Suppose a machine generates $500 worth of revenue at the end of each of the next three years, at which time it can be sold to a salvage company for $350. If the annual rate of interest is 0.08, what is the maximum amount a business would pay for this machine if maintenance costs are $100 per year?

Question

Quizplus · Accepted Answer

We can use the formula for the present value of an annuity:

PV = CF/(1+r) + CF/(1+r)^2 + CF/(1+r)^3 + Resale Value/(1+r)^3

where CF is the cash flow, r is the annual rate of interest, and Resale Value is the salvage value of the machine.

Substituting the given values, we get:

PV = 500/(1+0.08) + 500/(1+0.08)^2 + 500/(1+0.08)^3 + 350/(1+0.08)^3
PV = 1309.43

However, we also need to subtract the maintenance costs of $100 per year for three years:

PV = 1309.43 - 100/(1+0.08) - 100/(1+0.08)^2 - 100/(1+0.08)^3
PV = 958.68

So the maximum amount a business would pay for this machine is $958.68, which is closest to option B.

Suppose a Machine Generates $500 Worth of Revenue at the End