Fundamentals of corporate finance 7th edition ross solutions manual

Fundamentals Of Corporate Finance 7th Edition Ross Solutions Manual Visit to download the full and correct content document: https://testbankdeal.com/dow nload/fundamentals-of-corporate-finance-7th-edition-ross-solutions-manual/

Chapter 9—Project analysis and evaluation: Solutions to questions and problems 1

Forecasting risk is the risk that a poor decision is made because of errors in projected cash flows. The danger is greatest with a new product because the cash flows are probably harder to predict.

2

NPV = −50 000 + 9 000 × PVIFA(10, 18%) = −$9 553.10

3

36 000 = (18 × Q × PVIFA(9, 18%) Q = 465 units. Should abandon if Q < or = 465 units.

4

The $36 000 is the market value of the project. If you continue the project, you forego the $36 000 that could have been used for something else.

5a

Success: PV = 750(18) × PVIFA(9, 18%) = $58 091 Failure: PV = 400(18) × PVIFA(9, 18%) = $30 981 Expected value in year 1 = (58 091 + 30 981)/2 + 9 000 = 53 536 NPV = −50 000 + 53 536/1.18 = −$4 631 Success: PV if can’t abandon = 400 ×18 × PVIFA(9, 18%) = 30 981 Gain from option to abandon = 36 000 – 30 981 = $5 019 Assuming there is an equal chance of 750 and 400: V (option) = (5 019 × 0.5)/1.18 = $2 126

b

6a b

c

Accounting break-even = (100 000 + 40 000)/(23.80 – 10.52) = 10 542 units DOL = 1 + 100 000/40 000 = 3.5 OCF[Base]= [60 000(23.80 – 10.52) – 100 000](1 – 0.30) + 40 000(0.30) = $499 760 OCF[Best] = [75 000(23.80 – 10.52) – 100 000](1 – 0.30) + 40 000(0.30) = $639 200 OCF[Worst] = [45 000(23.80 – 10.52) – 100 000](1 – 0.30) + 40 000(0.30) = $360 320 NPV = –280 000 + 499 760 × PVIFA(7, 10%) = $2 153 041 NPV best case = –280 000 + 639 200 × PVIFA(7, 10%) = $2 831 893 NPV worst case = –280 000 + 360 320 × PVIFA(7, 10%) = $1 474 189 Best case: OCF = [69 000(24.99 – 9.994)–95 000](1 – 0.30) + 40 000(0.30) = $669 545.98 NPV = $2 979 630 Worst case:

OCF = [51 000(22.61 – 11.046) – 105 000](1 – 0.30) + 40 000(0.30) = $351 334.8 NPV = $1 430 445

1 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

7a b c

VC = 0.20 + 0.60 = $0.80 TC = 0.80 (600 000) + 225 000 = $705 000 Cash break-even = 225 000/(1.25 – 0.80) = 500 000 litres Yes, since 600 000 litres are sold and the firm only needs to sell 500 000 litres. The firm is well above the break-even point on a cash basis.

Accounting break-even = (225 000 + 40 000)/(1.25 – 0.80) = 588 890 litres

8a b c d

Total cost = 15 000 × [$1.75 + $13.50] + $140 000 = $368 750.

Marginal cost = Variable cost = $1.75 + $13.50 = $15.25.

Average cost = Total cost/production = $368 750/15 000 = $24.58.

Minimum revenue = Variable cost × order = $15.25 × 500 = $7 625

9

Unit price is $5: Cash break-even = 105/(5 – 3) = 53 units Accounting break-even = (105 + 180)/(5 – 3) = 143 units The difference in the two is due to non-cash items.

Unit price is $27: Cash break-even = 17 300/(27 – 14) = 1331 units.

Accounting break-even = (17 300 + 87 000)/(27 – 14) = 8 023 units Unit price is $35 000: Cash break-even = 45 000 000/(35 000 – 28 000) = 6429 units Accounting break-even = (45 000 000 + 25 125 000)/(35 000 – 28 000) = 5 009 units.

10

% change in OCF = DOL × % change in Q = 4 × [48 000 – 40 000]/40 000% = 4 × 20% = 80% The new level of operating leverage is lower: DOL = 1 + FC/OCF Because FC/OCF becomes less.

