The **Internal Rate of Return (IRR) **is a method used in capital budgeting decision that assumes flows from a project are reinvested at the same rate equal to the IRR. In reality, cash flows are rarely generated and reinvested at a return equal to this figure which is why many companies instead use the **modified IRR**.

Letâ€™s look at an example:

*Looking Glass Fashion is discussing a project that requires an initial investment of $2,750,000. The project’s expected cash flows can be found on the right.* *The WACC of Looking Glass is currently at 10% and the project has the same risk as an average one. *

Year | Cash Flow |

Year 1 | $375,000 |

Year 2 | -100,000 |

Year 3 | 425,000 |

Year 4 | 450,000 |

### Calculate Cash Outflows & Inflows

The first step in solving for a MIRR is to discount each cash **outflow **to the present using the companies WACC. The first cash outflow at t = 0 was -$2,750,000 (initial investment) but it does not need to be discounted since we are currently at t = 0. The next cash outflow occurs at t = 2 of -$100,000 so we must discount it by two years:

- PV of CF2 in Year 0: $100,000 / (1.10)^2 =
**-$82,645**

Now we must compound each cash inflow which occur at t= 1 and t = 3 to the project’s end year using the WACC. Note there is a cash inflow of $450,000 in year 4 but we do not need to compound because it’s value already equals t = 4.

- FV of CF1 in Year 4: $375,000 x (1.10)^3 =
**$499,125** - FV of CF3 in Year 4 : $425,000 x (1.10) =
**$467,500**

Now we know the terminal value (FV) of all cash inflows is **$1,416,625 **($499,125 + 467,500 + 450,000), and the present value (PV) of all the cash outflows is **-$2,832,645 **(-$2,750,000 + -82,645).

## Solve for MIRR

To finish the calculation, we use the PV of cash outflows at t =0 ($2,832,645) and terminal value of the cash inflows of t = 4 ($1,416,625). Make sure you indicate the number of periods (N) as 4 because the project lasts for four years.

*Financial Calculator*

Input | Keystroke | Output |

4 | N | |

-2,832,645 | PV | |

0 | PMT | |

$1,416,625 | FV | |

I/YR | 31.09 |

`Excel =MIRR(values,finance rate, reinvest_rate)`

We found that for Looking Glass Fashion project has a MIRR of -15.91%. **But what does this mean?** This figure represents the projects expected rate of return. If the MIRR is less than the cost of capital invested in the project, the company should reject the project.

### Summary

The general takeaways are:

- The IRR is a method that assumes the projects cash flows can be reinvested at the IRR which is usually incorrect. This leads to the IRR to overstate the projects true return
- The MIRR is a discount rate where the present value of a project’s cost equal the present value of it’s terminal value. A typical firm’s IRR will be greater than it’s MIRR