Fundamentals of Corporate Finance, 4th Edition Solution Manual.pdf (23)

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

1   1 − Fn (1 + i)n   PB = C   + i + (1 i)n     1   1 − (1.045)8   $1,000 $914.89 = $33    + (1.045)8 0.045     = $217.66+ $703.19  $920.85

Try a higher rate, i = 9.2%, i/2 = 4.6%.

1   1−   (1 + i)n  Fn  PB = C  + i + (1 i)n   

1  1 − (1.046)8   $1,000 $914.89 = $33    (1.046)8 0.046  +   = $216.78+ $697.82$914.60 

 The yield to maturity is approximately 9.2 percent. The effective annual yield can be

computed as:

EAY = (1+Quoted ratem)m − 1

= 1(.046)2−1 = 0.0941=9.41% Enter

8 i%

N Answer

$33

-$914.89

$1,000

PMT

PV

FV

4.5954%

The effective annual yield can be computed as:

EAY = (1+Quoted ratem)

m

−1

−1 = (1.045954)2 = 0.09399=9.4% LO 3

.

For exam and test prep, contact excellentessaywriters@gmail.com SM 8-40

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.21 Yield to maturity: Serengeti Corp. has five-year bonds outstanding that pay a coupon of 8.8 percent. If these bonds are priced at $1,064.86, what is the yield to maturity on these bonds? Assume semiannual coupon payments. What is the effective annual yield?

Solution: Years to maturity = n = 5 Frequency of payment = m = 2 Coupon rate = C = 8.8% Current market rate = i Semiannual coupon payments = $1,000 x (0.088/2) = $44 Present value of bond = PB = $1,064.86 0 i=?

1

2

3

10

├───────┼────────┼────────┼── ─────────┤Yrs. $44

44

$44

$44+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a premium bond, the market rate should be lower than 8.8 percent.

Try i = 7% or i/2 = 3.5%.

 1  1− (1 + i)n  FV  PB = C   i + (1 + i)n      1   1 −(1.035)10 $1,000 + $1,064.86= $44    0.035  (1.035)10   = $365.93+ $708.92  $1,074.85 Try a higher rate, i = 7.2%, i/2 = 3.6%.

.

SM 8-41

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

 1  1−(1+ i)n  Fn  PB=C   +  (1+ i) n i       1  1 − $1,068.86=$44   (1.036)10 + $1,000  0.036  (1.036)10     =$364.09 + $702.11 $1,066.20

The YTM is approximately 7.2 percent. The effective annual yield can be computed as:

EAY = (1+Quoted ratem)m − 1

= 1(.036)2−1 = 0.0733=7.33% Enter

10 N

Answer

$44 i%

PMT

-$1,064.86 $1,000 PV

FV

3.6156%

The effective annual yield can be computed as:

EAY = (1+ Quotedrate m)m − 1 −1 = 1(.036156)2 = 0.0736=7.36% LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.22 Yield to maturity: Adrienne Dawson is planning to buy 10-year zero coupon bonds

issued by the U.S. Treasury. If these bonds have a face value of $1,000 and are currently selling at $404.59, what is the expected return on them? Assume that interest compounds semiannually on similar coupon paying bonds.

.

SM 8-42

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: Years to maturity = n = 10 Frequency of payment = m = 2Coupon rate = C = 0% Current market rate = i Assume annual coupon payments.

Present value of bond = PB = $404.59 0 i=?

1

2

3

20

Period. ─────────┤ ├───────┼────────┼────────┼── $0

$0

$0+

$0

$1,000 To solve for the YTM, a trial-and-error approach has to be used.

Try YTM = 10%.

Fmn $1,000 = mn (1.05 1+i )20 m $404.59 $376.89 PB =

(

)

Try a lower rate, YTM = 9%.

$1,000 Fmn = mn (.0 1 45)20 1+i m $404.59 $414.64 PB =

(

)

Try YTM=9.25%.

$1,000 Fmn = mn 20 (1.04625) 1+i m $404.59  $404.85 PB =

(

)

The YTM is approximately9.25 percent.

(1+Quoted ratem)m −1 EAY =

( 625)2 = 1.04 −1

= 0.09464=9.46% The expected return from this investment is 9.46 percent.

Enter

.

20

$0

-$404.59

$1,000

SM 8-43

Fundamentals of Corporate Finance, 4th edition

N Answer

i%

Solutions Manual

PMT

PV

FV

4.63%

The effective annual yield can be computed as:

EAY = (1+Quoted ratem)m − 1 −1 = (1.046283)2 = 0.0947=9.47% LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.23 Realized yield: Brown & Co. issued seven-year bonds two years ago that can be called after two years. The bonds make semiannual coupon payments at a coupon rate of 7.875 percent. Each bond has a market value of $1,053.40, and the call price is $1,078.75. If an investor purchased the bonds at par value when they were originally issued and the bonds are called by the firm today, what is the investor’s realized yield?

Solution: Purchase price of bond = $1,000 Years investment held = n = 2 Coupon rate = C = 7.875% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.07875/2) = $39.375 Realized yield = i Call price of bond = CP = $1,078.75 Current market value = $1,053.40 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased.

.

SM 8-44

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

So, the realized return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate.

Try i = 10%, or i/2 = 5%.

1   1−(1+ mn  i 2)  C CP + PB =    i 2   (1+ i )mn 2 2     1   1 − (1.05)4 $1,078.75 + $1,000 = $39.375 (1.05)4  0.05    = $139.62+ $887.49 $1,027.11 Try a higher rate, i = 11.48% or i/2 = 5.74%.

1   1−(1+ mn  i 2) CP C  PB =   i 2  (1+ i )mn + 2 2      1  − 1 (1.0574)4  $1,078.75  = + $1,000 $39.375  0.0574  (1.0574)4   = $137.25+ $862.91  $1, 000.16

EAY=(1+Quoted ratem)m

-1

2 -1 =(1.0574)

= 0.11809 = 11.81% The realized rate of return is approximately 11.81 percent . Using a financial calculator provided an exact yield of 11.49 percent.

Enter

4 N

Answer

.

$39.375 -$1,000 $1,078.75 i%

PMT

PV

FV

5.74%

SM 8-45

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The effective annual yield can be computed as:

EAY=(1+Quoted ratem)

m

-1

=(1.0574) -1 2

= 0.1181 = 11.81% LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.24 Realized yield: Trevor Price bought 10-year bonds issued by Harvest Foods five years ago for $936.05. The bonds make semiannual coupon payments at a rate of 8.4 percent. If the current price of the bonds is $1,048.77, what is the yield that Trevor would earn by selling the bonds today?

Solution: Purchase price of bond = $936.05 Years investment held = n = 5 Coupon rate = C = 8.4% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.084/2) = $42 Realized yield = i Selling price of bond = PB = $1,048.77 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased.

So, the realized return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate.

Try i = 11%, or i/2 = 5.5%.

.

SM 8-46

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

 1  1 (1+ i m n  )  C − F 2n 2 PB=   + mn i 2   (1+ i 2) 2    1   1−(1.055)10  $1,048.77 $936.05= $42   +  0.0 5 5  (1.055)10     = $316.58+ $613.98 $930.56 

Try a lower rate, i = 10.8% or i/2 = 5.4%.  1  1 (1+ i m n  )  C − FV 2 PB=   + i 2   (1+ i 2) mn 2    1   1−(1.054)10 $1,048.77 $936.05= $42   +  0.0 5 4  (1.054)10     = $318.10+ $619.83 $937.94

EAY = (1+Quoted ratem)m − 1

= 1(.054)2−1 = 0.1109=11.09% The realized rate of return is approximately 11.09 percent . Using a financial calculator provided an exact yield of 11.14 percent.

Enter

10 N

Answer

i%

$42

-$936.05

$1,048.77

PMT

PV

FV

5.425%

The effective annual yield can be computed as:

.

SM 8-47

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

EAY = (1+Quoted ratem)m − 1 −1 = 1(.05425)2 = 0.1114=11.14% LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.25 Realized yield: You bought a six-year bond issued by Runaway Corp. four years ago. At that time, you paid $974.33 for the bond. The bond pays a coupon rate of 7.375 percent, and coupon payments are made semiannually. Currently, the bond is priced at $1,023.56.

What yield can you expect to earn on this bond if you sell it today?

Solution: Purchase price of bond = $974.33 Years investment held = n = 4 Coupon rate = C = 7.375% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.07375/2) = $36.875 Realized yield = i Selling price of bond = PB = $1,023.56 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased.

So, the realized return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate.

Try i = 9%, or i/2 = 4.5%.

.

SM 8-48

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

1   1−(1+ mn  i 2)  C F 2n + PB=     (1+ i ) mn i 2  2 2    1    $1,023.56 1 − $974.33= $3 6.8 7 5  (1.045)8 +  0.045  (1.045)8     = $243.22+ $719.75$962.98 Try a lower rate, i = 8.6% or i/2 = 4.3%.

1   1−(1+  mn i 2)  C  F 2n + = PB   (1+ i ) mn i 2  2 2    1    $1,023.56 1 − $974.33= $3 6.8 7 5  (1.043)8 + (1.043)8  0.043      = $245.22+ $730.87$976.09 EAY = (1+Quoted rate m) m −1

= 1.043)2 ( −1

= 0.08785= 8.78%

The realized rate of return is approximately 8.78 percent. Using a financial calculator provided an exact yield of 8.84 percent.

Enter

8

$36.875 -$974.33 $1,023.56 i%

N Answer

PMT

PV

FV

4.327%

The effective annual yield can be computed as:

EAY = (1+Quoted ratem)

( 327)2 = 1.04 −1

m

−1

= 0.0884=8.84% LO 3 .

SM 8-49

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

ADVANCED 8.26 Pullman Corp issued 10-year bonds four years ago with a coupon rate of 9.375 percent. At the time of issue, the bonds sold at par. Today bonds of similar risk and maturity must pay an annual coupon of 6.25 percent to sell at par value. Assuming semiannual coupon payments. a. What is the bond’s yield to maturity? b. What will be the current market price of the firm’s bonds?

Solution: a. Given that other bonds with similar risk must pay an annual coupon of 6.25 percent to sell at par, the yield to maturity must be 6.25 percent. b.

Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 9.375% Semiannual coupon = $1,000 × (0.09375/2) = $46.875 Current market rate = i = 6.25% Present value of bond = PB 0 6.25% 1

2

3

4

12

├───┼────┼───┼───┼─── ─────┤ $46.875 $46.875………

$46.875+ $1,000

n = 6; m = 2; C = 9.375%; i = YTM = 6.25%

.

SM 8-50

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

1   1   1− 1− 2n  12  F $1,000 (1.03125)   ( 1 + i )2  + = $46.875    PB = C 2n  2 0.03125 + (1.03125)12 i 2  (1 + i 2 )       = $463.13+ $691.25 = $1, 154.38

Enter

12

3.125%

N

i%

$46.875 PMT

Answer

$1,000 PV

FV

- $1,154.38

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.27 Showbiz, Inc., has issued eight-year bonds with a coupon of 6.375 percent and semiannual coupon payments. The market’s required rate of return on such bonds is 7.65 percent. a.

What is the market price of these bonds?

b.

If the above bond is callable after five years at an 8.5 percent premium on the face value, what is the expected return on this bond?

Solution: a.

Years to maturity = n = 8 Frequency of payment = m = 2 Coupon rate = C = 6.375% Semiannual coupon = $1,000 × (0.06375/2) = $31.875 Current market rate = i = 7.65% Present value of bond = PB 0 7.65%

.

1

2

3

16

SM 8-51

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

─────────┤Yrs. ├───────┼────────┼────────┼── $31.875

$31.875

$31.875+

$31.875

$1,000

1  mn  i F 2n 2   i + 1+ i 2 2   = $376.26+ $548.49=$924.75

 1 − PB= C    2  

(1+)

1   1−(1.03825)16  $1,000 + = $3 1.8 7 5   0.03825  (1.03825)16    

)mn

(

The firm can sell these bonds at $924.75 .

Financial Calculator Solution : Enter

16

3.825

N

i

Answer b.

31.875 PMT

1,000 PV

FV

-924.75

Purchase price of bond = $924.75 Years investment held = n = 5 Coupon rate = C = 6.375% Semiannual coupon = $1,000 × (0.06375/2) = $31.875 Frequency of payment = m = 2 Realized yield = i Call price of bond = CP = $1,000 × (1.085) = $1,085.00 To compute the expected return, either the trial-and-error approach or the financial calculator can be used. Try rates higher than the coupon rate.

Try i = 8%, or i/2 = 4%.

.

SM 8-52

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

 1  1 i (1+ 2)mn  CP C + PB =  i2 2   (1+i2)mn   1   1- (1.04)10  $1,085 + $924.75= $31.875   0.04  (1.04)10   = $258.54+ $732.99  $991.53

Try a higher rate, i = 9.67% or i/2 = 4.835%.

1   m n  1− (1+i2) C CP + PB =   (1+ i 2 2  i 2)mn    1   1 − (1.04835)10  $1,085 + $924.75 = $31.875  10  0.04835  (1.04835)   = $248.11+ $676.65  $924.77

The realized rate of return is approximately 9.67% percent. Using a financial calculator provided an exact yield of 9.6705 percent.

Enter

10 N

Answer

i%

$31.875 PMT

-$924.75 $1,085 PV

FV

4.835%

The effective annual yield can be computed as: EAY = (1+Quoted rate m) m − 1 =

(1.04835) −1 2

= 0.0990 = 9.90%

LO 2, LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-53

Fundamentals of Corporate Finance, 4th edition

8.28

Solutions Manual

Peabody Corp. has seven-year bonds outstanding. The bonds pay a coupon of 8.375 percent semiannually and are currently worth $1,063.49. The bonds can be called in three years at price of $1,075. a.

What is the yield to maturity of these bonds?

b.

What is the effective annual yield?

c.

What is the realized yield on the bonds if they are called?

d.

If you plan to invest in one of these bonds today, what is the expected yield on the investment? Explain.

Solution: a.

Years to maturity = n = 7 Frequency of payment = m = 2 Coupon rate = C = 8.375% Current market rate = i Semiannual coupon payments = $1,000 × (0.08375/2) = $41.875 Present value of bond = PB = $1,063.49 0i=?

1

2

3

14 Yrs.

├───────┼────────┼────────┼── ─────────┤ $41.875

$41.875

$41.875

$41.875+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a premium bond, the market rate should be lower than 8.375 percent.

Try i = 8% or i/2 = 4%.

.

SM 8-54

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

  1 1−  i F 2n   (1+ 2)n  + PB= C  mn  i  (1+ i 2) 2     1   1 − (1.04)14  $1,000  $1,063.49= $4 1.8 7 5  14 +  0.04  (1.04)     = $442.33+ $577.48  $1,019.81

Try a lower rate, i = 7.2%, or i/2 = 3.6%.

1   (1+ i 2)n  1− F2n B P=C + i   (1+ i )mn 2 2   1   (1.036)14  $1,000 1− $1,063.49=$41.875 +  0.036  (1.036)14    = $454.24 + $609.49  $1,063.73

The yield-to maturity is approximately 7.2 percent.

Financial Calculator Solution : Enter

14 N

Answer b.

i

41.875

-1,063.49

1,000

PMT

PV

FV

3.6 x 2=7.2

The effective annual yield can be computed as:

EAY = (1+Quoted rat em) m −1

−1 ( = 1.036)2

= 0.073296= 7.3%

.

SM 8-55

Fundamentals of Corporate Finance, 4th edition

c.

Solutions Manual

Purchase price of bond = $1,063.49 Years investment held = n = 3 Coupon rate = C = 8.375% Semiannual coupon payments = $1,000 x (0.08375/2) = $41.875 Frequency of payment = m = 2 Realized yield = i Selling price of bond = PB = $1,075 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased.

So, the realized return is going to be higher than the bond’s coupon. Try rates higher than the coupon rate.

Try i = 9%, or i/2 = 4.5%.

1   mn  1− (1+ i 2) F2n C  PB = 2   mn i 2 + (1+ i 2)        1  1− (1.045)6 $1,075  $1,063.49= $41.875  +(1.045)6  0.045     $215.99+ $825.49 $1,041.48 Try a lower rate, i = 8.2% or i/2 = 4.1%.

1   mn  1− (1+ i 2) F2n C  PB = 2   mn i 2 + (1+ i 2)        1  1 − (1.041)6 $1,075  $1,063.49= $41.875  + (1.041)6  0.041    = $218.80+ $844.70= $1,063.50 .

SM 8-56

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The realized rate of return is approximately 8.37 percent. Using a financial calculator provided an exact yield of 8.2 percent.

Enter

6

$41.875 -$1,063.49

N Answer

i%

PMT

$1075

PV

FV

4.1% x 2=8.2%

The effective annual yield can be computed as: EAY = (1+Quoted ratem) m − 1 =

(1.04100) −1 2

= 0.08368 = 8.368%

d.

Purchase price of bond = PB = $1,063.49 Years to maturity = n =7 Coupon rate = C = 8.375% Semiannual coupon payments = $1,000 × (0.08375/2) = $41.875 Frequency of payment = m = 2 Maturity value = FV = $1,000 Use the trial-and-error approach to compute the yield to maturity. Since we have a premium bond, market rates are lower than the bond’s coupon.

Try i = 7%, or i/2 = 3.5%.

  1 1−(1+ i mn  )  F2n C 2 + PB =    i  (1+ i ) m n 2  2 2      1  1 − (1.035)14 $1,000 + $1,063.49= $41.875  0.035  (1.035)14     = $457.30+ $617.78  $1, 075.08

.

SM 8-57

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Try a higher rate, i = 7.2%, or i/2 = 3.6%.

1   (1+ i 2)n  1− F2n P=   + C B i   (1+ i )mn 2 2    1   (1.036)14  $1,000 $1,063.49=$41.8751− +  0.036  (1.036)14   = $454.24 + $609.49  $1,063.73

The expected yield is approximately 7.2 percent which is the same as the yield to maturity obtained in (a). If the bond is not called and is held to maturity, then the expected yield is the yield to maturity.

Financial Calculator Solution : Enter

14 N

Answer

41.875

-1,063.49

1,000

PMT

PV

FV

i 3.6 x 2=7.2%

EAY = (1+Quoted rate m) m − 1 =

−1 (1.036) 2

= 0.073296 = 7.33% The expected yield is approximately 7.33 percent. Using a financial calculator provided an exact yield 7.334 percent.

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-58

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.29 The Maryland Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a rate of 9.875 percent. The current market rate for similar securities is 11 percent. a.

What is the current market value of one of these bonds?

b.

What will be the bond’s price if rates in the market (i) decrease to 9 percent or (ii) increase to 12 percent?

Refer to your answers in part b. How do the interest rate changes affect premium

c.

bonds and discount bonds?

Suppose the bond were to mature in 12 years. How do the interest rate changes in

d.

part b affect the bond prices?

Solution: a.

Years to maturity = n = 25 Frequency of payment = m = 2 Coupon rate = C = 9.875% Semiannual coupon = $1,000 × (0.09875/2) = $49.375 Current market rate = i = 11% Present value of bond = PB 0 11%

1

2

50 Yrs.

3

├───────┼────────┼────────┼── ─────────┤ $49.375

$49.375

$49.375

$49.375+ $1,000

 1 − PB= C    2  

1



1   1−(1.055)50  $1,000  = $4 9.3 7 5   0.0 5 5 + (1.055)50     

(1+ i 2 )2n F +  ( + i )mn i 2 2  1 2n

 = $835.99+ $6 8.7 7= $904.76

The Maryland bonds will sell at $904.76.

Enter

50 .

5.5%

$49.375

$1,000

SM 8-59

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

i

N

PMT

Answer b.

(i)

FV

PV -$904.76

Current market rate = i = 9%

1  1   2 n  i 1− 50   F 2n (1.045)  $1,000 2 = $4 9.3 7 5   + i  0.0 4 5 + (1.045)50  1+ i 2 2        = $975.75+ $110.71= $1,086.46

 1 − PB= C    2  

(1+)

(

)mn

The Maryland bonds will increase in price to sell at $1,086.46 .

Enter

50

4.5%

$49.375

N

i

PMT

FV

PV -$1,086.46

Answer (ii)

$1,000

Current market rate = i = 12%

 1 − PB= C    2  

1





1



1−(1.06)  $1,000 (1+ i 2 )2n F  = $4 9.3 7 5  +  ( i 0.06 + (1.06)50  i + )mn  1 2 2   50

2n



 = $778.24+ $5 4.2 9= $832.53

 

The Maryland bonds will drop in price to $832.53.

Enter

50

6%

$49.375

N

i

PMT

Answer c.

$1,000 PV

FV

-$832.53

Bonds, in general, decrease in price when interest rates go up. When interest rates decrease, bond prices increase.

d.

(i)

Current market rate = i = 9% Term to maturity = 12 years

.

SM 8-60

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

1  1   2n i 1− 24   F 2n (1.045)  $1,000 2 = $4 9.3 7 5  + i  0.0 4 5 + (1.045)24  1+ i 2 2        = $715.71+ $347.70= $1,063.42

 1 − PB= C    2  

(1+)

(

)mn

The Maryland bonds will increase in price to sell at $1,063.42 .

Enter

24

4.5%

N

i

$49.375 PMT

Answer (ii)

$1,000 PV

FV

-$1,063.42

Current market rate = i = 12%

1  1    n 2 i 1−  F 2n (1.06)24  $1,000 2 =   $4 9.3 7 5 + i  0.06 + (1.06)24  + i 1 2 2        = $619.67+ $246.98= $866.65

 1 − PB= C    2  

(1+)

)mn

(

The Maryland bonds will drop in price to $866.65.

Enter

24

6%

$49.375

N

i

PMT

Answer

$1,000 PV

FV

-$866.65

With shorter maturity, bond prices react the same way as in part b, but to a lesser extent.

When interest rates increase, the bond’s price declines; but the decline in price is less than that for a longer-term bond. Similarly, when interest rates decrease, bond prices increase with both longer-term and shorter-term bonds. However, longer-term bonds increasing more than shorter-term bonds.

LO 2, LO 3, LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-61

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.30 Rachette Corp. has 18-year bonds outstanding. These bonds, which pay interest semiannually, have a coupon rate of 9.735 percent and a yield to maturity of 7.95 percent. a. Compute the current price of these bonds. b. If the bonds can be called in five years at a premium of 13.5 percent over par value, what is the investor’s realized yield? c. If you bought one of these bonds today, what is your expected rate of return? Explain.

Solution: a.

Years to maturity = n = 18 Frequency of payment = m = 2 Coupon rate = C = 9.735% Semiannual coupon = $1,000 × (0.09735/2) = $48.675 Current market rate = i = 7.95% Present value of bond = PB 0

1

2

36

3

├───────┼────────┼────────┼── ─────────┤Yrs. $48.675

$48.675

$48.675+

$48.675

$1,000   1 1   1− 2n   1− 36 i2  F2n (1.03975)  $1,000    = PB = C   $48.675  2n 2 i  0.03975 + (1.03975)36 +  2           = $923.56+ $245.79 = $1, 169.34

(1+)

(1+) i2

.

The bond’s current price is at $1,169.34 Enter Answer b.

36

3.975%

N

i

$48.675 PMT

$1,000 PV

FV

-$1,169.34

Purchase price of bond = $1,169.34 (value today);

.

SM 8-62

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Call price = $1,135 To compute the realized return, either the trial-and-error approach or the financial calculator can be used.

Try rates lower than the coupon rate.

Try i = 8%, or i/2 = 4%.

  1 1−(1+ i mn  )  F2n C 2 + PB = 2    i   (1+ i )mn 2 2      1  1 − (1.04)10 $1,135 + $1,169.34= $48.675  0.04  (1.04)10     = $394.80+ $766.77  $1,161.56 Try a lower rate, i = 7.8% or i/2 = 3.9%.

  1 1−(1+ i mn  )  F2n C 2 + PB = 2    (1 i   + i )mn 2 2      1  1 − (1.039)10 $1,135 + $1,169.34= $48.675  0.039  (1.039)10     = $396.77+ $774.18  $1,170.95 EAY = (1+Quoted ratem)m − 1 =

−1 (1.039) 2

= 0.07952 = 7.95% The realized rate of return is approximately 7.95 percent. Using a financial calculator provided an exact yield of 7.834 percent.

.

SM 8-63

Fundamentals of Corporate Finance, 4th edition

Enter

10

$48.675 -$1,169.34 $1,135.00

N Answer

Solutions Manual

i

PMT

PV

FV

3.917 x 2 = 7.834%

The effective annual yield can be computed as:

EAY = (1+Quoted ratem) m − 1 =

(1.03917) −1 2

= 0.07987 = 7.99%

c.

Purchase price of bond = PB = $1,169.34 Years to maturity = n = 18 Coupon rate = C = 9.735% Semiannual coupon = $1,000 × (0.09735/2) = $48.675 Frequency of payment = m = 2 Maturity value = FV = $1,000

Use the trial-and-error approach to compute the yield to maturity. Since we have a premium bond, market rates are lower than the bond’s coupon.

Try i = 8%, or i/2 = 4.0%.

1   1−(1+ i mn  )  C F2n 2 + PB = 2     i  (1+ i )mn 2 2     1   1 − (1.04)36 $1,000 + $1,169.34 $48.675  0.04  (1.04)36      $920.36+ $243.67  $1,164.03 Try i = 7.9%, or i/2 = 3.95%.

.

SM 8-64

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

1   1−(1+ i mn  )  C F2n 2 + PB = 2     i  (1+ i )mn 2 2     1   1 − (1.0395)36  $1,000  $1,169.34 $48.675  0.0395 + (1.0395)36       $926.77+ $247.92  $1,174.69 Thus the expected yield is between 7.9 percent and 8 percent. Using a financial calculator provided an exact yield of 7.95 percent.

Enter

36

$48.675 -$1,169.34 $1,000 i

N Answer

PMT

PV

FV

3.975 x 2= 7.95%

The effective annual yield can be computed as:

EAY = (1+Quoted ratem) m − 1 =

(1.03975) −1 2

= 0.08108 = 8.11% LO 2, LO 3, LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.31 Zippy Corporation just sold $30 million of convertible bonds with a conversion ratio of 40. Each $1,000 bond is convertible into 25 shares of Zippy’s stock. a.

.

What is the conversion price of Zippy’s stock?

SM 8-65

Fundamentals of Corporate Finance, 4th edition

b.

Solutions Manual

If the current price of Zippy’s stock is $15 and the company’s annual stock return is normally distributed with a standard deviation of $5, what is the probability that investors will find it attractive to convert the bond into Zippy stock in the next year?

Solution: a.

The conversion price is $1,000/40 = $25.

b.

The stock price would have to increase by approximately two standard deviations (2  $5 = $10) for the price to increase to $25 and for conversion to become attractive to the investors. From Chapter 7we know that 95% of possible outcomes fall within two standard deviations of the mean (average) value in a normal distribution. This means that there is a 5 percent chance that the stock price will move up or down by $10 or more. Since the normal distribution is symmetric, this means that there is only a 2.5 percent chance that Zippy’s stock price will increase enough for it to become attractive for the investors to exercise the conversion option in the next year.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-66

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Sample Test Problems 8.1

Seven years ago Eastern Corporation issued 20-year bonds that had a $1000 face value, paid interest annually, and that had a coupon rate of 7 percent. If the market rate of interest is 5.5 percent today, what is the current market price of an Eastern Corporation bond? Are these bonds selling at a premium or discount? (LO 2) Solution: Years to maturity = n = 13 Coupon rate = C = 7% Annual coupon payment = $1,000 × 0.07 = $70 Current market rate = i = 5.5% Present value of bond = PB 0 1 2 3 4 13 ├───┼────┼───┼───┼─── ─────┤ $70 $70 $70 $70 $70 $1,000   1    1+ 1− + i)n  1− 13 (1 F $1,000   (1.055)  =  PB = C   $70 n   0.0 5 5 (1.055)13 i + (1 + i)       = $498.56 + $638.19  = $1,136.75 These bonds are selling at a premium.

Financial Calculator Solution : Enter Answer

13

5.5

70

N

i

PMT

1,000 PV

FV

-1,136.75

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-67

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

8.2 You are considering investing in a 10-year zero coupon bond that compounds interest semiannually. If the current market rate is 5.65 percent, what is the maximum price you should have pay for this bond? (LO 2) Solution: Years to maturity = n = 10 Coupon rate = C = 0% Current market rate = i = 5.65% Frequency of payments = m = 2

0 1 2 3 4 5 6 20 ─────┤ ├───┼────┼───┼───┼───┼────┼── $0 $0 $0 $0 $0 $0 $0 $1,000 F $1,000 mn P= = =$572.83 B mn 2x10 i (1 0.0565/2 + ) m

( 1 +)

Financial Calculator Solution: Enter

40

−1,100

1,000

N

i

PMT

Answer

PV

FV

3.31

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.3

Bigbox, Inc. has bonds outstanding that will mature in eight years. These bonds pay interest semiannually and have a coupon rate of 4.6 percent. If the bonds are currently selling at $888.92, what is the yield to maturity that an investor who buys them today can expect to earn? What is the effective annual yield? (LO 3) Solution: Years to maturity = n = 8 Coupon rate = C = 4.6% Current market rate = i

.

SM 8-68

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Semiannual coupon payment = $1,000 × (0.046/2) = 23 Present value of bond = PB = $888.92 0 1 2 3 16 ─────────┤ ├───────┼────────┼────────┼── (888.92) $23 $23 $23 $23 $1,000 To solve for the YTM, a trial-and-error approach has to be used. Since this bond is selling at a discount, we know that the market rate is higher than 4.6 percent.

Try i = 6% or i/2 = 3%.

1    1 i −  (1+ 2)n  FV =  PB C  + i + i   (1 2)n 2     1   1 −(1.03)16 $1,000 = $23   (1.03)16  0.03   +   = $288.91+ $623.16= $912.17  $888.92  Try a higher rate, i = 7%, i/2 = 3.5%.

1    1 i −  (1+ 2)n  FV =  PB C  + i i   (1+ 2)n 2      1  1 −(1.035)16 $1,000 = $23    0.0 3 5  + (1.035)16     = $278.17 + $576.71=$854.57  $888.92 Try a lower rate, i = 6.4%, i/2 = 3.2%.

.

SM 8-69

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

 1  1−(1+ i)n  FV  PB = C   i + (1+ i )n      1  − 1  (1.032)16 $1,000 $882.92=$23   0.032  +  (1.032)16    = =$284.54+$604.12 $888.66$888.92 The YTM is approximately 6.4 percent.

Using a financial calculator provides an exact YTM of Enter Answer

16 N

i% 6.395%

$23 PMT

6.395 percent

-$888.92 PV

$1,000 FV

The effective annual yield can be computed as: EAY=(1+Quoted ratem)m−1

=(1+0.063952 2) −1 = (1.03198)2 −1 = 0.064972 = 6.497%

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.4

Given a change in market interest rates, which will change more; the market price of a bond with 20 years until maturity or the market price of a bond with 5 years until maturity? Assume all the characteristics of these bonds are identical except the maturity dates. (LO 4 ) Solution: The price of the bond with 20 years to maturity will change more. The cash flows from the longer term bond are paid further in the future. As a result, these cash flows are more heavily discounted and therefore more sensitive to interest rate changes.

Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-70

Fundamentals of Corporate Finance, 4th edition

8.5

Solutions Manual

Which of the following classes of securities is likely to have the lowest corporate borrowing cost? (LO 5) a. AAA rated bonds. b. A rated bonds. c. BB rated bonds. d. C rated bonds. e. All of the above will have the same corporate borrowing cost.

Solution: a.

The issuers of AAA rated bonds should have the lowest borrowing cost because their default risk premium is lower than issuers with weaker credit ratings.

Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 8-71

Fundamentals of Corporate Finance,4th edition

Solutions Manual

Chapter 9 Stock Valuation Before You Go On Questions and Answers

Section 9.1 1. What is NASDAQ? The NASDAQ system is one of the largest electronic stock markets in the world, listing over three thousand companies. It was created in 1971 by the National Association of Securities Dealers.

2. How do dealers differ from brokers?

A dealer differs from a broker in that a dealer takes ownership of assets and is exposed to inventory risk, while a broker only facilitates a transaction on behalf of a client. Unlike brokers, dealers are subject to capital risk, because they must finance their inventories of securities.

3. List the major stock market indexes, and explain what they tell us.

The major U.S. Stock market indexes are the Dow Jones Industrial Average, New York Stock Exchange, Standard & Poor’s 500 Index, and NASDAQ Composite Index. A stock market index is essentially a listing of stocks that bear some commonality, such as being traded on the same market exchange. They are used to measure the stock market performance and many are used to benchmark the performance of portfolios, such as mutual funds.

.

SM 9-1

Fundamentals of Corporate Finance,4th edition

Solutions Manual

4. What does the price-earnings ratio tell us?

The price-earnings ratio is the firm’s current price divided by the current earnings. When valuing a company’s stock, it is useful to look at a company’s P/E ratio and compare it to that of similar firms. In general, a high P/E ratio means high projected earnings in the future. In addition, it also tells us how much investors are willing to pay per dollar of earnings.

5. Why do some people view preferred stock as a special type of a bond rather than a stock?

Just like debt, preferred stock is often callable and may be convertible into common stock.

Also, like debt, it has “credit” ratings that are similar to those issued to bonds. But most important, preferred stock has no voting rights and just like bonds pays fixed dividends. For these reasons, many analysts treat preferred stock as a special kind of debt rather than as an equity.

