In evaluating a project using the profitability index (PI), which of the following is a correct representation of PI and its acceptance criterion?

In evaluating a project using the profitability index (PI), which of the following is a correct representation of PI and its acceptance criterion?

• A. PI = NPV / initial investment; accept if PI > 1
• B. PI = PV of future cash flows / initial investment; accept if PI > 0
• C. PI = PV of future cash flows / initial investment; accept if PI > 1
• D. PI = PV of future cash flows - initial investment; accept if PI > 1

Answer: (C)

Profitability index shows how much value is created for each dollar invested. It is defined as the present value of the future cash inflows divided by the initial investment, with discounting at the project’s cost of capital. You accept a project when this ratio exceeds 1 because that means the present value of inflows is greater than the upfront cost, i.e., the project adds value and NPV is positive. If the PI is exactly 1, NPV is zero; if it’s less than 1, the project would destroy value. The other representations don’t match the standard definition or decision rule. Using NPV divided by the initial investment isn’t the usual PI and would lead to a different interpretation. Requiring PI > 0 would accept any positive ratio, even if the inflows barely cover the investment. Subtracting the initial investment in the numerator yields a difference rather than a ratio, which again changes the meaning and the acceptance threshold.

Profitability index shows how much value is created for each dollar invested. It is defined as the present value of the future cash inflows divided by the initial investment, with discounting at the project’s cost of capital. You accept a project when this ratio exceeds 1 because that means the present value of inflows is greater than the upfront cost, i.e., the project adds value and NPV is positive. If the PI is exactly 1, NPV is zero; if it’s less than 1, the project would destroy value.

The other representations don’t match the standard definition or decision rule. Using NPV divided by the initial investment isn’t the usual PI and would lead to a different interpretation. Requiring PI > 0 would accept any positive ratio, even if the inflows barely cover the investment. Subtracting the initial investment in the numerator yields a difference rather than a ratio, which again changes the meaning and the acceptance threshold.