Financing rate
%
Reinvestment rate
%
Initial investment
\$
Annual cash flows
Cash flow - year 1
\$
Cash flow - year 2
\$
Cash flow - year 3
\$
Cash flow - year 4
\$
Cash flow - year 5
\$
MIRR
MIRR
%

# MIRR Calculator - Modified Internal Rate of Return

By Bogna Haponiuk

This MIRR calculator (Modified Internal Rate of Return) helps you find out what is the IRR of an individual project, assuming that all profits will be reinvested 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 at your financing loan and reinvestment account. Read on to learn how to calculate the MIRR and to 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.

## 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.

`MIRR = [(FV(positive cash flows, reinvestment rate) / PV(negative cash flows, finance rate)] ^ (1/n) - 1`

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

• n is the number of time periods (typically, years) between now and the end of the project.

• FV stands for the future value of all positive cash flows. Every positive cash flow will be reinvested, increasing your total profit. The formula for FV is:

`FV = ∑ [Cᵢ * (1 + RR)ⁿ⁻ⁱ]`

• PV stands for the present value of all negative cash flows. The formula for PV is:

`PV = C₀ - ∑ [Cᵢ / (1 + FR)ⁱ]`

• RR is the reinvestment rate - an interest rate expressed as a percentage.

• FR is the finance rate.

Remember that you have to include only the positive `Cᵢ` terms when calculating the `FV` value, and only the negative `Cᵢ` terms when calculating the `PV` value!

As the formula is quite complicated, we strongly suggest using our MIRR calculator instead of determining its value by hand. In the 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:

timeCash flow
initial investment \$10,000
year 1 \$6000
year 2 -\$4000
year 3 \$8000
year 4 \$3000
year 5 \$7000

We will assume the 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:

`FV = 6000 * (1 + 0.12)⁴ + 8000 * (1 + 0.12)² + 3000 * (1 + 0.12) + 7000 = \$29,836`

1. Determine the present value of negative cash flows:

`PV = 10000 - (-4000) / (1 + 0.10)² = \$13,306`

1. Plug these values into the MIRR formula:

`MIRR = [FV / PV] ^ (1/n) - 1`

`MIRR = [29,836 / 13,306] ^ (1/5) - 1`

`MIRR = 17.53%`

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

Bogna Haponiuk