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So, the book value of the equipment at the end of three years, which will be the initial investment minus the accumulated depreciation, is: Book value in 3 years = $3,950,000 –($1,316,535 + 1,755,775 + 584,995) Book value in 3 years = $292,695 The asset is sold at a gain to book value, so this gain is taxable. Aftertax salvage value = $575,000 + ($292,695 –575,000)(.35) Aftertax salvage value = $476,193
CHAPTER 8 B-198 To calculate the OCF, we will use the tax shield approach, so the cash flow each year is: OCF = (Sales –Costs)(1 –tC) + tCDepreciation Year Cash Flow 0 –$4,400,000 = –$3,950,000 –450,000 1 1,578,787 = $1,720,000(.65) + .35($1,316,535) 2 1,732,521 = $1,720,000(.65) + .35($1,755,775) 3 2,248,942 = $1,837,500(.65) + .35($584,995) + $450,000 + 476,193 Remember to include the NWC cost in Year 0, and the recovery of the NWC at the end of the project. The NPV of the project with these assumptions is: NPV = –$4,400,000 + ($1,578,787/1.10) + ($1,732,521/1.102) + ($2,248,942/1.103) NPV = $156,759.92 6. First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation charge = $625,000/5 Annual depreciation charge = $125,000 The aftertax salvage value of the equipment is: Aftertax salvage value = $60,000(1 –.35) Aftertax salvage value = $39,000 Using the tax shield approach, the OCF is: OCF = $235,000(1 –.35) + .35($125,000) OCF = $196,500 Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is: NPV = 0 = –$625,000 + 55,000 + 196,500(PVIFAIRR%,5) + [($39,000 –55,000)/(1 + IRR)5] IRR = 20.90% 7.First, we will calculate the annual depreciation of the new equipment. It will be: Annual depreciation = $267,000/5 Annual depreciation = $53,400 Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so: Aftertax salvage value = MV + (BV –MV)tc
CHAPTER 8 B - 199 Very often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes: Aftertax salvage value = MV + (0 –MV)tcAftertax salvage value = MV(1 –tc) We will use this equation to find the aftertax salvage value since we know the book value is zero. So, the aftertax salvage value is: Aftertax salvage value = $30,000(1 –.34) Aftertax salvage value = $19,800 Using the tax shield approach, we find the OCF for the project is: OCF = $87,000(1 –.34) + .34($53,400) OCF = $75,576 Now we can find the project NPV. Notice that we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value. NPV = –$267,000 –11,000 + 75,576(PVIFA10%,5) + [($19,800 + 11,000)/1.105] NPV = $27,616.88 8.To find the BV at the end of four years, we need to find the accumulated depreciation for the first four years. We could calculate a table with the depreciation each year, but an easier way is to add the MACRS depreciation amounts for each of the first four years and multiply this percentage times the cost of the asset. We can then subtract this from the asset cost. Doing so, we get: BV