment 6.50% 7.50% 8.50% 9.50% 10.50% 10.50%

$2,245.93 $2,479.61 $2,717.46 $2,958.52 $3,201.98 $3,201.98 Sum =

PW(10/12%)

Excel Calculation for PW(10/12%)

-$25,546.32 =PV(0.10/12,12,-C2) -$25,530.89 =PV(0.10/12,12*(A3-1),,-PV(0.10/12,12,-C3)) -$25,327.72 =PV(0.10/12,12*(A4-1),,-PV(0.10/12,12,-C4)) -$24,960.81 =PV(0.10/12,12*(A5-1),,-PV(0.10/12,12,-C5)) -$24,454.17 =PV(0.10/12,12*(A6-1),,-PV(0.10/12,12,-C6)) -$206,117.66 =PV(0.10/12,60,,-PV(0.105/12,300,-C7)) -$331,937.56

=PMT(B4/12,336,-PV(B3/12,336,-C3)) =PMT(B7/12,300,-PV(B6/12,300,-C6))

M 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300

Type Loan Greatest PW? Conventional Interest-Only -$341,598.22 -$350,192.93 Conventional -$332,684.74 -$338,024.55 Conventional -$324,708.24 -$327,009.58 Conventional -$317,577.20 -$317,038.69 Interest-Only -$311,208.86 -$308,012.92 Interest-Only -$305,528.38 -$299,842.68 Interest-Only -$300,468.08 -$292,446.88 Interest-Only -$295,966.78 -$285,752.11 Interest-Only -$291,969.17 -$279,691.92 Interest-Only -$288,425.24 -$274,206.16 Interest-Only -$285,289.79 -$269,240.38 Interest-Only -$282,521.98 -$264,745.29 Interest-Only -$280,084.89 -$260,676.29 Interest-Only -$277,945.17 -$256,992.97 Interest-Only -$276,072.67 -$253,658.79 Interest-Only -$274,440.19 -$250,640.64 Interest-Only -$273,023.14 -$247,908.58 Interest-Only -$271,799.31 -$245,435.49 Interest-Only -$270,748.66 -$243,196.81 Interest-Only -$269,853.09 -$241,170.33 Interest-Only -$269,096.29 -$239,335.94 Interest-Only -$268,463.51 -$237,675.42 Interest-Only -$267,941.46 -$236,172.30 Interest-Only -$267,518.16 -$234,811.66 Interest-Only -$267,182.81 -$233,579.99 Interest-Only

TABLE 3.5 Present Worth Comparison of Several Mortgage Alternatives

Interest Rate

APR

Points

Prepaid Finance Costs

4.8750

4.9067

0.000

$1,266.77

4.7500

4.8470

0.750

$2,942.71

4.6250

4.7981

1.625

$4,899.90

4.5000

4.7380

2.375

$6,575.85

4.1250

4.2158

0.250

$1,759.92

4.0000

4.1648

0.750

$2,873.36

3.8750

4.1514

1.500

$4,549.31

3.7500

4.1195

3.750

$5,944.00

Conventional 30 year fixed rate ** Purchase Price $250,000 Loan Amount $225,000 10% down, MI included in monthly payment ($106.88)

4.875

5.2266

0.000

$1,266.77

4.750

5.1630

0.750

$2,942.71

4.625

5.1136

1.625

$4,899.90

4.500

5.0494

2.375

$6,575.85

Conventional 15 year fixed rate ** Purchase Price $250,000 Loan Amount $225,000 10% down, MI included in monthly payment ($110.63)

4.125

4.4381

0.250

$1,759.92

4.000

4.3881

0.750

$2,873.36

3.875

4.3697

1.500

$4,549.31

3.750

4.3391

2.125

$5,944.00

Conventional 30 year fixed rate *** Purchase Price $250,000 Loan Amount $225,000 Adjusted Loan Amount $227,812 10% down, MI financed into loan amount

4.875

5.0154

0.000

$4,084.90

4.750

4.9553

0.750

$5,760.70

4.625

4.9061

1.625

$7,717.75

4.500

4.8456

2.375

$9,393.55

Conventional 15 year fixed rate *** Purchase Price $250,000 Loan Amount $225,000 Adjusted Loan Amount $227,362 10% down, MI financed into loan amount

4.125

4.3706

0.250

$4,126.43

4.000

4.3194

0.750

$5,239.75

3.875

4.3059

1.500

$6,915.57

3.750

4.2739

2.125

$8,310.14

FHA 30 year fixed rate **** Purchase Price $250,000 Loan Amount $225,000 Adjusted Loan Amount $227,250 10% down, 1% MI financed in loan and 1.15% monthly MI in payment

4.500

5.1709

0.000

$3,416.26

4.375

5.1248

0.875

$5,515.51

FHA 15 year fixed rate **** Purchase Price $250,000 Loan Amount $225,000 Adjusted Loan Amount $227,250 10% down, 1% MI financed in loan and .25% monthly MI in payment

4.000

4.2829

0.000

$3,369.56

3.500

4.1791

2.500

$9,354.12

Some Representative Mortgage Alternatives Conventional 30 year fixed rate * Purchase Price $325,000 Loan Amount $225,000 Over 20% down, no MI Conventional 15 year fixed rate * Purchase Price $325,000 Loan Amount $225,000 Over 20% down, no MI

FHA 15 year fixed rate **** Purchase Price $250,000 Loan Amount $225,000 Adjusted Loan Amount $227,250 10% down, 1% MI financed in loan and .25% monthly MI in payment VA 30 year fixed rate****** Purchase Price $250,000 Loan Amount $255,375 (100% plus 2.15% VA funding fee)

4.500 4.375 4.250

4.7144 4.6635 4.5688

0.250 1.125 1.500

$6,783.27 $8,957.65 $9,882.03

ARM 3/1 30 YR * Purchase Price $325,000 Loan Amount $225,000 Over 20% down, no MI

3.250 2.875

3.0835 3.0795

0.000 1.000

$1,116.51 $3,331.84

ARM 5/1 30 YR * Purchase Price $325,000 Loan Amount $225,000 Over 20% down, no MI

3.750 3.375

3.2920 3.2395

0.000 1.000

$1,162.75 $3,378.07

* $100,000 Down payment ** 10% Down payment, monthly mortgage insurance payment 30 yr MMI $106.88 included in loan payment 15 yr MMI $110.63 included in loan payment *** 10% Down payment, up front mortgage insurance premium. 30 year UPFMIP $2,812.50 - Financed back into the loan amount; adjusted loan amo 15 year UPFMIP $2,362.50 - Financed back into the loan amount; adjusted loan amo **** 10% Down payment - up front mortgage insurance premium is 1% of the loan amount, financed back into the loan 30 year MMI is 1.15% *base loan amount, included in loan payment 15 year MMI is .25% * base loan amount, included in loan payment

***** Total Payment includes taxes and insurance. Taxes based on 1% of purchase price minus $350 applicable Arkansas hom ****** VA loan is standard 100% financing plus 2.15% VA funding fee financed into the loan Combined monthly taxes and insurance $308.33 for $325,000 purchase price and $237.50 for $250,000 purchase price

TABLE 3.5 ison of Several Mortgage Alternatives Principal and Interest Payment plus Monthly Mortgage Insurance if Applicable (PIP)

Buyer's TVOM = 6.50%

Total Payment PW (PIP) per PW(PITI) per including taxes and $000 $000 Financed insurance (PITI)***** Financed

$1,190.72

$1,499.05

$608.48

$766.04

$1,173.71

$1,482.04

$599.80

$613.68

$1,156.81

$1,465.14

$591.18

$606.70

$1,140.04

$1,448.37

$582.63

$599.77

$1,678.43

$1,986.76

$856.35

$1,013.66

$1,664.30

$1,972.63

$849.14

$1,006.45

$1,650.24

$1,958.57

$841.96

$999.27

$1,636.25

$1,944.58

$834.83

$992.14

$1,297.60

$1,535.10

$663.09

$784.46

$1,280.59

$1,518.09

$654.42

$775.79

$1,263.69

$1,501.19

$645.81

$767.18

$1,246.92

$1,484.42

$637.25

$758.63

$1,789.06

$2,097.39

$912.79

$1,070.10

$1,774.96

$2,083.26

$905.60

$1,062.89

$1,760.87

$2,069.20

$898.41

$1,055.72

$1,746.88

$2,055.21

$891.27

$1,048.58

$1,205.60

$1,443.10

$608.48

$728.35

$1,188.38

$1,425.88

$599.80

$719.68

$1,171.27

$1,408.77

$591.19

$711.06

$1,154.29

$1,391.79

$582.63

$702.51

$1,696.05

$1,933.55

$856.35

$976.26

$1,681.77

$1,919.27

$849.14

$969.05

$1,667.56

$1,905.06

$841.96

$961.88

$1,653.43

$1,890.93

$834.83

$954.74

$1,367.07

$1,604.57

$651.60

$764.80

$1,350.26

$1,587.76

$643.61

$1,188.07

$1,727.82

$1,965.32

$881.54

$1,002.72

$1,671.45

$1,908.95

$852.78

$973.96

$1,293.95 $1,275.05 $1,256.29

$1,531.45 $1,512.55 $1,493.79

$979.21 $933.51

$1,287.54 $1,241.84

$1,042.01 $994.72

$1,350.34 $1,303.05

$582.63 $574.14 $565.71

nced back into the loan amount; adjusted loan amount $227,812 nced back into the loan amount; adjusted loan amount $227,362 e loan amount, financed back into the loan amount, included in loan payment mount, included in loan payment

urchase price minus $350 applicable Arkansas homestead tax credit

ed into the loan

e and $237.50 for $250,000 purchase price

$689.58 $681.09 $672.66

Table 3.5 Loan Repayment (Amortization) Schedule A B C D E Beginning Loan Interest Principal Ending Year Balance Payment Payment Payment Balance 1 $10,000.00 $2,983.16 $1,500.00 $1,483.16 $8,516.84 2 $8,516.84 $2,983.16 $1,277.53 $1,705.63 $6,811.22 3 $6,811.22 $2,983.16 $1,021.68 $1,961.47 $4,849.74 4 $4,849.74 $2,983.16 $727.46 $2,255.69 $2,594.05 5 $2,594.05 $2,983.16 $389.11 $2,594.05 $0.00 note: the loan payment was calculated using Excel's PMT function; At = At-1; Ct = 0.15At; Dt = Bt - Ct; Et = At - Dt

t 1 2 3 4 5

A (P |F 15%,5-t +1) $2,983.16 0.49718 $2,983.16 0.57175 $2,983.16 0.65752 $2,983.16 0.75614 $2,983.16 0.86957

It Pt IPMT PPMT $1,499.99 $1,500.00 $1,483.17 $1,483.16 $1,277.54 $1,277.53 $1,705.62 $1,705.63 $1,021.67 $1,021.68 $1,961.49 $1,961.47 $727.47 $727.46 $2,255.69 $2,255.69 $389.09 $389.11 $2,594.07 $2,594.05

A Unpaid Beginning Balance of Year Before Payment 1 $10,000.00 2 $11,500.00 3 $13,225.00 4 $15,208.75 5 $12,953.06 6 $10,359.01 7 $7,375.85 8 $3,945.22 At+1 = It

$1,500.00 $1,725.00 $1,983.75 $2,281.31 $1,942.96 $1,553.85 $1,106.38 $591.78

C Unpaid Interest Before Payment $1,500.00 $3,225.00 $5,208.75 $7,490.06 $4,896.01 $1,912.86 $1,106.38 $591.78

0.15*At

Ct = Bt + Ht-1 Dt = At + Bt

Interest During Year

Amount Owed

Payment

Interest Payment

$11,500.00 $13,225.00 $15,208.75 $17,490.06 $14,896.01 $11,912.86 $8,482.23 $4,537.01

$0.00 $0.00 $0.00 $4,537.01 $4,537.01 $4,537.01 $4,537.01 $4,537.01

$0.00 $0.00 $0.00 $4,537.01 $4,537.01 $1,912.86 $1,106.38 $591.78

Et Ft = min(Ct,Et)

= min(Ct,Et)

$0.00 $0.00 $0.00 $0.00 $0.00 $2,624.15 $3,430.63 $3,945.22

H Unpaid Interest After Payment $1,500.00 $3,225.00 $5,208.75 $2,953.06 $359.01 $0.00 $0.00 $0.00

I Unpaid Balance After Payment $11,500.00 $13,225.00 $15,208.75 $12,953.06 $10,359.01 $7,375.85 $3,945.22 $0.00

Gt = Et - Ft

Ht = Ct - Ft

It = Dt - Et

Principal Payment

Payment 1 2 3 4 5

Deferred Type of Principal Payment Payment Payment $4,537.01 Interest-only P1 = $0.00 $4,537.01 Interest-only P2 = $0.00 P3 = $10,000 - $4,537.01(P|A 15%,2) = $2,624.14 $4,537.01 Transition P3 =10000+PV(15%,2,PMT(15%,5,FV(15%,3,,10000))) = $2,624.15 P4 = $4,537.01(P|F 15%, 5 - 4 + 1) = $3,430.61 $4,537.01 Normal P4 =PPMT(15%,4,5,FV(15%,3,,10000)) = $3,430.63 P5 = $4,537.01(P|F 15%, 5 - 5 + 1) = $3,945.25 $4,537.01 Normal P5 =PPMT(15%,5,5,FV(15%,3,,10000)) = $3,945.22

Interest Payment I1 = $4,537.01 - $0.00 = $4,537.01 I2 = $4,537.01 - $0.00 = $4,537.01 I3 = $4,537.01 - $2,624.14 = $1,912.87 I3 = $4,537.01 - $2,624.15 = $1,912.86 I4 = $4,537.01 - $3,430.61 = $1,106.40 I4 =IPMT(15%,4,5,FV(15%,3,,10000)) = $1,106.38 I5 = $4,537.01 - $3,945.25 = $591.76 I5 =IPMT(15%,5,5,FV(15%,3,,10000)) = $591.78

j= EOY

CF[A]

4% CF[B]

6% CF[C]

7% CF[D]

8% CF[E]

$18,000.00

-$10,000.00

-$10,000.00 -$28,000.00

$18,720.00

-$10,000.00

-$10,000.00 -$28,720.00

$19,468.80

-$10,000.00

-$10,000.00 -$29,468.80

$20,247.55

-$10,000.00

-$10,000.00 -$30,247.55

$21,057.45

$60,000.00

-$12,000.00

$25,000.00

$38,942.55

$21,899.75

$63,600.00

-$12,000.00

$25,000.00

$41,700.25

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

$22,775.74 $23,686.77 $24,634.24 $25,619.61 $26,644.40 $27,710.17 $28,818.58 $29,971.32 $31,170.18 $32,416.98 $33,713.66 $35,062.21 $36,464.70 $37,923.29 $39,440.22 $41,017.83 $42,658.54 $44,364.88 $46,139.47 $47,985.05 $49,904.46 $51,900.63 $53,976.66 $56,135.73 $58,381.16 $60,716.40 $63,145.06 $65,670.86 $68,297.69 $71,029.60 $73,870.79 $76,825.62 $79,898.64 $83,094.59 $86,418.37 $89,875.11 $93,470.11 $97,208.91 $101,097.27 $105,141.16 $109,346.81 $113,720.68

$67,416.00 $71,460.96 $75,748.62 $80,293.53 $85,111.15 $90,217.82 $95,630.88 $101,368.74 $107,450.86 $113,897.91 $120,731.79 $127,975.70 $135,654.24 $143,793.49 $152,421.10 $161,566.37 $171,260.35 $181,535.97 $192,428.13 $203,973.82 $216,212.24 $229,184.98 $242,936.08 $257,512.24 $272,962.98 $289,340.76 $306,701.20 $325,103.27 $344,609.47 $365,286.04 $387,203.20 $410,435.39 $435,061.52 $461,165.21 $488,835.12 $518,165.23 $549,255.14 $582,210.45 $617,143.08 $654,171.66 $693,421.96 $735,027.28

$75,000.00 $80,250.00 $85,867.50 $91,878.23 $98,309.70 $105,191.38 $112,554.78 $120,433.61 $128,863.96 $137,884.44 $147,536.35 $157,863.90 $168,914.37 $180,738.38 $193,390.06 $206,927.37 $221,412.28 $236,911.14 $253,494.92 $271,239.57 $290,226.33 $310,542.18 $332,280.13 $355,539.74 $380,427.52 $407,057.45 $435,551.47 $466,040.07 $498,662.88 $533,569.28 $570,919.13 $610,883.47 $653,645.31 $699,400.48 $748,358.52 $800,743.61 $856,795.66 $916,771.36 $980,945.36 $1,049,611.53 $1,123,084.34 $1,201,700.24

-$12,000.00 -$12,000.00 $90,000.00 $97,200.00 $104,976.00 $113,374.08 $122,444.01 $132,239.53 $142,818.69 $154,244.18 $166,583.72 $179,910.42 $194,303.25 $209,847.51 $226,635.31 $244,766.14 $264,347.43 $285,495.22 $308,334.84 $333,001.62 $359,641.75 $388,413.10 $419,486.14 $453,045.03 $489,288.64 $528,431.73 $570,706.27 $616,362.77 $665,671.79 $718,925.53 $776,439.57 $838,554.74 $905,639.12 $978,090.25 $1,056,337.47 $1,140,844.47 $1,232,112.02 $1,330,680.99 $1,437,135.47 $1,552,106.30 $1,676,274.81 $1,810,376.79

CF[B-A]

$25,000.00 $44,640.26 $25,000.00 $47,774.19 $90,000.00 $51,114.37 $97,200.00 $54,673.92 $104,976.00 $58,466.75 $113,374.08 $62,507.64 $122,444.01 $66,812.30 $132,239.53 $71,397.41 $142,818.69 $76,280.69 $154,244.18 $81,480.93 $166,583.72 $87,018.13 $179,910.42 $92,913.49 $194,303.25 $99,189.54 $209,847.51 $105,870.21 $226,635.31 $112,980.88 $244,766.14 $120,548.54 $264,347.43 $128,601.81 $285,495.22 $137,171.09 $308,334.84 $146,288.65 $333,001.62 $155,988.76 $359,641.75 $166,307.79 $388,413.10 $177,284.35 $419,486.14 $188,959.42 $453,045.03 $201,376.52 $489,288.64 $214,581.82 $528,431.73 $228,624.36 $570,706.27 $243,556.14 $616,362.77 $259,432.41 $665,671.79 $276,311.78 $718,925.53 $294,256.44 $776,439.57 $313,332.41 $838,554.74 $333,609.78 $905,639.12 $355,162.87 $978,090.25 $378,070.62 $1,056,337.47 $402,416.75 $1,140,844.47 $428,290.12 $1,232,112.02 $455,785.03 $1,330,680.99 $485,001.53 $1,437,135.47 $516,045.80 $1,552,106.30 $549,030.50 $1,676,274.81 $584,075.15 $1,810,376.79 $621,306.60

PW =

$376,468.65 $1,203,157.29

$1,479,707.57

$1,738,560.87

$1,828,637.82

29.04%

CF[C-B]

CF[D-C]

CF[E-C]

$0.00

-$72,000.00

$0.00

$37,000.00

-$75,600.00

$0.00

$37,000.00

$7,584.00 -$87,000.00 -$50,000.00 $8,789.04 -$92,250.00 -$55,250.00 $10,118.88 $4,132.50 $4,132.50 $11,584.69 $5,321.77 $5,321.77 $13,198.55 $6,666.30 $6,666.30 $14,973.56 $8,182.70 $8,182.70 $16,923.89 $9,889.23 $9,889.23 $19,064.87 $11,805.92 $11,805.92 $21,413.10 $13,954.73 $13,954.73 $23,986.53 $16,359.74 $16,359.74 $26,804.56 $19,047.37 $19,047.37 $29,888.20 $22,046.52 $22,046.52 $33,260.13 $25,388.88 $25,388.88 $36,944.88 $29,109.13 $29,109.13 $40,968.96 $33,245.25 $33,245.25 $45,361.00 $37,838.77 $37,838.77 $50,151.93 $42,935.15 $42,935.15 $55,375.17 $48,584.08 $48,584.08 $61,066.79 $54,839.92 $54,839.92 $67,265.75 $61,762.06 $61,762.06 $74,014.09 $69,415.42 $69,415.42 $81,357.20 $77,870.92 $77,870.92 $89,344.05 $87,206.01 $87,206.01 $98,027.50 $97,505.29 $97,505.29 $107,464.54 $108,861.12 $108,861.12 $117,716.69 $121,374.28 $121,374.28 $128,850.27 $135,154.80 $135,154.80 $140,936.80 $150,322.70 $150,322.70 $154,053.41 $167,008.91 $167,008.91 $168,283.24 $185,356.25 $185,356.25 $183,715.93 $205,520.45 $205,520.45 $200,448.07 $227,671.27 $227,671.27 $218,583.79 $251,993.81 $251,993.81 $238,235.27 $278,689.77 $278,689.77 $259,523.40 $307,978.95 $307,978.95 $282,578.38 $340,100.86 $340,100.86 $307,540.52 $375,316.36 $375,316.36 $334,560.91 $413,909.63 $413,909.63 $363,802.28 $456,190.11 $456,190.11 $395,439.87 $502,494.77 $502,494.77 $429,662.38 $553,190.47 $553,190.47 $466,672.96 $608,676.55 $608,676.55

MARR = 8% j HS 4% $376,469 5% $444,795 6% $533,070 7% $648,262 8% $800,000 9% $1,001,587 10% $1,271,457

BS $859,907 $1,011,322 $1,203,157 $1,448,207 $1,763,618 $2,172,416 $2,705,569

Note: PhD-1 denotes PhD student not on assistantship; PhD-2 denotes PhD student on ass

15.39%

14.20%

$0.00

20488%

MS $890,581 $1,044,015 $1,236,488 $1,479,708 $1,789,144 $2,185,273 $2,695,224

PhD-1 $884,626 $1,033,237 $1,217,791 $1,448,476 $1,738,561 $2,105,355 $2,571,457

PhD-2 $974,703 $1,123,314 $1,307,868 $1,538,552 $1,828,638 $2,195,432 $2,661,534

n assistantship; PhD-2 denotes PhD student on assistantship

Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

PW of Remaining Payments $225,000.00 $221,680.43 $218,191.02 $214,523.09 $210,667.50 $206,614.65 $202,354.45 $197,876.28 $193,169.01 $188,220.91 $183,019.65 $177,552.28 $171,805.19 $165,764.07 $159,413.88 $152,738.79 $145,722.20 $138,346.63 $130,593.70 $122,444.13 $113,877.60 $104,872.80 $95,407.29 $85,457.51 $74,998.68 $64,004.75 $52,448.36 $40,300.72 $27,531.58 $14,109.15 $0.00

Δ PW of Remaining Payments

Interest Paid

$3,319.57 $3,489.41 $3,667.93 $3,855.59 $4,052.85 $4,260.20 $4,478.16 $4,707.27 $4,948.11 $5,201.26 $5,467.37 $5,747.09 $6,041.12 $6,350.19 $6,675.08 $7,016.59 $7,375.57 $7,752.92 $8,149.58 $8,566.53 $9,004.80 $9,465.51 $9,949.78 $10,458.83 $10,993.92 $11,556.39 $12,147.64 $12,769.14 $13,422.43 $14,109.15

$11,174.61 $11,004.78 $10,826.25 $10,638.59 $10,441.33 $10,233.98 $10,016.02 $9,786.91 $9,546.08 $9,292.92 $9,026.82 $8,747.10 $8,453.06 $8,143.99 $7,819.10 $7,477.59 $7,118.61 $6,741.26 $6,344.61 $5,927.66 $5,489.38 $5,028.68 $4,544.40 $4,035.35 $3,500.26 $2,937.79 $2,346.54 $1,725.05 $1,071.75 $385.04

=PV(0.07/12,360-12*A8,-PMT(0.07/12,360,-225000)) =B9-B10 =12*PMT(0.07/12,360,-225000)-C12

Geometric Series Personal Investment Planner Name: ________________________________________________ Amount invested the first year ($): Annual increase in amount invested (%): Annual return on investment (%): Investment Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Amount Invested $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

Account Balance $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

Investment Year 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Amount Invested $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

$0.00 0.00% 0.00% Account Balance $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

er Date: ____________

$4,500.00 8.00% 6.00%

Investment Year

Amount Invested

Account Balance

Investment Year

Amount Invested

Account Balance

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$4,500.00 $4,860.00 $5,248.80 $5,668.70 $6,122.20 $6,611.98 $7,140.93 $7,712.21 $8,329.19 $8,995.52 $9,715.16 $10,492.38 $11,331.77 $12,238.31 $13,217.37 $14,274.76 $15,416.74 $16,650.08 $17,982.09 $19,420.65 $20,974.31

$4,500.00 $9,630.00 $15,456.60 $22,052.70 $29,498.06 $37,879.92 $47,293.65 $57,843.48 $69,643.28 $82,817.39 $97,501.60 $113,844.07 $132,006.48 $152,165.18 $174,512.46 $199,257.97 $226,630.19 $256,878.08 $290,272.85 $327,109.88 $367,710.78

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

$22,652.25 $24,464.43 $26,421.59 $28,535.31 $30,818.14 $33,283.59 $35,946.28 $38,821.98 $41,927.74 $45,281.96 $48,904.51 $52,816.87 $57,042.22 $61,605.60 $66,534.05 $71,856.77 $77,605.32 $83,813.74 $90,518.84 $97,760.35 $105,581.17

$412,425.67 $461,635.65 $515,755.37 $575,236.01 $640,568.31 $712,285.99 $790,969.43 $877,249.57 $971,812.29 $1,075,402.98 $1,188,831.67 $1,312,978.44 $1,448,799.37 $1,597,332.94 $1,759,706.96 $1,937,146.15 $2,130,980.24 $2,342,652.79 $2,573,730.80 $2,825,915.00 $3,101,051.07

ner Date: ____________

=G17*(1+$G$6)+F18

=F22*(1+$G$5)

$4,500.00 8.00% 10.96%

Investment Year

Amount Invested

Account Balance

Investment Year

Amount Invested

Account Balance

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

$4,500.00 $9,853.32 $16,182.32 $23,625.04 $32,337.19 $42,494.21 $54,293.67 $67,957.95 $83,737.18 $101,912.58 $122,800.15 $146,754.77 $174,174.87 $205,507.49 $241,254.10 $281,976.89 $328,306.00 $380,947.39 $440,691.71 $508,424.21 $585,135.69

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

$671,934.79 $770,061.62 $880,902.99 $1,006,009.32 $1,147,113.55 $1,306,152.10 $1,485,288.31 $1,686,938.44 $1,913,800.69 $2,168,887.46 $2,455,561.26 $2,777,574.69 $3,139,114.94 $3,544,853.25 $4,000,000.00 $4,510,365.99 $5,082,430.57 $5,723,417.47 $6,441,379.13 $7,245,290.50 $8,145,153.34

er Date: ____________

Left Side of Equality Time Period 0 1 2 3 4 PW =

Right Side of Equality

Cash Flow $0 $200 $300 $300 $400 $826.71

=NPV(15%,B5:B8)

Time Cash Flow Period 0 $0 1 $200 2 $268 3 $335 4 $403 PW = $826.71 X= $67.53

=200+2*E10 =NPV(15%,E5:E8)

Left Side of Equality

Right Side of Equality

Time Cash Flow Period 0 -$4,000 1 $1,500 2 $1,500 3 $1,500 4 $1,500 5 $1,500 PWLS = $1,686.18

Time Cash Flow Period 0 -$7,000 1 $1,500 2 $2,000 3 $2,500 4 $3,000 5 $3,500 PWRS = $2,117.08 PWLS-PWRS = i =

=NPV(E12,B5:B8)+B4

-$430.90 10% =NPV(E12,E5:E8)+E4

Left Side of Equality

Right Side of Equality

Time Cash Flow Period 0 -$4,000 1 $1,500 2 $1,500 3 $1,500 4 $1,500 5 $1,500 PWLS = $1,166.04

Time Cash Flow Period 0 -$7,000 1 $1,500 2 $2,000 3 $2,500 4 $3,000 5 $3,500 PWRS = $1,166.04 PWLS-PWRS = $0.00 i = 13.8677%

Interest Rate End of Period Sequential End of Period During Period Cash Flow Movement 5 12% $200.00 =C3 4 8% $0.00 =D3/(1+B3)+C4 3 8% $300.00 =D4/(1+B8)+C5 2 10% -$200.00 =D5/(1+B5)+C6 1 10% $200.00 =D6/(1+B6)+C7 0 =D7/(1+B7)+C8 Interest Rate End of Period End of Period During Period Cash Flow 5 12% $200.00 4 8% $0.00 3 8% $300.00 2 10% -$200.00 1 10% $200.00 0

Sequential Movement $200.00 $178.57 $465.34 $230.87 $409.89 $372.62

= PW

Interest Rate End of Period Sequential End of Period During Period Cash Flow Movement 0 1 10% $200.00 =C4 2 10% -$200.00 =D4*(1+B5)+C5 3 8% $300.00 =D5*(1+B6)+C6 4 8% $0.00 =D6*(1+B7)+C7 5 12% $200.00 =D7*(1+B8)+C8 Interest Rate End of Period End of Period During Period Cash Flow 0 1 10% $200.00 2 10% -$200.00 3 8% $300.00 4 8% $0.00 5 12% $200.00

Sequential Movement $200.00 $20.00 $321.60 $347.33 $589.01

= FW

Given

Determine

Interest Rate End of Period End of Period During Period Cash Flow 5 12% $200.00 4 8% $0.00 3 8% $300.00 2 10% -$200.00 1 10% $200.00 0 Interest Rate End of Period End of Period During Period Cash Flow 5 12% $96.99 4 8% $96.99 3 8% $96.99 2 10% $96.99 1 10% $96.99 0

Sequential Movement $200.00 $178.57 $465.34 $230.87 $409.89 $372.62

= PW

Sequential Movement $96.99 $183.58 $266.97 $344.18 $409.88 $372.62

= PW

MARR = 12% EOY CF[A] 0 -$15,500 1 -$8,750 2 -$8,750 3 -$8,750 4 -$21,750 5 -$8,750 6 -$8,750 7 -$8,750 8 -$21,750 9 -$8,750 10 -$8,750 11 -$8,750 12 -$21,750 13 -$8,750 14 -$8,750 15 -$8,750 16 -$21,750 17 -$8,750 18 -$8,750 19 -$8,750 20 -$21,750 21 -$8,750 22 -$8,750 23 -$8,750 24 -$21,750 25 -$8,750 26 -$8,750 27 -$8,750 28 -$21,750 29 -$8,750 30 -$8,750 31 -$8,750 32 -$21,750 33 -$8,750 34 -$8,750 35 -$8,750 36 -$21,750 37 -$8,750 38 -$8,750 39 -$8,750 40 -$21,750 41 -$8,750 42 -$8,750 43 -$8,750 44 -$21,750 45 -$8,750 46 -$8,750 47 -$8,750 48 -$21,750 49 -$8,750

CF[B] -$20,250 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850 -$23,100 -$5,850 -$5,850 -$5,850 -$5,850

CF[C] -$30,750 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175 -$3,175 -$3,175 -$3,175 -$3,175 -$30,675 -$3,175

AW PW

A B -$13,330.05 -$10,995.32 -$110,959.97 -$91,525.57

50 51 52 53 54 55 56 57 58 59 60 PW =

-$8,750 -$8,750 -$21,750 -$8,750 -$8,750 -$8,750 -$21,750 -$8,750 -$8,750 -$8,750 -$6,250 -$110,959.97

-$23,100 -$3,175 -$5,850 -$3,175 -$5,850 -$3,175 -$5,850 -$3,175 -$5,850 -$30,675 -$23,100 -$3,175 -$5,850 -$3,175 -$5,850 -$3,175 -$5,850 -$3,175 -$5,850 -$3,175 -$2,850 $75 -$91,525.57 -$85,352.36

C A/B A/C B/C -$10,253.71 1.212339 1.300022 1.072326 -$85,352.36 1.212339 1.300022 1.072326

Excavation Alternative

Useful Life

Initial Investment

A B C

4 yrs 5 yrs 6 yrs

$15,500 $20,250 $30,750

Annual Operating Cost $8,750 $5,850 $3,175

Terminal Salvage Value $2,500 $3,000 $3,250

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

TI t

MdT/N

$7,800.00 $7,464.89 $7,109.67 $6,733.15 $6,334.02 $5,910.96 $5,462.50 $4,987.14 $4,483.26 $3,949.15 $3,382.99 $2,782.86 $2,146.72 $1,472.42 $757.65

$306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 $306.67 km =

1 $33,462.90 $19,500.00 2 $33,462.90 $18,662.23 3 $33,462.90 $17,774.19 4 $33,462.90 $16,832.86 5 $33,462.90 $15,835.06 6 $33,462.90 $14,777.39 7 $33,462.90 $13,656.26 8 $33,462.90 $12,467.86 9 $33,462.90 $11,208.16 10 $33,462.90 $9,872.88 11 $33,462.90 $8,457.47 12 $33,462.90 $6,957.15 13 $33,462.90 $5,366.80 14 $33,462.90 $3,681.04 15 $33,462.90 $1,894.13 18 c = 3.5384615% = 0.02 + 5/325

A t -TI t -MdT/N -$313,500.00 = M (1-c) $25,356.23 $25,691.34 $26,046.56 $26,423.09 $26,822.21 $27,245.28 $27,693.73 $28,169.09 $28,672.97 $29,207.08 $29,773.24 $30,373.37 $31,009.51 $31,683.82 $32,398.58 3.942% =IRR(F2:F17)

Corporation

2006

βh

βp

2007

βh

βp

2008

βh

βp

2009

βh

βp

2010

βh

2011

βp

βh

βp

Boeing 1.04 1.03 0.91 0.90 1.39 1.14 1.24 1.25 1.27 1.10 Abbott Labs 0.65 0.63 0.21 0.59 0.14 0.37 0.20 0.54 0.22 0.60 Apple 1.52 1.50 1.32 1.33 2.36 1.35 1.67 0.87 1.50 0.87 AT&T 0.95 0.73 1.51 0.93 1.03 0.89 0.63 0.72 0.69 0.69 Caterpillar 1.58 1.25 1.46 1.29 1.32 1.22 1.76 1.65 1.77 1.35 Cisco 1.11 1.22 1.71 1.21 1.51 1.06 1.17 0.90 1.24 0.94 Coca Cola 0.75 0.46 0.66 0.52 0.72 0.57 0.59 0.52 0.59 0.52 Deere 1.54 1.29 1.27 1.45 1.47 1.39 1.75 1.69 1.56 1.31 Dell Computer 0.94 1.35 1.14 1.04 1.23 1.06 1.41 1.31 1.35 1.27 Dupont 1.11 0.96 1.13 1.02 0.98 1.02 1.36 1.31 1.37 1.09 Eastman Chemical 1.34 1.06 0.94 1.02 0.93 1.05 1.86 1.35 1.87 1.19 Exxon/Mobil 1.20 1.00 0.84 1.00 0.92 0.82 0.50 0.84 0.47 1.01 Federal Express 1.10 1.03 0.48 0.98 0.85 1.11 0.99 1.14 1.17 1.12 Ford 1.51 1.71 1.94 1.86 2.39 2.34 2.62 1.95 2.53 1.84 General Electric 0.84 0.89 0.71 0.93 0.63 1.15 1.43 1.62 1.57 1.46 General Motors 1.31 2.00 1.06 1.73 2.01 2.19 NA NA NA NA Hewlett Packard 1.18 1.20 1.85 0.97 0.13 0.47 1.04 0.79 1.04 0.86 Home Depot 1.17 1.06 1.44 1.05 0.87 1.27 0.65 0.90 0.74 1.07 IBM 1.01 0.84 1.64 0.87 0.99 0.72 0.79 0.69 0.75 0.62 Intel 1.26 1.68 1.85 1.45 1.64 1.05 1.18 0.74 1.15 0.83 J. B. Hunt Transport 1.28 1.32 1.07 1.33 0.66 1.11 1.06 1.04 0.95 1.03 Johnson & Johnson 0.60 0.55 0.20 0.54 0.39 0.35 0.53 0.54 0.58 0.52 Lockheed Martin 0.75 0.64 0.03 0.67 0.62 0.76 1.09 0.83 1.04 0.90 Lowe's 1.21 0.93 0.89 1.05 1.14 1.27 0.97 0.98 1.06 1.15 Merck 0.59 0.77 0.85 0.83 0.85 0.79 0.81 0.70 0.80 0.64 Microsoft 0.93 1.18 1.18 0.97 0.95 0.87 1.01 0.80 1.04 0.94 Motorola 1.44 1.44 1.36 1.46 2.14 1.80 1.97 1.32 1.75 1.36 Pepsi Cola 0.58 0.50 1.42 0.60 0.33 0.46 0.53 0.53 0.53 0.51 Pfizer 1.08 0.83 0.76 0.79 0.69 0.67 0.70 0.69 0.69 0.81 Procter & Gamble 0.59 0.64 0.24 0.53 0.66 0.56 0.56 0.69 0.56 0.59 Southwest Airlines 0.89 1.60 0.99 1.55 0.10 1.26 0.87 1.04 1.07 0.87 Starbuck's 1.01 0.99 0.70 1.30 1.22 1.25 1.20 1.08 1.30 0.94 Target 0.80 0.94 1.28 0.97 0.83 1.16 1.16 1.01 1.04 0.90 Texas Instruments 1.47 1.52 2.00 1.50 1.85 1.11 1.16 0.79 1.09 0.82 Tyco 1.17 1.19 1.29 1.04 0.68 1.21 1.25 1.22 1.25 1.01 Tyson Foods 0.72 0.98 0.90 0.96 0.88 1.20 1.38 1.08 1.19 1.06 United Parcel Service 0.89 0.83 0.53 0.90 0.86 0.96 0.80 0.90 0.83 0.91 United Technologies 1.05 0.99 0.73 0.87 1.06 1.03 0.95 0.98 0.99 0.98 Wal-Mart 0.84 0.82 0.60 0.84 0.14 0.74 0.20 0.64 0.28 0.64 Xerox 1.15 1.02 1.90 0.99 0.88 0.87 1.44 1.31 1.47 1.30 Source: Barra (July, 2006; June, 2007; June, 2008; June, 2009; June, 2010, June 2011)

1.27 0.30 1.33 0.66 1.73 1.21 0.60 1.53 1.41 1.39 1.92 0.48 1.17 2.41 1.64 NA 1.01 0.78 0.72 1.12 0.94 0.60 0.96 1.01 0.72 1.04 1.71 0.55 0.69 0.51 1.08 1.25 0.94 1.07 1.17 1.17 0.82 1.01 0.33 1.58

1.01 0.58 0.98 0.70 1.37 1.34 0.51 1.37 1.19 1.04 1.15 0.95 1.01 1.76 1.35 1.65 1.13 0.95 0.68 0.96 1.00 0.61 0.89 1.07 0.64 0.89 1.14 0.51 0.75 0.64 0.93 0.98 0.97 0.94 1.12 1.04 0.81 0.97 0.63 1.31

Note: Historical beta results are based on a 12-60-month regression against the S&P 500 depending on data availability 2011 data represents Motorola Solutions for Motorola

β 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

5% 8% 5.0% 5.3% 5.6% 5.9% 6.2% 6.5% 6.8% 7.1% 7.4% 7.7% 8.0% 8.3% 8.6% 8.9% 9.2% 9.5% 9.8% 10.1% 10.4% 10.7% 11.0%

9% 5.0% 5.4% 5.8% 6.2% 6.6% 7.0% 7.4% 7.8% 8.2% 8.6% 9.0% 9.4% 9.8% 10.2% 10.6% 11.0% 11.4% 11.8% 12.2% 12.6% 13.0%

E(r m ) 10% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0% 11.5% 12.0% 12.5% 13.0% 13.5% 14.0% 14.5% 15.0%

11% 5.0% 5.6% 6.2% 6.8% 7.4% 8.0% 8.6% 9.2% 9.8% 10.4% 11.0% 11.6% 12.2% 12.8% 13.4% 14.0% 14.6% 15.2% 15.8% 16.4% 17.0%

12% 5.0% 5.7% 6.4% 7.1% =$B$1+$A7*(F$3-$B$1) 7.8% 8.5% 9.2% 9.9% 10.6% Capital Asset Pricing Model 11.3% Security Market Li 12.0% 20.0% 18.0% 12.7% 16.0% 13.4% 14.0% 12.0% 14.1% 10.0% 14.8% 8.0% 6.0% 15.5% 4.0% 16.2% 2.0% 0.0% 16.9% 0.0 0.3 0.6 0.9 1.2 1.5 1.8 β 17.6% =$B$1+$A22*(F$3-$B$1) 18.3% 19.0% E(rcs)

rf =

t Pricing Model Security Market Lines 8% Market Return 9% Market Return 10% Market Return 11% Market Return 12% Market Return

