Question

Good Morning Food, Inc. is using the profitability index (PI) when evaluating projects. You have to find the PI for the company’s project, assuming the company’s cost of capital is 6.11 percent. The initial outlay for the project is $498,112. The project will produce the following end-of-the-year after-tax cash inflows of

Year 1: $148,444

Year 2: $92,435

Year 3: $171,330

Year 4: $436,132

Answer 1

We know that Profitability index (PI)can be computed using the following ratio:

PI = Present Value of Future Cashflow / Initial Investment

Initial Investment/outlay for the project = $498,112

Company’s cost of capital = 6.11% = 0.0611

Formula for Present Value of Future Cashflow:

Where C_T = Cashflow in the T^th Year r = Discount Rate / cost of capital

PV of Future Cashflow = ($148,444 / (1 + 0.0611)) + ($92,435 / (1 + 0.0611)²) + ($171,330 / (1 + 0.0611)³) + ($436,132 / (1 + 0.0611)⁴)

PV of Future Cashflow = ($148,444 / 1.0611) + ($92,435 / (1.0611)²) + ($171,330 / (1.0611)³) + ($436,132 / (1.0611)⁴)

PV of Future Cashflow = $139896.334 + ($92,435 / 1.12593321) + ($171,330 / 1.1947277) + ($436,132 / 1.267725)

PV of Future Cashflow = $139896.334 + $82096.3439 + $143405.0586 + $344,027.132

PV of Future Cashflow = $709,424.8685

Profitability index (PI) = $709,424.8685 / $498,112 = 1.4242 = 1.42

PI for the company’s project is 1.42

as PI > 1 the company should accept the project