Section 9.2 1.

What is the general formula used to calculate the price of a share of a stock? What does it mean?

The general formula developed to value a share of stock is as follows: P= 0

D3 D5 D1 D2 D4 + + + + +  2 3 4 (1 + R) (1 + R) 5 (1 + R) (1 + R) (1 + R)

It says that the price of a share of stock is the present value of all expected future dividends, or: Stock price = PV (all future cash dividends).

2. What are growth stocks, and why do they typically pay little or no dividends?

Growth stocks are defined as equity in any company whose earnings are growing faster than the average firm and the higher growth rate is expected to continue for some time. Instead of

.

SM 9-2

Fundamentals of Corporate Finance,4th edition

Solutions Manual

paying dividends, these firms reinvest the earnings back into the firm to pursue other highreturn investment opportunities.

Section 9.3 1.

What three different models are used to value stocks based on different dividend patterns?

Based on dividend patterns, we can use the following three models to value stock: (1) zerogrowth dividend model, (2) constant-growth dividend model, or (3) supernormal dividend growth model.

2. Explain why the growth rate g must always be less than the rate of return R for the constantgrowth rate model?

The constant-growth rate model assumes that the firm will grow at a constant rate forever.

Any growth rate that is greater than this sum would imply that the firm will eventually take over the entire economy. This is of course not possible. Mathematically, according to the model, if g becomes greater than R, then the value of the stock would be negative.

Section 9.4 1. Why can skipping payment of a preferred dividend be a bad signal?

A preferred dividend is treated like an interest payment on debt by financial markets and investors. Although the firm will not be in default, any delay or failure to pay the dividends by the firm will be treated seriously by the financial markets and make them think that the firm is in financial difficulty.

2. How is a preferred stock with a fixed maturity valued?

Any preferred stock with a defined maturity date is similar to a bond with a fixed maturity date. This similarity allows for the preferred stock to be valued in a similar fashion after making adjustments for differences in the preferred stock relative to a bond. Using Equation

.

SM 9-3

Fundamentals of Corporate Finance,4th edition

Solutions Manual

8.2, developed to value bonds, the coupons are replaced by the preferred dividends and the number of payments is adjusted to four a year to accommodate the fact that firms pay the dividends every quarter and not semi-annually. This results in the model represented by Equation 9.7.

Self- Study Problems

9.1

Ted McKay has just bought the common stock of Ryland Corp. The company expects to grow at the following rates for the next three years: 30 percent, 25 percent, and 15 percent. Last year the company paid a dividend of $2.50. Assume a required rate of return of 10 percent. Compute the expected dividends for the next three years and also the present value of these dividends.

Solution: Expected dividends for Ryland Corp and their present value: 0

10%

1

2

3

├─────────┼─────────┼─────────┼─────────┼────────── D0 = $2.50

D1

g1 = 30%

D2

D3

g2 = 25%

g3 = 15%

R = 10%

D1 = D0 × (1 + g1) = $2.50(1 + 0.30) = $3.25 D2 = D1 × (1 + g2) = $3.25(1 + 0.25) = $4.06 D3 =

D2 × (1 + g3) = $4.06(1 + 0.15) = $4.67

Present value of the dividends = PV(D1) + PV(D2) + PV(D3) = $2.95 + $3.36 + $3.51 = $9.82 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F)

.

SM 9-4

Fundamentals of Corporate Finance,4th edition

0 1 2 3

Solutions Manual

0 3.25 4.06 4.67

-1 1 1

Then solve by pressing NPV, enter the rate of 10% and compute NPV=9.82.

9.2

Merriweather Manufacturing Company has been growing at a rate of 6 percent for the past two years, and the CEO expects the company to continue to grow at this rate for the next several years. The company paid a dividend of $1.20 last year. If your required rate of return is 14 percent, what is the maximum price that you would be willing to pay for this company’s stock?

Solution: Present value of Merriweather stock: 0

14%

1

2

3

├─────────┼─────────┼─────────┼─────────┼────────── D0 = $1.20

D1

D2

D3

g = 6% R = 14% D1 = D0 × (1 + g) = $1.20(1 + 0.06) = $1.27

D1 P0 = (R−g) =

$1.2 7 (0.14−0.06)

= $15.88 The maximum price you should be willing to pay for this stock is 9.3

$15.88.

Clarion Corp. has been selling electrical supplies for the past 20 years. The company’s product line has changed very little in the past five years, and the company’s management does not expect to add any new items for the foreseeable future. Last year,

.

SM 9-5

Fundamentals of Corporate Finance,4th edition

Solutions Manual

the company paid a dividend of $4.45 to its common stockholders. The company is not expected to increase its dividends for the next several years. If your required rate of return for such firms is 13 percent, what is the current value of this company’s stock?

Solution: Present value of Clarion Corp. stock: 0

13%

1

2

3

Year

├─────────┼─────────┼─────────┼─────────┼────────── D0 = $4.45

D1

D2

D3

g = 0% R = 13% Since the company’s dividends are not expected to grow, D0 = D1 =D2=……..D∞ = $4.45 = D Current value of the stock

9.4

=

D/R

=

$4.45/0.13

=

$34.23

Barrymore Infotech is a fast-growing communications company. The company did not pay a dividend last year and is not expected to do so for the next two years. Last year the company’s growth accelerated, and management expects to grow the business at a rate of 35 percent for the next five years before growth slows to a more stable rate of 7 percent.

In the third year, management has forecasted a dividend payment of $1.10. Dividends will grow with the company thereafter. Calculate the value of the company’s stock at the end of its rapid growth period (i.e., at the end of five years). The required rate of return for such stocks is 17 percent. What is the current value of this stock?

Solution: Present value of Barrymore Infotech stock: 0 17% 1

2

3

4

5

6

7

8

├────┼────┼────┼────┼────┼────┼────┼────┤

.

SM 9-6

Fundamentals of Corporate Finance,4th edition D0

D1

D2

D3

D4

Solutions Manual D5

D6

g1 – g5 = 35% R = 17%g6 and beyond = 7% D0 = D1 = D2 = 0 D3 = $1.10 D4 = D3 × (1 + g4) = $1.10(1 + 0.35) = $1.485 D5 = D4 × (1 + g5) = $1.485(1 + 0.35) = $2.005 D6 = D5 × (1 + g6) = $2.005(1 + 0.07) = $2.145

Value of stock at

P5:

D6 P5 = (R−g) =

$2.145 (0.17−0.07)

= $21.45 Present value of the dividends in years 1 to 5 = PV(D1) + PV(D2) + PV(D3) + PV(D4) + PV(D5) = $0

Financial Calculator Solution :

$1.10 $1.485 $2.005 + + (1.17)3 + (1.17)4 + (1.17)5

= $0 $0 + $0.69+$0.79+$0.91 = + $0 $2.3 9

Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -0 1 1 0 1 2 3 1.10 1 4 1.485 1 5 2.005 1 Then solve by pressing NPV, enter the rate of 17% and compute NPV=2.39.

Current value of stock = PV(Dividends) + PV(P5) = $2.39 + [$21.45/(1.17)5] = $2.39 + $9.78 = $ 12.17

.

SM 9-7

Fundamentals of Corporate Finance,4th edition

9.5

Solutions Manual

You are interested in buying the preferred stock of a bank that pays a dividend of $1.80 every quarter. If you discount such cash flows at 8 percent, what is the value of this stock?

Solution: Present value of preferred bank stock: Quarterly dividend on preferred stock = D = $1.80 Required rate of return = 8% Current value of stock = D P0 = R $1.80  4 =

0.08

= $90.00

Discussion Questions 9.1

Why can the market price of a stock differ from its true (intrinsic) value?

Let us start by first defining the market price of a stock as the price that equates the demand for a stock with the supply of the stock. The role of the stock market is to bring buyers and sellers together in the most efficient way such that stocks are bought and sold at the market price. In reality, however, barriers of various kinds including the geographic separation of the two parties, strong demand that leads to overvaluation and vice versa, make the market price of a security slightly different than its true (intrinsic) value. The more efficient the market place, the smaller the deviation between the two.

LO: 1 Level: Basic Bloomcode: Comprehension

.

SM 9-8

Fundamentals of Corporate Finance,4th edition

Solutions Manual

AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.2

Why are investors and managers concerned about stock market efficiency?

The role of secondary markets is to bring buyers and sellers together. Ideally, we would like stock markets to be as efficient as possible. Markets are efficient when current market prices of securities traded reflect all available information relevant to the security.

If this is the case, security prices will be near or at their true value. The more efficient the market, the more likely this is to happen. This makes it easier for managers to price the stocks close to their intrinsic value.

What investors are most concerned about is having complete information regarding a stock’s current price and where that price information can be obtained.

Efficient markets allow them to trade at prices that are closer to the true value than otherwise possible.

Thus, both investors who provide funds and managers (firms) who raise money are concerned when high transaction costs lead to inefficient markets.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.3

Why are common stockholders considered to be more at risk than the holders of other types of securities?

In the hierarchy of lenders of funds to a firm, common stockholders have the most to lose. In the event of a firm becoming bankrupt, the law requires that creditors of different types, including bondholders, be paid off first. Next, preferred stockholders are paid off.

Finally, common stockholders receive their investment if any funds are still available.

Thus, common stockholders receive their money back last and are placed at most risk.

This feature of common equity is referred to as residual claim.

.

SM 9-9

Fundamentals of Corporate Finance,4th edition

Solutions Manual

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.4

Under what conditions does it make sense to use the constant-growth dividend model to value a stock?

It only makes sense to use the constant-growth dividend model to value the stock of a company that is already paying a dividend and when that dividend can reasonably be expected to grow at a constant rate forever⎯in other words, the stock of a mature company. As discussed in the chapter, the growth rate of such a company will be less than the sum of the long term rate of inflation and the real growth rate of the economy. It must also be less than the required rate of return on the stock.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.5

What does it mean when a company has a very high P/E ratio? Give examples of industries in which you believe high P/E ratios are justified.

A high P/E ratio implies that investors believe that the firm has good prospects for earnings growth in the future. In fact, they believe that the firm will have higher growth potential than firms with lower P/E ratios. Companies in industries that are fast growing like biotech or any hi-tech industry have high P/E ratios. In the past, firms like Cisco and Intel had very high P/E ratios. As these firms matured and settled to annual growth rates of 15 percent or less, their P/E ratios have declined.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic

.

SM 9-10

Fundamentals of Corporate Finance,4th edition

Solutions Manual

IMA: Corporate Finance AICPA: Measurement

9.6

Explain why preferred stock is considered to be a hybrid of equity and debt securities.

The law considers preferred stock as equity. Thus, holders are treated as the firm’s owners. Also, like common stockholders, preferred stockholders have to pay taxes on their dividend income. However, preferred stockholders do not have any voting rights. In addition, they receive only a fixed dividend just like bondholders. If a firm is liquidated, then they receive a stated value (par value) similar to bondholders. Preferred stock is rated by credit rating agencies just like bonds. Some preferred issues are convertible to the firm’s common stock just as convertible bonds. Some preferred issues are not perpetual and have a fixed maturity just like bonds.

Thus preferred stock is a hybrid security—like equity in some ways and like debt security in others.

LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.7

Why is stock valuation more difficult than bond valuation?

Despite the availability of mathematical models to value stocks, it is more difficult to apply valuation techniques to stocks than to bonds. First, unlike bonds, firms are not in default if dividends are not declared. This makes it difficult to determine the size and timing of the cash flows. Second, common stock, unlike bonds, does not have a fixed maturity, and hence, it is difficult to determine a terminal value unlike bonds, which have a maturity value. Next, it is easier to calculate the present value of a bond because the required rate of return is observable. In the case of stocks, it is rather difficult to estimate a required rate of return for many stocks and classify them into different risk groups.

LO: 2

.

SM 9-11

Fundamentals of Corporate Finance,4th edition

Solutions Manual

Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.8

You are currently thinking about investing in a stock valued at $25.00 per share.

The stock recently paid a dividend of $2.25 and its dividend is expected to grow at a rate of 5 percent for the foreseeable future. You normally require a return of 14 percent on stocks of similar risk. Is the stock overpriced, underpriced, or correctly priced?

D0 = $2.25 Required rate of return (R) = 14% Growth rate (g) = 5% Using Constant-growth model, the price of stock is:

P0 = =

D(1 + g) D1 0 =R R−g −g $2.25(1.05)

= $26.25

0.14 − 0.05 This stock is underpriced at $25. Using the constant-growth model, we arrived at a price of $26.25 for this stock. This makes the stock underpriced, and it should be considered a good buy.

LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.9

Stock A and Stock B are both priced at $50 per share. Stock A has a P/E ratio of 17, while Stock B has a P/E ratio of 24. Which is the more attractive investment, considering everything else to be the same, and why?

.

SM 9-12

Fundamentals of Corporate Finance,4th edition

Solutions Manual

Stock A is the more attractive investment because it has a lower P/E ratio. The lower the P/E ratio, the larger the amount of earnings supporting the stock price. This makes Stock A a more attractive investment than Stock B. LO: 1 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.10 Facebook does not pay dividends. How can it have a positive stock price?

Investors expect that Facebook will eventually start paying dividends and the value of its shares reflects the present value of these expected dividends. The fact that a company is not currently paying dividends does not mean that its stock is worthless. It is not uncommon for high growth firms not to pay dividends, since they often have to reinvest all of their earnings to maintain their high growth rate. However, if they are successful, as their growth rate slows over time they will begin to pay dividends.

LO: 3, 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems

BASIC 9.1

Stock Market Index: What is a stock market index?

Solution:

.

SM 9-13

Fundamentals of Corporate Finance,4th edition

Solutions Manual

A stock market index is used to measure the performance of the stock market. These indexes reflect the value of the stocks in a particular market, such as the NYSE or the NASDAQ, or across markets, and increase and decrease as the values of the stocks go up and down. Examples of stock market indexes include the Dow Jones Industrial Average, the New York Stock Exchange Index, the Standard & Poor’s 500 Index, and the NASDAQ Composite Index.

LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.2

Stock Market Index: What is the Dow Jones Industrial Average?

Solution: The Dow is the most widely published stock index and reflects the value of the stocks of 30 large companies. The value of the shares of these companies represents about 20 percent of the market value of all U.S. stocks.

LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.3

Stock Market Index: What does NASDAQ stand for? What is NASDAQ?

Solution: NASDAQ stands for National Association of Securities Dealers Automated Quotation system. NASDAQ is one of the largest electronic stock markets in the world, listing over three thousand companies. It is an OTC market and does not have any physical location.

Companies listed on NASDAQ had market capitalization of $10.2 trillion as of February 2017.

LO 1 Bloomcode: Knowledge AASCB: Analytic

.

SM 9-14

Fundamentals of Corporate Finance,4th edition

Solutions Manual

IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.4

Dividend yield: What is a dividend yield? What does it tell us?

Solution: A dividend yield is the ratio of the annual dividend payout and the current market price of a stock. It tells us what percentage return we would earn from dividends alone if we purchased the stock at its current price. Alternatively, it tells us what percentage of the firm’s stock value is being distributed to stockholders each year.

LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.5

Present value of dividends:Fresno Corp. is a fast-growing company whose management expects it to grow at a rate of 30 percent over the next two years and then slow down to a growth rate of 18 percent for the following three years. If the last dividend paid by the company was $2.15, estimate the dividends for the next five years.

Compute the present value of these dividends if the required rate of return is 14 percent.

Solution: 0

1

2

3

4

5

├───────┼────────┼───────┼────────┼───────┤ D0 = $2.15

g1-2 = 30%;

g3-5 = 18%;

R = 14%

D1 = D0 × (1 + g1) = $2.15(1.30) = $2.795 D2 = D1 × (1 + g2) = $2.795(1.30) = $3.634 D3 = D2 × (1 + g3) = $3.634(1.18) = $4.288 D4 = D3 × (1 + g4) = $4.288(1.18) = $5.06 D5 = D4 × (1 + g5) = $5.06(1.18) = $5.97

.

SM 9-15

Fundamentals of Corporate Finance,4th edition

Solutions Manual

$2.795 $3.634 $4.288 $5.06 $5.9 7 + (1.14)2 + + + (1.14)1 (1.14)3 (1.14)4 (1.14)5 = $2.45+$2.80+$2.89+$3.00+$3.10

PV( Dividends ) =

= $14.24

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2.795 1 2 3.634 1 3 4.288 1 4 5.06 1 5 5.97 1 Then solve by pressing NPV, enter the rate of 14% and compute NPV=14.24.

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.6

Zero growth: Nynet, Inc., paid a dividend of $4.18 last year. The company’s management does not expect to increase its dividend in the foreseeable future. If the required rate of return is 18.5 percent, what is the current value of the stock?

Solution: D0 = $4.18; g = 0;

LO 4

R = 18.5%

D $4.1 = $22.60 P0 = R = 8 0.18 5

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-16

Fundamentals of Corporate Finance,4th edition

9.7

Solutions Manual

Zero growth: Knight Supply Corp. has not grown for the past several years and management expects this lack of growth to continue. The firm last paid a dividend of $3.56. If you require a rate of return of 13 percent, what is the current value of this stock to you?

Solution: D0 = $3.56; g = 0;

R = 13%

D $3.56 = $27.38 P0 = R = 0.13

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.8

Zero growth: Ron Santana is interested in buying the stock of First National Bank. While the bank’s management expects no growth in the near future, Ron is attracted by the dividend income. Last year the bank paid a dividend of $5.65. If Ron requires a return of 14 percent on such stocks, what is the maximum price he should be willing to pay for a share of the bank’s stock?

Solution:

D0 = $5.65; g = 0; R = 14% D R $5.6 5 = $40.36 P0 = = 0.14 LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.9

Zero growth: The current stock price of Largent, Inc., is $44.72. If the required rate of return is 19 percent, what is the dividend paid by this firm if the dividend is not expected to grow in the future?

.

SM 9-17

Fundamentals of Corporate Finance,4th edition

Solutions Manual

Solution: P0 = $44.72;

R = 19%;

D = ?;

D P0= R $44.72=

D

0.19 D=$44.720.19= $8.50

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.10 Constant growth: Moriband Corp. paid a dividend of $2.15 yesterday. The company’s dividend is expected to grow at a steady rate of 5 percent for the foreseeable future. If investors in stocks of companies like Moriband require a rate of return of 15 percent, what should be the market price of Moriband stock?

Solution: D0 = $2.15;

P0 = =

g = 5%;

R = 15%

D1 D(1 + g) =0 R−g R −g $2.15(1.05) 0.15 − 0.05

= $22.58

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.11 Constant growth: Nyeil, Inc., is a consumer products firm that is growing at a constant rate of 6.5 percent. The firm’s last dividend was $3.36. If the required rate of return is 18

.

SM 9-18

Fundamentals of Corporate Finance,4th edition

Solutions Manual

percent, what is the market value of this stock if dividends grow at the same rate as the firm?

Solution: D0 = $3.36;

P0 =

g = 6.5%;

R = 18%

D1 $3.36(1.065) = R − g 0.18−0.065

= $31.12 LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.12 Constant growth: Reco Corp. is expected to pay a dividend of $2.25 next year. The forecast for the stock price a year from now is $37.50. If the required rate of return is 14 percent, what is the current stock price? Assume constant growth.

Solution: D1 = $2.25;

.

P1 = $37.50; R = 14%

SM 9-19

Fundamentals of Corporate Finance,4th edition

P1 = $37.50 =

Solutions Manual

D 1(1+g) D 2 = R −g R−g $2.25(1 + g ) 0.14−g

$37.50(0.14−g) = $2.25+2.25g $5.25−37.5g = 2.25+2.25g $5.25 − $2.25= 37.5g+2.25g g=

$3.00 = 7.55% $39.75

P0 =

D1 R−g

=

$2.25 0.14−0.0755

= $34.87

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.13 Constant growth: Proxicam, Inc., is expected to grow at a constant rate of 7 percent. If the company’s next dividend, which will be paid in a year, is $1.15 and its current stock price is $22.35, what is the required rate of return on this stock?

Solution: D1 = $1.15;

.

P0 = $22.35; g = 7%

SM 9-20

Fundamentals of Corporate Finance,4th edition

P0 =

Solutions Manual

D1 R−g

D R = 1+g P0 =

$1.15 + 0.07 $22.35

= 0.0515+ 0.07 = 12.15% LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.14 Preferred stock valuation: X-Centric Energy Company has issued perpetual preferred stock with a stated (par) value of $100 and a dividend of 4.5 percent. If the required rate of return is 8.25 percent, what is the stock’s current market price?

Solution: D = 4.5% ($100) = $4.50;

R = 8.25%

P0= D = $4.5 0 =$54.55 R 0.0825

LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.15 Preferred stock valuation: The First Bank of Flagstaff has issued perpetual preferred stock with a $100 par value. The bank pays a quarterly dividend of $1.65 on this stock.

What is the current price of this preferred stock given a required rate of return of 11.6 percent?

Solution: Quarterly dividend = $1.65 .

SM 9-21

Fundamentals of Corporate Finance,4th edition

Solutions Manual

Required rate of return = R = 11.6%  P0= (1.65 4) =$56.90 0.1 1 6

LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.16 Preferred stock valuation: The preferred stock of Axim Corp. is currently selling at $47.13. If the required rate of return is 12.2 percent, what is the dividend paid by this stock?

Solution: P0 = $47.13; R = 12.2%

D P0 =$47.13= 0.1 2 2 D = $47.130.122 = $5.75 LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.17 Preferred stock valuation: Each quarter, Sirkota, Inc., pays a dividend on its perpetual preferred stock. Today the stock is selling at $63.37. If the required rate of return for such stocks is 15.5 percent, what is the quarterly dividend paid by Sirkota?

Solution: P0 = $63.37; R = 15.5%

.

SM 9-22

Fundamentals of Corporate Finance,4th edition

Solutions Manual

D 0.1 5 5 D=$63.37  0.155 =$9.82

P0 = $63.37=

Annual dividend = $9.82 Quarterly dividend = $9.82 /4 = $2.46 LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

INTERMEDIATE 9.18 Constant growth: Kay Williams is interested in purchasing the common stock of Reckers, Inc., which is currently priced at $37.45. The company is expected to pay a dividend of $2.58 next year and to increase its dividend at a constant rate of 7 percent. a. What should the market value of the stock be if the required rate of return is 14 percent? b. Is this a good buy? Why or why not?

Solution: a.

P= 0 b.

D1 $2.58 = =$36.86 R − g 0.14 − 0.07

The stock is overpriced and not a good buy.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-23

Fundamentals of Corporate Finance,4th edition

Solutions Manual

9.19 Constant growth: The required rate of return is 23 percent. Ninex Corp. has just paid a dividend of $3.12 and is expected to increase its dividend at a constant rate of 5 percent.

What is the expected price of the stock three years from now?

Solution: R = 23%; P3 = =

D0 = $3.12;

g = 5%

D4 D(1 + g) 4 = 0 R−g R −g 3.12(1.05)4 0.23 − 0.05

= $21.07

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.20 Constant growth: Jenny Banks is interested in buying the stock of Fervan, Inc., which is increasing its dividends at a constant rate of 6 percent. Last year the firm paid a dividend of $2.65. The required rate of return is 16 percent. What is the current value of this stock?

What should be the price of the stock in year 5?

Solution: g = 6%, D0 = $2.65, R = 16% D P $2.65(1.06) 1 = = = $28.09 0 R − g 0.16 − 0.06

P5 =

D6 $2.65(1.06)6 = = $37.59 R−g 0.16 − 0.06

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-24

Fundamentals of Corporate Finance,4th edition

Solutions Manual

9.21 Constant growth: You own shares of Old World DVD Company and are interested in selling them. With so many people downloading music these days, sales, profits, and dividends at Old World have been declining 6 percent per year. The firm just paid a dividend of $1.15 per share. The required rate of return for a stock this risky is 15 percent. If dividends are expected to decline at 6 percent per year, what is a share of the stock worth today?

Solution: R = 15%; P0 = =

D0 = $1.15;

g = -6%

D1 D (1 +g) = 0 R −g R−g $1.15  (1 − 0.06) = $5.15 −( − 0.06) 0.15

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.22 Nonconstant growth: You own a company that competes with Old World DVD Company (in the previous problem). Instead of selling DVDs, however, your company sells music downloads from a web site. Things are going well now, but you know that it is only a matter of time before someone comes up with a better way to distribute music.

Your company just paid a $1.50 per share dividend, and you expect to increase the dividend 10 percent next year. However, you then expect your dividend growth rate to begin going down – to 5 percent the following year, 2 percent the next year, and to -3 percent per year thereafter. Based upon these estimates, what is the value of a share of your company’s stock? Assume that the required rate of return is 12 percent.

Solution: g1 = 10%, g2 = 5%, g3 =2%, D1 = $1.50 × 1.1 = $1.65, $1.7672,

.

g = -3%,

D0 = $1.50

R = 12%

D2 = $1.65 × 1.05 = $1.7325, D3 = $1.7325 ×1.02 =

D4 = $1.7672 × 0.97 = $1.7141.

SM 9-25

Fundamentals of Corporate Finance,4th edition

P3 =

D4 $1.7141 = = $11.43 R − g 0.12 − (−0.03)

P0 =

D1 D2 D3 P3 + + + 1 + R (1+ R)2 (1+ R)3 (1+ R)3

Solutions Manual

$1.65 $1.7325 $1.7672 $11.43 + + + 1.12 (1.12)2 (1.12)3 (1.12)3 P = $1.47 + $1.38 + $1.26 + $8.14 P0 = 0

P0 = $12.25 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 1.65 1 2 1.7325 1 3 1.7672 + 11.43 =13.1972 1 Then solve by pressing NPV, enter the rate of 12% and compute NPV=12.25.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.23 Nonconstant growth: Tre-Bien, Inc., is a fast-growing technology company.

Management projects rapid growth of 30 percent for the next two years, then a growth rate of 17 percent for the following two years. After that, a constant-growth rate of 8 percent is expected. The firm expects to pay its first dividend of $2.45 a year from now.

If dividends will grow at the same rate as the firm and the required rate of return on stocks with similar risk is 22 percent, what is the current price of the stock?

.

SM 9-26

Fundamentals of Corporate Finance,4th edition

Solutions Manual

Solution: g1 = g2 = 30%, D1 = $2.45,

g3 = g4 = 17%,

g = 8%,

D2 = $2.45 × 1.30 = $3.19,

D4 = $3.73 × 1.17 = $4.36,

D1 = $2.45,

R = 22%

D3 = $3.19 × 1.17 = $3.73

D5 = 4.36 × 1.08 = $4.71

P= 4

D5 $4.71 = =$33.63 R − g 0.22 − 0.08

P0 =

D3 D1 D2 D4 P4 + + + + (1+ R)2 (1+ R)3 (1+ R)4 (1+ R)4 1+R

P0 =

$2.45 $3.19 $3.73 ($4.36+33.63) + + + (1.22)4 1.22 (1.22)2 (1.22)3

P0 = $2.01+$2.14+$2.05+17.15 P0 = $23.35 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2.45 1 2 3.19 1 3 3.73 1 4 4.36 + 33.63 = 37.99 1 Then solve by pressing NPV, enter the rate of 22% and compute NPV=23.35.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.24 Nonconstant growth: Management of ProCor, a biotech firm, forecasted the following growth rates for the next three years: 35 percent, 28 percent, and 22 percent. Management

.

SM 9-27

Fundamentals of Corporate Finance,4th edition

Solutions Manual

then expects the company to grow at a constant rate of 9 percent forever. The company paid a dividend of $1.75 last week. If the required rate of return is 20 percent, what is the value of this stock?

Solution: g1 = 35%; g2 = 28%; g3 = 22%; g4 = 9%; D0 = $1.75; R = 20%

+ g 1 )=$1.751.35=$2.36 D 1 = D(1 0 D 2 = D(1 + g2 )=$2.361.28=$3.02 1

D 3 = D(1 + g 3 )=$3.021.22=$3.69 2

D

4

= D(1 + g )=$3.691.09=$4.02 3

P3 =

D4 $4.02 = = $36.57 R − g 0.20 − 0.09

P0 =

D1 D2 D3 P3 + + + 1 + R (1+ R)2 (1+ R)3 (1+ R)3

$2.36 $3.02 $3.69 $36.57 + + + 1.20 (1.20)2 (1.20)3 (1.20)3 P = $1.97+ $2.10 + $2.14 + $21.16

P0 = 0

P0 = $27.37 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2.36 1 2 3.02 1 3 3.69 + 36.57=40.26 1 Then solve by pressing NPV, enter the rate of 20% and compute NPV=27.37.

LO 5 Bloomcode: Application

.

SM 9-28

Fundamentals of Corporate Finance,4th edition

Solutions Manual

AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.25 Nonconstant growth: Revarop, Inc., is a fast-growth company that is expected to grow at a rate of 23 percent for the next four years. It is then expected to grow at a constant rate of 6 percent. Revarop’s first dividend, of $4.25, will be paid in year 3. If the required rate of return is 17 percent, what is the current value of the stock if dividends are expected to grow at the same rate as the company?

Solution: g1-4 = 23%; g = 6%; D3 = $4.25;

R = 17%

D4 = D3 × 1.23 = $4.25 × 1.23 = $5.23 P4 =

D5 $5.23 (1.06) = = $50.37 R−g 0.17 − 0.06

P0 =

D+P D3 D1 D2 + + 4 4 + (1+ R)2 (1+ R)3 (1+ R)4 1 +R

P0 = 0 + 0 +

$4.25

($5.23 + $50.37) (1.17)4 (1.17)3 +

P0 = $2.65 + $29.69 = $32.33

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 0 1 2 0 1 3 4.25 1 4 5.23 + 50.37 =55.60 1 Then solve by pressing NPV, enter the rate of 17% and compute NPV=32.33.

LO 5

.

SM 9-29

Fundamentals of Corporate Finance,4th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.26 Nonconstant growth: Quansi, Inc., management expects to pay no dividends for the next six years. It has projected a growth rate of 25 percent for the next seven years. After seven years, the firm will grow at a constant rate of 5 percent. Its first dividend, to be paid in year 7, will be $3.25. If the required rate of return is 24 percent, what is the stock worth today?

Solution: g = 5%; R = 24%; D7 = $3.25; D1 – D6 = 0

P7 =

$3.25 (1.05) D8 = = $17.96 R−g 0.24 − 0.05

P0 =

D 7+ P 7 $3.25 + $17.96 = = $4.71 (1.24)7 (1+R)7

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 0 6 2 3.25 + 17.96 = 21.21 1 Then solve by pressing NPV, enter the rate of 24% and compute NPV=4.71.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-30

Fundamentals of Corporate Finance,4th edition

Solutions Manual

9.27 Nonconstant growth: Staggert Corp. will pay dividends of $5.00, $6.25, $4`.75, and $3.00 in the next four years. Thereafter, management expects the dividend growth rate to be constant at 6 percent. If the required rate of return is 18.5 percent, what is the current value of the stock?

Solution: D1 = $5;

D2 = $6.25; D3 = 4.75; D4 = $3;

g = 6%; R = 18.5%;

P0 =

D1 D2 D3 D4 P4 + + + + 1 + R (1+R)2 (1+R)3 (1+R)4 (1+R)4

P4 =

$3  (1.06) D5 = = $25.44 R − g 0.185 − 0.06

P0 =

$6.25 $4.75 ($3+$25.44) $5 + (1.185)3+ (1.185)4 + 1.185 (1.185)2

P0 = $4.22+ $4.45 + $2.86 + $14.42 = $25.95 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -5 1 1 6.25 1 2 4.75 1 3 3 + 25.44 =28.44 1 4 Then solve by pressing NPV, enter the rate of 18.5% and compute NPV=25.95.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-31

Fundamentals of Corporate Finance,4th edition

Solutions Manual

9.28 Nonconstant growth: Diaz Corp. is expected to grow rapidly/ at a rate of 35 percent for the next seven years. The company’s first dividend, to be paid three years from now, will be $5. After seven years, the company (and the dividends it pays) will grow at a rate of 8.5 percent. What is the value of Diaz stock with a required rate of return of 14 percent?

Solution: g1-7 = 35%; D3 = $5.00; g = 8.5%; R = 14% D1 = D2 = 0;

D3 = $5

D4 = $5 × 1.35 = $6.75 D5 = $6.75 × 1.35 = $9.11 D6 =$9.11 × 1.35 = $12.30 D7 = $12.30 × 1.35 = $16.61 D8 = $16.61 × 1.085 = $18.02 P7 =

$18.02 D8 = = $327.64 R − g 0.14 − 0.085

P0 =

D+P 7 D1 D2 D3 D4 D5 D6 + + + + + 7 + (1+ R)2 (1+ R)3 (1+ R)4 (1+ R)5 (1+ R)6 (1+ R)7 1 +R

$6.75 $9.11 $12.30 ($16.61+$327.64) + + + (1.14)7 (1.14)3 (1.14)4 (1.14)5 (1.14)6 = $3.38+ $4.00+$4.73+$5.60+$137.58 = 0+0+

$5

+

= $155.29

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -0 0 2 1 5 1 2 6.75 1 3 9.11 1 4 12.30 1 5

.