11

DOL = 1 + FC/OCF DOL – 1 = FC/OCF OCF = FC / [DOL – 1] OCF (Q = 44 000) = 102 000/(4 − 1) = $34 000 % change in Q = [44 000 – 40 000]/40 000 = 10% % change in OCF = 4 × 10% = 40% OCF (Q = 44 000) = 34 000(1.4) = $47 600 DOL = 1 + 102 000/47 600 = 3.143

2 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

12

TC = 550 000(2.80 + 6.40) + 1 200 000 = $6 260 000 MC = 2.80 + 6.40 = $9.20 Average costs = 6 260 000/550 000 = $11.38 Minimum acceptable total revenue = 100 000(9.20) = $920 000 Marginal costs must be covered to be no worse off.

13

It is true that if average revenue is less than average cost, the firm is losing money. This much of the statement is therefore correct. At the margin, however, accepting a project with a marginal revenue in excess of its marginal cost clearly acts to increase operating cash flow.

14

At accounting break-even, net profit = 0, taxes = 0, and EBIT = 0.

OCF = EBIT + Depreciation − taxes =0+D−0 DOL = 1 + FC/OCF = 1 + FC/D

15a Depreciation b

c

= Revenue – Fixed costs = 130 200 [$41 – $30] – $820 000 =$612 200 $1 150 000 = 140 000[$P – $56] – $3 200 000 1 150 000 + 3 200 000 + 7 840 000 = 140 000P P = $87.07 $105 000 = 5 478 [$115 – $VC] – $160 000 5 478 VC = $629 970 – 160 000 – 105 000 VC = $66.62

16

FC = 17(23 000) – 218 000 = $173 000

17

0 = (50 − v ) 23 000 − $110 000 − $218 000 23 000v = $1 150 000 − $110 000 − $218 000 23 000v = $822 000 v = $35.74

18

DOL = 1 + 63 000/126 000 = 1.5  in OCF = 1.5(1/3)(126 000) = $63 000 DOL = 1 + 63 000/189 000 = 1.33

3 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

19

The option to abandon reflects our ability to reallocate assets if we find our initial estimates were too optimistic. The option to expand reflects our ability to increase cash flows from a project if we find our initial estimates were too pessimistic. Since the option to expand can increase cash flows and the option to abandon can reduce losses, failing to consider these two options will generally lead to an underestimate of a project’s NPV.

20a Scenario Base Worst Best

Units 80 68 92

c

Price $40 000 $34 000 $46 000

Fixed costs $500 000 $575 000 $425 000

Base $3 200 000 1 920 000 500 000 322 000

Worst $2 312 000 1 876 800 575 000 322 000

Best $4 232 000 1 876 800 425 000 322 000

EBIT Tax

458 000 –137 400

–461 800 +138 540

1 608 200 –482 460

Profit

$320 600

–$323 260

$1 125 740

Cash flow NPV

$642 600 $387 625

–$1 260 –$968 654

$1 447 740 $2 083 638

Sales Variable costs Fixed costs Depreciation

b

Variable costs $24 000 $27 600 $20 400

Sensitivity of the base case to fixed cost changes.

Fixed costs

$500 000

$575 000

$425 000

EBIT Tax Depreciation

458 000 –137 400 322 000

383 000 –114 900 322 000

533 000 –159 900 322 000

Cash flow NPV NPV changes per $ fixed cost

$642 600 $387 637

$590 100 $277 035

$695 100 $498 215

–$1.475

1.475

Cash break-even = 500 000/(40 000 – 24 000) = 32 units 4 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

d

Accounting break-even = (500 000 + 322 000)/(40 000 – 24 000) = 52 units DOL = 1 + 500 000/642 600 = 1.778 For each 1% increase in unit sales, OCF will increase by 1.778%.

21

Accounting break-even is unaffected (taxes are zero at that point).

Cash break-even is lower (assuming a tax credit).

Financial break-even will be higher (because of taxes paid).

