By Yuriy Smirnov Ph.D.

The profitability index (PI) is one of the methods used in capital budgeting for project valuation. In itself it is a modification of the net present value (NPV) method. The difference between them is that the NPV is an absolute measure, and the PI is a relative measure of a project. In other words, the profitability index is a ratio that shows how much profit results from a project per $1 of initial cost.

The profitability index can be calculated by dividing the present value of expected cash flows (PV) by the initial cost of a project (CF_{0}). The equation is as follows:

PI = | Present Value of Expected Cash Flows |

Initial Cost |

PV = | N | CF_{t} |

Σ | ||

(1 + r)^{t} |
||

t = 1 |

where CF_{t} is an expected cash flow at the end of designated year t, r is the discount rate, and N is the life of the project in years.

The breakeven value of a ratio is equal to 1. If a project has a profitability index greater than 1, it should be accepted; if lower than 1, it should be rejected. The value of 1 is the point of indifference regarding whether to accept or reject the project. In terms of net present value, a ratio greater than 1 means that the project’s NPV is positive and it should be accepted, and a value lower than 1 means a negative NPV.

Company C is considering two mutually exclusive projects with the same initial cost of $20,000K and cost of capital of 11%. Detailed information about the projects’ future cash flows is presented in the table below.

Initial Cost, CF_{0} |
Cash flows at the end of relevant year, CF_{t} |
|||||

0 | 1 | 2 | 3 | 4 | 5 | |

Project Y | -$20,000,000 | $9,000,000 | $8,000,000 | $7,000,000 | $5,000,000 | $4,000,000 |

Project Z | -$20,000,000 | $4,000,000 | $5,000,000 | $7,000,000 | $9,000,000 | $10,000,000 |

To find the present value of expected cash flows, we need to use the formula above.

PV_{Y} = |
$9,000,000 | + | $8,000,000 | + | $7,000,000 | + | $5,000,000 | + | $4,000,000 | = $25,386,887.43 |

(1 + 0.11)^{1} |
(1 + 0.11)^{2} |
(1 + 0.11)^{3} |
(1 + 0.11)^{4} |
(1 + 0.11)^{5} |

PV_{Z} = |
$4,000,000 | + | $5,000,000 | + | $7,000,000 | + | $9,000,000 | + | $10,000,000 | = $24,643,147.49 |

(1 + 0.11)^{1} |
(1 + 0.11)^{2} |
(1 + 0.11)^{3} |
(1 + 0.11)^{4} |
(1 + 0.11)^{5} |

The present value of future cash flows of Project Y is $25,386,887.43 and $24,643,147.49 for Project Z.

Using the equation above, we can calculate the profitability index as 1.269 for Project Y and 1.232 for Project Z.

PI of Project Y = | $25,386,887.43 | = 1.269 |

$20,000,000 |

PI of Project Y = | $24,643,147.49 | = 1.232 |

$20,000,000 |

If the projects were independent, both should be accepted. In case of mutually exclusive projects, Company C should accept Project Y and reject Project Z.

The net present value method will lead to the same decision because the NVP of Project Y of $5,386,887.43 is greater than the NPV of Project Z of $4,643,147.49.

The advantage of the profitability index method is that it mathematically leads to the same decision for independent projects as the NPV method.

Problems can arise, however, in case of mutually exclusive projects if they differ in size of investment. In such a case, the PI ranking can conflict with the NPV ranking, so many academic studies recommend using the net present value as a single screening criterion.

Alternatively, the profitability index can be calculated using our online calculator.

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