SM 9-32

Fundamentals of Corporate Finance,4th edition

6

Solutions Manual

16.61 + 327.64 =344.25

1

Then solve by pressing NPV, enter the rate of 14% and compute NPV=155.28.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.29 Nonconstant growth: Tin-Tin Waste Management, Inc., is growing rapidly. Dividends are expected to grow at rates of 30 percent, 35 percent, 25 percent, and 18 percent over the next four years. Thereafter, management expects dividends to grow at a constant rate of 7 percent. The stock is currently selling at $47.85, and the required rate of return is 16 percent. Compute the dividend for the current year (D0).

Solution: g1 = 30%; g 2 = 35%; g 3 = 25%; g 4 = 18%; g = 7%; R = 16%; P0 = $47.85

P0 = $47.85 =

D3 D1 D2 D4 P4 + + + + (1+ R 1) (1+ R 2)2 (1+ R 3)3 (1+ R 4)4 (1+ R 4)4 D0 (1.30) 1.16

+

D 0(1.30)(1.35) (1.16)2

+

D (1.30)(1.35)(1.25)(1.18) + 0 (1.16)4

D 0(1.30)(1.35)(1.25) (1.16)3

D 0(2.5886)(1.07) 0.16−0.07 + (1.16)4

$47.85=D [1.12+1.30+1.41+1.43+17.00] 0 D 0=

$47.85 =$2.15 $22.26

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

ADVANCED

.

SM 9-33

Fundamentals of Corporate Finance,4th edition

Solutions Manual

9.30 Equation 9.4 shows the relation between a stock’s value and the dividend that is expected next year if dividends grow at a constant rate forever. If a firm pays all of its earnings as dividends, show how Equation 9.4 can be rearranged to calculate that firm’s P/E ratio.

What does this tell us about the factors that determine a firm’s P/E ratio?

Solution: P= 0

D1 E1 , where, E 1is the earnings per share next year. −g= R R−g

Rearranging the formula:

1 P0 = E1 R − g This formula tells us that the P/E ratio is determined by both the risk of the dividend cash flows and the rate at which they are expected to grow.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.31 Riker Departmental Stores management has forecasted a growth rate of 40 percent for the next two years, followed by growth rates of 25 percent and 20 percent for the following two years. It then expects growth to stabilize at a constant rate of 7.5 percent forever. The firm paid a dividend of $3.50 recently. If the required rate of return is 18 percent, what is the current value of Riker’s stock?

Solution: g1-2= 40%; g 3 = 25%; g 4 = 20%; g = 7.5%; D0 = $3.50; R = 18%

.

SM 9-34

Fundamentals of Corporate Finance,4th edition

Solutions Manual

D 1 = D 0(1+g )=$3.501.40=$4.90 1 D 2 = D 1(1+g )=$4.901.40=$6.86 2 D 3 = D 2(1+g )=$6.861.25=$8.575 3 D4

= D 3(1+g )=$8.5751.20=$10.29 4

D 5 = D 4(1+g)=$10.291.075=$11.06 P4 =

$11.06 D = =$105.35 R−g5 0.18−0.075

P0 =

D1 D2 D3 D4 P4 + + + + (1+ R)2 (1+ R)3 (1+ R)4 (1+ R)4 1 +R

P0 =

$4.90 $6.86 $8.575 $10.29 $105.35 + + + + 1.18 (1.18)2 (1.18)3 (1.18)4 (1.18)4

P0 = $4.15 + $4.93 + $5.22 + $5.31 + $54.34 P0 = $73.94 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -0 4.90 1 1 6.86 1 2 8.575 1 3 10.29 + 105.35 =115.64 1 4 Then solve by pressing NPV, enter the rate of 18% and compute NPV=73.94.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-35

Fundamentals of Corporate Finance,4th edition

Solutions Manual

9.32 Courtesy Bancorp issued perpetual preferred stock a few years ago. The bank pays an annual dividend of $4.27 and your required rate of return is 12.2 percent. a.

What is the value of the stock given your required rate of return?

b.

Should you buy this stock if its current market price is $34.41? Explain.

Solution: a.

D = $4.27; R = 12.2% P0=

b.

D $4.27 = = R 0.122 $35.00

Since the stock is worth $35.00 but can be purchased for $34.41, you should buy this stock.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.33 Rhea Kirby owns shares in Ryoko Corp. Currently, the market price of the stock is $36.34. Management expects dividends to grow at a constant rate of 6 percent for the foreseeable future. Its last dividend was $3.25. Rhea’s required rate of return for such stocks is 16 percent. She wants to find out whether she should sell her shares or add to her holdings. a.

What is the value of this stock?

b.

Based on your answer to part a, should Rhea buy additional shares in Ryoko Corp? Why or why not?

Solution: $3.25  (1.06) D1 = =$34.45 0.16 − 0.06 R−g

a.

P= 0

b.

No, she should not buy more shares. This stock is overpriced with the stock selling at a higher price than what it is worth. She should sell her shares.

LO 4 Bloomcode: Analysis

.

SM 9-36

Fundamentals of Corporate Finance,4th edition

Solutions Manual

AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.34 Perry, Inc., paid a dividend of $2.50 yesterday. You are interested in investing in this company, which has forecasted a constant-growth rate of 7 percent for its dividends, forever. The required rate of return is 18 percent. a.

Compute the expected dividends D1, D2, D3, and D4.

b.

Compute the present value of these four dividends.

c.

What is the expected value of the stock four years from now (P4)?

d.

What is the value of the stock today based on the answers to parts b and c?

e.

Use the equation for constant growth (Equation 9.4) to compute the value of the stock today.

Solution: a.

D0 = $2.50 g = 7% R = 18% D 1 = $2.50 (1.07) = $2.675 D 2 = $2.5  (1.07) = $2.86 D3 =0 D4

= $3.063

= $2.5  (1.07) = $3.277 0

b.

2

3

$2.675 $2.86 $3.063 $3.277 $2.5 (1.07) + + + (1.18)4 = PV(Dividends) (1.18)1 (1.18)2 (1.18)3 4 = $2.27+2.05+$1.86+$1.69 0 = $7.87

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2.675 1

.

SM 9-37

Fundamentals of Corporate Finance,4th edition

Solutions Manual

2 2.86 1 3 3.063 1 4 3.277 1

Then solve by pressing NPV, enter the rate of 18% and compute NPV=7.87.

+ g) = $3.277(1.07) = $3.506 D 5 = D(1 4

c.

P4 =

D5 $3.506 = $31.88 = R − g 0.18 − 0.07

$31.88 PV(P4)= (1.18)4 = $16.44 PV(Dividends)+ P0 = PV(P4) $7.87 + $16.44 = $24.32 =

d.

e.

For a constant-growth stock: P0 =

D1 $2.675 = = $24.32 R − g 0.18 − 0.07

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.35 Zweite Pharma is a fast-growing drug company. Management forecasts that in the next three years, the company’s dividend growth rates will be 30 percent, 28 percent, and 24 percent, respectively. Last week it paid a dividend of $1.67. After three years, management expects dividend growth to stabilize at a rate of 8 percent. The required rate of return is 14 percent. a.

Compute the dividends for each of the next three years, and calculate their present value.

.

SM 9-38

Fundamentals of Corporate Finance,4th edition

b.

Solutions Manual

Calculate the price of the stock at the end of year 3, when the firm settles to a constant-growth rate.

c.

What is the current price of the stock?

Solution: g1 = 30%; g2 = 28%; g3 = 24%; g = 8%; D0 = $1.67; R = 14% + g 1 ) = $1.67  (1.30) = $2.171 D 1 = D(1 0 D 2 = D(1 + g 2 ) = $2.171 (1.28) = $2.779 1

D 3 = D(1 + g 3 ) = $2.779  (1.24) = $3.446 2

a.

PV(Dividends) =

D1 D2 D3 + + (1+ R)2 (1+ R)3 1 +R

=

$2.171 $2.779 $3.446 + + 1.14 (1.14)2 (1.14)3

= $1.90 + $2.14 + $2.33 =$6.37

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2.171 1 2 2.779 1 3 3.446 1 Then solve by pressing NPV, enter the rate of 14% and compute NPV=6.37. b.

.

SM 9-39

Fundamentals of Corporate Finance,4th edition

Solutions Manual

+ g) = $3.446(1.08) = $3.722 D 4 = D(1 3 P3 =

D4 $3.722 = $62.03 = R − g 0.14 − 0.08

$62.03 PV(P3)= (1.14)3 = $41.87 PV(Dividends)+ P0 = PV(P3) $6.37 + $41.87 = $48.24 =

c.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.36 Triton Inc., is expected to grow at a rate of 22 percent for the next five years and then

settle to a constant growth rate of 6 percent. The company recently paid a dividend of $2.35. The required rate of return is 15 percent. a.

Find the present value of the dividends during the rapid-growth period if dividends grow at the same rate as the company.

b.

What is the value of the stock at the end of year 5?

c.

What is the value of the stock today?

Solution: g1-5= 22%; g = 6%; D0 = $2.35; R = 15%

a.

.

SM 9-40

Fundamentals of Corporate Finance,4th edition

Solutions Manual

+ g 1) = $2.35 (1.22) = $2.867 D 1 = D(1 0 D 2 = D(1 + g2 ) = $2.867  (1.22) = $3.498 1

= D(1 + g 3 ) = $3.498 (1.22) = $4.267 D 2 = D(1 + g4 4 ) = $4.267  (1.22) = $5.206 D 3 = + ) = $5.206  (1.22) = $6.351 g D(1 5 4 D 3

PV ( Dividends )=

D3 D5 D1 D2 D4 + + + + (1+ R)2 (1+ R)3 (1+ R)4 (1+ R)5 1+R

=

$2.867 $3.498 $4.267 $5.206 $6.351 + + + + 1.15 (1.15)2 (1.15)3 (1.15)4 (1.15)5

= $2.49 + $2.65 + $2.81 + $2.98 + $3.16 = $14.09 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 0 -1 2.867 1 2 3.498 1 3 4.267 1 4 5.206 1 5 6.351 1 Then solve by pressing NPV, enter the rate of 15% and compute NPV=14.09. + g) = $6.351(1.06) = $6.732 D 6 = D(1 5

b.

.

P5 =

D6 $6.732 = $74.80 = R − g 0.15 − 0.06

SM 9-41

Fundamentals of Corporate Finance,4th edition

Solutions Manual

$74.80 PV(P 5) = (1.15)5 = $37.19 P0 =

c.

PV(Dividends)+PV(P ) 5

= $14.09 + $37.19 = $51.28

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.37 Ceebros Builders is expanding very fast and is expected to grow at a rate of 25 percent for the next four years. The company recently paid a dividend of $3.60 but is not expected to pay any dividends for the next three years. In year 4, management expects to pay a $5 dividend and thereafter to increase the dividend at a constant rate of 6 percent.

The required rate of return on such stocks is 20 percent. a.

Calculate the present value of the dividends during the fast-growth period.

b.

What is the value of the stock at the end of the fast-growth period (P4)?

c.

What is the value of the stock today?

d.

Would today’s stock value be affected by the length of time you intend to hold the stock?

Solution: a.

g1-4= 25% g = 6% D0 = $3.60 D4 = $5.00 R = 20% $5 = $2.41 PV( Dividends ) = 0 + 0 + 0 + (1.20)4 D5 $5.00  (1.06) = = $37.86 0.20 − 0.06 R −g

b.

P4 =

c.

P0= $2.4 1+

d.

No, the length of the holding period has no bearing on today’s stock price.

$3 7.8 6 = $20.67 (1.20) 4

.

SM 9-42

Fundamentals of Corporate Finance,4th edition

Solutions Manual

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Sample Test Problems

9.1

Which type of secondary market provides the most efficient market for financial securities? (LO 1 ) Solution: An auction market is the most efficient type of secondary market because the buyers and sellers in an auction market interact directly with each other and bargain over price.

Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.2

Is preferred stock a debt or an equity security? ( LO 2) Solution: Preferred stock represents an ownership interest in a corporation and is legally a form of equity. However, it does have characteristics that are similar to those of debt, such as no voting rights, fixed payments (dividends), and credit ratings similar to those issued to bonds.

Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.3

Burnes, Inc. is a mature firm that is growing at a constant rate of 5.5 percent per year.

The last dividend that the firm paid was $1.50 per share. If dividends are expected to grow at the same rate as the firm and the required rate of return on Burnes’s stock is 12 percent, what is the market value of the company’s stock? (LO 4) Solution:

.

SM 9-43

Fundamentals of Corporate Finance,4th edition

D0 = $1.50;

P0 =

g = 5.5%;

Solutions Manual

R = 12%

$1.50 1.055 D1 = = $24.35 R − g 0.12 − 0.055

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.4

Abacus Corporation will pay dividends of $2.25, $2.95, and $3.15 in the next three years.

After three years, the dividends are expected to grow at a constant rate of 4 percent per year. If the required rate of return is 14.5 percent, what is the current value of the Abacus common stock? (LO 4) Solution: gconstant = 4%; D1 = $2.25 D2 = $2.95 D3 = $3.15; R = 14.5% P3 =

$3.151.04 D4 = =$31.20 0.145−.04 R−g

$2.25 (1.145)2 $2.95 (1.145)3 $3.15 (1.145)3 $31.20 + + + (1.145) =$1.97+$2.25+$2.10+$20.78 = $27.10

P0 =

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -0 2.25 1 1 2.95 1 2 3.15 + 31.20 = 34.35 1 3 Then solve by pressing NPV, enter the rate of 14.5% and compute NPV=27.10.

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-44

Fundamentals of Corporate Finance,4th edition

9.5

Solutions Manual

The preferred stock of Wellcare Inc. is currently trading at $137.50 per share. If the required rate of return is 8 percent and this stock has no maturity date, what is the quarterly dividend paid by this stock? What is the quarterly dividend if the stock will mature in one year and it has a par value of $140? (LO 6) Solution: With no maturity date: PS0 = $137.5; R = 8.0% D PS 0=$137.50= 0.08

D=$137.500.08 =$11.00 Annual dividend = $11.00 Quarterly dividend = $11.00 /4 = $2.75 We can use Equation 9.7 to solve for the dividend with a one year maturity date:

PS0 =

D/m D/m + (1+i / m) (1+i / m)2

D/m+Pmn D/m + (1+i / m)3 + (1+i / m)4

D/m D/m + $140 D/m D/m + = $137.50= + + (1+0.08 / 4) (1+0.08 / 4)2 (1+0.08 / 4)3 (1 + 0.08 / 4) 4 D/m D/m+$140 D/m D/m = $137.50= + + + (1.02)4 1.02 (1.02)2 (1.02)3 Using a financial calculator to solve for PMT, we find that the quarterly dividend, $2.14.

Financial Calculator Solution : 4 N

2 i

-137.50 PV

PMT 2.14

D/m =

140 FV

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

.

SM 9-45

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

CHAPTER 10 The Fundamentals of Capital Budgeting

Before You Go On Questions and Answers Section 10.1 1.

Why are capital investments considered the most important decisions made by a firm’s management?

Capital investments are the most important decisions made by a firm’s management, because they usually involve large cash inflows and outflows. These cash flows, representing significant long-term projects that define the firm’s future line of business, are generally expected to significantly contribute to future revenues and once made, are not easily reversed.

2.

What are the differences between capital projects that are independent, mutually exclusive, and contingent?

A project is independent if accepting or rejecting the project does not affect the decision about implementing other projects. On the other hand, projects are mutually exclusive if the acceptance of one implies rejection of the other. Contingent projects are those in which the acceptance of one project is dependent on another project.

3. What is the cost of capital?

The cost of capital can be thought of as a “hurdle rate” or the minimum rate that a company expects to earn when investing in a project. It is the “opportunity cost”, or the rate of return that is possible from the next best alternative investment opportunity with similar risk.

.

SM 10-1

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

4. Describe the process of capital rationing?

Firms often have a limited amount of money for investment and qualified projects whose total cost exceeds this amount. In this situation managers of those firms must allocate the available money to the set of projects that add the most value to its shareholders. This allocation process is known as capital rationing.

Section 10.2 1.

What is the NPV of a project?

A project’s NPV is the difference between the present value of its expected future cash inflows and its outflows, including the present value of its cost. It is the recommended technique used to value capital investments, as it takes into account both the timing of the cash flows and their risk.

2.

If a firm accepts a project with a $10,000 NPV, what is the effect on the value of the firm?

If a firm accepts a project with a $10,000 NPV, it will increase its value by $10,000.

3.

What are the five steps used in NPV analysis?

The five-step process used in the NPV analysis can be listed as follows: (1) Determine the initial cost of the project.

(2) Estimate the project’s future cash flows over its expected life.

(3) Determine the riskiness of the project and the appropriate cost of capital.

(4) Compute the project’s NPV. (5) Make a decision. A project with a positive NPV adds value to the firm and should be accepted.

.

SM 10-2

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Section 10.3 1.

What is the payback period?

The payback period is defined as the number of years it takes to recover the project’s initial investment. All other things being equal, the project with the shortest payback period is usually the optimal investment.

2.

Why does the payback period provide a measure of a project’s liquidity risk?

The payback period determines how quickly you recover your investment in a project.

Thus, it serves as a good measure of the project’s liquidity.

3.

What are the main shortcomings of the payback method?

The payback method does not account for time value of money, nor does it distinguish between high- and low-risk projects. In addition, there is no rationale behind choosing the cutoff criteria. For all these reasons, the payback method is not the ideal capital decision rule.

Section 10.4 1.

What are the major shortcomings of using the Accounting Rate of Return (ARR) method as a capital budgeting method?

The biggest shortcoming of using ARR as a capital budgeting tool is that it uses historical, or book value data rather than cash flows and thus disregards the time value of money principle. In addition, as with the payback method, it fails to establish a rationale behind picking the appropriate hurdle rate.

Section 10.5 1.

.

What is the Internal Rate of Return (IRR) method?

SM 10-3

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The IRR, or the internal rate of return, is the discount rate that equates the present value of a project’s cost to the present value of its expected cash inflows. The IRR determines whether the project’s return rate is higher or lower than the required rate of return, which is the firm’s cost of capital. Normally, a project should be accepted if the IRR exceeds the firm’s cost of capital; otherwise the project should be rejected.

2.

Under what circumstances do the NPV and IRR decision rules always yield the same decision?

When a project has normal or conventional cash flows and when the project is completely independent of other projects, both of these decision rules will yield the same accept/reject decision.

3.

In capital budgeting, what is a conventional cash flow pattern?

A conventional project cash flow in capital budgeting is one in which an initial cash outflow is followed by one or more future cash inflows.

4.

Why should the NPV method be the primary decision tool used in making capital investment decisions?

Given all the different methods to evaluate capital investment decisions, the NPV method is the preferred valuation tool since it accounts for both the time value of money and the project’s risk. Furthermore, the NPV is not sensitive to nonconventional projects, and therefore it is superior to the IRR technique. Finally investment decisions made using NPV are always consistent with the goal of maximizing the value of the firm, even when discriminating between mutually exclusive projects.

Section 10.6

.

SM 10-4

Fundamentals of Corporate Finance, 4th edition

1.

Solutions Manual

What might cause a firm to face capital constraints?

A firm might face capital constraints because it can be difficult for outside investors (new creditors, bondholders, or stockholders) to accurately assess the risks and returns associated with the firm’s projects. This might cause the investors to require returns for their capital that are so high that they make positive-NPV projects unattractive, because those projects cannot produce the high returns required by investors.

2.

What decision criteria should managers use in selecting projects when a firm faces capital constraints?

When a firm faces capital constraints, the basic principle to follow when choosing a set of projects that create the greatest value in a given period, is to select the bundle of projects that yield the largest value per dollar invested.

3.

How can the Profitability Index (PI) help in choosing projects when a firm faces capital constraints? What are its limitations?

The basic concept underlying the PI is that managers should select the bundle of projects that creates the greatest value per dollar invested. The PI tells us the NPV per dollar invested for an individual project. In a single period, the PI can be used to identify the bundle of projects that yields the largest NPV per dollar invested. However, the PI will not necessarily help identify the most valuable bundle of projects if investments are being

.

SM 10-5

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

compared across more than one year and the timing of cash flows from early investments affects the firm’s ability to make subsequent investments.

Section 10.7 1.

What changes have taken place in the capital budgeting techniques used by U.S. companies?

Over the years, there has been a shift from using Payback and ARR as the primary capital budgeting tools to using NPV and IRR instead. Managers today understand the importance of the time value of money and discounting and thus regard ARR as an inaccurate and obsolete decision tool.

Self-Study Problems 10.1 The Management of Premium Manufacturing Company is evaluating two forklift systems to use in its plant that produces the towers for a windmill power farm. The costs and the cash flows from these systems are shown below. If the company uses a 12 percent discount rate for all projects, determine which forklift system should be purchased using the net present value (NPV) approach.

Otis

Year 0

Year 1

Year 2

Year 3

−$3,123,450

$979,225

$1,358,886

$2,111,497

−$4,137,410

$875,236

$1,765,225

$2,865,110

Forklifts Craigmore Forklifts S olu tion : NPV for Otis Forklifts: .

SM 10-6

Fundamentals of Corporate Finance, 4th edition n

NPV = t=0

Solutions Manual

CF t (1 +k) t

$979,225 $1,358,886 $2,111,497 + + (1.12)3 (1+ 0.12)1 (1.12)2 = −$3,123,450+ $874,308 + $1,083,296 + $1,502,922

= −$3,123,450+ = $337,075

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Otis Cash Flow (C) 0 -3,123,450 1 979,225 2 1,358,886 3 2,111,497

Frequency (F) -1 1 1

Then solve by pressing NPV, enter the rate of 12% and compute NPV= 337,075.

NPV for Craigmore Forklifts: n

NPV = t=0

CF t (1 +k) t

$875,236 $1,765,225 $2,865,110 = −$4,137,410+ (1+ 0.12)1 + + (1.12)2 (1.12)3 = −$4,137,410+ $781,461+$1,407,229+$2,039,227 = $9 0,6 0 6

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Craigmore Cash Flow (C) 0 -4,137,410 1 875,236 2 1,765,225 3 2,865,110

Frequency (F) -1 1 1

Then solve by pressing NPV, enter the rate of 12% and compute NPV= 90,606.

Premium should purchase the Otis forklift since it has a larger NPV. .

SM 10-7

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.2 Perryman Crafts Corp. management is evaluating two independent capital projects that will each cost the company $250,000. The two projects will provide the following cash flows: Year

Project A

Project B

1

$80,750

$32,450

2

$93,450

$76,125

3

$40,325

$153,250

4

$145,655

$96,110

Which project will be chosen if the company’s payback criterion is three years? What if the company accepts all projects as long as the payback period is less than five years?

Solution: Payback periods for Perryman projects A and B: Project A Cumulative Year

Cash Flow

Cash Flows

0

$(250,000)

$(250,000)

1

80,750

(169,250)

2

93,450

(75,800)

3

40,235

(35,565)

4

145,655

110,090

Project B Cumulative Year

.

Cash Flow

Cash Flows

0

$(250,000)

$(250,000)

1

32,450

(217,550)

2

76,125

(141,425) SM 10-8

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

3

153,250

11,825

4

96,110

107,935

Payback period for Project A:

Remaining cost to recover Payback period= Years before cost recovery+ Cash flow during the year $35, 565 $145,655 per year =3.24 years

=3+

Payback period for Project B:

Remaining cost to recover Payback period= Years before cost recovery+ Cash flow during the year $141, 425 $153,250 per year =2.92 years

=2+

If the payback period is three years, only project B will be chosen. If the payback criterion is five years, both A and B will be chosen.

10.3 Terrell Corp. management is considering purchasing a machine that will cost $117,250 and will be depreciated on a straight-line basis over a five-year period. The sales and expenses (excluding depreciation) for the next five years are shown in the following table. The company’s tax rate is 34 percent.

Year 1 Sales

$123,45

Year 2

Year 3

Year 4

Year 5

$176,87

$242,45

$255,44

$267,12

5

5

0

5

$137,41

$126,48

$141,28

$143,11

$133,55

0

8

9

2

6

Expenses 0

Terrell will accept all projects that provide an accounting rate of return (ARR) of at least 45 percent. Should the company accept the project? .

SM 10-9

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: Year 1

Year 2

Year 3

Year 4

Year 5

Sales

$123,450 $176,875

$242,455

$255,440

$267,125

Expenses

137,410

126,488

141,289

143,112

133,556

Depreciation

23,450

23,450

23,450

23,450

23,450

$ (37,410) $ 26,937

$ 77,716

$ 88,878

$110,119

EBIT Taxes (34%)

12,719

9,159

26,423

30,219

37,440

Net Income

$ (24,691) $ 17,778

$ 51,293

$ 58,659

$ 72,679

Beginning Book Value

117,250

93,800

70,350

46,900

23,450

Less: Depreciation

(23,450) (23,450) $ 93,800 $ 70,350

(23,450)

(23,450)

(23,450)

$ 46,900

$ 23,450

$

Ending Book Value

Average net income Average book value

0

= (–$24,691 + $17,778 + $51,293 + $58,659 + $72,679) / 5 = $35,143.60 = ($117,250 + $93,800 + $70,350 + $46,900 + $23,450 + $102)/6 = $58,625

Accounting rate of return

= $35,143.60 / $58,625 = 0.599 or 59.9%

The company should accept the project.

10.4 Refer to Problem 10.1. Compute the IRR for each of the two systems. Is the investment decision different from the one determined by NPV? Solution: IRR for two forklift systems: Otis Forklifts: First compute the IRR by the trial-and-error approach: NPV (Otis) = $337,075 > 0 Use a higher discount rate to get NPV = 0 At k = 15%, .

SM 10-10

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

$979,225 $1,358,886 $2,111,497 + (1.15)3 NPV Otis = −$3,123, 450+ (1+0.15)1 + (1.15)2 = −$3,123, 450+ $851,500+$1,027,513+$1,388,344 = $143, 907 Try a higher rate. At k = 17%,

NPV Otis = −$3,123, 450+ $836, 944+ $992, 685 +$1, 318, 357 = $24, 536 Try a higher rate. At k = 17.5%,

+ $833, 383+ $984, 254+ $1, 301, 598 NPV Otis = −$3, 123, 450 = −$4, 215 Thus the IRR for Otis is less than 17.5 percent. Using a financial calculator, you can find that the exact rate to be 17.43 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Otis Cash Flow (C) 0 -3,123,450 1 979,225 2 1,358,886 3 2,111,497

Frequency (F) -1 1 1

Then solve by pressing IRR to get 17.43% Craigmore Forklifts: First compute the IRR by the trial-and-error approach: NPV (Craigmore) = $90,606 > 0 Use a higher discount rate to get NPV = 0 At k = 15%, $875,236 $1,765,225 $2,865,110 + + (1.12)3 (1.15)1 (1.12)2 = −$4,137, 410+ $761,075+$1,334,764+$1,883,856 = −$157, 715

NPV Craigmore = −$4,137, 410+

Try a lower rate. At k = 13%, .

SM 10-11

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NPV Craigmore = −$4,137, 410+ $774, 545+ $1, 382, 430+ $1, 985, 665 = $5,230 Try a higher rate. At k = 13.1%,

NPV Craigmore = −$4,137, 410+ $773, 860+ $1, 379, 987+ $1, 980, 403 = −$3,161 Thus the IRR for Craigmore is less than 13.1 percent. The exact rate is 13.06 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Craigmore Cash Flow (C) 0 -4,137,410 1 875,236 2 1,765,225 3 2,865,110

Frequency (F) -1 1 1

Then solve by pressing IRR to get 13.06% Based on the IRR, we would still pick Otis over Craigmore forklift systems. The decision is the same as that indicated by NPV since both projects are conventional.

10.5 You are considering a project that has an initial outlay of $1 million. The profitability index of the project is 2.24. What is the NPV of the project?

Solution: You can use Equation 10.6 to solve for the NPV:

PI

=

2.24 =

NPV + Initial investment Initial investment NPV+$1,000,000 $1, 000, 000

Therefore: NPV = $1,240,000

.

SM 10-12

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Discussion Questions 10.1 Explain why the cost of capital is referred to as the “hurdle” rate in capital budgeting.

Solution The cost of capital is the minimum required return on any new investment that allows a firm to break even. Since we are using the cost of capital as a benchmark or “hurdle” to compare the return earned by any project, it is sometimes referred to as the hurdle rate.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective a.Sykes, Inc. management is considering two projects: a plant expansion and a

10.2

new computer system for the firm’s production department. Classify these projects as independent, mutually exclusive, or contingent projects and explain your reasoning. b. A company is building a new plant on the outskirts of Smallesville. The town has offered to donate the land, and as part of the agreement, the company will have to build an access road from the main highway to the plant. How will the project of building the road be classified in the capital budgeting analysis? c. Management of your firm is currently considering the upgrading of the operating systems of all the firm’s computers. One alternative is to choose the Linux operating system that a local computer services firm has offered to install and maintain. Microsoft has also put in a bid to install the new Windows operating system for businesses. How would these projects be classified?

Solution .

SM 10-13

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

a. These two projects are independent projects. Accepting or rejecting one will not influence the decision on the other project. The cash flows of the two projects are unrelated. b. This is a contingent project. Acceptance of the road-building project is contingent on the new plant being a financially viable project. If the new plant will not have a positive value, then the firm will not even consider this project. However, the cost of building the road will have to be considered along with the cost of building the new plant in the capital budgeting analysis. c. These are two mutually exclusive projects. The company’s computers need only one operating system. Either the Linux or the Windows operating system needs to be installed, not both. Hence, the selection of one will eliminate the other from consideration.

LO: 1 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.3 In the context of capital budgeting, what is “capital rationing”?

Solution Capital rationing implies that a firm does not have the resources necessary to fund all of the available projects. In other words, funding needs exceed funding resources. Thus, the available capital will be allocated to the projects that will benefit the firm and its shareholders the most. Projects that create the largest increase in shareholder wealth will be accepted until all the available resources have been allocated.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions .

SM 10-14

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

AICPA: Industry/Sector Perspective

10.4 Provide two conditions under which a set of projects might be characterized as mutually exclusive.

Solution When projects are mutually exclusive, acceptance of one project precludes the acceptance of others. Typically, mutually exclusive projects perform the same function and so only one of them needs to be accepted. A funding or resource constraint can also cause projects to be mutually exclusive.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.5 a.A firm invests in a project that is expected to earn a return of 12 percent. If the appropriate cost of capital is also 12 percent, did the firm make the right decision. Explain. b. What is the impact on the firm if it accepts a project with a negative NPV? Solution a. We would normally argue that a firm should only accept projects in which the project’s return exceeds the cost of capital. In other words, only if the net present value exceeds zero should a project be accepted. But in reality, projects with a zero NPV should also be accepted because the project earns a return that equals the cost of capital. For some firms like the one above, this could be the situation because they may not have projects that provide a return greater than the cost of capital for the firm. When a firm takes on positive NPV projects, the value of the firm b. increases. By .

SM 10-15

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

the same token, when a project undertaken has a negative NPV, the value of the firm will decrease by the amount of the net present value.

LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.6 Identify the weaknesses of the payback period method.

Solution There are several critical weaknesses in the payback period approach of evaluating capital projects.

▪ ▪ ▪ ▪

The payback period ignores the time value of money by not discounting future cash flows.

When projects, it ignores between thethat projects.

A firm comparing may establish payback criteriarisk withdifferences no economic basis for decision and thereby run the risk of losing out on good projects.

The method ignores cash flows beyond the payback period, thus leading to nonselection of projects that may produce cash flows well beyond the payback period or more cash flows than accepted projects. This leads to a bias against longer-term projects.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.7 What are the strengths and weaknesses of the accounting rate of return approach?

Solution

.

SM 10-16

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The biggest advantage of Accounting Rate of Return (ARR) approach is that it is easy to compute since accounting data is readily available, whereas estimating cash flows is more difficult. However, the disadvantages outweigh this specific advantage. Similar to the payback, it does not discount cash flows, but merely averages net income over time. No economic rationale is used in establishing an ARR cutoff rate. Finally, the ARR uses net income to evaluate the project and not cash flows or market data. This is a serious flaw in this approach.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.8 Under what circumstances might the IRR and NPV approaches produce conflicting results?

Solution IRR and the NPV methods of evaluating capital investment projects might produce dissimilar results under two circumstances. First, if the project’s cash flows are not conventional—that is, if the sign of the cash flow changes more than once during the life of a project—then multiple IRRs can be obtained as solutions. Therefore, we would be unable to identify the correct IRR for decision making. (See Learning by Doing Application 10.3.) The second situation occurs when two or more projects are mutually exclusive. The project with the highest IRR may not necessarily be the one with the highest NPV and thereby be the right choice. There is an important reason for this. IRR assumes that all cash flows received during the life of a project are reinvested at the IRR, whereas the NPV method assumes that they are reinvested at the cost of capital. Since the cost of capital is the better proxy for opportunity cost, NPV uses the better proxy, while the IRR may use an unrealistically higher rate as proxy.

LO: 5 .

SM 10-17

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.9 The modified IRR (MIRR) alleviates two concerns with using the IRR method for evaluating capital investments. What are they?

Solution IRR assumes that the cash flows from a project are reinvested at the project’s IRR, while the NPV assumes that they are invested at the firm’s cost of capital. The NPV assumption is correct more often than not. The MIRR assumes that each operating cash flow is reinvested at the firm’s cost of capital.

The second appeal of MIRR is that under this method all of the compounded operating cash flow values are summed up to get the project’s terminal value. Since most projects generate positive total net operating cash flows, MIRR does not suffer from issues associated with unconventional cash flows.

LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.10 Elkridge Construction Company has an overall (composite) cost of capital of 12 percent. This cost of capital reflects the cost of capital for an Elkridge Construction project with average risk. However, the firm takes on projects of various risk levels.