MARR = 10% (ignores salvage value until EOY = 10) EOY CF Cum(PW) 0 -$500,000 -$500,000.00 =B3 1 $92,500 -$415,909.09 =NPV($B$1,$B$4:B4)+$B$3 2 $92,500 -$339,462.81 =NPV($B$1,$B$4:B5)+$B$3 3 $92,500 -$269,966.19 =NPV($B$1,$B$4:B6)+$B$3 4 $92,500 -$206,787.45 =NPV($B$1,$B$4:B7)+$B$3 5 $92,500 -$149,352.22 =NPV($B$1,$B$4:B8)+$B$3 6 $92,500 -$97,138.39 =NPV($B$1,$B$4:B9)+$B$3 7 $92,500 -$49,671.26 =NPV($B$1,$B$4:B10)+$B$3 8 $92,500 -$6,519.33 =NPV($B$1,$B$4:B11)+$B$3 9 $92,500 $32,709.70 =NPV($B$1,$B$4:B12)+$B$3 10 $142,500 $87,649.62 =NPV($B$1,$B$4:B13)+$B$3 PW = $87,649.62 =NPV(B1,B4:B13)+B3 Present Worth of the Investment (ignores salvage value until EOY = 10) $100,000 $0 -$100,000 0

-$200,000 -$300,000 -$400,000 -$500,000

Investment Year

f the Investment

alue until EOY = 10)

tment Year

EOY 0

CF(A) -$300,000.00

CF(B) -$450,000.00

CF(B-A) -$150,000.00

MARR

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

IRR =

12.87%

12.11%

10.56%

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

$400,000 $350,000 $300,000

Present Worth

$250,000 $200,000 $150,000 $100,000 $50,000 $0 0%

10%

12%

14%

-$50,000 -$100,000 -$150,000

MARR Alternative A

Alternative B

16%

18%

20%

PW(A)

PW(B)

PW(B-A)

$250,000.00 $350,000.00 $100,000.00 $220,921.75 $307,704.36 $86,782.61 $194,042.18 $268,606.80 $74,564.63 $169,161.16 $232,416.23 $63,255.07 $146,099.27 $198,871.66 $52,772.39 $124,695.42 $167,738.79 $43,043.37 $104,804.79 $138,806.96 $34,002.18 $86,296.98 $111,886.52 $25,589.54 $69,054.48 $86,806.51 $17,752.03 $52,971.17 $63,412.62 $10,441.44 $37,951.19 $41,565.37 $3,614.18 $23,907.76 $21,138.56 -$2,769.20 $10,762.27 $2,017.84 -$8,744.42 -$1,556.61 -$15,900.52 -$14,343.91 -$13,113.64 -$32,710.75 -$19,597.11 -$23,967.73 -$48,498.51 -$24,530.78 -$34,172.49 -$63,341.80 -$29,169.31 -$43,776.80 -$77,311.71 -$33,534.91 -$52,825.25 -$90,473.10 -$37,647.84 -$61,358.58 -$102,885.21 -$41,526.63 -$69,414.04 -$114,602.23 -$45,188.20

EOY 0 1

CF(A) CF(B) CF(B-A) ($300,000.00) ($450,000.00) ($150,000.00) $55,000.00 $80,000.00 $25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

IRR =

12.87%

12.11%

10.56%

$45,000

Present Worth

$40,000

$35,000

$30,000

$25,000

$20,000 10.0% 10.1% 10.2% 10.3% 10.4% 10.5% 10.6% 10.7% 10.8% 10.9% 11.0%

MARR Alternative A

Alternative B

MARR

PW(A)

PW(B)

PW(B-A)

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10.0% 10.1% 10.2% 10.3% 10.4% 10.5% 10.6% 10.7% 10.8% 10.9% 11.0% 11.1% 11.2% 11.3% 11.4% 11.5% 11.6% 11.7% 11.0%11.8% 11.9% 12.0%

$250,000 $220,922 $194,042 $169,161 $146,099 $124,695 $104,805 $86,297 $69,054 $52,971 $37,951 $36,504 $35,067 $33,639 $32,221 $30,813 $29,413 $28,023 $26,642 $25,270 $23,908 $22,554 $21,209 $19,873 $18,546 $17,227 $15,917 $14,616 $13,323 $12,038 $10,762

$350,000 $307,704 $268,607 $232,416 $198,872 $167,739 $138,807 $111,887 $86,807 $63,413 $41,565 $39,461 $37,370 $35,294 $33,231 $31,182 $29,146 $27,124 $25,116 $23,121 $21,139 $19,170 $17,213 $15,270 $13,340 $11,422 $9,516 $7,623 $5,743 $3,874 $2,018

$100,000 $86,783 $74,565 $63,255 $52,772 $43,043 $34,002 $25,590 $17,752 $10,441 $3,614 $2,956 $2,303 $1,654 $1,010 $369 ($267) ($899) ($1,526) ($2,150) ($2,769) ($3,385) ($3,996) ($4,603) ($5,206) ($5,806) ($6,401) ($6,993) ($7,580) ($8,164) ($8,744)

MARR = EOY 0 1 2 3 4 5 6 7 8 9 10

10% SVgeometric Cum(PWgeom) CF -$500,000 $500,000 n/a $92,500 $397,500 -$54,545.45 $92,500 $316,013 -$78,295.45 $92,500 $251,230 -$81,213.42 $92,500 $199,728 -$70,370.67 $92,500 $158,784 -$50,760.10 $92,500 $126,233 -$25,883.17 $92,500 $100,355 $1,826.83 $92,500 $79,782 $30,699.75 $92,500 $63,427 $59,608.94 $92,500 $50,424 $87,813.27

SVgradient Cum(PWgrad) $500,000 n/a $455,000 -$2,272.73 =PV($B$1,A4,-B4,-E4)+$B$3 $410,000 -$619.83 =PV($B$1,A5,-B5,-E5)+$B$3 $365,000 $4,263.71 =PV($B$1,A6,-B6,-E6)+$B$3 $320,000 $11,776.86 =PV($B$1,A7,-B7,-E7)+$B$3 $275,000 $21,401.14 =PV($B$1,A8,-B8,-E8)+$B$3 $230,000 $32,690.62 =PV($B$1,A9,-B9,-E9)+$B$3 $185,000 $45,262.99 =PV($B$1,A10,-B10,-E10)+$B$3 $140,000 $58,791.71 =PV($B$1,A11,-B11,-E11)+$B$3 $95,000 $72,998.98 =PV($B$1,A12,-B12,-E12)+$B$3 $50,000 $87,649.62 =PV($B$1,A13,-B13+E13,-E13)+$B$3

Present Worth of the Investment (including salvage value) $100,000.00 $80,000.00 $60,000.00 $40,000.00 $20,000.00 $0.00 -$20,000.00 1 -$40,000.00 -$60,000.00 -$80,000.00 -$100,000.00

geometric

gradient

Investment Year

MARR : # years used: Annual Investment: Annual Savings: Salvage Value geometric: Present Worth:

10% 10 = DPBP $500,000 $92,500 $49,794 =B3*(1-0.206)^B2 $87,570.11 =PV(B1,B2,-B4,-B5)-B3

# years used: Annual Investment: Annual Savings: Salvage Value gradient: Present Worth:

10 = DPBP $500,000 $92,500 $50,000 =B9-B8*45000 $87,649.62 =PV(B1,B8,-B10,-B11)-B9

The difference in present worths is due to round-off error in the geometric series rate needed to obtain exactly a $50,000 salvage value after 10 years.

MARR : # years used: Annual Investment: Annual Savings: Salvage Value geometric: Present Worth:

10% 6.951875214 = DPBP $500,000 $92,500 $100,585 =B3*(1-0.206)^B2 $0.00 =PV(B1,B2,-B4,-B5)-B3

# years used: Annual Investment: Annual Savings: Salvage Value gradient: Present Worth:

2.169974472 = DPBP $500,000 $92,500 $402,351 =B9-B8*45000 $0.00 =PV(B1,B8,-B10,-B11)-B9

MARR = 10% DPBP = 6.273148349 (P|G MARR,DPBP ) = 10.5029 Initial Investment = $150,000.00 First Year Savings = $45,000.00 Gradient Step = -$5,000.00 Present Worth = $0.00 =(1-(1+B1*B2)*(1+B1)^-B2)/B1^2

$50,000 $0 0

-$50,000

Present Worth

-$100,000 -$150,000 -$200,000 -$250,000 -$300,000 -$350,000 -$400,000 -$450,000

Investment Year Alternative A

Alternative B

Alternative C

EOY 0 1 2 3 4 5 6 7 8 9 10 PW =

CF(A) -$300,000.00 $72,000.00 $72,000.00 $72,000.00 $72,000.00 $72,000.00 $72,000.00 $72,000.00 $72,000.00 $72,000.00 $72,000.00 $23,574.21

CumPW(A) -$300,000.00 -$238,983.05 -$187,273.77 -$143,452.35 -$106,315.55 -$74,843.69 -$48,172.62 -$25,570.01 -$6,415.27 $9,817.57 $23,574.21

CF(B) -$450,000.00 $103,000.00 $103,000.00 $103,000.00 $103,000.00 $103,000.00 $103,000.00 $103,000.00 $103,000.00 $103,000.00 $103,000.00 $12,890.89

CumPW(B) -$450,000.00 -$362,711.86 -$288,738.87 -$226,049.89 -$172,923.63 -$127,901.38 -$89,746.94 -$57,412.66 -$30,010.73 -$6,788.75 $12,890.89

CF(C) -$150,000.00 $50,000.00 $45,000.00 $40,000.00 $35,000.00 $30,000.00 $25,000.00 $20,000.00 $15,000.00 $10,000.00 $5,000.00 $2,942.05

CumPW(C) -$150,000.00 -$107,627.12 -$75,308.82 -$50,963.58 -$32,910.97 -$19,797.70 -$10,536.91 -$4,258.41 -$267.84 $1,986.73 $2,942.05

Beginning Scholarship Amount = $12,500.00 Size of the Gift = $300,000.00 EOY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Scholarship Cost $12,500.00 $13,062.50 $13,650.31 $14,264.58 $14,906.48 $15,577.27 $16,278.25 $17,010.77 $17,776.26 $18,576.19 $19,412.12 $20,285.66 $21,198.52 $22,152.45 $23,149.31 $24,191.03 $25,279.63 $26,417.21 $27,605.98 $28,848.25 $30,146.43 $31,503.01 $32,920.65 $34,402.08 $35,950.17 '=B28*(1+$L$1)

Size of Endowment $314,500.00 $329,742.50 $345,769.01 $362,623.65 $380,353.29 $399,007.81 $418,640.27 $439,307.12 $461,068.50 $483,988.48 $508,135.32 $533,581.84 $560,405.69 $588,689.75 $618,522.51 $649,998.51 $683,218.75 $718,291.22 $755,331.45 $794,463.02 $835,818.27 $879,538.90 $925,776.75 $974,694.58 $1,026,466.92

EOY 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Annual Endowment Growth Rate = 9.0% Annual Increase in Tuition = 4.5% Scholarship Cost $37,567.93 $39,258.49 $41,025.12 $42,871.25 $44,800.46 $46,816.48 $48,923.22 $51,124.76 $53,425.38 $55,829.52 $58,341.85 $60,967.23 $63,710.76 $66,577.74 $69,573.74 $72,704.56 $75,976.26 $79,395.19 $82,967.98 $86,701.54 $90,603.11 $94,680.25 $98,940.86 $103,393.19 $108,045.89

Size of Endowment $1,081,281.01 $1,139,337.81 $1,200,853.10 $1,266,058.63 $1,335,203.45 $1,408,555.28 $1,486,402.04 $1,569,053.46 $1,656,842.89 $1,750,129.23 $1,849,299.02 $1,954,768.70 $2,066,987.13 $2,186,438.23 $2,313,643.93 $2,449,167.33 $2,593,616.12 $2,747,646.38 $2,911,966.58 $3,087,342.03 $3,274,599.71 $3,474,633.44 $3,688,409.59 $3,916,973.26 $4,161,454.97

EOY 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

Scholarship Cost $112,907.95 $117,988.81 $123,298.31 $128,846.73 $134,644.83 $140,703.85 $147,035.53 $153,652.12 $160,566.47 $167,791.96 $175,342.60 $183,233.02 $191,478.50 $200,095.03 $209,099.31 $218,508.78 $228,341.68 $238,617.05 $249,354.82 $260,575.78 $272,301.69 $284,555.27 $297,360.26 $310,741.47 $324,724.84 '=L28*1.09

Size of Endowment $4,423,077.96 $4,703,166.16 $5,003,152.81 $5,324,589.83 $5,669,158.08 $6,038,678.46 $6,435,123.99 $6,860,633.03 $7,317,523.53 $7,808,308.69 $8,335,713.87 $8,902,695.11 $9,512,459.16 $10,168,485.45 $10,874,549.83 $11,634,750.54 $12,453,536.41 $13,335,737.64 $14,286,599.21 $15,311,817.35 $16,417,579.22 $17,610,606.08 $18,898,200.37 $20,288,296.93 $21,789,518.82 '=L28*1.09-H29

EOY 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Scholarship Cost $339,337.45 $354,607.64 $370,564.98 $387,240.41 $404,666.23 $422,876.21 $441,905.63 $461,791.39 $482,572.00 $504,287.74 $526,980.69 $550,694.82 $575,476.09 $601,372.51 $628,434.27 $656,713.82 $686,265.94 $717,147.91 $749,419.56 $783,143.44 $818,384.90 $855,212.22 $893,696.77 $933,913.12 $975,939.21

Size of Endowment $23,411,238.06 $25,163,641.85 $27,057,804.63 $29,105,766.64 $31,320,619.41 $33,716,598.95 $36,309,187.23 $39,115,222.69 $42,153,020.73 $45,442,504.85 $49,005,349.60 $52,865,136.24 $57,047,522.42 $61,580,426.93 $66,494,231.08 $71,821,998.06 $77,599,711.94 $83,866,538.11 $90,665,106.98 $98,041,823.17 $106,047,202.36 $114,736,238.36 $124,168,803.04 $134,410,082.20 $145,531,050.38

Beginning Scholarship Amount = $12,500.00 Size of the Gift = $273,678.79 EOY 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Size of Endowment $285,809.88 $298,470.27 $311,682.28 $325,469.11 $339,854.85 $354,864.51 $370,524.06 $386,860.46 $403,901.64 $421,676.60 $440,215.37 $459,549.09 $479,709.99 $500,731.44 $522,647.96 $545,495.25 $569,310.19 $594,130.90 $619,996.70 $646,948.14 $675,027.05 $704,276.47 $734,740.70 $766,465.29 $799,496.99

EOY 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Size of Endowment $833,883.79 $869,674.84 $906,920.46 $945,672.05 $985,982.08 $1,027,903.99 $1,071,492.13 $1,116,801.66 $1,163,888.43 $1,212,808.87 $1,263,619.82 $1,316,378.38 $1,371,141.68 $1,427,966.69 $1,486,909.95 $1,548,027.29 $1,611,373.48 $1,677,001.90 $1,744,964.10 $1,815,309.33 $1,888,084.06 $1,963,331.38 $2,041,090.35 $2,121,395.29 $2,204,274.98

EOY 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

Size of Endowment $2,289,751.77 $2,377,840.62 $2,468,547.97 $2,561,870.55 $2,657,794.07 $2,756,291.68 $2,857,322.41 $2,960,829.30 $3,066,737.47 $3,174,951.88 $3,285,354.95 $3,397,803.88 $3,512,127.72 $3,628,124.19 $3,745,556.05 $3,864,147.32 $3,983,578.90 $4,103,483.95 $4,223,442.69 $4,342,976.74 $4,461,542.96 $4,578,526.55 $4,693,233.68 $4,804,883.25 $4,912,597.90 '=L28*1.09-H29

EOY 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Size of Endowment $5,015,394.26 $5,112,172.10 $5,201,702.61 $5,282,615.44 $5,353,384.60 $5,412,313.01 $5,457,515.55 $5,486,900.56 $5,498,149.61 $5,488,695.33 $5,455,697.22 $5,396,015.15 $5,306,180.43 $5,182,364.16 $5,020,342.66 $4,815,459.68 $4,562,585.11 $4,256,069.87 $3,889,696.59 $3,456,625.85 $2,949,337.28 $2,359,565.42 $1,678,229.54 $895,357.07 $0.00

EOY CF(1) CumCF(1) CF(2) CumCF(2) 0 -$10,000 -$10,000 -$10,000 -$10,000 1 $5,000 -$5,000 $5,000 -$5,000 2 $5,000 $0 $4,000 -$1,000 3 $0 $0 $3,000 $2,000 4 $0 $0 $2,000 $4,000 5 $1,000 $1,000 $1,000 $5,000 PBP = 2 yrs 2.33 yrs PW(10%) = -$701.39 $2,092.13

CF(3) CumCF(3) -$10,000 -$10,000 $2,500 -$7,500 $2,500 -$5,000 $2,500 -$2,500 $2,500 $0 $12,500 $12,500 4 yrs $5,686.18

EOY CF(A) CumPW(A) CF(B) CumPW(B) CF(B-A) CumPW(B-A) 0 ($300,000.00) ($300,000.00) ($450,000.00) ($450,000.00) ($150,000.00) ($150,000.00) 1 $55,000.00 ($250,000.00) $80,000.00 ($377,272.73) $25,000.00 ($127,272.73) 2 $55,000.00 ($204,545.45) $80,000.00 ($311,157.02) $25,000.00 ($106,611.57) 3 $55,000.00 ($163,223.14) $80,000.00 ($251,051.84) $25,000.00 ($87,828.70) 4 $55,000.00 ($125,657.40) $80,000.00 ($196,410.76) $25,000.00 ($70,753.36) 5 $55,000.00 ($91,506.73) $80,000.00 ($146,737.06) $25,000.00 ($55,230.33) 6 $55,000.00 ($60,460.66) $80,000.00 ($101,579.14) $25,000.00 ($41,118.48) 7 $55,000.00 ($32,236.97) $80,000.00 ($60,526.49) $25,000.00 ($28,289.53) 8 $55,000.00 ($6,579.06) $80,000.00 ($23,205.90) $25,000.00 ($16,626.85) 9 $55,000.00 $16,746.31 $80,000.00 $10,721.91 $25,000.00 ($6,024.40) 10 $55,000.00 $37,951.19 $80,000.00 $41,565.37 $25,000.00 $3,614.18 PW = $37,951.19 $41,565.37 $3,614.18

MARR = 10% Planning SVgeometric FWgeometric SVgradient CF Horizon 0 -$500,000 $500,000 $0.00 $500,000 1 $92,500 $397,000 -$60,500.00 $455,000 2 $92,500 $315,218 -$95,532.00 $410,000 3 $92,500 $250,283 -$109,041.91 $365,000 4 $92,500 $198,725 -$104,032.72 $320,000 5 $92,500 $157,787 -$82,745.78 $275,000 6 $92,500 $125,283 -$46,803.32 $230,000 7 $92,500 $99,475 $2,679.67 $185,000 8 $92,500 $78,983 $65,008.32 $140,000 9 $92,500 $62,713 $139,840.33 $95,000 10 $142,500 $49,794 $230,421.06 $50,000 FW = $227,340.55 =FV(B1,A13,,-NPV(B1,B4:B13)-B3)

FWgradient $0.00 =B3+E3 -$2,500.00 =FV($B$1,A4,-B4,-$B$3)+$E4 -$750.00 =FV($B$1,A5,-B5,-$B$3)+$E5 $5,675.00 =FV($B$1,A6,-B6,-$B$3)+$E6 $17,242.50 =FV($B$1,A7,-B7,-$B$3)+$E7 $34,466.75 =FV($B$1,A8,-B8,-$B$3)+$E8 $57,913.43 =FV($B$1,A9,-B9,-$B$3)+$E9 $88,204.77 =FV($B$1,A10,-B10,-$B$3)+$E10 $126,025.24 =FV($B$1,A11,-B11,-$B$3)+$E11 $172,127.77 =FV($B$1,A12,-B12,-$B$3)+$E12 $227,340.55 =FV($B$1,A13,-B13+C13,-$B$3)+$E13 Future Worth of the SMP Machine Investment

geometric

gradient

$250,000 $200,000 $150,000 $100,000 $50,000 $0 -$50,000

-$100,000 -$150,000 Length of the Planning Horizon (Yrs)

FWgradient $0.00 -$2,500.00 -$750.00 $5,675.00 $17,242.50 $34,466.75 $57,913.43 $88,204.77 $126,025.24 $172,127.77 $227,340.55

Geometric Gradient n = 6.951875214 2.16997447 FW = $0.00 $0.00 =FV($B$1,C17,-92500,500000)+500000-45000*C17 =FV($B$1,B17,-92500,500000)+500000*(1-0.206)^B17

MARR = 10% Planning SVgeometric FWgeometric CF Horizon 0 -$500,000 $500,000 $0.00 1 $92,500 $397,164 -$60,335.90 2 $92,500 $315,479 -$95,271.36 3 $92,500 $250,594 -$108,731.42 4 $92,500 $199,054 -$103,703.95 5 $92,500 $158,114 -$82,419.40 6 $92,500 $125,594 -$46,492.29 7 $92,500 $99,763 $2,967.85 8 $92,500 $79,245 $65,269.88 9 $92,500 $62,946 $140,074.01 10 $142,500 $50,000 $227,340.55 FW = $227,340.55 =FV(B1,A13,,-NPV(B1,B4:B13)-B3) n= FW =

3.20992665 -$109,440.80

EOY 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Deposit $5,000.00 $8,000.00 $11,000.00 $14,000.00 $17,000.00 $20,000.00 $23,000.00 $26,000.00 $29,000.00 $32,000.00 $35,000.00 $38,000.00 $41,000.00 $44,000.00 $47,000.00 $50,000.00 $53,000.00 $56,000.00 Gradient =

Balance EOY $5,000.00 41 $13,325.00 42 $25,191.13 43 $40,828.55 44 $60,482.40 45 $84,413.76 46 $112,900.65 47 $146,239.20 48 $184,744.74 49 $228,753.15 50 $278,622.11 51 $334,732.55 52 $397,490.16 53 $467,327.02 54 $544,703.28 55 $630,108.99 56 $724,066.07 57 $827,130.37 58 $3,000.00

Deposit $59,000.00 $62,000.00 $65,000.00 $68,000.00 $71,000.00 $74,000.00 $77,000.00 $80,000.00 $83,000.00 $86,000.00 $89,000.00 $92,000.00 $95,000.00 $98,000.00 $101,000.00 $104,000.00 $107,000.00 $110,000.00

Balance $939,893.84 $1,062,986.94 $1,197,081.09 $1,342,891.37 $1,501,179.30 $1,672,755.96 $1,858,485.10 $2,059,286.63 $2,276,140.26 $2,510,089.38 $2,762,245.19 $3,033,791.12 $3,325,987.55 $3,640,176.74 $3,977,788.22 $4,340,344.46 $4,729,466.85 $5,146,882.19 =E18+$C$20

=E19+1.065*F18

EOY 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Deposit $5,000.00 $7,901.67 $10,803.34 $13,705.02 $16,606.69 $19,508.36 $22,410.03 $25,311.70 $28,213.38 $31,115.05 $34,016.72 $36,918.39 $39,820.06 $42,721.74 $45,623.41 $48,525.08 $51,426.75 $54,328.43 Gradient =

Balance EOY $5,000.00 41 $13,226.67 42 $24,889.75 43 $40,212.60 44 $59,433.11 45 $82,804.62 46 $110,596.95 47 $143,097.46 48 $180,612.17 49 $223,467.01 50 $272,009.09 51 $326,608.07 52 $387,657.66 53 $455,577.14 54 $530,813.07 55 $613,841.00 56 $705,167.41 57 $805,331.72 58 $2,901.67

Deposit $57,230.10 $60,131.77 $63,033.44 $65,935.11 $68,836.79 $71,738.46 $74,640.13 $77,541.80 $80,443.47 $83,345.15 $86,246.82 $89,148.49 $92,050.16 $94,951.83 $97,853.51 $100,755.18 $103,656.85 $106,558.52

Balance $914,908.38 $1,034,509.19 $1,164,785.73 $1,306,431.92 $1,460,186.78 $1,626,837.37 $1,807,221.93 $2,002,233.16 $2,212,821.79 $2,440,000.35 $2,684,847.19 $2,948,510.75 $3,232,214.11 $3,537,259.86 $3,865,035.26 $4,217,017.73 $4,594,780.73 $5,000,000.00 =E18+$C$20

=E19+1.065*F18

=FV(A14,36,-5000)+2901.67206*(((1+A14)^36-(1+36*A14))/A14^2)

Size of the Investment Portfolio $10,000,000 $9,000,000 $8,000,000 $7,000,000 $6,000,000 $5,000,000 $4,000,000

Annual Return on Investments

10.0%

9.5%

9.0%

8.5%

8.0%

7.5%

7.0%

6.5%

6.0%

5.5%

5.0%

$3,000,000

4.5%

Size of the Investment Portfolio $3,405,608.20 $3,665,472.67 $3,951,689.33 $4,267,232.69 $4,615,429.27 $5,000,000.00 $5,425,107.75 $5,895,410.65 $6,416,121.75 $6,993,075.95 $7,632,804.90 $8,342,620.92 $9,130,711.02

4.0%

Annual Return on Investments 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0%

Annual Return on Investment 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0%

3% $602,827.11 $659,700.04 $723,384.45 $794,761.41 $874,828.95 $964,717.59 $1,065,707.98 $1,179,250.82 $1,306,989.35 $1,450,784.88 $1,612,745.56 $1,795,258.93 $2,001,028.73

Rate of Increase in Annual Investments 4% 5% 6% 7% $710,296.02 $843,941.79 $1,010,829.86 $1,220,001.61 $773,445.91 $914,437.67 $1,089,957.85 $1,309,312.75 $843,941.79 $992,882.77 $1,177,717.93 $1,408,031.51 $922,717.61 $1,080,269.25 $1,275,166.62 $1,517,285.60 $1,010,829.86 $1,177,717.93 $1,383,495.62 $1,638,345.09 $1,109,473.78 $1,286,495.10 $1,504,049.43 $1,772,640.76 $1,220,001.61 $1,408,031.51 $1,638,345.09 $1,921,784.67 $1,343,943.31 $1,543,943.91 $1,788,094.57 $2,087,593.51 $1,483,029.91 $1,696,059.28 $1,955,229.96 $2,272,114.82 $1,639,219.94 $1,866,442.27 $2,141,932.00 $2,477,656.61 $1,814,729.25 $2,057,426.11 $2,350,662.17 $2,706,820.71 $2,012,064.72 $2,271,647.59 $2,584,198.93 $2,962,540.46 $2,234,062.33 $2,512,086.44 $2,845,678.57 $3,248,123.06

8% $1,483,029.91 $1,584,399.05 $1,696,059.28 $1,819,217.29 $1,955,229.96 $2,105,623.47 $2,272,114.82 $2,456,636.14 $2,661,361.97 $2,888,740.18 $3,141,526.60 $3,422,824.21 $3,736,127.17

Size of the Investment Portfolio

=5000*((1+$A15)^36-(1+B$2)^36)/($A15-B$2)

$4,000,000 $3,500,000 $3,000,000 $2,500,000 $2,000,000 $1,500,000 $1,000,000

Annual Return on Investment

10.0%

9.5%

9.0%

8.5%

8.0%

7.5%

7.0%

6.5%

6.0%

5.5%

5.0%

4.5%

4.0%

$500,000

EOY 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Deposit Balance EOY Deposit $5,000.00 $5,000.00 41 $49,875.00 $7,500.00 $12,900.00 42 $52,368.75 $10,000.00 $23,932.00 43 $54,987.19 $12,500.00 $38,346.56 44 $57,736.55 $15,000.00 $56,414.28 45 $60,623.37 $17,500.00 $78,427.43 46 $63,654.54 $20,000.00 $104,701.62 47 $66,837.27 $22,500.00 $135,577.75 48 $70,179.13 $25,000.00 $171,423.97 49 $73,688.09 $27,500.00 $212,637.89 50 $77,372.49 $30,000.00 $259,648.92 51 $81,241.12 $32,500.00 $312,920.83 52 $85,303.18 $35,000.00 $372,954.50 53 $89,568.33 $37,500.00 $440,290.86 54 $94,046.75 $40,000.00 $515,514.13 55 $98,749.09 $42,500.00 $599,255.26 56 $103,686.54 $45,000.00 $692,195.68 57 $108,870.87 $47,500.00 $795,071.34 58 $114,314.41 Gradient = $2,500.00 Geometric = 5.0% ROI = 8.0% =B19+(1+$C$22)*C18

Balance $908,552.04 $1,033,604.96 $1,171,280.54 $1,322,719.53 $1,489,160.47 $1,671,947.85 $1,872,540.94 $2,092,523.35 $2,333,613.31 $2,597,674.87 $2,886,729.98 $3,202,971.56 $3,548,777.61 $3,926,726.57 $4,339,613.79 $4,790,469.43 $5,282,577.86 $5,819,498.50

=E18*(1+$C$21) 1+$C$22)*C18

=E2*(1+$C$21)

=E16+(1+$C$22)*F15

Annual Return on Investment 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0%

3% $2,809,930.78 $3,033,555.95 $3,280,374.71 $3,553,040.23 $3,854,522.48 $4,188,146.69 $4,557,636.45 $4,967,162.09 $5,421,394.89 $5,925,567.82 $6,485,543.71 $7,107,891.57 $7,799,972.13

Rate of Increase in Annual Investments 4% 5% 6% 7% $2,959,850.36 $3,127,030.79 $3,313,582.98 $3,521,875.02 $3,187,706.58 $3,359,454.70 $3,550,941.57 $3,764,568.52 $3,438,924.71 $3,615,418.73 $3,812,029.08 $4,031,191.05 $3,716,165.42 $3,897,591.39 $4,099,522.22 $4,324,427.91 $4,022,406.54 $4,208,958.72 $4,416,415.60 $4,647,282.67 $4,360,981.51 $4,552,862.75 $4,766,060.22 $5,003,115.70 $4,735,622.51 $4,933,044.62 $5,152,206.59 $5,395,687.32 $5,150,508.86 $5,353,693.05 $5,579,053.23 $5,829,206.24 $5,610,321.25 $5,819,498.50 $6,051,300.83 $6,308,383.87 $6,120,302.47 $6,335,714.06 $6,574,213.18 $6,838,495.16 $6,686,325.65 $6,908,223.56 $7,153,685.29 $7,425,446.76 $7,314,970.55 $7,543,617.97 $7,796,319.81 $8,075,853.54 $8,013,609.17 $8,249,281.01 $8,509,512.68 $8,797,124.16

8% $3,754,562.56 $4,003,027.53 $4,275,633.74 $4,575,075.48 $4,904,365.72 $5,266,874.60 $5,666,372.68 $6,107,079.37 $6,593,717.23 $7,131,572.86 $7,726,565.11 $8,385,321.53 $9,115,264.07

=(5000+2500*((1+$A15)^18-(1+18*$A15))/($A15*((1+$A15)^18-1)))*(((1+$A15)^18-1)/$A15)*(1+$A15)^18 +47500*(1+B$2)*((1+$A15)^18-(1+B$2)^18)/($A15-B$2)

Size of the Investment Portfolio for Various Geometric Rates of Increase in Annual Investments after Age 40 3%

7.0%

7.5%

$10,000,000

$9,000,000

Fuure Worth

$8,000,000

$7,000,000

$6,000,000

$5,000,000

$4,000,000

$3,000,000

$2,000,000 4.0%

4.5%

5.0%

5.5%

6.0%

6.5%

8.0%

Annual Return on Investment

8.5%

9.0%

9.5%

10.0%

Planning Horizon 8.2725408 9.6137761

Geometric Series Rate (A) = -85.800% CF(A) SV(A) FW(A) -$300,000.00 $300,000.00 $0.00 $55,000.00 $42,599.95 -$232,400.05 $55,000.00 $6,049.19 -$241,450.81 $55,000.00 $858.98 -$216,391.02 $55,000.00 $121.98 -$183,853.02 $55,000.00 $17.32 -$147,355.18 $55,000.00 $2.46 -$107,107.29 $55,000.00 $0.35 -$62,820.38 $55,000.00 $0.05 -$14,102.75 $55,000.00 $0.01 $39,486.93 $55,000.00 $0.00 $98,435.62

Geometric Series Rate (B) = -86.364% CF(B) SV(B) FW(B) -$450,000.00 $450,000.00 $0.00 $80,000.00 $61,360.84 -$353,639.16 $80,000.00 $8,367.00 -$368,133.00 $80,000.00 $1,140.90 -$333,009.10 $80,000.00 $155.57 -$287,409.43 $80,000.00 $21.21 -$236,300.29 $80,000.00 $2.89 -$179,950.76 $80,000.00 $0.39 -$117,948.62 $80,000.00 $0.05 -$49,743.86 $80,000.00 $0.01 $25,281.70 $80,000.00 $0.00 $107,809.86

FW(B-A) $0.00 -$121,239.12 -$126,682.18 -$116,618.08 -$103,556.40 -$88,945.11 -$72,843.47 -$55,128.24 -$35,641.11 -$14,205.23 $9,374.25

$200,000

FW(A)

FW(B-A) $100,000

$0.00 $75,000.00

-$35,641.11 $0.00

Future Worth

Planning Horizon 0 1 2 3 4 5 6 7 8 9 10

-$100,000

-$200,000

-$300,000

-$400,000 Length of the Planning Horizon (Yrs)

Alternative A

Alternative B

=FV(A27,10,-55000,300000)

=FV(A3,10,-80000,450000)

Future Worth as a Function of MARR Alternative A

Alternative B

$500,000

-$500,000 -$1,000,000

-$1,500,000 -$2,000,000

MARR

24%

22%

20%

18%

16%

14%

12%

10%

FW(B) $350,000.00 $339,897.05 $327,430.19 $312,347.97 $294,378.64 $273,228.82 $248,582.13 $220,097.73 $187,408.75 $150,120.72 $107,809.86 $60,021.27 $6,267.11 -$53,975.39 -$121,265.98 -$196,203.52 -$279,428.25 -$371,624.12 -$473,521.31 -$585,898.74 -$709,586.82 -$845,470.23 -$994,490.89 -$1,157,651.01 -$1,336,016.31 -$1,530,719.35

FW(A) $250,000.00 $244,035.05 $236,536.33 $227,338.45 $216,262.61 $203,115.70 $187,689.41 $169,759.23 $149,083.44 $125,402.03 $98,435.62 $67,884.20 $33,425.97 -$5,284.01 -$48,615.16 -$96,962.82 -$150,749.72 -$210,427.57 -$276,478.69 -$349,417.72 -$429,793.41 -$518,190.47 -$615,231.57 -$721,579.33 -$837,938.47 -$965,058.06

MARR 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25%

Planning Horizon 0 1 2 3 4 5 6 7 8 9 10

CF(B-A) -$150,000.00 $25,000.00 $25,000.00 $25,000.00 $25,000.00 $25,000.00 $25,000.00 $25,000.00 $25,000.00 $25,000.00 $25,000.00

Future Worth of Incremental Cash Flow $10,000 -$10,000 1

-$30,000 -$50,000 -$70,000 -$90,000 -$110,000

-$130,000

Length of Planning Horizon (Yrs)

SV(B-A) $150,000.00 $18,760.88 $2,317.82 $281.92 $33.60 $3.89 $0.43 $0.05 $0.00 $0.00 $0.00

FW(B-A) $0.00 -$121,239.12 -$126,682.18 -$116,618.08 -$103,556.40 -$88,945.11 -$72,843.47 -$55,128.24 -$35,641.11 -$14,205.23 $9,374.25

EOY

CF(A)

CF(B)

CF(B-A)

-$300,000.00

-$450,000.00

-$150,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$55,000.00

$80,000.00

$25,000.00

$100,000 $50,000

-$100,000 -$150,000 -$200,000 -$250,000 -$300,000 MARR

20%

18%

16%

14%

12%

10%

-$50,000

MARR 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

FW(B-A) $100,000.00 $95,861.99 $90,893.86 $85,009.53 $78,116.04 $70,113.12 $60,892.72 $50,338.50 $38,325.31 $24,718.69 $9,374.25 -$7,862.92 -$27,158.85 -$48,691.38 -$72,650.82 -$99,240.70 -$128,678.53 -$161,196.55 -$197,042.62 -$236,481.02 -$279,793.41

EOY 0 1 2 3 4 5 6 FW =

CF(1) -$10,000 $5,000 $5,000 $10,000

CF(2) CF(3) -$14,500 -$20,000 $5,000 $0 $5,000 $3,000 $5,000 $6,000 $5,000 $9,000 $5,000 $12,000 $5,000 $15,000 $10,990.36 $11,955.52 $13,403.27

MARR 10% 11% 12% 13% 14% 15% 16% 17% 18%

Investment 1

$11,800 $11,600 $11,400 $11,200 $11,000 $10,800 $10,600 $10,400 $10,200 $10,000 $9,800 10%

11%

12%

13%

FW (1)

FW (2)

FW (3)

$10,967.44 $10,987.81 $10,990.36 $10,974.00 $10,937.59 $10,879.96 $10,799.90 $10,696.16 $10,567.46

$12,890.42 $12,443.29 $11,955.52 $11,425.23 $10,850.49 $10,229.31 $9,559.64 $8,839.36 $8,066.30

$16,037.08 $14,760.61 $13,403.27 $11,961.87 $10,433.09 $8,813.55 $7,099.77 $5,288.16 $3,375.04

Investment 2

14% MARR

15%

Investment 3

16%

17%

18%

EOY 0 1 2 3 4 5 6 FW =

CF(1) -$10,000 $5,000 $5,000 $10,000

CF(2) -$14,500 $5,000 $5,000 $5,000 $5,000 $5,000 $5,000 $10,990.36 $11,955.52

CF(3) -$20,000 $0 $3,000 $6,000 $9,000 $12,000 $15,000 $13,403.27

EOY 0 1 2 3 4 5 6 FW =

CF(1') CF(2) CF(3) -$10,000 -$15,000 -$20,000 $5,000 $5,000 $0 $5,000 $5,000 $3,000 $0 $5,000 $6,000 $5,000 $5,000 $9,000 $5,000 $5,000 $12,000 $10,000 $7,500 $15,000 $18,813.08 $13,468.60 $13,403.27

MARR =

10%

Planning SVgeometric AW geometric SVgradient CF Horizon 0 -$500,000 $500,000 n/a $500,000 1 $92,500 $397,000 -$60,500.00 $455,000 2 $92,500 $315,218 -$45,491.43 $410,000 3 $92,500 $250,283 -$32,943.17 $365,000 4 $92,500 $198,725 -$22,416.01 $320,000 5 $92,500 $157,787 -$13,553.55 $275,000 6 $92,500 $125,283 -$6,066.06 $230,000 7 $92,500 $99,475 $282.45 $185,000 8 $92,500 $78,983 $5,684.59 $140,000 9 $92,500 $62,713 $10,297.92 $95,000 10 $137,500 $49,794 $14,251.63 $50,000 AW = $14,264.57 =PMT(B1,10,500000,-50000)+92500

AW gradient

Excel Formula for AW gradient

n/a -$2,500.00 =PMT($B$1,A4,-$B$3,-E4)+B4 -$357.14 =PMT($B$1,A5,-$B$3,-E5)+B5 $1,714.50 =PMT($B$1,A6,-$B$3,-E6)+B6 $3,715.26 =PMT($B$1,A7,-$B$3,-E7)+B7 $5,645.57 =PMT($B$1,A8,-$B$3,-E8)+B8 $7,506.01 =PMT($B$1,A9,-$B$3,-E9)+B9 $9,297.27 =PMT($B$1,A10,-$B$3,-E10)+B10 $11,020.15 =PMT($B$1,A11,-$B$3,-E11)+B11 $12,675.58 =PMT($B$1,A12,-$B$3,-E12)+B12 $14,264.57 =PMT($B$1,A13,-$B$3,-E13)+B13-45000

geometric

gradient

$20,000

Annual Worth

$10,000 $0 1

-$10,000 -$20,000 -$30,000 -$40,000

-$50,000 -$60,000 -$70,000

Planning Horizon

MARR = 10% Planning SVgeometric AW geometric SVgradient AW gradient CF Horizon 0 -$500,000 $500,000 n/a $500,000 n/a 1 $92,500 $397,000 -$60,500.00 $455,000 -$2,500.00 2 $92,500 $315,218 -$45,491.43 $410,000 -$357.14 3 $92,500 $250,283 -$32,943.17 $365,000 $1,714.50 4 $92,500 $198,725 -$22,416.01 $320,000 $3,715.26 5 $92,500 $157,787 -$13,553.55 $275,000 $5,645.57 6 $92,500 $125,283 -$6,066.06 $230,000 $7,506.01 7 $92,500 $99,475 $282.45 $185,000 $9,297.27 8 $92,500 $78,983 $5,684.59 $140,000 $11,020.15 9 $92,500 $62,713 $10,297.92 $95,000 $12,675.58 10 $137,500 $49,794 $14,251.63 $50,000 $14,264.57 AW = $14,264.57 =PMT(B1,10,500000,-50000)+92500 geometric gradient n = 6.95187521 2.1699745 AW = $0.00 $0.00 =PMT($B$1,C17,500000,-500000+45000*C17)+92500 =PMT($B$1,B17,500000,-500000*(1-0.206)^B17)+92500

