Consider a $10,000 machine that will reduce pretax operating costs by $3,000 per year over a 5-year period. assume no changes in net working capital and a zero scrap value after five years. for simplicity, assume straight-line depreciation to zero, a marginal tax rate of 34 percent, and a required return of 10 percent. the net present value of acquiring this machine is: a) $83.b) $449.c) $689.d) $827.e) $1,235.

A) $83

Explanation:

First, find aftertax OCF per year

aftertax OCF = (Operating benefit - depreciation)*(1-tax) +depreciation

Depreciation per year = 10,000/5 = 2,000

Tax = 34%

aftertax OCF per year = (3,000 - 2,000)*(1-0.34) + 2,000

= 660 +2,000

= 2,660

Next, find the PV of the aftertax OCF per year. It is an annuity;

PMT = 2,660

N = 5

I/Y = 10%

FV = 0

then CPT PV = 10,083.493

Subtract the initial cost of the machine to find the Net Present Value (NPV);

NPV = -$10,000 + $10,083.493

NPV = $83.493

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