# Modified Internal Rate of Return (MIRR)

## What is Modified Internal Rate of Return (MIRR)?

Definition: The Modified Internal Rate of Return (MIRR) is a financial formula that is used to compare the return that a project can provide. As its name suggests, it is a modified version of the Internal Rate of Return (IRR) calculation.

## What does MIRR mean?

What is the difference between MIRR and IRR? To understand this, you must first know that both calculations use the cash flows from a project to work out the return that a company will earn.

A project could have a large cash outflow at the beginning and subsequently there could be inflows in the following years. In the IRR calculation, it is assumed that the inflows are reinvested by the company at the same rate as the IRR. However, this may not be a correct assumption because a firm may not have the opportunity to reinvest inflows at this rate.

The MIRR calculation assumes that the inflows are reinvested at the firm’s cost of capital. This could be a more realistic assumption. When calculating MIRR it is also assumed that the initial outlays are financed at the firm’s financing cost.

## Example of MIRR

The following example will help to explain the difference between IRR and MIRR.

Consider a project that results in an outflow of \$250,000 in year 1 and provides a positive cash flow of \$45,000 in years 2, 3, 4, and 5. At the end of year 5, the project provides an inflow of \$295,000, which is the original investment of \$250,000 along with a return of \$45,000.

The cash flows can be summarized as follows:

• Year 1: -\$250,000
• Year 2: \$45,000
• Year 3: \$45,000
• Year 4: \$45,000
• Year 5: \$45,000
• End of Year 5: \$295,000

The IRR for these cash flows is 18%. Remember that the IRR calculation assumes that cash flows are reinvested at the IRR. However, when we calculate MIRR, the reinvestment rate is the firm’s cost of capital. Let us assume the cost of capital to be 10%.

To calculate the MIRR, we assume that the first inflow of \$45,000 is reinvested at 10% per year. At the end of the fifth year, this amount will increase to \$65,885.

Similarly, the second inflow of \$45,000 will increase to \$59,895 by the end of the fifth year. Here is the calculation for the entire period: We can see that the total inflows are equal to \$524,730 at the end of five years. (\$65,885 + \$59,895 + 54,450 + \$49,500 + \$295,000). Remember that this calculation has been done by using a reinvestment rate of 10%, which is the company’s cost of capital. Now, using the initial outflow of \$250,000 and the inflow of \$524,730 at the end of the fifth year, we can calculate the MIRR: It should be noted that the MIRR is 15.98%, which is lower than the IRR of 18%. That’s because the reinvestment of the inflows is assumed to be at the company’s cost of capital of 10% instead of at the IRR.

## Summary

MIRR is considered to be a more realistic measure than IRR because it is not always possible for a firm to reinvest cash inflows at the project’s rate.