MARR

20%

18%

16%

14%

12%

10%

Annual Worth

AW $47,500.00 =PMT(A2,10,500000,-50000)+92500 $44,488.07 =PMT(A3,10,500000,-50000)+92500 $41,403.06 =PMT(A4,10,500000,-50000)+92500 $38,246.27 =PMT(A5,10,500000,-50000)+92500 $35,019.08 =PMT(A6,10,500000,-50000)+92500 $31,722.94 =PMT(A7,10,500000,-50000)+92500 $28,359.42 =PMT(A8,10,500000,-50000)+92500 $24,930.12 =PMT(A9,10,500000,-50000)+92500 $21,436.73 =PMT(A10,10,500000,-50000)+92500 $17,880.96 =PMT(A11,10,500000,-50000)+92500 $14,264.57 =PMT(A12,10,500000,-50000)+92500 $10,589.36 =PMT(A13,10,500000,-50000)+92500 $6,857.13 =PMT(A14,10,500000,-50000)+92500 $60,000.00 $3,069.70 =PMT(A15,10,500000,-50000)+92500 -$771.09 =PMT(A16,10,500000,-50000)+92500 $40,000.00 -$4,663.43 =PMT(A17,10,500000,-50000)+92500 -$8,605.49 =PMT(A18,10,500000,-50000)+92500 $20,000.00 -$12,595.47 =PMT(A19,10,500000,-50000)+92500 $0.00 -$16,631.59 =PMT(A20,10,500000,-50000)+92500 -$20,712.09 =PMT(A21,10,500000,-50000)+92500 -$20,000.00 -$24,835.24 =PMT(A22,10,500000,-50000)+92500 -$40,000.00 MARR = 13.800% AW = $0.00

MARR 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

Planning Horizon 0 1 2 3 4 5 6 7 8 9 10

Geometric Series Rate (A) = -85.800% CF(A) SV(A) AW(A) -$300,000.00 $300,000.00 n/a $55,000.00 $42,599.95 -$232,400.05 $55,000.00 $6,049.19 -$114,976.58 $55,000.00 $858.98 -$65,374.93 $55,000.00 $121.98 -$39,614.96 $55,000.00 $17.32 -$24,136.41 $55,000.00 $2.46 -$13,881.90 $55,000.00 $0.35 -$6,621.61 $55,000.00 $0.05 -$1,233.20 $55,000.00 $0.01 $2,907.84 $55,000.00 $0.00 $6,176.38

Geometric Series Rate (B) = -86.364% CF(B) SV(B) AW(B) -$450,000.00 $450,000.00 n/a $80,000.00 $61,360.84 -$353,639.16 $80,000.00 $8,367.00 -$175,301.43 $80,000.00 $1,140.90 -$100,606.98 $80,000.00 $155.57 -$61,928.34 $80,000.00 $21.21 -$38,705.39 $80,000.00 $2.89 -$23,322.95 $80,000.00 $0.39 -$12,432.43 $80,000.00 $0.05 -$4,349.80 $80,000.00 $0.01 $1,861.76 $80,000.00 $0.00 $6,764.57 Annual Worths

DPBP A = 8.273

DPBP B = 8.674

AW A = $0.00

AW B = $0.00

Design A

$50,000.00 $0.00 -$50,000.00 1 -$100,000.00 -$150,000.00 -$200,000.00 -$250,000.00 -$300,000.00 -$350,000.00 -$400,000.00

Design B

Length of the Planning Horizon

CF(B) -$450,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 AW(A)

AW(B)

12%

CF(A) -$300,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00

EOY 0 1 2 3 4 5 6 7 8 9 10

$40,000 $30,000 $20,000 $10,000

-$20,000 -$30,000 MARR

20%

18%

16%

14%

10%

-$10,000

MARR 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

AW(A) $25,000.00 $23,325.38 $21,602.04 $19,830.85 $18,012.72 $16,148.63 $14,239.61 $12,286.75 $10,291.15 $8,253.97 $6,176.38 $4,059.57 $1,904.75 -$286.87 -$2,514.06 -$4,775.62 -$7,070.32 -$9,396.98 -$11,754.39 -$14,141.39 -$16,556.83

AW(B) $35,000.00 $32,488.07 $29,903.06 $27,246.27 $24,519.08 $21,722.94 $18,859.42 $15,930.12 $12,936.73 $9,880.96 $6,764.57 $3,589.36 $357.13 -$2,930.30 -$6,271.09 -$9,663.43 -$13,105.49 -$16,595.47 -$20,131.59 -$23,712.09 -$27,335.24

MARR = Capital Investment = Planning SVgeometric Horizon 0 $500,000 1 $397,164 2 $315,479 3 $250,594 4 $199,054 5 $158,114 6 $125,594 7 $99,763 8 $79,245 9 $62,946 10 $50,000 11 $39,716 12 $31,548 13 $25,059 14 $19,905 15 $15,811 16 $12,559 17 $9,976 18 $7,924 19 $6,295 20 $5,000 21 $3,972 22 $3,155 23 $2,506 24 $1,991 25 $1,581 26 $1,256 27 $998 28 $792 29 $629 30 $500

10% $500,000 CR geometric n/a $152,835.88 $137,867.30 $125,349.36 $114,845.17 $106,000.08 $98,525.74 $92,187.17 $86,792.54 $82,184.87 $78,235.43 $74,838.35 $71,906.37 $69,367.38 $67,161.57 $65,239.24 $63,558.95 $62,086.01 $60,791.33 $59,650.39 $58,642.51 $57,750.14 $56,958.35 $56,254.40 $55,627.40 $55,067.96 $54,568.02 $54,120.58 $53,719.60 $53,359.80 $53,036.58

SVnegligible $500,000 $455,000 $410,000 $365,000 $320,000 $275,000 $230,000 $185,000 $140,000 $95,000 $50,000 $5,000 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0

CR negligible n/a $550,000.00 $288,095.24 $201,057.40 $157,735.40 $131,898.74 $114,803.69 $102,702.75 $93,722.01 $86,820.27 $81,372.70 $76,981.57 $73,381.66 $70,389.26 $67,873.11 $65,736.89 $63,908.31 $62,332.07 $60,965.11 $59,773.43 $58,729.81 $57,812.19 $57,002.53 $56,285.91 $55,649.89 $55,084.04 $54,579.52 $54,128.82 $53,725.51 $53,364.04 $53,039.62

Geometrically Decreasing Sa

$180,000 $160,000

CR(geometrically decreasing SV)

$140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $0 1 2 3 4 5

Geometrically Decreasing Salvage Value

Decreasing Gradient Salvage Value

$600,000

$400,000

$300,000

$200,000

$100,000

$0 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Age (Yrs)

CR (decreasing gradient SV)

$500,000

At Bt Ita Et t 0 -$10,000 -$10,000 1 $2,525 -$10,000 -$2,000 -$9,475 2 $2,525 $9,475 $1,895 -$8,845 3 $2,525 $8,845 $1,769 -$8,089 4 $3,840 $8,089 $1,618 -$5,867 5 $3,840 $5,867 $1,173 -$3,200 6 $3,840 $3,200 $640 $0 a Based on i = 0.20. $3,007.06

EOY CF 0 -$1,000 1 $4,100 2 -$5,580 3 $2,520

Investment Initial Investment Annual Return Salvage Value Internal Rate of Return

1 $15,000.00 $3,750.00 $15,000.00 25.00%

2 $25,000.00 $5,000.00 $25,000.00 20.00%

3 $40,000.00 $9,250.00 $40,000.00 23.13%

4 $50,000.00 $11,250.00 $50,000.00 22.50%

5 $70,000.00 $14,250.00 $70,000.00 20.36%

Investment Initial Investment Annual Return Salvage Value Present Worth Internal Rate of Return

1 $15,000.00 $3,750.00 $15,000.00 $4,718.79 25.00%

2 $25,000.00 $5,000.00 $25,000.00 $2,247.04 20.00%

3 $40,000.00 $9,250.00 $40,000.00 $9,212.88 23.13%

4 $50,000.00 $11,250.00 $50,000.00 $10,111.69 22.50%

5 $70,000.00 $14,250.00 $70,000.00 $7,415.24 20.36%

Investment Δ Investment Δ Annual Return Δ Salvage Value Δ IRR > MARR ? Defender

1 $15,000.00 $3,750.00 $15,000.00 25.00% Yes 1

2-1 $10,000.00 $1,250.00 $10,000.00 12.50% No 1

3-1 $25,000.00 $5,500.00 $25,000.00 22.00% Yes 3

4-3 $10,000.00 $2,000.00 $10,000.00 20.00% Yes 4

5-4 $20,000.00 $3,000.00 $20,000.00 15.00% No 4

Incremental IRR Analysis $75,000.00 $50,000.00 $25,000.00

MARR CF(2-1)

$16,760.78 $17,647.70 $15,702.99

CF(3-2)

25%

20%

-$25,000.00

15%

$0.00

10%

CF(3-2) $18,439,609.05 $8,678,504.49 $4,520,312.50 $2,541,136.60 $1,515,000.00 $945,573.30 $611,625.51 $406,593.92 $275,761.59 $189,485.60 $130,957.03 $90,262.17 $61,350.32 $40,415.72 $25,000.00 $13,476.96 $4,747.72 -$1,944.70 -$7,130.92 -$11,188.80 -$14,391.40 -$16,938.63 -$18,978.70 -$20,622.68 -$21,954.73 -$23,039.21 -$23,925.78 -$24,653.11 -$25,251.50 -$25,744.93 -$26,152.43 -$26,489.27 -$26,767.74 -$26,997.78 -$27,187.50

CF(3-2) -$25,000 -$10,000 $0 $5,000 $15,000 $40,000 13.41%

CF(2-1) -$19,522,736.63 -$8,248,650.86 -$3,797,656.25 -$1,851,735.42 -$935,000.00 -$478,861.82 -$243,004.12 -$118,109.48 -$51,414.59 -$16,193.42 $1,635.74 $9,733.85 $12,376.59 $11,997.35 $10,000.00 $7,200.26 $4,071.85 $886.92 -$2,202.29 -$5,115.20 -$7,813.98 -$10,286.05 -$12,533.47 -$14,566.40 -$16,399.18 -$18,047.89 -$19,528.96 -$20,858.35 -$22,051.08 -$23,121.02 -$24,080.85 -$24,942.01 -$25,714.81 -$26,408.48 -$27,031.25

CF(2-1) -$25,000 -$45,000 $55,000 $50,000 $40,000 -$65,000 16.41%

MARR -70% -65% -60% -55% -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%

CF(3) -$150,000 -$35,000 $75,000 $75,000 $75,000 $95,000 18.01%

-5%

CF(2) -$125,000 -$25,000 $75,000 $70,000 $60,000 $55,000 19.39%

-10%

CF(1) -$100,000 $20,000 $20,000 $20,000 $20,000 $120,000 20.00%

Present Worth

EOY 0 1 2 3 4 5 IRR =

MARR 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28%

ERR MARR 0.4654% 30% 2.3768% 32% 4.2999% 34% 6.2338% 36% 8.1775% 38% 10.1302% 40% 12.0911% 42% 14.0592% 44% 16.0339% 46% 18.0144% 48% 20.0000% 50% 21.9900% 52% 23.9837% 54% 25.9805% 56% 27.9799% 58%

ERR 29.9812% 31.9840% 33.9877% 35.9919% 37.9962% 40.0000% 42.0030% 44.0049% 46.0052% 48.0037% 50.0000% 51.9939% 53.9850% 55.9732% 57.9581%

Investment Initial Investment Annual Return Salvage Value External Rate of Return

1 $15,000.00 $3,750.00 $15,000.00 21.27%

2 $25,000.00 $5,000.00 $25,000.00 19.02%

3 $40,000.00 $9,250.00 $40,000.00 20.47%

4 $50,000.00 $11,250.00 $50,000.00 20.19%

5 $70,000.00 $14,250.00 $70,000.00 19.19%

Investment Δ Investment Δ Annual Return Δ Salvage Value Δ ERR > MARR ? Defender

1 $15,000.00 $3,750.00 $15,000.00 21.27% Yes 1

2-1 $10,000.00 $1,250.00 $10,000.00 14.70% No 1

3-1 $25,000.00 $5,500.00 $25,000.00 19.97% Yes 3

4-3 $10,000.00 $2,000.00 $10,000.00 19.02% Yes 4

5-4 $20,000.00 $3,000.00 $20,000.00 16.30% No 4

EOY 0 1 2 3 4 5 6 7 8 9 10 MIRR A =

CF(A) -$7,585,000.00 -$1,237,500.00 $1,695,500.00 $2,002,800.00 $2,345,700.00 $2,450,500.00 $2,575,600.00 $2,735,000.00 $3,005,300.00 $3,857,500.00 $5,285,000.00 18.9046%

CF(B) -$10,285,000.00 -$1,575,500.00 $2,455,700.00 $2,657,500.00 $2,877,500.00 $3,025,000.00 $3,250,300.00 $3,565,800.00 $3,750,000.00 $4,252,500.00 $8,750,000.00 MIRR B-A =

CF(B-A) -$2,700,000.00 -$338,000.00 $760,200.00 $654,700.00 $531,800.00 $574,500.00 $674,700.00 $830,800.00 $744,700.00 $395,000.00 $3,465,000.00 17.9244%

Present Worth $500,000 $400,000 $300,000 $200,000 $100,000

24%

22%

20%

18%

16%

14%

12%

10%

-$100,000

-$200,000

MARR

16%

18%

20%

22%

24%

16%

18%

20%

22%

24%

14%

12%

10%

$500,000 $250,000 $0 -$250,000 -$500,000 -$750,000 -$1,000,000 -$1,250,000 -$1,500,000 -$1,750,000

Future Worth

AW $47,500.00 $44,488.07 $41,403.06 $38,246.27 $35,019.08 $31,722.94 $28,359.42 $24,930.12 $21,436.73 $17,880.96 $14,264.57 $10,589.36 $6,857.13 $3,069.70 -$771.09 -$4,663.43 -$8,605.49 -$12,595.47 -$16,631.59 -$20,712.09 -$24,835.24 -$28,999.35 -$33,202.74 -$37,443.81 -$41,720.96 -$46,032.65

PW FW $475,000.00 $475,000.00 $421,360.02 $465,443.60 $371,906.53 $453,351.98 $326,248.46 $438,450.65 $284,036.07 $420,442.77 $244,956.14 $399,007.75 $208,727.79 $373,799.68 $175,098.76 $344,445.76 $143,842.20 $310,544.53 $114,753.88 $271,664.16 $87,649.62 $227,340.55 $62,363.18 $177,075.34 $38,744.29 $120,333.89 $16,656.94 $56,543.10 -$4,022.11 -$14,910.86 -$23,404.67 -$94,684.93 -$41,592.28 -$183,481.63 -$58,677.30 -$282,051.69 -$74,743.79 -$391,196.73 -$89,868.41 -$511,772.16 -$104,121.05 -$644,690.12 -$117,565.61 -$790,922.62 -$130,260.48 -$951,504.77 -$142,259.13 -$1,127,538.21 -$153,610.57 -$1,320,194.59 -$164,359.74 -$1,530,719.35

MARR

14%

12%

10%

$50,000 $40,000 $30,000 $20,000 $10,000 $0 -$10,000 -$20,000 -$30,000 -$40,000 -$50,000

Annual Worth

-500000 92500 92500 92500 92500 92500 92500 92500 92500 92500 142500 13.8003% $0.00 $0.00

13.8003% $27,451.43

MARR 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25%

MARR

$50

$40

Future Worth

$30

$20

$10

$0 10%

15%

20%

25%

30%

35%

-$10

-$20

MARR

40%

45%

50%

55%

CF -$4,000 $16,400 -$22,320 $10,080

Guess IRR FW 0% 20.0% $160.00 1% 20.0% $145.24 2% 20.0% $131.33 3% 20.0% $118.25 4% 20.0% $105.98 5% 20.0% $94.50 6% 20.0% $83.78 7% 20.0% $73.79 8% 20.0% $64.51 9% 20.0% $55.92 10% 20.0% $48.00 11% 20.0% $40.72 12% 20.0% $34.05 13% 20.0% $27.97 14% 20.0% $22.46 15% 20.0% $17.50 16% 20.0% $13.06 17% 20.0% $9.11 18% 20.0% $5.63 19% 20.0% $2.60 20% 20.0% $0.00 21% 20.0% -$2.20 22% 20.0% -$4.03 23% 20.0% -$5.51 24% 20.0% -$6.66 25% 20.0% -$7.50 26% 20.0% -$8.06 27% 20.0% -$8.37 28% 20.0% -$8.45 29% 50.0% -$8.32 30% 40.0% -$8.00 31% 40.0% -$7.52 32% 40.0% -$6.91 33% 40.0% -$6.19 34% 40.0% -$5.38 35% 40.0% -$4.50 36% 40.0% -$3.58 37% 40.0% -$2.65 38% 40.0% -$1.73 39% 40.0% -$0.84 40% 40.0% $0.00 41% 40.0% $0.76 42% 40.0% $1.41 43% 40.0% $1.93 44% 40.0% $2.30 45% 50.0% $2.50 46% 50.0% $2.50 47% 50.0% $2.27 48% 50.0% $1.79 49% 50.0% $1.04 50% 50.0% $0.00 51% 50.0% -$1.36 52% 50.0% -$3.07 53% 50.0% -$5.15 54% 50.0% -$7.62 55% 50.0% -$10.50 56% 50.0% -$13.82 57% 50.0% -$17.61 58% 50.0% -$21.89 59% 50.0% -$26.68 60% 50.0% -$32.00 61% 50.0% -$37.88 62% 50.0% -$44.35 63% 50.0% -$51.43 64% 50.0% -$59.14 65% 50.0% -$67.50 66% 50.0% -$76.54 67% 50.0% -$86.29 68% 50.0% -$96.77 69% 50.0% -$108.00 70% 50.0% -$120.00 71% 50.0% -$132.80 72% 50.0% -$146.43 73% 50.0% -$160.91 74% 50.0% -$176.26 75% 50.0% -$192.50 76% 50.0% -$209.66 77% 50.0% -$227.77 78% 50.0% -$246.85 79% 50.0% -$266.92 80% 50.0% -$288.00

Value Obtained from the Excel® IRR Worksheet Function 60% 50% 40%

IRR

EOY 0 1 2 3

30% 20%

10% 0% 0%

20%

40%

60%

Guess

80%

100%

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 IRR =

CF Cum CF i FW -$250,000 -$250,000 -50% $2.96 $45,000 -$205,000 -45% $3.73 $55,000 -$150,000 -40% $4.76 $65,000 -$85,000 -35% $6.16 $75,000 -$10,000 -30% $8.07 $85,000 $75,000 -25% $10.71 -$55,000 $20,000 -20% $14.33 $85,000 $105,000 -15% $19.21 $75,000 $180,000 -10% $25.63 $65,000 $245,000 -5% $33.59 $55,000 $300,000 0% $42.50 $45,000 $345,000 5% $50.32 $35,000 $380,000 10% $52.15 $25,000 $405,000 15% $37.74 $15,000 $420,000 20% -$12.83 $5,000 $425,000 19.12% i = 8.5469% $52.70

($0,000s) $60

$40 $20 $0 -50% -40% -$20

Future Worth

-40% -30% -20% -10% 0%

TVOM

10% 20%

EOY 0 1 2 3 4 5 6 7 8 9 10 IRR =

CF(A) -$7,585,000.00 -$1,237,500.00 $1,695,500.00 $2,002,800.00 $2,345,700.00 $2,450,500.00 $2,575,600.00 $2,735,000.00 $3,005,300.00 $3,857,500.00 $5,285,000.00 19.39%

CF(B) -$10,285,000.00 -$1,575,500.00 $2,455,700.00 $2,657,500.00 $2,877,500.00 $3,025,000.00 $3,250,300.00 $3,565,800.00 $3,750,000.00 $4,252,500.00 $8,750,000.00 18.93% IRR(D2:D12) =IRR(B2:B12)

CF(B-A) -$2,700,000.00 -$338,000.00 $760,200.00 $654,700.00 $531,800.00 $574,500.00 $674,700.00 $830,800.00 $744,700.00 $395,000.00 $3,465,000.00 17.61%

=C5-B5

EOY 0 1 2 3 4 5

CF(1) -$100,000 $20,000 $20,000 $20,000 $20,000 $120,000

-20%

Incremental IRR Comparison of Alter

-30%

CF(3-2) $1,843.96 $867.85 $452.03 $254.11 $151.50 $94.56 $61.16 $40.66 $27.58 $18.95 $13.10 $9.03 $6.14 $4.04 $2.50 $1.35 $0.47 -$0.19 -$0.71 -$1.12 -$1.44 -$1.69 -$1.90 -$2.06 -$2.20 -$2.30 -$2.39 -$2.47 -$2.53 -$2.57 -$2.62 -$2.65 -$2.68 -$2.70 -$2.72

CF(3-2) -$25,000 -$10,000 $0 $5,000 $15,000 $40,000 13.41%

-40%

CF(2-1) -$1,952.27 -$824.87 -$379.77 -$185.17 -$93.50 -$47.89 -$24.30 -$11.81 -$5.14 -$1.62 $0.16 $0.97 $1.24 $1.20 $1.00 $0.72 $0.41 $0.09 -$0.22 -$0.51 -$0.78 -$1.03 -$1.25 -$1.46 -$1.64 -$1.80 -$1.95 -$2.09 -$2.21 -$2.31 -$2.41 -$2.49 -$2.57 -$2.64 -$2.70

CF(2-1) -$25,000 -$45,000 $55,000 $50,000 $40,000 -$65,000 16.41%

-50%

MARR -70% -65% -60% -55% -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%

CF(3) -$150,000 -$35,000 $75,000 $75,000 $75,000 $95,000 18.01%

-60%

CF(2) -$125,000 -$25,000 $75,000 $70,000 $60,000 $55,000 19.39%

-70%

CF(1) -$100,000 $20,000 $20,000 $20,000 $20,000 $120,000 20.00%

PW (x $10,000)

EOY 0 1 2 3 4 5 IRR =

MARR CF(2-1)

CF(2) CF(3) -$125,000 -$150,000 -$25,000 -$35,000 $75,000 $75,000 $70,000 $75,000 $60,000 $75,000 $55,000 $95,000

Comparison of Alternatives $2,000 $1,500 $1,000 $500

-$1,000 -$1,500 -$2,000 MARR CF(3-2)

20%

-$500

10%

-10%

-20%

CF(3-2) -$25,000 -$10,000 $0 $5,000 $15,000 $40,000 13.41%

Incremental IRR Comparison of Alter $8 $7 $6 $5 $4 $3 $2 $1

$0 -$1

CF(2-1) -$25,000 -$45,000 $55,000 $50,000 $40,000 -$65,000 16.41%

MARR -70% -65% -60% -55% -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%

CF(3) -$150,000 -$35,000 $75,000 $75,000 $75,000 $95,000 18.01%

-5%

CF(2) -$125,000 -$25,000 $75,000 $70,000 $60,000 $55,000 19.39%

-10%

CF(1) -$100,000 $20,000 $20,000 $20,000 $20,000 $120,000 20.00%

PW (x $10,000)

EOY 0 1 2 3 4 5 IRR =

-$2 MARR CF(2-1)

MARR CF(2-1)

CF(3-2)

25%

20%

15%

10%

Comparison of Alternatives

EOY 0 1 2 3 4 5 6 7 8 9 10 ERR =

CF MARR -$500,000 0% $92,500 1% $92,500 2% $92,500 3% $92,500 4% $92,500 5% $92,500 6% $92,500 7% $92,500 8% $92,500 9% $142,500 10% 11.79118% 11% 12% =MIRR(B2:B12,,10%) 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25%

ERR 6.91% 7.37% 7.83% 8.31% 8.79% 9.27% 9.76% 10.26% 10.77% 11.28% 11.79% 12.31% 12.84% 13.37% 13.91% 14.45% 15.00% 15.55% 16.10% 16.67% 17.23% 17.80% 18.37% 18.95% 19.53% 20.12%

IRR 13.80% 13.80% 20% 13.80% 13.80% 13.80% 16% 13.80% 13.80% 12% 13.80% 13.80% 8% 13.80% 13.80% 13.80% 4% 13.80%0% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80% 13.80%

Relationship Among MARR

9% 12%

MARR

nship Among ERR, IRR, and MARR

MARR = ERR = IRR = 13.8%

12% 15% 18% 21% 24%

MARR

EOY

-$4,000

$16,400

-$22,320

3 ERR =

$10,080 12.0911%

EQ 8.2

$0.00

=FV(B6,3,,4000)+FV(12%,2,,-16400)+FV(B6,1,,22320)+10080

EOY CF CF(+) CF(-) CF 0 -$250,000 $0 $250,000 -$250,000 1 $45,000 $45,000 $0 $0 2 $55,000 $55,000 $0 $0 3 $65,000 $65,000 $0 $0 4 $75,000 $75,000 $0 $0 =IF(B8<0,-B8,0) 5 $85,000 $85,000 $0 $0 6 -$55,000 $0 $55,000 -$55,000 =-D8 7 $85,000 $85,000 $0 $0 8 $75,000 $75,000 $0 $0 9 $65,000 $65,000 $0 $0 =IF(B11<0,0,B11) 10 $55,000 $55,000 $0 $0 11 $45,000 $45,000 $0 $0 12 $35,000 $35,000 $0 $0 13 $25,000 $25,000 $0 $0 14 $15,000 $15,000 $0 $0 15 $5,000 $5,000 $0 $2,605,119 ERR = 16.2483% =IRR(E2:E17)

EOY 0 1 2 3 4 5 6 7 8 9 10

CF(A) -$7,585,000.00 -$1,237,500.00 $1,695,500.00 $2,002,800.00 $2,345,700.00 $2,450,500.00 $2,575,600.00 $2,735,000.00 $3,005,300.00 $3,857,500.00 $5,285,000.00 ERR A =

CF(A) CF(B) -$7,585,000.00 -$10,285,000.00 -$1,237,500.00 -$1,575,500.00 $0.00 $2,455,700.00 $0.00 $2,657,500.00 $0.00 $2,877,500.00 $0.00 $3,025,000.00 $0.00 $3,250,300.00 $0.00 $3,565,800.00 $0.00 $3,750,000.00 $0.00 $4,252,500.00 $49,090,929.92 $8,750,000.00 18.9938% =IRR(C2:C12) =FV(18.5%,9,,-NPV(18.5%,B4:B12))

CF(B-A) -$2,700,000.00 -$338,000.00 $760,200.00 $654,700.00 $531,800.00 $574,500.00 $674,700.00 $830,800.00 $744,700.00 $395,000.00 $3,465,000.00 ERR B-A =

CF(B-A) -$2,700,000.00 -$338,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $15,610,551.99 17.9848% =IRR(F2:F12)

EOY CF(1) CF(2) CF(2-1) 0 -$100,000 -$125,000 -$25,000 1 $20,000 -$25,000 -$45,000 2 $20,000 $75,000 $55,000 3 $20,000 $70,000 $50,000 4 $20,000 $60,000 $40,000 5 $120,000 $55,000 -$65,000 ERR 1 = 18.6198% ERR 2-1 =

CF (2-1) CF(3) -$25,000 -$150,000 -$45,000 -$35,000 $0 $75,000 $0 $75,000 $0 $75,000 $130,773 $95,000 15.3604%

CF(3-2) -$25,000 -$10,000 $0 $5,000 $15,000 $40,000 ERR 3-2 =

CF (3-2) -$25,000 -$10,000 $0 $0 $0 $63,863 13.5670%

=IRR(H2:H7)

=MIRR(B2:B7,,15%) =FV(15%,4,,-NPV(15%,D4:D6))+D7 =IRR(E2:E7)

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 MIRR = MIRR =

CF PW(-) FW(+) -$250,000 -$250,000 $0 $45,000 $0 $318,407 $55,000 $0 $338,403 $65,000 $0 $347,766 $75,000 $0 $348,929 $85,000 $0 $343,872 =IF(B8<0,PV(10%,A8,,-B8),0) -$55,000 -$31,046 $0 $85,000 $0 $260,017 =IF(B9>0,B9*(1.15^(15-A9)),0) $75,000 $0 $199,501 $65,000 $0 $150,349 $55,000 $0 $110,625 $45,000 $0 $78,705 $35,000 $0 $53,231 $25,000 $0 $33,063 $15,000 $0 $17,250 $5,000 $0 $5,000 -$281,046 $2,605,119 =SUM(D2:D17) 16.003% =RATE(15,,C18,D18) 16.003% =MIRR(B2:B17,10%,15%)

EOY CF PW(-) FW(+) 0 -$275,000 -$275,000 $0 1 $45,000 $0 $318,407 2 $55,000 $0 $338,403 3 $65,000 $0 $347,766 4 $75,000 $0 $348,929 5 $85,000 $0 $343,872 =IF(B8<0,PV(2%,A8,,-B8),0) 6 -$55,000 -$48,838 $0 7 $85,000 $0 $260,017 =IF(B9>0,B9*(1.15^(15-A9)),0 8 $75,000 $0 $199,501 9 $65,000 $0 $150,349 10 $55,000 $0 $110,625 11 $45,000 $0 $78,705 12 $35,000 $0 $53,231 13 $25,000 $0 $33,063 14 $15,000 $0 $17,250 15 $5,000 $0 $5,000 IRR = 16.756% -$323,838 $2,605,119 =SUM(D2:D17) MIRR = 14.912% =RATE(15,,C18,D18) MIRR = 14.912% =MIRR(B2:B17,2%,15%)

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Finance Rate -$275,000 0.00% $45,000 1.00% $55,000 2.00% $65,000 3.00% $75,000 4.00% $85,000 5.00% -$55,000 6.00% $85,000 7.00% $75,000 8.00% $65,000 9.00% $55,000 10.00% $45,000 11.00% $35,000 12.00% $25,000 13.00% $15,000 14.00% $5,000 15.00% 16.00% 17.00% 18.00% 19.00% 20.00% CF

MIRR 14.7680% 14.8423% 14.9123% 14.9783% 15.0405% 15.0992% 15.1545% 15.2066% 15.2558% 15.3022% 15.3460% 15.3874% 15.4264% 15.4633% 15.4981% 15.5310% 15.5621% 15.5915% 15.6193% 15.6456% 15.6705%

ERR

17.0%

IRR

16.2483% 16.7556% 16.2483% 16.7556% 16.5% 16.2483% 16.7556% 16.2483% 16.7556% 16.0% 16.7556% 16.2483% 16.2483% 16.7556% 15.5% 16.7556% 16.2483% 16.2483% 16.7556% 16.2483% 15.0% 16.7556% 16.2483% 16.7556% 16.2483% 14.5% 16.7556% 16.2483% 16.7556% 16.2483% 16.7556% 14.0% 16.2483% 16.7556% 16.2483% 16.7556% 13.5% 16.7556% 16.2483% 2% 16.2483% 0% 16.7556% 16.2483% 16.7556% 16.2483% 16.7556% 16.2483% 16.7556% 16.2483% 16.7556%

MIRR

ERR = 16.2488%

10%

12%

14%

16%

Finance Rate ERR = 16.2488%

IRR = 16.7556%

18%

20%

t 0 1 2 3 4 5 6 7 8 9 10

SF d t

SF B t

$28,235.43 $31,058.97 $34,164.87 $37,581.35 $41,339.49 $45,473.44 $50,020.78 $55,022.86 $60,525.15 $66,577.66

$500,000.00 $471,764.57 $440,705.60 $406,540.73 $368,959.38 $327,619.89 $282,146.45 $232,125.67 $177,102.81 $116,577.66 $50,000.00

SLN d t

SLN B t

$45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00

$500,000.00 $455,000.00 $410,000.00 $365,000.00 $320,000.00 $275,000.00 $230,000.00 $185,000.00 $140,000.00 $95,000.00 $50,000.00

DB d t

DB B t

$103,000.00 $81,782.00 $64,934.91 $51,558.32 $40,937.30 $32,504.22 $25,808.35 $20,491.83 $16,270.51 $12,918.79

$500,000.00 $397,000.00 $315,218.00 $250,283.09 $198,724.78 $157,787.47 $125,283.25 $99,474.90 $78,983.07 $62,712.56 $49,793.77

DDB d t

DDB B t

$100,000.00 $80,000.00 $64,000.00 $51,200.00 $40,960.00 $32,768.00 $26,214.40 $20,971.52 $16,777.22 $13,421.77

$500,000.00 $400,000.00 $320,000.00 $256,000.00 $204,800.00 $163,840.00 $131,072.00 $104,857.60 $83,886.08 $67,108.86 $53,687.09

VDB d t

VDB B t

$100,000.00 $80,000.00 $64,000.00 $51,200.00 $40,960.00 $32,768.00 $26,214.40 $20,971.52 $16,943.04 $16,943.04

$500,000.00 $400,000.00 $320,000.00 $256,000.00 $204,800.00 $163,840.00 $131,072.00 $104,857.60 $83,886.08 $66,943.04 $50,000.00

SF d t t 0 1 $31,372.70 2 $34,509.97 3 $37,960.96 4 $41,757.06 5 $45,932.77 6 $50,526.04 7 $55,578.65 8 $61,136.51 9 $67,250.16 10 $73,975.18

SF B t

SLN d t

$500,000.00 $468,627.30 $50,000.00 $434,117.34 $50,000.00 $396,156.37 $50,000.00 $354,399.31 $50,000.00 $308,466.54 $50,000.00 $257,940.50 $50,000.00 $202,361.85 $50,000.00 $141,225.34 $50,000.00 $73,975.18 $50,000.00 ($0.00) $50,000.00

SLN B t

DDB d t

$500,000.00 $450,000.00 $100,000.00 $400,000.00 $80,000.00 $350,000.00 $64,000.00 $300,000.00 $51,200.00 $250,000.00 $40,960.00 $200,000.00 $32,768.00 $150,000.00 $26,214.40 $100,000.00 $20,971.52 $50,000.00 $16,777.22 $0.00 $13,421.77

DDB B t

VDB d t

$500,000.00 $400,000.00 $100,000.00 $320,000.00 $80,000.00 $256,000.00 $64,000.00 $204,800.00 $51,200.00 $163,840.00 $40,960.00 $131,072.00 $32,768.00 $104,857.60 $32,768.00 $83,886.08 $32,768.00 $67,108.86 $32,768.00 $53,687.09 $32,768.00

VDB B t $500,000.00 $400,000.00 $320,000.00 $256,000.00 $204,800.00 $163,840.00 $131,072.00 $98,304.00 $65,536.00 $32,768.00 $0.00

EOY 0 1 2 3 4 5 6 PW = EOY 0 1 2 3 4 5 6

SLH d

200%DBH d

MACRS d

SLN d

DDB d

DDB/SLN d

$50,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $50,000.00 $361,847.83 B $500,000.00 $450,000.00 $350,000.00 $250,000.00 $150,000.00 $50,000.00 $0.00

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $34,560.00 $12,960.00 $363,382.91 B $500,000.00 $400,000.00 $240,000.00 $144,000.00 $86,400.00 $51,840.00 $38,880.00

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $386,630.21 B $500,000.00 $400,000.00 $240,000.00 $144,000.00 $86,400.00 $28,800.00 $0.00

$100,000.00 $100,000.00 $100,000.00 $100,000.00 $100,000.00 $0.00 $379,078.68 B $500,000.00 $400,000.00 $300,000.00 $200,000.00 $100,000.00 $0.00 $0.00

$200,000.00 $120,000.00 $72,000.00 $43,200.00 $25,920.00 $0.00 $380,686.86 B $500,000.00 $300,000.00 $180,000.00 $108,000.00 $64,800.00 $38,880.00 $38,880.00

$200,000.00 $120,000.00 $72,000.00 $54,000.00 $54,000.00 $0.00 $405,498.88 B $500,000.00 $300,000.00 $180,000.00 $108,000.00 $54,000.00 $0.00 $0.00

SYD dt

0 1 $81,818.18 2 $73,636.36 3 $65,454.55 4 $57,272.73 5 $49,090.91 6 $40,909.09 7 $32,727.27 8 $24,545.45 9 $16,363.64 10 $8,181.82

Bt $500,000.00 $418,181.82 $344,545.45 $279,090.91 $221,818.18 $172,727.27 $131,818.18 $99,090.91 $74,545.45 $58,181.82 $50,000.00

n 1 2 3 4 5

1.000000 0.666667 0.500000 0.400000 0.333333

0.333333 0.333333 0.300000 0.266667

SYD d3

0.166667 0.200000 0.200000

0.100000 0.133333

MARR = 10% MARR = 20% n PW(SYD) PW(DDB) PW(SYD) PW(DDB) 3 $0.86 $0.87 $0.74 $0.77 4 $0.83 $0.84 $0.71 $0.72 5 $0.81 $0.81 $0.67 $0.68

DDB d3

0.066667

1.000000 0.666667 0.500000 0.400000

0.222222 0.250000 0.240000

0.111111 0.125000 0.144000

0.125000 0.086400

0.129600

Table 9.C.2 Depletion Allowance Calculation for Example 9.C.1 50% of Taxable Taxable Income Income Depletion Barrels Gross Operating Before Before Percentage Cost Allowance Income Cost Depletion Depletion Depletion Depletion Used EOY Sold A B C D E = C-D F = 0.5D G = 0.15C H I 0 -$140,000 -$140,000 -$70,000 1 15,000 $300,000 $75,000 $225,000 $112,500 $45,000 $43,750 $45,000 2 13,000 $260,000 $104,000 $156,000 $78,000 $39,000 $37,424 $39,000 3 10,000 $200,000 $110,000 $90,000 $45,000 $30,000 $28,000 $30,000 4 6,000 $120,000 $84,000 $36,000 $18,000 $18,000 $15,600 $18,000 5 3,000 $60,000 $51,000 $9,000 $4,500 $9,000 $6,000 $6,000 6 1,000 $20,000 $20,000 $0 $0 $3,000 $2,000 $2,000

SF B t $500,000.00 $471,764.57 $440,705.60 $406,540.73 $368,959.38 $327,619.89 $282,146.45 $232,125.67 $177,102.81 $116,577.66 $50,000.00

$500,000 $400,000

Book Value

t 0 1 2 3 4 5 6 7 8 9 10

$300,000

$200,000 $100,000 $0 0

End of Year

$500,000

Book Value

$400,000

$300,000

$200,000

$100,000

$0 0

DDB

VDB

End of Year SF

SLN

VDB B t

$500,000.00 $400,000.00 $320,000.00 $256,000.00 $204,800.00 $163,840.00 $131,072.00 $104,857.60 $83,886.08 $66,943.04 $50,000.00

1 2 3 4 5 6 7 8 9 10

SLN d t

DDB d t

$45,000.00 $100,000.00 $38,888.89 $80,000.00 $33,750.00 $64,000.00 $29,428.57 $51,200.00 $25,800.00 $40,960.00 $22,768.00 $32,768.00 $20,268.00 $26,214.40 $18,285.87 $20,971.52 $16,943.04 $16,777.22

SLN dt > DDB dt? No No No No No No No No Yes

VDB d t

$100,000.00 $80,000.00 $64,000.00 $51,200.00 =B5-B6 $40,960.00 $32,768.00 $26,214.40 $20,971.52 $16,943.04 $16,943.04 =DDB(500000,50000,10,A7)

=(B5-50000)/(10-A5) =B8-VDB(500000,50000,10,A8,A9,2,FALSE)

$500,000

$400,000

Book Value

$300,000

$200,000

$100,000

($100,000)

End of Year SF

SLN

DDB

VDB

SLH SLN

200%DBH DDB

MACRS DDB/SLN

$500,000

Book Value

$400,000

$300,000

$200,000

$100,000

$0 0

End of Year

n DDB(d1)

SYD(d1)

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

0.333333 0.285714 0.250000 0.222222 0.200000 0.181818 0.166667 0.153846 0.142857 0.133333 0.125000 0.117647 0.111111 0.105263 0.100000 0.095238 0.090909 0.086957 0.083333 0.080000 0.076923 0.074074 0.071429 0.068966 0.066667 0.064516 0.062500 0.060606 0.058824 0.057143 0.055556 0.054054 0.052632 0.051282 0.050000 0.048780 0.047619 0.046512 0.045455 0.044444 0.043478 0.042553 0.041667 0.040816 0.040000 0.039216 0.038462 0.037736 0.037037 0.036364 0.035714 0.035088 0.034483 0.033898 0.033333 0.032787 0.032258 0.031746 0.031250 0.030769 0.030303 0.029851 0.029412 0.028986 0.028571 0.028169 0.027778 0.027397 0.027027 0.026667 0.026316 0.025974 0.025641 0.025316 0.025000 0.024691 0.024390 0.024096 0.023810 0.023529 0.023256 0.022989 0.022727 0.022472 0.022222 0.021978 0.021739 0.021505 0.021277 0.021053 0.020833 0.020619 0.020408 0.020202 0.020000 0.019802

