# Profitability Index

Profitability Index is a capital budgeting tool used to rank projects based on their profitability. It is calculated by dividing the present value of all cash inflows by the initial investment. Projects with higher profitability index are better.

While the net present value gives us the absolute value that a project adds, it is wrong to compare the net present values of different investments directly. Let’s say there are two projects, A and B, each with initial investment outlay of \$10 million and net present values of \$2 million and \$2.2 million respectively. It is wrong to conclude that Project B is better just because it has higher net present value. We need to calculate the net present value added by each project per \$1 of initial investment i.e. their profitability index.

Projects with higher profitability index are better. However, actual decision should attempt to maximize the total net present value of the project keeping in view the available funds for initial investment using capital rationing.

## Formula

Profitability index can be computed using the following formula:

 Profitability Index = Present Value of Cash Flows Initial Investment

Since NPV equals the present value of cash flows minus initial investment, we can write the present value of future value as the sum of net present value and initial investment:

 Profitability Index = Initial Investment + Net Present Value Initial Investment

This gives us another formula for profitability index:

 Profitability Index = 1 + Net Present Value Initial Investment

## Example

Your company has \$100 million available for investment in the following potential investment opportunities:

Project NPV Initial Investment
A \$5 million \$15 million
B \$15 million \$50 million
C \$10 million \$10 million
D \$20 million \$60 million
E \$12 million \$35 million

Rank the projects based on profitability and identify the projects that should be accepted keeping in view the company’s capital budget constraints.

Solution

Let’s first find profitability indices of each project:

Project Profitability Index
A 1 + 5/15 = 1.33
B 1 + 15/50 = 1.30
C 1 + 10/10 = 2.00
D 1 + 20/60 = 1.33
E 1 + 12/35 = 1.34

The ranking based on profitability index is: Project C, Project E, Project A and D and Project B. Now, we need to maximize total net present value that can be achieved using \$100 million investment by applying the concept of capital rationing capital rationing.