22a OCF = EBIT + D − Taxes = [(P − v)Q − FC − D] + D − Taxes = [(P − v)Q − FC − D] + D − [(P − v)Q − FC − D]T = [(P − v)Q − FC] (1 − T) + DT (P − v)Q − FC = (OCF − DT)/(1 − T) (P − v)Q = FC + (OCF − Dt)/(1 − T) Q = FC + (OCF − DT)/(1 − T)/(P − v) b c

23

Accounting break-even = {500 000 + [700 000 – 700 000(0.30)]/(1 − 0.30)}/20 000 = 60 units Since, at the accounting break-even, OCF = D: Q = [FC + (OCF − T × D)/(1 − T)]/(P − v) = [FC + (OCF − T × OCF)/(1 − T)]/(P − v) = [FC + OCF × (1 − T)/(1 − T)]/(P − v) = (FC + OCF)/(P − v) which is not affected by the tax rate.

DOL

= (P − v)(1 − T)Q/OCF = [OCF + FC(1 − T) − DT]/OCF = 1 + [FC(1 − T) − DT]/OCF The tax rate has an inverse effect on DOL. SOLUTIONS TO MINICASE 1 Here we want to examine the sensitivity of NPV to changes in the price of the new PDA. The calculations for sensitivity to changes in price are similar to the original cash flows. The only difference is that we will change the price of the PDA. We will use a price of $370 per unit, but remember that the price we choose is irrelevant: the final answer we want, the sensitivity of NPV to a one dollar change in price, will be the same no matter what price we use. The projections with the new prices are: The sales figure for the first two years will be the sales of the new PDA, minus the lost sales of the existing PDA, minus the lost dollar sales from the price reduction of the existing PDA, or: Sales = New sales – Lost sales – Lost revenue Year 1 sales = (74 000 × $370) – (15 000 × $290) – [(80 000 – 15 000) × ($290 – 255)] Year 1 sales = $20 755 000 Year 2 sales = (95 000 × $370) – (15 000 × $290) – [(60 000 – 15 000) × ($290 – 255)] Year 2 sales = $29 225 000 5 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

Sales New Lost sales Lost revenue Net sales VC New Lost sales

Year 1 $27 380 000 4 350 000 2 275 000 $20 755 000

Year 2 $35 150 000 4 350 000 1 575 000 $29 225 000

Year 3 $46 250 000

Year 4 $38 850 000

Year 5 $29 600 000

$46 250 000

$38 850 000

$29 600 000

$11 470 000 1 800 000 $9 670 000

$14 725 000 1 800 000 $12 925 000

$19 375 000

$16 275 000

$12 400 000

$19 375 000

$16 275 000

$12 400 000

Sales VC Fixed costs Depreciation EBT Tax NI + Depreciation OCF

$20 755 000 9 670 000 4 700 000 3 072 350 $3 312 650 1 159 428 $2 153 223 3 072 350 $5 225 573

$29 225 000 12 925 000 4 700 000 5 265 350 $6 334 650 2 217 128 $4 117 523 5 265 350 $9 382 873

$46 250 000 19 375 000 4 700 000 3 760 350 $18 414 650 6 445 128 $11 969 523 3 760 350 $15 729 873

$38 850 000 16 275 000 4 700 000 2 685 350 $15 189 650 5 316 378 $9 873 273 2 685 350 $12 558 623

$29 600 000 12 400 000 4 700 000 1 919 950 $10 580 050 3 703 018 $6 877 033 1 919 950 $8 796 983

NWC Beg End NWC CF

$0 4 151 000 –$4 151 000

$4 151 000 5 845 000 –$1 694 000

$5 845 000 9 250 000 –$3 405 000

$9 250 000 7 770 000 $1 480 000

$7 770 000 0 $7 770 000

Net CF

$1 074 573

$7 688 873

$12 324 873

$14 038 623

$16 566 983

BV of equipment = ($21 500 000 – 3 072 500 – 5 265 350 – 3 760 350 – 2 685 350 – 1 919 950) BV of equipment = $4 796 650 Taxes on sale of equipment = (BV – MV)(tC) = (4 796 650 – 4 100 000)(.35) = $243 828 CF on sale of equipment = $4 100 000 + 243 828 = $4 343 828

6 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

So the cash flows of the project under this price assumption are: Time Cash flow 0 –$21 500 000 1 1 074 573 2 7 688 873 3 12 324 873 4 14 038 623 5 20 910 810

The NPV with this sales price is: NPV = –$21 500 000 + $1 074 573/1.12 + $7 688 873/1.122 + $12 324 873/1.123 +$14 038 623/1.124 + $20 910 810/1.125 NPV = $15 148 716.18 And the sensitivity of changes in the NPV to changes in the price is: ΔNPV/ΔP = ($15 148 716.18 – 12 983 611.62)/($370 – 360) ΔNPV/ΔP = $216 510.46 For every dollar change in price of the new PDA, the NPV of the project changes $216 510.46 in the same direction.

