In this article, we will cover how to calculate modified internal rate of return (MIRR). This includes the overview, key definition, formula, example calculation as well as advantages and limitations of MIRR.

## Overview

The conventional method of internal rate of return IRR assumes all cash flows arising from a project to be reinvested in the same project. It also discounts all future cash inflows to the net present value. It sets the NPV of the total cash flows to zero i.e. finds breakeven against the WACC. However, in practical terms, many cash flows cannot be reinvested into the project again. The IRR calculations assume two different costs of interest rate, which may give different IRR or multiple IRRs.

## Problems with the IRR Approach

The IRR method assumes the reinvestment of all cash inflows associated with the project. It also considers IRR the only cost of financing which may not be correct. Many projects offer cash flows with project activities on an ongoing basis and are difficult to predict in absolute terms in advance. Uneven cash flows make the IRR calculation difficult and may often result in multiple IRRs. IRR also considers the best investment option with a higher IRR; in fact, any other project with the same IRR may offer higher NPV.

## What is Modified Internal Rate of Return MIRR?

The project’s initial investment rate and the subsequent cash flows can be reinvested at different costs. The adjustment made with these different costs or rates of return is the modified internal rate of return. The MIRR assumes the reinvestment with the company’s cost of capital. Also, the MIRR uses the terminal value of cash inflows adjusted with WACC to the present value. That offers greater flexibility to the management with reinvestments and calculations of MIRR from time to time, unlike the IRR that needs to be calculated before the project commencement.

## How to Calculate Modified Internal Rate of Return?

The MIRR is computed by taking into account for time value of money

**MIRR Formula:**

The MIRR formula can be calculated in two simple steps.

- The first step is to calculate the terminal value of the cash inflows.
- The MIRR formula using the terminal cash flows discounted at company cost of capital

The Formula for MIRR is:

MIRR = (Terminal Cash inflows/ PV of cash out flows) ^^{n}– 1

n = the number of years for the project

Terminal Value= future value of cash inflows to be reinvested in the project at the cost of capital.

Or, we can calculate the MIRR by using the below formula:

MIRR = (PV_{R}/PV_{I}) ^^{ (1/n)}× (1+r_{e}) -1

Where:

PV_{R }= The PV of the return phase (This represents the PV of cash inflow)

PV_{I} = The PV of the investment phase (This represents the PV of cash outflow)

r_{e} = Cost of capital

## Working Example

Suppose we have a simple projection of a project with an initial investment of $ 1,000. The project is assumed to be completed in three years with cash inflows as below. The company uses a WACC of 10%. The cash inflows in MIRR calculations can be reinvested into the project. The cash inflows compounded at the company WACC rate give the modified returns. The total cash inflows at the end of the year adjusted with company WACC is then used to calculate the MIRR.

Year | Cash flow | Multiplier @ 10% | Re-Invested Amount |

1 | 400 | 1.100^2 | 484 |

2 | 600 | 1.100^1 | 660 |

3 | 300 | 1.100^0 | 300 |

1,444 |

The present value of cash outflow remained at US$1,000.

Thus, we can calculate the MIRR by using the below formula:

MIRR = (Terminal Cash inflows/ PV of cash out flows) ^

^{n}– 1

MIRR = (1444/1000) ^^{3} – 1

Hence, **MIRR = 0.1303 or 13.03% or 13%**

Alternatively, by using the second formula, we have the present value as per the below table:

Year | Cash flow | Discount factor @ 10% | Present value |

1 | 400 | 0.909 | 364 |

2 | 600 | 0.826 | 496 |

3 | 300 | 0.751 | 225 |

1,085 |

The present value of initial investment is US$1,000.

Thus, we can calculate the MIRR by using the second formula as below:

MIRR = (PV

_{R}/PV_{I}) ^^{ (1/n)}× (1+r_{e}) -1

Where:

PV_{R }= US$1,085

PV_{I} = US$1,000

r_{e} = 10%

Hence, MIRR = [(1,085/1,000)] ^^{ (1/3)} × (1+0.10)-1

MIRR = 13.01% or 13%

Both formula provide the same MIRR rate which is at 13%.

**Interpretation of the MIRR Method**

MIRR includes the reinvestment of cash inflows at the company cost of capital. That implies it creates a cushion of error or margin if the project returns are less than expected. Generally, the company should undergo with a higher MIRR than the WACC. The reinvestment of cash inflows at the WACC would also mean that if the during the project the WACC rate changes, the MIRR can be adjusted.

