# MIRR Calculator - Modified Internal Rate of Return

Created by Bogna Szyk and Wei Bin Loo
Reviewed by Steven Wooding
Based on research by
Mackie, Peter; Nellthorp, John; Laird, James When and How to Use NPV, IRR, and Modified IRR;; 2005
Last updated: Jun 05, 2023

This MIRR calculator (modified internal rate of return) helps you find out what is the IRR of an individual project, assuming that you will reinvest all profits each year. It is a modified version of our IRR calculator that allows you to specify not only the value of each cash flow but also the interest rate of your financing loan and reinvestment account. Read on to learn how to calculate the MIRR and discover a handy MIRR formula.

## What is the modified internal rate of return?

MIRR, or modified internal rate of return, is a variation of the IRR metric. Similarly, it shows you what return (expressed as a percentage of the initial investment) you can expect on a given project. Knowing the IRR or MIRR, you can easily compare mutually exclusive investments and choose the one that is most profitable.

Just like the IRR calculator, the MIRR calculator takes into account the present value of each cash flow. The main difference between these two metrics lies in the approach to the cash inflows: in MIRR, we assume that each cash inflow is reinvested at a steady rate, called the reinvestment rate.

If you want to learn more about the present vs. future value of money, check out our time value of money calculator.

π‘ We also have the dedicated present value calculator and future value calculator.

## MIRR formula

The MIRR formula is substantially different from the IRR formula - you will notice that, while the future value of positive cash flows is still taken into consideration, the MIRR metric is not that similar to the NPV equation (net present value calculator).

$\footnotesize {\rm MIRR} = \left(\frac{{\rm FV}(C_i^+, {\rm RR})}{{\rm PV}(C_i^-, {\rm FR})}\right)^{\!\!(1/n)}\! - 1$

What are all the elements of this equation? Let's list them here:

• $n$ β Number of time periods (typically, years) between now and the end of the project.

• $\rm FV$ β Future value of all positive cash flows. Every positive cash flow will be reinvested, increasing your total profit. The formula for FV is:

$\footnotesize \qquad {\rm FV} = \sum_{i\ =\ 1}^n\left[C_i^+\times(1 + {\rm RR})^{n - i}\right]$
• $\rm PV$ β Present value of all negative cash flows. The formula for PV is:
$\footnotesize \qquad {\rm PV} = C_0 - \sum_{i\ =\ 1}^n\left[\frac{C_i^-}{(1 + {\rm FR})^i}\right]$
• $\rm RR$ β Reinvestment rate β an interest rate expressed as a percentage.

• $\rm FR$ β Finance rate β loan interest rate.

• $C_i^+$ β Positive cash flow amounts.

• $C_i^-$ β Negative cash flow amounts.

Remember that you have to include only the positive $C_i^+$ terms when calculating the $\rm FV$ value and only the negative $C_i^-$ terms when calculating the $\rm PV$ value!

As the formula is quite complicated, we strongly suggest using our MIRR calculator instead of determining its value by hand. In advanced mode, this tool can process up to 9 cash flows.

## How to calculate MIRR: an example

Let's try to find the value of the MIRR metric for the following case:

Time

Cash flow

Initial investment

$10,000 Year 1$6000

Year 2

-$4000 Year 3$8000

Year 4

$3000 Year 5$7000

We will assume a financing rate of 10% and the reinvestment rate of 12%. The number of years $n = 5$.

1. Determine the future value of positive cash flows:
\footnotesize \qquad \begin{align*} {\rm FV} &= 6000 \times (1 + 0.12)^4 +\\ &\quad\ 8000 \times (1 + 0.12)^2 +\\ &\quad\ 3000 \times (1 + 0.12) + 7000\\ &= \29,\!836 \end{align*}
1. Determine the present value of negative cash flows:
\footnotesize \qquad \begin{align*} {\rm PV} &= 10,\!000 - \frac{(-4000)}{(1 + 0.10)^2}\\ &= \13,\!306 \end{align*}
1. Plug these values into the MIRR formula:
\footnotesize \qquad \begin{align*} {\rm MIRR} &= \left(\frac{FV}{PV}\right)^{(1/n)} - 1\\[1em] &= \left(\frac{28,\!836}{13,\!306}\right)^{(1/5)} - 1\\[1em] &= 17.53\% \end{align*}

The MIRR of this case is equal to 17.53%. By comparison, the IRR metric is 24.38%. These two values are significantly different; remember that by no means can they be used interchangeably!

Bogna Szyk and Wei Bin Loo
Financing rate
%
Reinvestment rate
%
Initial investment
$Annual cash flows Year 1$
Year 2
$Year 3$
Year 4
$Year 5$
Result
MIRR
%
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