The company’s experience suggests that low-risk projects have a cost of capital of 10 percent and high-risk projects have a cost of capital of 15 percent. Which of the following projects should the company not select to maximize shareholder wealth? .

SM 10-18

Fundamentals of Corporate Finance, 4th edition

Project

Solutions Manual

Expected Return Risk

1. Single-family homes

13%

Low

2. Multifamily residential

12

Average

3. Commercial

18

High

4. Single-family homes

9

Low

5. Commercial

13

High

Required

Expected

Return

Return

Solution Project

Risk

1. Single-family homes

Low

10%

13%

Accept

2. Multifamily residential

Average

12

12

Accept / Indifferent

3. Commercial

High

15

18

Accept

4. Single-family homes

Low

10

9

Reject

5. Commercial

High

15

13

Reject

Decision

LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.11 High Tech Monopoly Co. has plenty of cash to fund any conceivable positive NPV project. Can you describe a situation in which capital rationing could still occur?

Solution: Financial capital is not the only constrainable item within the firm. This might occur, for example, when human capital is in short supply, as is the case with most high-technology firms. Even if every positive NPV project could be funded, the firm might not have .

SM 10-19

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

enough employees to manage the projects. Therefore, even with ample financial capital, firms will more than likely still be rationing projects.

LO: 6 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.12 The profitability index is a tool for measuring a project’s benefits relative to its costs.

How might this help to eliminate bias in project selection?

Solution: Since the profitability index is a modified pure-return-type measure, it offers a method to maximize the use of capital that is employed by the firm. This could help eliminate some types of bias if the measure were to be employed universally. However, it does not necessarily maximize the use of capital that is not employed, which could in some circumstances be problematic.

LO: 6 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Questions and Problems .

SM 10-20

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

BASIC 10.1 Net present value: Riggs Corp. management is planning to spend $650,000 on a newmarketing campaign. They believe that this action will result in additional cash flows of $325,000 over the next three years. If the discount rate is 17.5 percent, what is the NPV on this project?

Solution: Initial investment = $650,000 Annual cash flows = $325,000 Length of project = n = 3 years Required rate of return = k = 17.5% Net present value = NPV n NCFt $325,000 $325,000 $325,000 + + NPV =  (1+k)t = −$650,000+ (1.175)1 (1.175)2 (1.175)3 t=0 = −$650,000+ 276,596 + $235,401 + $200,341

= $62,337

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -650,000 -1 325,000 3 Then solve by pressing NPV, enter the rate of 17.5% and compute NPV=62,337.34.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 10-21

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.2 Net present value: Kingston, Inc. management is considering purchasing a new machine at a cost of $4,133,250. They expect this equipment to produce cash flows of $814,322, $863,275, $937,250, $1,017,112, $1,212,960, and $1,225,000 over the next six years. If the appropriate discount rate is 15 percent, what is the NPV of this investment?

Solution: Cost of new machine = $4,133,250 Length of project = n = 6 years Required rate of return = k = 15% NCFt t t=0 (1+ k ) n

NPV = 

$814,322 $863,275 $937,250 $1,017,112 $1,212,960 $1,225,000 + + + + + (1.15)1 (1.15)2 (1.15)3 (1.15)4 (1.15)5 (1.15)6 = −$4,133,250+ $708,106+$652,760+$616257+$581,537+$603,055+$529,601 = −$441,933 = −$4,133,250+

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -4,133,250 1 814,322 2 863,275 937,250 3 1,017,112 4 5 1,212,960 1,225,000 6

Frequency (F) -1 1 1 1 1 1

Then solve by pressing NPV, enter the rate of 15% and compute NPV= -441,933 LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.3 Net present value:Crescent Industries management is planning to replace some existing .

SM 10-22

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

machinery in its plant. The cost of the new equipment and the resulting cash flows are shown in the accompanying table. If the firm uses an 18 percent discount rate for projects like this, should management go ahead with the project?

Year

Cash Flow

0

−$3,300,000

1

875,123

2

966,222

3

1,145,000

4

1,250,399

5

1,504,445

Solution: Initial investment = $3,300,000 Length of project = n = 5 years Required rate of return = k = 18% n NCFt NPV =  (1+k)t t=0

$875,123 $966,222 $1,145,000 $1,250,399 $1,504,455 + + + + (1.18)1 (1.18)2 (1.18)3 (1.18)4 (1.18)5 = −$3,300,000+ $741,630+ $693,926 + $696,882 + $644,942 + $657,607

= −$3,300,000+ = $134,986

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -3,300,000 1 875,123 2 966,222 3 1,145,000 4 1,250,399 5 1,504,455

Frequency (F) -1 1 1 1 1

Then solve by pressing NPV, enter the rate of 18% and compute NPV= 134,986

.

SM 10-23

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Since the NPV is positive, the firm should accept the project.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.4 Net present value: Management of Franklin Mints, a confectioner, is considering purchasing a new jelly bean-making machine at a cost of $312,500. They project that the cash flows from this investment will be $121,450 for the next seven years. If the appropriate discount rate is 14 percent, what is the NPV for the project?

Solution: Initial investment = $312,500 Annual cash flows = $121,450 Length of project = n = 7 years Required rate of return = k = 14% n NCFt NPV =  (1+k)t t=0

= −$312,500+

$121,450 $121,450 $121,450 $121,450 $121,450 + + + + (1.14)1 (1.14)2 (1.14)3 (1.14)4 (1.14)5

$121,450 $121,450 + (1.14)6 (1.14)7 = −$312,500 + $106,535 +$93,452+ $81,975+ $71,908+ $63,077+ $55,331+$48,536 +

= $208,315 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -312,500 -1 121,450 7 Then solve by pressing NPV, enter the rate of 14% and compute NPV= 208,315

.

SM 10-24

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.5 Net present value: Blanda Incorporated management is considering investing in two alternative production systems. The systems are mutually exclusive, and the cost of the new equipment and the resulting cash flows are shown in the accompanying table. If the firm uses a 9 percent discount rate for production system projects, in which system should the firm invest?

Year 0 1 2 3

System 1 -15,000 15,000 15,000 15,000

System 2 -45,000 32,000 32,000 32,000

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: System 1 Cash Flow (C) Frequency (F) 0 -15,000 -1 15,000 3 Then solve by pressing NPV, enter the rate of 9% and compute NPV= 22,969.42 Using a financial calculator, enter the cash flows as follows: System 2 Cash Flow (C) Frequency (F) 0 -45,000 -1 32,000 3 Then solve by pressing NPV, enter the rate of 9% and compute NPV= 36,001.43 The NPV of System 1 is $22,969.42 and the NPV of System 2 is $36,001.43. Since the NPV of the System 2 is larger than the NPV for System 1, and the investments are mutually exclusive, the firm should take System 2.

LO 2 .

SM 10-25

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.6 Payback: Refer to problem 10.5. What are the payback periods for Production Systems 1 and 2? If the systems are mutually exclusive and the firm always chooses projects with the lowest payback period, in which system should the firm invest?

Solution System 1 has a payback of exactly one year. System 2 has a payback of 1.41 years.

Given the shorter payback period for System 1, the investment should be made in System 1 based on the payback criteria.

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.7 Payback: Quebec, Inc., is purchasing machinery at a cost of $3,768,966. The company’s management expects the machinery to produce cash flows of $979,225, $1,158,886, and $1,881,497 over the next three years, respectively. What is the payback period?

Solution: Cumulative Year

CF

Cash Flow

0

$(3,768,966)

$(3,768,966)

1

979,225

(2,789,741)

2

1,158,886

(1,630,855)

3

1,881,497

250,642

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 2 + ($1,630,855 / $1,881,497) = 2.87 years .

SM 10-26

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.8 Payback: Northern Specialties just purchased inventory-management computer software at a cost of $1,645,276. Cost savings from the investment over the next six years will produce the following cash flow stream: $212,455, $292,333, $387,479, $516,345, $645,766, and $618,325. What is the payback period on this investment?

Solution: Cumulative Year

CF

Cash Flow

0

$(1,645,276)

$(1,645,276)

1

212,455

(1,432,821)

2

292,333

(1,140,488)

3

387,479

(753,009)

4

516,345

(236,664)

5

645,766

409,102

6

618,325

1,027,427

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4 + ($236,664 / $645,766) = 4.37 years LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.9 Payback: Nakamichi Bancorp has made an investment in banking software at a cost of .

SM 10-27

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

$1,875,000. Management expects productivity gains and cost savings over the next several years. If, as a result of this investment, the firm is expected to generate additional cash flows of $586,212, $713,277, $431,199, and $318,697 over the next four years, what is the investment’s payback period?

Solution: Cumulative Year

CF

Cash Flow

0

$(1,875,000)

$(1,875,000)

1

586,212

(1,288,788)

2

713,277

(575,511)

3

431,199

(144,312)

4

318,697

174,385

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($144,312 / $318,697) = 3.45 years LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.10

Average accounting rate of return (ARR):

Capitol Corp. management is expecting a

project to generate after-tax income of $63,435 in each of the next three years. The average book value of the project’s equipment over that period will be $212,500. If the firm’s investment decision on any project is based on an ARR of 37.5 percent, should this project be accepted?

Solution: Annual after-tax income = $63,435 Average after-tax income = ($63,435 +$63,435 + $63,435) / 3 = $63,435

.

SM 10-28

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Average book value of equipment = $212,500 Accounting rate of return = =

Average after-tax income Average book value $63,435 =29.9% $212,500

Since the project’s ARR is below the acceptance rate of 37.5 percent, the project should be rejected.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.11 Internal rate of return: Refer to Problem 10.4. What is the IRR that Franklin Mints management can expect on this project?

Solution: Initial investment = $312,500 Annual cash flows = $121,450 Length of project = n = 7 years Required rate of return = k = 14% To determine the IRR, a trial-and-error approach can be used. Set NPV = 0.

Since the project had a positive NPV of $208,315, try IRR > k.

Try IRR = 25%.

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

 1  1 − (1.25)7   0  −$312,500+$121,450    0.25       −$312,500+$383,920 $71,420

.

SM 10-29

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Try a higher rate, IRR = 34%.

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

 1  1 − (1.34)7   0  −$312,500+$121,450    0.34       −$312,500+$311,161 −$1,339 Try a lower rate, IRR = 33.8%.

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

  1 1 − (1.338)7  0 = −$312,500+ $121,450    0.3 3 8      = −$312,500+ $312,515= $15  0 The IRR of the project is approximately 33.8 percent. Using a financial calculator, we find that the IRR is 33.802 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -312,500 -1 121,750 7 Then solve by pressing IRR to get 33.802%.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 10-30

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.12Internal rate of return: Hathaway, Inc., a resort management company, is refurbishing one of its hotels at a cost of $7.8 million. Management expects that this will lead to additional cash flows of $1.8 million for the next six years. What is the IRR of this project? If the appropriate cost of capital is 12 percent, should Hathaway go ahead with this project?

Solution: Initial investment = $7,800,000 Annual cash flows = $1,800,000 Length of project = n = 6 years Required rate of return = k = 12% To determine the IRR, a trial-and-error approach can be used. Set NPV = 0.

Try IRR = 12%.

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

 1  1  − (1.12)6  0  −$7,800,000+$1,800,000    0.12       −$7,800,000+$7,400,533  −$399,467 Since NPV < 0, try a lower rate, IRR = 10%.

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

 1  1 − (1.10)6  0  −$7,800,000+$1,800,000    0.10       −$7,800,000+$7,839,469 $39,469 Try IRR = 10.2%.

.

SM 10-31

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

  1 1  − (1.102)6  0  −$7,800,000+ $1,800,000    0.1 0 2       −$7,800,000+ $7,793,735  − $6,265 Try IRR = 10.15%.

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

  1 1 − (1.1015)6  0  −$7,800,000+$1,800,000    0.1015       −$7,800,000+$7,805,129 $5,129 The IRR of the project is between 10.15 percent and 10.2 percent. Using a financial calculator, we find that the IRR is 10.1725 percent. Since IRR < k, reject the project.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -7,800,000 -1 1,800,000 6 Then solve by pressing IRR to get 10.1725% LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.13 Profitability index: What is the profitability index, and why is it helpful in the capital rationing process?

.

SM 10-32

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: The profitability index is a measure of the value a project generates for each dollar invested in that project. It is computed as the ratio of NPV plus initial investment divided by initial investment. In the capital rationing process, we can calculate the profitability index for each potential investment and choose the projects with the largest indexes until we run out of capital. This follows the basic principle that we need to choose the set of projects that creates the greatest value given the limited capital available.

LO 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

INTERMEDIATE 10.14 Net present value:Champlain Corp. management is investigating two computer systems. The Alpha 8300 costs $3,122,300 and will generate cost savings of $1,345,500 in each of the next five years. The Beta 2100 system costs $3,750,000 and will produce cost savings of $1,125,000 in the first three years and then $2 million for the next two years. If the company’s discount rate for similar projects is 14 percent, what is the NPV for the two systems? Which one should be chosen based on the NPV? Solution: Cost of Alpha 8300 = $3,122,300 Annual cost savings = $1,345,500 Length of project = n = 5 years Required rate of return = k = 14%

.

SM 10-33

Fundamentals of Corporate Finance, 4th edition

NCF t=−$3,122,300+$1,345,500 NPV =  t=0 (1+k) t n

= −$3,122,300+$4,619,210 = $1,496,910

Solutions Manual

 1  1 − (1.14)5     0.14     

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Alpha Cash Flow (C) Frequency (F) 0 -3,122,300 -1 1,345,500 5 Then solve by pressing NPV, enter the rate of 14% and compute NPV=1,496,910 Cost of Beta 2100 = $3,750,000 Length of project = n = 5 years Required rate of return = k = 14%

1   1−  (1.14) 3  $2,0 0 0,0 0 0$2,0 0 0,0 0 0 =−$3,750,000+$1,125,500 + NPV =  0.14 t=0 (1+ k)t (1.14)4 (1.14)5 +      = −$3,750,000+$2,611,836+$1,184,161+1,038,737  n

NCF t

= $1,084,734 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Beta Cash Flow (C) Frequency (F) 0 -375,000,000 -1 1,125,500 5 Then solve by pressing NPV, enter the rate of 14% and compute NPV=1,084,734 Based on the NPV, the Alpha 8300 system should be chosen.

LO 2 Bloomcode: Analysis .

SM 10-34

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.15 Net present value: Briarcrest Condiments is a spice-making firm. Recently, it developed a new process for producing spices. The process requires new machinery that would cost $1,968,450, have a life of five years, and would produce the cash flows shown in the following table. What is the NPV if the discount rate is 15.9 percent?

Year

Cash Flow

1

$512,496

2

(242,637)

3

814,558

4

887,225

5

712,642

Solution: Cost of equipment = $1,968,450 Length of project = n = 5 years Required rate of return = k = 15.9% NCFt t t=0 (1+ k ) n

NPV = 

$512,496 $242,637 $814,558 $887,225 $712,642 − + + + (1.159)1 (1.159)2 (1.159)3 (1.159)4 (1.159)5 = −$1,968,450+ $442,188 − $180,630 + $523,205 + 491,700 + 340,764

= −$1,968,450+ = −$351,223

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -1,968,450 1 $512,496 2 (242,637) .

Frequency (F) -1 1 SM 10-35

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

3 814,558 1 4 887,225 1 5 712,642 1

Then solve by pressing NPV, enter the rate of 15.9% and compute NPV=-351,223 LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.16 Net present value:Cranjet Industries is expanding its product line and its production capacity. The costs and expected cash flows of the two independent projects are given in the following table. The firm uses a discount rate of 16.4 percent for such projects. a.

What are the NPVs of the two projects?

b

Should both projects be accepted? Or either? Or neither? Explain your reasoning.

Product Line

Production Capacity

Year

Expansion

Expansion

0

$(2,575,000)

$(8,137,250)

1

600,000

2,500,000

2

875,000

2,500,000

3

875,000

2,500,000

4

875,000

3,250,000

5

875,000

3,250,000

Solution: a.

Required rate of return = k =16.4% Product Line Expansion: Cost of product line expansion = $2,575,000

.

SM 10-36

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

n NCFt NPV =  t=0 (1+k) t

$600,000 $875,000 $875,000 $875,000 $875,000 + + + + (1.164)1 (1.164)2 (1.164)3 (1.164)4 (1.164)5 = −$2, 575, 000+ $515, 464 + $645, 806 + $554, 816 + 476, 646 + 409, 490

= −$2, 575, 000+ = $27, 222

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Product Line Cash Flow (C) 0 -2,575,000 1 600,000 2 875,000

Frequency (F) -1 4

Then solve by pressing NPV, enter the rate of 16.4% and compute NPV=27,222 Production Capacity Expansion: Cost of production capacity expansion = $8,137,250

NPV =

NCFt t =0 (1+k) t n

1   1 − (1.164)3  $3,250,000 $3,250,000  = −$8,137,250+$2,500,000   + (1.164)5  0.164 + (1.164)4     = −$8,137,250+$5,578,116+ $1,770,400+$1,520,962 = $732,228 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Production Capacity Cash Flow (C) 0 -8,137,250 1 2,500,000 2 3,250,000

Frequency (F) -3 2

Then solve by pressing NPV, enter the rate of 16.4% and compute NPV=732,227.95 .

SM 10-37

Fundamentals of Corporate Finance, 4th edition

b.

Solutions Manual

Since they are independent, and both have NPV > 0, both projects should be accepted.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.17 Net present value:Emporia Mills management is evaluating two alternative heating systems. Costs and projected energy savings are given in the following table. The firm uses 11.5 percent to discount such project cash flows. Which system should be chosen?

Year

System 100

System 200

0

$(1,750,000)

$(1,735,000)

1

275,223

750,000

2

512,445

612,500

3

648,997

550,112

4

875,000

384,226

Solution: Required rate of return = k = 11.5% System 100: Cost of System 100 = $1,750,000 n NCFt $275,223 $512,445 $648,997 $875,000 + + (1.115)3 + NPV =  (1+ k)t =−$1,750,000+ (1.115)4 (1.115)1 (1.115)2 t=0 = −$1,750,000 + $246,837 + $412,190 + $468,186 + 566,120 = −$56,667

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: .

SM 10-38

Fundamentals of Corporate Finance, 4th edition

System 100 01234

Cash Flow (C) -1,750,000 275,223 512,445 648,997 875,000

Solutions Manual

Frequency (F) -1111

Then solve by pressing NPV, enter the rate of 11.5% and compute NPV= -56,667.41 System 200: Cost of System 200 = $1,735,000 n NCFt $750,000 $612,500 $550,112 $384,226 + + + NPV =  (1+ k)t =−$1,735,000+ (1.115)1 (1.115)2 (1.115)3 (1.115)4 t=0 = −$1,735,000 + $672,646 + $492,670 + $396,850 + 248,592 = $75,758

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: System 200 Cash Flow (C) 0 -1,735,000 1 750,000 2 612,500 3 550,112 4 384,226

Frequency (F) -1 1 1 1

Then solve by pressing NPV, enter the rate of 11.5% and compute NPV= 75,758 Since System 200 has a positive NPV, select that system. Reject System 100 as it has negative NPV. LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.18 Payback: Creative Solutions, Inc., has just invested $4,615,300 in new equipment. The .

SM 10-39

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

firm uses a payback period criteria of not accepting any project that takes more than four years to recover its costs. Management anticipates cash flows of $644,386, $812,178, $943,279, $1,364,997, $2,616,300, and $2,225,375 over the next six years. Does this investment meet the firm’s payback criteria?

Solution: Cumulative Year

CF

Cash Flow

0

$(4,615,300)

$(4,615,300)

1

644,386

(3,970,914)

2

812,178

(3,158,736)

3

943,279

(2,215,457)

4

1,364,997

(850,460)

5

2,616,300

1,765,840

6

2,225,375

3,991,215

Remaining cost to recover Payback period= Years before cost recovery+ Cash flow during the year = 4 + $850, 460 $2, 616, 300 = 4.33 years

Since the project payback period exceeds the firm’s target of four years, it should not have been accepted.

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.19 Discounted payback: Timeline Manufacturing Co. management is evaluating two projects. The company uses payback criteria of three years or less. Project A has a cost of $912,855, and project B’s cost is $1,175,000. Cash flows from both projects are given in the following table. What are their discounted payback periods, and which will be .

SM 10-40

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

accepted with a discount rate of 8 percent?

Year

Project A

Project B

1

$ 86,212

$586,212

2

313,562

413,277

3

427,594

231,199

4

285,552

Solution: Project A Cumulative Year

Cumulative

CF

PVCF

PVCF

1

86,212

$(912,855)

(826,643) 79,826 2 313,562 (513,081) 268,829 3

(833,029)

427,594 (85,487) 339,438 4 285,552 200,065 209,889

(564,200)

0

CF $(912,855)

$(912,855)

$(912,855)

(224,762) (14,873) The payback period of Project A exceeds three years.

Project B Cumulative Year 0

CF

Cumulative

CF

$(1,175,000) $(1,175,000)

PVCF

PVCF

$(1,175,000)

$(1,175,000)

1

586,212

(588,788)

542,789

(632,211)

2

413,277

(175,511)

354,318

(277,893)

3

231,199

55,688

183,533

(94,359)

The payback period of Project B exceeds three years.

Since the firm’s acceptance criteria is three years, neither project will be accepted.

LO 3 Bloomcode: Analysis .

SM 10-41

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.20 Payback: Regent Corp. management is evaluating three competing types of equipment.

Costs and cash flow projections for all three are given in the following table. Which would be the best choice based on payback period?

Year

Type 1

Type 2

Type 3

0

$(1,311,450)

$(1,415,888)

$(1,612,856)

1

212,566

586,212

786,212

2

269,825

413,277

175,000

3

455,112

331,199

175,000

4

285,552

141,442

175,000

5

121,396

175,000

6

175,000

Solution: Type 1

Type 2

Cumulative Year 0 1 2 3 4 5

CF

CF

Type 3

Cumulative CF

CF

Cumulative CF

CF

$(1,311,450)

$(1,311,450) $(1,415,888)

$(1,415,888) $(1,612,856)

($1,612,856)

212,566

(1,098,884) 586,212

(829,676) 786,212

(826,644)

269,825

(829,059) 413,277

(416,399) 175,000

(651,644)

455,112

(373,947) 331,199

(85,200) 175,000

(476,644)

285,552

(88,395) 141,442

56,242 175,000

(301,644)

121,396

33,001

175,000

(126,644)

175,000

48,356

6

Type 1:

.

SM 10-42

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Remaining cost to recover Payback period= Years before cost recovery+ Cash flow during the year = 4 + $88, 395 $121, 396 = 4.73 years

Type 2: Remaining cost to recover Payback period= Years before cost recovery+ Cash flow during the year = 3+

$85, 200

$141, 442 = 3.6 years

Type 3: Remaining cost to recover Payback period= Years before cost recovery+ Cash flow during the year = 5+

$126, 644

$175, 000 = 5.72 years

Select Type 2 because it has the lowest payback period.

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.21 Discounted payback: Nugent Communication Corp. is investing $9,365,000 in new technologies. The company’s management expects significant benefits in the first three years after installation (as can be seen by the following cash flows), and smaller constant benefits in each of the next four years. What is the discounted payback period for the project assuming a discount rate of 10 percent?

Years Cash flows .

1

2

3

4–7

$2,265,433

$4,558,721

$3,378,911

$1,250,000 SM 10-43

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: Discount rate = k = 10% Cumulative Year 0

CF

CF

$(9,365,000) $(9,365,000)

Cumulative PVCF

PVCF

$(9,365,000)

$(9,365,000)

1

2,265,433

(7,099,567)

2,059,485

(7,305,515)

2

4,558,721

(2,540,846)

3,767,538

(3,537,977)

3

3,378,911

838,065

2,538,626

(999,352)

4

1,250,000

2,088,065

853,767

(145,585)

5

1,250,000

3,338,065

776,152

630,567

6

1,250,000

4,588,065

705,592

1,336,159

7

1,250,000

5,838,065

641,448

1,977,607

Discounted PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4 + ($145,585 / $776,152) = 4.19 years LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.22 Modified internal rate of return (MIRR): Morningside Bakeries recently purchased equipment at a cost of $650,000. Management expects the equipment to generate cash flows of $275,000 in each of the next four years. The cost of capital is 14 percent. What is the MIRR for this project?

Solution: PV of costs = $650,000 .

SM 10-44

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Length of project = n = 4 years Cost of capital = k = 14% Annual cash flows = CFt = $275,000 − − TV=CF1(1+k)n1+CF2(1+k)n2++CFn(1+k)n−n

=$275,000(1.14)3+$275,000(1.14)2+$275,000(1.14)1+$275,000(1.14)0 = $407,425 + $357,390 + $313,500 + $275,000 = $1,353,315 Financial Calculator Solution : Find the Terminal Value of the annual cash inflows by using a financial calculator as follows: 4 14 0 275,000 N i PV PMT FV -1,353,315

Now we can solve for the MIRR using Equation 10.5.

PVC ost s=

TV (1+ MIRR)t

$1,353,315 (1+ MIRR)4 $1,353,315 (1+ MIRR) 4 = =2.0820 $650,000 = 1 (1+ MIRR) (2.0820) 4 = 1.2012 = MIRR 0.2012=20.1% $650,000=

Financial Calculator Solution : 4 N

i 20.12

-650,000 PV

0 PMT

1,353,315 FV

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective .

SM 10-45

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.23 Modified internal rate of return (MIRR): Management of Sycamore Home Furnishings is considering acquiring a new machine that can create customized window treatments. The equipment will cost $263,400 and will generate cash flows of $85,000 over each of the next six years. If the cost of capital is 12 percent, what is the MIRR on this project?

Solution: PV of costs = $263,400 Length of project = n = 6 years Cost of capital = k = 12% Annual cash flows = CFt = $85,000 − − TV=CF1(1+k)n1+CF(1+k)n2++CF(1+k)n−n 2 n

= $85,000(1.12)5 + $85,000(1.12)4 + $85,000(1.12)3 + $85,000(1.12)2 + $85,000(1.12)1 + $85,000(1.12)0 = $149,799 + $133,749 + $119,419 + $106,624 + $95,200 + $85,000 = $689,791 Financial Calculator Solution : Find the Terminal Value of the annual cash inflows by using a financial calculator as follows: 6 12 0 85,000 N i PV PMT FV -689,791.07 Now we can solve for the MIRR using Equation 10.5.

TV (1 + MIRR )t $689, 791 $263, 400= (1 + MIRR )6 $689, 791 (1 + MIRR )6 = =2.6188 $263, 400 PV Costs =

(1 + MIRR ) = (2.6188) 6 = 1.1740 MIRR = 0.1740=17.4% 1

Financial Calculator Solution: .

SM 10-46

Fundamentals of Corporate Finance, 4th edition

6 N

i 17.40

-263,400 PV

Solutions Manual

0 PMT

689,791 FV

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.24 Internal rate of return: Management of Great Flights, Inc., an aviation firm, is considering purchasing three aircraft for a total cost of $161 million. The company would lease the aircraft to an airline. Cash flows from the proposed leases are shown in the following table. What is the IRR of this project?

Years

Cash Flow

1–4

$23,500,000

5–7

$72,000,000

8–10

$80,000,000

Years

Cash Flow

1–4

$23,500,000

5–7

$72,000,000

8–10

$80,000,000

Solution:

Initial investment = $161,000,000 Length of project = n = 10 years Required rate of return = k = To determine the IRR, the trial-and-error approach can be used. Set NPV=0.

Try a higher rate than k = 15%; try IRR = 22%. .

SM 10-47

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

1   1    1(1.22)4 −  1 − (1.22)3 1  $72,000,000    0  −$161,000,000+$23,500,000  0.22  (1.22)4  0.22 +          1   − 1  (1.22)3  1  + $80,000,000     0.22  (1.22)7     −$161,000,000+ $58,600,552+$66,374,346+$40,614,233 $4,589,131 Try IRR = 23%.

NPV = 0 =

NCFt (1+ IR R) t =0 t n

1   1    1 (1.23)4 −  1 − (1.23)3 1  $72,000,000    0  −$161,000,000+ $23,500,000   0.23  (1.23)4  0.23 +          1   − 1  (1.23)3  1  + $80,000,000     0.23  (1.23)7     −$161,000,000+ $57,534,386+$63,271,035+$37,778,708 −$2,415,871 Try IRR = 22.7%.

.

SM 10-48

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt (1+ IR R) t t =0 n

NPV = 0 = 

1 1     1−(1.227)4 1 − (1.227)3 1  $72,000,000    0  −$161,000,000+ $23,500,000   0.2 2 7  (1.227)4  0.2 2 7 +          1   − 1 (1.227)3  1  + $80,000,000     (1.227)7  0.2 2 7       −$161,000,000+ $57,850,786+ $64,183,552+ $38,605,355 −$360,307 The IRR of the project is between 22 and 23 percent. Using a financial calculator, we find that the IRR is 22.65 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -161,000,000 1 23,500,000 2 72,000,000 3 80,000,000

Frequency (F) -4 3 3

Then solve by pressing IRR to get 22.65% LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.25 Internal rate of return: Refer to problem 10.5. Compute the IRR for both production System 1 and production System 2. Which has the higher IRR? Which production system has the higher NVP? Explain why the IRR and NPV rankings of Systems 1 and 2 are different?

.

SM 10-49

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution The IRR of System 1 is 83.93 percent and the IRR of System 2 is 50.07 percent. The NPV of System 1 is $22,969.42 and the NPV of System 2 is $36,001.43. System 1 delivers a higher IRR because it requires a lower initial investment and the cost is recovered the first year. Thus, even with lower cash inflows in the years after startup, System 1 is able to deliver a higher return on the initial investment. System 2 has a higher initial investment but delivers a higher net cash flow for the firm.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: System 1 Cash Flow (C) Frequency (F) 0 -15,000 -1 15,000 3 Then solve by pressing IRR to get 83.93%. Then solve by pressing NPV, enter the rate of 9% and compute NPV= 22,969.42 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: System 2 Cash Flow (C) Frequency (F) 0 -45,000 -1 32,000 3 Then solve by pressing IRR to get 50.07%. Then solve by pressing NPV, enter the rate of 9% and compute NPV= 36,001.43 LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.26 Internal rate of return: Ancala Corporation management is considering investments in two new golf apparel lines for next season: golf hats and belts. Due to a funding constraint, these lines are mutually exclusive. A summary of each project’s estimated .

SM 10-50

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

cash flows over its three -year life, as well as the IRR and NPV of each are outlined below. The CFO of the firm has decided to manufacture the belts; however, the CEO is questioning this decision given that the IRR is higher for manufacturing hats. Explain to the CEO why the IRRs and NPVs of the belt and hat projects disagree? Is the CFO’s decision the correct?

Year 0 1 2 3 NPV IRR

Golf Belts -$1,000 1,000 500 500 $697.97 54%

Golf Hats -$500 500 300 300 $427.87 61%

Solution The IRRs and NPVs of the belt and hat lines disagree because of the differences in the scale of the project. Golf hats deliver a higher IRR because they require a lower initial investment. Thus, even with lower cash inflows in the years after startup, the golf hat project is able to deliver a higher return on the initial investment. While the golf belts project does cost more, it delivers a higher net cash flow for Ancala’s investors. This NPV factors in the initial cost of the project, and reflects the total net cash flow for the firm’s shareholders.

The CFO’s decision to choose the golf belts project is the right choice because it yields the higher net cash flows for Ancala’s investors.

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.27 Internal rate of return: Compute the IRR on the following cash flow streams: a.

An initial investment of $25,000 followed by a single cash flow of $37,450 in year 6.

.

SM 10-51

Fundamentals of Corporate Finance, 4th edition

b.

Solutions Manual

An initial investment of $1 million followed by a single cash flow of $1,650,000 in year 4.

c.

An initial investment of $2 million followed by cash flows of $1,650,000 and $1,250,000 in years 2 and 4, respectively.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective Solution: a.

Try IRR = 7%. n NCF t NPV = 0=  t=0 (1+ IRR)t $37,450 0  −$25,000+ (1.07)6  −$25,000+ $2 4,9 5 5 −$45

Try IRR = 6.97%. n NCF t NPV = 0=  t=0 (1+ IRR)t $37,450 0  −$25,000+ (1.0697)6  −$25,000+ $2 4,9 9 7 −$3

The IRR of the project is approximately 6.97 percent. Using a financial calculator, we find that the IRR is 6.968 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) -25,000 -0 0 5 1 37,450 1 2 Then solve by pressing IRR which gives the result 6.968% .

SM 10-52

Fundamentals of Corporate Finance, 4th edition

b.

Solutions Manual

Try IRR = 12%. n NCFt NPV = 0=  t=0 (1+IRR)t

$1,650,000 (1.12)4  −$1,000,000+ $1,048,605 $48,605

0  −$1,000,000+

Try IRR = 13%. n NCFt NPV = 0=  t=0 (1+IRR)t

$1,650,000 (1.13)4  −$1,000,000+ $1,011,976$11,976

0  −$1,000,000+

Try IRR = 13.3%. n NCFt NPV = 0=  t=0 (1+IRR)t

$1,650,000 (1.133)4  −$1,000,000+ $1,001,300$1,300

0  −$1,000,000+

The IRR of the project is approximately 13.3 percent. Using a financial calculator, we find that the IRR is 13.337 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -1,000,000 1 0 2 1,650,000

Frequency (F) -3 1

Then solve by pressing IRR which gives an answer of 13.337% Alternatively:

.

