# How to Calculate the MIRR

## Introduction

The Modified Internal Rate of Return (MIRR) is based on the formula for the Internal Rate of Return (IRR) with one major difference. The IRR assumes any positive cash flows are reinvested at the internal rate of return, while the MIRR assumes that any positive cash flows are reinvested at the cost of capital.

## MIRR

The calculation of a MIRR involves a number of values and mathematic calculations. The formula for MIRR is:

The MIRR formula
Image Credit: Ron Price

Cash Flows (a.k.a. terminal cash flows) is the future value (FV) of the sum of all cash in-flows re-invested at the cost of capital. Outlay is the present value (PV) of the capital invested in the project or equipment.

## Cost of Capital

In an MIRR calculation, the interest rate of the FV and PV calculations is replaced by the cost of capital. The MIRR measures cash in-flows from an investment against the cost of acquiring the capital. In other words, MIRR measures whether or not an investment should cover the expense (typically, interest amounts) or opportunity cost (compared to other investment opportunities) of funding the investment.

The sources of capital may charge a variety of rates for funds. Therefore, when calculating MIRR, the accuracy of the result is improved by using a weighted average cost of capital, or WACC. A company has two primary sources of capital: debt, including long-term debt or bonds; and equity, such as common stock and preferred stock. A WACC is a company's cost of raising money. A WACC is calculated by multiplying the cost of each capital source (debt and/or equity) by the weight (ratio) of each capital source (actual percentage of total capital) and adding the two results together.

## The Decision Rule

If you compare the result of an MIRR to an IRR on the same investment, the IRR typically yields what appears to be a better rate of return. However, the MIRR reinvests its returns at the cost of capital and not a fixed interest rate. The result of an MIRR calculation indicates whether or not an investment returns cash in-flows greater than its cost of the capital outflows. Here's an example:

Suppose ABC Corp. wants to make an investment of \$500,000 for new equipment for the company's factory. The acquisition and installation of this equipment is expected to reduce costs by 15% and have an effective production life of three years. At present, the WACC is at 12%.

The FV of the projected cash in-flows from this investment are:

The cash flows of the ABC investment.
Image Credit: Ron Price

The PV of the required investment to purchase the equipment is \$500,000.00. As shown in the above cash in-flows, the cash in-flows seem to break-even against the investment. However, notice that the FV of the in-flows is much higher.

The calculation of the MIRR is

The MIRR calculation for ABC.
Image Credit: Ron Price

After finding the cube root of the FV of the cash in-flows divided by the PV of the intitial investment, the MIRR = 1.08 – 1, or 0.08. The investment will produce an MIRR of 8%.