# Profitability Index Calculator

Instructions: Use this step-by-step Profitability Index Calculator to compute the profitability index ($$PI$$) of a stream of cash flows by indicating the yearly cash flows ($$F_t$$), starting at year $$t = 0$$, and the discount rate ($$r$$) (Type in the cash flows for each year from $$t=0$$ to $$t = n$$. The first cash flow must be negative. Type '0' if there is no cash flow for a year):

Interest Rate $$(r)$$ =
Type the yearly cash flows (comma or space separated)

## Profitability Index Calculator

More about the this PI calculator so you can better understand how to use this solver

The profitability index of a stream of cash flows $$F_t$$ depends on the discount interest rate $$r$$, and the cash flows themselves. It is computed as the present value ($$PV$$) after the initial investment $$I$$.

### How do you calculate the profitability index (PI)?

First, we let:

$PV = \displaystyle \sum_{i=1}^n \frac{F_i}{(1+i)^i}$

be the present value ($$PV$$) after the initial investment. The profitability index is therefore:

$PI = \frac{PV}{I}$

Other ways to evaluate a project include using instead a NPV calculator or also a IRR calculator . Those two metrics are the most common ones used to evaluate and make the decision of whether or not a project should be undertaken.

### Example of the calculation of the profitability index

Question: Assume that you act as the manager company, and you are asked to evaluate a project. This project requires a payment of $10,000 to get started. Then, it is expected that the project will bring a revenue of$3,000 at the end of the first year, and then another \$4,000 at the end of the following 3 years. Suppose that the discount rate is 4.5%, compute the profitability index of the project.

Solution:

This is the information we have been provided with:

• The cash flows provided are: -10000, 3000, 4000, 4000, 4000 and the discount rate is $$r = 0.045$$.

Therefore, the initial investment is $$I = 10000$$, and the present value (PV) of cash flows after the initial investment associated to these cash flows are computed using the following formula

$PV = \displaystyle \sum_{i=1}^n {\frac{F_i}{(1+i)^i}}$

The following table shows the cash flows and discounted cash flows:

 Period Cash Flows Discounted Cash Flows 1 3000 $$\displaystyle \frac{ 3000}{ (1+0.045)^{ 1}} = \text{\textdollar}2870.81$$ 2 4000 $$\displaystyle \frac{ 4000}{ (1+0.045)^{ 2}} = \text{\textdollar}3662.92$$ 3 4000 $$\displaystyle \frac{ 4000}{ (1+0.045)^{ 3}} = \text{\textdollar}3505.19$$ 4 4000 $$\displaystyle \frac{ 4000}{ (1+0.045)^{ 4}} = \text{\textdollar}3354.25$$ $$Sum = 13393.16$$

Based on the cash flows provided the PV is computed as follows:

$\begin{array}{ccl} PV & = & \displaystyle \frac{ 3000}{ (1+0.045)^{ 1}}+\frac{ 4000}{ (1+0.045)^{ 2}}+\frac{ 4000}{ (1+0.045)^{ 3}} +\frac{ 4000}{ (1+0.045)^{ 4}} \\\\ \\\\ & = & \text{\textdollar}2870.81+\text{\textdollar}3662.92+\text{\textdollar}3505.19+\text{\textdollar}3354.25 \\\\ \\\\ & = & \text{\textdollar}13393.16 \end{array}$

Therefore, the profitability index is ($$PI$$) computed as.

$\begin{array}{ccl} PI & = & \displaystyle \frac{PV}{I} \\\\ \\\\ & = &\displaystyle \frac{13393.17}{10000} \\\\ \\\\ & = & 1.3393 \end{array}$

Therefore, the profitability indexe associated to the provided cash flows and the discount rate of $$r = 0.045$$ is $$PI =1.3393$$.