SM 10-53

Fundamentals of Corporate Finance, 4th edition

4 N

i 13.337 c.

-1,000,000 PV

0 PMT

Solutions Manual

1,650,000 FV

Try IRR = 15%. n NCFt NPV = 0=  t=0 (1+IRR)t

$1,650,000 $1,250,000 + 0  −$2,0 0 0,0 0+0 (1.15)2 (1.15)4  −$2,0 0 0,0 0+0$1,247,637 + $714,692  −$37,671 Try IRR = 14%. n NCFt NPV = 0=  t=0 (1+IRR)t

$1,650,000 $1,250,000 + 0  −$2,0 0 0,0 0+0 (1.14)2 (1.14)4  −$2,0 0 0,0 0+0$1,269,621+ $740,100  $9,721 The IRR of the project is between 14 and 15 percent. Using a financial calculator, we find that the IRR is 14.202 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) -2,000,000 0 0 1 1,650,000 2 3 0 4 1,250,000

Frequency (F) -1 1 1 1

Then solve by pressing IRR which gives an answer of 14.202% 10.28 Internal rate of return: Compute the IRR for the following project cash flows: a.

An initial outlay of $3,125,000 followed by annual cash flows of $565,325 for the next eight years.

.

SM 10-54

Fundamentals of Corporate Finance, 4th edition

b.

Solutions Manual

An initial investment of $33,750 followed by annual cash flows of $9,430 for the next five years.

c.

An initial outlay of $10,000 followed by annual cash flows of $2,500 for the next seven years.

Solution: a.

Initial investment = $3,125,000 Annual cash flows = $565,325 Length of investment = n = 8 years Try IRR = 8%. n NCF t=−$3,125,000+$565,325 NPV =  t=0 (1+k) t

= −$3,125,000+$3,248,719 = $123,719

 1  1 − (1.08)8     0.08     

Try a higher rate, IRR = 9%.

 1  − 1  n (1.09)8 NCF    t=−$3,125,000+ = NPV  $565,325 t=0 (1+k) t  0.09      = −$3,125,000+$3,128,972 = $3,972 The IRR of the project is approximately 9 percent. Using a financial calculator, we find that the IRR is 9.034 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) -3,125,000 -0 565,325 8 1 .

SM 10-55

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Then solve by pressing IRR where we find it is 9.034% b.

Initial investment = $33,750 Annual cash flows = $9,430 Length of investment = n = 5 years Try IRR = 12%.

 1  − 1  n (1.12)5 NCF tt    $33,750+ = = − NPV  $9,430 t=0 (1+k)  0.12      = −$33,750+$33,993 = $243 Try IRR = 12.3%.

  1 1−   (1.123)5 NCF tt  = −$33,750+$9,430   NPV =  t=0 (1+k)  0.1 2 3      = −$33,750+$33742 = −$8 0 n

The IRR of the project is approximately 12.3 percent. Using a financial calculator, we find that the IRR is 12.29 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -33,750 -1 9,430 5 Then solve by pressing IRR where we find it is 12.29% c.

Initial investment = $10,000 Annual cash flows = $2,500 Length of investment = n = 7 years

.

SM 10-56

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Try IRR = 16%.

 1  1− (1.16)7 NCF tt  = −$10,000+$2,5 0 0  NPV =  t=0 (1+k)  0.16      = −$10,000+$1 0,0 9 6 = $96 n

Try IRR = 16.3%.

  1 1− (1.163)7 NCFt  $10,000+$2,500   − = NPV =  t  0.1 6 3  t=0 (1+ k)     = −$10,000+$1 0,0 0 8 =$80 n

The IRR of the project is approximately 16.3 percent. Using a financial calculator, we find that the IRR is 16.327 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -10,000 -1 2,500 7 Then solve by pressing IRR where we find it is 16.327% LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.29 Profitability index: Suppose that you could invest in the following projects but have only $30,000 to invest. How would you make your decision and in which projects would you invest?

.

SM 10-57

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Project

Cost

NPV

A

$ 8,000

$4,000

B

11,000

7,000

C

9,000

5,000

D

7,000

4,000

Solution: One would compute the profitability index for each of the projects as follows:

PI=

NPV+Initial investment Initial investment

The profitability indexes of the projects are: PI A=

$4, 000 + $8, 000 =1.50 $8,000

PI B=

$7, 000 + $11, 000 =1.64 11,000

$5, 000 + $9, 000 =1.56 $9, 000 $4, 000 + $7, 000 $7, 000 =1.57 PI D= PI C=

With $30,000, you should invest in B, D, and C. The total cost is $27,000, and the total NPV is $16,000.

LO 6 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 10-58

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.30 Profitability index: Suppose that you could invest in the same projects as in the previous problem, but have only $25,000 to invest. Which projects would you chose?

Solution: The profitability indexes of the projects are: A: 1.50; B: 1.64; C: 1.56; D: 1.57 With $25,000, you cannot invest in all of B, D, and C, since the total cost is $27,000. You may think that you should then invest in only B and D, since they have the highest profitability indexes. This will yield a total NPV of $11,000, and you are left with $7,000 of idle capital.

If you give up project B, however, which has the highest profitability index and highest cost, and invest instead in A, C, and D, which require less capital, you will get a total NPV of $13,000, and you are left with less idle capital ($1,000). From this example you can see that capital rationing with indivisible projects are sometimes complicated and require a careful thought of all possibilities (or linear/integer programming).

LO 6 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

ADVANCED

.

SM 10-59

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.31Management of Draconian Measures, Inc., is evaluating two independent projects. The company uses a 13.8 percent discount rate for such projects. The costs and cash flows for the projects are shown in the following table. What are their NPVs? Year

Project 1

Project 2

0

$(8,425,375)

$(11,368,000)

1

3,225,997

2,112,589

2

1,775,882

3,787,552

3

1,375,112

3,125,650

4

1,176,558

4,115,899

5

1,212,645

4,556,424

6

1,582,156

7

1,365,882

Solution: Project 1: Cost of Project 1 = $8,425,375 Length of project = n = 7 years Required rate of return = k = 13.8% NCFt (1+ k) t t=0 n

NPV = 

= −$8,425,375+

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.138)1 (1.138)2 (1.138)3 (1.138)4 (1.138)5

$1,582,156 $1,365,882 + (1.138)7 (1.138)6 = −$8,425,375 + $2,834,795 + $1,371,291+ $933,064 + 701,527 + $635,364 + $728,443 + $552,608 +

= −$668,283

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 1 Cash Flow (C) Frequency (F) 0 -8,425,375 -1 3,225,997 1 .

SM 10-60

Fundamentals of Corporate Finance, 4th edition

2 3 4 5 6 7

1,775,882 1,375,112 1,176,558 1,212,645 1,582,156 1,365,882

Solutions Manual

1 1 1 1 1 1

Then solve by pressing NPV, enter the rate of 13.8% and compute NPV= -668,283 Since Project 1 NPV is negative, we reject this project.

Project 2: Cost of Project 2 = $11,368,000 Length of project = n = 5 years Required rate of return = k = 13.8% NCFt t t=0 (1+ k ) n

NPV = 

$2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556,424 + + + + (1.138)5 (1.138)1 (1.138)2 (1.138)3 (1.138)4 = −$11,368,000+ $1,856,405 + $2,924,651+ $2,120,868 + $2,454,119 + $2,387,332 = $375,375 = −$11,368,000+

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) 0 -11,368,000 1 2,112,589 2 3,787,552 3 3,125,650 4 4,115,899 5 4,556,424

Frequency (F) -1 1 1 1 1

Then solve by pressing NPV, enter the rate of 13.8% and compute NPV= 375,375 Since Project 2 NPV is positive, we accept this project.

LO 2 Bloomcode: Analysis AASCB: Analytic .

SM 10-61

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.32 Refer to Problem 10.31. a.

What are the IRRs for the projects?

b.

Does the IRR criterion suggest a different decision than the NPV criterion?

c.

Explain how you would expect the management of Draconian Measures to decide

which project(s) to invest in.

Solution: a.

Project 1: At the required rate of return of 13.8 percent, Project 1 has a NPV of $(668,283).

To find the IRR, try lower rates.

Try IRR = 11%.

NCFt (1+ k) t t=0 n

NPV = 

= −$8,425,375+

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.11)1 (1.11)2 (1.11)3 (1.11)4 (1.11)5

$1,582,156 $1,365,882 + (1.11)7 (1.11)6 = −$8,425,375+ $2,906,304+$1,441,346+$1,005,470+$775,035+ $719,646 + $845,885 +$657,889 +

= −$73,801

Try a lower rate, IRR=10.7%.

NCFt (1+ k) t t=0 n

NPV = 

= −$8,425,375+

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.107)1 (1.107)2 (1.107)3 (1.107)4 (1.107)5

$1,582,156 $1,365,882 + (1.107)7 (1.107)6 = −$8,425,375+$2,914,180+$1,449,168+$1,013,667+$783,471+$729,450 + $859,733+$670,471 +

= −$5,235 .

SM 10-62

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The IRR of the project is approximately 10.7 percent. Using a financial calculator, we find that the IRR is 10.677 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 1 Cash Flow (C) 0 -8,425,375 1 3,225,997 2 1,775,882 3 1,375,112 4 1,176,558 5 1,212,645 6 1,582,156 7 1,365,882

Frequency (F) -1 1 1 1 1 1 1

Then solve by pressing IRR to get 10.677% Project 2: At the required rate of return of 13.8 percent, Project 2 has a NPV of $ 375,375.

To find the IRR, try higher rates.

Try IRR = 15%. n NCFt NPV = 0=  + IRR t ) t =0 (1 $2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556,424 + + + + 0 = −$11,368,000+ (1.15)3 (1.15)4 (1.15)5 (1.15)1 (1.15)2 = −$11,368,000+ $1,837,034+$2,863,933+ $2055,166+$2,353,279+$2,265,348 ,

= $6,760

Try IRR = 15.1%. n NCFt NPV = 0=  + IRR t ) t =0 (1 $2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556,424 + + + + 0 = −$11,368,000+ (1.151)5 (1.151)3 (1.151)4 (1.151)1 (1.151)2 = −$11,368,000+ $1,835,438+$2,858,959+ $ 2049,814+$2,345,111+$2,255,524 ,

= −$23,154

The IRR of the project is between 15 and 15.1 percent. Using a financial calculator, we find that the IRR is 15.023 percent. .

SM 10-63

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) 0 -11,368,000 1 2,112,589 2 3,787,552 3 3,125,650 4 4,115,899 5 4,556,424

Frequency (F) -1 1 1 1 1

Then solve by pressing IRR to get 15.023%. b.

Based on the IRR, Project 1 will be rejected and Project 2 will be accepted. These decisions are identical to those based on NPV. (Given that Project 1 had a negative NPV, the IRR will always be less than the required rate of return 13.8%.)

c.

Management would use the decision spelled out by NPV, although in this case the IRR has come up with the same decision.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.33 Management of Dravid, Inc., is currently evaluating three projects that are independent.

The cost of funds can be either 13.6 percent or 14.8 percent depending on their financing plan. All three projects cost the same at $500,000. Expected cash flow streams are shown in the following table. Which projects would be accepted at a discount rate of 14.8 percent? What if the discount rate was 13.6 percent?

.

Year

Project 1

Project 2

Project 3

1

$0

$0

$245,125

2

125,000

0

212,336

3

150,000

500,000

112,500 SM 10-64

Fundamentals of Corporate Finance, 4th edition

4

375,000

Solutions Manual

500,000

74,000

Solution: Cost of projects = $500,000 Length of project = n = 4 years Required rate of return = k = 14.8% Project 1:

NCF t $0 $125,000 $150,000 $375,000 + = −$500,000+ + + t (1.148)1 (1.148)2 (1.148)3 (1.148)4 t=0 (1+k) n

NPV = 

= −$500,000+ $0 + $94,848+$99,144+$215,906 = −$90,103 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 1 Cash Flow (C) 0 -500,000 1 0 2 125,000 3 150,000 4 375,000

Frequency (F) -1 1 1 1

Then solve by pressing NPV, enter the rate of 14.8% and compute NPV= -90,103 Also solve by pressing NPV, enter the rate of 13.6% and compute NPV= -75,645.18 Project 2:

$0 NCF $500,000 $500,000 $0 + + = −$500,000+ + tt 1 (1.148) (1.148)2 (1.148)3 (1.148)4 t=0 (1+k) n

NPV = 

= −$500,000+ $0 + $0+$330,479 + $287,874 = $118,353 .

SM 10-65

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) 0 -500,000 1 0 2 500,000

Frequency (F) -2 2

Then solve by pressing NPV, enter the rate of 14.8% and compute NPV=118,353 Also solve by pressing NPV, enter the rate of 13.6% and compute NPV= 141,295 Project 3:

NCFt $245,125 $212,336 $112,500 $7 4,0 0 0 + = −$500,000+ + + t (1+ (1.148)1 (1.148)2 (1.148)3 (1.148)4 k) t=0 = −$500,000+ $213,524+$161,116+$74,358+$42,605 = −$8,397 n

NPV = 

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 3 Cash Flow (C) 0 -500,000 1 213,524 2 161,116 3 74,358 4 42,605

Frequency (F) -1 1 1 1

Then solve by pressing NPV, enter the rate of 14.8% and compute NPV=-8,397 Also solve by pressing NPV, enter the rate of 13.6% and compute NPV= -1,491 At a discount rate of 14.8 percent, only project 2 will be accepted. At a discount rate of 13.6 percent, the NPVs of the three projects are -$75,645, $141,295, and $1,491 respectively. Both projects 2 and 3 have positive NPVs and will be accepted.

.

Year

Project 1

PVCF

Project 2

PVCF

Project 3

PVCF

0

$(500,000)

$(500,000)

$(500,000)

$(500,000)

$(500,000)

$(500,000)

SM 10-66

Fundamentals of Corporate Finance, 4th edition

123

−

4 NPV

Solutions Manual

−

−

−

245,125

215,779

125,000

96,862

−

−

212,336

164,538

150,000

102,319

500,000

341,063

112,500

76,739

375,000

225,175 (75,645)

500,000

300,232

74,000

44,434 1,491

141,29 5

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.34 Management of Intrepid, Inc., is considering investing in three independent projects. The costs and the cash flows are given in the following table. The appropriate cost of capital is 14.5 percent. Compute the project IRRs and identify the projects that should be accepted.

Year

Project 1

Project 2

Project 3

0

$(275,000)

$(312,500)

$(500,000)

1

63,000

153,250

212,000

2

85,000

167,500

212,000

3

85,000

112,000

212,000

4

100,000

212,000

Solution: Project 1: Cost of Project 1 = $275,000 Length of project = n = 4 years Required rate of return = k = 14.5%

.

SM 10-67

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt t t=0 (1+ k ) n

NPV = 

$63,000 $85,000 $85,000 $100,000 + (1.145)2 + + (1.145)4 (1.145)1 (1.145)3 = −$275,000+ 55,022+$64,835+$56,624+$58,181 = −$40,338 = −$275,000+

At the required rate of return of 14.5 percent, Project 1 has a NPV of $(40,338). To find the IRR, try lower rates.

Try IRR = 7.6%. n NCF t NPV = 0=  t =0(1+ IRR)t $63,000 $85,000 $85,000 $100,000 + + + 0 = −$275,000+ (1.076)1 (1.076)2 (1.076)3 (1.076)4 = −$275,000+ 58,550+$73,417+$68,231+$74,602

= −$200 0

The IRR of the project is approximately 7.6 percent. Using a financial calculator, we find that the IRR is 7.57 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 1 Cash Flow (C) 0 -275,000 1 63,000 2 85,000 3 85,000 4 100,000

Frequency (F) -1 1 1 1

Then compute IRR to get 7.57% Project 2: Cost of Project 2 = $312,500 Length of project = n = 3 years Required rate of return = k = 14.5%

.

SM 10-68

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt $153,250 $167,500 $112,000 $312,500+ + = − + (1+ k) t (1.145)1 (1.145)2 (1.145)3 t=0 = −$312,500+ $ 133,843+$127,763+$74,611 = $23,717 n

NPV = 

At the required rate of return of 14.5 percent, Project 2 has a NPV of $23,717. To find the IRR, try higher rates.

Try IRR =19%. n NCF t NPV = 0=  t =0(1+ IRR)t

$153,250 $167,500 $112,000 + + (1.19)1 (1.19)2 (1.19)3 = −$312,500+ $128,782+$118,283 +$66,463 = $1,027

0 = −$312,500+

Try IRR=19.2%.

NCF t + t=0 (1 IRR)t $153,250 $167,500 $112,000 0 = −$312,500+ + + (1.192)3 (1.192)1 (1.192)2 +$ = −$312,500+ $128,565+$117,886 66,129 n

NPV =0= 

=$80 0

The IRR of the project is approximately 19.2 percent. Using a financial calculator, we find that the IRR is 19.22 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) 0 -312,500 1 153,250 2 167,500 3 112,000

Frequency (F) -1 1 1

Then compute IRR to get 19.22%.

Project 3: Cost of Project 3 = $500,000 .

SM 10-69

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Length of project = n = 4 years Required rate of return = k = 14.5%

  1 1−  (1.145)4 NCF tt  = −$500,000+$212,000   NPV =  t=0 (1+k)  0.1 4 5      = −$500,000+$611,429 = $111,429 n

At the required rate of return of 14.5 percent, Project 3 has a NPV of $111,429. To find the IRR, try higher rates.

Try IRR =25%.

NPV = 0 =

NCFt (1+ IRR)t =0 t n

 1  1−(1.25)4  0 = −$500,000+$212,000    0.25      = −$500,000+$500,659  $659 Try IRR=25.1%.

NPV = 0 =

NCFt (1+ IR R) t =0 t n

  1 1−(1.251)4  0 = −$500,000+ $212,000    0.2 5 1      = −$500,000+ $500,659 = −$2310 The IRR of the project is approximately 25.1 percent. Using a financial calculator, we find that the IRR is 25.07 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) Frequency (F) .

SM 10-70

Fundamentals of Corporate Finance, 4th edition

0 1

Solutions Manual

-500,000 212,000

-4

Then compute IRR to get 25.07%.

Only Projects 2 and 3 will be accepted as the IRRs exceed the required rate of return of 14.5 percent.

Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.35 Jekyll & Hyde Corp. management is evaluating two mutually exclusive projects. The cost of capital is 15 percent. Costs and cash flows for each project are given in the following table. Which project should be accepted?

Year

Project 1

Project 2

0

$(1,250,000)

$(1,250,000)

1

250,000

350,000

2

350,000

350,000

3

450,000

350,000

4

500,000

350,000

5

750,000

350,000

Solution: Project 1: Cost of project = $1,250,000 Length of project = n = 5 years Required rate of return = k = 15%

.

SM 10-71

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt t t=0 (1+ k ) n

NPV = 

$250,000 $350,000 $450,000 $500,000 $750,000 + + + + (1.15)1 (1.15)2 (1.15)4 (1.15)5 (1.15)3 = −$1,250,000+ $217,391+$264,650 +$295,882+ $285,877+$372,883 = −$1,250,000+ = $186,683

At the required rate of return of 15 percent, Project 1 has an NPV of $186,683.Based on the positive NPV, Project 1 should be accepted.

To find the IRR, try higher rates.

Try IRR = 20%.

NCFt )t t =0 (1+ k n

NPV = 0= 

$500,000 $750,000 0 = −$1,250,000+ $250,000 + $350,000 + $450,000 + + 3 (1.20)4 (1.20)5 (1.20)1 (1.20)2 (1.20) = −$1,250,000+ $208,333+$243,056 +$260,417 + $241,127+$301,408  $4,340

Try IRR = 20.1%. n NCFt NPV = 0=  t =0 (1+IRR)t

$250,000 $350,000 $450,000 $500,000 $750,000 + + + + (1.201)4 (1.201)5 (1.201)1 (1.201)2 (1.201)3 +$ = −$1,250,000+ $208,160+$242,651 259,767 + $240,324+$300,155

0 = −$1,250,000+ = $1,057 0

The IRR of the project is approximately 20.1 percent. Using a financial calculator, we find that the IRR is 20.132 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 1 Cash Flow (C) 0 -1,250,000 1 250,000 2 350,000 .

Frequency (F) -1 1 SM 10-72

Fundamentals of Corporate Finance, 4th edition

3 4 5

450,000 500,000 750,000

Solutions Manual

1 1 1

Then solve by pressing IRR to get 20.132%.

Project 2: Cost of project = $1,250,000 Length of project = n = 5 years Required rate of return = k = 15%

 1  1−  (1.15)5 NCF    t=−$1,250,000+ NPV =  $350,000 t=0 (1+k) t  0.15      = −$1,250,000+$1,173,254 = −$76,746 n

At the required rate of return of 15 percent, Project 2 has an NPV of $(76,746). Based on the negative NPV, Project 2 should be rejected.

To find the IRR, try lower rates.

Try IRR = 12%.

NPV = 0 =

NCFt (1+ IR R) t =0 t n

 1  1 − (1.12)5  0 = −$1,250,000+$350,000    0.12      = −$1,250,000+$1,261,672 = $11,672 Try IRR = 12.4%.

.

SM 10-73

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt (1+ IRR)t t =0 n

NPV = 0 = 

  1 1 − (1.124)5  0 = −$1,250,000+$350,000    0.1 2 4      = −$1,250,000+$1,249,269 = −$731 0 The IRR of the project is approximately 12.4 percent. Using a financial calculator, we find that the IRR is 12.376 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) Frequency (F) 0 -1,250,000 -1 350,000 5 Then solve by pressing IRR to get 12.376%.

Given a required rate of return of 15 percent, Project 1 will be accepted as the IRR of 20.1 percent exceeds the required rate of return. Project 2 will be rejected.

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.36 Management of Larsen Automotive, a manufacturer of auto parts, is considering investing in two projects. The company typically compares project returns to a cost of funds of 17 percent. Compute the IRRs based on the cash flows in the following table.

Which project(s) will be accepted?

Year .

Project 1

Project 2 SM 10-74

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

0

$(475,000)

$(500,000)

1

300,000

117,500

2

110,000

181,300

3

125,000

244,112

4

140,000

278,955

Solution: Project 1: Cost of project = $475,000 Length of project = n = 4 years Required rate of return = k = 17% NCFt t t=0 (1+ k ) n

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.17)1 (1.17)2 (1.17)3 (1.17)4 = −$475,000+ $256,410+$80,356+$78,046+$74,711 = $14,524

= −$475,000+

At the required rate of return of 17 percent, Project 1 has an NPV of $14,524. To find the IRR, try higher rates.

Try IRR = 19%.

NCFt t t=0 (1+ k ) n

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.19)1 (1.19)2 (1.19)3 (1.19)4 = −$475,000+ $252,101+$77,678+$74,177+$69,814  −$1,230 = −$475,000+

Try IRR = 18.8%.

.

SM 10-75

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt t t=0 (1+ k ) n

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.188)1 (1.188)2 (1.188)3 (1.188)4 = −$475,000+ $252,525+$77,940+$74,552+$70,285 = $302 0 = −$475,000+

The IRR of the project is approximately 18.8 percent. Using a financial calculator, we find that the IRR is 18.839 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 1 Cash Flow (C) 0 -475,000 1 300,000 2 110,000 3 125,000 4 140,000

Frequency (F) -1 1 1 1

Then solve by pressing IRR to get 18.839%.

Project 2: Cost of project = $500,000 Length of project = n = 4 years Required rate of return = k = 17% NCFt t=0 (1+ k) t n

NPV = 

$117, 500 $181, 300 $244, 112 $278, 955 + + + (1.17)4 (1.17)3 (1.17)2 (1.17)1 = −$500, 000+ $100,427 + $132, 442+ $152, 416+ $148, 864 = $34, 150

= −$500, 000+

At the required rate of return of 17 percent, Project 2 has an NPV of $34,150. To find the IRR, try higher rates.

Try IRR = 20%. .

SM 10-76

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

n NCF t NPV = 0=  + t=0 (1 IRR)t $117,500 $181,300 $244,112 $278,955 + (1.20)4 + + 0 = −$500, 000+ (1.20)3 (1.20)1 (1.20)2 = −$500, 000+ $97,917+$125,903+ $141, 269 + $134, 527 = −$385 0

The IRR of the project is approximately 20 percent. Using a financial calculator, we find that the IRR is 19.965 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) 0 -500,000 1 117,500 2 181,300 3 244,112 4 278,955

Frequency (F) -1 1 1 1

Then solve by pressing IRR to get 19.965%.

Both projects can be accepted since their IRRs exceed the cost of capital of 17 percent.

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.37 Compute the IRR for each of the following projects:

.

Year

Project 1

Project 2

Project 3

0

$(10,000)

$(10,000)

$(10,000)

1

4,750

1,650

800

2

3,300

3,890

1,200

3

3,600

5,100

2,875

4

2,100

2,750

3,400 SM 10-77

Fundamentals of Corporate Finance, 4th edition

5

Solutions Manual

800

6,600

Solution: Project 1: Cost of project = $10,000 Length of project = n = 4 years NCF t t=0 (1 + IRR)t $4,750 $3,300 $3,600 $2,100 0 = −$1 0,0 0 + + + + 0 (1.16)1 (1.16)2 (1.16)3 (1.16)4 = −$1 0,0 0 + 0 $4,095+$2,452 + $2,3 0 + $1,1 6 0 6 =$13 0 n

NPV =0= 

The IRR of the project is approximately 16 percent. Using a financial calculator, we find that the IRR is 16.076 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 1 Cash Flow (C) 0 -10,000 1 4,750 2 3,300 3 3,600 4 2,100

Frequency (F) -1 1 1 1

Then solve by computing IRR to get 16.076% Project 2: Cost of project = $10,000 Length of project = n = 5 years

.

SM 10-78

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCF t + t=0 (1 IRR)t $1,650 $3,890 $5,100 $2,750 $800 0 = −$1 0,0 0 + + + + + 0 (1.137)1 (1.137)2 (1.137)3 (1.137)4 (1.137)5 = −$1 0,0 0 + 0 $1,451+$3,009+$3,470+$1,645+$421 n

NPV =0= 

=−$4 0

The IRR of the project is approximately 13.7 percent. Using a financial calculator, we find that the IRR is 13.685 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project 2 Cash Flow (C) 0 -10,000 1 1,650 2 3,890 3 5,100 4 2,750 5 800

Frequency (F) -1 1 1 1 1

Then solve by computing IRR to get 13.685%.

Project 3: Cost of project = $10,000 Length of project = n = 5 years n NCF t NPV = 0=  t =0(1+ IRR)t

$1,200 $2,875 $3,400 $800 $6,600 + + + + 3 (1.109)1 (1.109)2 (1.109) (1.109)4 (1.109)5 = −$1 0,0 0 + 0 $721+$976+$2,108+$2,248 + $3,934

0 0 = −$1 0,0 0 + = −$13 0

The IRR of the project is approximately 10.9 percent. Using a financial calculator, we find that the IRR is 10.862 percent.

Financial Calculator Solution :

.

SM 10-79

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Using a financial calculator, enter the cash flows as follows: Project 3 Cash Flow (C) Frequency (F) 01234 -10,000 800 -11111 5 1,200 2,875 3,400 6,600

Then solve by computing IRR to get 10.862%.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 9.38 Primus Corp. management is planning to convert an existing warehouse into a new plant that will increase its production capacity by 45 percent. The cost of this project will be $7,125,000. It will result in additional cash flows of $1,875,000 for the next eight years.

The discount rate is 12 percent. a.

What is the payback period?

b.

What is the NPV for this project?

c.

What is the IRR?

Solution: a.

Year

.

Project 1

Cumulative CF

0

$(7,125,000)

$(7,125,000)

1

1,875,000

(5,250,000)

2

1,875,000

(3,375,000)

3

1,875,000

(1,500,000)

4

1,875,000

375,000

5

1,875,000

2,250,000 SM 10-80

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

6

1,875,000

4,125,000

7

1,875,000

6,000,000

8

1,875,000

7,875,000

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($1,500,000 / $1,875,000) = 3.80 years b.

Cost of this project = $7,125,000 Required rate of return = 12% Length of project = n = 8 years

NPV =

NCFt t =0 (1+k) t n

 1  1 − (1.12)8  = −$7,125,000+$1,875,000    0.12      = −$7,125,000+$9,314,325 = $2,189,325 c.

To compute the IRR, try rates higher than 12 percent.

Try IRR = 20%.

NPV = 0 =

NCFt t =0 (1+k) t n

 1  1 − (1.20)8  0 = −$7,125,000+$1,875,000    0.20      = −$7,125,000+$7,194,675 = $69,675 Try IRR = 20.3%.

.

SM 10-81

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt (1+k)t t =0 n

NPV = 0 = 

  1 1 − (1.203)8  0 = −$7,125,000+$1,875,000    0.2 0 3      = −$7,125,000+$7,130,832 = $5,832 The IRR of the project is approximately 20.3 percent. Using a financial calculator, we find that the IRR is 20.328 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -7,125,000 -1 1,875,000 8 Then solve by computing IRR to get 20.328% LO 2, LO 3, LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.39 Quasar Tech Co. management is investing $6 million in new machinery that will produce the next-generation routers. Sales to its customers will amount to $1,750,000 for the next three years and then increase to $2.4 million for three more years. The project is expected to last six years and operating costs, excluding depreciation, will be $898,620 annually.

The machinery will be depreciated to a salvage value of $0 over 6 years using the straight-line method. The company’s tax rate is 30 percent, and the cost of capital is 16 percent.

.

a.

What is the payback period?

b.

What is the average accounting return (ARR)?

SM 10-82

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

c.

Calculate the project NPV.

d.

What is the IRR for the project?

Solution: a.

Year

Net Income

Depreciation

0

Project 1

Cumulative

Cash Flows

CF

$(6,000,000)

$(6,000,000)

1

$(104,034)

$1,000,000

895,966

(5,104,034)

2

$(104,034)

$1,000,000

895,966

(4,208,068)

3

$(104,034)

$1,000,000

895,966

(3,312,102)

4

350,966

$1,000,000

1,350,966

(1,961,136)

5

350,966

$1,000,000

1,350,966

(610,170)

6

350,966

$1,000,000

1,350,966

740,796

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 5 + ($610,170 / $1,350,966) = 5.45 years b.

Year 1 Sales

Year 2

Year 3

Year 4

Year 5

Year 6

$ 1,750,000 $ 1,750,000 $ 1,750,000 $ 2,400,000 $ 2,400,000 $ 2,400,000

Expenses

898,620

898,620

898,620

898,620

898,620

898,620

Depreciation

1,000,000

1,000,000

1,000,000

1,000,000

1,000,000

1,000,000

$(1,48,620) $(1,48,620) $(1,48,620)

$ 501,380

$ 501,380

$ 501,380

44,586

(150,414)

(150,414)

(150,414)

Net income

$ (104,034) $ (104,034) $ (104,034)

$ 350,966

$ 350,966

$ 350,966

Beginning BV

6,000,000

5,000,000

4,000,000

3,000,000

2,000,000

1,000,000

Less:

1,000,000

1,000,000

1,000,000

1,000,000

1,000,000

1,000,000

EBIT Taxes (30%)

44,586

44,586

Depreciation Ending BV

.

$ 5,000,000 $ 4,000,000 $ 3,000,000 $ 2,000,000 $ 1,000,000

$

SM 10-83

0

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Average after-tax income = $123,466 Average book value of equipment = $3,000,000 Accounting rate of return = =

c.

Average after-tax income Average book value $123,466 =4.1% $3,000,000

Cost of this project = $6,000,000 Required rate of return = k =16% Length of project = n = 6 years

NPV =

NCFt t =0 (1+k) t n

1   1   −   1 (1.16)3 1 − (1.16)3 1  $1,350,966    = −$6,000,000+ $895,966  0.16  (1.16)3  0.16 +          = −$6,000,000+ $2,012,241+$1,943,833 = −$2,043,927 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -6,000,000 895,966 1 1,350,966 2

Frequency (F) -3 3

Then solve by pressing NPV, enter the rate of 16% and compute NPV= -2,043,927.

Also compute IRR to get 3.145% d.

To compute the IRR, try rates lower than 16 percent.

Try IRR = 3%.

.

SM 10-84

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

NCFt (1+ IRR)t t =0 n

NPV = 0 = 

1  1    1 − (1.03)3  1 − (1.03)3 1   +   0 = −$6,000,000+$895,966   $1,350,966  0.03  0.03  (1.03)3         = −$6,000,000+$2,5 3 4,3 4+0$3,497,084 = $31,424 Try IRR = 3.1%.

NCFt (1+ IRR)t t =0

NPV = 0 −

n

1  1    1 − (1.031)3 1 − (1.031)3 1  $1,350,966    0 = −$6,000,000+$895,966    0.0 3 1 +  0.0 3 1  (1.031)3         = −$6,000,000+$2,529,475+ $3,480,225 = $9,700 The IRR of the project is approximately 3.1 percent. Using a financial calculator, we find that the IRR is 3.145 percent.

LO 2, LO 3, LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.40 Management of Skywards, Inc., an airline caterer, is purchasing refrigerated trucks at a total cost of $3.25 million. After-tax net income from this investment is expected to be $750,000 for the next five years. Annual depreciation expense will be $650,000. The cost of capital is 17 percent.

.

a.

What is the discounted payback period?

b.

Compute the ARR.

c.