0.400000 0.333333 0.285714 0.250000 0.222222 0.200000 0.181818 0.166667 0.153846 0.142857 0.133333 0.125000 0.117647 0.111111 0.105263 0.100000 0.095238 0.090909 0.086957 0.083333 0.080000 0.076923 0.074074 0.071429 0.068966 0.066667 0.064516 0.062500 0.060606 0.058824 0.057143 0.055556 0.054054 0.052632 0.051282 0.050000 0.048780 0.047619 0.046512 0.045455 0.044444 0.043478 0.042553 0.041667 0.040816 0.040000 0.039216 0.038462 0.037736 0.037037 0.036364 0.035714 0.035088 0.034483 0.033898 0.033333 0.032787 0.032258 0.031746 0.031250 0.030769 0.030303 0.029851 0.029412 0.028986 0.028571 0.028169 0.027778 0.027397 0.027027 0.026667 0.026316 0.025974 0.025641 0.025316 0.025000 0.024691 0.024390 0.024096 0.023810 0.023529 0.023256 0.022989 0.022727 0.022472 0.022222 0.021978 0.021739 0.021505 0.021277 0.021053 0.020833 0.020619 0.020408 0.020202 0.020000

DDB(d2) DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB DDB

0.240000 0.222222 0.204082 0.187500 0.172840 0.160000 0.148760 0.138889 0.130178 0.122449 0.115556 0.109375 0.103806 0.098765 0.094183 0.090000 0.086168 0.082645 0.079395 0.076389 0.073600 0.071006 0.068587 0.066327 0.064209 0.062222 0.060354 0.058594 0.056933 0.055363 0.053878 0.052469 0.051132 0.049861 0.048652 0.047500 0.046401 0.045351 0.044348 0.043388 0.042469 0.041588 0.040742 0.039931 0.039150 0.038400 0.037678 0.036982 0.036312 0.035665 0.035041 0.034439 0.033857 0.033294 0.032749 0.032222 0.031712 0.031217 0.030738 0.030273 0.029822 0.029385 0.028960 0.028547 0.028145 0.027755 0.027376 0.027006 0.026647 0.026297 0.025956 0.025623 0.025299 0.024984 0.024676 0.024375 0.024082 0.023795 0.023516 0.023243 0.022976 0.022715 0.022460 0.022211 0.021967 0.021728 0.021495 0.021267 0.021043 0.020824 0.020609 0.020399 0.020193 0.019992 0.019794 0.019600

SYD(d2) 0.266667 SYD 0.238095 SYD 0.214286 SYD 0.194444 SYD 0.177778 SYD 0.163636 SYD 0.151515 SYD 0.141026 SYD 0.131868 SYD 0.123810 SYD 0.116667 SYD 0.110294 SYD 0.104575 SYD 0.099415 SYD 0.094737 SYD 0.090476 SYD 0.086580 SYD 0.083004 SYD 0.079710 SYD 0.076667 SYD 0.073846 SYD 0.071225 SYD 0.068783 SYD 0.066502 SYD 0.064368 SYD 0.062366 SYD 0.060484 SYD 0.058712 SYD 0.057041 SYD 0.055462 SYD 0.053968 SYD 0.052553 SYD 0.051209 SYD 0.049933 SYD 0.048718 SYD 0.047561 SYD 0.046458 SYD 0.045404 SYD 0.044397 SYD 0.043434 SYD 0.042512 SYD 0.041628 SYD 0.040780 SYD 0.039966 SYD 0.039184 SYD 0.038431 SYD 0.037707 SYD 0.037010 SYD 0.036338 SYD 0.035690 SYD 0.035065 SYD 0.034461 SYD 0.033878 SYD 0.033314 SYD 0.032768 SYD 0.032240 SYD 0.031729 SYD 0.031234 SYD 0.030754 SYD 0.030288 SYD 0.029837 SYD 0.029398 SYD 0.028973 SYD 0.028559 SYD 0.028157 SYD 0.027767 SYD 0.027387 SYD 0.027017 SYD 0.026657 SYD 0.026306 SYD 0.025965 SYD 0.025632 SYD 0.025308 SYD 0.024992 SYD 0.024684 SYD 0.024383 SYD 0.024089 SYD 0.023803 SYD 0.023523 SYD 0.023249 SYD 0.022982 SYD 0.022721 SYD 0.022466 SYD 0.022217 SYD 0.021973 SYD 0.021734 SYD 0.021500 SYD 0.021272 SYD 0.021048 SYD 0.020829 SYD 0.020614 SYD 0.020404 SYD 0.020198 SYD 0.019996 SYD 0.019798 SYD 0.019604 SYD

DDB(d3) SYD(d3)

DDB(d4) SYD(d4)

0.144000 0.200000 SYD 0.148148 0.190476 SYD 0.145773 0.178571 SYD 0.140625 0.166667 SYD 0.134431 0.155556 SYD 0.128000 0.145455 SYD 0.121713 0.136364 SYD 0.115741 0.128205 SYD 0.110150 0.120879 SYD 0.104956 0.114286 SYD 0.100148 0.108333 SYD 0.095703 0.102941 SYD 0.091594 0.098039 SYD 0.087791 0.093567 SYD 0.084269 0.089474 SYD 0.081000 0.085714 SYD 0.077961 0.082251 SYD 0.075131 0.079051 SYD 0.072491 0.076087 SYD 0.070023 0.073333 SYD 0.067712 0.070769 SYD 0.065544 0.068376 SYD 0.063507 0.066138 SYD 0.061589 0.064039 SYD 0.059781 0.062069 SYD 0.058074 0.060215 SYD 0.056460 0.058468 SYD 0.054932 0.056818 SYD 0.053482 0.055258 SYD 0.052107 0.053782 SYD 0.050799 0.052381 SYD 0.049554 0.051051 SYD 0.048368 0.049787 SYD 0.047237 0.048583 SYD 0.046157 0.047436 SYD 0.045125 0.046341 SYD 0.044137 0.045296 SYD 0.043192 0.044297 SYD 0.042286 0.043340 SYD 0.041416 0.042424 SYD 0.040582 0.041546 SYD 0.039780 0.040703 SYD 0.039009 0.039894 SYD 0.038267 0.039116 SYD 0.037552 0.038367 SYD 0.036864 0.037647 SYD 0.036200 0.036953 SYD 0.035560 0.036284 SYD 0.034942 0.035639 SYD 0.034344 0.035017 SYD 0.033767 0.034416 SYD 0.033209 0.033835 SYD 0.032669 0.033273 SYD 0.032146 0.032729 SYD 0.031639 0.032203 SYD 0.031148 0.031694 SYD 0.030672 0.031200 SYD 0.030210 0.030722 SYD 0.029762 0.030258 SYD 0.029327 0.029808 SYD 0.028905 0.029371 SYD 0.028494 0.028946 SYD 0.028095 0.028534 SYD 0.027707 0.028133 SYD 0.027330 0.027743 SYD 0.026962 0.027364 SYD 0.026604 0.026995 SYD 0.026256 0.026636 SYD 0.025917 0.026287 SYD 0.025586 0.025946 SYD 0.025263 0.025614 SYD 0.024949 0.025290 SYD 0.024642 0.024975 SYD 0.024343 0.024667 SYD 0.024051 0.024367 SYD 0.023766 0.024074 SYD 0.023487 0.023788 SYD 0.023215 0.023509 SYD 0.022949 0.023236 SYD 0.022689 0.022969 SYD 0.022435 0.022709 SYD 0.022187 0.022454 SYD 0.021944 0.022205 SYD 0.021706 0.021961 SYD 0.021473 0.021723 SYD 0.021246 0.021490 SYD 0.021023 0.021261 SYD 0.020804 0.021038 SYD 0.020590 0.020819 SYD 0.020381 0.020605 SYD 0.020176 0.020395 SYD 0.019974 0.020189 SYD 0.019777 0.019987 SYD 0.019584 0.019790 SYD 0.019394 0.019596 SYD 0.019208 0.019406 SYD

0.086400 0.133333 SYD 0.098765 0.142857 SYD 0.104123 0.142857 SYD 0.105469 0.138889 SYD 0.104557 0.133333 SYD 0.102400 0.127273 SYD 0.099583 0.121212 SYD 0.096451 0.115385 SYD 0.093204 0.109890 SYD 0.089963 0.104762 SYD 0.086795 0.100000 SYD 0.083740 0.095588 SYD 0.080818 0.091503 SYD 0.078037 0.087719 SYD 0.075398 0.084211 SYD 0.072900 0.080952 SYD 0.070536 0.077922 SYD 0.068301 0.075099 SYD 0.066188 0.072464 SYD 0.064188 0.070000 SYD 0.062295 0.067692 SYD 0.060502 0.065527 SYD 0.058802 0.063492 SYD 0.057190 0.061576 SYD 0.055658 0.059770 SYD 0.054202 0.058065 SYD 0.052817 0.056452 SYD 0.051498 0.054924 SYD 0.050241 0.053476 SYD 0.049042 0.052101 SYD 0.047896 0.050794 SYD 0.046801 0.049550 SYD 0.045754 0.048364 SYD 0.044751 0.047233 SYD 0.043790 0.046154 SYD 0.042869 0.045122 SYD 0.041984 0.044135 SYD 0.041135 0.043189 SYD 0.040319 0.042283 SYD 0.039534 0.041414 SYD 0.038778 0.040580 SYD 0.038050 0.039778 SYD 0.037349 0.039007 SYD 0.036672 0.038265 SYD 0.036020 0.037551 SYD 0.035389 0.036863 SYD 0.034781 0.036199 SYD 0.034192 0.035559 SYD 0.033623 0.034941 SYD 0.033072 0.034343 SYD 0.032539 0.033766 SYD 0.032023 0.033208 SYD 0.031522 0.032668 SYD 0.031037 0.032145 SYD 0.030567 0.031638 SYD 0.030110 0.031148 SYD 0.029667 0.030672 SYD 0.029236 0.030210 SYD 0.028818 0.029762 SYD 0.028411 0.029327 SYD 0.028015 0.028904 SYD 0.027631 0.028494 SYD 0.027257 0.028095 SYD 0.026892 0.027707 SYD 0.026537 0.027329 SYD 0.026192 0.026962 SYD 0.025855 0.026604 SYD 0.025527 0.026256 SYD 0.025207 0.025916 SYD 0.024894 0.025586 SYD 0.024590 0.025263 SYD 0.024292 0.024949 SYD 0.024002 0.024642 SYD 0.023719 0.024343 SYD 0.023442 0.024051 SYD 0.023171 0.023765 SYD 0.022907 0.023487 SYD 0.022649 0.023215 SYD 0.022396 0.022949 SYD 0.022149 0.022689 SYD 0.021907 0.022435 SYD 0.021671 0.022187 SYD 0.021439 0.021944 SYD 0.021213 0.021706 SYD 0.020991 0.021473 SYD 0.020773 0.021245 SYD 0.020561 0.021022 SYD 0.020352 0.020804 SYD 0.020148 0.020590 SYD 0.019947 0.020381 SYD 0.019751 0.020175 SYD 0.019558 0.019974 SYD 0.019369 0.019777 SYD 0.019184 0.019584 SYD 0.019002 0.019394 SYD 0.018824 0.019208 SYD

DDB(d5)

SYD(d5)

0.051840 0.066667 SYD 0.065844 0.095238 DDB 0.074374 0.107143 DDB 0.079102 0.111111 DDB 0.081322 0.111111 DDB 0.081920 0.109091 DDB 0.081477 0.106061 DDB 0.080376 0.102564 DDB 0.078865 0.098901 DDB 0.077111 0.095238 DDB 0.075222 0.091667 DDB 0.073273 0.088235 DDB 0.071310 0.084967 DDB 0.069366 0.081871 DDB 0.067462 0.078947 DDB 0.065610 0.076190 DDB 0.063819 0.073593 DDB 0.062092 0.071146 DDB 0.060432 0.068841 DDB 0.058839 0.066667 DDB 0.057311 0.064615 DDB 0.055848 0.062678 DDB 0.054447 0.060847 DDB 0.053105 0.059113 DDB 0.051820 0.057471 DDB 0.050589 0.055914 DDB 0.049410 0.054435 DDB 0.048280 0.053030 DDB 0.047196 0.051693 DDB 0.046157 0.050420 DDB 0.045159 0.049206 DDB 0.044201 0.048048 DDB 0.043281 0.046942 DDB 0.042396 0.045884 DDB 0.041545 0.044872 DDB 0.040725 0.043902 DDB 0.039936 0.042973 DDB 0.039176 0.042082 DDB 0.038444 0.041226 DDB 0.037737 0.040404 DDB 0.037055 0.039614 DDB 0.036396 0.038853 DDB 0.035759 0.038121 DDB 0.035144 0.037415 DDB 0.034549 0.036735 DDB 0.033974 0.036078 DDB 0.033417 0.035445 DDB 0.032877 0.034833 DDB 0.032354 0.034242 DDB 0.031847 0.033670 DDB 0.031356 0.033117 DDB 0.030879 0.032581 DDB 0.030416 0.032063 DDB 0.029967 0.031560 DDB 0.029530 0.031073 DDB 0.029106 0.030601 DDB 0.028694 0.030143 DDB 0.028293 0.029698 DDB 0.027903 0.029266 DDB 0.027523 0.028846 DDB 0.027153 0.028438 DDB 0.026794 0.028042 DDB 0.026443 0.027656 DDB 0.026101 0.027280 DDB 0.025768 0.026915 DDB 0.025443 0.026559 DDB 0.025127 0.026213 DDB 0.024818 0.025875 DDB 0.024516 0.025546 DDB 0.024222 0.025225 DDB 0.023934 0.024912 DDB 0.023653 0.024607 DDB 0.023379 0.024309 DDB 0.023111 0.024018 DDB 0.022848 0.023734 DDB 0.022592 0.023457 DDB 0.022342 0.023186 DDB 0.022096 0.022921 DDB 0.021856 0.022662 DDB 0.021622 0.022409 DDB 0.021392 0.022161 DDB 0.021167 0.021919 DDB 0.020946 0.021682 DDB 0.020731 0.021450 DDB 0.020519 0.021223 DDB 0.020312 0.021001 DDB 0.020109 0.020784 DDB 0.019910 0.020570 DDB 0.019714 0.020361 DDB 0.019523 0.020157 DDB 0.019335 0.019956 DDB 0.019151 0.019759 DDB 0.018970 0.019567 DDB 0.018792 0.019377 DDB 0.018618 0.019192 DDB 0.018447 0.019010 DDB

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% $0.92 $0.89 $0.85 $0.82 $0.79 $0.76 $0.74 $0.71 $0.69 $0.67 $0.65 $1.00 $0.96 $0.91 $0.88 $0.84 $0.81 $0.78 $0.75 $0.72 $0.69 $0.67 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.87 $0.83 $0.80 $0.76 $0.73 $0.71 $0.68 $0.66 $0.63 $0.61 $0.59 $0.95 $0.91 $0.86 $0.83 $0.79 $0.76 $0.73 $0.70 $0.67 $0.64 $0.62 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.81 $0.78 $0.74 $0.71 $0.68 $0.66 $0.63 $0.61 $0.58 $0.56 $0.54 $0.89 $0.85 $0.81 $0.77 $0.73 $0.70 $0.67 $0.64 $0.62 $0.59 $0.57 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.76 $0.73 $0.69 $0.66 $0.64 $0.61 $0.58 $0.56 $0.54 $0.52 $0.50 $0.83 $0.79 $0.75 $0.72 $0.68 $0.65 $0.62 $0.60 $0.57 $0.55 $0.53 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.72 $0.68 $0.65 $0.62 $0.59 $0.57 $0.54 $0.52 $0.50 $0.48 $0.47 $0.78 $0.74 $0.70 $0.67 $0.63 $0.61 $0.58 $0.55 $0.53 $0.51 $0.49 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.67 $0.64 $0.61 $0.58 $0.55 $0.53 $0.51 $0.49 $0.47 $0.45 $0.43 $0.73 $0.69 $0.65 $0.62 $0.59 $0.56 $0.54 $0.52 $0.49 $0.47 $0.45 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.63 $0.60 $0.57 $0.55 $0.52 $0.50 $0.48 $0.46 $0.44 $0.42 $0.41 $0.68 $0.65 $0.61 $0.58 $0.55 $0.53 $0.50 $0.48 $0.46 $0.44 $0.42 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.60 $0.57 $0.54 $0.51 $0.49 $0.47 $0.45 $0.43 $0.41 $0.40 $0.38 $0.64 $0.61 $0.58 $0.55 $0.52 $0.50 $0.47 $0.45 $0.43 $0.41 $0.40 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.57 $0.54 $0.51 $0.49 $0.46 $0.44 $0.42 $0.41 $0.39 $0.37 $0.36 $0.60 $0.57 $0.54 $0.51 $0.49 $0.47 $0.44 $0.42 $0.41 $0.39 $0.37 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.54 $0.51 $0.48 $0.46 $0.44 $0.42 $0.40 $0.38 $0.37 $0.35 $0.34 $0.57 $0.54 $0.51 $0.49 $0.46 $0.44 $0.42 $0.40 $0.38 $0.37 $0.35 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.51 $0.48 $0.46 $0.44 $0.42 $0.40 $0.38 $0.36 $0.35 $0.33 $0.32 $0.54 $0.51 $0.49 $0.46 $0.44 $0.42 $0.40 $0.38 $0.36 $0.35 $0.33 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.49 $0.46 $0.44 $0.42 $0.40 $0.38 $0.36 $0.35 $0.33 $0.32 $0.31 $0.51 $0.49 $0.46 $0.44 $0.42 $0.40 $0.38 $0.36 $0.34 $0.33 $0.32 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.47 $0.44 $0.42 $0.40 $0.38 $0.36 $0.34 $0.33 $0.32 $0.30 $0.29 $0.49 $0.46 $0.44 $0.42 $0.40 $0.38 $0.36 $0.34 $0.33 $0.31 $0.30 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.45 $0.42 $0.40 $0.38 $0.36 $0.34 $0.33 $0.31 $0.30 $0.29 $0.28 $0.47 $0.44 $0.42 $0.40 $0.38 $0.36 $0.34 $0.33 $0.31 $0.30 $0.29 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.43 $0.40 $0.38 $0.36 $0.35 $0.33 $0.32 $0.30 $0.29 $0.28 $0.27 $0.45 $0.42 $0.40 $0.38 $0.36 $0.34 $0.33 $0.31 $0.30 $0.29 $0.27 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.41 $0.39 $0.37 $0.35 $0.33 $0.32 $0.30 $0.29 $0.28 $0.26 $0.25 $0.43 $0.40 $0.38 $0.36 $0.35 $0.33 $0.31 $0.30 $0.29 $0.27 $0.26 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.39 $0.37 $0.35 $0.34 $0.32 $0.30 $0.29 $0.28 $0.27 $0.25 $0.24 $0.41 $0.39 $0.37 $0.35 $0.33 $0.31 $0.30 $0.29 $0.27 $0.26 $0.25 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.38 $0.36 $0.34 $0.32 $0.31 $0.29 $0.28 $0.27 $0.26 $0.24 $0.23 $0.40 $0.37 $0.35 $0.33 $0.32 $0.30 $0.29 $0.27 $0.26 $0.25 $0.24 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.37 $0.35 $0.33 $0.31 $0.30 $0.28 $0.27 $0.26 $0.25 $0.24 $0.23 $0.38 $0.36 $0.34 $0.32 $0.31 $0.29 $0.28 $0.26 $0.25 $0.24 $0.23 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.35 $0.33 $0.32 $0.30 $0.29 $0.27 $0.26 $0.25 $0.24 $0.23 $0.22 $0.37 $0.35 $0.33 $0.31 $0.29 $0.28 $0.27 $0.25 $0.24 $0.23 $0.22 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.34 $0.32 $0.31 $0.29 $0.28 $0.26 $0.25 $0.24 $0.23 $0.22 $0.21 $0.35 $0.33 $0.32 $0.30 $0.28 $0.27 $0.26 $0.25 $0.23 $0.22 $0.21 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.33 $0.31 $0.30 $0.28 $0.27 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.34 $0.32 $0.31 $0.29 $0.27 $0.26 $0.25 $0.24 $0.23 $0.22 $0.21 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.32 $0.30 $0.29 $0.27 $0.26 $0.25 $0.23 $0.22 $0.21 $0.20 $0.20 $0.33 $0.31 $0.30 $0.28 $0.27 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.31 $0.29 $0.28 $0.26 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.32 $0.30 $0.29 $0.27 $0.26 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.30 $0.28 $0.27 $0.26 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.31 $0.29 $0.28 $0.26 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.29 $0.28 $0.26 $0.25 $0.24 $0.22 $0.21 $0.20 $0.19 $0.19 $0.18 $0.30 $0.28 $0.27 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.28 $0.27 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.29 $0.28 $0.26 $0.25 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.18 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.28 $0.26 $0.25 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.18 $0.17 $0.28 $0.27 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.27 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.28 $0.26 $0.25 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.17 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.26 $0.25 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.17 $0.16 $0.27 $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.25 $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.16 $0.26 $0.25 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.17 $0.16 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.25 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.17 $0.16 $0.15 $0.26 $0.24 $0.23 $0.22 $0.20 $0.19 $0.19 $0.18 $0.17 $0.16 $0.15 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.24 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.25 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.16 $0.15 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.24 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.16 $0.15 $0.14 $0.24 $0.23 $0.22 $0.21 $0.19 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.24 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.16 $0.15 $0.14 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.23 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.16 $0.15 $0.14 $0.14 $0.23 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.23 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.16 $0.15 $0.14 $0.14 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.22 $0.20 $0.19 $0.18 $0.17 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.22 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.22 $0.20 $0.19 $0.18 $0.17 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.13 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.20 $0.19 $0.18 $0.17 $0.16 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.21 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.13 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.12 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.12 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.20 $0.18 $0.17 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.20 $0.19 $0.18 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.13 $0.12 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.20 $0.18 $0.17 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.19 $0.18 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.19 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.18 $0.17 $0.16 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 $0.19 $0.18 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.18 $0.17 $0.16 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.18 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.18 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.17 $0.17 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 $0.11 $0.18 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.18 $0.17 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 $0.11 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.17 $0.16 $0.15 $0.15 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.17 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.17 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.16 $0.15 $0.15 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.17 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.16 $0.15 $0.15 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.10 $0.16 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.16 $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.10 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.16 $0.15 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.10 $0.09 $0.15 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.15 $0.14 $0.13 $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.10 $0.09 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.15 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.15 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.15 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.14 $0.14 $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.10 $0.09 $0.09 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.14 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.14 $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.08 $0.14 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.08 $0.14 $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.13 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.13 $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.13 $0.12 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.12 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.13 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.12 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.07 $0.12 $0.12 $0.11 $0.11 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.08 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.12 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.12 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.12 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.11 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.11 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.11 $0.11 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.07 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.11 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.11 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.11 $0.10 $0.09 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.11 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.10 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.06 $0.10 $0.09 $0.09 $0.08 $0.08 $0.08 $0.07 $0.07 $0.06 $0.06 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.06 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.06 $0.10 $0.09 $0.09 $0.08 $0.08 $0.07 $0.07 $0.07 $0.06 $0.06 $0.06 SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD SYD

EOY BTCF DWO 0 -$500,000.00 1 $124,166.67 $45,000.00 2 $124,166.67 $45,000.00 3 $124,166.67 $45,000.00 4 $124,166.67 $45,000.00 5 $124,166.67 $45,000.00 6 $124,166.67 $45,000.00 7 $124,166.67 $45,000.00 8 $124,166.67 $45,000.00 9 $124,166.67 $45,000.00 10 $174,166.67 $45,000.00 MARRBT = 16.667% PW BT = $96,229.49 FW BT = $449,547.99 AW BT = $20,406.41 IRR BT = 21.64% ERR BT = 18.74%

$79,166.67 $79,166.67 $79,166.67 $79,166.67 $79,166.67 $79,166.67 $79,166.67 $79,166.67 $79,166.67 $79,166.67

$31,666.67 $31,666.67 $31,666.67 $31,666.67 $31,666.67 $31,666.67 $31,666.67 $31,666.67 $31,666.67 $31,666.67 MARRAT = PW AT = FW AT = AW AT = IRR AT = ERR AT =

ATCF -$500,000.00 $92,500.00 $92,500.00 $92,500.00 $92,500.00 $92,500.00 $92,500.00 $92,500.00 $92,500.00 $92,500.00 $142,500.00 10% $87,649.62 $227,340.55 $14,264.57 13.80% 11.79%

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF DWO TI T ATCF -$500,000.00 -$500,000.00 $124,166.67 $100,000.00 $24,166.67 $9,666.67 $114,500.00 $124,166.67 $160,000.00 -$35,833.33 -$14,333.33 $138,500.00 $124,166.67 $96,000.00 $28,166.67 $11,266.67 $112,900.00 $124,166.67 $57,600.00 $66,566.67 $26,626.67 $97,540.00 $124,166.67 $57,600.00 $66,566.67 $26,626.67 $97,540.00 $124,166.67 $28,800.00 $95,366.67 $38,146.67 $86,020.00 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 $174,166.67 $0.00 $174,166.67 $69,666.67 $104,500.00 PW = $123,988.64 FW = $321,594.61 AW = $20,178.58 IRR = 16.12% ERR = 12.46%

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67 B 10 =

DWO

$100,000.00 $24,166.67 $9,666.67 $80,000.00 $44,166.67 $17,666.67 $64,000.00 $60,166.67 $24,066.67 $51,200.00 $72,966.67 $29,186.67 $40,960.00 $83,206.67 $33,282.67 $32,768.00 $91,398.67 $36,559.47 $26,214.40 $97,952.27 $39,180.91 $20,971.52 $103,195.15 $41,278.06 $16,777.22 $107,389.45 $42,955.78 $13,421.77 $107,057.81 $42,823.12 $53,687.09 PW = FW = AW = IRR = ERR =

ATCF -$500,000.00 $114,500.00 $106,500.00 $100,100.00 $94,980.00 $90,884.00 $87,607.20 $84,985.76 $82,888.61 $81,210.89 $131,343.55 $105,429.72 $273,457.54 $17,158.20 14.88% 12.12%

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF TI T ATCF -$500,000.00 -$500,000.00 -$200,000.00 -$300,000.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $124,166.67 $124,166.67 $49,666.67 $74,500.00 $174,166.67 $174,166.67 $69,666.67 $104,500.00 PW = $169,336.56 FW = $439,215.43 AW = $27,558.75 IRR = 21.64% ERR = 15.03%

EOY 0 1 2 3 4 5 6 7 8 9 10 PW(A) = EOY 0 1 2 3 4 5 6 7 8 9 10 PW(B) =

BTCF(A) -$300,000.00 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $37,954.92 BTCF(B) -$450,000.00 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $37,283.84

DWO(A)

TI(A)

$30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00 $30,000.00

$41,666.67 $41,666.67 $41,666.67 $41,666.67 $41,666.67 $41,666.67 $41,666.67 $41,666.67 $41,666.67 $41,666.67

DWO(B)

TI(B)

$45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00 $45,000.00

$58,333.33 $58,333.33 $58,333.33 $58,333.33 $58,333.33 $58,333.33 $58,333.33 $58,333.33 $58,333.33 $58,333.33

T(A) $16,666.67 $16,666.67 $16,666.67 $16,666.67 $16,666.67 $16,666.67 $16,666.67 $16,666.67 $16,666.67 $16,666.67 PW(A) = T(B) $23,333.33 $23,333.33 $23,333.33 $23,333.33 $23,333.33 $23,333.33 $23,333.33 $23,333.33 $23,333.33 $23,333.33 PW(B) =

ATCF(A) -$300,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $55,000.00 $37,951.19 ATCF(B) -$450,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $80,000.00 $41,565.37

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF(A) -$300,000.00 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67

DWO(A)

TI(A)

$42,870.00 $73,470.00 $52,470.00 $37,470.00 $26,790.00 $26,760.00 $26,790.00 $13,380.00 $0.00 $0.00

$28,796.67 -$1,803.33 $19,196.67 $34,196.67 $44,876.67 $44,906.67 $44,876.67 $58,286.67 $71,666.67 $71,666.67

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF(B) -$450,000.00 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33

DWO(B)

TI(B)

$64,305.00 $110,205.00 $78,705.00 $56,205.00 $40,185.00 $40,140.00 $40,185.00 $20,070.00 $0.00 $0.00

$39,028.33 -$6,871.67 $24,628.33 $47,128.33 $63,148.33 $63,193.33 $63,148.33 $83,263.33 $103,333.33 $103,333.33

T(A) $11,518.67 -$721.33 $7,678.67 $13,678.67 $17,950.67 $17,962.67 $17,950.67 $23,314.67 $28,666.67 $28,666.67 PW(A) = T(B) $15,611.33 -$2,748.67 $9,851.33 $18,851.33 $25,259.33 $25,277.33 $25,259.33 $33,305.33 $41,333.33 $41,333.33 PW(B) =

ATCF(A) -$300,000.00 $60,148.00 $72,388.00 $63,988.00 $57,988.00 $53,716.00 $53,704.00 $53,716.00 $48,352.00 $43,000.00 $43,000.00 $50,790.36 ATCF(B) -$450,000.00 $87,722.00 $106,082.00 $93,482.00 $84,482.00 $78,074.00 $78,056.00 $78,074.00 $70,028.00 $62,000.00 $62,000.00 $60,824.10

EOY 0 1 2 3 4 5 6 7 8 9 10 EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF(A) DWO(A) TI(A) T(A) ATCF(A) -$300,000.00 -$300,000.00 $71,666.67 $99,990.00 -$28,323.33 -$11,329.33 $82,996.00 $71,666.67 $133,350.00 -$61,683.33 -$24,673.33 $96,340.00 $71,666.67 $44,430.00 $27,236.67 $10,894.67 $60,772.00 $71,666.67 $22,230.00 $49,436.67 $19,774.67 $51,892.00 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00 PW(A) = $64,084.76 BTCF(B) DWO(B) TI(B) T(B) ATCF(B) -$450,000.00 -$450,000.00 $103,333.33 $64,305.00 $39,028.33 $15,611.33 $87,722.00 $103,333.33 $110,205.00 -$6,871.67 -$2,748.67 $106,082.00 $103,333.33 $78,705.00 $24,628.33 $9,851.33 $93,482.00 $103,333.33 $56,205.00 $47,128.33 $18,851.33 $84,482.00 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.00 $103,333.33 $40,140.00 $63,193.33 $25,277.33 $78,056.00 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.00 $103,333.33 $20,070.00 $83,263.33 $33,305.33 $70,028.00 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.00 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.00 PW(B) = $60,824.10

EOY 0 1 2 3 4 5

BTCF -$125,000.00 -$500.00 -$500.00 -$500.00 -$500.00 $24,500.00

DWO $41,662.50 $55,562.50 $18,512.50 $9,262.50 $0.00

-$42,162.50 -$16,865.00 -$56,062.50 -$22,425.00 -$19,012.50 -$7,605.00 -$9,762.50 -$3,905.00 $24,500.00 $9,800.00 AW =

ATCF -$125,000.00 $16,365.00 $21,925.00 $7,105.00 $3,405.00 $14,700.00 -$19,840.63

EOY BTCF(P) 0 -$90,000.00 1 -$18,750.00 2 -$18,750.00 3 -$18,750.00 4 -$18,750.00 5 -$3,750.00 PW(P) = -$140,045.81 EOY BTCF(L) 0 -$29,500.00 1 -$38,500.00 2 -$38,500.00 3 -$38,500.00 4 -$38,500.00 5 -$9,000.00 PW(L) = -$132,783.18

DWO(P)

TI(P)

T(P)

$29,997.00 $40,005.00 $13,329.00 $6,669.00 $0.00

-$48,747.00 -$58,755.00 -$32,079.00 -$25,419.00 -$3,750.00

DWO(L)

TI(L) -$29,500.00 -$38,500.00 -$38,500.00 -$38,500.00 -$38,500.00 -$9,000.00

-$19,498.80 -$23,502.00 -$12,831.60 -$10,167.60 -$1,500.00 PW(P) = T(L) -$11,800.00 -$15,400.00 -$15,400.00 -$15,400.00 -$15,400.00 -$3,600.00 PW(L) =

$0.00 $0.00 $0.00 $0.00 $0.00

ATCF(P) -$90,000.00 $748.80 $4,752.00 -$5,918.40 -$8,582.40 -$2,250.00 -$96,486.74 ATCF(L) -$17,700.00 -$23,100.00 -$23,100.00 -$23,100.00 -$23,100.00 -$5,400.00 -$90,926.87

Present Worth

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR = 10% interest rate = 12% income tax rate = 40% BT&LCF PPMT IPMT DWO TI Tax ATCF -$500,000.00 -$300,000.00 -$200,000.00 $124,166.67 $0.00 $36,000.00 $100,000.00 -$11,833.33 -$4,733.33 $92,900.00 $124,166.67 $0.00 $36,000.00 $160,000.00 -$71,833.33 -$28,733.33 $116,900.00 $124,166.67 $0.00 $36,000.00 $96,000.00 -$7,833.33 -$3,133.33 $91,300.00 $124,166.67 $0.00 $36,000.00 $57,600.00 $30,566.67 $12,226.67 $75,940.00 $124,166.67 $0.00 $36,000.00 $57,600.00 $30,566.67 $12,226.67 $75,940.00 $124,166.67 $0.00 $36,000.00 $28,800.00 $59,366.67 $23,746.67 $64,420.00 $124,166.67 $0.00 $36,000.00 $0.00 $88,166.67 $35,266.67 $52,900.00 $124,166.67 $0.00 $36,000.00 $0.00 $88,166.67 $35,266.67 $52,900.00 $124,166.67 $0.00 $36,000.00 $0.00 $88,166.67 $35,266.67 $52,900.00 $174,166.67 $300,000.00 $36,000.00 $0.00 $138,166.67 $55,266.67 -$217,100.00 PW AT = $175,603.01 $300,000 FW AT = $455,468.98 $250,000 AW AT = $28,578.58 IRR AT = 41.54% $200,000 ERR AT = 17.16% $150,000

ATCF -$200,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $974,217.47

$100,000

=IRR(I4:I14)

$50,000 $0 -20% -13% -6% -$50,000

15% 22% 29% 36% 43% 50%

-$100,000 -$150,000 MARR

=FV(10%,10,,-NPV(10%,H5:H13))+H14

MARR

-20%

-$120,214.85

-19%

-$29,580.15

-18%

$44,520.76

-17%

$104,731.01

-16%

$153,270.45

-15%

$192,005.64

-14%

$222,507.81

-13%

$246,100.91

-12%

$263,901.51

-11%

$276,852.02

-10%

$285,748.42

-9%

$291,263.36

-8%

$293,965.53

-7%

$294,335.89

-6%

$292,781.21

-5%

$289,645.61

-4%

$285,220.06

-3%

$279,750.57

-2%

$273,445.00

-1%

$266,478.82

$259,000.02

$251,133.24

$242,983.26

$234,637.99

$226,170.99

$217,643.61

$209,106.84

$200,602.83

$192,166.24

$183,825.34

10%

$175,603.01

11%

$167,517.54

12%

$159,583.33

13%

$151,811.50

14%

$144,210.39

15%

$136,785.99

16%

$129,542.33

17%

$122,481.82

18%

$115,605.45

19%

$108,913.09

20%

$102,403.67

21%

$96,075.34

22%

$89,925.61

23%

$83,951.50

24%

$78,149.61

25%

$72,516.23

26%

$67,047.41

27%

$61,739.01

28%

$56,586.80

29%

$51,586.43

30%

$46,733.53

31%

$42,023.73

32%

$37,452.66

33%

$33,015.98

34%

$28,709.43

35%

$24,528.81

36%

$20,469.99

37%

$16,528.95

38%

$12,701.74

39%

$8,984.55

40%

$5,373.64

41%

$1,865.39

42%

-$1,543.70

43%

-$4,857.02

44%

-$8,077.87

45%

-$11,209.43

46%

-$14,254.76

47%

-$17,216.82

48%

-$20,098.48

49%

-$22,902.49

50%

-$25,631.51

Plan 2

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR = 10% interest rate = 12% income tax rate = 40% BT&LCF PPMT IPMT DWO TI Tax ATCF -$500,000.00 -$300,000.00 -$200,000.00 $124,166.67 $30,000.00 $36,000.00 $100,000.00 -$11,833.33 -$4,733.33 $62,900.00 $124,166.67 $30,000.00 $32,400.00 $160,000.00 -$68,233.33 -$27,293.33 $89,060.00 $124,166.67 $30,000.00 $28,800.00 $96,000.00 -$633.33 -$253.33 $65,620.00 $124,166.67 $30,000.00 $25,200.00 $57,600.00 $41,366.67 $16,546.67 $52,420.00 $124,166.67 $30,000.00 $21,600.00 $57,600.00 $44,966.67 $17,986.67 $54,580.00 $124,166.67 $30,000.00 $18,000.00 $28,800.00 $77,366.67 $30,946.67 $45,220.00 $124,166.67 $30,000.00 $14,400.00 $0.00 $109,766.67 $43,906.67 $35,860.00 $124,166.67 $30,000.00 $10,800.00 $0.00 $113,366.67 $45,346.67 $38,020.00 $124,166.67 $30,000.00 $7,200.00 $0.00 $116,966.67 $46,786.67 $40,180.00 $174,166.67 $30,000.00 $3,600.00 $0.00 $170,566.67 $68,226.67 $72,340.00 PW = $156,374.28 FW = $405,594.61 AW = $25,449.19 IRR = 28.51% ERR = 16.54%

Plan 3

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR = 10% interest rate = 12% income tax rate = 40% BT&LCF PPMT IPMT DWO TI Tax ATCF -$500,000.00 -$300,000.00 -$200,000.00 $124,166.67 $17,095.25 $36,000.00 $100,000.00 -$11,833.33 -$4,733.33 $75,804.75 $124,166.67 $19,146.68 $33,948.57 $160,000.00 -$69,781.90 -$27,912.76 $98,984.18 $124,166.67 $21,444.28 $31,650.97 $96,000.00 -$3,484.30 -$1,393.72 $72,465.14 $124,166.67 $24,017.59 $29,077.65 $57,600.00 $37,489.02 $14,995.61 $56,075.81 $124,166.67 $26,899.71 $26,195.54 $57,600.00 $40,371.13 $16,148.45 $54,922.97 $124,166.67 $30,127.67 $22,967.58 $28,800.00 $72,399.09 $28,959.64 $42,111.78 $124,166.67 $33,742.99 $19,352.26 $0.00 $104,814.41 $41,925.76 $29,145.66 $124,166.67 $37,792.15 $15,303.10 $0.00 $108,863.57 $43,545.43 $27,525.99 $124,166.67 $42,327.21 $10,768.04 $0.00 $113,398.63 $45,359.45 $25,711.97 $174,166.67 $47,406.47 $5,688.78 $0.00 $168,477.89 $67,391.16 $53,680.26 PW = $160,734.89 FW = $416,904.92 AW = $26,158.86 IRR = 31.65% ERR = 16.68%

MARR = 10% interest rate = 12% income tax rate = 40% EOY BT&LCF PPMT IPMT DWO TI Tax ATCF ATCF 0 -$500,000.00 -$300,000.00 -$200,000.00 -$200,000.00 1 $124,166.67 $0.00 $0.00 $100,000.00 $24,166.67 $9,666.67 $114,500.00 $0.00 2 $124,166.67 $0.00 $0.00 $160,000.00 -$35,833.33 -$14,333.33 $138,500.00 $0.00 3 $124,166.67 $0.00 $0.00 $96,000.00 $28,166.67 $11,266.67 $112,900.00 $0.00 4 $124,166.67 $0.00 $0.00 $57,600.00 $66,566.67 $26,626.67 $97,540.00 $0.00 5 $124,166.67 $0.00 $0.00 $57,600.00 $66,566.67 $26,626.67 $97,540.00 $0.00 6 $124,166.67 $0.00 $0.00 $28,800.00 $95,366.67 $38,146.67 $86,020.00 $0.00 7 $124,166.67 $0.00 $0.00 $0.00 $124,166.67 $49,666.67 $74,500.00 $0.00 8 $124,166.67 $0.00 $0.00 $0.00 $124,166.67 $49,666.67 $74,500.00 $0.00 9 $124,166.67 $0.00 $0.00 $0.00 $124,166.67 $49,666.67 $74,500.00 $0.00 10 $174,166.67 $300,000.00 $631,754.46 $0.00 -$457,587.79 -$183,035.12 -$574,552.68 $939,413.16 PW AT = $162,184.44 After-Tax Present Worth FW AT = $420,664.67 AW AT = $26,394.77 IRR AT = 53.49% =IRR(H4:H14,50%) $175,000 ERR AT = 16.73% =IRR(I4:I14) $150,000

=FV(10%,10,,-NPV(10%,H5:H13))+H14

$125,000 $100,000

$75,000 $50,000 $25,000 $0 -4%

11% 16% 21% 26% 31% 36% 41% 46% 51% 56%

-$25,000

MARR

MARR -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% 6% 7% 8% 9.328% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30% 31% 32% 33% 34% 35% 36% 37% 38% 39% 40% 41% 42% 43% 44% 45% 46% 47% 48% 49% 50% 51% 52% 53% 54% 55% 56% 57% 58% 59% 60%

