# Modified Internal Rate of Return (MIRR)

## Definition

Modified Internal Rate of Return, shortly referred to as MIRR, is the internal rate of return of an investment that is modified to account for the difference between re-investment rate and investment return.

Topic Contents:

## Formula

Terminal Value of Cash Inflows

Present Value of Cash Outflows

- 1

Where:

n | = | The number of years of investment. |

Terminal Value | = | Future value of the net cash inflows from investment assumed to be re-invested at the rate of cost of capital (or a specified re-investment rate where relevant) over the investment period.Example A 3 year investment has cash inflows of $100,000 each year. Cost of capital is 10%. Solution $100,000 x 1.1 ^{2} = 121,000 (Year 1 inflows re-invested for 2 years)
$100,000 x 1.1 = 110,000 (Year 2 inflows re-invested for 1 years)$100,000 x 1.0 = 100,000 (Year 3 inflows cannot be re-invested) Terminal Value331,000 |

Present Value | = | Present value of the net cash outflows incurred during the investment period discounted at the cost of capital.
Example A project requires an initial investment of $100,000 and shall incur net cash outflows of $50,000 annually in years 1 and 2 on account of trading losses. Cost of capital is 10%. Solution $100,000 ÷ 1.0 = 100,000 (initial investment) $50,000 ÷ 1.1 = 45,455 (Year 1 cash outflows) $50,000 ÷ 1.1 ^{2} = 41,322 (Year 2 cash outflows)Terminal Value186,777 |

## Explanation

The calculation of IRR implicitly assumes that the positive cash flows earned during the life of a project are re-invested at the rate of the IRR until the end of the investment period. This could cause the IRR to be overly optimistic. **MIRR** was developed to counter this assumption.

The re-investment assumption of IRR and how it necessitates the use of MIRR can be explained through an illustrative example Expand Text Collapse Text

*Suppose an investment has the following expected cash flows:*

Year | $ |

0 | (250,000) |

1 | 50,000 |

2 | 100,000 |

3 | 200,000 |

*Cost of capital may be assumed to equal 13%.*

*Based on the above, we get an IRR of 15.1% (see calculation).*

*In arriving at this IRR, we have implicitly assumed the following*

- $50,000 cash inflows in year 1 will be re-invested at 15.1% until the termination of investment at the end of year 3 (i.e. 2 years in total)
- $100,000 cash inflows in year 2 will be re-invested at 15.1% until the termination of investment at the end of year 3 (i.e. 1 year in total)

In order to obtain proof regarding the existence of the re-investment assumption above, we can calculate the net present value of the investment (which should equal zero) including the re-investment using the IRR as our discount rate:

Year | $ | Value at the end of investment |

1 | 50,000 | 66,240 (50,000 x 1.151^{2}) |

2 | 100,000 | 115,100 (100,000 x 1.151) |

3 | 100,000 | 200,000 (200,000 x 1.000) |

Total Terminal Value | 381,340 | |

Discount Factor (1 / 1.151^{3}) | 0.6558 | |

Present Value of Cash inflows | 250,083 (83 is rounding difference) | |

Present Value of Cash outflows | 250,000 | |

Net Present Value ≈ | - |

*Since the NPV calculated is equal to zero, we may conclude that the re-investment assumptions stated above are correct.*

*As you can observe from the working above, the IRR calculation assumes that the cash inflows shall be re-invested at the rate of the investment's IRR which in this case is significantly higher than the (probably more achievable) rate of the cost of capital. In other words, IRR inflates the rate of return of an investment due to its variance with the cost of capital which causes the need for MIRR.*

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MIRR calculates the return on investment based on the more prudent assumption that the cash inflows from a project shall be re-invested at the rate of the cost of capital. As a result, MIRR usually tends to be lower than IRR.

The decision rule for MIRR is very similar to IRR, i.e. an investment should be accepted if the MIRR is greater than the cost of capital. However, when evaluating multiple investments that are mutually exclusive *(i.e. where selection of one investment would result in the abandonment of another investment)*, it is preferable to select investments with the highest NPV rather than the highest MIRR because NPV analysis offers a better measure of the impact of an investment on the wealth of the investor. Like IRR, MIRR should still be used to assess the sensitivity of the proposed investments in such cases.

## Example

Mr. A is considering an investment of $250,000 in a startup.

The cost of capital for the investment is 13%.

Following cash flows are expected:

Year | $ |

0 | (250,000) |

1 | 50,000 |

2 | 100,000 |

3 | 200,000 |

Calculate MIRR for the proposed investment and interpret your answer.

## Solution

Step 1: Calculate the Terminal value of Inflows:

Cash Inflow | Duration | Rate | Working | Terminal Value |

50,000 | 2 years | 13% | (50,000 x 1.13^{2}) | 63,845 |

100,000 | 1 years | 13% | (100,000 x 1.13) | 113,000 |

200,000 | 0 years | 13% | - | 200,000 |

376,845 |

Step 2: Calculate the Present value of Outflows:

Cash Inflow | Duration | Rate | Working | Terminal Value |

250,000 | 0 year | - | 250,000 |

Step 3: Calculate MIRR

Terminal Value of Cash Inflows

Present Value of Cash Outflows

- 1

**376,845**

**250,000**

- 1

= 1.1466 − 1

= 0.1466

= 14.66%

Step 4: Interpret

The investment should be accepted by Mr. A because the cost of capital (i.e. 13%) is lower than the MIRR (i.e. 14.66%).

The cost of capital will need to increase by more than 12.8%* before the investment becomes financially unviable.

^{*} | 14.66% - 13% | = | 12.8% |

13% |

## Advantages

- MIRR overcomes 2 major drawbacks of IRR including the elimination of multiple IRRs in case of investments with unusual timing of cash flows and secondly the re-investment problem discussed earlier.
- Helps in the measurement of sensitivity of an investment towards variation in the cost of capital.

## Limitations

- As with IRR, MIRR may lead to sub-optimal decision making when multiple investment options are being considered. As MIRR does not quantify the impact of different investments on the wealth of investors in absolute terms, NPV provides a more effective theoretical basis for selecting investments that are mutually exclusive (i.e. where the selection of one investment results in the abandonment of another investment, e.g. due to shortage of funds).
- MIRR can be hard to understand for people belonging from a non-financial background. The theoretical basis for MIRR is also disputed among academics.