A machine will cost $28 000. It is estimated that it will generate $8000 in after-tax savings each year during its five-year life. What is the profitability index assuming a hurdle rate of 10 per cent?

Question

Quizplus · Accepted Answer

The profitability index (PI) is calculated by dividing the present value (PV) of future cash flows by the initial investment. Here, the future cash flows are the annual savings of $8000 over 5 years. Using a discount rate (hurdle rate) of 10%, the PV of future cash flows can be calculated using the formula for the present value of an annuity: PV = P * [(1 - (1 + r)^-n) / r], where P is the annual payment, r is the annual interest rate, and n is the number of periods. Substituting the given values: PV = 8000 * [(1 - (1 + 0.1)^-5) / 0.1] ≈ $30,244. The profitability index is then: PI = PV of future cash flows / Initial Investment = $30,244 / $28,000 ≈ 1.08.

A Machine Will Cost $28 000