# Modified Internal Rate of Return (MIRR): Definition and Formula

> **Definition**
>
> The modified internal rate of return can provide a realistic return for an investment with various and irregular cash flows.

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

The modified internal rate of return (MIRR) is a measure of the profitability of a project or other investment.

It assumes that positive cash flows are reinvested at the firm's cost of capital and that the initial outlays are financed at the firm's financing cost.

By contrast, the traditional [internal rate of return (IRR)](https://www.investopedia.com/terms/i/irr.asp) assumes the [cash flows](https://www.investopedia.com/terms/c/cashflow.asp) from a project are reinvested at the IRR itself. The MIRR, therefore, more accurately reflects the cost and profitability of a project.

### Key Takeaways

*   Modified internal rate of return (MIRR) improves on internal rate of return (IRR) by assuming that positive cash flows are reinvested at the firm's cost of capital.
*   MIRR is used to rank investments or projects that a firm or investor may undertake.
*   MIRR is designed to generate one solution, eliminating the issue of multiple IRRs.

![Modified Internal Rate of Return (MIRR): A calculation used to rank investments or projects of unequal size.](https://www.investopedia.com/thmb/bYvRyE4w_jfAKFRnGG_gOQw2S_g=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/mirr.asp-final-08103c3132f543d1b6db0e2960006cc6.png)

*A reliable estimation of return is crucial to capitalizing on the best investment opportunities. — Investopedia / Julie Bang*

## Formula and Calculation of MIRR

Given the variables, the formula for MIRR is expressed as:

$\begin{aligned} & MIRR = \sqrt[n]{\frac{FV(\text{Positive cash flows} \times \text{Cost of capital})}{PV(\text{Initial outlays} \times \text{Financing cost})}} - 1\\ &\textbf{where:}\\ &FVCF(c)=\text{the future value of positive cash flows at the cost of capital for the company}\\ &PVCF(fc)=\text{the present value of negative cash flows at the financing cost of the company}\\ &n=\text{number of periods}\\ \end{aligned}$

Meanwhile, the internal rate of return (IRR) is a discount rate that makes the [net present value (NPV)](https://www.investopedia.com/terms/n/npv.asp) of all cash flows from a particular project equal to zero. Both MIRR and IRR calculations rely on the formula for NPV.

## How Does the MIRR Work?

The MIRR calculation is a solution to two major problems that exist with the popular IRR calculation.

The first main problem with IRR is that multiple solutions can be found for the same project.

The second problem is that the assumption that positive cash flows are reinvested at the IRR is considered impractical in practice.

With the MIRR, only a single solution exists for a given project, and the reinvestment rate of positive cash flows is much more valid in practice.

The MIRR allows project managers to change the assumed rate of reinvested growth from stage to stage in a project.

While the most common way to do this is to input the average estimated cost of capital, there is flexibility to add any specific anticipated reinvestment rate.

## The Difference Between MIRR and IRR

Even though the IRR metric is popular among business managers, it tends to overstate the profitability of a project and can lead to [capital budgeting](https://www.investopedia.com/terms/c/capitalbudgeting.asp) mistakes based on an overly optimistic estimate.

The MIRR compensates for this flaw and gives managers more control over the assumed reinvestment rate from future cash flow.

An IRR calculation acts like an inverted compounding growth rate. It has to discount the growth from the initial investment in addition to reinvested cash flows.

However, the IRR does not paint a realistic picture of how cash flows are actually pumped back into future projects.

Cash flows are often reinvested at the cost of capital, not at the same rate at which they were generated in the first place. IRR also assumes that the growth rate remains constant from project to project. It is very easy to overstate potential [future value](https://www.investopedia.com/terms/f/futurevalue.asp) with basic IRR figures.

Another major issue with IRR occurs when a project has different periods of positive and negative cash flows.

In these cases, the IRR produces more than one number, causing uncertainty and confusion. MIRR solves this issue as well.

## The Difference Between MIRR and FMRR

The [financial management rate of return (FMRR)](https://www.investopedia.com/terms/f/financial-management-rate-of-return.asp) is a metric most often used to evaluate the performance of a real estate investment and pertains to a [real estate investment trust (REIT)](https://www.investopedia.com/terms/r/reit.asp).

The MIRR improves on the standard internal rate of return (IRR) value by adjusting for differences in the assumed reinvestment rates of initial cash outlays and subsequent cash inflows.

FMRR takes things a step further by specifying cash outflows and cash inflows at two different rates known as the “safe rate” and the “reinvestment rate.”

The safe rate assumes that funds required to cover negative cash flows are earning interest at a rate easily attainable and can be withdrawn when needed at a moment’s notice (i.e., within a day of account deposit).

In this instance, a rate is safe because the funds are highly [liquid](https://www.investopedia.com/terms/l/liquidasset.asp) and safely available with minimal risk when needed.