PW -$12,692.97 $22,099.59 $51,321.21 $75,720.99 $95,947.34 $112,561.97 $126,051.87 $136,839.58 $145,291.93 $151,727.62 $156,423.69 $159,621.03 $161,529.26 $162,380.12 $162,184.44 $161,228.48 $159,583.33 $157,353.86 $154,631.37 $151,495.36 $148,015.02 $144,250.53 $140,254.21 $136,071.53 $131,741.94 $127,299.66 $122,774.29 $118,191.45 $113,573.23 $108,938.63 $104,303.99 $99,683.27 $95,088.39 $90,529.46 $86,015.01 $81,552.20 $77,146.98 $72,804.28 $68,528.06 $64,321.54 $60,187.21 $56,126.97 $52,142.18 $48,233.79 $44,402.31 $40,647.94 $36,970.58 $33,369.89 $29,845.32 $26,396.12 $23,021.43 $19,720.22 $16,491.39 $13,333.73 $10,245.98 $7,226.81 $4,274.86 $1,388.72 -$1,433.01 -$4,191.77 -$6,888.99 -$9,526.12 -$12,104.58 -$14,625.80 -$17,091.18

interest rate = 12% DWO

Tax

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

-$35,833.33 -$95,833.33 -$31,833.33 $6,566.67 $6,566.67 $35,366.67 $64,166.67 $64,166.67 $64,166.67 $114,166.67

-$14,333.33 -$38,333.33 -$12,733.33 $2,626.67 $2,626.67 $14,146.67 $25,666.67 $25,666.67 $25,666.67 $45,666.67 PW AT = FW AT = AW AT = IRR AT = ERR AT =

After-Tax Present Worth $250,000 $200,000 $150,000 $100,000 $50,000

-$50,000

MARR

25%

23%

21%

19%

17%

15%

13%

11%

-1%

-3%

-5%

Method 1

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR = 10% income tax rate = 40% BT&LCF PPMT IPMT -$500,000.00 -$500,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $124,166.67 $0.00 $60,000.00 $174,166.67 $500,000.00 $60,000.00

MARR -5% ATCF -4% $0.00 -3% $78,500.00 -2% $102,500.00 -1% $76,900.00 0% $61,540.00 1% $61,540.00 2% $50,020.00 3% $38,500.00 4% $38,500.00 5% $38,500.00 6% -$431,500.00 7% $210,012.58 8% $544,718.55 9% $34,178.58 10% n/a 11% n/a 12% 13% 14.332% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25%

PW -$37,403.49 $2,902.80 $37,621.80 $67,474.35 $93,085.96 $115,000.02 $133,689.06 $149,564.37 $162,984.28 $174,261.25 $183,667.98 $191,442.63 $197,793.40 $202,902.37 $206,928.90 $210,012.58 $212,275.70 $213,825.47 $214,755.93 $215,174.26 $215,078.78 $214,607.14 $213,790.45 $212,677.71 $211,311.95 $209,730.95 $207,967.89 $206,051.87 $204,008.43 $201,859.98 $199,626.15

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR = 10% income tax rate = 40% BT&LCF PPMT IPMT DWO -$500,000.00 -$500,000.00 $124,166.67 $0.00 $83,333.33 $100,000.00 $124,166.67 $0.00 $83,333.33 $160,000.00 $124,166.67 $0.00 $83,333.33 $96,000.00 $124,166.67 $0.00 $83,333.33 $57,600.00 $124,166.67 $0.00 $83,333.33 $57,600.00 $124,166.67 $0.00 $83,333.33 $28,800.00 $124,166.67 $0.00 $83,333.33 $0.00 $124,166.67 $0.00 $83,333.33 $0.00 $124,166.67 $0.00 $83,333.33 $0.00 $174,166.67 $500,000.00 $83,333.33 $0.00

-$59,166.66 -$119,166.66 -$55,166.66 -$16,766.66 -$16,766.66 $12,033.34 $40,833.34 $40,833.34 $40,833.34 $90,833.34

0 1 2 3 4 5 6 7 8 9 10

-$500,000.00 -$500,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $124,166.67 $50,000.00 $174,166.67 $50,000.00

$83,333.33 $100,000.00 $75,000.00 $160,000.00 $66,666.67 $96,000.00 $58,333.33 $57,600.00 $50,000.00 $57,600.00 $41,666.67 $28,800.00 $33,333.33 $0.00 $25,000.00 $0.00 $16,666.67 $0.00 $8,333.33 $0.00

-$59,166.66 -$110,833.33 -$38,500.00 $8,233.34 $16,566.67 $53,700.00 $90,833.34 $99,166.67 $107,500.00 $165,833.34

0 1 2 3 4 5 6 7 8 9 10

-$500,000.00 -$500,000.00 $124,166.67 $22,696.59 $124,166.67 $26,479.35 $124,166.67 $30,892.58 $124,166.67 $36,041.34 $124,166.67 $42,048.23 $124,166.67 $49,056.27 $124,166.67 $57,232.31 $124,166.67 $66,771.03 $124,166.67 $77,899.53 $174,166.67 $90,882.79

$83,333.33 $100,000.00 $79,550.57 $160,000.00 $75,137.34 $96,000.00 $69,988.58 $57,600.00 $63,981.69 $57,600.00 $56,973.65 $28,800.00 $48,797.61 $0.00 $39,258.89 $0.00 $28,130.39 $0.00 $15,147.13 $0.00

-$59,166.66 -$115,383.90 -$46,970.67 -$3,421.91 $2,584.98 $38,393.02 $75,369.06 $84,907.78 $96,036.28 $159,019.54

0 1 2

-$500,000.00 -$500,000.00 $124,166.67 $0.00 $124,166.67 $0.00

$0.00 $100,000.00 $0.00 $160,000.00

$24,166.67 -$35,833.33

3 4 5 6 7 8 9 10

$124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

$0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $500,000.00 $1,835,812.08

$96,000.00 $28,166.67 $57,600.00 $66,566.67 $57,600.00 $66,566.67 $28,800.00 $95,366.67 $0.00 $124,166.67 $0.00 $124,166.67 $0.00 $124,166.67 $0.00 -$1,661,645.41

interest rate = 16.667% Tax -$23,666.67 -$47,666.67 -$22,066.67 -$6,706.67 -$6,706.67 $4,813.33 $16,333.33 $16,333.33 $16,333.33 $36,333.33 PW = -$23,666.67 -$44,333.33 -$15,400.00 $3,293.33 $6,626.67 $21,480.00 $36,333.33 $39,666.67 $43,000.00 $66,333.33 PW = -$23,666.67 -$46,153.56 -$18,788.27 -$1,368.76 $1,033.99 $15,357.21 $30,147.62 $33,963.11 $38,414.51 $63,607.82 PW = $9,666.67 -$14,333.33

ATCF $0.00 $64,500.00 $88,500.00 $62,900.00 $47,540.00 $47,540.00 $36,020.00 $24,500.00 $24,500.00 $24,500.00 -$445,500.00 $123,988.64 $0.00 $14,500.00 $43,500.00 $22,900.00 $12,540.00 $17,540.00 $11,020.00 $4,500.00 $9,500.00 $14,500.00 $49,500.00 $123,988.64 $0.00 $41,803.42 $64,290.31 $36,925.02 $19,505.52 $17,102.76 $2,779.54 -$12,010.87 -$15,826.36 -$20,277.76 $4,528.94 $123,988.64 $0.00 $114,500.00 $138,500.00

P1-P4 $117,442.66 interest rate =

10.0000000000%

P2-P4 $117,442.66 interest rate =

12.4588137081%

P3-P4 $117,442.66 interest rate =

12.1230478963%

$11,266.67 $112,900.00 $26,626.67 $97,540.00 $26,626.67 $97,540.00 $38,146.67 $86,020.00 $49,666.67 $74,500.00 $49,666.67 $74,500.00 $49,666.67 $74,500.00 -$664,658.17 -$1,496,987.25 PW = $6,545.98

Plan 1

10% Interest Rate = 16.66667% EOY PPMT IPMT TI 0 -$100,000.00 1 $0.00 $16,666.67 -$16,666.67 2 $0.00 $16,666.67 -$16,666.67 3 $0.00 $16,666.67 -$16,666.67 4 $0.00 $16,666.67 -$16,666.67 5 $100,000.00 $16,666.67 -$16,666.67

Plan 2

0 1 2 3 4 5

Plan 3

0 1 2 3 4 5

Plan 4

0 1 2 3 4 5

Income Tax Rate = 40% ATCF $100,000.00 -$6,666.67 -$10,000.00 -$6,666.67 -$10,000.00 -$6,666.67 -$10,000.00 -$6,666.67 -$10,000.00 -$6,666.67 -$110,000.00 PW = $0.00 IRR = 10.000% -$100,000.00 $100,000.00 $20,000.00 $16,666.67 -$16,666.67 -$6,666.67 -$30,000.00 $20,000.00 $13,333.33 -$13,333.33 -$5,333.33 -$28,000.00 $20,000.00 $10,000.00 -$10,000.00 -$4,000.00 -$26,000.00 $20,000.00 $6,666.67 -$6,666.67 -$2,666.67 -$24,000.00 $20,000.00 $3,333.33 -$3,333.33 -$1,333.33 -$22,000.00 PW = $0.00 IRR = 10.000% $100,000.00 $100,000.00 $14,350.57 $16,666.67 -$16,666.67 -$6,666.67 -$24,350.57 $16,742.33 $14,274.90 -$14,274.90 -$5,709.96 -$25,307.27 $19,532.72 $11,484.52 -$11,484.52 -$4,593.81 -$26,423.43 $22,788.17 $8,229.06 -$8,229.06 -$3,291.63 -$27,725.61 $26,586.20 $4,431.03 -$4,431.03 -$1,772.41 -$29,244.82 PW = $0.00 IRR = 10.000% $100,000.00 $100,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $100,000.00 $116,139.40 -$116,139.40 -$46,455.76 -$169,683.64 PW = -$5,360.19 IRR = 11.155% T

P4-P3 -$5,360.19 interest rate = 13.534088021379% P4-P2 -$5,360.19 interest rate = 13.739282411356% P1-P4 $5,360.19 interest rate = 9.99999999955% P1-P2 -$2,692.73 interest rate = 16.66666666667%

Interest Rate 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

After-Tax Present Worth P1 P2 P3 P4 $37,907.87 $24,184.26 $24,184.26 $37,907.87 $35,633.40 $22,733.21 $22,867.80 $36,007.47 $33,358.92 $21,282.15 $21,532.80 $34,030.31 $31,084.45 $19,831.10 $20,179.54 $31,974.07 $28,809.98 $18,380.04 $18,808.29 $29,836.40 $26,535.51 $16,928.99 $17,419.33 $27,614.92 $24,261.04 $15,477.93 $16,012.94 $25,307.18 $21,986.56 $14,026.87 $14,589.39 $22,910.69 $19,712.09 $12,575.82 $13,148.98 $20,422.92 $17,437.62 $11,124.76 $11,691.97 $17,841.28 $15,163.15 $9,673.71 $10,218.64 $15,163.15 $12,888.68 $8,222.65 $8,729.28 $12,385.83 $10,614.20 $6,771.59 $7,224.16 $9,506.62 $8,339.73 $5,320.54 $5,703.56 $6,522.71 $6,065.26 $3,869.48 $4,167.75 $3,431.29 $3,790.79 $2,418.43 $2,617.01 $220.47 $1,516.31 $967.37 $1,051.61 -$3,085.67 -$758.16 -$483.69 -$528.18 -$6,517.12 -$3,032.63 -$1,934.74 -$2,122.10 -$10,067.91 -$5,307.10 -$3,385.80 -$3,729.87 -$13,741.13 -$7,581.57 -$4,836.85 -$5,351.24 -$17,539.91

P1 1 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 3 3 3 3

Rank Ordered Preference P2 P3 3 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 4 3 3 2 3 2 3 2 1 2 1 2 1 2 1 2

P4 1 1 1 1 1 1 1 1 1 1 1 2 2 2 4 4 4 4 4 4 4

Borrower's After-Tax Present Worth $40,000

Present Worth of Borrower's Cash Flows

MARR =

Plan 1

Plan 2

Plan 3

Plan 4

$30,000

$20,000

$10,000

Plan 2 is best $0

-$10,000

Plan 4 is best

Plan 1 is best

-$20,000

Interest Rate Paid by Borrower

$40,000

$30,000

ATMARR = 10% $20,000

$10,000

ATMARR/(1 - itr) = 16.667%

$0 0%

10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

Plan 4 is best -$10,000

Plan 1 is best

Interest Rate on Borrowed Capital

-$20,000

Plan 1

Plan 2

Plan 3

Plan 4

Plan 2 is best if borrowing is required

Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

BTLCF -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87 -$2,338.87

IPMT $2,039.04 $2,037.37 $2,035.69 $2,034.00 $2,032.29 $2,030.58 $2,028.86 $2,027.13 $2,025.39 $2,023.64 $2,021.88 $2,020.11 $2,018.33 $2,016.53 $2,014.73 $2,012.92 $2,011.09 $2,009.26 $2,007.41 $2,005.56 $2,003.69 $2,001.81 $1,999.93 $1,998.03 $1,996.12 $1,994.19 $1,992.26 $1,990.32 $1,988.36 $1,986.39

TI -$2,039.04 -$2,037.37 -$2,035.69 -$2,034.00 -$2,032.29 -$2,030.58 -$2,028.86 -$2,027.13 -$2,025.39 -$2,023.64 -$2,021.88 -$2,020.11 -$2,018.33 -$2,016.53 -$2,014.73 -$2,012.92 -$2,011.09 -$2,009.26 -$2,007.41 -$2,005.56 -$2,003.69 -$2,001.81 -$1,999.93 -$1,998.03 -$1,996.12 -$1,994.19 -$1,992.26 -$1,990.32 -$1,988.36 -$1,986.39

T -$713.66 -$713.08 -$712.49 -$711.90 -$711.30 -$710.70 -$710.10 -$709.50 -$708.89 -$708.27 -$707.66 -$707.04 -$706.41 -$705.79 -$705.16 -$704.52 -$703.88 -$703.24 -$702.60 -$701.95 -$701.29 -$700.64 -$699.97 -$699.31 -$698.64 -$697.97 -$697.29 -$696.61 -$695.93 -$695.24

ATLCF -$1,625.20 -$1,625.79 -$1,626.38 -$1,626.97 -$1,627.56 -$1,628.16 -$1,628.77 -$1,629.37 -$1,629.98 -$1,630.59 -$1,631.21 -$1,631.83 -$1,632.45 -$1,633.08 -$1,633.71 -$1,634.35 -$1,634.98 -$1,635.63 -$1,636.27 -$1,636.92 -$1,637.58 -$1,638.23 -$1,638.89 -$1,639.56 -$1,640.23 -$1,640.90 -$1,641.58 -$1,642.26 -$1,642.94 -$1,643.63

Month 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 BTPW =

IPMT $1,984.42 $1,982.43 $1,980.42 $1,978.41 $1,976.39 $1,974.35 $1,972.30 $1,970.24 $1,968.17 $1,966.08 $1,963.99 $1,961.88 $1,959.75 $1,957.62 $1,955.47 $1,953.32 $1,951.14 $1,948.96 $1,946.76 $1,944.55 $1,942.33 $1,940.10 $1,937.85 $1,935.59 $1,933.31 $1,931.02 $1,928.72 $1,926.41 $1,924.08 $1,921.74

TI -$1,984.42 -$1,982.43 -$1,980.42 -$1,978.41 -$1,976.39 -$1,974.35 -$1,972.30 -$1,970.24 -$1,968.17 -$1,966.08 -$1,963.99 -$1,961.88 -$1,959.75 -$1,957.62 -$1,955.47 -$1,953.32 -$1,951.14 -$1,948.96 -$1,946.76 -$1,944.55 -$1,942.33 -$1,940.10 -$1,937.85 -$1,935.59 -$1,933.31 -$1,931.02 -$1,928.72 -$1,926.41 -$1,924.08 -$1,921.74

T ATLCF -$694.55 -$1,644.32 -$693.85 -$1,645.02 -$693.15 -$1,645.72 -$692.44 -$1,646.42 -$691.74 -$1,647.13 -$691.02 -$1,647.85 -$690.31 -$1,648.56 -$689.58 -$1,649.28 -$688.86 -$1,650.01 -$688.13 -$1,650.74 -$687.39 -$1,651.47 -$686.66 -$1,652.21 -$685.91 -$1,652.95 -$685.17 -$1,653.70 -$684.42 -$1,654.45 -$683.66 -$1,655.21 -$682.90 -$1,655.97 -$682.14 -$1,656.73 -$681.37 -$1,657.50 -$680.59 -$1,658.27 -$679.82 -$1,659.05 -$679.03 -$1,659.83 -$678.25 -$1,660.62 -$677.45 -$1,661.41 -$676.66 -$1,662.21 -$675.86 -$1,663.01 -$675.05 -$1,663.82 -$674.24 -$1,664.63 -$673.43 -$1,665.44 -$672.61 -$332,585.39 ATPW = -$323,302.93

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF DWO TI T ITC ATCF -$500,000.00 -$500,000.00 $124,166.67 $95,000.00 $29,166.67 $11,666.67 $50,000.00 $162,500.00 $124,166.67 $152,000.00 -$27,833.33 -$11,133.33 $0.00 $135,300.00 $124,166.67 $91,200.00 $32,966.67 $13,186.67 $0.00 $110,980.00 $124,166.67 $54,720.00 $69,446.67 $27,778.67 $0.00 $96,388.00 $124,166.67 $54,720.00 $69,446.67 $27,778.67 $0.00 $96,388.00 $124,166.67 $27,360.00 $96,806.67 $38,722.67 $0.00 $85,444.00 $124,166.67 $0.00 $124,166.67 $49,666.67 $0.00 $74,500.00 $124,166.67 $0.00 $124,166.67 $49,666.67 $0.00 $74,500.00 $124,166.67 $0.00 $124,166.67 $49,666.67 $0.00 $74,500.00 $174,166.67 $0.00 $174,166.67 $69,666.67 $0.00 $104,500.00 PW = $161,710.59 FW = $419,435.61 AW = $26,317.65 =0.95*500000*0.32 IRR = 18.39% ERR = 13.13%

EOY 0 1 2 3 4 5 6 7 8 9 10

Section 179 Deduction

BTCF DWO TI T ATCF -$1,500,000.00 -$1,500,000.00 $372,500.00 $500,000.00 $200,000.00 -$327,500.00 -$131,000.00 $503,500.00 $372,500.00 $0.00 $320,000.00 $52,500.00 $21,000.00 $351,500.00 $372,500.00 $0.00 $192,000.00 $180,500.00 $72,200.00 $300,300.00 $372,500.00 $0.00 $115,200.00 $257,300.00 $102,920.00 $269,580.00 $372,500.00 $0.00 $115,200.00 $257,300.00 $102,920.00 $269,580.00 $372,500.00 $0.00 $57,600.00 $314,900.00 $125,960.00 $246,540.00 $372,500.00 $0.00 $0.00 $372,500.00 $149,000.00 $223,500.00 $372,500.00 $0.00 $0.00 $372,500.00 $149,000.00 $223,500.00 $372,500.00 $0.00 $0.00 $372,500.00 $149,000.00 $223,500.00 $522,500.00 $0.00 $0.00 $522,500.00 $209,000.00 $313,500.00 PW = $399,131.99 FW = $1,035,245.60 AW = =(1500000-500000)*0.32 $64,956.89 IRR = 16.90% ERR = 12.63%

Bonus Depreciation = 100% EOY BTCF DWO TI T ATCF 0 -$500,000.00 -$500,000.00 1 $124,166.67 $500,000.00 -$375,833.33 -$150,333.33 $274,500.00 2 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 3 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 4 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 5 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 6 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 7 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 8 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 9 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 10 $174,166.67 $0.00 $174,166.67 $69,666.67 $104,500.00 PW = $151,154.74 Bonus Depreciation = 50% EOY BTCF DWO TI T ATCF 0 -$500,000.00 -$500,000.00 1 $124,166.67 $300,000.00 -$175,833.33 -$70,333.33 $194,500.00 2 $124,166.67 $80,000.00 $44,166.67 $17,666.67 $106,500.00 3 $124,166.67 $48,000.00 $76,166.67 $30,466.67 $93,700.00 4 $124,166.67 $28,800.00 $95,366.67 $38,146.67 $86,020.00 5 $124,166.67 $28,800.00 $95,366.67 $38,146.67 $86,020.00 6 $124,166.67 $14,400.00 $109,766.67 $43,906.67 $80,260.00 7 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 8 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 9 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00 10 $174,166.67 $0.00 $174,166.67 $69,666.67 $104,500.00 PW = $137,571.69

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF(A) -$300,000.00 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67 $71,666.67

DWO(A) $42,870.00 $73,470.00 $52,470.00 $37,470.00 $26,790.00 $26,760.00 $26,790.00 $13,380.00 $0.00 $0.00 $0.00

TI(A) -$42,870.00 -$1,803.33 $19,196.67 $34,196.67 $44,876.67 $44,906.67 $44,876.67 $58,286.67 $71,666.67 $71,666.67 $71,666.67

EOY 0 1 2 3 4 5 6 7 8 9 10

BTCF(B) -$450,000.00 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33 $103,333.33

DWO(B) $64,305.00 $110,205.00 $78,705.00 $56,205.00 $40,185.00 $40,140.00 $40,185.00 $20,070.00 $0.00 $0.00 $0.00

TI(B) -$64,305.00 -$6,871.67 $24,628.33 $47,128.33 $63,148.33 $63,193.33 $63,148.33 $83,263.33 $103,333.33 $103,333.33 $103,333.33

T(A) ATCF(A) -$17,148.00 -$282,852.00 -$721.33 $72,388.00 $7,678.67 $63,988.00 $13,678.67 $57,988.00 $17,950.67 $53,716.00 $17,962.67 $53,704.00 $17,950.67 $53,716.00 $23,314.67 $48,352.00 $28,666.67 $43,000.00 $28,666.67 $43,000.00 $28,666.67 $43,000.00 PW(A) = $59,447.76 T(B) ATCF(B) -$25,722.00 -$424,278.00 -$2,748.67 $106,082.00 $9,851.33 $93,482.00 $18,851.33 $84,482.00 $25,259.33 $78,074.00 $25,277.33 $78,056.00 $25,259.33 $78,074.00 $33,305.33 $70,028.00 $41,333.33 $62,000.00 $41,333.33 $62,000.00 $41,333.33 $62,000.00 PW(B) = $73,810.19

$14,362.43

EOY CF(1) CF(2) CF(2) - CF(1) 0 $0.00 -$450,000.00 -$450,000.00 1 -$120,000.00 -$10,000.00 $110,000.00 2 -$125,000.00 -$15,000.00 $110,000.00 3 -$130,000.00 -$20,000.00 $110,000.00 4 -$135,000.00 -$25,000.00 $110,000.00 5 -$140,000.00 $170,000.00 $310,000.00 BTEUAC(2-1) = $889.06

EOY (t )

O&M 1,t

O&M 2,t

-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

--$4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000

--------$36,000 --30,000 $1,000 24,600 2,000 19,800 3,000 15,600 4,000 12,000 5,000 9,000 6,000 6,600 7,000 4,800 8,000 3,600 9,000 3,000

S 2,t

EOY CF(1) CF(2) CF(2) - CF(1) 0 $0.00 -$27,000.00 -$27,000.00 1 -$7,000.00 $0.00 $7,000.00 2 -$8,000.00 -$1,000.00 $7,000.00 3 -$9,000.00 -$2,000.00 $7,000.00 4 -$10,000.00 -$3,000.00 $7,000.00 5 -$9,000.00 $8,000.00 $17,000.00

EOY CF(1) 0 $0.00 1 -$7,000.00 2 -$8,000.00 3 -$9,000.00 4 -$10,000.00 5 -$40,000.00 6 $0.00 7 -$1,000.00 8 -$2,000.00 9 -$3,000.00 10 $11,000.00

CF(2) -$27,000.00 $0.00 -$1,000.00 -$2,000.00 -$3,000.00 -$4,000.00 -$5,000.00 -$6,000.00 -$7,000.00 -$8,000.00 -$6,000.00 =-4000+15000

=-11000-31000+2000 $8,532.34

$8,615.25

$82.90

EOY 0 1 2 3 4 5

CF(1) CF(2) CF(3) CF(4) $0.00 -$26,000.00 -$28,000.00 $1,500.00 -$7,000.00 $0.00 -$500.00 -$7,500.00 -$8,000.00 -$1,000.00 -$1,000.00 -$8,300.00 -$9,000.00 -$2,000.00 -$1,500.00 -$9,100.00 =-7500-1600 -$10,000.00 -$3,000.00 -$2,000.00 -$9,900.00 -$9,000.00 $8,000.00 $10,500.00 -$3,200.00 =-36000+10000

$8,426.18

$7,699.23

=-2500+13000 =-40000+12000

$7,786.14

$7,318.41

EOY BTCF(1) 0 $0.00 1 -$120,000.00 2 -$125,000.00 3 -$130,000.00 4 -$135,000.00 5 -$140,000.00

DW(1) TI(1) T(1) $0.00 $0.00 $0.00 $0.00 -$120,000.00 -$48,000.00 $0.00 -$125,000.00 -$50,000.00 $0.00 -$130,000.00 -$52,000.00 $0.00 -$135,000.00 -$54,000.00 $0.00 -$140,000.00 -$56,000.00 ATEUAC(1) =

ATCF(1) $0.00 -$72,000.00 -$75,000.00 -$78,000.00 -$81,000.00 -$84,000.00 $77,430.38

EOY BTCF(2) DW(2) TI(2) T(2) ATCF(2) 0 -$450,000.00 $0.00 $0.00 $0.00 -$450,000.00 1 -$10,000.00 $100,000.00 -$60,000.00 -$24,000.00 $14,000.00 2 -$15,000.00 $160,000.00 -$175,000.00 -$70,000.00 $55,000.00 3 -$20,000.00 $96,000.00 -$116,000.00 -$46,400.00 $26,400.00 4 -$25,000.00 $57,600.00 -$82,600.00 -$33,040.00 $8,040.00 5 $170,000.00 $28,800.00 $83,600.00 $33,440.00 $136,560.00 ATEUAC(2) = $74,311.49 =-10000-100000+50000 =-170000-28800-57600

-$3,118.88

EOY 0 1 2 3 4 5

BTCF(1) $0.00 -$7,000.00 -$8,000.00 -$9,000.00 -$10,000.00 -$9,000.00

DWO(1) $0.00 $2,223.00 $0.00 $0.00 $0.00 $0.00

=-11000+2000 =-36000+9000 EOY 0 1 2 3 4 5

BTCF(2) -$27,000.00 $0.00 -$1,000.00 -$2,000.00 -$3,000.00 $8,000.00

TI(1) $0.00 -$9,223.00 -$8,000.00 -$9,000.00 -$10,000.00 -$9,000.00

T(1) $0.00 -$3,689.20 -$3,200.00 -$3,600.00 -$4,000.00 -$3,600.00 EUAC(1) = =2223.00+11998.80

ATCF(1) $0.00 -$3,310.80 -$4,800.00 -$5,400.00 -$6,000.00 -$5,400.00 $4,886.68

DWO(2) $0.00 $14,221.80 $16,002.00 $5,331.60 $2,667.60 $0.00

TI(2) $0.00 -$5,221.80 -$17,002.00 -$7,331.60 -$5,667.60 $8,000.00

T(2) $0.00 -$2,088.72 -$6,800.80 -$2,932.64 -$2,267.04 $3,200.00 EUAC(2) =

ATCF(2) -$27,000.00 $2,088.72 $5,800.80 $932.64 -$732.96 $4,800.00 $4,339.91

DWO(2-1) $0.00 $11,998.80 $16,002.00 $5,331.60 $2,667.60 $0.00

TI(2-1) $0.00 $4,001.20 -$9,002.00 $1,668.40 $4,332.40 $17,000.00

T(2-1) $0.00 $1,600.48 -$3,600.80 $667.36 $1,732.96 $6,800.00 EUAC(2-1) =

ATCF(2-1) -$27,000.00 $5,399.52 $10,600.80 $6,332.64 $5,267.04 $10,200.00 -$546.77

=-4000+12000 EOY 0 1 2 3 4 5

BTCF(2-1) -$27,000.00 $7,000.00 $7,000.00 $7,000.00 $7,000.00 $17,000.00

EOY 0 1 2 3 4 5

BTCF(1) DWO(1) TI(1) T(1) ATCF(1) $0.00 $0.00 $0.00 $0.00 $0.00 -$7,000.00 $2,223.00 -$9,223.00 -$3,689.20 -$3,310.80 -$8,000.00 $0.00 -$8,000.00 -$3,200.00 -$4,800.00 -$9,000.00 $0.00 -$9,000.00 -$3,600.00 -$5,400.00 -$10,000.00 $0.00 -$10,000.00 -$4,000.00 -$6,000.00 -$9,000.00 $0.00 -$9,000.00 -$3,600.00 -$5,400.00 =-11000+2000 EUAC(1) = $4,886.68 EOY BTCF(2) DWO(2) TI(2) T(2) ATCF(2) 0 -$27,000.00 $0.00 $0.00 $0.00 -$27,000.00 1 $0.00 $11,222.10 -$11,222.10 -$4,488.84 $4,488.84 2 -$1,000.00 $12,001.50 -$13,001.50 -$5,200.60 $4,200.60 3 -$2,000.00 $3,998.70 -$5,998.70 -$2,399.48 $399.48 4 -$3,000.00 $2,000.70 -$5,000.70 -$2,000.28 -$999.72 5 $8,000.00 $0.00 $8,000.00 $3,200.00 $4,800.00 =-4000+12000 EUAC(2) = $4,274.50 $612.17

EOY BTCF(1) DWO(1) TI(1) T(1) ATCF(1) 0 $0.00 $0.00 $0.00 $0.00 $0.00 1 -$7,000.00 $2,223.00 -$9,223.00 -$3,689.20 -$3,310.80 2 -$8,000.00 $0.00 -$8,000.00 -$3,200.00 -$4,800.00 3 -$9,000.00 $0.00 -$9,000.00 -$3,600.00 -$5,400.00 4 -$10,000.00 $0.00 -$10,000.00 -$4,000.00 -$6,000.00 5 -$40,000.00 $0.00 -$40,000.00 -$16,000.00 -$24,000.00 6 $0.00 $10,332.30 -$10,332.30 -$4,132.92 $4,132.92 7 $1,000.00 $13,779.50 -$12,779.50 -$5,111.80 $6,111.80 8 -$2,000.00 $4,591.10 -$6,591.10 -$2,636.44 $636.44 9 -$3,000.00 $2,297.10 -$5,297.10 -$2,118.84 -$881.16 10 $11,000.00 $0.00 $11,000.00 $4,400.00 $6,600.00 EUAC(1) = $3,519.49 =-11000-31000+2000 =-7000-2223 =-14221.80+9000 EOY BTCF(2) DWO(2) TI(2) 0 -$27,000.00 $0.00 $0.00 1 $0.00 $14,221.80 -$5,221.80 2 -$1,000.00 $16,002.00 -$17,002.00 3 -$2,000.00 $5,331.60 -$7,331.60 4 -$3,000.00 $2,667.60 -$5,667.60 5 -$4,000.00 $0.00 -$4,000.00 6 -$5,000.00 $0.00 -$5,000.00 7 -$6,000.00 $0.00 -$6,000.00 8 -$7,000.00 $0.00 -$7,000.00 9 -$8,000.00 $0.00 -$8,000.00 10 -$6,000.00 $0.00 -$6,000.00

T(2) ATCF(2) $0.00 -$27,000.00 -$2,088.72 $2,088.72 -$6,800.80 $5,800.80 -$2,932.64 $932.64 -$2,267.04 -$732.96 -$1,600.00 -$2,400.00 -$2,000.00 -$3,000.00 -$2,400.00 -$3,600.00 -$2,800.00 -$4,200.00 -$3,200.00 -$4,800.00 -$2,400.00 -$3,600.00 EUAC(2) = $4,854.88

$1,335.38

EOY BTCF(1) 0 $0.00 1 -$7,000.00 2 -$8,000.00 3 -$9,000.00 4 -$10,000.00 5 -$9,000.00

DWO(1) TI(1) T(1) $0.00 $0.00 $0.00 $2,223.00 -$9,223.00 -$3,689.20 $0.00 -$8,000.00 -$3,200.00 $0.00 -$9,000.00 -$3,600.00 $0.00 -$10,000.00 -$4,000.00 $0.00 -$9,000.00 -$3,600.00 EUAC(1) =

ATCF(1) $0.00 -$3,310.80 -$4,800.00 -$5,400.00 -$6,000.00 -$5,400.00 $4,886.68

EOY BTCF(2) DWO(2) TI(2) T(2) ATCF(2) =35000*0.3333+2223 0 -$26,000.00 $0.00 $0.00 $0.00 -$26,000.00 1 $0.00 $13,888.50 -$4,888.50 -$1,955.40 $1,955.40 2 -$1,000.00 $15,557.50 -$16,557.50 -$6,623.00 $5,623.00 =-13888.50+9000 3 -$2,000.00 $5,183.50 -$7,183.50 -$2,873.40 $873.40 4 -$3,000.00 $2,593.50 -$5,593.50 -$2,237.40 -$762.60 5 $8,000.00 $0.00 $8,000.00 $3,200.00 $4,800.00 EUAC(2) = $4,169.90

$716.78

EOY BTCF(3) DWO(3) TI(3) T(3) ATCF(3) =37000*0.3333+2223 0 -$28,000.00 $0.00 $0.00 $0.00 -$28,000.00 1 -$500.00 $14,555.10 -$6,055.10 -$2,422.04 $1,922.04 2 -$1,000.00 $16,446.50 -$17,446.50 -$6,978.60 $5,978.60 =-500-14555.10+9000 3 -$1,500.00 $5,479.70 -$6,979.70 -$2,791.88 $1,291.88 4 -$2,000.00 $2,741.70 -$4,741.70 -$1,896.68 -$103.32 5 $10,500.00 $0.00 $10,500.00 $4,200.00 $6,300.00 EUAC(3) = $4,161.21

$725.47

EOY 0 1 2 3 4 5

BTCF(4) $1,500.00 -$7,500.00 -$8,300.00 -$9,100.00 -$9,900.00 -$3,200.00

DWO(4) $0.00 $2,223.00 $0.00 $0.00 $0.00 $0.00

TI(4) T(4) -$7,500.00 -$3,000.00 -$723.00 -$289.20 -$8,300.00 -$3,320.00 -$9,100.00 -$3,640.00 -$9,900.00 -$3,960.00 -$3,200.00 -$1,280.00 EUAC(4) = =30000*0.0741

ATCF(4) $4,500.00 -$7,210.80 -$4,980.00 -$5,460.00 -$5,940.00 -$1,920.00 $4,108.08

=-7500+9000

=-7500+9000-2223

$778.59

EOY CF(1) CF(2) CF(2) - CF(1) 0 -$50,000.00 -$500,000.00 -$450,000.00 1 -$120,000.00 -$10,000.00 $110,000.00 2 -$125,000.00 -$15,000.00 $110,000.00 3 -$130,000.00 -$20,000.00 $110,000.00 4 -$135,000.00 -$25,000.00 $110,000.00 5 -$140,000.00 $170,000.00 $310,000.00 BTEUAC(2-1) = $889.06

EOY CF(1) CF(2) CF(2) - CF(1) 0 -$9,000.00 -$36,000.00 -$27,000.00 1 -$7,000.00 $0.00 $7,000.00 2 -$8,000.00 -$1,000.00 $7,000.00 3 -$9,000.00 -$2,000.00 $7,000.00 4 -$10,000.00 -$3,000.00 $7,000.00 5 -$9,000.00 $8,000.00 $17,000.00 BTEUAC = $11,111.02 $10,682.39

-$428.64

EOY CF(1) CF(2) CF(3) 0 -$9,000.00 -$35,000.00 -$37,000.00 1 -$7,000.00 $0.00 -$500.00 2 -$8,000.00 -$1,000.00 -$1,000.00 3 -$9,000.00 -$2,000.00 -$1,500.00 4 -$10,000.00 -$3,000.00 -$2,000.00 5 -$9,000.00 $8,000.00 $10,500.00

CF(4) -$7,500.00 -$7,500.00 -$8,300.00 -$9,100.00 -$9,900.00 -$3,200.00

$11,111.02 $10,384.07 $10,470.98 $10,003.25

EOY BTCF(1) 0 -$50,000.00 1 -$120,000.00 2 -$125,000.00 3 -$130,000.00 4 -$135,000.00 5 -$140,000.00

DW(1) TI(1) T(1) $0.00 $0.00 $0.00 $0.00 -$170,000.00 -$68,000.00 $0.00 -$125,000.00 -$50,000.00 $0.00 -$130,000.00 -$52,000.00 $0.00 -$135,000.00 -$54,000.00 $0.00 -$140,000.00 -$56,000.00 ATEUAC(1) =

ATCF(1) -$50,000.00 -$52,000.00 -$75,000.00 -$78,000.00 -$81,000.00 -$84,000.00 $85,823.93

EOY BTCF(2) DW(2) TI(2) T(2) ATCF(2) 0 -$500,000.00 $0.00 $0.00 $0.00 -$500,000.00 1 -$10,000.00 $100,000.00 -$110,000.00 -$44,000.00 $34,000.00 2 -$15,000.00 $160,000.00 -$175,000.00 -$70,000.00 $55,000.00 3 -$20,000.00 $96,000.00 -$116,000.00 -$46,400.00 $26,400.00 4 -$25,000.00 $57,600.00 -$82,600.00 -$33,040.00 $8,040.00 5 $170,000.00 $28,800.00 $83,600.00 $33,440.00 $136,560.00 ATEUAC(2) = $82,705.05

-$3,118.88

EOY BTCF(1) 0 -$9,000.00 1 -$7,000.00 2 -$8,000.00 3 -$9,000.00 4 -$10,000.00 5 -$9,000.00

DWO(1) TI(1) T(1) $0.00 $0.00 $0.00 $2,223.00 -$18,223.00 -$7,289.20 $0.00 -$8,000.00 -$3,200.00 $0.00 -$9,000.00 -$3,600.00 $0.00 -$10,000.00 -$4,000.00 $0.00 -$9,000.00 -$3,600.00 EUAC(1) = =-7000-2223-9000

ATCF(1) -$9,000.00 $289.20 -$4,800.00 -$5,400.00 -$6,000.00 -$5,400.00 $6,351.40

EOY BTCF(2) DWO(2) TI(2) T(2) ATCF(2) 0 -$36,000.00 $0.00 $0.00 $0.00 -$36,000.00 1 $0.00 $14,221.80 -$14,221.80 -$5,688.72 $5,688.72 2 -$1,000.00 $16,002.00 -$17,002.00 -$6,800.80 $5,800.80 3 -$2,000.00 $5,331.60 -$7,331.60 -$2,932.64 $932.64 4 -$3,000.00 $2,667.60 -$5,667.60 -$2,267.04 -$732.96 5 $8,000.00 $0.00 $8,000.00 $3,200.00 $4,800.00 EUAC(2) = $5,804.63 =2223+11998.80 $546.77

EOY BTCF(1) DWO(1) TI(1) T(1) ATCF(1) 0 -$9,000.00 $0.00 $0.00 $0.00 -$9,000.00 1 -$7,000.00 $2,223.00 -$18,223.00 -$7,289.20 $289.20 2 -$8,000.00 $0.00 -$8,000.00 -$3,200.00 -$4,800.00 3 -$9,000.00 $0.00 -$9,000.00 -$3,600.00 -$5,400.00 4 -$10,000.00 $0.00 -$10,000.00 -$4,000.00 -$6,000.00 5 -$40,000.00 $0.00 -$40,000.00 -$16,000.00 -$24,000.00 6 $0.00 $10,332.30 -$10,332.30 -$4,132.92 $4,132.92 7 $1,000.00 $13,779.50 -$12,779.50 -$5,111.80 $6,111.80 8 -$2,000.00 $4,591.10 -$6,591.10 -$2,636.44 $636.44 9 -$3,000.00 $2,297.10 -$5,297.10 -$2,118.84 -$881.16 10 $11,000.00 $0.00 $11,000.00 $4,400.00 $6,600.00 EUAC(1) = $4,407.24 =-7000-2223-9000 EOY BTCF(2) DWO(2) TI(2) 0 -$36,000.00 $0.00 $0.00 1 $0.00 $14,221.80 -$14,221.80 2 -$1,000.00 $16,002.00 -$17,002.00 3 -$2,000.00 $5,331.60 -$7,331.60 4 -$3,000.00 $2,667.60 -$5,667.60 5 -$4,000.00 $0.00 -$4,000.00 6 -$5,000.00 $0.00 -$5,000.00 7 -$6,000.00 $0.00 -$6,000.00 8 -$7,000.00 $0.00 -$7,000.00 9 -$8,000.00 $0.00 -$8,000.00 10 -$6,000.00 $0.00 -$6,000.00

T(2) ATCF(2) $0.00 -$36,000.00 -$5,688.72 $5,688.72 -$6,800.80 $5,800.80 -$2,932.64 $932.64 -$2,267.04 -$732.96 -$1,600.00 -$2,400.00 -$2,000.00 -$3,000.00 -$2,400.00 -$3,600.00 -$2,800.00 -$4,200.00 -$3,200.00 -$4,800.00 -$2,400.00 -$3,600.00 EUAC(2) = $5,742.62

