Question

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.

Answer 1

A) $83

Step-by-step 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