A corporation is considering purchasing a machine that will save $150,000 per ye

Question

A corporation is considering purchasing a machine that will save $150,000 per year before taxes. The cost of operating the machine (including maintenance) is $30,000 per year. The machine will be needed for five years, after which it will have a zero salvage value. MACRS depreciation will be used, assuming a three-year class life. The marginal income tax rate is 40%. If the firm wants 15% return on investment after taxes, how much can it afford to pay for this machine? [use closes approximate value] Answer Choices: a. $250,000 b. $300,000 c. $350,000 d. $400,000

Explanation / Answer

Lets solve this question using the options given.

lets assume option B as right option i.e., 300,000. Now calculate cash flows as follows

In MACRS 3 year method, machine is depreciated 33.33% in year 1, 44.45% in year 2, 14.81% in year 3 and 7.41% in year 4. Machine depreciation value column are calculated using these numbers. They add upto 300,000

NPV of these cash flows calculated in excel as =NPV(15%,G2:G7) = $81,369.74

So company can afford it at this price.

lets assume option C as right option i.e., 350,000. Now calculate cash flows as follows

Cash flows are calculated as follows

NPV of these cash flows calculated in excel as =NPV(15%,G2:G7) = $51,207.60

Company can even affors machine at this price as well.

lets assume option D as right option i.e., 400,000. Now calculate cash flows as follows

Cash flows are calculated as follows

NPV of these cash flows calculated in excel as =NPV(15%,G2:G7) = $21,045.56

So company can afford this machine at this price as well.Since $400,000 is the highest value in the options we will go for it. So option D is correct.

Cash flow Tax Rate After tax Cash Flow Machine Depreciation value Depreciation Tax Shield Total net cash flows Year 0 -300000 40% -300000 0 0 -300000 Year 1 150000 40% 90000 99990 39996 129996 Year 2 150000 40% 90000 133350 53340 143340 Year 3 150000 40% 90000 44430 17772 107772 Year 4 150000 40% 90000 22230 8892 98892 Year 5 150000 40% 90000 0 0 90000

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