# Modified Internal Rate Of Return - MIRR

## What is 'Modified Internal Rate Of Return - MIRR'

Modified internal rate of return (MIRR) assumes that positive cash flows are reinvested at the firm's cost of capital, and the initial outlays are financed at the firm's financing cost. By contrast, the traditional internal rate of return (IRR) assumes the cash flows from a project are reinvested at the IRR. The MIRR more accurately reflects the cost and profitability of a project.

## BREAKING DOWN 'Modified Internal Rate Of Return - MIRR'

The MIRR is used to rank investments or projects of unequal size. The 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 reinvestment rate of positive cash flows is much more valid in practice.

## Calculating the Modified Internal Rate of Return and Example

The formula for the MIRR takes into account three variables. They are:

FVCF(c) = the future value of positive cash flows at the cost of capital for the company

PVCF(fc) = the present value of negative cash flows at the financing cost of the company

n = number of periods

Given the variables, the formula for MIRR is:

MIRR = ( FVCF(c) / PVCF(fc) ) ^ ( 1 / n ) -1

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) = 0:

NPV = 0 = -195 + 121/(1+ IRR) + 131/(1 + IRR), when IRR = 18.66%.

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 of the positive cash flows is computed as:

\$121(1.12) + \$131 = \$266.52 = Future Value of positive cash flows at t = 2

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 2 periods.

Finally, adjust this ratio for the time period using the formula for MIRR given:

MIRR = (\$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.