=0-14221.80 $1,335.38

EOY BTCF(1) 0 -$9,000.00 1 -$7,000.00 2 -$8,000.00 3 -$9,000.00 4 -$10,000.00 5 -$9,000.00

DWO(1) TI(1) $0.00 $0.00 $2,223.00 -$18,223.00 $0.00 -$8,000.00 $0.00 -$9,000.00 $0.00 -$10,000.00 $0.00 -$9,000.00

T(1) $0.00 -$7,289.20 -$3,200.00 -$3,600.00 -$4,000.00 -$3,600.00 EUAC(1) =

ATCF(1) -$9,000.00 $289.20 -$4,800.00 -$5,400.00 -$6,000.00 -$5,400.00 $6,351.40

=-7000-2223-9000

EOY BTCF(2) DWO(2) TI(2) T(2) ATCF(2) =35000*0.3333+2223 0 -$35,000.00 $0.00 $0.00 $0.00 -$35,000.00 1 $0.00 $13,888.50 -$13,888.50 -$5,555.40 $5,555.40 2 -$1,000.00 $15,557.50 -$16,557.50 -$6,623.00 $5,623.00 =-13888.50+0 3 -$2,000.00 $5,183.50 -$7,183.50 -$2,873.40 $873.40 4 -$3,000.00 $2,593.50 -$5,593.50 -$2,237.40 -$762.60 5 $8,000.00 $0.00 $8,000.00 $3,200.00 $4,800.00 EUAC(2) = $5,634.61

$716.78

EOY BTCF(3) DWO(3) TI(3) T(3) ATCF(3) =37000*0.3333+2223 0 -$37,000.00 $0.00 $0.00 $0.00 -$37,000.00 1 -$500.00 $14,555.10 -$15,055.10 -$6,022.04 $5,522.04 2 -$1,000.00 $16,446.50 -$17,446.50 -$6,978.60 $5,978.60 =-500-14555.10 3 -$1,500.00 $5,479.70 -$6,979.70 -$2,791.88 $1,291.88 4 -$2,000.00 $2,741.70 -$4,741.70 -$1,896.68 -$103.32 5 $10,500.00 $0.00 $10,500.00 $4,200.00 $6,300.00 EUAC(3) = $5,625.93

$725.47

EOY 0 1 2 3 4 5

BTCF(4) -$7,500.00 -$7,500.00 -$8,300.00 -$9,100.00 -$9,900.00 -$3,200.00

DWO(4) $0.00 $2,223.00 $0.00 $0.00 $0.00 $0.00

TI(4) -$7,500.00 -$9,723.00 -$8,300.00 -$9,100.00 -$9,900.00 -$3,200.00

T(4) -$3,000.00 -$3,889.20 -$3,320.00 -$3,640.00 -$3,960.00 -$1,280.00 EUAC(4) =

ATCF(4) -$4,500.00 -$3,610.80 -$4,980.00 -$5,460.00 -$5,940.00 -$1,920.00 $5,572.80

=-7500-2223

$778.59

EOY BTCF(1) 0 $0.00 1 -$7,000.00 2 -$8,000.00 3 -$9,000.00 4 -$10,000.00 5 -$9,000.00

DWO(1) TI(1) T(1) ATCF(1) $0.00 $0.00 $0.00 $0.00 $2,223.00 -$9,223.00 -$3,689.20 -$3,310.80 $0.00 -$8,000.00 -$3,200.00 -$4,800.00 $0.00 -$9,000.00 -$3,600.00 -$5,400.00 $0.00 -$10,000.00 -$4,000.00 -$6,000.00 $0.00 -$9,000.00 -$3,600.00 -$5,400.00 EUAC(1) = $4,886.68 Section 1031 Deferral EOY BTCF(2) DWO(2) TI(2) T(2) ATCF(2) 0 -$26,000.00 $0.00 $0.00 $0.00 -$26,000.00 1 $0.00 $14,221.80 -$13,321.80 -$5,328.72 $4,000.00 $9,328.72 2 -$1,000.00 $16,002.00 -$17,002.00 -$6,800.80 $5,800.80 3 -$2,000.00 $5,331.60 -$7,331.60 -$2,932.64 $932.64 4 -$3,000.00 $2,667.60 -$5,667.60 -$2,267.04 -$732.96 5 $8,000.00 $0.00 $8,000.00 $3,200.00 $4,800.00 EUAC(2) = $2,375.16 Section 1031 Deferral EOY BTCF(3) DWO(3) TI(3) T(3) ATCF(3) 0 -$28,000.00 $0.00 $0.00 $0.00 -$28,000.00 1 -$500.00 $13,332.00 -$13,832.00 -$5,532.80 $4,800.00 $9,832.80 2 -$1,000.00 $17,780.00 -$18,780.00 -$7,512.00 $6,512.00 3 -$1,500.00 $5,924.00 -$7,424.00 -$2,969.60 $1,469.60 4 -$2,000.00 $2,964.00 -$4,964.00 -$1,985.60 -$14.40 5 $10,500.00 $0.00 $10,500.00 $4,200.00 $6,300.00 EUAC(3) = $2,128.44 Section 1031 Deferral EOY BTCF(4) DWO(4) TI(4) T(4) ATCF(4) 0 $1,500.00 $0.00 -$7,500.00 -$3,000.00 $4,500.00 1 -$7,500.00 $0.00 -$7,500.00 -$3,000.00 -$4,500.00 2 -$8,300.00 $0.00 -$8,300.00 -$3,320.00 -$4,980.00 3 -$9,100.00 $0.00 -$9,100.00 -$3,640.00 -$5,460.00 4 -$9,900.00 $0.00 -$9,900.00 -$3,960.00 -$5,940.00 5 -$3,200.00 $0.00 -$3,200.00 -$1,280.00 -$1,920.00 EUAC(4) = $3,468.70

$2,511.52

$2,758.23

$1,417.97

Life CR O&M EUAO&MC EUAC 1 $11,500.00 $2,500.00 $2,500.00 $14,000.00 2 $6,151.16 $3,000.00 $2,732.56 $8,883.72 3 $4,379.77 $3,600.00 $2,982.36 $7,362.13 4 $3,502.65 $4,320.00 $3,250.24 $6,752.90 5 $2,983.16 $5,184.00 $3,537.05 $6,520.21 6 $2,642.37 $6,220.80 $3,843.63 $6,486.00 7 $2,403.60 $7,464.96 $4,170.86 $6,574.46 8 $2,228.50 $8,957.95 $4,519.60 $6,748.10 9 $2,095.74 $10,749.54 $4,890.74 $6,986.48 10 $1,992.52 $12,899.45 $5,285.19 $7,277.71

Life 1 2 3 4 5 6 7 8 9 10

CR $11,500.00 $6,151.16 $4,379.77 $3,502.65 $2,983.16 $2,642.37 $2,403.60 $2,228.50 $2,095.74 $1,992.52

O&M EUAO&MC EUAC $2,500.00 $2,500.00 $14,000.00 $4,000.00 $3,197.67 $9,348.84 =PMT(15%,A3,-NPV(15%,$C$2:C3)) $5,500.00 $3,860.69 $8,240.46 $7,000.00 $4,489.39 $7,992.04 optimum =PMT(15%,A5,-10000) $8,500.00 $5,084.22 $8,067.38 $10,000.00 $5,645.79 $8,288.15 =B7+D7 $11,500.00 $6,174.77 $8,578.38 $13,000.00 $6,671.99 $8,900.49 =C8+1500 $14,500.00 $7,138.34 $9,234.08 $16,000.00 $7,574.79 $9,567.31

$16,000 $14,000 $12,000 $10,000 $8,000 $6,000 $4,000 $2,000 $0

CR EUAO&M C

Life (yrs)

9 10

Life 1 2 3 4 5 6 7 8 9 10

CR $11,500.00 $6,151.16 $4,379.77 $3,502.65 $2,983.16 $2,642.37 $2,403.60 $2,228.50 $2,095.74 $1,992.52

O&M EUAO&MC $2,500.00 $2,500.00 $5,000.00 $3,662.79 $7,500.00 $4,767.82 $10,000.00 $5,815.64 $12,500.00 $6,807.04 $15,000.00 $7,742.98 $17,500.00 $8,624.62 $20,000.00 $9,453.32 $22,500.00 $10,230.56 $25,000.00 $10,957.99

$16,000 $14,000 $12,000 $10,000 $8,000 $6,000 $4,000 $2,000 $0

EUAC $14,000.00 $9,813.95 $9,147.59 optimum $9,318.30 $9,790.19 $10,385.35 $11,028.23 $11,681.82 $12,326.30 $12,950.51

CR EUAO&M C

5 6 7 Life (yrs)

9 10

Life 1 2 3 4 5 6 7 8 9 10

CR $23,000.00 $12,302.33 $8,759.54 $7,005.31 $5,966.31 $5,284.74 $4,807.21 $4,457.00 $4,191.48 $3,985.04

EUAC $25,500.00 $15,965.12 $13,527.36 $12,820.95 $12,773.35 optimum $13,027.71 $13,431.83 $13,910.32 $14,422.04 $14,943.03

$30,000 $25,000 $20,000

$15,000

EUAO&M C

$10,000 $5,000 $0 1

Life (yrs)

9 10

Life 1 2 3 4 5 6 7 8 9 10

CR $20,300.00 $10,225.56 $6,867.66 $5,188.90 $4,181.79 $3,510.50 $3,031.12 $2,671.68 $2,392.20 $2,168.68

O&M EUAO&MC $2,500.00 $2,500.00 $5,000.00 $3,740.69 $7,500.00 $4,975.19 $10,000.00 $6,203.48 $12,500.00 $7,425.56 $15,000.00 $8,641.45 $17,500.00 $9,851.14 $20,000.00 $11,054.63 $22,500.00 $12,251.93 $25,000.00 $13,443.04

EUAC $22,800.00 $13,966.25 $11,842.85 $11,392.37 optimum $11,607.35 $12,151.96 $12,882.26 $13,726.31 $14,644.13 $15,611.72

$25,000 $20,000 $15,000

$10,000

EUAO&M C

$5,000 $0 1

Life (yrs)

9 10

Life 1 2 3 4 5 6 7 8 9 10

SV $8,000.00 $6,400.00 $5,120.00 $4,096.00 $3,276.80 $2,621.44 $2,097.15 $1,677.72 $1,342.18 $1,073.74

CR $3,500.00 $3,174.42 $2,905.33 $2,682.37 $2,497.16 $2,342.90 $2,214.10 $2,106.28 $2,015.78 $1,939.64

O&M EUAO&MC $2,500.00 $2,500.00 $2,750.00 $2,616.28 $3,025.00 $2,733.98 $3,327.50 $2,852.84 $3,660.25 $2,972.59 $4,026.28 $3,092.96 $4,428.90 $3,213.68 $4,871.79 $3,334.47 $5,358.97 $3,455.08 $5,894.87 $3,575.24

$7,000 $6,000 $5,000 $4,000 $3,000 $2,000 $1,000 $0

EUAC $6,000.00 $5,790.70 $5,639.31 $5,535.21 $5,469.75 $5,435.87 $5,427.78 optimum $5,440.75 $5,470.86 $5,514.88

CR EUAO&MC EUAC

Life (yrs)

Life 1 2 3 4 5 6 7 8 9 10

SV $7,500.00 $5,625.00 $4,218.75 $3,164.06 $2,373.05 $1,779.79 $1,334.84 $1,001.13 $750.85 $563.14

CR $4,000.00 $3,534.88 $3,164.87 $2,869.00 $2,631.20 $2,439.05 $2,282.99 $2,155.57 $2,051.01 $1,964.79

EUAC $6,500.00 $6,151.16 $5,898.85 $5,721.84 $5,603.79 $5,532.01 $5,496.67 $5,490.04 optimum $5,506.09 $5,540.03

$7,000 $6,000 $5,000 CR

$4,000

EUAO&MC

$3,000

EUAC

$2,000 $1,000 $0 1

5 6 7 Life (yrs)

Life 1 2 3 4 5 6 7 8 9 10

SV $8,000.00 $6,400.00 $5,120.00 $4,096.00 $3,276.80 $2,621.44 $2,097.15 $1,677.72 $1,342.18 $1,073.74

O&M -$2,500.00 -$2,750.00 -$3,025.00 -$3,327.50 -$3,660.25 -$4,026.28 -$4,428.90 -$4,871.79 -$5,358.97 -$5,894.87

DWO

$2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00 $0.00 $0.00 $0.00

DWO

$2,000.00 $1,600.00 $960.00 $576.00 $576.00 $576.00 $0.00 $0.00 $0.00 $0.00

-$4,500.00 -$5,950.00 -$4,945.00 -$4,479.50 -$4,812.25 -$4,602.28 -$4,428.90 -$4,871.79 -$5,358.97 -$5,894.87

-$4,500.00 -$4,350.00 -$3,985.00 -$3,903.50 -$4,236.25 -$4,602.28 -$4,428.90 -$4,871.79 -$5,358.97 -$5,894.87

assumes replacement occurs in a later year assumes replacement occurs in current year 3 does not include salvage value or realized gain (loss) from replacement 4 includes tax on realized gain (loss) 2

geometric rate geometric rate o

=-PMT(9%,A6,-(-10000+NPV(9%,$C$2:C Replace after 1 Year EOY CFBT 0 -$10,000.00 1 $5,500.00

Replace after 2 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 $3,650.00

Replace after 3 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 -$2,750.00 3 $2,095.00

Replace after 4 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 -$2,750.00 3 -$3,025.00 4 $768.50

Replace after 5 Years

DWO $2,000.00

DWO $2,000.00 $1,600.00

DWO $2,000.00 $3,200.00 $960.00

DWO $2,000.00 $3,200.00 $1,920.00 $576.00

TI -$4,500.00

TI -$4,500.00 -$4,350.00

TI -$4,500.00 -$5,950.00 -$2,705.00

TI -$4,500.00 -$5,950.00 -$4,945.00 -$2,111.50

T -$1,800.00 ATPW = ATEUAC = T -$1,800.00 -$1,740.00 ATPW = ATEUAC = T -$1,800.00 -$2,380.00 -$1,082.00 ATPW = ATEUAC = T -$1,800.00 -$2,380.00 -$1,978.00 -$844.60 ATPW = ATEUAC =

Replace after 7 Years EOY 0 1 2 3 4 ATCF 5 -$10,000.00 6 -$700.00 7 $5,390.00 -$6,105.55 $3,470.81 Replace after 8 Years EOY ATCF 0 -$10,000.00 1 -$700.00 2 -$370.00 3 $3,177.00 4 -$8,500.40 5 $3,358.12 6 7 ATCF 8 -$10,000.00 -$700.00 -$370.00 Replace after 9 Years -$1,047.00 EOY $1,613.10 0 -$10,619.34 1 $3,277.86 2 3 ATCF -$10,000.00 $7,300.00 -$3,302.75 $3,600.00

EOY 0 1 2 3 4 5

CFBT DWO TI -$10,000.00 -$2,500.00 $2,000.00 -$2,750.00 $3,200.00 -$3,025.00 $1,920.00 -$3,327.50 $1,152.00 -$383.45 $576.00

Replace after 6 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 -$2,750.00 3 -$3,025.00 4 -$3,327.50 5 -$3,660.25 6 -$1,404.84

DWO $2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00

ATCF 4 -$10,000.00 5 -$4,500.00 -$1,800.00 -$700.00 6 -$5,950.00 -$2,380.00 -$370.00 7 -$4,945.00 -$1,978.00 -$1,047.00 8 -$4,479.50 -$1,791.80 -$1,535.70 9 -$2,111.45 -$844.58 $461.13 ATPW = -$12,550.33 ATEUAC = $3,226.59 Replace after 10 Years EOY TI T ATCF 0 -$10,000.00 1 -$4,500.00 -$1,800.00 -$700.00 2 -$5,950.00 -$2,380.00 -$370.00 3 -$4,945.00 -$1,978.00 -$1,047.00 4 -$4,479.50 -$1,791.80 -$1,535.70 5 -$4,812.25 -$1,924.90 -$1,735.35 6 -$1,980.84 -$792.33 -$612.50 7 ATPW = -$14,343.10 8 ATEUAC = $3,197.36 9 10

1,3

-$1,800.00 -$2,380.00 -$1,978.00 -$1,791.80 -$1,924.90 -$1,840.91 -$1,771.56 -$1,948.72 -$2,143.59 -$2,357.95

2,3

-$1,800.00 -$1,740.00 -$1,594.00 -$1,561.40 -$1,694.50 -$1,840.91 -$1,771.56 -$1,948.72 -$2,143.59 -$2,357.95

ToRG

2,4

$8,000.00 $0.00 $6,400.00 $0.00 $3,840.00 $512.00 $2,304.00 $716.80 $1,152.00 $849.92 $0.00 $1,048.58 $0.00 $838.86 $0.00 $671.09 $0.00 $536.87 $0.00 $429.50

ATEUAC $3,600.00 $3,470.81 $3,358.12 $3,277.86 $3,226.59 $3,197.36 $3,188.24 $3,197.29 $3,221.10 $3,257.26

geometric rate of decrease in SV = 20% geometric rate of increase in O&M = 10%

,-(-10000+NPV(9%,$C$2:C6)-NPV(9%,$H$2:H5)+PV(9%,A6,,I6)+PV(9%,A6,,K6)),-B6)

lace after 7 Years CFBT -$10,000.00 -$2,500.00 -$2,750.00 -$3,025.00 -$3,327.50 -$3,660.25 -$4,026.28 -$2,331.75

DWO

CFBT -$10,000.00 -$2,500.00 -$2,750.00 -$3,025.00 -$3,327.50 -$3,660.25 -$4,026.28 -$4,428.90 -$3,194.07

DWO

CFBT -$10,000.00 -$2,500.00 -$2,750.00 -$3,025.00

DWO

$2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00

TI -$4,500.00 -$5,950.00 -$4,945.00 -$4,479.50 -$4,812.25 -$4,602.28 -$2,331.75

T -$1,800.00 -$2,380.00 -$1,978.00 -$1,791.80 -$1,924.90 -$1,840.91 -$932.70 ATPW = ATEUAC =

ATCF -$10,000.00 -$700.00 -$370.00 -$1,047.00 -$1,535.70 -$1,735.35 -$2,185.37 -$1,399.05 -$16,046.28 $3,188.24

lace after 8 Years

$2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00 $0.00

TI -$4,500.00 -$5,950.00 -$4,945.00 -$4,479.50 -$4,812.25 -$4,602.28 -$4,428.90 -$3,194.07

T -$1,800.00 -$2,380.00 -$1,978.00 -$1,791.80 -$1,924.90 -$1,840.91 -$1,771.56 -$1,277.63 ATPW = ATEUAC =

ATCF -$10,000.00 -$700.00 -$370.00 -$1,047.00 -$1,535.70 -$1,735.35 -$2,185.37 -$2,657.34 -$1,916.44 -$17,696.40 $3,197.29

lace after 9 Years

$2,000.00 $3,200.00 $1,920.00

TI -$4,500.00 -$5,950.00 -$4,945.00

T -$1,800.00 -$2,380.00 -$1,978.00

ATCF -$10,000.00 -$700.00 -$370.00 -$1,047.00

-$3,327.50 -$3,660.25 -$4,026.28 -$4,428.90 -$4,871.79 -$4,016.79

lace after 10 Years CFBT -$10,000.00 -$2,500.00 -$2,750.00 -$3,025.00 -$3,327.50 -$3,660.25 -$4,026.28 -$4,428.90 -$4,871.79 -$5,358.97 -$4,821.13

$1,152.00 $1,152.00 $576.00 $0.00 $0.00 $0.00

DWO $2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00 $0.00 $0.00 $1.00

-$4,479.50 -$4,812.25 -$4,602.28 -$4,428.90 -$4,871.79 -$4,016.79

TI -$4,500.00 -$5,950.00 -$4,945.00 -$4,479.50 -$4,812.25 -$4,602.28 -$4,428.90 -$4,871.79 -$5,358.97 -$4,822.13

-$1,791.80 -$1,924.90 -$1,840.91 -$1,771.56 -$1,948.72 -$1,606.72 ATPW = ATEUAC =

-$1,535.70 -$1,735.35 -$2,185.37 -$2,657.34 -$2,923.08 -$2,410.08 -$19,311.26 $3,221.10

ATCF -$10,000.00 -$700.00 -$370.00 -$1,047.00 -$1,535.70 -$1,735.35 -$2,185.37 -$2,657.34 -$2,923.08 -$3,215.38 -$2,892.28 -$20,903.78 $3,257.23

-$1,800.00 -$2,380.00 -$1,978.00 -$1,791.80 -$1,924.90 -$1,840.91 -$1,771.56 -$1,948.72 -$2,143.59 -$1,928.85 ATPW = ATEUAC =

Life 1 2 3 4 5 6 7 8 9 10

SV $7,500.00 $5,625.00 $4,218.75 $3,164.06 $2,373.05 $1,779.79 $1,334.84 $1,001.13 $750.85 $563.14

O&M -$2,500.00 -$3,125.00 -$3,906.25 -$4,882.81 -$6,103.52 -$7,629.39 -$9,536.74 -$11,920.93 -$14,901.16 -$18,626.45

DWO

$2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00 $0.00 $0.00 $0.00

DWO

$2,000.00 $1,600.00 $960.00 $576.00 $576.00 $576.00 $0.00 $0.00 $0.00 $0.00

-$4,500.00 -$6,325.00 -$5,826.25 -$6,034.81 -$7,255.52 -$8,205.39 -$9,536.74 -$11,920.93 -$14,901.16 -$18,626.45

-$4,500.00 -$4,725.00 -$4,866.25 -$5,458.81 -$6,679.52 -$8,205.39 -$9,536.74 -$11,920.93 -$14,901.16 -$18,626.45

geometric rate geometric rate o

=-PMT(9%,A6,-(-10000+NPV(9%,$C$4:C6 Replace after 1 Year EOY CFBT 0 -$10,000.00 1 $5,000.00

Replace after 2 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 $2,500.00

Replace after 3 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 -$3,125.00 3 $312.50

Replace after 4 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 -$3,125.00 3 -$3,906.25 4 -$1,718.75

Replace after 5 Years

DWO $2,000.00

DWO $2,000.00 $1,600.00

DWO $2,000.00 $3,200.00 $960.00

DWO $2,000.00 $3,200.00 $1,920.00 $576.00

TI -$5,000.00

TI -$4,500.00 -$5,500.00

TI -$4,500.00 -$6,325.00 -$4,487.50

TI -$4,500.00 -$6,325.00 -$5,826.25 -$4,598.75

T -$2,000.00 ATPW = ATEUAC = T -$1,800.00 -$2,200.00 ATPW = ATEUAC = T -$1,800.00 -$2,530.00 -$1,795.00 ATPW = ATEUAC = T -$1,800.00 -$2,530.00 -$2,330.50 -$1,839.50 ATPW = ATEUAC =

Replace after 7 Years EOY 0 1 2 3 4 ATCF 5 -$10,000.00 6 -$700.00 7 $4,700.00 -$6,686.31 $3,800.96 Replace after 8 Years EOY ATCF 0 -$10,000.00 1 -$700.00 2 -$595.00 3 $2,107.50 4 -$9,515.62 5 $3,759.19 6 7 ATCF 8 -$10,000.00 -$700.00 -$595.00 Replace after 9 Years -$1,575.75 EOY $120.75 0 -$12,274.23 1 $3,788.67 2 3 ATCF -$10,000.00 $7,000.00 -$3,577.98 $3,900.00

EOY CFBT DWO 0 -$10,000.00 1 -$2,500.00 2 -$3,125.00 3 -$3,906.25 4 -$4,882.81 5 -$3,730.47

Replace after 6 Years EOY CFBT 0 -$10,000.00 1 -$2,500.00 2 -$3,125.00 3 -$3,906.25 4 -$4,882.81 5 -$6,103.52 6 -$5,849.61

TI $2,000.00 $3,200.00 $1,920.00 $1,152.00 $576.00

DWO $2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00

ATCF 4 -$10,000.00 5 -$4,500.00 -$1,800.00 -$700.00 6 -$6,325.00 -$2,530.00 -$595.00 7 -$5,826.25 -$2,330.50 -$1,575.75 8 -$6,034.81 -$2,413.93 -$2,468.89 9 -$5,458.47 -$2,183.39 -$1,547.08 ATPW = -$15,114.29 ATEUAC = $3,885.77 Replace after 10 Years EOY TI T ATCF 0 -$10,000.00 1 -$4,500.00 -$1,800.00 -$700.00 2 -$6,325.00 -$2,530.00 -$595.00 3 -$5,826.25 -$2,330.50 -$1,575.75 4 -$6,034.81 -$2,413.93 -$2,468.89 5 -$7,255.52 -$2,902.21 -$3,201.31 6 -$6,425.61 -$2,570.24 -$3,279.37 7 ATPW = -$18,144.80 8 ATEUAC = $4,044.84 9 10

1,3

-$1,800.00 -$2,530.00 -$2,330.50 -$2,413.93 -$2,902.21 -$3,282.16 -$3,814.70 -$4,768.37 -$5,960.46 -$7,450.58

2,3

-$1,800.00 -$1,890.00 -$1,946.50 -$2,183.53 -$2,671.81 -$3,282.16 -$3,814.70 -$4,768.37 -$5,960.46 -$7,450.58

$8,000.00 $6,400.00 $3,840.00 $2,304.00 $1,152.00 $0.00 $0.00 $0.00 $0.00 $0.00

ToRG

2,4

-$200.00 -$310.00 $151.50 $344.03 $488.42 $711.91 $533.94 $400.45 $300.34 $225.25

ATEUAC $3,900.00 $3,800.96 $3,759.19 $3,788.67 $3,885.77 $4,044.84 $4,266.60 $4,552.97 $4,905.63 $5,328.42

geometric rate of decrease in SV = 25% geometric rate of increase in O&M = 25%

-(-10000+NPV(9%,$C$4:C6)-NPV(9%,$H$4:H5)+PV(9%,A6,,I6)+PV(9%,A6,,K6)),-B6)

ce after 7 Years CFBT -$10,000.00 -$2,500.00 -$3,125.00 -$3,906.25 -$4,882.81 -$6,103.52 -$7,629.39 -$8,201.90

DWO

CFBT -$10,000.00 -$2,500.00 -$3,125.00 -$3,906.25 -$4,882.81 -$6,103.52 -$7,629.39 -$9,536.74 -$10,919.80

DWO

CFBT -$10,000.00 -$2,500.00 -$3,125.00 -$3,906.25

DWO

$2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00

TI -$4,500.00 -$6,325.00 -$5,826.25 -$6,034.81 -$7,255.52 -$8,205.39 -$8,201.90

T -$1,800.00 -$2,530.00 -$2,330.50 -$2,413.93 -$2,902.21 -$3,282.16 -$3,280.76 ATPW = ATEUAC =

ATCF -$10,000.00 -$700.00 -$595.00 -$1,575.75 -$2,468.89 -$3,201.31 -$4,347.24 -$4,921.14 -$21,473.57 $4,266.60

ce after 8 Years

$2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00 $0.00

TI -$4,500.00 -$6,325.00 -$5,826.25 -$6,034.81 -$7,255.52 -$8,205.39 -$9,536.74 -$10,919.80

T -$1,800.00 -$2,530.00 -$2,330.50 -$2,413.93 -$2,902.21 -$3,282.16 -$3,814.70 -$4,367.92 ATPW = ATEUAC =

ATCF -$10,000.00 -$700.00 -$595.00 -$1,575.75 -$2,468.89 -$3,201.31 -$4,347.24 -$5,722.05 -$6,551.88 -$25,199.86 $4,552.97

ce after 9 Years

$2,000.00 $3,200.00 $1,920.00

TI -$4,500.00 -$6,325.00 -$5,826.25

T -$1,800.00 -$2,530.00 -$2,330.50

ATCF -$10,000.00 -$700.00 -$595.00 -$1,575.75

-$4,882.81 -$6,103.52 -$7,629.39 -$9,536.74 -$11,920.93 -$14,150.31

$1,152.00 $1,152.00 $576.00 $0.00 $0.00 $0.00

CFBT -$10,000.00 -$2,500.00 -$3,125.00 -$3,906.25 -$4,882.81 -$6,103.52 -$7,629.39 -$9,536.74 -$11,920.93 -$14,901.16 -$18,063.32

DWO

-$6,034.81 -$7,255.52 -$8,205.39 -$9,536.74 -$11,920.93 -$14,150.31

-$2,413.93 -$2,902.21 -$3,282.16 -$3,814.70 -$4,768.37 -$5,660.13 ATPW = ATEUAC =

-$2,468.89 -$3,201.31 -$4,347.24 -$5,722.05 -$7,152.56 -$8,490.19 -$29,410.44 $4,905.63

ATCF -$10,000.00 -$700.00 -$595.00 -$1,575.75 -$2,468.89 -$3,201.31 -$4,347.24 -$5,722.05 -$7,152.56 -$8,940.70 -$10,837.59 -$34,195.78 $5,328.39

ce after 10 Years

$2,000.00 $3,200.00 $1,920.00 $1,152.00 $1,152.00 $576.00 $0.00 $0.00 $0.00 $1.00

TI -$4,500.00 -$6,325.00 -$5,826.25 -$6,034.81 -$7,255.52 -$8,205.39 -$9,536.74 -$11,920.93 -$14,901.16 -$18,064.32

-$1,800.00 -$2,530.00 -$2,330.50 -$2,413.93 -$2,902.21 -$3,282.16 -$3,814.70 -$4,768.37 -$5,960.46 -$7,225.73 ATPW = ATEUAC =

Year

CPI

1983 = 100.0 CPI %

Year

CPI

1983 = 100.0 CPI %

30.0 30.3 30.7 31.1 31.6 32.5 33.5 34.9 36.8 39.0 40.7 42.0 44.6 49.5 54.0 57.1 60.8 65.5 72.9 82.7 91.3 96.9 100.0 104.3 108.0

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

109.6 113.6 118.3 124.0 130.7 136.2 140.3 144.5 148.2 152.4 156.9 160.5 163.0 166.6 172.2 177.1 179.9 184.0 188.9 195.3 201.6 207.3 215.3 214.5 218.1

110.0 114.1 118.8 124.5 131.2 136.7 140.9 145.1 148.8 153.0 157.5 161.1 163.7 167.3 172.9 177.8 180.6 184.7 189.7 196.1 202.4 208.2 216.2 215.4 218.9

1.0 1.0 1.3 1.3 1.6 2.9 3.1 4.2 5.5 5.7 4.4 3.2 6.2 11.0 9.1 5.8 6.5 7.6 11.3 13.5 10.3 6.2 3.2 4.3 3.6

1.9 3.6 4.1 4.8 5.4 4.2 3.0 3.0 2.6 2.8 3.0 2.3 1.6 2.2 3.4 2.8 1.6 2.3 2.7 3.4 3.2 2.8 3.8 -0.4 1.6

1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Consumer Price Index 250.0 16.0%

225.0 14.0%

200.0

10.0%

150.0 8.0%

125.0 6.0%

100.0

75.0

4.0%

50.0 2.0%

25.0 0.0%

0.0 -2.0%

Calendar Year

Page 2

CPI-Based Inflation Rate

Figure 12.1

12.0%

175.0

Year

CPI

1983 = 100.0 CPI %

30.0 30.3 30.7 31.1 31.6 32.5 33.5 34.9 36.8 39.0 40.7 42.0 44.6 49.5 54.0 57.1 60.8 65.5 72.9 82.7 91.3 96.9 100.0 104.3 108.0

1.0 1.0 1.3 1.3 1.6 2.9 3.1 4.2 5.5 5.7 4.4 3.2 6.2 11.0 9.1 5.8 6.5 7.6 11.3 13.5 10.3 6.2 3.2 4.3 3.6

Year

CPI

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

109.6 113.6 118.3 124.0 130.7 136.2 140.3 144.5 148.2 152.4 156.9 160.5 163.0 166.6 172.2 177.1 179.9 184.0 188.9 195.3 201.6 207.3 215.3 214.5 218.1

1983 = 100.0 CPI %

110.0 114.1 118.8 124.5 131.2 136.7 140.9 145.1 148.8 153.0 157.5 161.1 163.7 167.3 172.9 177.8 180.6 184.7 189.7 196.1 202.4 208.2 216.2 215.4 218.9

1.9 3.6 4.1 4.8 5.4 4.2 3.0 3.0 2.6 2.8 3.0 2.3 1.6 2.2 3.4 2.8 1.6 2.3 2.7 3.4 3.2 2.8 3.8 -0.4 1.6

Year

1960 = 1983 = CPI 100.0 100.0 CPI %

1961 29.9 1962 30.2 1963 30.6 1964 31.0 1965 31.5 1966 32.4 1967 33.4 1968 34.8 1969 36.7 1970 38.8 1971 40.5 1972 41.8 1973 44.4 1974 49.3 1975 53.8 1976 56.9 1977 60.6 1978 65.2 1979 72.6 1980 82.4 1981 90.9 1982 96.5 1983 99.6 1984 103.9 1985 107.6 1986 109.6 1987 113.6 1988 118.3 1989 124.0 1990 130.7 1991 136.2 1992 140.3 1993 144.5 1994 148.2 1995 152.4 1996 156.9 1997 160.5 1998 163.0 1999 166.6 2000 172.2 2001 177.1 2002 179.9 2003 184.0 2004 188.9

101.0 102.0 103.4 104.7 106.4 109.5 112.8 117.6 124.0 131.1 136.8 141.2 150.0 166.6 181.8 192.2 204.7 220.3 245.3 278.4 307.1 326.0 336.5 351.0 363.5 370.3 383.8 399.7 418.9 441.6 460.1 474.0 488.2 500.7 514.9 530.1 542.2 550.7 562.8 581.8 598.3 607.7 621.5 638.2

30.0 1.0% 30.3 1.0% 30.7 1.3% 31.1 1.3% 31.6 1.6% 32.5 2.9% 33.5 3.1% 34.9 4.2% 36.8 5.5% 39.0 5.7% 40.7 4.4% 42.0 3.2% 44.6 6.2% 49.5 11.0% 54.0 9.1% 57.1 5.8% 60.8 6.5% 65.5 7.6% 72.9 11.3% 82.7 13.5% 91.3 10.3% 96.9 6.2% 100.0 3.2% 104.3 4.3% 108.0 3.6% 110.0 1.9% 114.1 3.6% 118.8 4.1% 124.5 4.8% 131.2 5.4% 136.7 4.2% 140.9 3.0% 145.1 3.0% 148.8 2.6% 153.0 2.8% 157.5 3.0% 161.1 2.3% 163.7 1.6% 167.3 2.2% 172.9 3.4% 177.8 2.8% 180.6 1.6% 184.7 2.3% 189.7 2.7%

2005 195.3 2006 201.6 2007 207.3 2008 215.3 2009 214.5 2010 218.1

659.8 681.1 700.5 727.4 724.8 736.7

196.1 3.4% 202.4 3.2% 208.2 2.8% 216.2 3.8% 215.4 -0.4% 218.9 1.6%

1983 = 100 % HEPI Change Year --1961 25.6

1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

26.5 27.6 28.6 29.8 31.3 32.9 34.9 37.1 39.5 42.1 44.3 46.7 49.9 54.3 57.8 61.5 65.7 70.5 77.5 85.8 93.9 100.0 104.8 110.8

3.5% 4.2% 3.6% 4.2% 5.0% 5.1% 6.1% 6.3% 6.5% 6.6% 5.2% 5.4% 6.9% 8.8% 6.4% 6.4% 6.8% 7.3% 9.9% 10.7% 9.4% 6.5% 4.8% 5.7%

Year

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

1983 = % 100 HEPI Change

116.3 120.9 126.2 132.8 140.8 148.2 153.5 157.9 163.3 168.1 173.0 178.4 184.7 189.1 196.9 206.5 215.0 221.2 231.5 239.8 251.8 260.3 273.2 279.3 281.8

5.0% 4.0% 4.4% 5.2% 6.0% 5.3% 3.6% 2.9% 3.4% 2.9% 2.9% 3.1% 3.5% 2.4% 4.1% 4.9% 4.1% 2.9% 4.7% 3.6% 5.0% 3.4% 5.0% 2.2% 0.9%

1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Higher Education Price Index 300 12.0%

250 10.0%

200 8.0%

150 6.0%

100 4.0%

50 2.0%

0 0.0%

Academic Fiscal Year

Page 6

HEPI-Based Inflation Rate

Figure 12.2

Year

1983 = 100 % HEPI Change

25.6 26.5 27.6 28.6 29.8 31.3 32.9 34.9 37.1 39.5 42.1 44.3 46.7 49.9 54.3 57.8 61.5 65.7 70.5 77.5 85.8 93.9 100.0 104.8 110.8 116.3 120.9 126.2 132.8 140.8 148.2 153.5 157.9 163.3 168.1 173.0 178.4 184.7 189.1 196.9 206.5 215.0 221.2 231.5

---

3.5% 4.2% 3.6% 4.2% 5.0% 5.1% 6.1% 6.3% 6.5% 6.6% 5.2% 5.4% 6.9% 8.8% 6.4% 6.4% 6.8% 7.3% 9.9% 10.7% 9.4% 6.5% 4.8% 5.7% 5.0% 4.0% 4.4% 5.2% 6.0% 5.3% 3.6% 2.9% 3.4% 2.9% 2.9% 3.1% 3.5% 2.4% 4.1% 4.9% 4.1% 2.9% 4.7%

2005 2006 2007 2008 2009 2010

239.8 251.8 260.3 273.2 279.3 281.8

3.6% 5.0% 3.4% 5.0% 2.2% 0.9%

Academic Fiscal Year 2010

2007

2004

2001

1998

1995

1992

1989

1986

1983

1980

1977

1974

1971

1968

1965

1962

Index Value

HEPI CPI

300

250

200

150

100

Academic Fiscal Year 1995

1992

1989

1986

1983

1980

1977

1974

1971

1968

1965

1962

Index Value

HEPI CPI

300

250

200

150

100

2010

2007

2004

2001

1998

1995

Page 12

Academic Fiscal Year 2010

2008

2006

2004

2002

2000

1998

1996

1994

1992

HEPI

1990

1988

1986

1984

1982

1980

1978

1976

1974

1972

1970

1968

1966

1964

1962

Index-Based Inflation Rate

Figure 12.4

CPI

14%

12%

10%

Monthly Academic Fiscal Year

1983 = 100HEPI

% Change

CPI

1983 = 100 CPI

% Change

July

1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987

25.6 26.5 27.6 28.6 29.8 31.3 32.9 34.9 37.1 39.5 42.1 44.3 46.7 49.9 54.3 57.8 61.5 65.7 70.5 77.5 85.8 93.9 100.0 104.8 110.8 116.3 120.9

3.5% 4.2% 3.6% 4.2% 5.0% 5.1% 6.1% 6.3% 6.5% 6.6% 5.2% 5.4% 6.9% 8.8% 6.4% 6.4% 6.8% 7.3% 9.9% 10.7% 9.4% 6.5% 4.8% 5.7% 5.0% 4.0%

29.8 30.1 30.4 30.8 31.2 31.9 32.9 34.0 35.7 37.8 39.7 41.2 42.8 46.6 51.8 55.5 58.7 62.6 68.5 77.6 86.6 94.1 98.2 101.8 105.8 108.8 111.2

30.3 30.6 31.0 31.4 31.8 32.5 33.5 34.6 36.3 38.5 40.5 41.9 43.6 47.5 52.8 56.5 59.8 63.8 69.8 79.1 88.3 95.9 100.0 103.7 107.8 110.9 113.3

1.0% 1.2% 1.4% 1.3% 2.2% 3.2% 3.3% 4.9% 5.9% 5.2% 3.6% 4.0% 8.9% 11.1% 7.1% 5.8% 6.7% 9.4% 13.3% 11.6% 8.6% 4.3% 3.7% 3.9% 2.9% 2.2%

29.6 30 30.3 30.7 31.1 31.6 32.5 33.4 34.9 36.8 39 40.7 41.9 44.3 49.4 54.2 57.1 61 65.7 73.1 82.7 91.6 97.5 99.9 104.1 107.8 109.5

29.6 29.9 30.3 30.7 31 31.6 32.7 33.5 35 37 39 40.8 42 45.1 50 54.3 57.4 61.2 66 73.8 83.3 92.3 97.7 100.2 104.5 108 109.7

1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

126.2 132.8 140.8 148.2 153.5 157.9 163.3 168.1 173.0 178.4 184.7 189.1 196.9

4.4% 5.2% 6.0% 5.3% 3.6% 2.9% 3.4% 2.9% 2.9% 3.1% 3.5% 2.4% 4.1%

115.8 121.2 127.0 133.9 138.2 142.5 146.2 150.4 154.5 158.9 161.7 164.5 169.3

118.0 123.5 129.4 136.4 140.8 145.2 149.0 153.2 157.4 161.9 164.8 167.6 172.5

4.1% 4.6% 4.8% 5.5% 3.2% 3.1% 2.6% 2.9% 2.7% 2.9% 1.8% 1.7% 2.9%

113.8 118.5 124.4 130.4 136.2 140.5 144.4 148.4 152.5 157 160.5 163.2 166.7

114.4 119 124.6 131.6 136.6 140.9 144.8 149 152.9 157.3 160.8 163.4 167.1

August

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

206.5 215.0 221.2 231.5 239.8 251.8 260.3 273.2 279.3 281.8

4.9% 4.1% 2.9% 4.7% 3.6% 5.0% 3.4% 5.0% 2.2% 0.9%

175.1 178.2 182.1 186.1 191.7 199.0 204.1 211.7 214.7 216.7

178.4 181.6 185.5 189.6 195.3 202.7 208.0 215.7 218.7 220.8

3.4% 1.8% 2.2% 2.2% 3.0% 3.8% 2.6% 3.7% 1.4% 1.0%

172.8 177.5 180.1 183.9 189.4 195.4 203.5

172.8 177.5 180.7 184.6 189.5 196.4 203.9

208.299

207.917

219.964

219.086

215.351

215.834

218.011

July

218.312

August

300 250 200 150

HEPI CPI

100 50

1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

Monthly CPI Values from Bureau of Labor, U.S. Department of Commerce September

October

November December January February

March

29.6 30 30.4 30.7 31.1 31.6 32.7 33.6 35.1 37.1 39.2 40.8 42.1 45.2 50.6 54.6 57.6 61.4 66.5 74.6 84 93.2 97.9 100.7 105 108.3 110.2

