# Modified Internal Rate of Return (MIRR) vs. Regular Internal Rate of Return (IRR)

## Modified Internal Rate of Return (MIRR) vs. Regular Internal Rate of Return (IRR): An Overview

When determining whether to undertake a new project, business managers often consider its internal rate of return (IRR). This metric is an estimate of the potential annual profit of the project after its costs. The internal rate of return metric is popular among business and project managers. It is also used by government agencies like the United States Environmental Protection Agency to select projects.

Unfortunately, IRR tends to overstate the potential profitability of a project and can lead to capital budgeting mistakes based on an overly optimistic estimate. A variation, the modified internal rate of return, compensates for this flaw and gives managers more control over the assumed reinvestment rate from future cash flows.

This variation, called the modified internal rate of return (MIRR) strives to improve the original formula. Let's compare the two and understand how these two approaches differ.

• The standard internal rate of return calculation is a widely used technique to determine an expected profitability rate for a project.
• IRR calculations may overstate the potential future value of a project as it may use unrealistic discount rates for all cash flows.
• The modified internal rate of return is used to avoid distorting the cost of reinvested growth from stage to stage in a project.
• Modified internal rate of return allows for adjusting the assumed rate of reinvested growth for different stages of a project.
• Modified internal rate of return can also only return one answer, while internal rate of return may be harder to analyze when reporting multiple valid calculations for an irregular set of cash flow.
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## Internal Rate of Return (IRR)

IRR is often used to analyze cash flow over a period of time. It is calculated by summing the present value of each cash flow over the life of a project. The calculation often has an initial cash outlay (the initial investment) along with subsequent annual cash inflows (resulting revenue generated from the initial investment).

The discount rate used to find the present value of the cash flows is set so the net present value of the series is equal to 0. This discount rate is the internal rate of return; it is the required investment return rate to break even on a project when considering the timing of the cash flow of a project. In general, projects with higher IRRs are more favorable than projects with lower IRRs, as the expected rate of return on these projects is greater.

IRR is often used to compare different options or choose between projects. For example, a company that is considering expanding into a new product line might compare the internal rate of return if it accomplishes that expansion by building a new factory, buying a competitor, or importing the products. All else being equal, the option with the highest IRR is most favorable.

### The Drawback to IRR

There are several disadvantages when using IRR. First, IRR does not give you the return on investment in terms of dollars. A project may yield an IRR of 10%; however, you won't know if the project will generate \$10,000 or \$10 million of cash flow. For this reason, larger projects with lower yields but higher net cash proceeds may be put at an analytical disadvantage when using IRR.

IRR does not consider differences in the duration of projects. Imagine a one-year project with an IRR of 10% and a five-year project with an IRR of 8%. While the one-year project is more favorable because of its higher IRR, the company may want to consider a longer-term project that will yield a return over a longer period of time.

IRR calculations also assume all cash flow will be reinvested at the same rate over the term of the entire project. This means the initial cash outlay and subsequent cash inlays will have the same earning potential, even if these cash flow span years.

Last, a series of cash flow may end up having two valid IRR calculations. This problem arises when a project has non-normal cash flow over its life and generally occurs when the direction of cash flow changes. When this occurs, a project has more than one internal rate of return and may be more difficult to analyze.

## Modified Internal Rate of Return (MIRR)

To fix the last two issues above related to IRR, a different calculation was created. The MIRR uses a lot of similar concepts as IRR, but there are slightly differences to help improve the original formula. The MIRR is calculated by incorporating the future value of positive cash flows and the present value of cash flows taken at different discount rates.

Similar to IRR, MIRR is used to analyze the profitability of a project. MIRR is often compared to an internally required rate of return. If a project's MIRR is higher than this expected return, a project is favorable; if a project's MIRR is lower, it is often not recommended.

Both formulas can be difficult to manually calculate. Both can be calculated in Excel using specific formulas (=IRR and = MIRR).

## Key Differences

There are several differences between IRR and MIRR, and these differences are what make the general view that MIRR demonstrates a more realistic picture of a project. These differences are discussed below.

• They use different rates. IRR relies on a single reinvestment rate for all cash flows. This may not be realistic, especially for projects with a long timespan. In addition, a company may have a different rate of return for cash inlays as opposed to cost of capital rates for cash outlays.
• They consider inflation differently. Because IRR does not factor in the cost of capital as part of its equation, IRR does not incorporate inflation. Meanwhile, MIRR can reflect this cost.
• They provide a different number of solutions. When a project has irregular cash flow, it may return multiple IRR results. This makes analysis difficult, as both percentages can be interpreted as the rate of return. Alternatively, based on the format of the formula, MIRR will only generate one result. This often means MIRR is easier to analyze.
• They are defined differently. IRR is the discount rate at which the net present value of a series of cash flow is equal to zero. Alternatively, MIRR is defined at the rate of return where the NPV of the project inflows is equal to the initial investment. Though these definitions aren't widely different, they do vary as they use different approaches to the discount rate(s) used.
• They vary in accuracy. Because MIRR incorporates more information and allows for more flexibility, it is often considered the more accurate and more useful calculation.
Internal Rate of Return (IRR)
• Uses a single discount rate for all cash flows

• Does not incorporate a company's cost of capital

• May return more than one result depending on the sequence and direction of cash flows

• Is not considered highly accurate

Modified Internal Rate of Return (MIRR)
• Uses different discount rate for different types of cash flows

• Incorporates a company's cost of capital

• Will always return a single result regardless of the sequence and direction of cash flows

• Is considered to be highly accurate

## What Is Internal Rate of Return?

IRR is a capital budgeting technique used to calculate the profitability of a project. It is calculated by finding the present value of a series of cash flows that equals \$0. This discount rate is often compared to a company's required rate of return, and projects with higher IRR calculations are seen as more favorable.

## How Is IRR Different than MIRR?

IRR and MIRR both analyze the cash flow of a project to determine its long-term profitability rate. However, these two calculations are slightly different. MIRR uses different discount rates and treats cash outlays differently than IRR. As MIRR incorporates more information, it is often considered more accurate.

## Is MIRR Better than IRR?

In general, MIRR is considered better than IRR. MIRR incorporates more information and more accurately reflects expected rates of return around cash outlays. MIRR also incorporates external costs like inflation due to the incorporation of cost of capital. Because MIRR also only returns one calculated figure, it is often considered easier to analyze as well.

## Why Is MIRR Different than IRR?

MIRR has several differences to IRR. Most notably, MIRR incorporates different rates in its calculation. While IRR uses only one expected rate of return for all cash flows, MIRR incorporates both expected investment growth rates as well as the cost of capital rates. Based on the set up of the formula, MIRR also only yields one calculation every time, whereas IRR might return two results for a single project.

## What Does IRR and MIRR Tell You?

Both IRR and MIRR result in a calculated percent. This percent represents the profitability of a project through the analysis of project cash flows over the life of the project. IRR and MIRR are often used to compare projects and select more ideal endeavors. They are also used to test the overall profitability of a project.

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#### What Is MIRR?

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1. United States Environmental Protection Agency. "Project Planning and Financing."