The reinvestment rate includes a rate to be received when positive cash flows are reinvested in a similar intermediate or long-term investment with comparable risk.

The reinvestment rate is higher than the safe rate because it is not liquid (i.e., it pertains to another investment) and thus requires a higher-risk [discount rate](https://www.investopedia.com/terms/d/discountrate.asp).

## Limitations of MIRR

The first limitation of the MIRR is that it requires you to compute an estimate of the cost of capital in order to make a decision. This calculation can be subjective and vary depending on the assumptions made.

In addition, the MIRR can provide information that leads to sub-optimal decisions that do not maximize value when several investment options are being considered at once.

The MIRR does not actually quantify the various impacts of different investments in absolute terms; NPV often provides a more effective theoretical basis for selecting investments that are [mutually exclusive](https://www.investopedia.com/terms/m/mutuallyexclusive.asp). It may also fail to produce optimal results in the case of [capital rationing](https://www.investopedia.com/terms/c/capitalrationing.asp).

The MIRR can also be difficult to understand for people who do not have a financial background. Moreover, the theoretical basis for MIRR is also disputed among academics.

## Example of How to Use MIRR

A basic IRR calculation is as follows. Assume that a two-year project with an initial outlay of $195 and a cost of capital of 12% will return $121 in the first year and $131 in the second year. To find the IRR of the project so that the [net present value (NPV)](https://www.investopedia.com/terms/n/npv.asp) = 0 when _IRR_ = 18.66%:

﻿ $NPV = 0 = -195 + \frac{121}{(1 + IRR)} + \frac{131}{(1+IRR)^2}$﻿

To calculate the MIRR of the project, assume that the positive cash flows will be reinvested at the 12% cost of capital. Therefore, the [future value](https://www.investopedia.com/terms/f/futurevalue.asp) of the positive cash flows when _t_ = 2 is computed as:

﻿ $\$121\times 1.12 + \$131 = \$266.52$﻿

Next, divide the future value of the cash flows by the present value of the initial outlay, which was $195, and find the geometric return for two periods. Finally, adjust this ratio for the time period using the formula for MIRR, given:

﻿ $MIRR = \frac{\$266.52}{\$195}^{1/2} - 1 = 1.1691 - 1 = 16.91\%$﻿

In this particular example, the IRR gives an overly optimistic picture of the potential of the project, while the MIRR gives a more realistic evaluation of the project.

## What Is MIRR in Simple Terms?

The modified internal rate of return is a way for businesses to estimate the return on investment of a project by taking into account variable cash flows.

## When Should You Use MIRR?

MIRR is used for evaluating the profitability and cost of an investment or project, and is used in capital budgeting. Businesses use the MIRR to identify which project can provide the most attractive returns. It is particularly useful for variable cash flows that can change from each stage of a given project since the MIRR allows businesses to change the assumed rate of reinvested growth of each stage of a project.

## Why Is IRR Flawed?

The problem with IRR is that it can overstate a project's profitability. This is because it doesn't account for variations in cash flows within a project.

> **Article Sources**
>
> 1.  Financial Industry Regulatory Authority. “[Regulatory Notice](https://www.finra.org/sites/default/files/2020-06/Regulatory-Notice-20-21.pdf),” Page 6.
>     
> 2.  Kierulff, Herbert. “[MIRR: A Better Measure](https://www.sciencedirect.com/science/article/abs/pii/S0007681308000359).” _Business Horizons_, vol. 51, no 4, 2008, pp. 326-328.
>     
> 3.  New York University Stern School of Business. “[Chapter 5: Measuring Return on Investments](https://pages.stern.nyu.edu/~adamodar/pdfiles/acf2E/Chap5.pdf),” Pages 12-13.
>     
> 4.  Microsoft. “[Go With the Cash Flow: Calculate NPV and IRR in Excel](https://support.microsoft.com/en-us/office/go-with-the-cash-flow-calculate-npv-and-irr-in-excel-9e3d78bb-f1de-4f8e-a20e-b8955851690c).”
>     
> 5.  New York University Stern School of Business. “[Chapter 5: Measuring Return on Investments](https://pages.stern.nyu.edu/~adamodar/pdfiles/acf2E/Chap5.pdf),” Page 67.
>     
> 6.  New York University Stern School of Business. “[Chapter 5: Measuring Return on Investments](https://pages.stern.nyu.edu/~adamodar/pdfiles/acf2E/Chap5.pdf),” Pages 62-63.
>     
> 7.  New York University Stern School of Business. “[Chapter 5: Measuring Return on Investments](https://pages.stern.nyu.edu/~adamodar/pdfiles/acf2E/Chap5.pdf),” Page 64.
>     
> 8.  Cary, David, and Michael Dunn. “[Adjustment of Modified Internal Rate of Return for Scale and Time Span Differences](http://www.csun.edu/~vcfin003/mirr.pdf).” _Allied Academics International Conference_, vol. 2, no 2, 1997, pp. 57.