# Modified Rate of Return: Definition & Example

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• 0:04 Modified Internal Rate…
• 3:04 Calculating the MIRR
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Lesson Transcript
Instructor: James Walsh

M.B.A. Veteran Business and Economics teacher at a number of community colleges and in the for profit sector.

In this lesson, we'll explain the three different approaches to the modified rate of return. In addition, we'll compare the modified rate of return to the internal rate of return.

## Modified Internal Rate of Return

The internal rate of return (IRR) is a performance metric in the form of an interest rate that is used in business to measure the attractiveness of a particular project or business investment. The higher a project's internal rate of return, the more attractive the project becomes for the business. Think of the IRR as a measure of the potential return on a project. However, the modified internal rate of return (MIRR) is a modified version of the internal rate of return and is also used to measure how appealing or lucrative an investment is to a potential investor.

When a company invests money in a project, the company usually makes an initial investment during the early phases of the project. This is negative cash flow. As the project progresses, the project will yield cash profits resulting in positive cash flow. When cash flows change from negative to positive throughout the project lifecycle, there can be several internal rates of return for each change (from positive to negative). The modified rate of return addresses the issue of multiple IRRs by accounting for the positive and negative cash flows separately.

For example, a company invests \$10,000 into the creation of a new machine. Some other companies started hearing about the new machine and offered to invest as well, for a total of \$10,000. During the project, the company had to invest another \$15,000. The cash flow in this scenario is moving from negative to positive and back to negative again. The MIRR allows a company to determine the return on investment while accounting for these cash flow changes.

The MIRR is also useful because the conventional IRR assumes that profits are reinvested in the same project and will return the rate calculated in the IRR. This is often not realistic because maybe a project doesn't require any additional funds. The MIRR solves this problem by allowing profits to be reinvested at more realistic rates that reflect market conditions. It allows the user to set the reinvestment rate to get a more realistic result.

The MIRR solves for the limitations of the IRR and accounts for what the company does with positive cash flows when received such as reinvesting at a specific reinvestment interest rate. The MIRR also assumes a finance rate for any negative cash flows. The MIRR is used to compare projects with non-conventional cash flow methods, whereas the IRR is not useful to measure non-conventional cash flow.

The formula for the modified internal rate of return is:

FV = Future Value

PV = Present Value

n = number of periods

## Calculating the MIRR

There are three different approaches to the modified internal rate of return that business analysts and investors use to review potential investment returns. The three approaches to calculating the modified rate of return are the discounting approach, reinvestment approach, and combination approach.

#### MIRR: Discounting Approach

Discounting cash flows of a project is the exact opposite of compounding interest on an investment. The MIRR discounting approach involves discounting all negative cash flows of a project back to the initial start of the project. The negative cash flows are discounted at an assumed finance rate.

For example, a project has an initial capital outlay of \$1000 and a finance rate of 10%. The cash flow in year one is \$2500, cash flow in year two at -\$3000, and cash flow of \$4000 in year three. We will use a reinvestment rate of 8%.

-1000 + -3000/((1.10)(1.10)) = \$3479.34

\$3479.34 is the sum of negative cash flow discounted to year of initial investment.

Now, for the numerator, we will calculate the future value of the positive cash flows. Since \$2500 is received at the end of year one, we will find what it is worth at the end of year three at the reinvestment rate of 8%:

\$2500 * 1.08 * 1.08 = \$2,916

Then add the \$4000 at the end of year three for a total positive return of:

\$2916 + \$4,000 = \$6,916

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