What is the NPV on this investment?

d.

Calculate the IRR. SM 10-85

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: a.

Year 0 1 2 3 4 5

Cumulative CF PVCF $(3,250,000) $(3,250,000) (1,850,000) 1,196,581 (450,000) 1,022,719 950,000 874,119 2,350,000 747,110 3,750,000 638,556

CF $(3,250,000) 1,400,000 1,400,000 1,400,000 1,400,000 1,400,000

Cumulative PVCF $(3,250,000) (2,053,419) (1,030,700) (156,581) 590,529 1,229,085

Discount payback period = Years before recovery + (Remaining cost / Next year’s CF) = 3 + ($156,581 / $747,110) = 3.21 years b.

Net income Beginning BV Less: Depreciation Ending BV

Year 1 $ 750,000 3,250,000 650,000

Year 2 $ 750,000 2,600,000 650,000

Year 3 $ 750,000 1,950,000 650,000

Year 4 $ 750,000 1,300,000 650,000

$2,600,000 $1,950,000 $1,300,000 $ 650,000

Year 5 $ 750,000 650,000 650,000 $

0

Average after-tax income = $750,000 Average book value of equipment = $1,625,000

Accounting rate of return = =

c.

Average after-tax income Average book value $750,000 = 46.2% $1,625,000

Cost of this project = $3,250,000 Required rate of return = k =17% Length of project = n = 5 years

.

SM 10-86

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

 1  1−  (1.17)5  NCF    t = −$3,250,000+ $1,400,000 NPV =  t=0 (1+ )  0.17  k t     = −$3,250,000+ $4,479,085 =$1,229,085 n

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -3,250,000 -1 1,400,000 5 Then solve by pressing NPV, enter the rate of 17% and compute NPV= 1,229,085. d.

To compute the IRR, try rates much higher than 17 percent.

Try IRR = 30%.

NPV = 0 =

NCFt (1+ IRR)t =0 t n

1   1 − (1.30)5  0 = −$3,250,000+$1,400,000    0.30      = −$3,250,000+$3,409,798 = $159,798 Try IRR = 32.5%.

NPV = 0 =

NCFt (1+ IRR)t =0 t n

1   1 − (1.325)5  0 = −$3,250,000+$1,400,000    0.3 2 5      = −$3,250,000+$3,252,904 = $2,904 0 The IRR of the project is approximately 32.5 percent. .

SM 10-87

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -3,250,000 -1 1,400,000 5 Then compute IRR to get 32.548%.

LO 2, LO 3, LO 4, LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.41 Trident Corp. management is evaluating two independent projects. The costs and expected cash flows are given in the following table. The cost of capital is 10 percent.

Year

A

B

0

$(312,500)

$(395,000)

1

121,450

153,552

2

121,450

158,711

3

121,450

166,220

4

121,450

132,000

5

121,450

122,000

a.

Calculate the projects’ NPV.

b.

Calculate the projects’ IRR.

c.

Which project should be chosen based on NPV? Based on IRR? Is there a conflict?

d.

If you are the decision maker for the firm, which project or projects will be accepted? Explain your reasoning.

Solution:

.

SM 10-88

Fundamentals of Corporate Finance, 4th edition

a.

Solutions Manual

Project A: Cost of this project = $312,500 Annual cash flows = $121,450 Required rate of return = k = 10% Length of project = n = 5 years

 1  1− n (1.10)5 NCFt    = = + − NPV  312,500 $121,450 )  0.10  t=0(1+ k t     = −$312,500+ 460,391 = $147,891 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project A Cash Flow (C) Frequency (F) 0 -312,500 -1 121,450 5 Then solve by pressing NPV, enter the rate of 10% and compute NPV=147,891.

Project B: Cost of this project = $395,000 Required rate of return = k = 10% Length of project = n = 5 years NCFt t t=0 (1+ k ) n

NPV = 

$153,552 $158,711 $166,220 $132,000 $122,000 + + + + = −$395,000+ (1.10)1 (1.10)2 (1.10)3 (1.10)4 (1.10)5 = −395,000 + $139,593 + $131,166 + $124,884 + 90,158 + 75,752 = $166,553

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project B Cash Flow (C) Frequency (F) .

SM 10-89

Fundamentals of Corporate Finance, 4th edition

0 1 2 3 4 5

-395,000 153,552 158,711 166,220 132,000 122,000

Solutions Manual

-1 1 1 1 1

Then solve by pressing NPV, enter the rate of 10% and compute NPV= 166,553 b.

Project A: Since NPV > 0, to compute the IRR, try rates higher than 10 percent.

Try IRR = 27%.

NPV = 0 =

NCFt (1+ IR R) t =0 t n

 1  1−(1.27)5  0 = −312,500+ $121,450   0.27      = −$312,500+ 313,666  $1,166 Try IRR = 27.2%,

NPV = 0 =

NCFt (1+ IRR)t =0 t n

  1 1 − (1.272)5  0 = −312,500+$121,450    0.2 7 2      = −$312,500+312,418 = −$82 0 The IRR of Project A is approximately 27.2 percent. Using a financial calculator, we find that the IRR is 27.187 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project A Cash Flow (C) Frequency (F) .

SM 10-90

Fundamentals of Corporate Finance, 4th edition

0 1

-312,500 121,450

Solutions Manual

-5

Then solve by pressing IRR to get 27.187% Project B: Since NPV > 0, to compute the IRR, try rates higher than 10 percent.

Try IRR = 26%. n NCF t NPV = 0=  t =0(1+ IRR)t $153,552 $158,711 $166,220 $132,000 $122,000 0 = −$395,000+ + + + + (1.26)1 (1.26)2 (1.26)3 (1.26)4 (1.26)5 = −$395,000+ $121,867+$99,969+$83,094+$52,371+$38,416

 $717

Try IRR = 26.1%. n NCF t NPV = 0=  t =0(1+ IRR)t

$153,552 $158,711 $166,220 $132,000 $122,000 + + + + (1.261)1 (1.261)2 (1.261)3 (1.261)4 (1.261)5 = −$395,000+ $121,770+$99,811+$82,897+$52,205+$38,263

0 = −$395,000+ = −$54 0

The IRR of Project B is approximately 26.1 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project B Cash Flow (C) 0 -395,000 1 153,552 2 158,711 3 166,220 4 132,000 5 122,000

Frequency (F) -1 1 1 1 1

Then solve by pressing IRR to get 26.093%. .

SM 10-91

Fundamentals of Corporate Finance, 4th edition

c.

Solutions Manual

Since both projects have positive NPVs and they are independent projects, both should be accepted under the NPV decision criteria. Under the IRR decision criteria, since both projects have IRRs greater than the cost of capital, both will be accepted. Thus, there is no conflict between the NPV and IRR decisions.

d.

Based on NPV, both projects will be accepted.

LO 2, LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.42 Management of Tyler, Inc., is considering switching to a new production technology. The cost of the required equipment will be $4 million. The discount rate is 12 percent. The cash flows that management expects the new technology to generate are as follows.

Years

CF

1-2

0

3–5

$845,000

6–9

$1,450,000

a.

Compute the payback and discounted payback periods for the project.

b.

What is the NPV for the project? Should the firm go ahead with the project?

c.

What is the IRR, and what would be the decision based on the IRR?

Solution: a.

Year

.

Cash Flows

PVCF

Cumulative

Cumulative

CF

PVCF

SM 10-92

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

0

$(4,000,000)

$(4,000,000)

$(4,000,000)

$(4,000,000)

1

--

--

(4,000,000)

(4,000,000)

2

--

--

(4,000,000)

(4,000,000)

3

845,000

601,454

(3,155,000)

(3,398,546)

4

845,000

537,013

(2,310,000)

(2,861,533)

5

845,000

479,476

(1,465,000)

(2,382,057)

6

1,450,000

734,615

(15,000)

(1,647,442)

7

1,450,000

655,906

1,435,000

(991,536)

8

1,450,000

585,631

2,885,000

(405,905)

9

1,450,000

522,885

4,335,000

116,979

Remaining cost to recover Payback period= Years before cost recovery+ Cash flow during the year = 6 + $15, 000 $1, 450, 000 = 6.01 years Discounted Payback period= Years before cost recovery+ =8+

Remaining cost to recover Cash flow during the year

$405, 905

$522, 885 = 8.8 years

b.

Cost of this project = $4,000,000 Required rate of return = k = 12% Length of project = n = 9 years

 1  1−  (1.12)3 NCFt  1 = −$4,0 0 0,0 0+00 + 0 +$845,000   NPV =  (1+k)t  0.12  (1.12)2 t =0      1  1−(1.12)4  1  + $1,450,000  (1.12)5  0.12     = −$4,0 0 0,0 0+ 00 + 0 + $1,617,943+$2,499,037 = $116,980 n

.

SM 10-93

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Since NPV > 0, the project should be accepted.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -4,000,000 1 0 3 845,000 4 1,450,000

Frequency (F) -2 3 4

Compute the NPV using a discount rate of 12% to get $116,980. Then solve by pressing IRR to get 12.539% c.

Given a positive NPV, to compute the IRR, one should try rates higher than 12 percent.

Try IRR = 12.5%.

1   − 1 (1.125)3   n NCFt 1    + 0 + − 0 = = + NPV  $4,0 0 0,0 0 0 $845,000 (1+k)t  0.1 2 5  (1.125)2 t =0      1  1−(1.125)4  1  + $1,450,000  (1.125)5  0.125     = −$4,0 0 0,0 0+ 00 + 0 + $1,589,915+$2,418,479 = $8,394 The IRR is approximately 12.5 percent. Using a financial calculator, we find that the IRR is 12.539 percent. Based on the IRR exceeding the cost of capital of 12 percent, the project should be accepted.

LO 2, LO 3, LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective .

SM 10-94

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.43 You are analyzing two proposed capital investments with the following cash flows: Year 0

Project X $(20,000)

Project Y $(20,000)

1

13,000

7,000

2

6,000

7,000

3

6,000

7,000

4

2,000

7,000

The cost of capital for both projects is 10 percent. Calculate the profitability index (PI) for each project. Which project, or projects, should be accepted if you have unlimited funds to invest? Which project should be accepted if they are mutually exclusive?

Solution: The PI calculations are as follows: The NPV is needed first:

$13,000 $6,000 $6,000 $2,000 + + + =$2,650.78 (1.1)1 (1.1)2 (1.1)3 (1.1)4 $7,000 $7,000 $7,000 $7,000 + + + =$2,189.06 NPVy = −$2 0,0 0 +0 (1.1)1 (1.1)2 (1.1)3 (1.1)4 NPVx = −$2 0,0 0 +0

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project X Cash Flow (C) 0 -20,000 1 13,000 2 6,000 3 2,000 .

Frequency (F) -1 2 1 SM 10-95

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Then solve by pressing NPV, enter the rate 10% and compute NPV=2,650.78.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Project Y Cash Flow (C) Frequency (F) 0 -20,000 -1 7,000 4 Then solve by pressing NPV, enter the rate of 10% and compute NPV=2,189.06

NPV + Initial Investment $22, 650.78 = $20, 000 = 1.1325 Initial Investment $22,189.06 NPV+Initial Investment $20, 000 = = 1.1095 PI y = Initial Investment PIx =

Both methods rank Project X over Project Y. Therefore, both should be accepted if they are independent and sufficient resources are available. If the projects are mutually exclusive, we should choose the project with the higher PI at r = 10%, which in this case is Project X. LO 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

CFA Problems 10.44Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent.

Year .

SM 10-96

Fundamentals of Corporate Finance, 4th edition

C ASH FLOW

Solutions Manual

0

1

2

3

4

5

–50,000

15,000

15,000

20,000

10,000

5,000

NPV

IRR

a.

$1,905

10.9%

b.

$1,905

26.0%

c.

$3,379

10.9%

d.

$3,379

26.0%

SOLUTION: c is correct.

NPV = −$50, 000+

$15, 000 $15, 000 $20, 000 $10, 000 $5, 000 + + + + (1.08)1 (1.08)2 (1.08)3 (1.08)4 (1.08)5

NPV = –$50,000 + $13,888.89 + $12,860.08 + $15,876.64 + $7,350.30 + $3,402.92 NPV = –$50,000 + $53,378.83 = $3,378.83 Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -50,000 -1 15,000 2 2 20,000 1 3 10,000 1 4 5,000 1 Then solve by pressing NPV, enter the rate of 8% and compute NPV=3,378.83

Then find IRR with the calculator to get 10.879%.

Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective .

SM 10-97

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.45 Given the following cash flows for a capital project, calculate its payback period and discounted payback period. The required rate of return is 8 percent.

Year CASH FLOW

0

1

2

3

4

5

–50,000

15,000

15,000

20,000

10,000

5,000

2

3

4

5

The discounted payback period is a.

0.16 year longer than the payback period.

b.

0.80 year longer than the payback period.

c.

1.01 years longer than the payback period.

d.

1.85 years longer than the payback period.

SOLUTION: c is correct.

YEAR

0

1

CASH FLOW

–$50,000 $15,000

$15,000

$20,000

$10,000

$5,000

–50,000

–35,000

–20,000

0

10,000

15,000

–50,000

13,888.89

12,860.08

15,876.64

7,350.30

3,402.92

–

–

– –$24.09

$3,378.83

CUMULATIVE CASH FLOW

DISCOUNTED CASH FLOW

CUMULATIVEDCF

–$50,000 $36,111.11 $23,251.03 $7,374.38

As the table shows, the cumulative cash flow offsets the initial investment in exactly three years. The payback period is 3.00 years. The discounted payback period is between four and five years. The discounted payback period is 4 years plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The discounted payback period is 4.01 – 3.00 = 1.01 years longer than the payback .

SM 10-98

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

period.

LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.46An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2, and $120 in Year 3. The required rate of return is 20 percent. The net present value is closest to a.

$42.22

b.

$58.33

c.

$68.52

d.

$98.95

SOLUTION: b is correct.

80 120 40 NCFt = −$100+ + + = $58.33 (1+k)t 1.20 1.2 0 2 1.203 t =0 n

NPV = 

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) -100 0 40 1 80 2 120 3

Frequency (F) -1 1 1

Then solve by pressing NPV, enter the rate of 20% and compute NPV= 58.33 LO 2 Bloomcode: Application AASCB: Analytic .

SM 10-99

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.47 An investment of $150,000 is expected to generate an after-tax cash flow of $100,000 in one year and another $120,000 in two years. The cost of capital is 10 percent. What is the internal rate of return? a.

28.19 percent

b.

28.39 percent

c.

28.59 percent

d.

28.79 percent

SOLUTION: d is correct. The IRR can be found using a financial calculator or with trial and error. Using trial and error, the total PV is equal to zero if the discount rate is 28.79 percent.

C ASH

PRESENT ALUE

F LOW

V 28.19%

28.39%

28.59%

28.79%

012

–150,000

–150,000

–150,000

–150,000

–150,000

Total

100,000

78,009

77,888

77,767

77,646

120,000

73,025

72,798

72,572

72,346 –

1,034

686

338

8

YEAR

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) -150,000 -0 100,000 1 1 120,000 1 2

.

SM 10-100

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Then solve for a more precise IRR which is 28.7855 percent that has a total PV closer to zero.

LO 5 Bloomcode: Application AASCB: AnalyticIMA: Investment Decisions AICPA: Industry/Sector Perspective

10.48 An investment requires an outlay of $100 and produces after-tax cash flows of $40 annually for four years. A project enhancement increases the required outlay by $15 and the annual after-tax cash flows by $5. How will the enhancement affect the project’s NPV profile? The vertical intercept of the NPV profile of the project shifts: a.

up and the horizontal intercept shifts left.

b.

up and the horizontal intercept shifts right.

c.

down and the horizontal intercept shifts left.

d.

down and the horizontal intercept shifts right.

SOLUTION: a is correct. The vertical intercept changes from $60 to $65, and the horizontal intercept changes from 21.86 percent to 20.68 percent.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Sample Test Problems 10.1 Testco Corporation is considering adding a new product line. The cost of the factory and equipment to produce this product is $1,780,000. Company management expects net cash flows from the sale of this product to be $450,000 in each of the next eight years. If Testco uses a discount rate of 12 percent for projects like this, what is the net present value of this project? What is the internal rate of return?

Solution: .

SM 10-101

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Investment = $1,780,000 Annual net cash flow = NCF = $450,000 Discount rate = k = 12% Length of project = n = 8 years

1   1 − (1.12)8  NCFt   = −$1, 780, 000 + $450, 000 NPV=0(1+ k)t 0.12   t=   = −$1,780,000+ $2,235,438  NPV=$455,437.90 n

Determine the IRR using trial and error: Since NPV > 0, try IRR > k

.

Try IRR = 20%

1   1 − (1.20)8  NCF  NPV= 0 =  t = −$1,500,000 + $450, 000 t=0 (1+ IRR)t  0.20    = −$1, 780, 000 + $1, 726, 722   −$53, 278 n

Try IRR = 19%

1 1− (1.19)8 NCF t = −$1,780,000 +$450, 000  NPV = 0=  0.19 t=0(1+ IRR)t = −$1, 780, 000 + $1, 779, 465 n

= −$535 0

The IRR is approximately 19 percent.

Financial Calculator Solution : Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -1,780,000 -1 450,000 8 We find that the IRR is 18.99 percent.

LO 2 & 5) .

SM 10-102

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.2 Flowers Unlimited is considering purchasing an additional delivery truck which will have a seven year useful life. The new truck will cost $42,000. Cost savings with this truck are expected to be $12,800 for the first two years, $8,900 for the following two years, and $5,000 for the last 3 years of the truck’s useful life. What is the payback period for this project?

What is the discounted payback period for this project with a discount rate of 10 percent?

(LO 3 ) Solution: Discount rate = k = 10% Year 0 1 2 3 4 5 6 7

NCF $(42,000) 12,800 12,800 8,900 8,900 5,000 5,000 5,000

Cumulative NCF $(42,000) (29,200) (16,400) (7,500) 1,400 6,400 11,400 16,400

PV(NCF) $(42,000) 11,636 10,579 6,687 6,079 3,105 2,822 2,566

Cumulative PV(NCF) $(42,000) (30,364) (19,785) (13,098) (7,019) (3,914) (1,092) 1,474

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($7,500 / $8,900) = 3.84 years Discounted PB = Years before cost recovery + (Remaining cost to recover/ PV Cash flow during the year) = 6 + ($1,092 / $2,566) = 6.43 years Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.3 What is the average accounting rate of return (ARR) on a piece of equipment that will cost $1.2 million and that will result in pretax cost savings of $380,000 for the first three years and then $280,000 for the following three years? Assume that the machinery will be depreciated to a salvage value of 0 over 6 years using the straight-line method and the company’s tax rate is 32 percent. If the acceptance decision is based on the project exceeding an ARR of 20 percent, should this machinery be purchased? (LO 4) .

SM 10-103

Fundamentals of Corporate Finance, 4th edition

Solution:

Solutions Manual

Cost savings Depreciation EBIT Taxes (32%) Net income

Year 1 $ 380,000 200,000 $ 180,000 57,600 $ 122,400

Year 2 $ 380,000 200,000 $ 180,000 57,600 $ 122,400

Year 3 $ 380,000 200,000 $ 180,000 57,600 $ 122,400

Year 4 $ 280,000 200,000 $ 80,000 25,600 $ 54,400

Year 5 $ 280,000 200,000 $ 80,000 25,600 $ 54,400

Year 6 $ 280,000 200,000 $ 80,000 25,600 $ 54,400

Beg. book value Less: Depreciation End. book value

1,200,000 200,000 $ 1,000,000

5,000,000 200,000 $ 800,000

4,000,000 200,000 $ 600,000

3,000,000 200,000 $ 400,000

2,000,000 200,000 $ 200,000

1,000,000 200,000 0 $

Average after-tax income (years 1 through 9) = $88,400 Average book value of equipment (years 0 through 6) = $600,000 Accounting rate of return = =

Average after-tax income Average book value $88, 400 = 14.7% $600, 000

Since the project’s ARR is below the acceptance rate of 20 percent, the machinery should not be purchased.

Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.4 What do we know about that project’s IRR if we know that it has a positive NPV? (LO 2 & 5) Solution: If a project has a positive NPV, the IRR of that project is greater than the required rate of return. Since the IRR is the discount rate that makes the NPV equal zero, a positive NPV results from the project’s IRR being greater than the required rate of return.

Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective .

SM 10-104

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

10.5 West Street Automotive is considering adding state safety inspections to their service offerings. The equipment necessary to perform these inspections will cost $557,000 and will generate cash flows of $195,000 over each of the next five years. If the cost of capital is 14 percent, what is the MIRR on this project? (LO 5) Solution: Investment (cost) = $557,000 Annual net cash flow = NCFt = $195,000 Length of project = n = 5 years Cost of capital = k = 14% k)n 2− + +kn1 TV= NCF 1(1 ) −+ NCF (1+ 2

+ NCF n(1+ k)n n−

+ $195, 000 1.14 + $195, 000 = $195, 000  (1.14)4 + $195, 000  (1.14)3 + $195, 000  (1.14)2 = $329, 347 + $288, 901+ $253, 422 + $222, 300 + $195, 000 = $1, 288, 970 Financial Calculator Solution :

5 N

14 i

0 PV

195,000 PMT

FV 1,288,970

Solve for the MIRR:

TV (1 + MIRR ) n $1, 288, 970 $557, 000= (1 + MIRR )5 $1, 288, 970 (1+ MIRR) 5 = =2.3141 $557, 000 PV Cost =

(1 + MIRR ) = (2.3141)1/5 =1.1827 MIRR = 0.1827 =18.3% Financial Calculator Solution : 5 N

i 18.27

-557,000 PV

0 PMT

1,288,970 FV

Bloomcode: Application .

SM 10-105

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.6 You are chairperson of the investment committee at your firm. Five projects have been submitted to your committee for approval this month. The investment required and the project profitability index for each of these projects are presented in the following table: LO( 6) Pro je c t A B C D E

Investment $20,000 50,000 70,000 10,000 80,000

PI 2.500 2.000 1.750 1.000 0.800

If you have $500,000 available for investments, which of these projects would you approve? Assume that you do not have to worry about having enough resources for future investments when making this decision.

Solution: Definitely accept projects A, B, and C. They all have a positive NPV as can be seen by PI greater than 1. Project D just returns the opportunity cost of capital, so you would be indifferent with regards to accepting this project. Do not accept project E; it has a negative NPV. Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 10-106

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Chapter 11 Cash Flows and Capital Budgeting

Before You Go On Questions and Answers

Section 11.1 1. Why do we care about incremental cash flows at the firm level when we evaluate a project?

We care about incremental cash flows at the firm level because they reflect the impact of the project on a firm’s future investment outlays and cash flows from operations. This is what the stockholders care about. The NPV of a project is the difference between the present value of the expected cash flows from the firm with the project and the present value of the expected cash flows from the firm without the project. Our NPV estimate will be incorrect if we do not account for all of the incremental cash flows at the firm level.

2. Why is D&A first subtracted and then added back in FCF calculations?

By subtracting D&A, calculating the tax obligation, and then adding back D&A, we are accounting for the fact that D&A is a noncash charge that reduces the firm’s tax obligation by the

.

SM 11-1

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

product of D&A and the tax rate (D&A x t). If we did not do this, we would overstate the tax obligation and understate FCF.

3. What types of investments should be included in FCF calculations?

All investments directly associated with the project should be included in FCF calculations. These can include both investments in tangible and intangible assets. They can also include investments in additions to working capital, such as for the credit a firm extends to its customers and inventories.

Section 11.2 1. What are the five general rules for calculating FCF?

(1) Include cash flows and only cash flows in your calculations.

(2) Include the impact of the project on cash flows from other product lines.

(3) Include all opportunity costs.

(4) Forget sunk costs.

(5) Include only after-tax cash flows in the cash flow calculations.

2. What is the difference between nominal and real dollars? Why is it important not to mix them in an NPV analysis?

.

SM 11-2

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

When most people talk about dollar amounts, they are referring to nominal dollars. Nominal dollars do not take into account changes in purchasing power. Real dollars are dollar amounts that are adjusted for changes in purchasing power (or inflation). For example, 100 real dollars have the same purchasing power whether they are received today or at some future date. It is important not to mix nominal and real dollars in an NPV analysis because the discount rate is either a nominal rate, which is used to discount nominal dollars, or a real rate, which is used to discount real dollars. Since the discount rate must be either a nominal rate or a real rate, if real and nominal dollars are mixed in an NPV analysis, the NPV will be calculated incorrectly.

3. What is a progressive tax system? What is the difference between a firm’s marginal and average tax rates?

A progressive tax system is one in which the marginal tax rate at low levels of income is lower than the marginal tax rate at high levels of income. A firm’s marginal tax rate is the rate that it pays on the last dollar earned while the average tax rate is the average rate paid on the firm’s total earnings (tax paid divided by taxable income).

4. How can FCF in the terminal year of a project’s life differ from FCF in the other years?

FCF in the terminal year can differ from FCF in other years in several ways. The terminal year cash flows can include cash flows from the asset sales, including the actual proceeds from the sales themselves and taxes due or received if there is a gain or loss on the sale. Terminal year cash flows can also include cash flows associated with recovery of working capital. .

SM 11-3

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

5. Why is it important to understand that cash flow forecasts in an NPV analysis are expected values?

It is important to recognize that we are forecasting expected cash flows in an NPV analysis because uncertainties regarding future cash flows that are unique to the project should be reflected in the cash flow forecasts.

Section 11.3 1. What is the difference between variable and fixed costs, and what are examples of each?

Variable costs vary directly with unit sales. Fixed costs do not vary with unit sales. For an example of each, see the video game player scenario on page 379. Variable costs are those associated with purchasing the components for the player, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses.

2. How are working capital items forecast? Why are accounts receivable typically forecast as a percentage of revenue and accounts payable and inventories as percentages of the cost of good sold?

Working capital items are forecast using 1) cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4) accounts payable.

Accounts receivable are forecast as a percentage of revenue as this represents the amount of money that must be set aside to finance purchases by customers. Inventories are forecast as a percentage of the cost of goods sold because the COGS represent a measure of the amount of .

SM 11-4

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

money invested in inventories. Accounts payable are forecast this way because the COGS is a measure of the amount of money actually owed to suppliers.

Section 11.4 1. When can we not simply compare the NPVs of two mutually exclusive projects?

If we expect to replace at least one of the projects at the end of its life, we cannot simply compare the NPVs. Doing so would ignore the subsequent investment(s). You can only directly compare the NPVs of mutually exclusive projects under one condition—that is, if you expect to terminate the project that is chosen (e.g., sell the lawn mower) on or before the end of the life of the shorterlived project.

2. When choosing between mutually exclusive projects of unequal lives, how can we ensure that the best decision is made?

We can effectively make the lives of mutually exclusive projects equal by repeating one or both investments and comparing the Net Present Values of both projects, or by creating the Equivalent Annual Cost (EAC) of both projects and choosing the less expensive one.

3. How do we decide when to harvest an asset?

.

SM 11-5

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

We choose the harvest date that maximizes the NPV of the asset. To identify this date, we compare the NPVs expected from harvesting the asset for each of the feasible harvest dates. The best date to harvest the asset is the date that produces the largest NPV, once the NPVs for all of the alternative harvest dates have been discounted to the same point in time.

4. Under what circumstance would you replace an old machine that is still operating with a new one?

You should replace the old machine when the EAC of the new machine is lower than the EAC of the old machine (if revenues are the same for both machines) or when the annualized cash inflow from the replacement is greater.

.

SM 11-6

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Self-Study Problems

11.1

Explain why the announcement of a new investment is usually accompanied by a change in the firm’s stock price.

Solution: A firm’s investments cause changes in its future after-tax cash flows and stockholders are the residual claimants (owners) of those cash flows. Therefore, the stock price should increase when stockholders expect an investment to have a positive NPV, and decrease when it is expected to have a negative NPV.

11.2

In calculating the NPV of a project, should we use all of the after-tax cash flows associated with the project, or incremental after-tax cash flows from the project? Why?

Solution: We should use incremental cash flows of the project. Incremental cash flows reflect the amount by which the firm’s total cash flows will change if the project is adopted. In other words, incremental cash flows represent the net difference in cash revenues, costs, and investment outlays (in net working capital and capital expenditures) at the firm level with and without the project, which is precisely what the stockholders care about.

.

SM 11-7

Fundamentals of Corporate Finance, 4th d edition

11.3

Solutions Manual

You are considering opening another restaurant in the TexasBurgers chain. The new restaurant will have annual revenue of $300,000 and operating expenses of $150,000. The annual depreciation and amortization for the assets used in the restaurant will equal $50,000.

An annual capital expenditure of $10,000 will be required to offset wear-and-tear on the assets used in the restaurant, but no additions to working capital will be required. The marginal tax rate will be 40 percent. Calculate the incremental annual free cash flow for the project.

Solution: The incremental annual free cash flow is calculated as:

FCF = ($300, 000− $150, 000− $50, 000) (1 − 0.4)+ $50, 000)− $10, 000 = $100, 000

11.4 Sunglass Heaven, Inc., is launching a new store in a shopping mall in Houston. The annual revenue of the store depends on the weather conditions in the summer in Houston. The annual revenue will be $240,000 in a sizzling summer, with probability of 0.3; $80,000 in a cool summer, with probability of 0.2; and $150,000 in a normal summer, with probability of 0.5.

What is the expected annual revenue of the store?

Solution: The expected annual revenue is: (0.3 × $240,000) + (0.2 × $80,000) + (0.5 × $150,000) = $163,000

.

SM 11-8

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

11.5 Sprigg Lane Manufacturing, Inc., needs to purchase a new central air-conditioning system for a plant. There are two choices. The first system costs $50,000 and is expected to last 10 years, and the second system costs $72,000 and is expected to last 15 years. Assume that the opportunity cost of capital is 10 percent. Which air-conditioning system should Sprigg Lane purchase?

Solution: The equivalent annual cost for each system is:

(1.1)10 = = $8,137.27 EAC 1 (0.1)($50,000) (1.1)10 − 1 (1.1)15 = $9,466.11 EAC 2 = (0.1)($72,000) (1.1)15 − 1 Therefore Sprigg Lane should purchase the first one.

Discussion Questions 11.1

Do you agree or disagree with the following statement given the discussion in this chapter? We can calculate future cash flows precisely and obtain an exact value for the NPV of an investment.

The statement is not true. The nature of the real business world includes those risks which cannot be forecasted or foreseen such as changes in a nation’s economic policy, fluctuation in inflation and interest rates and the like. Given this, it is almost certain that the cash flows generated by a project will differ from the forecasts used to decide whether to proceed with .

SM 11-9

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

the project. However, techniques discussed in this chapter provide an important and useful framework that helps minimize errors and ensures that forecasts are internally consistent.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2

What are the differences between cash flows used in capital budgeting calculations and past accounting earnings?

Cash flows used in capital budgeting calculations are forward looking; they are incremental after-tax cash flows based on forecasts. Accounting earnings are backward looking; they represent a record of past performance and may not accurately reflect cash flows.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.3 Suppose that FRA Corporation already has divisions in both Dallas and Houston. FRA is now considering setting up a third division in Austin. This expansion will require that

.

SM 11-10

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

one senior manager from Dallas and one from Houston relocate to Austin. Ignore relocation expenses. Is their annual compensation relevant to the decision to expand?

The annual compensations of existing senior managers are not incremental to the new investment and therefore are not relevant for capital budgeting analysis. This is consistent with our Rule 1 for incremental cash flow calculations: Include cash flows and only cash flows; do not include allocated costs unless they reflect cash flows.

LO: 1, 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4 MusicHeaven, Inc., is a producer of media players which currently have either 20 gigabytes or 30 gigabytes of storage. Now the company is considering launching a new production line making mini media players with 5 gigabytes of storage. Analysts forecast that MusicHeaven will be able to sell 1 million such mini media players if the investment is made. In making the investment decision, discuss what the company should consider other than the sales of the mini media players.

The company’s launch of the new mini media players may reduce its current sales of media players of bigger storage. This impact has to be considered. This is consistent with our Rule 2

.

SM 11-11

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

for incremental cash flow calculations: Include the impact of the project on cash flows from other product lines.

LO: 1, 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5 QualityLiving Trust is a real estate investment company that builds and remodels apartment buildings in northern California. It is currently considering remodeling a few idle buildings that it owns in San Jose into luxury apartment buildings. The company bought those buildings eight months ago. How should the market value of the buildings be treated in evaluating this project?

Although the buildings are not currently in use, the company can sell them at their market value rather than remodel them into apartments. Therefore, the market value of the buildings is the opportunity cost of the project and should be considered as a cash outflow in the investment decision. This is consistent with our Rule 3 for incremental cash flow calculations: Include all opportunity costs.

LO: 1, 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective .

SM 11-12

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

11.6 High-End Fashions, Inc., bought a production line of ankle-length skirts last year at a cost of $500,000. This year, however, miniskirts are in and ankle-length skirts are completely out of fashion. High-End has the option to rebuild the production line and use it to produce miniskirts with an annual operating cost of $300,000 and expected revenue of $700,000. How should the company treat the $500,000 cost of the old production line in evaluating the rebuilding plan?

The cost of the old production line occurred in the past. It cannot be changed whether or not the company rebuilds it into the miniskirt production line. Therefore, High-End should not consider the cost of $500,000. This is consistent with our Rule 4 for incremental cash flow calculations: Forget sunk costs.

