Questions-Making Capital Investment Decision

Q1) Massey Machine Shop is considering a four-year project to improve its production efficiency. Buying a new machine press for $480,000 is estimated to result in $195,000 in annual pretax cost savings. The press falls in the MACRS five-year class, and it will have a salvage value at the end of the project of $81,000. (year 1: 20%, year 2: 32%, year 3: 19.20%, year 4: 11.52%, year 5: 11.52%, year 6: 5.76%) The press also requires an initial investment in spare parts inventory of $21,000, along with an additional $2,600 in inventory for each succeeding year of the project. The shop’s tax rate is 30 percent and its discount rate is 8 percent. First, we will calculate the depreciation each year, which will be:  D1 = $480,000(.2000) = $96,000D2 = $480,000(.3200) = $153,600D3 = $480,000(.1920) = $92,160D4 = $480,000(.1152) = $55,296  The book value of the equipment at the end of the project is:  BV4 = $480,000 − ($96,000 + 153,600 + 92,160 + 55,296) = $82,944  The asset is sold at a loss to book value, so this creates a tax refund.  After-tax salvage value = $81,000 + ($82,944 − 81,000)(.30) = $81,583.20  So, the OCF for each year will be:  OCF1 = $195,000(1 − .30) + .30($96,000) = $165,300.00OCF2 = $195,000(1 − .30) + .30($153,600) = $182,580.00OCF3 = $195,000(1 − .30) + .30($92,160) = $164,148.00OCF4 = $195,000(1 − .30) + .30($55,296) = $153,088.80  Now we have all the necessary information to calculate the project NPV. We need to be careful with the NWC in this project. Notice the project requires $21,000 of NWC at the beginning, and $2,600 more in NWC each successive year. We will subtract the $21,000 from the initial cash flow and subtract $2,600 each year from the OCF to account for this spending. In Year 4, we will add back the total spent on NWC, which is $28,800. The $2,600 spent on NWC capital during Year 4 is irrelevant. Why? Well, during this year the project required an additional $2,600, but we would get the money back immediately. So, the net cash flow for additional NWC would be zero. With all this, the equation for the NPV of the project is:   NPV = −$480,000 − 21,000 + ($165,300.00 − 2,600) / 1.08 + ($182,580.00 − 2,600) / 1.082            + ($164,148.00 − 2,600) / 1.083 + ($153,088.80 + 28,800 + 81,583.20) / 1.084NPV = $125,853.79

Q2) Hagar Industrial Systems Company (HISC) is trying to decide between two different conveyor belt systems. System A costs $260,000, has a four-year life, and requires $80,000 in pretax annual operating costs. System B costs $366,000, has a six-year life, and requires $74,000 in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Whichever system is chosen, it will not be replaced when it wears out. The tax rate is 30 percent and the discount rate is 9 percent. NPV for both convertor belt systems? Both projects only have costs associated with them, not sales, so we will use these to calculate the NPV of each project. Using the tax shield approach to calculate the OCF, the NPV of System A is:  OCFA = −$80,000(1 − .30) + .30($260,000 / 4)OCFA = −$36,500.00 NPVA = −$260,000 − $36,500.00(PVIFA9%,4)NPVA = −$378,249.78 And the NPV of System B is: OCFB = −$74,000(1 − .30) + .30($366,000 / 6)OCFB = −$33,500.00 NPVB = −$366,000 − $33,500.00(PVIFA9%,6)NPVB = −$516,278.27 If the equipment will be replaced at the end of its useful life, the correct capital budgeting technique is EAC. Using the above NPVs, the EAC for each system is:    EACA = –$378,249.78 / (PVIFA9%,4)EACA = –$116,753.85 (or pv=-378,249.78, i=9, n=4, fv=0 and pmt=) EACB = – $516,278.27 / (PVIFA9%,6)EACB = –$115,088.64 If the conveyor belt system will be continually replaced, we should choose System B since it has the less negative EAC.

Q3) Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs $3,054,000 and will last for six years. Variable costs are 35 percent of sales, and fixed costs are $200,000 per year. Machine B costs $5,238,000 and will last for nine years. Variable costs for this machine are 30 percent and fixed costs are $135,000 per year. The sales for each machine will be $10.2 million per year. The required return is 10 percent and the tax rate is 35 percent. Both machines will be depreciated on a straight-line basis. The company plans to replace the machine when it wears out on a perpetual basis NPVs and EACs? OCF(A) -3,570,000 (VC)-200,000(FC)-509,000(Dep)=-4,279,000(EBT)-1,497,000(Tax)=-2,781,350(NI) => OCF=-2,2781,350+509,000(Dep)=-2,272,305 OCF(B) -3,060,000 (VC)-135,000(FC)-582,000(Dep)=-3,777,000(EBT)-1,32,950(Tax)=-2,455,050(NI) => OCF=-2,2781,350+582,000(Dep)=-1,873,050 The NPV and EAC for Machine A is: NPVA = −$3,054,000 − $2,272,350(PVIFA10%,6)NPVA = −$12,950,676.65 EACA = −$12,950,676.65 / (PVIFA10%,6)EACA = −$2,973,570.94 And the NPV and EAC for Machine B is: NPVB = −$5,238,000 − 1,873,050(PVIFA10%,9)NPVB = −$16,024,939.56 EACB = −$16,024,939.56 / (PVIFA10%,9)EACB = −$2,782,579.14 You should choose Machine B since it has a less negative EAC