29.8 30 30.4 30.8 31.1 31.7 32.9 33.7 35.3 37.3 39.4 40.9 42.3 45.6 51.1 54.9 57.9 61.6 67.1 75.2 84.8 93.4 98.2 101 105.3 108.7 110.3

29.8 30 30.4 30.8 31.2 31.7 32.9 33.8 35.4 37.5 39.6 40.9 42.4 45.9 51.5 55.3 58 61.9 67.4 75.9 85.5 93.7 98 101.2 105.3 109 110.4

29.8 30 30.4 30.9 31.2 31.8 32.9 33.9 35.5 37.7 39.8 41.1 42.5 46.2 51.9 55.5 58.2 62.1 67.7 76.7 86.3 94 97.6 101.3 105.3 109.3 110.5

29.8 30 30.4 30.9 31.2 31.8 32.9 34.1 35.6 37.8 39.8 41.1 42.6 46.6 52.1 55.6 58.5 62.5 68.3 77.8 87 94.3 97.8 101.9 105.8 109.6 111.2

29.8 30.1 30.4 30.9 31.2 32 32.9 34.2 35.8 38 39.9 41.3 42.9 47.2 52.5 55.8 59.1 62.9 69.1 78.9 87.9 94.6 97.9 102.4 106 109.3 111.6

29.8 30.1 30.5 30.9 31.3 32.1 33 34.3 36.1 38.2 40 41.4 43.3 47.8 52.7 55.9 59.5 63.4 69.8 80.1 88.5 94.5 97.9 102.6 106.4 108.8 112.1

29.8 30.2 30.5 30.9 31.4 32.3 33.1 34.4 36.3 38.5 40.1 41.5 43.6 48 52.9 56.1 60 63.9 70.6 81 89.1 94.9 98.6 103.1 106.9 108.6 112.7

29.8 30.2 30.5 30.9 31.4 32.3 33.2 34.5 36.4 38.6 40.3 41.6 43.9 48.6 53.2 56.5 60.3 64.5 71.5 81.8 89.8 95.8 99.2 103.4 107.3 108.9 113.1

115 119.8 125 132.7 137.2 141.3 145.1 149.4 153.2 157.8 161.2 163.6 167.9

115.3 120.2 125.6 133.5 137.4 141.8 145.6 149.5 153.7 158.3 161.6 164 168.2

115.4 120.3 125.9 133.8 137.8 142 145.8 149.7 153.6 158.6 161.5 164 168.3

115.4 120.5 126.1 133.8 137.9 141.9 145.8 149.7 153.5 158.6 161.3 163.9 168.3

115.7 121.1 127.4 134.6 138.1 142.6 146.2 150.3 154.4 159.1 161.6 164.3 168.8

116 121.6 128 134.8 138.6 143.1 146.7 150.9 154.9 159.6 161.9 164.5 169.8

116.5 122.3 128.7 135 139.3 143.6 147.2 151.4 155.7 160 162.2 165 171.2

117.1 123.1 128.9 135.2 139.5 144 147.4 151.9 156.3 160.2 162.5 166.2 171.3

117.5 123.8 129.2 135.6 139.7 144.2 147.5 152.2 156.6 160.1 162.8 166.2 171.5

April

May

173.7 178.3 181 185.2 189.9 198.8 202.9

174 177.7 181.3 185 190.9 199.2 201.8

174.1 177.4 181.3 184.5 191 197.6 201.5

174 176.7 180.9 184.3 190.3 196.8 201.8

175.1 177.1 181.7 185.2 190.7 198.3

175.8 177.8 183.1 186.2 191.8 198.7

176.2 178.8 184.2 187.4 193.3 199.8

176.9 179.8 183.8 188 194.6 201.5

177.7 179.8 183.5 189.1 194.4 202.5

202.416

203.499

205.352

206.686

207.949

208.490

208.936

210.177

210.036

211.080

211.693

213.528

214.823

216.632

218.783

216.573

212.425

210.228

211.143

212.193

212.709

213.240

213.856

215.969

216.177

216.330

215.949

216.687

216.741

217.631

218.009

218.178

219.179

220.223

221.309

223.467

218.439

September

218.711

October

218.803

November

December January

February March

12% 10%

Series2

Series3

8% 6% 4% 2%

Academic Fiscal Year

2010

2007

2004

2001

1998

1995

1992

1989

1986

1983

1980

1977

1974

1971

1968

1965

1962

Index, Centered on 1983

14%

224.906

April

May

June

Average

29.8 29.75 30.2 30.05833 30.6 30.425 31 30.84167 31.6 31.23333 32.4 31.90833 33.3 32.91667 34.7 34.00833 36.6 35.66667 38.8 37.775 40.6 39.725 41.7 41.15 44.2 42.80833 49 46.625 53.6 51.79167 56.8 55.45833 60.7 58.69167 65.2 62.63333 72.3 68.5 82.7 77.63333 90.6 86.625 97 94.10833 99.5 98.15 103.7 101.7833 107.6 105.7917 109.5 108.8167 113.5 111.2333 118 115.8417 124.1 121.1917 129.9 126.975 136 133.9167 140.2 138.2083 144.4 142.525 148 146.2083 152.5 150.4083 156.7 154.5 160.3 158.9083 163 161.7417 166.2 164.5417 172.4 169.2917

1983 = 100 CPI % Change

30.31 30.62 31.00 31.42 31.82 32.51 33.54 34.65 36.34 38.49 40.47 41.93 43.62 47.50 52.77 56.50 59.80 63.81 69.79 79.10 88.26 95.88 100.00 103.70 107.79 110.87 113.33 118.03 123.48 129.37 136.44 140.81 145.21 148.96 153.24 157.41 161.90 164.79 167.64 172.48

1.0% 1.2% 1.4% 1.3% 2.2% 3.2% 3.3% 4.9% 5.9% 5.2% 3.6% 4.0% 8.9% 11.1% 7.1% 5.8% 6.7% 9.4% 13.3% 11.6% 8.6% 4.3% 3.7% 3.9% 2.9% 2.2% 4.1% 4.6% 4.8% 5.5% 3.2% 3.1% 2.6% 2.9% 2.7% 2.9% 1.8% 1.7% 2.9%

Fiscal Year

1983 = 100 HEPI

% Change

Fiscal Year

1983 = 100 HEPI

1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

25.6 26.5 27.6 28.6 29.8 31.3 32.9 34.9 37.1 39.5 42.1 44.3 46.7 49.9 54.3 57.8 61.5 65.7 70.5 77.5 85.8 93.9 100.0 104.8 110.8

3.5% 4.2% 3.6% 4.2% 5.0% 5.1% 6.1% 6.3% 6.5% 6.6% 5.2% 5.4% 6.9% 8.8% 6.4% 6.4% 6.8% 7.3% 9.9% 10.7% 9.4% 6.5% 4.8% 5.7%

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

116.3 120.9 126.2 132.8 140.8 148.2 153.5 157.9 163.3 168.1 173.0 178.4 184.7 189.1 196.9 206.5 215.0 221.2 231.5 239.8 251.8 260.3 273.2 279.3 281.8

Fiscal Year

1983 = 100CPI

% Change

Fiscal Year

1983 = 100CPI

1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972

30.3 30.6 31.0 31.4 31.8 32.5 33.5 34.6 36.3 38.5 40.5 41.9

1.0% 1.2% 1.4% 1.3% 2.2% 3.2% 3.3% 4.9% 5.9% 5.2% 3.6%

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

110.9 113.3 118.0 123.5 129.4 136.4 140.8 145.2 149.0 153.2 157.4 161.9

178 175.0917 179.9 178.1917 183.7 182.1083 189.7 186.0917 194.5 191.6917 202.9 198.9917 208.352 204.1378 218.815 211.7022 215.693 214.6578 217.965 216.7351 June

178.39 181.55 185.54 189.60 195.30 202.74 207.99 215.69 218.70 220.82

3.4% 1.8% 2.2% 2.2% 3.0% 3.8% 2.6% 3.7% 1.4% 1.0%

1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

43.6 47.5 52.8 56.5 59.8 63.8 69.8 79.1 88.3 95.9 100.0 103.7 107.8

4.0% 8.9% 11.1% 7.1% 5.8% 6.7% 9.4% 13.3% 11.6% 8.6% 4.3% 3.7% 3.9%

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

164.8 167.6 172.5 178.4 181.6 185.5 189.6 195.3 202.7 208.0 215.7 218.7 220.8

Fiscal Year

1960 = 100CPI

% Change

Fiscal Year

1960 = 100CPI

1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

101.0 102.0 103.4 104.7 106.4 109.5 112.8 117.6 124.0 131.1 136.8 141.2 150.0 166.6 181.8 192.2 204.7 220.3 245.3 278.4 307.1 326.0 336.5 351.0 363.5

1.0% 1.3% 1.3% 1.6% 2.9% 3.1% 4.2% 5.5% 5.7% 4.4% 3.2% 6.2% 11.0% 9.1% 5.8% 6.5% 7.6% 11.3% 13.5% 10.3% 6.2% 3.2% 4.3% 3.6%

1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

370.3 383.8 399.7 418.9 441.6 460.1 474.0 488.2 500.7 514.9 530.1 542.2 550.7 562.8 581.8 598.3 607.8 621.6 638.2 659.8 681.1 700.5 727.4 724.8 736.7

% Change

5.0% 4.0% 4.4% 5.2% 6.0% 5.3% 3.6% 2.9% 3.4% 2.9% 2.9% 3.1% 3.5% 2.4% 4.1% 4.9% 4.1% 2.9% 4.7% 3.6% 5.0% 3.4% 5.0% 2.2% 0.9%

% Change

2.9% 2.2% 4.1% 4.6% 4.8% 5.5% 3.2% 3.1% 2.6% 2.9% 2.7% 2.9%

FY 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

HEPI % CPI % HEPI CPI 3.52% 1.04% 26.5 30.6 4.15% 1.22% 27.6 31.0 3.62% 1.37% 28.6 31.4 4.20% 1.27% 29.8 31.8 5.03% 2.16% 31.3 32.5 5.11% 3.16% 32.9 33.5 6.08% 3.32% 34.9 34.6 6.30% 4.88% 37.1 36.3 6.47% 5.91% 39.5 38.5 6.58% 5.16% 42.1 40.5 5.23% 3.59% 44.3 41.9 5.42% 4.03% 46.7 43.6 6.85% 8.92% 49.9 47.5 8.82% 11.08% 54.3 52.8 6.45% 7.08% 57.8 56.5 6.40% 5.83% 61.5 59.8 6.83% 6.72% 65.7 63.8 7.31% 9.37% 70.5 69.8 9.93% 13.33% 77.5 79.1 10.71% 11.58% 85.8 88.3 9.44% 8.64% 93.9 95.9 6.50% 4.29% 100 100.0 4.80% 3.70% 104.8 103.7 5.73% 3.94% 110.8 107.8 4.96% 2.86% 116.3 110.9 3.96% 2.22% 120.9 113.3 4.38% 5.23% 6.02% 5.26% 3.58% 2.87% 3.42% 2.94% 2.91% 3.12% 3.53% 2.38% 4.12%

4.14% 4.62% 4.77% 5.47% 3.20% 3.12% 2.58% 2.87% 2.72% 2.85% 1.78% 1.73% 2.89%

126.2 132.8 140.8 148.2 153.5 157.9 163.3 168.1 173.0 178.4 184.7 189.1 196.9

118.0 123.5 129.4 136.4 140.8 145.2 149.0 153.2 157.4 161.9 164.8 167.6 172.5

1.8% 1.7% 2.9% 3.4% 1.8% 2.2% 2.2% 3.0% 3.8% 2.6% 3.7% 1.4% 1.0%

% Change

1.9% 3.6% 4.1% 4.8% 5.4% 4.2% 3.0% 3.0% 2.6% 2.8% 3.0% 2.3% 1.6% 2.2% 3.4% 2.8% 1.6% 2.3% 2.7% 3.4% 3.2% 2.8% 3.8% -0.4% 1.6%

2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

4.88% 4.12% 2.88% 4.66% 3.59% 5.00% 3.38% 4.96% 2.23% 0.90%

3.43% 1.77% 2.20% 2.19% 3.01% 3.81% 2.59% 3.71% 1.40% 0.97%

206.5 215.0 221.2 231.5 239.8 251.8 260.3 273.2 279.3 281.8

178.4 181.6 185.5 189.6 195.3 202.7 208.0 215.7 218.7 220.8

EOY 0 1 2 3 4 5 P =

$C $T $2,500.00 $2,500.00 $2,700.00 $2,808.00 $2,916.00 $3,153.95 $3,149.28 $3,542.51 $3,401.22 $3,978.95 $3,673.32 $4,469.16 $12,160.14 $12,160.14

Payment Plan

End of Year

Interest Accrued During Year

0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5

D Total Money Owed Before Yearly Payment

Interest Payment

Principal Payment

$1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00

$11,500.00 $11,500.00 $11,500.00 $11,500.00 $11,500.00

$1,500.00 $1,500.00 $1,500.00 $1,500.00 $1,500.00

$0.00 $0.00 $0.00 $0.00 $10,000.00

$1,500.00 $1,200.00 $900.00 $600.00 $300.00

$11,500.00 $9,200.00 $6,900.00 $4,600.00 $2,300.00

$1,500.00 $1,200.00 $900.00 $600.00 $300.00

$2,000.00 $2,000.00 $2,000.00 $2,000.00 $2,000.00

$1,500.00 $1,277.53 $1,021.68 $727.46 $389.11

$11,500.00 $9,794.37 $7,832.90 $5,577.20 $2,983.16

$1,500.00 $1,277.53 $1,021.68 $727.46 $389.11

$1,483.16 $1,705.63 $1,961.47 $2,255.69 $2,594.05

$1,500.00 $1,725.00 $1,983.75 $2,281.31 $2,623.51

$11,500.00 $13,225.00 $15,208.75 $17,490.06 $20,113.57

$0.00 $0.00 $0.00 $0.00 $10,113.57

$0.00 $0.00 $0.00 $0.00 $10,000.00

G Total Payment

$1,500.00 $1,500.00 $1,500.00 $1,500.00 $11,500.00 $3,500.00 $3,200.00 $2,900.00 $2,600.00 $2,300.00 $2,983.16 $2,983.16 $2,983.16 $2,983.16 $2,983.16 $0.00 $0.00 $0.00 $0.00 $20,113.57

End of Year 1 2 3 4 5 PW(12.32%) PW(14.40%) PW(16.48%)

Plan 1 Payment $1,500.00 $1,500.00 $1,500.00 $1,500.00 $11,500.00 $10,958.47 $10,204.02 $9,520.78

Plan 2 Payment $3,500.00 $3,200.00 $2,900.00 $2,600.00 $2,300.00 $10,619.37 $10,133.31 $9,683.52

Plan 3 Payment $2,983.16 $2,983.16 $2,983.16 $2,983.16 $2,983.16 $10,668.90 $10,143.72 $9,659.35

Plan 4 Payment $0.00 $0.00 $0.00 $0.00 $20,113.57 $11,251.33 $10,265.00 $9,380.64

EOY 0 1 2 3 4 5 6 7 8 9 10

$TBTCF -$500,000.00 $129,133.34 $134,298.67 $139,670.62 $145,257.44 $151,067.74 $157,110.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

$TDWO $100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

$TTI

$TT

$29,133.34 $11,653.33 -$25,701.33 -$10,280.53 $43,670.62 $17,468.25 $87,657.44 $35,062.98 $93,467.74 $37,387.10 $128,310.45 $51,324.18 $163,394.87 $65,357.95 $169,930.66 $67,972.26 $176,727.89 $70,691.16 $257,809.22 $103,123.69 PW $T =

=1.04^A7*124166.67

FW $T = AW $T =

=1.04^A12*(50000+124166.67)

IRR c = ERR c =

$TATCF -$500,000.00 $117,480.00 $144,579.20 $122,202.37 $110,194.47 $113,680.64 $105,786.27 $98,036.92 $101,958.40 $106,036.73 $154,685.53 $109,201.18 =NPV(14.4%,F3:F12)+F2 $419,264.00 =FV(14.4%,10,,-F13) $21,263.15 =PMT(14.4%,10,-F13) 19.99% =IRR(F2:F12) 16.68% =MIRR(F2:F12,,14.4%)

EOY 0 1 2 3 4 5 6 7 8 9 10

$CBTCF -$500,000.00 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $124,166.67 $174,166.67

$CDWO

$CTI

$CT

$96,153.85 $147,928.99 $85,343.65 $49,236.72 $47,343.00 $22,761.06 $0.00 $0.00 $0.00 $0.00

$28,012.82 -$23,762.32 $38,823.02 $74,929.95 $76,823.67 $101,405.61 $124,166.67 $124,166.67 $124,166.67 $174,166.67

$11,205.13 -$9,504.93 $15,529.21 $29,971.98 $30,729.47 $40,562.24 $49,666.67 $49,666.67 $49,666.67 $69,666.67 PW $C = FW $C =

=500000*0.1152*1.04^-5

AW $C = IRR r = ERR r =

$CATCF -$500,000.00 $112,961.54 $133,671.60 $108,637.46 $94,194.69 $93,437.20 $83,604.43 $74,500.00 $74,500.00 $74,500.00 $104,500.00 $109,201.18 =NPV(10%,F3:F12)+F2 $283,239.74 =FV(10%,10,,-F13) $17,771.99 =PMT(10%,10,-F13) 15.38% =IRR(F2:F12) 12.19% =MIRR(F2:F12,,10%)

After-Tax Present Worth 500 400 300

$000s

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% interest rate = income tax rate = 40% inflation rate = $TBTCF $TPPMT $TIPMT $TDWO $TTI -$500,000.00 -$300,000.00 $129,133.34 $0.00 $36,000.00 $100,000.00 -$6,866.66 $134,298.67 $0.00 $36,000.00 $160,000.00 -$61,701.33 $139,670.62 $0.00 $36,000.00 $96,000.00 $7,670.62 $145,257.44 $0.00 $36,000.00 $57,600.00 $51,657.44 $151,067.74 $0.00 $36,000.00 $57,600.00 $57,467.74 $157,110.45 $0.00 $36,000.00 $28,800.00 $92,310.45 $163,394.87 $0.00 $36,000.00 $0.00 $127,394.87 $169,930.66 $0.00 $36,000.00 $0.00 $133,930.66 $176,727.89 $0.00 $36,000.00 $0.00 $140,727.89 $257,809.22 $300,000.00 $36,000.00 $0.00 $221,809.22

0.36

0.42

200 100 0 -100

0.06

0.12

0.18

0.24 MARRr

0.3

0.48

interest rate = 12% inflation rate = 4% $TTax $TATCF $TATCF -$200,000.00 -$200,000.00 -$2,746.67 $95,880.00 $0.00 -$24,680.53 $122,979.20 $0.00 $3,068.25 $100,602.37 $0.00 $20,662.98 $88,594.47 $0.00 $22,987.10 $92,080.64 $0.00 $36,924.18 $84,186.27 $0.00 $50,957.95 $76,436.92 $0.00 $53,572.26 $80,358.40 $0.00 $56,291.16 $84,436.73 $0.00 $88,723.69 -$166,914.47 $1,613,044.36 PW $T = $220,132.29 FW $T = $845,169.87 AW $T = $42,863.15 IRR c = 47.70% =IRR(H4:H14) ERR c = 23.21% =IRR(I4:I14) IRR r = 42.02% =(H18-H2)/(1+H2) ERR r =

18.48% =(H19-H2)/(1+H2)

MARR 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30%

PWr $376.64 $339.36 $305.35 $274.32 $246.00 $220.13 $196.47 $174.81 $154.94 $136.70 $119.91 $104.45 $90.18 $77.00 $64.78 $53.46

32%

$42.94

34% 36% 38% 40% 42% 44% 46% 48% 50%

$33.14 $24.02 $15.50 $7.54 $0.08 -$6.91 -$13.47 -$19.65 -$25.46

$458.64 $415.86 $376.64 $340.73 $307.85 $277.76 $250.19 $224.93 $201.75 $180.46 $160.87 $142.84 $126.20 $110.84 $96.63 $83.46 $71.24 $59.89 $49.32 $39.47 $30.27 $21.67 $13.62 $6.07 -$1.02 -$7.69

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT -$500,000.00 -$300,000.00 $129,133.34 $30,000.00 $36,000.00 $134,298.67 $30,000.00 $32,400.00 $139,670.62 $30,000.00 $28,800.00 $145,257.44 $30,000.00 $25,200.00 $151,067.74 $30,000.00 $21,600.00 $157,110.45 $30,000.00 $18,000.00 $163,394.87 $30,000.00 $14,400.00 $169,930.66 $30,000.00 $10,800.00 $176,727.89 $30,000.00 $7,200.00 $257,809.22 $30,000.00 $3,600.00

$TDWO $100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

interest rate = 12% inflation rate = 4% $TTI $TTax $TATCF -$200,000.00 -$6,866.66 -$2,746.67 $65,880.00 -$58,101.33 -$23,240.53 $95,139.20 $14,870.62 $5,948.25 $74,922.37 $62,457.44 $24,982.98 $65,074.47 $71,867.74 $28,747.10 $70,720.64 $110,310.45 $44,124.18 $64,986.27 $148,994.87 $59,597.95 $59,396.92 $159,130.66 $63,652.26 $65,478.40 $169,527.89 $67,811.16 $71,716.73 $254,209.22 $101,683.69 $122,525.53 PW $T = $182,165.68 FW $T = $699,401.91 AW $T =

$35,470.47

IRR c =

35.34%

ERR c =

22.05%

IRR r =

30.13%

ERR r =

17.36%

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT -$500,000.00 -$300,000.00 $129,133.34 $17,095.25 $36,000.00 $134,298.67 $19,146.68 $33,948.57 $139,670.62 $21,444.28 $31,650.97 $145,257.44 $24,017.59 $29,077.65 $151,067.74 $26,899.71 $26,195.54 $157,110.45 $30,127.67 $22,967.58 $163,394.87 $33,742.99 $19,352.26 $169,930.66 $37,792.15 $15,303.10 $176,727.89 $42,327.21 $10,768.04 $257,809.22 $47,406.47 $5,688.78

$TDWO

$TTI

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

-$6,866.66 -$59,649.90 $12,019.65 $58,579.79 $67,272.20 $105,342.87 $144,042.61 $154,627.56 $165,959.85 $252,120.44

interest rate = 12% inflation rate = 4% $TTax $TATCF -$200,000.00 -$2,746.67 $78,784.75 -$23,859.96 $105,063.38 $4,807.86 $81,767.51 $23,431.91 $68,730.28 $26,908.88 $71,063.61 $42,137.15 $61,878.05 $57,617.04 $52,682.57 $61,851.02 $54,984.39 $66,383.94 $57,248.70 $100,848.18 $103,865.79 PW $T = $191,157.40 FW $T = $733,924.46 AW $T =

$37,221.30

IRR c =

38.58%

ERR c =

22.34%

IRR r =

33.25%

ERR r =

17.63%

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT -$500,000.00 -$300,000.00 $129,133.34 $0.00 $0.00 $134,298.67 $0.00 $0.00 $139,670.62 $0.00 $0.00 $145,257.44 $0.00 $0.00 $151,067.74 $0.00 $0.00 $157,110.45 $0.00 $0.00 $163,394.87 $0.00 $0.00 $169,930.66 $0.00 $0.00 $176,727.89 $0.00 $0.00 $257,809.22 $300,000.00 $631,754.46

$TDWO $100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

After-Tax Present Worth $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 $0 -$50,000

0.06

0.12

0.18

0.24

0.3 MARRr

0.36

0.42

0.48

0.54

0.6

$TTI $29,133.34 -$25,701.33 $43,670.62 $87,657.44 $93,467.74 $128,310.45 $163,394.87 $169,930.66 $176,727.89 -$373,945.24

interest rate = 12% inflation rate = 4% $TTax $TATCF -$200,000.00 $11,653.33 $117,480.00 -$10,280.53 $144,579.20 $17,468.25 $122,202.37 $35,062.98 $110,194.47 $37,387.10 $113,680.64 $51,324.18 $105,786.27 $65,357.95 $98,036.92 $67,972.26 $101,958.40 $70,691.16 $106,036.73 -$149,578.10 -$524,367.15 PW $T = $232,335.64 FW $T = $892,023.06 AW $T =

$45,239.33

IRR c =

58.76%

ERR c =

23.57%

IRR r =

52.66%

ERR r =

18.82%

$TATCF -$200,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1,659,897.55

MARR PW 0% $295,587.86 2% $298,928.05 4% $295,763.27 6% $288,046.12 8% $277,217.84 10% $264,340.50 12% $250,194.32 14% $235,349.69 16% $220,220.57 18% $205,104.26 20% $190,211.10 22% $175,686.61 24%

$161,628.20

26%

$148,097.63

28%

$135,130.42

30%

$122,742.89

32%

$110,937.49

34% 36% 38% 40% 42% 44% 46% 48% 50% 52% 54% 56% 58% 60%

$99,706.77 $89,036.40 $78,907.37 $69,297.70 $60,183.63 $51,540.53 $43,343.62 $35,568.36 $28,190.83 $21,187.94 $14,537.60 $8,218.75 $2,211.47 -$3,503.05

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT $TDWO $TTI -$500,000.00 -$100,000.00 $129,133.34 $0.00 $12,000.00 $100,000.00 $17,133.34 $134,298.67 $0.00 $12,000.00 $160,000.00 -$37,701.33 $139,670.62 $0.00 $12,000.00 $96,000.00 $31,670.62 $145,257.44 $0.00 $12,000.00 $57,600.00 $75,657.44 $151,067.74 $0.00 $12,000.00 $57,600.00 $81,467.74 $157,110.45 $0.00 $12,000.00 $28,800.00 $116,310.45 $163,394.87 $0.00 $12,000.00 $0.00 $151,394.87 $169,930.66 $0.00 $12,000.00 $0.00 $157,930.66 $176,727.89 $0.00 $12,000.00 $0.00 $164,727.89 $257,809.22 $100,000.00 $12,000.00 $0.00 $245,809.22 PW $T = $146,178.22 =NPV($D$1+$H$2+$H$2*$D$1,H5:H14)+H4 FW $T = $561,232.62 =FV($D$1+$H$2+$H$2*$D$1,10,,-C15) AW $T =

$28,463.15 =PMT($D$1+$H$2+$H$2*$D$1,10,-C15)

IRR r =

19.44% =(IRR(H4:H14)-H2)/(1+H2)

ERR r =

13.48% =(MIRR(H4:H14,,H2+D1+D1*H2)-H2)/(1+H2)

interest rate = 12% inflation rate = 4% $TTax $TATCF -$400,000.00 $6,853.33 $110,280.00 -$15,080.53 $137,379.20 $12,668.25 $115,002.37 $30,262.98 $102,994.47 $32,587.10 $106,480.64 $46,524.18 $98,586.27 $60,557.95 $90,836.92 $63,172.26 $94,758.40 $65,891.16 $98,836.73 $98,323.69 $47,485.53 H14)+H4

2)/(1+H2)

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT $TDWO $TTI -$500,000.00 -$100,000.00 $129,133.34 $10,000.00 $12,000.00 $100,000.00 $17,133.34 $134,298.67 $10,000.00 $10,800.00 $160,000.00 -$36,501.33 $139,670.62 $10,000.00 $9,600.00 $96,000.00 $34,070.62 $145,257.44 $10,000.00 $8,400.00 $57,600.00 $79,257.44 $151,067.74 $10,000.00 $7,200.00 $57,600.00 $86,267.74 $157,110.45 $10,000.00 $6,000.00 $28,800.00 $122,310.45 $163,394.87 $10,000.00 $4,800.00 $0.00 $158,594.87 $169,930.66 $10,000.00 $3,600.00 $0.00 $166,330.66 $176,727.89 $10,000.00 $2,400.00 $0.00 $174,327.89 $257,809.22 $10,000.00 $1,200.00 $0.00 $256,609.22 PW $T = $133,522.68 =NPV($D$1+$H$2+$H$2*$D$1,H5:H14)+H4 FW $T = $512,643.30 =FV($D$1+$H$2+$H$2*$D$1,10,,-C15) AW $T =

$25,998.93 =PMT($D$1+$H$2+$H$2*$D$1,10,-C15)

IRR r =

18.03% =(IRR(H4:H14)-H2)/(1+H2)

ERR r =

13.21% =(MIRR(H4:H14,,H2+D1+D1*H2)-H2)/(1+H2)

interest rate = 12% inflation rate = 4% $TTax $TATCF -$400,000.00 $6,853.33 $100,280.00 -$14,600.53 $128,099.20 $13,628.25 $106,442.37 $31,702.98 $95,154.47 $34,507.10 $99,360.64 $48,924.18 $92,186.27 $63,437.95 $85,156.92 $66,532.26 $89,798.40 $69,731.16 $94,596.73 $102,643.69 $143,965.53 H14)+H4

2)/(1+H2)

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT $TDWO $TTI -$500,000.00 -$100,000.00 $129,133.34 $5,698.42 $12,000.00 $100,000.00 $17,133.34 $134,298.67 $6,382.23 $11,316.19 $160,000.00 -$37,017.52 $139,670.62 $7,148.09 $10,550.32 $96,000.00 $33,120.29 $145,257.44 $8,005.86 $9,692.55 $57,600.00 $77,964.89 $151,067.74 $8,966.57 $8,731.85 $57,600.00 $84,735.89 $157,110.45 $10,042.56 $7,655.86 $28,800.00 $120,654.59 $163,394.87 $11,247.66 $6,450.75 $0.00 $156,944.11 $169,930.66 $12,597.38 $5,101.03 $0.00 $164,829.63 $176,727.89 $14,109.07 $3,589.35 $0.00 $173,138.54 $257,809.22 $15,802.16 $1,896.26 $0.00 $255,912.96 PW $T = $136,519.92 =NPV($D$1+$H$2+$H$2*$D$1,H5:H14)+H4 FW $T = $524,150.82 =FV($D$1+$H$2+$H$2*$D$1,10,,-C15) AW $T =

$26,582.54 =PMT($D$1+$H$2+$H$2*$D$1,10,-C15)

IRR r =

18.37% =(IRR(H4:H14)-H2)/(1+H2)

ERR r =

13.28% =(MIRR(H4:H14,,H2+D1+D1*H2)-H2)/(1+H2)

interest rate = 12% inflation rate = 4% $TTax $TATCF -$400,000.00 $6,853.33 $104,581.59 -$14,807.01 $131,407.26 $13,248.12 $108,724.08 $31,185.96 $96,373.07 $33,894.36 $99,474.97 $48,261.84 $91,150.20 $62,777.65 $82,918.80 $65,931.85 $86,300.39 $69,255.42 $89,774.06 $102,365.18 $137,745.62 :H14)+H4

2)/(1+H2)

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% interest rate = income tax rate = 40% inflation rate = $TBTCF $TPPMT $TIPMT $TDWO $TTI -$500,000.00 -$100,000.00 $129,133.34 $0.00 $0.00 $100,000.00 $29,133.34 $134,298.67 $0.00 $0.00 $160,000.00 -$25,701.33 $139,670.62 $0.00 $0.00 $96,000.00 $43,670.62 $145,257.44 $0.00 $0.00 $57,600.00 $87,657.44 $151,067.74 $0.00 $0.00 $57,600.00 $93,467.74 $157,110.45 $0.00 $0.00 $28,800.00 $128,310.45 $163,394.87 $0.00 $0.00 $0.00 $163,394.87 $169,930.66 $0.00 $0.00 $0.00 $169,930.66 $176,727.89 $0.00 $0.00 $0.00 $176,727.89 $257,809.22 $100,000.00 $210,584.82 $0.00 $47,224.40 PW $T = $150,246.00 =NPV($D$1+$H$2+$H$2*$D$1,H5:H14)+H4 FW $T = $576,850.35 =FV($D$1+$H$2+$H$2*$D$1,10,,-C15) AW $T = $29,255.21 =PMT($D$1+$H$2+$H$2*$D$1,10,-C15) IRR r = 20.50% =(IRR(H4:H14)-H2)/(1+H2) ERR r = 13.56% =(MIRR(I4:I14,,H2+D1+D1*H2)-H2)/(1+H2)

interest rate = 12% inflation rate = 4% $TTax $TATCF -$400,000.00 $11,653.33 $117,480.00 -$10,280.53 $144,579.20 $17,468.25 $122,202.37 $35,062.98 $110,194.47 $37,387.10 $113,680.64 $51,324.18 $105,786.27 $65,357.95 $98,036.92 $67,972.26 $101,958.40 $70,691.16 $106,036.73 $18,889.76 -$71,665.36

$TATCF -$400,000.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $2,112,599.34

=FV(14.4%,10,,-NPV(14.4%,H5:H13))+H14

Plan 1

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT -$500,000.00 -$500,000.00 $129,133.34 $0.00 $120,000.00 $134,298.67 $0.00 $120,000.00 $139,670.62 $0.00 $120,000.00 $145,257.44 $0.00 $120,000.00 $151,067.74 $0.00 $120,000.00 $157,110.45 $0.00 $120,000.00 $163,394.87 $0.00 $120,000.00 $169,930.66 $0.00 $120,000.00 $176,727.89 $0.00 $120,000.00 $257,809.22 $500,000.00 $120,000.00

$TDWO

$TTI

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

-$90,866.66 -$145,701.33 -$76,329.38 -$32,342.56 -$26,532.26 $8,310.45 $43,394.87 $49,930.66 $56,727.89 $137,809.22

interest rate = 24% inflation rate = 4% $TTax $TATCF $0.00 -$36,346.67 $45,480.00 -$58,280.53 $72,579.20 -$30,531.75 $50,202.37 -$12,937.02 $38,194.47 -$10,612.90 $41,680.64 $3,324.18 $33,786.27 $17,357.95 $26,036.92 $19,972.26 $29,958.40 $22,691.16 $34,036.73 $55,123.69 -$417,314.47 PW $T = $109,201.18 FW $T = $419,264.00 AW $T = $21,263.15

Plan 2

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT -$500,000.00 -$500,000.00 $129,133.34 $50,000.00 $120,000.00 $134,298.67 $50,000.00 $108,000.00 $139,670.62 $50,000.00 $96,000.00 $145,257.44 $50,000.00 $84,000.00 $151,067.74 $50,000.00 $72,000.00 $157,110.45 $50,000.00 $60,000.00 $163,394.87 $50,000.00 $48,000.00 $169,930.66 $50,000.00 $36,000.00 $176,727.89 $50,000.00 $24,000.00 $257,809.22 $50,000.00 $12,000.00

$TDWO

$TTI

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

-$90,866.66 -$133,701.33 -$52,329.38 $3,657.44 $21,467.74 $68,310.45 $115,394.87 $133,930.66 $152,727.89 $245,809.22

interest rate = 24% inflation rate = 4% $TTax $TATCF $0.00 -$36,346.67 -$4,520.00 -$53,480.53 $29,779.20 -$20,931.75 $14,602.37 $1,462.98 $9,794.47 $8,587.10 $20,480.64 $27,324.18 $19,786.27 $46,157.95 $19,236.92 $53,572.26 $30,358.40 $61,091.16 $41,636.73 $98,323.69 $97,485.53 PW $T = $109,201.18 FW $T = $419,264.00 AW $T = $21,263.15

Plan 3

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT -$500,000.00 -$500,000.00 $129,133.34 $15,801.06 $120,000.00 $134,298.67 $19,593.32 $116,207.74 $139,670.62 $24,295.72 $111,505.35 $145,257.44 $30,126.69 $105,674.38 $151,067.74 $37,357.09 $98,443.97 $157,110.45 $46,322.79 $89,478.27 $163,394.87 $57,440.26 $78,360.80 $169,930.66 $71,225.93 $64,575.14 $176,727.89 $88,320.15 $47,480.91 $257,809.22 $109,516.99 $26,284.08

$TDWO

$TTI

$100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

-$90,866.66 -$141,909.07 -$67,834.73 -$18,016.93 -$4,976.23 $38,832.18 $85,034.07 $105,355.53 $129,246.98 $231,525.14

interest rate = 24% inflation rate = 4% $TTax $TATCF $0.00 -$36,346.67 $29,678.94 -$56,763.63 $55,261.24 -$27,133.89 $31,003.45 -$7,206.77 $16,663.15 -$1,990.49 $17,257.17 $15,532.87 $5,776.51 $34,013.63 -$6,419.82 $42,142.21 -$8,012.61 $51,698.79 -$10,771.97 $92,610.06 $29,398.10 PW $T = $109,201.18 FW $T = $419,264.00 AW $T = $21,263.15

Plan 4

EOY 0 1 2 3 4 5 6 7 8 9 10

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT -$500,000.00 -$500,000.00 $129,133.34 $0.00 $0.00 $134,298.67 $0.00 $0.00 $139,670.62 $0.00 $0.00 $145,257.44 $0.00 $0.00 $151,067.74 $0.00 $0.00 $157,110.45 $0.00 $0.00 $163,394.87 $0.00 $0.00 $169,930.66 $0.00 $0.00 $176,727.89 $0.00 $0.00 $257,809.22 $500,000.00 $3,797,212.75

$TDWO $100,000.00 $160,000.00 $96,000.00 $57,600.00 $57,600.00 $28,800.00 $0.00 $0.00 $0.00 $0.00

$TTI $29,133.34 -$25,701.33 $43,670.62 $87,657.44 $93,467.74 $128,310.45 $163,394.87 $169,930.66 $176,727.89 -$3,539,403.54

interest rate = 24% inflation rate = 4% $TTax $TATCF $0.00 $11,653.33 $117,480.00 -$10,280.53 $144,579.20 $17,468.25 $122,202.37 $35,062.98 $110,194.47 $37,387.10 $113,680.64 $51,324.18 $105,786.27 $65,357.95 $98,036.92 $67,972.26 $101,958.40 $70,691.16 $106,036.73 -$1,415,761.41 -$2,623,642.12 PW $T = -$114,439.91 FW $T = -$439,377.42 AW $T = -$22,283.22

No Borrowing

500

450

After-Tax Present Worth ($000s)

400

350 10% + 4% + 10%(4%) = 14.4% P1 = P4 300

250

200

[10% + 4% + 10%(4%)] P1 = P2 = P3 = No 150

100

P1 preferred

P4 preferred 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Interest Rate on Borrowed Capital

0.2

No Borrowing

[10% + 4% + 10%(4%)]/(1 - 40%) = 24% P1 = P2 = P3 = No Borrowing

0.22

0.24

0.26

0.28

P2 preferred if borrowing is required

0.3

interest rate

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32%

$478,971.56 $448,157.37 $417,343.17 $386,528.97 $355,714.77 $324,900.57 $294,086.37 $263,272.17 $232,457.97 $201,643.78 $170,829.58 $140,015.38 $109,201.18 $78,386.98 $47,572.78 $16,758.58 -$14,055.61

$352,416.19 $332,148.27 $311,880.36 $291,612.44 $271,344.52 $251,076.60 $230,808.69 $210,540.77 $190,272.85 $170,004.93 $149,737.01 $129,469.10 $109,201.18 $88,933.26 $68,665.34 $48,397.43 $28,129.51

$352,416.19 $337,146.22 $320,825.06 $303,487.37 $285,173.15 $265,926.58 $245,794.88 $224,827.26 $203,073.95 $180,585.38 $157,411.45 $133,600.98 $109,201.18 $84,257.35 $58,812.58 $32,907.59 $6,580.63

Plan 3

EOY 0 1 2 3 4 5 6 7 8 9 10

No Borrowing

$478,971.56 $109,201.18 $461,859.83 $109,201.18 $441,446.35 $109,201.18 $417,176.49 $109,201.18 $388,415.75 $109,201.18 $354,440.08 $109,201.18 $314,425.28 $109,201.18 $267,435.33 $109,201.18 $212,409.64 $109,201.18 $148,149.10 $109,201.18 $73,300.86 $109,201.18 -$13,658.27 $109,201.18 -$114,439.91 $109,201.18 -$230,963.69 $109,201.18 -$365,378.63 $109,201.18 -$520,086.17 $109,201.18 -$697,765.25 $109,201.18

