Corporate_Finance_9th_edition_Solutions_Manual_FINAL0

# The equation for the npv of the project is npv 0

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Unformatted text preview: ompany still has in the project. To calculate the aftertax salvage value, we first need the book value of the equipment. The book value at the end of the five years will be the purchase price, minus the total depreciation. So, the ending book value is: Ending book value = \$18,000,000 – (\$2,574,000 + 4,410,000 + 3,150,000 + 2,250,000 + 1,602,000) Ending book value = \$4,014,000 171 The market value of the used equipment is 20 percent of the purchase price, or \$3.6 million, so the aftertax salvage value will be: Aftertax salvage value = \$3,600,000 + (\$4,014,000 – 3,600,000)(.35) Aftertax salvage value = \$3,744,900 The aftertax salvage value is included in the total cash flows are capital spending. Now we have all of the cash flows for the project. The NPV of the project is: NPV = –\$19,500,000 + \$4,911,400/1.18 + \$5,112,000/1.182 + \$7,605,750/1.183 + \$7,037,250/1.184 + \$10,989,350/1.185 NPV = \$1,395,937.88 And the IRR is: NPV = 0 = –\$19,500,000 + \$4,911,400/(1 + IRR) + \$5,112,000/(1 + IRR)2 + \$7,605,750/(1 + IRR)3 + \$7,037,250/(1 + IRR)4 + \$10,989,350/(1 + IRR)5 IRR = 20.72% We should accept the project. 29. To find the initial pretax cost savings necessary to buy the new machine, we should use the tax shield approach to find the OCF. We begin by calculating the depreciation each year using the MACRS depreciation schedule. The depreciation each year is: D1 = \$540,000(0.3330) = \$179,820 D2 = \$540,000(0.4440) = \$237,760 D3 = \$540,000(0.1480) = \$79,920 D4 = \$540,000(0.0740) = \$39,960 Using the tax shield approach, the OCF each year is: OCF1 = (S – C)(1 – 0.35) + 0.35(\$179,820) OCF2 = (S – C)(1 – 0.35) + 0.35(\$237,760) OCF3 = (S – C)(1 – 0.35) + 0.35(\$79,920) OCF4 = (S – C)(1 – 0.35) + 0.35(\$39,960) OCF5 = (S – C)(1 – 0.35) Now we need the aftertax salvage value of the equipment. The aftertax salvage value is: After-tax salvage value = \$50,000(1 – 0.35) = \$32,500 To find the necessary cost reduction, we must realize that we can split the cash flows each year. The OCF in any given year is the cost reduction (S – C) times one minus the tax rate, which is an annuity for the project life, and the depreciation tax shield. To calculate the necessary cost reduction, we would require a zero NPV. The equation for the NPV of the project is: NPV = 0 = – \$540,000 – 45,000 + (S – C)(0.65)(PVIFA12%,5) + 0.35(\$179,820/1.12 + \$237,760/1.122 + \$79,920/1.123 + \$39,960/1.124) + (\$45,000 + 32,500)/1.125 172 Solving this equation for the sales minus costs, we get: (S – C)(0.65)(PVIFA12%,5) = \$389,135.07 (S – C) = \$166,076.70 30. To find the bid price, we need to calculate all other cash flows for the project, and then solve for the bid price. The aftertax salvage value of the equipment is: Aftertax salvage value = \$60,000(1 – 0.35) = \$39,000 Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the NPV of the project is: NPV = 0 = – \$830,000 – 75,000 + OCF(PVIFA14%,5) + [(\$75,000 + 39,000) / 1.145] Solving for the OCF, we find the OCF that makes the project NPV equal to zero is: OCF = \$845,791.97 / PVIFA14%,5 = \$246,365.29 The easiest way to calculate the bid price is the tax shield approach, so: OCF = \$246,365.29 = [(P – v)Q – FC ](1 – tc) + tcD \$246,365.29 = [(P – \$8.50)(130,000) – \$210,000 ](1 – 0.35) + 0.35(\$830,000/5) P = \$12.34 31. a. This problem is basically the same as the previous problem, except that we are given a sales price. The cash flow at Time 0 for all three parts of this question will be: Capital spending Change in NWC Total cash flow –\$830,000 –75,000 –\$905,000 We will use the initial cash flow and the salvage value we already found in that problem. Using the bottom up approach to calculating the OCF, we get: Assume price per unit = \$14 and units/year = 130,000 Year 1 2 3 Sales \$1,820,000 \$1,820,000 \$1,820,000 Variable costs 1,105,000 1,105,000 1,105,000 Fixed costs 210,000 210,000 210,000 Depreciation 166,000 166,000 166,000 EBIT \$339,000 \$339,000 \$339,000 Taxes (35%) 118,650 118,650 118,650 Net Income \$220,350 \$220,350 \$220,350 Depreciation 166,000 166,000 166,000 Operating CF \$386,350 \$386,350 \$386,350 4 \$1,820,000 1,105,000 210,000 166,000 \$339,000 118,650 \$220,350 166,000 \$386,350 5 \$1,820,000 1,105,000 210,000 166,000 \$339,000 118,650 \$220,350 166,000 \$386,350 173 Year Operating CF Change in NWC Capital spending Total CF 1 \$386,350 0 0 \$386,350 2 \$386,350 0 0 \$386,350 3 \$386,350 0 0 \$386,350 4 \$386,350 0 0 \$386,350 5 \$386,350 75,000 39,000 \$500,350 With these cash flows, the NPV of the project is: NPV = – \$830,000 – 75,000 + \$386,350(PVIFA14%,5) + [(\$75,000 + 39,000) / 1.145] NPV = \$480,578.86 If the actual price is above the bid price that results in a zero NPV, the project will have a positive NPV. As for the cartons sold, if the number of cartons sold increases, the NPV will increase, and if the costs increase, the NPV will decrease. b. To find the minimum number of cartons sold to still breakeven, we need to use the tax shield approach to calculating OCF, and solve the problem similar to finding a bid price. Using the initial cash flow and salvage value we already calculated, the equation for a zero NPV of the project is: NPV = 0 = – \$830,000 – 75,000...
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## This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of Texas-Tyler.

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