# 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):

## 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

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 \( PI =1.3393\).