Modified Internal Rate of Return (MIRR)

What Is Modified Internal Rate of Return (MIRR)?

The modified internal rate of return (MIRR) 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) assumes the cash flows from a project are reinvested at the IRR itself. The MIRR, therefore, more accurately reflects the cost and profitability of a project.

Formula and Calculation of MIRR

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

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

Meanwhile, the internal rate of return (IRR) is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. Both MIRR and IRR calculations rely on the formula for NPV.

What MIRR Can Tell You

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 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. The most common method is to input the average estimated cost of capital, but there is flexibility to add any specific anticipated reinvestment rate.

The Difference Between MIRR and IRR

Even though the internal rate of return (IRR) metric is popular among business managers, it tends to overstate the profitability of a project and can lead to capital budgeting mistakes based on an overly optimistic estimate. The modified internal rate of return (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 assumes that the growth rate remains constant from project to project. It is very easy to overstate potential future value 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) is a metric most often used to evaluate the performance of a real estate investment and pertains to a real estate investment trust (REIT). The modified internal rate of return (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.”

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 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.

Limitations of Using MIRR

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

As with IRR, 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. 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. It may also fail to produce optimal results in the case of capital rationing.

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) = 0 when IRR = 18.66%:

 $NPV = 0 = -195 + \frac{121}{(1 + IRR)} + \frac{131}{(1+IRR)^2}$NPV=0=−195+(1+IRR)121​+(1+IRR)2131​

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 when t = 2 is computed as:

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

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