BUAD 306 Fall 2015 Professor Kenneth Ahern Practice Problems 5 Answers 1 An asset used in a four year project falls in the seven year MACRS class for tax purposes The asset has an acquisition cost of 9 000 000 and will be sold for 4 000 000 at the end of the project If the tax rate is 35 percent what is the aftertax salvage value of the asset Year 1 2 3 4 5 6 7 8 MACRS DEPRECIATION ALLOWANCES Three Year Five Year Seven Year 33 33 20 00 14 29 44 45 32 00 24 49 14 81 19 20 17 49 7 41 11 52 12 49 11 52 8 93 5 76 8 92 8 93 4 46 ANSWER To find the BV at the end of four years we need to find the accumulated depreciation for the first four years We 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 BV4 9 000 000 9 000 000 0 1429 0 2449 0 1749 0 1249 BV4 2 811 600 The asset is sold at a gain to book value so this gain is taxable Aftertax salvage value 4 000 000 4 000 000 2 811 600 35 Aftertax salvage value 3 584 060 2 In the context of capital budgeting describe what an opportunity cost is and give an example ANSWER An opportunity cost is the value of the next best alternative use It is the value foregone by using an asset in a project For example if a firm uses land to build a factory the opportunity cost of the land is the market value of the land 3 Johnson Controls Inc is considering a new three year expansion project that requires an initial fixed asset investment of 2 7 million The fixed asset will be depreciated straight line to zero over its three year tax life after which time it will be worthless The project is estimated to generate 2 080 000 in annual sales with costs of 775 000 If the tax rate is 35 percent what is the OCF for this project ANSWER OCF Sales Costs 1 T T Depreciation OCF 2 080 000 775 000 1 0 35 0 35 2 700 000 3 OCF 1 163 250 4 Suppose the required return on the project is 12 percent What is the project s NPV ANSWER Since we have the OCF we can find the NPV as the initial cash outlay plus the PV of the OCFs which are an annuity so the NPV is NPV 2 700 000 1 163 250 PVIFA12 3 NPV 93 930 22 5 XYZ Corp is considering a four year project to improve its production efficiency Buying a new machine press for 470 000 is estimated to result in 190 000 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 80 000 The press requires an initial investment in spare parts inventory of 20 000 along with an additional 2 500 in inventory for each succeeding year of the project If the tax rate is 35 and its discount rate is 9 should the company buy and install the machine press ANSWER First we will calculate the depreciation each year which will be D1 470 000 0 2000 94 000 D2 470 000 0 3200 150 400 D3 470 000 0 1920 90 240 D4 470 000 0 1152 54 144 The book value of the equipment at the end of the project is BV4 470 000 94 000 150 400 90 240 54 144 81 216 The asset is sold at a loss to book value so this creates a tax refund After tax salvage value 80 000 81 216 80 000 0 35 80 425 60 So the OCF for each year will be OCF1 190 000 1 0 35 0 35 94 000 156 400 OCF2 190 000 1 0 35 0 35 150 400 176 140 OCF3 190 000 1 0 35 0 35 90 240 155 084 OCF4 190 000 1 0 35 0 35 54 144 142 450 40 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 20 000 of NWC at the beginning and 2 500 more in NWC each successive year We will subtract the 20 000 from the initial cash flow and subtract 2 500 each year from the OCF to account for this spending In Year 4 we will add back the total spent on NWC which is 27 500 The 2 500 spent on NWC capital during Year 4 is irrelevant Why Well during this year the project required an additional 2 500 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 470 000 20 000 156 400 2 500 1 09 176 140 2 500 1 092 155 084 2 500 1 093 142 450 40 27 500 80 425 60 1 09 4 NPV 92 537 49 6 You are considering whether compact fluorescent lamps CFLs are better than incandescent lightbulbs Suppose a typical 60 watt incandescent lightbulb costs 0 45 and lasts for 1 000 hours A 15 watt CFL which provides the same light costs 3 40 and lasts for 12 000 hours A kilowatt hour of electricity costs 0 121 A kilowatt hour is 1 000 watts for 1 hour If you require a 10 percent return and use a light fixture 500 hours per year what is the equivalent annual cost of each lightbulb Which one is a better value ANSWER A kilowatt hour is 1 000 watts for 1 hour A 60 watt bulb burning for 500 hours per year uses 30 000 watt hours or 30 kilowatt hours Since the cost of a kilowatt hour is 0 121 the cost per year is Cost per year 30 0 121 Cost per year 3 63 The 60 watt bulb will last for 1 000 hours which is two years of use at 500 hours per year So the NPV of the 60 watt bulb is NPV 0 45 3 63 PVIFA10 2 NPV 6 75 And the EAC is EAC 6 75 PVIFA10 2 EAC 3 89 Now we can find the EAC for the 15 watt CFL A 15 watt bulb burning for 500 hours per year uses 7 500 watts or 7 5 kilowatts And since the cost of a kilowatt hour is 0 121 the cost per year is Cost per year 7 5 0 121 Cost per year 0 9075 The 15 watt CFL will last for 12 000 hours which is 24 years of use at 500 hours per year So the NPV of the CFL is NPV 3 40 0 9075 …