LO: 1, 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.7

How is the MACRS depreciation method under IRS rules different from the straightline depreciation allowed under GAAP rules? What is the implication on incremental after-tax free cash flows from firms’ investments?

.

SM 11-13

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

GAAP allows the straight-line depreciation method. In contrast, an “accelerated” method of depreciation, Modified Accelerated Cost Recovery System (MACRS), has been used for U.S. federal tax calculations. The advantage of MACRS, relative to straight-line depreciation, is that it enables a firm to deduct depreciation changes sooner, thereby realizing the tax saving sooner and increasing the present value of the tax savings.

LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.8

Explain the difference between marginal and average tax rates, and identify which of these rates is used in capital budgeting and why?

The marginal tax rate is the rate paid on the next dollar earned. The average tax rate is the dollar value of total taxes paid divided by total income. The marginal tax rate is the appropriate rate to use in capital budgeting analysis because this is the tax rate that will be paid on the incremental income earned by the project.

LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 11-14

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

11.9 Under what circumstances will the sale of an asset result in a taxable gain? How do you estimate the taxes or tax benefits associated with the sale of an asset?

The sale of an asset results in a taxable gain when the selling price of the asset exceeds its book value.

Tax on the sale of an asset = (Selling price of asset – Book value of asset) × Tax rate (t) LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.10 When two mutually exclusive projects have different lives, how can an analyst determine which is better? What is the underlying assumption in this method?

When we choose from mutually exclusive projects with different lives, instead of electing the project with higher NPV or lower net present value of costs, we should choose the project with higher Equivalent Annual Revenue or lower Equivalent Annual Cost. The underlying assumption is that we will continue to operate with the same equivalent annual revenue or equivalent annual cost in the future.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective .

SM 11-15

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

11.11 What is the opportunity cost of using an existing asset? Give an example of the opportunity cost of using the excess capacity of a machine.

The opportunity cost of using an existing asset in a project is the present value of the change in the firm’s cash flows that is attributed to the fact that this asset is being used in the project.

For example, by using the excess capacity of a machine, you may accelerate the wear-andtear of the machine and hence will need to replace it sooner. The present value of the added annualized costs is the opportunity cost of using the excess capacity.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.12 You are providing financial advice to a shrimp farmer who will be harvesting his last crop of farm-raised shrimp. His current shrimp crop is very young and will, therefore, grow and become more valuable as their weight increases. Describe how you would determine the appropriate time to harvest the entire crop of shrimp.

Assuming that the price of shrimp is directly (and linearly) related to the weight of the shrimp, then the optimal point in time to harvest the shrimp would be where the rate of weight increase is no longer greater than the opportunity cost of capital for the shrimp farmer. .

SM 11-16

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Alternatively, the appropriate time is when the value increase of the shrimp is no longer greater than the opportunity cost of capital.

LO: 5 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Questions and Problems

BASIC 11.1Calculating project cash flows: Why do we use forecasted incremental after-tax free cash flows instead of forecasted accounting earnings in estimating the NPV of a project?

Solution: Accounting earnings can differ from cash flows for a number of reasons, making accounting earnings an unreliable measure of the costs and benefits of a project. For example, ease of manipulating earnings components such as accounts receivable and depreciation may result in distorted estimation of capital budgeting; using forecasted cash flows eliminates such .

SM 11-17

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

possibilities. In addition, because there is time value of money, cash flows better reflect the actual available funds to be distributed to shareholders at each point in time.

LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2 The FCF calculation: How do we calculate incremental after-tax free cash flows from forecasted earnings of a project? What are the common adjustment items?

Solution: We need to adjust for the depreciation and amortization tax shield, capital expenditures, and changes in working capital (including receivables and payables).

LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.3 The FCF calculation: How do we adjust for depreciation when we calculate incremental aftertax free cash flow from EBITDA? What is the intuition for the adjustment?

Solution:

.

SM 11-18

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

There are two ways to adjust for depreciation: (1) subtract depreciation from EBITDA, multiply it by (1 – tax rate), and then add depreciation back; (2) add the tax shield from depreciation (depreciation multiplied by tax rate) to revenue. These two methods yield the same results. The intuition is that although depreciation itself is not a cash inflow or outflow, an increase in depreciation will result in a decrease in taxable income. This saving on tax is treated as a cash inflow in calculating incremental after-tax free cash flows.

LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4 Nominal versus real cash flows: What is the difference between nominal and real cash flows? Which rate of return should we use to discount each type of cash flow?

Solution: Nominal cash flows are cash flows stated as we usually think of them. They represent the actual cash flow that we expect a project to generate in the future, without any adjustment, for changes in purchasing power over time. Real cash flows are cash flows stated so that their purchasing power remains constant. We should use nominal rate of return to discount future nominal cash flows and real rate of return to discount future real cash flows. By doing this, we will get meaningful present values of cash flows and purchasing power.

LO 2 Bloomcode: Analysis .

SM 11-19

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5 Taxes and depreciation: What is the difference between average tax rate and the marginal tax rate? Which one should we use in calculating incremental after-tax cash flows?

Solution: In a progressive tax system, the marginal tax rate is different from the average tax rate. The average tax rate is the total amount of tax divided by total amount of money earned, while the marginal tax rate is the rate paid on the last dollar earned. Since a firm already pays taxes, the appropriate tax rate used for the firm’s new project is the tax rate that the firm will pay on any additional profits that are earned because the project is adopted. Therefore, we use the marginal tax rate in calculating incremental after-tax cash flows.

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.6 Computing terminal-year FCF: Healthy Potions, Inc., a pharmaceutical company, bought a machine at a cost of $2 million five years ago that produces pain-reliever medicine. The machine has been depreciated over the past five years, and the current book value is $800,000. The company decides to sell the machine now at its market price of $1 million. The .

SM 11-20

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

marginal tax rate is 30 percent. What are the relevant cash flows? How do they change if the market price of the machine is $600,000 instead?

Solution: The relevant cash flows include the sale price of the machine, as well as the tax on the capital gain: $1,000,000 – 0.3 × ($1,000,000 – $800,000) = $940,000 When the market price of the machine is changed to $600,000, the relevant cash flows include the sale price and tax saving on capital loss: $600,000 + 0.3 × ($800,000 – $600,000) = $660,000 LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.7 Cash flows from operations: What are variable costs and fixed costs? What are some examples of each? How are these costs estimated in forecasting operating expenses?

Solution: Variable costs vary directly with unit sales, while fixed costs do not. Variable costs are those associated with purchasing the components for the product, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses. .

SM 11-21

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

11.8 Cash flows from operations: When forecasting operating expenses, explain the difference between a fixed cost and a variable cost.

Solution: While forecasting operating expenses, fixed costs are based on the cost of manufacturing space, administrative expenses required for administration of the project, and so forth. While variable costs vary directly with the number of units sold, they can be forecasted by multiplying the variable cost per unit (that has been estimated to be produced) by the number of units expected to be sold each year.

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 11.9 Investment cash flows: Zippy Corporation just purchased computing equipment for $20,000.

The equipment will be depreciated using a five-year MACRS depreciation schedule. If the equipment is sold at the end of its fourth year for $12,000, what are the after-tax proceeds from the sale, assuming the marginal tax rate is 35 percent??

Solution: The 5-year depreciation schedule allows us to depreciate 20 percent of the value of the equipment in year 1, 32 percent in year two, 19.20 percent in year 3, and 11.52 percent in year .

SM 11-22

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

four after the purchase. The associated depreciation charges in years 1 through 4 in order are $4,000, $6,400, $ 3,840, and $2,304 respectively. Total depreciation at the end of year 4 $16,544, so the book value of the equipment when sold is $3,456. Since the equipment is sold for $12,000 the tax on the sale of the asset is equal to ($12,000-$3,456) × 0.35 = $2,990.40.

The total after tax proceeds are $12,000 - $2,990.40 = $9,009.60 LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.10 Investment cash flows: Six Twelve, Inc., is considering opening up a new convenience store in downtown New York City. The expected annual revenue at the new store is $800,000. To estimate the increase in working capital, analysts estimate the ratio of cash and cashequivalents to revenue to be 0.03 and the ratios of receivables, inventories, and payables to revenue to be 0.05, 0.10, and 0.04, respectively, in the same industry. What is the expected incremental cash flow related to working capital when the store is opened?

Solution: Cash flow related to working capital in year0 = $800,000 × (0.03 + 0.05 + 0.10 - 0.04) = $112,000 LO 2 Bloomcode: Application .

SM 11-23

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.11 Investment cash flows: Keswick Supply Company wants to set up a division that provides copy and fax services to businesses. Customers will be given 20 days to pay for such services. The annual revenue of the division is estimated to be $25,000. Assuming that the customers take the full 20 days to pay, what is the incremental cash flow associated with accounts receivable?

Solution: The average accounts receivable balance will be (20days/365days/year) ×100% ×25,000 = 5.48% × 25,000 = $1,370.

Alternatively, the average daily credit sale = $25,000 / 365 = $68.49, and it takes 20 days, on average, to collect the sale.

Therefore, the incremental cash flow related to working capital when the store is opened: 20 × $68.49 = $1,369.86, or about $1,370.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 11-24

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

11.12Expected cash flows: Define expected cash flows, and explain why this concept is important in evaluating projects.

Solution: Expected cash flows are probability-weighted averages of the future cash flows generated by a project under alternative scenarios. In the real business world there are a lot of uncertainties.

Future cash flows may vary across different states of the world. It is not possible to estimate a unique number of cash flow for all states. We can estimate the expected cash flows across different states and use that as an estimation of future cash flows. The cash flows that are discounted in an NPV analysis are the expected incremental cash flows the project will produce.

LO 2 Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.13 Projects with different lives: Explain the concept of equivalent annual cost and how it is used to compare projects with different lives.

Solution: The equivalent annual cost (EAC) is the annualized cost of an investment stated in nominal dollars. In other words, it is the annual payment from an annuity with a life equal to that of a project that has the same NPV as the project. Since it is a measure of the annual cost or cash .

SM 11-25

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

inflow from a project, the EAC for one project can be compared directly with the EAC from another project, regardless of the lives of those two projects.

LO 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.14. Replace an existing asset: Explain how we determine the optimal time to replace an existing asset with a new one.

Solution: The optimal time to replace an existing asset with a new one is if the benefits of replacing the machine exceed the costs.

LO 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.15.Projects with different lives:If you had to choose between one project with an expected life of five years and a second project with an expected life of six years, how could you do this without using the equivalent annual cost concept?

Solution:

.

SM 11-26

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

You can effectively make the lives of the projects the same by assuming repeated investments over some identical period and compare the NPVs. LO 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

INTERMEDIATE

11.16Nominal versus real cash flows: You are buying a sofa. You will pay $200 today and make three consecutive annual payments of $300 in the future. The real rate of return is 10 percent, and the expected inflation rate is 4 percent. What is the actual price of the sofa?

Solution: We can calculate it in two different ways: (1)

Use nominal dollars and nominal rate of return: Nominal rate of return = (1 + 10%) × (1 + 4%) - 1 = 14.4% Price = 200 + 300 / (1 + 14.4%) + 300/(1 + 14.4%)2 + 300 / (1 + 14.4%)3 = $891.84

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 200 0 300 1 .

Frequency (F) -3 SM 11-27

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Then solve by pressing NPV, enter the rate of 14.4% and compute NPV= 891.84 (2)

Use real dollars and a real rate of return: Real annual payments are: 300 / (1 + 4%) = 288.46, 300 / (1 + 4%)2 = 277.37, and 300 / (1 + 4%)3 = 266.70 Price = 200 + 288.46/(1 + 10%) + 277.37/(1 + 10%)2+266.7 / (1+10%)3 =891.84

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 200 1 288.46 2 277.37 3 266.7

Frequency (F) -1 1 1

Then solve by pressing NPV, enter the rate of 10% and compute NPV= 891.84 Note that we get identical results as long as we are consistent in using nominal or real cash flows and corresponding discount rates.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.17Nominal versus real cash flows: You are graduating in two years. You want to invest your current savings of $5,000 in bonds and use the proceeds to purchase a new car when you graduate and start to work. You can invest the money in either Bond A, a two-year bond with a 3 percent annual interest rate, or Bond B, an inflation-indexed two-year bond paying 1 .

SM 11-28

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

percent real interest above the inflation rate (assume this bond makes annual interest payments). The inflation rate over the next two years is expected to be 1.5 percent. Assume that both bonds are default free and have the same market price. Which bond should you invest in?

Solution: The nominal interest rate is 3 percent for bond A, and (1 + 1%) × (1 +1.5%) – 1 = 2.52% for the inflation-indexed bond B. You should invest in bond A. LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.18 Marginal and average tax rates: Given the U.S. Corporate Tax Rate Schedule in Exhibit 11.6, what was the marginal tax rate and average tax rate of a corporation that had a taxable income of $12 million in 2016?

Solution: The marginal tax rate is 35 percent.

The total tax payable is 3,400,000 + (12,000,000-10,000,000) ×35% = $4,100,000 Therefore the average tax rate = 4,100,000 / 12,000,000 = 34.2% LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions .

SM 11-29

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

AICPA: Industry/Sector Perspective

11.19 Investment cash flows: Healthy Potions, Inc., is considering investing in a new production line for eye drops. Other than investing in the equipment, the company needs to increase its cash and cash equivalents by $10,000, increase the level of inventory by $30,000, increase accounts receivable by $25,000, and increase accounts payable by $5,000 at the beginning of the project. Healthy Potions will recover these changes in working capital at the end of the project 10 years later. Assume the appropriate discount rate is 12 percent. What are the present values of the relevant investment cash flows?

Solution: The relevant cash flow related to working capital at the beginning of the project is: $10,000 +$30,000+$25,000 - $5,000 = $60,000 The present value of relevant cash flow related to working capital at the end of the project is: $60,000 / (1 + 0.12)10 = $19,318.39 LO 1 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.20Cash flows from operations: Given the soaring price of gasoline, Ford is considering introducing a new production line of gas-electric hybrid sedans. The expected annual unit .

SM 11-30

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

sales of the hybrid cars is 30,000; the price is $22,000 per car. Variable costs of production are $10,000 per car. The fixed overhead including salary of top executives is $80 million per year.

However, the introduction of the hybrid sedan will decrease Ford’s sales of regular sedans by 10,000 cars per year; the regular sedans have a unit price of $20,000, a unit variable cost of $12,000, and fixed costs of $250,000 per year. Depreciation costs of the production plant are $50,000 per year. The marginal tax rate is 40 percent. What is the incremental annual cash flow from operations?

Solution: Step One: Revenue: $22,000 × 30,000 cars =$660,000,000 Step Two: Op Exp: $10,000 × 30,000 cars = $300,000,000, plus lost net revenue from regular sedans = ($20,000 – $12,000) × 10,000 cars = $80,000,000; total Op Exp = $380,000,000 Step Three: D&A: $50,000 Step Four: Plug information into the text book template as below.

= = x = + = =

ΔNR ΔOpEx ΔEBITDA ΔD&A ΔEBIT (1-t) ΔNOPAT ΔD&A ΔCFO ΔCapEx ΔAWC ΔFCF

660,000,000 -380,000,000 280,000,000 -50,000 279,950,000 0.60 167,970,000 50,000 168,020,000 0 0 168,020,000

Alternatively, the incremental annual cash flow from operations is: .

SM 11-31

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

(($22,000-$10,000) ×30,000-($20,000-$12,000) ×10,000) × (1-0.4) + $50,000 ×0.4 = $168,020,000 Note that the fixed costs are not included in the incremental cash flows calculations, since they exist regardless of the hybrid sedan investment.

LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.21 FCF and NPV for a project: Archer Daniels Midland Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12 million. This investment will consist of $2 million for land and $10 million for trucks and other equipment. The land, all trucks, and all other equipment are expected to be sold at the end of 10 years for a price of $5 million, which is $2 million above book value. The farm is expected to produce revenue of $2 million each year, and annual cash flow from operations equals $1.8 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this investment.

Solution: Cash flow of investment in year 0 is: $(12,000,000) Annual cash flows from operations = $1,800,000 Present value of free cash flows:

.

SM 11-32

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

PV(FCF 1−10) =Annual CF  PV Annuity factor  1-1 (1.10)10 =$1,800,000   0.10     = $11,060220.79 Financial Calculator Solution: 10 N

10 i

PV 11,060,220.79

-1,800,000 PMT

0 FV

Book value of asset = $3,000,000 Sale price of asset = $5,000,000 Tax on sale of an asset = (Selling price of asset - Book value of asset) × t = $2,000,000 × 0.35 = $700,000 PV of after-tax salvage value in year 10 is:

 ($5,000,000− $700, 000)

10 N

10 i

1 = $1,657,836.15 (1.10)10

PV 1,657,836.15

0 PMT

-4,300,000 FV

NPV = −$12,000,000 +$11,060,220.79+ 1, 657, 836.15 = $718, 056.94 Since NPV > 0, project should be accepted.

LO 1 Bloomcode: Application AASCB: Analytic .

SM 11-33

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.22 Projects with different lives: You are trying to choose between purchasing one of two machines for a factory. Machine A costs $15,000 to purchase and has a three-year life.

Machine B costs $17,700 to purchase but has a four year life. Regardless of which machine you purchase, it will have to be replaced at the end of its operating life. Which machine should you choose? Assume a marginal tax rate of 35 percent and a discount rate of 15 percent.

Solution Since the machines have difference purchase costs and different operating lives, you should choose the machine that has the lowest equivalent annual cost (EAC).  (1+ k)t  EAC A = kNPVA   t (1+k) −1 = (0.15)(−$15, 000) 

EAC B =(0.15)(−$17,700)

(1.15)3 = −$6, 569.65 (1.15)3−1

(1.15)4 = −$6,199.70 (1.15)4−1

You should choose machine B because it has the lower equivalent annual cost.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.23Projects with different lives: You are starting a family pizza parlor and need to buy a motorcycle for delivery orders. You have two models in mind. Model A costs $9,000 and is .

SM 11-34

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

expected to run for 6 years; Model B is more expensive, with a price of $14,000, and has an expected life of 10 years. The annual maintenance costs are $800 for Model A and $700 for Model B. Assume that the opportunity cost of capital is 10 percent. Which one should you buy?

Solution: You need to first calculate the NPV of costs for each of the motorcycles:

1    1 − (1.10)6=−  −  $12,484.21 NPV A = −$9, 000+ ( $800) 0.10     Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Motorcycle A Cash Flow (C) 0 -9,000 1 -800

Frequency (F) -6

Then solve by pressing NPV, enter the rate of 10% and compute NPV=-12,484.21.

1    1−  (1.10)10 =− −  $18,301.20 NPV B = −$14, 000+ ( $700) 0.10     Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Motorcycle A Cash Flow (C) 0 -14,000 1 -700 .

Frequency (F) -10 SM 11-35

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Then solve by pressing NPV, enter the rate of 10% and compute NPV=-18,301.20 Then you need to calculate the EAC of each model:  (1+k) t  EAC A = kNPVA   (1+ k)t−1 = (0.10)(−$12, 484.21)

(1.10)6 = −$2, 866.47 (1.10)6−1

Financial Calculator Solution: 6 N

10 i

 EAC B = (0.10)( −$18, 301.20)

-12,484.21 PV

0 FV

PMT 2866.47

(1.10)10 = −$2,978.44 (1.10)10 − 1

Financial Calculator Solution: 10 N

10 i

-18,301.20 PV

0 FV

PMT 2,978.44

Since EAC is lower for Model A, you should buy Model A. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.24 When to harvest an asset: Predator LLC, a leveraged-buyout specialist, recently bought a company and wants to determine the optimal time to sell it. The partner in charge of this investment has estimated the after-tax cash flows from a sale at different times to be as follows: $700,000 if sold one year later; $1,000,000 if sold two years later; $1,200,000 if sold

.

SM 11-36

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

three years later; and $1,300,000 if sold four years later. The opportunity cost of capital is 12 percent. When should Predator sell the company? Why?

Solution: The NPV of each choice is: 1 $625,000 NPV 1 =$700,000 / (1.12)= 2 $797,194 NPV 2 =$1,000,000 / (1.12)= 3 $854,136 NPV 3 =$1,200,000 / (1.12)= 4 $826,174 NPV 4 = $1,300,000 / (1.12)=

Selling the company in 3 years provides the highest NPV. LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.25 Replace an existing asset: Bell Mountain Vineyards is considering updating its current manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. The Bell Mountain’s opportunity cost of capital is 10 percent, and the costs and values of investments made at different times in the future are as follows: Year

Cost

Value of Future Savings (at time of purchase)

0

$5,000

$7,000

1

4,500 .

7,000 SM 11-37

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

2 4,000 7,000 3 3,600 7,000 4 3,300 7,000 5 3,100 7,000

When should Bell Mountain buy the new accounting system?

Solution: The NPV of each choice is: NPV0 = Future savings – Cost = $7,000 - $5,000 = $2,000 1 $2,273 NPV 1 =$2,500 / (1.1)= 2 2,479 NPV 2 =$3,000 / (1.1)=$ 3 NPV 3 =$3,400 /(1 .1)=$2,554 4 $2,527 NPV 4 =$3,700 / (1.1)= 5 $2,422 NPV 5 =$3,900 / (1.1)=

Therefore the company should purchase the system in year 3.

LO 4 Bloomcode: AAnalysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.26 Replace an existing asset: You have a 2000 Nissan that is expected to run for another three years, but you are considering buying a new Hyundai before the Nissan wears out. You will donate the Nissan to Goodwill when you buy the new car. The annual maintenance cost is .

SM 11-38

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

$1,500 per year for the Nissan and $200 for the Hyundai. The price of your favorite Hyundai model is $18,000, and it is expected to run for 15 years. Your opportunity cost of capital is 3 percent. Ignore taxes. When should you buy the new Hyundai?

Solution: NPV of cost of the new car is:

1    1−  (1.03)15 =− −  $20,387.59 NPV Hyundai = −$18, 000+ ( $200) 0.03     Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Hyundai Cash Flow (C) 0 -18,000 1 -200

Frequency (F) -15

Then solve by pressing NPV, enter the rate of 3% and compute NPV=-20,387.59 Then you need to calculate the EAC of each model: EAC of the new car is:  (1+ k)t  EAC Hyundai = kNPV t  (1+ kt) − 1 = (0.03)(−$20,387.59) 

(1.03)15 = −$1,707.80 (1.03)15 − 1

Financial Calculator Solution : 15 N

.

3 i

-20,387.59 PV

PMT 1,707.80

0 FV

SM 11-39

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Since the EAC of the new car is $1,707.8 and exceeds that of the Nissan ($ ($1,500), you should drive the 2000 Nissan for three more years and then buy a new Hyundai.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.27Replace an existing asset:Assume that you are considering replacing your old Nissan with a new Hyundai, as in the previous problem. However, the annual maintenance cost of the old Nissan increases as time goes by. It is $1,200 in the first year, $1,500 in the second year, and $1,800 in the third year. When should you replace it with the new Hyundai in this case?

Solution:  (1+ k)t  EAC Hyundai = kNPV t  (1+ kt) − 1 = (0.03)(−$20,387.59) 

(1.03)15 = −$1,707.80 (1.03)15 − 1

The EAC of the Hyundai remains at $1,707.80, as calculated above.

Comparing this amount with the annual maintenance costs of the Nissan and you will see that in year 2 it is cheaper to drive the Nissan, but in year 3 it is cheaper to drive the Hyundai.

Therefore, the optimal time to replace the old car is at the end of year 2.

LO 4 Bloomcode: Application AASCB: Analytic .

SM 11-40

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.28 When to harvest an existing asset: Anaconda Manufacturing Company currently own a mine that is known to contain a certain amount of gold. Since Anaconda does not have any goldmining expertise, the company plans to sell the entire mine and base the selling price on a fixed multiple of the spot price for gold at the time of the sale. Analysts at Anaconda have forecast the spot price for gold and have determined that the price will increase by 14 percent, 12 percent, 9 percent, and 6 percent during the next one, two, three, and four years, respectively. If Anaconda’s opportunity cost of capital is 10 percent, what is the optimal time for Anaconda to sell the mine?

Solution: The rate of gold price appreciation is greater than the opportunity cost of capital for the next two years and then it drops below the opportunity cost of capital. Therefore, Anaconda should sell the gold at the beginning of the third year (or at the end of the second year).

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.29 Replace an existing asset: You are thinking about delivering pizzas in your spare time. Since you must use your own car to deliver the pizzas, you will wear out your current car one year earlier, .

SM 11-41

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

which is one year from today, than if you did not take on the delivery job. You estimate that when you purchase a new car, regardless of when that occurs, you will pay $20,000 for the car and it will last you five years. If your opportunity cost of capital is 7 percent, what is the opportunity cost of using your car to deliver pizzas?

Solution:

 (1+0.07)5  EAC New Car = 0.07 −$20, 000 =− $4,877.81  (1+ 0.07)5−1 Financial Calculator Solution : 5 N

7 i

-20,000.00 PV

PMT 4,877.81 Therefore, the opportunity cost of wearing out your car a year earlier is

0 FV

NPVUsingyourcar=−$4,877.81/(1.07)1=−$4,558,70 Financial Calculator Solution: 1 N

7 i

PV -4,558.70

0 PMT

4,877.81 FV

LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 11-42

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

ADVANCED

11.30 You are the CFO of SlimBody, Inc., a retailer of the exercise machine Slimbody6 and related accessories. Your firm is considering opening up a new store in Los Angeles. The store will have a life of 20 years. It will generate annual sales of 5,000 exercise machines, and the price of each machine is $2,500. The annual sales of accessories will be $600,000, and the operating expenses of running the store, including labor and rent, will amount to 50 percent of the revenues from the exercise machines. The initial investment in the store will equal $30 million and will be fully depreciated on a straight-line basis over the 20-year life of the store.

Your firm will need to invest $2 million in additional working capital immediately, and recover it at the end of the investment. Your firm’s marginal tax rate is 30 percent. The opportunity cost of opening up the store is 10 percent. What are the incremental free cash flows from this project at the beginning of the project as well as in years 1-19 and 20? Should you approve it?

Solution: Step One: Initial outlay = $30,000,000 + $2,000,000 (WC requirement) = $32,000,000 Step Two: ΔNR for years 1- 20: $2,500 × 5,000 machines = $12,500,000 plus $600,000 = $13,100,000 Step Three: ΔOpExp for years 1- 20: $1,250 × 5,000 machines = $6,250,000 Step Four: ΔD&A for years 1- 20: $30,000,000 / 20 years = $1,500,000 / year Step Five: Plug information into the text book template as below.

Step Six: Yr 20 recapture of WC requirements that were funded in year 0. .

SM 11-43

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Yrs 1-19 1

ΔNR Δ

O

p

E

Δ

E

B

I

Δ

D

&

Δ

E

B

(

1

-

t

3

x

T

D

A

6

A

I

,

-

,

-

T

1

6

0

2

8

1

0

5

5

5

,

0

0

0

0

0

0

,

0

0

0

0

0

0

Yr 20

0

0

0

5

,

3

5

0

0

,

0

0

0

3

,

7

4

5

,

0

0

)

0

P

A

.

3

,

-

6

,

-

1

6

0

2

8

1

0

5

5

5

,

0

0

0

0

0

,

0

0

0

0

0

0

0

0

0

0

0

5

,

3

5

0

,

0

0

0

0

3

,

7

4

5

,

0

0

0

7

0

.

7

Δ

N

O

Δ

D

&

A

1

,

5

0

0

,

0

0

0

1

,

5

0

0

,

0

0

0

Δ

C

F

O

5

,

2

4

5

,

0

0

0

5

,

2

4

5

,

0

0

0

Δ

C

a

p

Δ

A

W

Δ

F

C

E

T

1

x

-

3

C

F

-

-

3

0

,

0

0

0

,

0

0

0

0

2

,

0

0

0

,

0

0

0

0

2

,

0

0

0

,

0

0

0

2

,

0

0

0

,

0

0

0

0

7

,

2

4

5

,

0

0

0

5

,

2

4

5

,

0

0

0

Therefore the NPV of the project is:

1   1− (1.10)19  1  7, 245, 000  NPV = −$32, 000, 000+ $5, 245, 000  (1.10)20  0.10 +      = $12, 950, 928.97 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) Frequency (F) 0 -32,000,000 -5,245,000 19 1 7,245,000 1 2 Then solve by pressing NPV, enter the rate of 10% and compute NPV=12,950,928.97.

You should approve the project since it has a positive NPV. Alternative Solution: Incremental cash flows in year 0 is: FCF0 = -$30,000,000-$2,000,000= -$32,000,000 Annual incremental cash flows through the life of the investment are: FCFt = (($2,500 × 2,500) + $600,000) × (1-0.3) + (0.3 × $1,500,000) = $5,245,000 .

SM 11-44

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Additional incremental cash flows at the end of the project are: $2,000,000 Therefore the NPV of the project is:

1   1− (1.10)19  1  7, 245, 000  NPV = −$32, 000, 000+ $5, 245, 000  (1.10)20  0.10 +      = $12, 950, 928.97 You should approve the project since it has a positive NPV. LO 1, 3, 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.31Merton Shovel Corporation has decided to bid for a contract to supply shovels to the Honduran Army. The Honduran Army intends to buy 1,000 shovels per year for the next three years. To supply these shovels, Merton will have to acquire manufacturing equipment at a cost of $150,000. This equipment will be depreciated on a straight-line basis over its five-year lifetime. At the end of the third year, Merton can sell the equipment for exactly its book value ($60,000). Additional fixed costs will be $36,000 per year, and variable costs will be $3.00 per shovel. An additional investment of $25,000 in net working capital will be required when the project is initiated. This investment will be recovered at the end of the third year. Merton Shovel has a 35 percent marginal tax rate and a 17 percent required rate of return on the project. What is the lowest possible per shovel price that Merton can offer for the contract and still create value for its stockholders?

Solution Year 0 cash flow = Cap Exp + Add WC = -$150,000 – $25,000 = -$175,000 Year 3: Cap Exp + Add WC = $60,000 + $25,000 = $85,000 .

SM 11-45

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

We can’t directly solve for CF Opns since revenue depends on what we are going to charge per shovel. Since CF Opns must be the same in years 1, 2, and 3 of the project this is a three year annuity and we can solve for the total value of CF Opns as: Present value of CF Opns = CF Opns × [(1-1/(1.17)3)/0.17] NPV of the shovel contract = -$175,000 + $85,000/(1.17)3 + OCF [(1-1/(1.17)3)/0.17] Set NPV = 0 and solve for CF Opns: CF Opns = $55,181 Now solve CF Opns formula for the price of each shovel (P): CF Opns = [Revenue – OpEx – D&A) × (1 – t)] + D&A $55,181 = [(P × 1000) – ($3.00 × 1000) – $36,000 - $30,000] × (1-0.35) + $30,000 P = $107.74 This is the minimum bid price for a shovel. If Merton Shovel charges less than this price per shovel, the NPV of the contract will be less than zero.

LO 1,3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.32 Rocky Mountain Lumber, Inc., is considering purchasing a new wood saw that costs $50,000.

The saw will generate revenues of $100,000 per year for five years. The cost of materials and labor needed to generate these revenues will total $60,000 per year, and other cash expenses will be $10,000 per year. The machine is expected to sell for $1,000 at the end of its five-year life and will be depreciated on a straight-line basis over five years to zero. Rocky Mountain’s tax rate is 34 percent, and its opportunity cost of capital is 10 percent. Should the company purchase the saw? Explain why or why not?

Solution: .

SM 11-46

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Step One: Initial outlay = $50,000 Step Two: ΔNR for years 1- 5: $100,000 Step Three: ΔOpExp for years 1- 5: $60,000 + $10,000 = $70,000 Step Four: ΔD&A for years 1- 5: $50,000 / 5 years = $10,000 / year Step Five: Plug into the text book template as below.

Step Six: Yr 5: Capital recovery = $1,000 – (0.34 × $1,000 gain on sale) = $660.

Yrs 1-4 1

ΔNR

0

0

Yr 5 ,

0

0

0

0

0

0

1

-

0

0

0

0

3

0

0

0

-

0

0

2

6

6

0

,

0

0

0

0

0

0

0

0

0

0

0

0

0

0

6

6

E

Δ

O

p

Δ

E

B

Δ

D

&

E

Δ

(

1

I

B

-

t

x

T

-

D

A

3

A

I

7

-

T

2

0

0

1

,

0

0

)

,

0

0

A

0

0

1

,

0

0

,

0

0

.

Δ

N

O

P

1

3

,

2

0

0

1

3

,

2

0

0

Δ

D

&

A

1

0

,

0

0

0

1

0

,

0

0

0

Δ

C

F

O

2

3

,

2

0

0

2

3

,

2

0

0

Δ

C

a

p

6

6

0

Δ

A

W

Δ

F

C

8

6

0

E

T

.

7

x

-

5

0

,

0

0

C

F

-

5

0

,

0

0

0

0

0

0

0

2

3

,

2

0

0

0

2

3

,

Therefore, NPV of investment is: NPV = −$50,000 +

$23, 200 $23, 200 $23, 200 $23, 200 $23, 860 + + + + (1.10) (1.10)2 (1.10)3 (1.10)4 (1.10)5

=$38,356

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -50,000 1 23,200 2 23,860

Frequency (F) -4 1

Then solve by pressing NPV, enter the rate of 10% and compute NPV=38,356 Since NPV > 0, the company should buy the machine.

.

