# Profitability Index

Profitability Index is a capital budgeting tool used to compare different projects based on the net present value added by each project per $1 of initial investment.

While 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.

## Formula

$$ Profitability\ Index\\=\frac{Present\ Value\ of\ Future\ Cash\ Flows}{Initial\ Investment} $$

Profitability index can also be calculated from net present value as follows:

$$ Profitability\ Index\\=\ 1+\frac{Net\ Present\ Value}{Initial\ Investment} $$

## 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