MARR r = 10% income tax rate = 40% $TBTCF $TPPMT $TIPMT $TDWO -$500,000.00 $0.00 $129,133.34 $0.00 $0.00 $100,000.00 $134,298.67 $0.00 $0.00 $160,000.00 $139,670.62 $0.00 $0.00 $96,000.00 $145,257.44 $0.00 $0.00 $57,600.00 $151,067.74 $0.00 $0.00 $57,600.00 $157,110.45 $0.00 $0.00 $28,800.00 $163,394.87 $0.00 $0.00 $0.00 $169,930.66 $0.00 $0.00 $0.00 $176,727.89 $0.00 $0.00 $0.00 $257,809.22 $0.00 $0.00 $0.00

interest rate

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30%

$TTI $29,133.34 -$25,701.33 $43,670.62 $87,657.44 $93,467.74 $128,310.45 $163,394.87 $169,930.66 $176,727.89 $257,809.22

479.0 448.2 417.3 386.5 355.7 324.9 294.1 263.3 232.5 201.6 170.8 140.0 109.2 78.4 47.6 16.8

352.4 332.1 311.9 291.6 271.3 251.1 230.8 210.5 190.3 170.0 149.7 129.5 109.2 88.9 68.7 48.4

interest rate = 30% inflation rate = 4% $TTax $TATCF -$500,000.00 $11,653.33 $117,480.00 -$10,280.53 $144,579.20 $17,468.25 $122,202.37 $35,062.98 $110,194.47 $37,387.10 $113,680.64 $51,324.18 $105,786.27 $65,357.95 $98,036.92 $67,972.26 $101,958.40 $70,691.16 $106,036.73 $103,123.69 $154,685.53 PW $T = $109,201.18

352.4 337.1 320.8 303.5 285.2 265.9 245.8 224.8 203.1 180.6 157.4 133.6 109.2 84.3 58.8 32.9

479.0 461.9 441.4 417.2 388.4 354.4 314.4 267.4 212.4 148.1 73.3 -13.7 -114.4 -231.0 -365.4 -520.1

No Borrowing

109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2 109.2

50%

45%

Upper Bound on Lender's Interest Rate

40%

35%

30%

25%

2% inflation 4% inflation 6% inflation

20%

15%

10%

0% 0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1

0.11 0.12 0.13 0.14 0.15 0.16

Borrower's Real Minimum Attractive Rate of Return

2% inflation 4% inflation 6% inflation

0.16 0.17 0.18 0.19

0.2

MARR r

MARR c

MARR c /(1-itr )

MARR c

MARR c /(1-itr )

MARR c

MARR c /(1-itr )

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2% 2%

2.00% 3.02% 4.04% 5.06% 6.08% 7.10% 8.12% 9.14% 10.16% 11.18% 12.20% 13.22% 14.24% 15.26% 16.28% 17.30% 18.32% 19.34% 20.36% 21.38% 22.40%

3.33% 5.03% 6.73% 8.43% 10.13% 11.83% 13.53% 15.23% 16.93% 18.63% 20.33% 22.03% 23.73% 25.43% 27.13% 28.83% 30.53% 32.23% 33.93% 35.63% 37.33%

4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4% 4%

4.00% 5.04% 6.08% 7.12% 8.16% 9.20% 10.24% 11.28% 12.32% 13.36% 14.40% 15.44% 16.48% 17.52% 18.56% 19.60% 20.64% 21.68% 22.72% 23.76% 24.80%

6.67% 8.40% 10.13% 11.87% 13.60% 15.33% 17.07% 18.80% 20.53% 22.27% 24.00% 25.73% 27.47% 29.20% 30.93% 32.67% 34.40% 36.13% 37.87% 39.60% 41.33%

6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6% 6%

6.00% 7.06% 8.12% 9.18% 10.24% 11.30% 12.36% 13.42% 14.48% 15.54% 16.60% 17.66% 18.72% 19.78% 20.84% 21.90% 22.96% 24.02% 25.08% 26.14% 27.20%

10.00% 11.77% 13.53% 15.30% 17.07% 18.83% 20.60% 22.37% 24.13% 25.90% 27.67% 29.43% 31.20% 32.97% 34.73% 36.50% 38.27% 40.03% 41.80% 43.57% 45.33%

Annual Sales 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000 22000 23000 24000 25000 26000 27000 28000 29000 30000 31000

Cost

Revenue

$274,579 $277,579 $280,579 $283,579 $286,579 $289,579 $292,579 $295,579 $298,579 $301,579 $304,579 $307,579 $310,579 $313,579 $316,579 $319,579 $322,579 $325,579 $328,579 $331,579 $334,579 $337,579 $340,579 $343,579 $346,579 $349,579 $352,579 $355,579 $358,579 $361,579 $364,579 $367,579

$0 $17,500 $35,000 $52,500 $70,000 $87,500 $105,000 $122,500 $140,000 $157,500 $175,000 $192,500 $210,000 $227,500 $245,000 $262,500 $280,000 $297,500 $315,000 $332,500 $350,000 $367,500 $385,000 $402,500 $420,000 $437,500 $455,000 $472,500 $490,000 $507,500 $525,000 $542,500

$600,000

$500,000

$400,000

$300,000

Loss regio $200,000

$100,000

$0 0

3,000

6,000

9,000

Profit Annual cost

Loss region

Annual revenue

break-even point 18,937 units

9,000 12,000 15,000 18,000 21,000 24,000 27,000 30,000 Annual Sales (units)

$1,400,000

$1,200,000

Annual Worth

$1,000,000

Annual Revenue (II) $800,000 AWII(15%) Annual Cost (II) $600,000

Annual Revenue (I) AWI(15%)

$400,000

Annual Cost (I)

$200,000 break-even point 18,937 units

break-even point 14,814 units $0

5000

10000

15000 Annual Sales (Units)

20000

25000

30000

Product I Annual Sales 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000 22000 23000 24000 25000 26000 27000 28000 29000 30000

Product II

Cost

Revenue

Cost

Revenue

$456,616 $467,041 $477,466 $487,891 $498,316 $508,741 $519,166 $529,591 $540,016 $550,441 $560,866 $571,291 $581,716 $592,141 $602,566 $612,991 $623,416 $633,841 $644,266 $654,691 $665,116 $675,541 $685,966 $696,391 $706,816 $717,241 $727,666 $738,091 $748,516 $758,941 $769,366

$0 $41,250 $82,500 $123,750 $165,000 $206,250 $247,500 $288,750 $330,000 $371,250 $412,500 $453,750 $495,000 $536,250 $577,500 $618,750 $660,000 $701,250 $742,500 $783,750 $825,000 $866,250 $907,500 $948,750 $990,000 $1,031,250 $1,072,500 $1,113,750 $1,155,000 $1,196,250 $1,237,500

n = 2.1699745 $0.00 =PMT(10%,B1,500000,-500000+45000*B1)+92500 n = 6.9466429 geometric rate = -20.5672% =RATE(10,,-500000,50000) $0.00 =PMT(10%,B4,500000,-500000*(1+B5)^B4)+92500

$70,000

$60,000

$40,000

Annual Worth

$50,000

Initial investment

Annual savings

$30,000

$20,000 Salvage

$10,000 MARR

$0 -50% -$10,000

-$20,000

-$30,000

-$40,000

-40% Planning horizon

-30%

-20%

-10%

10%

20%

30%

40%

50%

MARR = 10% EOY 0 1 2 3 4 5 6 7 8 9 10 10 IRR =

% Error for Initial Parameter Investment -$500,000.00 -50% $54,950.92 $92,500.00 -40% $46,813.65 $92,500.00 -30% $38,676.38 $92,500.00 -20% $30,539.11 $92,500.00 -10% $22,401.84 $92,500.00 0% $14,264.57 $92,500.00 10% $6,127.30 $92,500.00 20% -$2,009.97 $92,500.00 30% -$10,147.24 $92,500.00 40% -$18,284.51 $92,500.00 50% -$26,421.78 $50,000.00 Break-Even = $587,649.62 13.800% CF

Annual Salvage Receipts Value -$31,985.43 $12,695.94 -$22,735.43 $13,009.66 -$13,485.43 $13,323.39 -$4,235.43 $13,637.12 $5,014.57 $13,950.85 $14,264.57 $14,264.57 $23,514.57 $14,578.30 $32,764.57 $14,892.03 $42,014.57 $15,205.75 $51,264.57 $15,519.48 $60,514.57 $15,833.21 $78,235.43 -$177,340.55

Planning Horizon -$31,208.87 -$15,823.32 -$4,932.47 $3,150.19 $9,361.76 $14,264.57 $18,216.59 $21,456.51 $24,149.66 $26,414.20 $28,336.80 7.5767

MARR $31,722.94 $28,359.42 $24,930.12 $21,436.73 $17,880.96 $14,264.57 $10,589.36 $6,857.13 $3,069.70 -$771.09 -$4,663.43 13.800%

30%

20%

10%

0% -50%

-10%

-20%

-30%

-40%

-50%

-40%

-30%

-20%

-10%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Eqpt Cost =

$4,250,000

EOY

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

-7,250,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 -2,550,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000 1,700,000

% Error for Parameter -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Labor Savings = 70 Equipment Labor Investment Savings $879,688.17 -$446,223.07 $843,347.04 -$349,973.07 $807,005.92 -$253,723.07 $770,664.80 -$157,473.07 $734,323.67 -$61,223.07 $697,982.55 $35,026.93 $661,641.43 $131,276.93 $625,300.30 $227,526.93 $588,959.18 $323,776.93 $552,618.06 $420,026.93 $516,276.93 $516,276.93 $479,935.81 $612,526.93 $443,594.68 $708,776.93 $407,253.56 $805,026.93 $370,912.44 $901,276.93 $334,571.31 $997,526.93 $298,230.19 $1,093,776.93 $261,889.07 $1,190,026.93 $225,547.94 $1,286,276.93 $189,206.82 $1,382,526.93 $152,865.69 $1,478,776.93

-50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%

-0.45798 -0.4391 -0.42022 -0.40135 -0.38247 -0.36359 -0.34471 -0.32583 -0.30695 -0.28807 -0.2692 -0.25032 -0.23144 -0.21256 -0.19368 -0.1748 -0.15593 -0.13705 -0.11817 -0.09929 -0.08041 -0.06153 -0.04265 -0.02378 -0.0049 0.013982 0.03286 0.051739 0.070617 0.089496 0.108374

Estimation errors for Design B

40%

30%

20%

10%

0% -50%

-40%

-30%

-20%

-10%

10%

20%

30%

40%

Estimation errors for Design A -10%

-20%

-30%

-40%

50%

x -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

y -35% -32% -28% -25% -21% -18% -14% -11% -8% -4% -1% 3% 6% 10% 13% 16% 20% 23% 27% 30% 34%

Estimation errors for Design B

50%

40%

30%

20%

10%

0% -50%

-40%

-30%

-20%

n=7

-30%

-40%

n = 10

10%

20%

30%

40%

Estimation errors for Design A

-10%

-20%

-10%

n=8

n=9

50%

x -50% -45% -40% -35% -30% -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

n =7 y -27% -24% -20% -17% -13% -10% -6% -3% 0% 4% 7% 11% 14% 18% 21% 24% 28% 31% 35% 38% 42%

n =8 y -30% -27% -24% -20% -17% -13% -10% -6% -3% 0% 4% 7% 11% 14% 18% 21% 25% 28% 31% 35% 38%

n =9 y -33% -30% -26% -23% -19% -16% -12% -9% -6% -2% 1% 5% 8% 12% 15% 18% 22% 25% 29% 32% 36%

n = 10 y -35% -32% -28% -25% -21% -18% -14% -11% -8% -4% -1% 3% 6% 10% 13% 16% 20% 23% 27% 30% 34%

Design A $285,000 $65,000 $285,000 $40,000 $285,000 $55,000 $310,000 $65,000 $310,000 $40,000 $310,000 $55,000 $300,000 $65,000 $300,000 $40,000 $300,000 $55,000

$400,000 $85,000 B B B B B B B B B

$400,000 $70,000 A B A A B B A B A

$400,000 $80,000 A B B B B B A B B

$510,000 $85,000 A B A A B A A B A

Design B $510,000 $70,000 A A A A A A A A A

$510,000 $80,000 A B A A B A A B A

=IF(PV(10%,10,-$B12)-$A12>PV(10%,10,-E$3)-E$2,"A","B")

$450,000 $85,000 A B B A B B A B B

$450,000 $70,000 A B A A B A A B A

$450,000 $80,000 A B A A B B A B B

EOY 0 1 2 3 4 5 6 7 8 9 10 PW = IRR =

CF -$500,000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?

=RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.18 =RiskOutput("PW(SMP)") + NPV(10%,B3:B12)+B2 =RiskOutput("IRR(SMP)") + IRR(B2:B12)

0.095,0.131,0.178,0.183,0.181,0.162})+RiskDiscrete({40000,45000,50000,55000,60000}, {0.1,0.2,0.4,0.2,0.1})

Initial Investment = Annual Savings = Salvage Value = PW = IRR =

$500,000 #NAME? #NAME? #NAME? #NAME?

=RiskDiscrete({40000,45000,50000,55000,60000}, {0.1,0.2,0.4,0.2,0.1}) =RiskOutput("PW(SMP) =") + PV(10%,10,-C2,-C3)-500000 =RiskOutput() + RATE(10,C2,-C1,C3)

=RiskDiscrete({75000,80000,85000,90000,95000,100000,105000}, {0.07,0.095,0.131,0.178,0.183,0.181,0.162})

t 1 2 3

MARR #NAME? #NAME? FW =

Annual Investment #NAME? #NAME? #NAME? #NAME?

=RiskDiscrete({4000,4250,4500,4750,5000}, {0.2,0.2,0.2,0.2,0.2}) =RiskDiscrete({4000,4250,4500,4750,5000}, {0.2,0.2,0.2,0.2,0.2}) =RiskDiscrete({4000,4250,4500,4750,5000}, {0.2,0.2,0.2,0.2,0.2}) =RiskOutput("Portfolio Value =") + (C2*(1+B2)+C3)*(1+B3)+C4

=RiskDiscrete({0.06,0.065,0.07,0.075,0.08}, {0.2,0.2,0.2,0.2,0.2})

EOY 0 1 2 3 4 5 6 7 8 9 10 PW = IRR =

CF(A) -$300,000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?

CF(B) -$450,000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?

CF(B-A) -$150,000 #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME? #NAME?

=RiskNormal(55000, 5000) =RiskNormal(80000, 7500) =C5-B5

=RiskOutput("PW(B-A)") + NPV(10%,D3:D12)+D2 =RiskOutput("IRR(B-A)") + IRR(D2:D12)

=RiskOutput("IRR(B)") + IRR(C2:C12) =RiskOutput("PW(A)") + NPV(10%,B3:B12)+B2

MARR = 10% Initial Investment = Annual Revenue = PW = IRR =

A #NAME? #NAME? #NAME? #NAME?

B #NAME? #NAME? #NAME? #NAME?

B-A #NAME? #NAME? #NAME? #NAME?

=D3-C3 =D4-C4 =RiskOutput("PW(B-A)") + PV(C1,10,-E4)-E3 =RiskOutput("IRR(B-A)") + RATE(10,E4,-E3)

=RiskOutput("IRR(B)") + RATE(10,D4,-D3) =RiskOutput("PW(A)") + PV(C1,10,-C4)-C3 =RiskDiscrete({285000,300000,310000}, {0.2,0.5,0.3})

MARR PW(B-A) 0% $285.00 1% $263.85 2% $244.30 3% $226.21 4% $209.44 5% $193.87 6% $179.40 7% $165.94 8% $153.40 9% $141.71 10% $130.78 11% $120.57 12% $111.01 13% $102.05 14% $93.64 15% $85.75 16% $78.33 17% $71.34 18% $64.76 19% $58.56 20% $52.70 21% $47.16 22% $41.93 23% $36.97 24% $32.27 25% $27.82 26% $23.59 27% $19.58 28% $15.76 29% $12.12 30% $8.66 31% $5.36 32% $2.22 33% -$0.79 34% -$3.66 35% -$6.40 36% -$9.02 37% -$11.53 38% -$13.94 39% -$16.25 40% -$18.46 41% -$20.58 42% -$22.62 43% -$24.58 44% -$26.46 45% -$28.27 46% -$30.02 47% -$31.70 48% -$33.32 49% -$34.88 50% -$36.39

PW(B-A) $350.00 $300.00 $250.00

Present Worth

EOY CF(A) CF(B) CF(B-A) 0 -$285,000 -$400,000 -$115,000 1 $40,000 $80,000 $40,000 2 $40,000 $80,000 $40,000 3 $40,000 $80,000 $40,000 4 $40,000 $80,000 $40,000 5 $40,000 $80,000 $40,000 6 $40,000 $80,000 $40,000 7 $40,000 $80,000 $40,000 8 $40,000 $80,000 $40,000 9 $40,000 $80,000 $40,000 10 $40,000 $80,000 $40,000 IRR = 6.691% 15.098% 32.734%

$200.00 $150.00 $100.00 $50.00 $0.00 -$50.00

5% 10% 15% 20% 25% 30%

-$100.00 MARR

30% 35% 40% 45% 50%

MARR

Parameter Initial Investment (A) Initial Investment (B) Annual Revenue (A) Annual Revenue (B) PW A PW B

Optimistic Pessimistic Most Likely Expected $285,000 $310,000 $300,000 $299,166.67 $400,000 $510,000 $450,000 $451,666.67 $65,000 $40,000 $55,000 $54,166.67 $85,000 $70,000 $80,000 $79,166.67 $114,396.86 -$64,217.32 $37,951.19 $33,664.05 $122,288.20 -$79,880.30 $41,565.37 $34,778.23

A $75,000 $80,000 $85,000 $90,000 $95,000 $100,000 $105,000 Sum

p(A) 0.070 0.095 0.131 0.178 0.183 0.181 0.162 1.000

E(A) = $92,500 V(A) = 81,400,001.7 SD(A) = $9,022.19

Ap(A) $5,250 $7,600 $11,135 $16,020 $17,385 $18,100 $17,010 $92,500

A2p(A) 393,750,000 608,000,000 946,475,000 1,441,800,000 1,651,575,000 1,809,999,998 1,786,050,000 8,637,649,998

SV $40,000 $45,000 $50,000 $55,000 $60,000 Sum

p(SV) 0.10 0.20 0.40 0.20 0.10 1.00

E(SV) = $50,000 V(SV) = 30,000,000 SD(SV) = $5,477.23

SV2p(SV) SVp(SV) $4,000 160,000,000 $9,000 405,000,000 $20,000 1,000,000,000 $11,000 605,000,000 $6,000 360,000,000 $50,000 2,530,000,000

E(A) = $92,500 V(A) = 81,400,001.7 SD(A) = $9,022.19 EOY (t ) 0 1 2 3 4 5 6 7 8 9 10

E(CF) -$500,000 $92,500 $92,500 $92,500 $92,500 $92,500 $92,500 $92,500 $92,500 $92,500 $142,500

E(SV) = $50,000 V(SV) = 30,000,000 SD(SV) = $5,477.23 (1.10)-t E(CF)(1.10)-t 1.0000 -$500,000.00 0.9091 $84,090.91 0.8264 $76,446.28 0.7513 $69,496.62 0.6830 $63,178.74 0.6209 $57,435.22 0.5645 $52,213.84 0.5132 $47,467.13 0.4665 $43,151.93 0.4241 $39,229.03 0.3855 $54,939.92 E(PW) = $87,649.62

(1.10)-2t V(CF)(1.10)-2t 0.0 1.0000 0.00 81,400,001.7 0.8264 67,272,728.68 81,400,001.7 0.6830 55,597,296.43 81,400,001.7 0.5645 45,948,178.87 81,400,001.7 0.4665 37,973,701.54 81,400,001.7 0.3855 31,383,224.41 81,400,001.7 0.3186 25,936,549.10 81,400,001.7 0.2633 21,435,164.55 81,400,001.7 0.2176 17,715,012.02 81,400,001.7 0.1799 14,640,505.80 111,400,001.7 0.1486 16,558,900.41 V(PW) = 334,461,261.82 SD(PW) = $18,288.28 Pr(PW>0)* = 0.999999177 =NORMSDIST(D27/H2 * Central Limit Theorem approximation V(CF)

=NORMSDIST(D27/H28)

Annual Savings $75,000 $80,000 $85,000 $90,000 $95,000 $100,000 $105,000

PW(Annual Savings) $460,842.53 $491,565.37 $522,288.20 $553,011.04 $583,733.88 $614,456.71 $645,179.55

p(A)PW(A)2 p(A) p(A)PW(A) 0.070 $32,258.98 $14,866,308,810.88 0.095 $46,698.71 $22,955,468,589.24 0.131 $68,419.75 $35,734,830,810.85 0.178 $98,435.97 $54,436,175,348.62 0.183 $106,823.30 $62,356,378,347.48 0.181 $111,216.66 $68,337,825,823.37 0.162 $104,519.09 $67,433,576,766.13 SUM = $568,372.46 $326,120,564,496.57 V[PW(A)] = 3,073,314,444.39

EOY (t )

(1.10)-2t

V(A t )

V(At)(1.10)-2t

V(B t )

V(Bt)(1.10)-2t

V(B t -A t )

V(Bt-At)(1.10)-2t

0 1 2 3 4 5 6 7 8 9 10

1.0000 0.8264 0.6830 0.5645 0.4665 0.3855 0.3186 0.2633 0.2176 0.1799 0.1486

0 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000 25,000,000

0.0000 20661157.0248 17075336.3841 14111848.2513 11662684.5052 9638582.2357 7965770.4428 6583281.3577 5440728.3948 4496469.7477 3716090.7006

0 56,250,000 56,250,000 56,250,000 56,250,000 56,250,000 56,250,000 56,250,000 56,250,000 56,250,000 56,250,000

0.0000 46487603.3058 38419506.8643 31751658.5655 26241040.1368 21686810.0304 17922983.4962 14812383.0547 12241638.8882 10117056.9324 8361204.0764

81,250,000 81,250,000 81,250,000 81,250,000 81,250,000 81,250,000 81,250,000 81,250,000 81,250,000 81,250,000

67148760.3306 55494843.2484 45863506.8169 37903724.6420 31325392.2661 25888753.9390 21395664.4124 17682367.2829 14613526.6801 12077294.7770

V [PW (A )] = 101351949.0447 SD [PW (A )] = $10,067.37 Pr[PW (A ) > 0]* = 0.999918

V [PW (B-A )] = 329393834.3954 SD [PW (B-A )] = $18,149.21 Pr[PW (B-A ) > 0]* = 0.578922 V [PW (B )] = 228041885.3507 SD [PW (B )] = $15,101.06 Pr[PW (B ) > 0]* = 0.997043 *Central Limit Theorem approximations

Design A Initial Annual Probability Investment Savings $285,000 0.200 $40,000 $300,000 0.500 $55,000 $310,000 0.300 $65,000 Design B Initial Annual Investment Probability Savings $400,000 0.25005 $70,000 $450,000 0.54200 $80,000 $510,000 0.20800 $85,000

Design A $285,000

$65,000

$285,000

$40,000

$285,000

$55,000

$310,000

$65,000

$310,000

$40,000

$310,000

$55,000

$300,000

$65,000

$300,000

$40,000

$300,000

$55,000

Probability 0.150 0.625 0.225 Probability 0.125 0.625 0.250

$400,000 $85,000 B 0.002813 B 0.001875 B 0.007814 B 0.004220 B 0.002813 B 0.011721 B 0.007033 B 0.004688 B 0.019535

$400,000 $70,000 A 0.001407 B 0.000938 A 0.003907 A 0.002110 B 0.001407 B 0.005861 A 0.003516 B 0.002344 A 0.009768

$400,000 $80,000 A 0.007033 B 0.004688 B 0.019535 B 0.010549 B 0.007033 B 0.029303 A 0.017582 B 0.011721 B 0.048838

$510,000 $85,000 A 0.002340 B 0.001560 A 0.006500 A 0.003510 B 0.002340 A 0.009750 A 0.005850 B 0.003900 A 0.016250

Design B $510,000 $70,000 A 0.001170 A 0.000780 A 0.003250 A 0.001755 A 0.001170 A 0.004875 A 0.002925 A 0.001950 A 0.008125

$510,000 $80,000 A 0.005850 B 0.003900 A 0.016250 A 0.008775 B 0.005850 A 0.024375 A 0.014625 B 0.009750 A 0.040625

$450,000 $85,000 A 0.006098 B 0.004065 B 0.016938 A 0.009146 B 0.006098 B 0.025406 A 0.015244 B 0.010163 B 0.042344

$450,000 $70,000 A 0.003049 B 0.002033 A 0.008469 A 0.004573 B 0.003049 A 0.012703 A 0.007622 B 0.005081 A 0.021172

$450,000 $80,000 A 0.015244 B 0.010163 A 0.042344 A 0.022866 B 0.015244 B 0.063516 A 0.038109 B 0.025406 B 0.105859

0.002813 0.001875 0.007814 0.004220 0.002813 0.011721 0.007033 0.004688 0.019535

0.000000 0.000938 0.000000 0.000000 0.001407 0.005861 0.000000 0.002344 0.000000

0.000000 0.004688 0.019535 0.010549 0.007033 0.029303 0.000000 0.011721 0.048838

0.000000 0.001560 0.000000 0.000000 0.002340 0.000000 0.000000 0.003900 0.000000

0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

0.000000 0.003900 0.000000 0.000000 0.005850 0.000000 0.000000 0.009750 0.000000

0.000000 0.004065 0.016938 0.000000 0.006098 0.025406 0.000000 0.010163 0.042344

0.000000 0.002033 0.000000 0.000000 0.003049 0.000000 0.000000 0.005081 0.000000

0.000000 0.010163 0.000000 0.000000 0.015244 0.063516 0.000000 0.025406 0.105859

0.002813 0.029222 0.044287 0.014769 0.043832 0.135806 0.007033 0.073054 0.216576 0.5673909

72 48 61 26 05

71 05 86 48 42

87 12 49 46 50

95 09 48 47 49

73 42 39 60 18

76 86 90 75 92

60 10 13 80 78

87 66 07 73 02

33 68 80 97 72

84 74 82 13 82

11 73 39 40 09

77 26 32 56 71

40 97 86 22 64

78 62 85 12 20

07 71 19 66 07

21 70 85 67 69

36 41 78 28 40

53 69 30 56 15

86 18 27 29 99

73 92 18 38 29

23 18 67 66 93

40 99 02 10 44

63 49 03 50 25

18 83 40 06 83

53 84 34 71 60

99 90 58 40 76

76 28 82 35 25

97 57 90 91 8

86 73 50 72 34

13 05 54 73 99

19 25 62 47 85

84 76 31 25 09

84 84 29 46 07

01 73 24 28 53

41 12 81 88 92

53 76 95 97 23

92 36 69 78 78

51 83 11 04 62

39 61 10 27 83

08 53 12 59 31

93 89 15 57 44

90 85 80 94 71

23 58 86 93 33

66 67 91 01 53

65 30 79 05 46

86 70 92 45 93

06 11 40 72 88

48 28 16 82 48

99 60 16 6 33

94 52 3 56 31

Investment Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

RN 72 5 40 67 25 93 44 48 32 99 84 9 94 49 97 63 25 46 86 9 78 20 6 24 67

Year 1 Value $5,000 $2,000 $4,000 $5,000 $3,000 $5,000 $4,000 $4,000 $4,000 $5,000 $5,000 $2,000 $5,000 $4,000 $5,000 $5,000 $3,000 $4,000 $5,000 $2,000 $5,000 $3,000 $2,000 $3,000 $5,000

RN 48 11 9 66 62 89 71 42 56 2 76 90 71 46 86 49 84 7 93 48 62 18 83 28 91

Year 2 Value $4,000 $3,000 $2,000 $5,000 $5,000 $5,000 $5,000 $4,000 $4,000 $2,000 $5,000 $5,000 $5,000 $4,000 $5,000 $4,000 $5,000 $2,000 $5,000 $4,000 $5,000 $3,000 $5,000 $3,000 $5,000

RN 61 73 23 93 47 15 5 77 71 10 31 85 87 50 22 3 84 23 33 47 85 83 1 53 1

Year 3 Value $5,000 $5,000 $3,000 $5,000 $4,000 $3,000 $2,000 $5,000 $5,000 $3,000 $4,000 $5,000 $5,000 $4,000 $3,000 $2,000 $5,000 $3,000 $4,000 $4,000 $5,000 $5,000 $2,000 $4,000 $2,000

RN 26 39 18 19 85 57 86 26 40 44 25 80 12 40 64 50 29 58 95 49 12 40 73 66 53

Year 4 Value $3,000 $4,000 $3,000 $3,000 $5,000 $4,000 $5,000 $3,000 $4,000 $4,000 $3,000 $5,000 $3,000 $4,000 $5,000 $4,000 $3,000 $4,000 $5,000 $4,000 $3,000 $4,000 $5,000 $5,000 $4,000 % Negative =

Present Worth MARR = 20% $1,284.72 -$1,427.47 -$2,094.91 $1,979.17 $698.30 $1,304.01 $374.23 $451.39 $933.64 -$779.32 $1,400.46 $443.67 $1,979.17 $354.94 $1,786.27 $30.86 $312.50 -$1,612.65 $2,364.97 -$1,311.73 $1,979.17 -$594.14 -$1,292.44 -$690.59 $725.31 32.0%

Investment Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

RN 72 5 40 66 47 15 86 56 2 31 80 50 25 93 53 39 88 21 76 35 69 62 97 10 18

Year 1 Stratum 19 2 11 17 12 4 22 15 1 8 21 13 7 24 14 10 23 6 20 9 18 16 25 3 5

Latin Hypercube Simulation

RN 48 11 23 93 85 57 42 71 44 25 12 97 29 33 66 60 79 67 53 36 90 82 72 6 3

Year 2 Stratum 13 3 6 24 22 15 11 18 12 7 4 25 8 9 17 16 20 17 14 10 23 21 19 2 1

RN 61 73 18 25 93 44 77 40 84 9 49 22 7 12 67 53 90 69 97 2 83 33 29 38 56

Year 3 Stratum 16 19 5 7 24 12 20 11 22 3 13 6 2 4 17 14 23 18 25 1 21 9 8 10 15

RN 26 39 67 62 89 71 32 99 76 85 46 49 23 18 1 41 92 58 10 53 4 80 73 13 31

Year 4 Stratum 7 10 17 16 23 18 9 25 20 22 12 13 6 5 1 11 24 15 3 14 2 21 19 4 8

Investment Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

RN 72 5 40 66 47 15 86 56 2 31 80 50 25 93 53 39 88 21 76 35 69 62 97 10 18

Year 1 Value $5,000 $2,000 $4,000 $5,000 $4,000 $3,000 $5,000 $4,000 $2,000 $4,000 $5,000 $4,000 $3,000 $5,000 $4,000 $4,000 $5,000 $3,000 $5,000 $4,000 $5,000 $5,000 $5,000 $3,000 $3,000

RN 48 11 23 93 85 57 42 71 44 25 12 97 29 33 66 60 79 67 53 36 90 82 72 6 3

Year 2 Value $4,000 $3,000 $3,000 $5,000 $5,000 $4,000 $4,000 $5,000 $4,000 $3,000 $3,000 $5,000 $3,000 $4,000 $5,000 $5,000 $5,000 $5,000 $4,000 $4,000 $5,000 $5,000 $5,000 $2,000 $2,000

RN 61 73 18 25 93 44 77 40 84 9 49 22 7 12 67 53 90 69 97 2 83 33 29 38 56

Year 3 Value $5,000 $5,000 $3,000 $3,000 $5,000 $4,000 $5,000 $4,000 $5,000 $2,000 $4,000 $3,000 $2,000 $3,000 $5,000 $4,000 $5,000 $5,000 $5,000 $2,000 $5,000 $4,000 $3,000 $4,000 $4,000

RN 26 39 67 62 89 71 32 99 76 85 46 49 23 18 1 41 92 58 10 53 4 80 73 13 31

Year 4 Value $3,000 $4,000 $5,000 $5,000 $5,000 $5,000 $4,000 $5,000 $5,000 $5,000 $4,000 $4,000 $3,000 $3,000 $2,000 $4,000 $5,000 $4,000 $3,000 $4,000 $2,000 $5,000 $5,000 $3,000 $4,000 % Negative =

Present Worth MARR = 20% $1,284.72 -$1,427.47 -$435.96 $1,786.27 $2,110.34 $3.86 $1,766.98 $1,531.64 -$250.77 -$1,014.66 $493.83 $470.68 -$2,812.50 $127.31 $663.58 $1,049.38 $2,943.67 $794.75 $1,284.72 -$802.47 $1,496.91 $2,364.97 $1,786.27 -$2,349.54 -$1,867.28 32.0% 439.9691358

Investment Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

RN 72 5 40 67 19 93 44 86 26 99 76 9 49 22 63 58 33 18 83 28 91 1 70 53 36

Year 1 Value $5,000 $2,000 $4,000 $5,000 $3,000 $5,000 $4,000 $5,000 $3,000 $5,000 $5,000 $2,000 $4,000 $3,000 $5,000 $4,000 $4,000 $3,000 $5,000 $3,000 $5,000 $2,000 $5,000 $4,000 $4,000

RN 48 11 23 66 25 89 71 42 56 2 84 80 71 97 29 93 47 62 6 53 19 12 79 36 35

Year 2 Value $4,000 $3,000 $3,000 $5,000 $3,000 $5,000 $5,000 $4,000 $4,000 $2,000 $5,000 $5,000 $5,000 $5,000 $3,000 $5,000 $4,000 $5,000 $2,000 $4,000 $3,000 $3,000 $5,000 $4,000 $4,000

Latin Hypercube Simulation (Greedy Algorithm)

RN 61 73 9 93 47 15 5 77 40 44 31 25 85 64 3 23 83 53 39 18 34 71 88 99 56

Year 3 Value $5,000 $5,000 $2,000 $5,000 $4,000 $3,000 $2,000 $5,000 $4,000 $4,000 $4,000 $3,000 $5,000 $5,000 $2,000 $3,000 $5,000 $4,000 $4,000 $3,000 $4,000 $5,000 $5,000 $5,000 $4,000

RN 26 39 18 62 85 57 48 32 71 10 90 94 46 40 7 78 12 20 1 73 66 53 81 30 97

Year 4 Value $3,000 $4,000 $3,000 $5,000 $5,000 $4,000 $4,000 $4,000 $5,000 $3,000 $5,000 $5,000 $4,000 $4,000 $2,000 $5,000 $3,000 $3,000 $2,000 $5,000 $5,000 $4,000 $5,000 $4,000 $5,000 % Negative =

Present Worth

Present Worth MARR = 20% $1,284.72 -$1,427.47 -$1,979.17 $2,943.67 -$690.59 $1,304.01 -$108.02 $1,766.98 $3.86 -$682.87 $2,364.97 -$713.73 $1,628.09 $794.75 -$1,628.09 $952.93 $451.39 -$266.20 -$1,165.12 -$574.85 $976.08 -$1,427.47 $2,943.67 $933.64 $837.19 44.0% 340.8950617

Year 1 2 3 4 5

Pessimistic (0.1) 25,000 33,000 41,000 49,000 57,000 Pessimistic Most Likely Optimistic Year 0.1 0.7 0.2 6 60,000 65,000 70,000 7 67,000 73,000 79,000 8 74,000 81,000 88,000 9 81,000 89,000 97,000 10 88,000 97,000 106,000 0.01

0.07

0.02

Annual Demand for Leased Space Most Likely (0.5) 50,000 60,000 70,000 80,000 90,000 Pessimistic Most Likely Optimistic 0.3 0.4 0.3 95,000 100,000 105,000 104,000 110,000 114,000 113,000 120,000 123,000 122,000 130,000 132,000 131,000 140,000 141,000 0.15

0.2

0.15

Optimistic (0.4) 60,000 72,000 84,000 96,000 108,000 Pessimistic 0.2 115,000 126,000 137,000 148,000 159,000 0.08

Optimistic (0.4) 60,000 72,000 84,000 96,000 108,000 Most Likely Optimistic 0.5 0.3 120,000 125,000 132,000 138,000 144,000 151,000 156,000 164,000 168,000 177,000 0.2

0.12

Demand BOY 1 2 3 4 5 6 7 8 9 10

BOY 1 2 3 4 5 6 7 8 9 10 PW = E(PW|P) = E(PW) =

BOY 1 2 3 4

80,000 87,000 94,000 101,000 108,000

{P,P} $562,500 $562,500 $562,500 $562,500 $702,500 $672,500 $850,500 $1,056,500 $1,290,500 $1,552,500 $4,210,878 $4,847,985 $7,252,129

{P,P} $562,500 $562,500 $562,500 $562,500 $702,500 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $5,123,379 $5,123,379 $6,152,317

{P,P} $1,125,000 $1,125,000 $1,125,000 $1,125,000

Pessimistic 50,000 58,000 66,000 74,000 82,000 90,000 98,000 106,000 114,000 122,000

100,000 109,000 118,000 127,000 136,000

105,000 113,000 121,000 129,000 137,000

Most Likely 60,000 71,000 82,000 93,000 104,000 115,000 124,000 133,000 142,000 151,000

Optimistic 75,000 87,000 99,000 111,000 123,000 125,000 135,000 145,000 155,000 165,000

130,000 139,000 148,000 157,000 166,000

Yearly Lease Payments with 75,000 Sq Ft DC (no expansion) {P,ML} {P,O} {ML,P} {ML,ML} {ML,O} {O,P} $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $730,500 $562,500 $562,500 $674,500 $674,500 $674,500 $946,500 $562,500 $562,500 $886,500 $886,500 $886,500 $1,210,500 $702,500 $702,500 $1,142,500 $1,142,500 $1,142,500 $1,522,500 $892,500 $1,112,500 $1,222,500 $1,442,500 $1,662,500 $1,772,500 $1,114,500 $1,378,500 $1,474,500 $1,738,500 $2,002,500 $2,098,500 $1,368,500 $1,680,500 $1,758,500 $2,070,500 $2,382,500 $2,460,500 $1,654,500 $2,018,500 $2,074,500 $2,438,500 $2,802,500 $2,858,500 $1,972,500 $2,392,500 $2,422,500 $2,842,500 $3,262,500 $3,292,500 $4,790,067 $5,369,255 $6,070,900 $6,650,088 $7,229,276 $8,163,686 E(PW|ML) = $6,650,088 E(PW|O) = $8,605,716

Yearly Lease Payments with 75K Sq. Ft. DC, Plus 75K SQ. Ft. Expansion {P,ML} {P,O} {ML,P} {ML,ML} {ML,O} {O,P} $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $562,500 $730,500 $562,500 $562,500 $674,500 $674,500 $674,500 $946,500 $562,500 $562,500 $886,500 $886,500 $886,500 $1,210,500 $702,500 $702,500 $1,142,500 $1,142,500 $1,142,500 $1,522,500 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,500,000 $1,640,000 $1,696,000 $1,500,000 $1,500,000 $1,500,000 $1,530,000 $1,950,000 $1,980,000 $5,123,379 $5,123,379 $5,672,674 $5,681,202 $5,846,358 $6,655,252 E(PW|ML) = $5,728,190 E(PW|O) = $6,939,710

{P,ML} $1,125,000 $1,125,000 $1,125,000 $1,125,000

Yearly Lease Payments with 150K Sq. Ft. DC {P,O} {ML,P} {ML,ML} {ML,O} $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000

{O,P} $1,125,000 $1,125,000 $1,125,000 $1,125,000

5 6 7 8 9 10 PW = E(PW|P) = E(PW) =

$1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $6,493,032 $6,493,032 $6,714,781 $6,124,778

$1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $6,493,032

$1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $6,493,032 E(PW|ML) =

$1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $6,493,032 $6,548,548

$1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,155,000 $6,501,560

$1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,265,000 $1,575,000 $6,666,716 E(PW|O) =

$1,125,000 $1,125,000 $1,125,000 $1,125,000 $1,321,000 $1,605,000 $6,693,551 $6,978,009

Optimistic 75,000 87,000 99,000 111,000 123,000 135,000 145,000 155,000 165,000 175,000

145,000 156,000 167,000 178,000 189,000

{O,ML} $562,500 $730,500 $946,500 $1,210,500 $1,522,500 $1,882,500 $2,242,500 $2,642,500 $3,082,500 $3,562,500 $8,499,028

{O,O} $562,500 $730,500 $946,500 $1,210,500 $1,522,500 $2,102,500 $2,506,500 $2,954,500 $3,446,500 $3,982,500 $9,078,216

{O,ML} $562,500 $730,500 $946,500 $1,210,500 $1,522,500 $1,500,000 $1,500,000 $1,630,000 $1,920,000 $2,250,000 $6,854,101

{O,O} $562,500 $730,500 $946,500 $1,210,500 $1,522,500 $1,500,000 $1,644,000 $1,942,000 $2,284,000 $2,670,000 $7,272,031

{O,ML} $1,125,000 $1,125,000 $1,125,000 $1,125,000

{O,O} $1,125,000 $1,125,000 $1,125,000 $1,125,000

ion)

Expansion

$1,125,000 $1,125,000 $1,125,000 $1,255,000 $1,545,000 $1,875,000 $6,892,399

$1,125,000 $1,125,000 $1,269,000 $1,567,000 $1,909,000 $2,295,000 $7,310,329