 # Profitability Index, PI By Yuriy Smirnov Ph.D.

## Definition

The profitability index (PI) is one of the methods used in capital budgeting for project valuation. In itself it is a modification of the net present value (NPV) method. The difference between them is that the NPV is an absolute measure, and the PI is a relative measure of a project. In other words, the profitability index is a ratio that shows how much profit results from a project per \$1 of initial cost.

## Formula

The profitability index can be calculated by dividing the present value of expected cash flows (PV) by the initial cost of a project (CF0). The equation is as follows:

 PI = Present Value of Expected Cash Flows Initial Cost

 PV = N CFt Σ (1 + r)t t = 1

where CFt is an expected cash flow at the end of designated year t, r is the discount rate, and N is the life of the project in years.

## Decision Rule

The breakeven value of a ratio is equal to 1. If a project has a profitability index greater than 1, it should be accepted; if lower than 1, it should be rejected. The value of 1 is the point of indifference regarding whether to accept or reject the project. In terms of net present value, a ratio greater than 1 means that the project’s NPV is positive and it should be accepted, and a value lower than 1 means a negative NPV.

## Example

Company C is considering two mutually exclusive projects with the same initial cost of \$20,000K and cost of capital of 11%. Detailed information about the projects’ future cash flows is presented in the table below.

 Initial Cost, CF0 Cash flows at the end of relevant year, CFt 0 1 2 3 4 5 Project Y -\$20,000,000 \$9,000,000 \$8,000,000 \$7,000,000 \$5,000,000 \$4,000,000 Project Z -\$20,000,000 \$4,000,000 \$5,000,000 \$7,000,000 \$9,000,000 \$10,000,000

To find the present value of expected cash flows, we need to use the formula above.

 PVY = \$9,000,000 + \$8,000,000 + \$7,000,000 + \$5,000,000 + \$4,000,000 = \$25,386,887.43 (1 + 0.11)1 (1 + 0.11)2 (1 + 0.11)3 (1 + 0.11)4 (1 + 0.11)5

 PVZ = \$4,000,000 + \$5,000,000 + \$7,000,000 + \$9,000,000 + \$10,000,000 = \$24,643,147.49 (1 + 0.11)1 (1 + 0.11)2 (1 + 0.11)3 (1 + 0.11)4 (1 + 0.11)5

The present value of future cash flows of Project Y is \$25,386,887.43 and \$24,643,147.49 for Project Z.

Using the equation above, we can calculate the profitability index as 1.269 for Project Y and 1.232 for Project Z.

 PI of Project Y = \$25,386,887.43 = 1.269 \$20,000,000

 PI of Project Y = \$24,643,147.49 = 1.232 \$20,000,000

If the projects were independent, both should be accepted. In case of mutually exclusive projects, Company C should accept Project Y and reject Project Z.

The net present value method will lead to the same decision because the NVP of Project Y of \$5,386,887.43 is greater than the NPV of Project Z of \$4,643,147.49.