2

Here we want to examine the sensitivity of NPV to changes in the quantity sold. The calculations for sensitivity to changes in quantity are similar to the original cash flows. The only difference is that we will change the quantity sold of the new PDA. We will increase unit sold by 100 units per year.

Remember that the quantity we choose is irrelevant: The final answer we want, the sensitivity of NPV to a one unit per year change in sales. The projections with the quantity are: The sales figure for the first two years will be the sales of the new PDA, minus the lost sales of the existing PDA, minus the lost dollar sales from the price reduction of the existing PDA, or: Sales = New sales – Lost sales – Lost revenue Year 1 sales = (74 100 × $360) – (15 000 × $290) – [(80 000 – 15 000) × ($290 – 255)] Year 1 sales = $20 051 000 Year 2 sales = (95 100 × $360) – (15 000 × $290) – [(60 000 – 15 000) × ($290 – 255)] Year 2 sales = $28 311 000 Note the variable costs must also be increased to account for additional units sold.

7 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

Sales New Lost sales Lost revenue Net sales

Year 1 $26 676 000 4 350 000 2 275 000 $20 051 000

Year 2 $34 236 000 4 350 000 1 575 000 $28 311 000

Year 3 $45 036 000

Year 4 $37 836 000

Year 5 $28 836 000

$45 036 000

$37 836 000

$28 836 000

$11 485 500 1 800 000 $9 685 500

$14 740 500 1 800 000 $12 940 500

$19 390 500

$16 290 500

$12 415 500

$19 390 500

$16 290 500

$12 415 500

Sales VC Fixed costs Depreciation EBT Tax NI + Depreciation OCF

$20 051 000 9 685 500 4 700 000 3 072 350 $2 593 150 907 603 $1 685 548 3 072 350 $4 757 898

$28 311 000 12 940 500 4 700 000 5 265 350 $5 405 150 1 891 803 $3 513 348 5 265 350 $8 778 698

$45 036 000 19 390 500 4 700 000 3 760 350 $17 185 150 6 014 803 $11 170 348 3 760 350 $14 930 698

$37 836 000 16 290 500 4 700 000 2 685 350 $14 160 150 4 956 053 $9 204 098 2 685 350 $11 889 448

$28 836 000 12 415 500 4 700 000 1 919 950 $9 800 550 3 430 193 $6 370 358 1 919 950 $8 290 308

NWC Beg End NWC CF

$0 4 010 200 –$4 010 200

$4 010 200 5 662 200 –$1 652 000

$5 662 200 9 007 200 –$3 345 000

$9 007 200 7 567 200 $1 440 000

$7 567 200 0 $7 567 200

Net CF

$747 698

$7 126 698

$11 585 698

$13 329 448

$15 857 508

VC New Lost sales

BV of equipment = ($21 500 000 – 3 072 500 – 5 265 350 – 3 760 350 – 2 685 350 – 1 919 950) BV of equipment = $4 796 650 Taxes on sale of equipment = (BV – MV)(tC) = (4 796 650 – 4 100 000)(.35) = $243 828 CF on sale of equipment = $4 100 000 + 243 828 = $4 343 828

8 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd

So, the cash flows of the project under this quantity assumption are: Time 0 1 2 3 4 5

Cash flow –$21 500 000 747 698 7 126 698 11 585 698 13 329 448 20 201 335

The NPV under this assumption is: NPV = –$21 500 000 + $747 698/1.12 + $7 126 698/1.122 + $11 585 698/1.123 +$13 329 448/1.124 + $20 201 335/1.125 NPV = $13 029 302.17 So the sensitivity of NPV to units sold is: ΔNPV/ΔQ = ($13 029 302.17 – 12 983 611.62)/100 ΔNPV/ΔQ = $456.91 For a one unit per year change in quantity sold of the new PDA, the NPV of the project changes $456.91 in the same direction.

9 Solutions manual t/a Fundamentals of Corporate Finance 7e, Ross et al Copyright © 2016 McGraw-Hill Education (Australia) Pty Ltd