# Modified Internal Rate of Return (MIRR)

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.

Let’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.

### 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

``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