## Modified IRR with Different Rates for Return and Investment Phases

When a company use different discount rates for each phase, the above formula cannot be used. This is because there is no single cost of capital any more. In case of different rates for return and investment phases, the below formula is used to calculate the MIRR:

MIRR = (-FV/PV) ^^{ [1/ (n-1)] }-1

Where:

FV = The future value of cash inflow (at return phase)

PV = The present value of cash outflow (at investment phase)

n = Number of periods

**Example**

ABC Co is considering one investment project with a cost of initial investment of US$130,000. This project will give return of US$50,000 in year 1, US$45,000 in year 2, US$47,000 in year 4, US$50,000 in year 5 and US$42,000 in year 6. There is an additional investment in year 3 for US$30,000.

The discount rate for investment phase is at 13% while the discount rate for return phase is at 11%.

Required: Calculate the modified internal rate of return (MIRR) for this project.

**Solution:**

In order to calculate the MIRR of this project, let’s separate the table into different investment and return phases as follow:

Present value of investment phase:

Year | Cash flow | Discount factor @ 13% | Present value |

(130,000) | 1.000 | (130,000) | |

3 | (30,000) | 0.693 | (20,790) |

Total | (150,790) |

Re-invested amount for the return phase:

Year | Cash flow | Factor @ 11% | Compound rate | Value |

1 | 50,000 | (1+11%)^5 | 1.685 | 84,253 |

2 | 45,000 | (1+11%)^4 | 1.518 | 68,313 |

3 | [Outflow] | |||

4 | 47,000 | (1+11%)^2 | 1.232 | 57,909 |

5 | 50,000 | (1+11%)^1 | 1.110 | 55,500 |

6 | 42,000 | (1+11%)^0 | 1.000 | 42,000 |

Total | 307,975 |

Therefore, we can calculate the modified internal rate of return (MIRR) as per the formula below:

MIRR = (-FV/PV) ^

^{ [1/ (n-1)] }-1

Where:

FV = US$307,975

PV = -US$150,790

n = 6 years

Therefore, MIRR = (-307,975/-150,790) ^^{ (1/5) }-1

MIRR = 15.35%

Thus, the modified rate of return (MIRR) for this project at different rates of return and investment phases is at 15.35%.

## Advantages of MIRR

The modified internal rate of return offers a clearer rate of return or project cost than IRR. Its main advantages include:

- MIRR offers a single and unique rate of return
- It eliminates the possibility of multiple rates of returns unlike IRR
- It includes the project inflows at the company cost of capital and compounds the values at the terminal value to calculate the MIRR
- Unlike IRR it can accommodate any future cash flows arising with project activities
- There is conflict between NPV and IRR methods in many cases; however, MIRR will give indication the same as NPV, which is the correct theoretical method.

## Limitations of the MIRR

Similar to other project appraisal methods, the MIRR approach also offers some limitations:

- It requires the cost of capital to compound the future cash inflows that can change with the capital structure of financing
- The weighted average cost of capital also basis on some assumptions which may not be an accurate rate of return
- Unlike the NPV method, both IRR and MIRR methods do not provide information in absolute profitability terms of investment appraisal
- MIRR is a relatively harder concept to grasp than simple payback or IRR calculations

## MIRR Vs IRR

Both IRR and MIRR offer a calculated cost of capital employed in an investment or project. Both value the cash inflows higher than the absolute profitability of the project. IRR and MIRR both assume the same basis that all cash inflows arising from the project can be reinvested in the project.

Further comparative points for IRR and MIRR:

- IRR evaluates the future cash flows at the point where NPV is zero; MIRR calculates the terminal cash flow value to be equal to the initial investment.
- IRR computes the cash inflows using trial and error methods which may give multiple IRRs. MIRR offers a unique rate of return which can be used to rank the investment options.
- IRR assumes that all cash inflows arising during the project can be invested at the rate of the project i.e. the IRR. On the other hand, MIRR considers the reinvestment rate of WACC for the company i.e. the total cost of capital.
- MIRR is more flexible with including unexpected cash flows arising during the project lifespan. Whereas IRR would often provide different results if the project goes through unforeseen cash flows like one time spending in the future.

## Conclusion

Although MIRR also does offer some limitations like IRR in terms of absolute terms of profitability, it’s nonetheless a superior project appraisal method than IRR. Its inclusion of the weighted average cost of capital for project cash inflow reinvestments make it a better and accurate measure of appraisals. Unlike IRR it offers a single and unique percentage value that can be compared with the company WACC. In terms of project ranking, it offers better appraisal as the rate of return with MIRR is closer to the company WACC.