# Profitability Index (PI) explained with formula and example

Profitability index in another decision making technique of capital budgeting i.e. deciding whether to make investment in long term projects or not.

## Definition

Also known as “benefit / cost” ratio can be defined as

“Ratio of present value of net cash flows of the project to initial investment cost.”

Profitability index has close resembles with net present value. In NPV initial cost is subtracted from present value of net cash flows. Whereas in PI, present value of net cash flows is divided by the initial cost.

The difference between NPV & PI is the way each technique prioritizes / ranks the projects.

## Formula

Formula can be created from definition i.e.

 Profitability index  = Present value of net cash flows received from project Initial Cost for the project

Or, in mathematical terms

 PI  = ∑ n t=1 FCFt (1 + r)t IC

Where
FCF = Future cash flows
r = the discount rate. Normally this is required rate of return for particular investment.
t = are number of periods (usually year wise) in which cash flows are generated.
n = is the total life of the project / investment; and
IC = Initial cost of starting the project or making the investment.
All the elements of this formula are explained in detail while discussing net present value. You may refer for further understanding. Here an example of calculating PI is presented.

## Example

Suppose initial cost of a project is \$ 80,000. Cash flows received in return will be 20,000 per annum. Total project life is 6 years. Calculate profitability index of the project if company’s overall required rate of return is 8%.

#### Solution

Step wise approach can be used.

#### Step 1: Determine the future cash flows of the investment / Project

Predict / forecast all the relevant future cash flows of the investment. Future cash flows comprise inflows, outflows, taxes and salvage value.
In this example a single amount i.e. \$ 20,000 is given. However how to calculate complex future cash flows is discussed elsewhere in these pages.

#### Step 2: Determine the required rate of return for the investment / project

Ideally required rate of return for each project should be determined separately. However for the sake of simplicity companies use their overall required rate of return for the purpose which is 8% as per example.
(Required rate of return takes into account the riskiness of project and cost of capital. How to calculate the required rate of return is explained separately.)

#### Step 3: Discount the future cash flows with required rate of return

Step 3 involves concept of time value of money.
Discount the future cash flows of investment (determined in step 1) with the discount rate (determined in step 2).

 DCF= 20,000 + 20,000 + 20,000 + 20,000 + 20,000 + 20,000 (1 + 0.08) 1 (1 + 0.08) 2 (1 + 0.08) 3 (1 + 0.08) 4 (1 + 0.08) 5 (1 + 0.08) 6

Alternatively annuity formula can be used since cash flows are uniform over the period.

 DCF= \$92,459

#### Step 4: Divide “discounted cash flows” with initial cost of investment

 PI= DCF Initial cost of investment
 PI= \$ 92,459 \$ 80,000
 PI= 1.15

#### Step 5: Interpret the profitability index

As PI is greater than 1 the project should be accepted.
Complete interpretation of PI is explained below.

## Interpretation of profitability index

The result of PI will be either greater than, less than or equal to 1.

#### When PI is greater than 1 i.e. PI > 1

Accept the project.
Greater than 1 PI means the projects net present value exceeds its cost. Projects with positive net present values fulfill the goal of maximization of shareholder value and should therefore be accepted.

#### When PI is equal to 1 i.e. PI = 1

Accept the project.
PI = 1 means, net present value and initial cost of investment are equal. It means the project is at least recovering the required rate of return (remember cash flows were discounted using the required rate of return). Therefore project should be accepted.

#### When PI is less than 1 i.e. PI < 1

Reject the project.
It means project has failed to recover even the cost of the project. Accepting such project will harm the goal of maximizing the shareholder’s wealth and it should therefore be rejected.