Profitability index

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Mathematical economic formula

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Profitability index (PI), also known as profit investment ratio (PIR) and value investment ratio (VIR), is the ratio of payoff to investment of a proposed project. It is a useful tool for ranking projects because it allows you to quantify the amount of value created per unit of investment. Under capital rationing, PI method is suitable because PI method indicates relative figure i.e. ratio instead of absolute figure.

The ratio is calculated as follows:

${\text{Profitability index}}={\frac {\text{PV of future cash flows}}{\text{Initial investment}}}=1+{\frac {\text{NPV}}{\text{Initial investment}}}$

Assuming that the cash flow calculated does not include the investment made in the project, a profitability index of 1 indicates break-even. Any value lower than one would indicate that the project's present value (PV) is less than the initial investment. As the value of the profitability index increases, so does the financial attractiveness of the proposed project.

The PI is similar to the Return on Investment (ROI), except that the net profit is discounted.

Example

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We assume an investment opportunity with the following characteristics:

Investment = $40,000
Life of the Machine = 5 Years

CFAT Year CFAT 1 18000 2 12000 3 10000 4 9000 5 6000

Calculate Net present value at 6% and PI:

Year CFAT PV@10% PV 1 18000 0.909 16362 2 12000 0.827 9924 3 10000 0.752 7520 4 9000 0.683 6147 5 6000 0.621 3726 Total present value 43679 (-) Investment 40000 NPV 3679 PI = 43679/40000 = 1.092 > 1 = Accept the project