Question

Peter wants to buy a computer which he expects to save him $4000 each year in bookkeeping costs. The computer will last for five years and will have no salvage value. If Peter's required rate of return is 12%, what is the maximum price Peter should be willing to pay for the computer?

1) $20,000
2) $14,420
3) $11,340
4) $10,830

Answer 1

The maximum price Peter should pay for the computer, according to a present value calculation of an annuity with a 12% rate of return over 5 years, is $13,586.20. Option 3, $11,340, is the highest amount he should pay without exceeding the calculated present value.

Step-by-step explanation:

The maximum price Peter should be willing to pay for the computer is calculated using the concept of the present value of a series of cash flows. In this case, we need to find the present value of $4000 each year for five years at Peter's required rate of return of 12%. The formula for present value (PV) of an annuity (series of equal payments) is:

PV = Pmt × [(1 - (1 + r)^{-n}) / r]

Where Pmt is the annual payment ($4000), r is the interest rate (12% or 0.12), and n is the number of periods (5 years).

Substituting the values in:

PV = $4000 × [(1 - (1 + 0.12)^{-5}) / 0.12]

Calculating this, we get:

PV = $4000 × [(1 - (1 + 0.12)^{-5}) / 0.12] = $13,586.20

So, the maximum price Peter should be willing to pay for the computer based on his required rate of return is $13,586.20. Among the options provided, the closest one without going over is option 3) $11,340.