# Modified Internal Rate of Return (MIRR)

Definition: The modified internal rate of return, or MIRR, is a financial formula used to measure the return of a project and compare it with other potential projects. It uses the traditional internal rate of return of a project and adapted to assume the difference between the reinvestment rate and the investment return.

## What Does the Modified Internal Rate of Return Mean?

MIRR is a revised version of the internal rate of return (IRR), which calculates a reinvestment rate and accounts even or uneven cash flows. In fact, MIRR portrays more accurately than IRR the cost and profitability of a project because it considers the cost of capital as the reinvested rate for a firm’s positive cash flows and the financing cost as the discount rate for the firm’s negative cash flows.

If the MIRR is higher than the expected return, the investment should be undertaken. If the MIRR is lower than the expected return, the project should be rejected. Also, if two projects are mutually exclusive, the project with the higher MIRR should be undertaken.

To calculate the MIRR formula of a project, we need to know: the future value of a firm’s positive cash flows discounted at the firm’s cost of capital and the present value of a firm’s negative cash flows discounted at the cost of the firm.

Let’s look at an example.

## Example

Helen works for a construction company and she is asked to calculate the MIRR for two mutually exclusive projects to determine which project should be selected.

Project A has a total life of 3 years with a cost of capital 12% and a financing cost 14%. Project B has a total life of 3 years with a cost of capital 15% and a financing cost 18%.

The expected cash flows of the projects are in the table below:

Year | Project A | Project B |

0 | -1,000 | -800 |

1 | -2,000 | -700 |

2 | 4,000 | 3,000 |

3 | 5,000 | 1,500 |

Helen calculates the future value of the positive cash flows discounted at the cost of capital.

Project A: 4,000 x ( 1 + 12% )1 + 5,000 = 9,480

Project B: 3,000 x ( 1 + 15% )1 + 1,500 = 4,950

Then, she calculates the present value of the negative cash flows discounted at the financing cost.

Project A: -1,000 + ( -2,000 ) / ( 1 + 14% )1 = -3,000

Project B: - 800 + ( -700 / 1 + 18%)1 = -1,500

To calculate the MIRR for each project Helen uses the formula:

MIRR = (Future value of positive cash flows / present value of negative cash flows) (1/n) – 1.

Therefore:

Project A: 9,480 / (3000)1/3 -1 = 5.3%

Project B: 4,950 / (1500)1/3 -1 = 10.0%

Given that these are mutually exclusive projects project B should be undertaken because it has a higher MIRR than project A.

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