SM 11-47

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Alternatively: The annual operating cash flows from year 1 to 5 are: ($100,000-$60,000-$10,000) × (1-0.34) + 0.34 ×10,000=$23,200 The after-tax terminal value in year 5 is: $1,000 - (0.34)($1,000-$0) = $660 Therefore, NPV of investment is: NPV = −$50,000 +

$23, 200 $23, 200 $23, 200 $23, 200 $23, 860 + + + + (1.10) (1.10)2 (1.10)3 (1.10)4 (1.10)5

=$38,356

Therefore the company should buy the machine.

LO 1,3,4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.33 A beauty product company is developing a new fragrance named Happy Forever. There is a probability of 0.5 that consumers will love Happy Forever, and in this case, annual sales will be 1 million bottles; a probability of 0.4 that consumers will find the smell acceptable and annual sales will be 200,000 bottles; and a probability of 0.1 that consumers will find the smell unpleasant and annual sales will be only 50,000 bottles. The selling price is $38, and the variable cost is $8 per bottle. Fixed production costs will be $1 million per year, and depreciation will be $1.2 million. Assume that the marginal tax rate is 40 percent. What are the expected annual incremental after-tax free cash flows from the new fragrance?

Solution: Step One: Expected sales units: (0.5) ×1,000,000 + (0.4) ×200,000 + (0.1) ×50,000 = 585,000 units .

SM 11-48

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Step Two: ΔNR: 585,000 units × $38 = $22,230,000 Step Three: ΔOpExp: 585,000 units x $8 + $1,000,000 = $5,680,000 Step Four: ΔD&A: $1,200,000 Step Five: Plug into the text book template as below.

= = x = + = =

ΔNR ΔOpEx ΔEBITDA ΔD&A ΔEBIT (1-t) ΔNOPAT ΔD&A ΔCFO ΔCapEx ΔAWC ΔFCF

22,230,000 -5,680,000 16,550,000 -1,200,000 15,350,000 0.60 9,210,000 1,200,000 10,410,000 0 0 10,410,000

Alternatively, the expected annual incremental cash flows are: (((0.5 ×1,000,000+0.4 ×200,000+0.1 ×50,000) × ($38-$8)) -1,000,000) × (1 - 0.4) +1,200,000 ×0.4 = $10,410,000 LO 1,3,4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.34 Great Fit, Inc., is a company that manufactures clothing. The company has a production line that produces women’s tops of regular sizes. The same machine could be used to produce petite sizes as well. However, the remaining life of the machines will be reduced from four years to two years if the petite size production is added. The cost of identical machines with a .

SM 11-49

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

life of eight years is $2 million. Assume the opportunity cost of capital is 8 percent. What is the opportunity cost of adding petite sizes?

Solution: The opportunity cost is the incremental costs of the machine in year 3 and year 4 if petite sizes are in production. The EAC of the machine is:  (1+ k)t  EAC A = kNPVA   (1+ k)t−1 = (0.08)(−$2, 000, 000)

(1.08)8 = −$348, 029.52 (1.08)8−1

The present value of such cost in year 3 and year 4 is: $348,029.52 $348,029.52 + (1.08)4 (1.08)3 = $532, 089.14

NPV =

LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.35 Biotech Partners LLC has been farming a new strain of radioactive-material-eating bacteria that the electrical utility industry can use to help dispose of its nuclear waste. Two opposing factors affect Biotech’s decision of when to harvest the bacteria. The bacteria are currently growing at a 22 percent annual rate, but due to known competition from other top firms, .

SM 11-50

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Biotech analysts estimate that the price for the bacteria will decline according to the schedule below. If the opportunity cost of capital is 10 percent, then when should Biotech harvest the entire bacteria colony at one time?

Year

Change in Price Due to Competition

1

5%

2

-2

3

-8

4

-10

5

-15

6

-25

Solution: Change in revenue: Yr 1

(1.05)(1.22) = 1.2810 or 28.1%

Yr 2

(0.98)(1.22) = 1.1956 or 19.56%

Yr 3

(0.92)(1.22) = 1.1224 or 12.24%

Yr 4

(0.9)(1.22) = 1.0980 or 9.80%

Yr 5

(0.85)(1.22) = 1.037 or 3.70%

Yr 6

(0.75)(1.22) = 0.9150 or -8.50%

Since the change in revenue is higher than the 10% opportunity cost of capital for the first three years, Biotech should sell its bacteria colony at the beginning of the third year or at the end of the second year. .

SM 11-51

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.36 ACME Manufacturing is considering replacing an existing production line with a new line that has a greater output capacity and operates with less labor than the existing line. The new line would cost $1 million, have a five-year life, and be depreciated using MACRS over three years. At the end of five years, the new line could be sold as scrap for $200,000 (in Year 5 dollars). Because the new line is more automated, it would require fewer operators, resulting in a savings of $40,000 per year before tax and unadjusted for inflation (in today’s dollars).

Additional sales with the new machine are expected to result in additional net cash inflows, before tax, of $60,000 per year (in today’s dollars). If ACME invests in the new line, a onetime investment of $10,000 in additional working capital will be required. The tax rate is 35 percent, the opportunity cost of capital is 10 percent, and the annual rate of inflation is 3 percent. What is the NPV of the new production line?

Solution: t=

0.35

rate =

0.1

NPV of the New Line 0

1

2

3

4

$66,950

$68,959

$71,027

$73,158

5

(Revenue Op Exp)(1-t)

.

$75,353

SM 11-52

Fundamentals of Corporate Finance, 4th d edition

plus Tax x Deprec

Solutions Manual $116,655

minus Cap Exp

$155,575

$51,835

$25,935

$(200,000)

$1,000,000

plus tax on Salvage

$(70,000)

minus Add WC

$10,000

Net Cash Flows

$(1,010,000)

$183,605

$224,534

$122,862

$99,093

$215,353

PV of Net Cash Flows

$(1,010,000)

$166,914

$185,565

$92,308

$67,682

$133,717

Net Present Value

$(363,814)

$(10,000)

LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.37 The alternative to investing in the new production line in Problem 11.36 is to overhaul the existing line, which currently has both a book value and a salvage value of $0. It would cost $300,000 to overhaul the existing line, but this expenditure would extend its useful life to five years. The line would have a $0 salvage value at the end of five years. The overhaul outlay would be capitalized and depreciated using MACRS over three years. Should ACME replace or renovate the existing line? .

SM 11-53

Fundamentals of Corporate Finance, 4th d edition

t=

Solutions Manual

0.35

rate =

0.1

Renovate Old Line 0

1

2

3

4

$34,997

$46,673

$15,551

$7,781

5

(Revenue Op Ex)(1-t)

plus Tax × Deprec

minus Cap Exp

$300,000

plus tax on Salvage

minus Add WC

Net Cash Flows

$(300,000)

$34,997

$46,673

$15,551

$7,781

$0

PV of Net Cash Flows

$(300,000)

$31,815

$38,572

$11,683

$5,314

$0

Net Present Value

$(212,615)

NPV new - NVP old

$(151,199)

Renovating the old line is less costly.

LO 4 Bloomcode: Analysis AASCB: Analytic .

SM 11-54

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

IMA: Investment Decisions AICPA: Industry/Sector Perspective

CFA Problems 11.38. FITCO is considering the purchase of new equipment. The equipment costs $350,000, and an additional $110,000 is needed to install it. The equipment will be depreciated straight-line to zero over a five-year life. The equipment will generate additional annual revenues of $265,000, and it will have annual cash operating expenses of $83,000. The equipment will be sold for $85,000 after five years. An inventory investment of $73,000 is required during the life of the investment. FITCO is in the 40 percent tax bracket, and its cost of capital is 10 percent. What is the project NPV?

a.

$47,818

b.

$63,658

c.

$80,189

d.

$97,449

Solution:

d is correct.

Outlay = FCInv + NWCInv – Salvage0 + T × (Salvage0 – Book0) Outlay = (350,000 + 110,000) + 73,000 – 0 + 0 = $533,000 The installed cost is $350,000 + $110,000 = $460,000, so the annual depreciation is $460,000/5 = $92,000. The annual after-tax operating cash flow for Years 1–5 is CF = (Sales – Costs – Deprec)(1 – T) + Deprec = (265,000 – 83,000 – 92,000)(1 – 0.40) + 92,000 CF = $146,000 .

SM 11-55

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

The terminal year after-tax non-operating cash flow in Year 5 is TermialOCF = Salvage5 + NWCInv – T(Salvage5 – B5) = 85,000 + 73,000 – 0.40(85,000 – 0) TermialOCF = $124,000 The NPV is NPV = −533, 000+

146, 000 124, 000 + t 1.105 1 .10 t= 1  = $97,449 5

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -533,000 1 146,000 2 270,000

Frequency (F) -41

Then solve by pressing NPV, enter the rate of 10% and compute NPV=97,449.11 LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective

11.39 After estimating a project’s NPV, the analyst is advised that the fixed capital outlay will be revised upward by $100,000. The fixed capital outlay is depreciated straight-line over an eight-year life. The tax rate is 40 percent, and the required rate of return is 10 percent. No changes in cash operating revenues, cash operating expenses, or salvage value are expected.

What is the effect on the project NPV? .

SM 11-56

Fundamentals of Corporate Finance, 4th d edition

a.

$100,000 decrease

b.

$73,325 decrease

C.

$59,988 decrease

d.

No change

Solutions Manual

Solution:

b is correct. The additional annual depreciation is $100,000/8 = $12,500. The depreciation tax savings is 0.40 ($12,500) = $5,000. The change in project NPV is −100, 000+

5, 000 = −100, 000+ 26, 675= −$73, 325 1 (1.10)t t= 8

Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) -100,000 0 5,000 1

Frequency (F) -8

Then solve by pressing NPV, enter the rate of 10% and compute NPV=-73,325 LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective

11.40. When assembling the cash flows to calculate an NPV or IRR, the project’s after-tax interest expenses should be subtracted from the cash flows for:

.

SM 11-57

Fundamentals of Corporate Finance, 4th d edition

a.

The NPV calculation, but not the IRR calculation. The

b.

IRR calculation, but not the NPV calculation. Both the

c.

NPV calculation and the IRR calculation. Neither the

d.

NPV calculation nor the IRR calculation.

Solutions Manual

Solution: d is correct. Financing costs are not subtracted from the cash flows for either the NPV or the IRR. The effects of financing costs are captured in the discount rate used.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Sample Test Problems

11.1 You purchased 100 shares of stocks of an oil company, Texas Energy, Inc., at $50 per share.

The company has 1 million shares outstanding. Ten days later, Texas Energy announced an investment in an oil field in east Texas. The probability that the investment will be successful and generate an NPV of $10 million is 0.2; the probability that the investment will be a failure and generate an NPV of negative $1 million is 0.8. How would you expect the stock price to change upon the company’s announcement of the investment?

Solution:

.

SM 11-58

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

The expected change in the stock price should be equal to the expected NPV of the project divided by the number of shares outstanding.

The expected NPV of the project is (0.2 × $10,000,000) + (0.8 × –$1,000,000) = $1,200,000 Therefore, the change in Texas Energy’s stock price should equal $1,200,000 / 1,000,000 shares = $1.2 per share when the investment is announced. The total value of your shares should increase by 100 shares × $1.20 per share = $120.

Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2 A division of Virginia City Highlands Manufacturing is considering purchasing for 1,500,000 a machine that automates the process of inserting electronic components onto computer motherboards. The annual cost of operating the machine will be $50,000, but it will save the company $370,000 in labor costs each year. The machine will have a useful life of 10 years, and its salvage value in 10 years is estimated to be $300,000. Straight-line depreciation will be used in calculating taxes for this project, and the marginal corporate tax rate is 32 percent. If the appropriate discount rate is 12 percent, what is the NPV of this project?

Solution: The incremental after-tax free cash flow (FCF) in year 0 is: FCF0 = –$1,500,000 The FCF in years 1 through 9 is: .

SM 11-59

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Annual Depreciation = ($1,500,000 – $300,000) / 10 = $120,000 per year FCFt = [($370,000 – $50,000) × (1 – 0.32)] + [ 0.32 × $120,000] = $256,000 The FCF in year 10 is: FCF10 = $256,000 + $300,000 – [(Salvage Value – Book Value) × 0.032] = $556,000 Therefore, the NPV of the project is:

 1   1 –   (1.12)9  1     + $556,000 $256,000 NPV = –$1,500,000 +    (1.12 )10   0.12           = –$1,500,000 + $1,346,032 + $179,017 = $43,049 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -1,500,000 1 256,000 2 556,000

Frequency (F) -91

Then solve by pressing NPV, enter the rate of 12% and compute NPV=43,049 Virginia City Highlands Manufacturing should approve the project since it has a positive NPV. Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 11-60

Fundamentals of Corporate Finance, 4th d edition

11.3

Solutions Manual

After examining the NPV analysis for a potential project that would increase the firm’s output by 5 percent, an analyst’s manager tells the analyst to increase the initial fixed capital outlay in the analysis by $480,000. The initial fixed capital outlay would be fully depreciated on a straight-line basis over a 12-year life, regardless of whether it is increased. If the firm’s average tax rate is 28 percent, its marginal tax rate is 35 percent, and the required rate of return is 10 percent, what is the effect of the adjustment on the project NPV?

Solution: The additional annual depreciation is $480,000 / 12 = $40,000.

For a project such as this we would use the marginal tax rate. Therefore, the annual depreciation tax savings is 0.35 × $40,000 = $14,000.

The change in the overall NPV of the project is:

 1   1−   (1.10)12     + Change in NPV = – $480,000 $14,000   0.10          = –$480,000 + $95,392    = –$384,608 Financial Calculator Solution: Using a financial calculator, enter the cash flows as follows: Cash Flow (C) 0 -480,000 1 14,000

Frequency (F) -12

Then solve by pressing NPV, enter the rate of 10% and compute NPV=-384,608 The NPV will be reduced by $384,608 .

SM 11-61

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4 Which of the following are relevant cash flows in the evaluation of a proposal to produce a new product? a. Decrease in the cash flows of a substitute product. b. Alternative of leasing an existing building that will be used for manufacturing this product. c. The cost of a new machine required to produce this product. d. Salvage value of the new machine at the end of its useful life. e. Increase in net working capital at the beginning of the project’s life. f. Cost to develop a product prototype last year.

Solution: a, b, c, d, and e are all relevant cash flows. f is a sunk cost and is therefore not relevant.

Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5

Managers of Central Embroidery have decided to purchase a new monogram machine and are considering two alternative machines. The first machine costs $100,000 and is expected to last five years. The second machine costs $160,000 and is expected to last eight years. Assume

.

SM 11-62

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

that the opportunity cost of capital is 8 percent. Which machine should Central Embroidery purchase?

Solution: The equivalent annual cost for each system is:  (1.08)5  EAC Machine 1 = 0.08 × $100,000 ×   = $25,045.65 (1.08) 5 – 1 

Financial Calculator Solution : 5 N

8 i

-100,000 PV

PMT 25,045.65

0 FV

 (1.08)8  EAC Machine 2 = 0.08 × $160,000 ×   = $27,842.37 (1.08) 8 – 1

Financial Calculator Solution: 8 N

8 i

-160,000 PV

PMT 27,842.37

0 FV

Central Embroidery should purchase the first machine because it has a lower EAC. Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.6

You have inherited an apple orchard and want to sell it in the next four years. An expert in apple orchard valuation has estimated the after-tax cash flow you would receive if you sold at the end of each of the next four years as follows: $1,000,000 if you sell in one year;

.

SM 11-63

Fundamentals of Corporate Finance, 4th d edition

Solutions Manual

$1,300,000 if you sell in two years; $1,500,000 if you sell in three years; and $1,600,000 if you sell in four years. Your opportunity cost of capital is 10 percent. When should you sell the orchard?

Solution: The NPV in today’s dollars for each alternative is: NPV=1 $1,0 00,000 / (1.10)1= $909,091 NPV=2 $1,3

2

NPV=3 $1,500,000 / (1.103 ) = $1,126,972 NPV=4 $1, 600,000 / (1.10)4= $1,092,822 You should sell the orchard in 3 years because the present value of the NPV is highest in year three. After year three, the value of the orchard is expected to increase at a rate that is less than your opportunity cost of capital. Therefore it is better for you to sell the orchard after three years and invest the proceeds elsewhere.

Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

.

SM 11-64

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Chapter 12 Evaluating Project Economics

Before You Go On Questions and Answers

Section 12.1 1.

Why do analysts care about how sensitive EBITDA and EBIT are to changes in revenue?

Comparing the sensitivity of EBITDA to changes in revenue can help you better understand risks and returns associated with alternative options. For example, if we assume that the sensitivity of EBITDA to changes in revenue is higher for one alternative than for the other. This means that EBITDA for the more sensitive alternative will decline more when revenue is lower than expected. A larger decline in EBITDA reduces the value of the project more and has a greater impact on the amount of cash the firm has available to fund other positive NPV projects. Conversely, EBITDA will increase more when revenue is greater than expected if the level of sensitivity is higher.

2.

How is the proportion of fixed costs in a project’s cost structure related to the sensitivity of EBITDA and EBIT to changes in revenue?

.

SM 12-1

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The greater the proportion of fixed costs, the more sensitive EBITDA and EBIT will be to changes in revenue.

Section 12.2 1.

How does operating leverage change when there is an increase in the proportion of a project’s costs that are fixed?

An increase in the proportion of a project’s costs that are fixed increases the operating leverage of the project.

2.

What do the degree of pretax cash flow operating leverage (Cash Flow DOL) and the degree of accounting operating leverage (Accounting DOL) tell us?

Cash Flow DOL provides us with a measure of how sensitive pretax operating cash flows are to changes in revenue. Cash Flow DOL changes with the level of revenue. Accounting DOL is a measure of how sensitive accounting operating profits (EBIT) are to changes in revenue. Accounting DOL focuses on EBIT, whereas Cash Flow DOL focuses on EBITDA.

Section 12.3 1.

How is the per-unit contribution related to the accounting operating profit breakeven point?

.

SM 12-2

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

The per unit contribution is how much is left from the sale of a single unit after paying the variable costs associated with that unit. This is the amount that is available to help cover FC and D&A for the project. When we calculate the accounting operating profit break-even point, we divide the sum of FC and D&A by the per unit contribution to determine how many units must be sold to cover FC and D&A.

2.

What is the difference between the pretax operating cash flow break-even point and the accounting operating profit break-even point?

The pretax operating cash flow break-even point is the number of units that must be sold in a particular year for cash inflows to exactly equal cash outflows. The accounting operating profit break-even point is the number of units that must be sold in a particular year for the project to have operating profits of $0—in other words, to break even on an accounting operating profit basis.

Section 12.5 1.

How is a sensitivity analysis used in project analysis?

Sensitivity analysis is used to examine the sensitivity of a project’s NPV to changes in an individual assumption.

2. .

How does a scenario analysis differ from a sensitivity analysis?

SM 12-3

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Scenario analysis recognizes that variables typically do not change one at a time. A change in economic or market conditions will usually cause several assumptions to change. Scenario analysis recognizes this by examining a project under alternative scenarios in which each assumption can change under each scenario.

3.

What is a simulation analysis, and what can it tell us?

Simulation analysis involves creating a large number of scenarios, often using random numbers and probability distributions, to evaluate the effects of different scenarios. Simulation analysis uses a computer to generate a large number of scenarios quickly, and calculate the range of outcomes (standard deviation, inter-quartile range, etc) and the probabilities of particular outcomes.

Self-Study Problems

12.1 The Yellow Shelf Company sells all of its shelves for $100 per shelf, and incurs $50 in variable costs to produce each. If the fixed costs for the firm are $2,000,000 per year, what will the EBIT for the firm be if it produces and sells 45,000 shelves next year?

Assume that depreciation and amortization is included in the fixed costs.

.

SM 12-4

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: Revenue

$100 per unit × 45,000 units =

$4,500,000

VC

$50 per unit × 45,000 units =

2,250,000

FC + D&A

2,000,000

EBIT

$ 250,000

12.2 Hydrogen Batteries sells its specialty automobile batteries for $85 each, while its current variable cost per unit is $65. Total fixed costs (including depreciation and amortization expense) are $150,000 per year. Management expects to sell 10,000 batteries next year, but is concerned that variable cost will increase next year due to material cost increases.

What is the maximum variable cost per unit increase that will keep the EBIT from becoming negative?

Solution: The forecasted EBIT for Hydrogen Batteries is: Revenue

$85 per unit × 10,000 units = $850,000

VC

$65 per unit × 10,000 units = 650,000

FC + D&A

150,000

EBIT

$ 50,000

Therefore, total variable cost may increase by $50,000, which means that if the firm produces and sells 10,000 batteries, then the variable cost per unit may increase by $5 ($50,000 / 10,000 units = $5 per unit).

.

SM 12-5

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

12.3 The Vinyl CD Co. is going to take on a project that is expected to increase its EBIT by $90,000, its fixed cost cash expenditures by $100,000, and its depreciation and amortization by $80,000 next year. If the project yields an additional 10 percent in revenue, what percentage increase in the project’s EBIT will result from the additional revenue?

Solution:

Accounting DOL

= 1+

FC+D&A EBIT

= 1+

$100, 000 + $80, 000 $90, 000

=3 Therefore, a 10 percent additional increase in revenue should result in approximately a 30 percent increase in EBIT.

12.4

You are considering investing in a business that has monthly fixed costs of $5,500 and sells a single product that costs $35 per unit to make. This product sells for $90 per unit.

What is the annual pretax operating cash flow break-even point for this business?

Solution: You can solve for the monthlypretax operating cash flow break-even point using Equation 12.4:

EBITDABreak-Even=

FC $5,500 = =100units per month Price−UnitVC $90−$35

Therefore, the annual EBITDA break-even point is 100  12 = 1,200 units. .

SM 12-6

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

12.5 Belt Bottoms, Inc. is considering a five-year project with an initial investment of $20,000. What annual free cash flow (FCF) would be required for this project to have an NPV of $0 if the opportunity cost capital is 11 percent?

Solution: If the FCF is equal in each of the five years, then we can solve for FCF using the present value of an ordinary annuity formula: $20,000=

𝑭𝑪𝑭𝒕 .𝟏𝟏

× (𝟏 −

𝟏 )𝟓)→ (𝟏𝟏𝟏 .

FCF = $5,411.41

We can also use a financial calculator to solve this problem: N=5; I/Y=11; PV=-20,000;FV=0 → CPT → PMT=5,411.11 If using a spreadsheet to solve this problem:

Discussion Questions 12.1 You are involved in the planning process for a firm that is expected to have a large increase in sales next year. Which type of firm would benefit the most from that sales increase: a firm with low fixed costs and high variable costs or a firm with high fixed costs and low variable costs?

Solution:

.

SM 12-7

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Under the circumstances described, the firm with the high fixed costs would incur lower total future costs associated with the increased sales than the firm with the low fixed costs due to the higher variable cost per unit of sales. Therefore, the firm with the high fixed costs structure would benefit the most.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.2 You own a firm with a single new product that is about to be introduced to the public for the first time. Your marketing analysis suggests that the annual demand for this product could be anywhere between 500,000 units and 5,000,000 units. Given such a wide range, discuss the safest cost structure alternative for your firm.

Solution: Since there is a great deal of variability concerning the demand for the product, then the safest alternative would be to create a cost structure that limits the variability of the firm’s EBIT. This means that you would create a cost structure that is composed of high unit variable costs with low fixed costs. Although this would not enable the firm to maximize earnings if the 5,000,000 unit forecast occurs, it limits the downside profitability for the firm in the event that the 500,000 unit forecast occurs.

LO: 1 .

SM 12-8

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.3 Discuss the interpretation of the degree of accounting operating leverage and degree of pretax cash flow operating leverage.

Solution: While the degree of accounting operating leverage is defined as: Accounting DOL = 1 + (FC + D&A) / (EBIT) it is used to interpret the percentage change in EBIT that will be driven by a given percentage change in net revenue. Similarly, the degree of pretax cash flow operating leverage is defined as: Cash Flow DOL = 1 + FC / (EBIT + D&A) but it is used to interpret the percentage change in EBITDA (or pretax operating cash flow) that will be driven by a given percentage change in net revenue.

LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

.

SM 12-9

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

12.4 Explain how EBITDA differs from incremental after-tax free cash flows (FCF) and discuss the types of businesses for which this difference would be especially small or large.

Solution: Depreciation and amortization, taxes, capital expenditures, and working capital are not reflected in EBITDA. If any of these is not equal to zero, then EBITDA is likely to differ from FCF, which is equal to EBIT(1-T) + depreciation—increases in working capital— capital expenditures. The type of businesses that require large capital expenditures (and therefore have large depreciation expenses per year) such as heavy manufacturing, are likely to have substantial differences between EBITDA and FCF. Conversely, smaller firms that have smaller capital expenditures, such as firms in retail sales, will likely have small differences between FCF and EBITDA for. Setting aside depreciation and special tax subsidies, taxes will always create a difference between EBITDA and FCF for a profitable firm.

LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

.

SM 12-10

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

12.5 Describe how the pretax operating cash flow break-even point is related to the economic break-even point.

Solution: The pre-tax operating cash flow break-even point establishes the number of units that must be sold in a given year to break even for a particular year. The economic break-even calculation looks at cash flows over the course of an entire project and tells us how many units must be sold to achieve an NPV of $0. The NPV calculation is useful when deciding whether to undertake a project in an economic sense. The cash flow break-even calculation is useful when considering whether to abandon a project or to make changes to a project’s cost structure.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.6 Is it possible to have a crossover point where the accounting break-even point is the same for two alternatives - that is, above the break-even point for a low-fixed-cost alternative but below the break-even point for a high-fixed-cost alternative? Explain.

.

SM 12-11

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: No. Above the low fixed cost break-even sales level implies that income is positive.

Below the high fixed cost break-even sales level implies that income is negative.

However, the cross-over point is defined as the sales level at which the income level for both alternatives is the same. Therefore, it cannot occur.

LO: 3 Level: Basic Bloomcode: Comrpehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.7 What is the fundamental difference between a sensitivity analysis and a scenario analysis?

Solution: A sensitivity analysis is a form of “what if” analysis that is very useful for identifying key individual assumptions in models used for financial analysis such as an NPV calculation.

Scenario analysis identifies relationships across several key individual assumptions, and is therefore a good way of estimating how project values might vary under different economic scenarios.

LO: 5 Level: Basic Bloomcode: Comprehension .

SM 12-12

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.8 The economics break-even calculation assumes that the number of units sold is the same each year during the life of the project. It is possible for the NPV of a project to be negative if unit sakes are not the same each year and the average unit sales are higher than that estimated using the economic break-even calculation.

Solution: Yes. This is possible, if, for example, actual unit sales are lower than the average in the early years of a project’s life and higher than the average in the latter years of a project’s life. This is due to the time value of money. Unit sales in early years have a greater present value than unit sales in later years.

Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.9 How does the pretax operating cash flow for a project differ from the economic profit for that project?

Solution: The pretax operating cash flow is a measure of the extent to which revenues exceed cash operating expenses. It does not account for taxes or the opportunity cost of the .

SM 12-13

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

capital that is invested in the project. Economic profit is a measure of the extent to which revenues exceed cash operating expenses, taxes, and the opportunity cost of the capital invested in a project. Economic profit accounts for all of the costs associated with producing a project’s revenue.

Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.10 What is the advantage of using a simulation analysis instead of a scenario analysis to assess the risk of a project?

Solution: Simulation analysis is like a scenario analysis except that in simulation analysis an analyst uses a computer to examine a large number of scenarios in a short period of time. This description from the text suggests that simulation analysis allows for more efficient use of the analyst’s time. In addition, since an analyst can examine a very large number of scenarios (typically in the thousands) in a simulation analysis, this analytical tool can enable the analyst to get a more complete picture of the risks associated with a project.

Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective .

SM 12-14

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Questions and Problems

BASIC 12.1

Fixed and variable costs:Define variable costsand fixed costs , and give an example of each.

Solution: Fixed costs are costs that in the short term cannot be changed regardless of how much output the project produces. One example is the in-home technical computer support business (discussed in Learning by Doing Application 12.1). Regardless of the number of house calls the technical support firm makes, it will incur the full cost of advertising.

Variable costs are costs that depend on the number of units of output produced by the project. An example is the gas that the technical support firm uses to make house calls.

The cost to keep the vehicles gassed up is directly related to the number of service calls the firm makes.

LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

.

SM 12-15

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

12.2 EBIT: Describe the role that the mix of variable versus fixed costs has in the variation of earnings before interest and taxes (EBIT) for the firm.

Solution: By definition, variable costs do not occur unless matching sales or matching revenues also occur, whereas fixed costs are not a function of the level of sales. Therefore, a large mix of fixed costs within a firm’s cost structure will make the firm’s EBIT very reactive to a change in the level of sales for the firm. The greater the proportion of fixed costs, (compared to variable costs), the greater the variability in EBIT for the firm. LO 1

Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.3 EBIT: The Generic Publications Textbook Company sells all of its books for $100 per book, and it currently costs $50 in variable costs to produce each text. The fixed costs, which include depreciation and amortization for the firm, are currently $2 million per year. The firm is considering changing its production technology, which will increase the fixed costs for the firm by 50 percent but decrease the variable costs per unit by 50 percent. If the firm expects to sell 45,000 books next year, should the firm switch technologies?

.

SM 12-16

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

Solution: The current EBIT for the firm is: Revenue

$100 per book × 45,000 books

=

$4,500,000

VC

$50 per book × 45,000 books

=

2,250,000

FC + D&A

2,000,000

EBIT

$250,000

If the fixed costs increase by 50 percent, then they will be $2,000,000 × 1.5 = $3,000,000, while the unit variable costs would be 0.5 × $50 = $25.

The new EBIT for the firm would then be: Revenue

$100 per book × 45,000 books

=

$4,500,000

VC

$25 per book × 45,000 books

=

1,125,000

FC + D&A EBIT

3,000,000 $ 375,000

Since the EBIT after the technology change is $125,000 higher, the firm should adopt the new production technology.

LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.4 EBIT: WalkAbout Kangaroo Shoe Stores forecasts that it will sell 9,500 pairs of shoes next year. The firm buys its shoes for $50 per pair from the wholesaler and sells them for .

SM 12-17

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

$75 per pair. If the firm will incur fixed costs plus depreciation and amortization of $100,000, then what is the percent increase in EBIT if the actual sales next year equal 11,500 pairs of shoes instead of 9,500?

Solution: The forecasted EBIT for the firm is: Revenue

$75 per pair × 9,500 pairs

=

$712,500

VC

$50 per pair × 9,500 pairs

=

475,000

FC + D&A

100,000

EBIT

$137,500

The actual EBIT for the firm is: Revenue

$75 per pair × 11,500 pairs

=

$862,500

VC

$50 per pair × 11,500 pairs

=

575,000

FC + D&A

100,000

EBIT

$187,500

Therefore, the percent increase in EBIT would be ($187,500 – $137,500) / $137,500 = 0.3636 = 36.36%.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

.

SM 12-18

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

12.5 Cash Flow DOL: The law firm of Dewey, Cheatem, and Howe has monthly fixed costs of $100,000, EBIT of $250,000, and depreciation charges on its office furniture and computers of $5,000. Calculate the Cash Flow DOL for this firm.

Solution:

CashFlowDOL=1+

$100,000 FC EBITDA =1+ $250,000+$5,000 =1.392

LO 2

12.6. Cash Flow DOL: The degree of pretax cash flow operating leverage at Rackit Corporation is 2.7 when it sells 100,000 units of its new tennis racket and its EBITDA is $95,000. Ignoring the effects of taxes, what are the fixed costs for Rackit Corporation?

Solution: Cash Flow DOL = 1 + FC/EBITDA 2.7 = 1 + FC / ($95,000) FC = $161,500 LO 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

.

SM 12-19

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

12.7 Accounting DOL: Explain how the value of accounting operating leverage can be used.

Solution: Accounting operating leverage gives us the ratio by which the firm can convert revenues into EBIT. That is, if the firm’s operating leverage is 3, then a 15 percent increase will convert to a 45 percent (15% x 3) increase in EBIT for the firm.

LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.8 Accounting DOL: Caterpillar, Inc. is a manufacturer of large earth-moving and mining equipment. This firm, and other heavy equipment manufacturers, have accounting degrees of operating leverage that are relatively high. Explain why.

Solution: Caterpillar and other heavy equipment manufacturers are heavily dependent on assets in place, like manufacturing equipment and facilities, for production. These investments result in relatively high fixed costs compared to variable costs of production, leading to a high degree of operating leverage. To illustrate, in 2009, CAT saw a 37% decrease in revenue and an 88% drop in operating income relative to their 2008 results. However, .

SM 12-20

Fundamentals of Corporate Finance, 4th edition

Solutions Manual

for the third quarter of 2010, CAT saw a 53% increase in sales and a 329% jump in operating profit.

LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.9

Break-even analysis:Why is the per-unit contribution important in a break-even analysis?

Solution: Per-unit contribution is critical to break-even analysis in order for a firm to determine how many units are required to be sold to cover the firm’s fixed costs. The underlying known variable is the dollar amount of the contribution margin the firm will generate from each unit sold in order to make the above calculation.

EBITDA Break-even = FC / (Price – Unit VC) and EBIT break-even = (FC + D&A) / (Price – Unit VC) demonstrate the calculation for EBITDA and EBIT break-even points respectively. The term in the denominator (Price-Unit VC) represents the per-unit cash flow contribution.

LO 3 Bloomcode: Comprehension .

SM 12-21