## Comparing IRR and MIRR

Every business will make a long term investment on various projects with the aim of generating benefits in future years. A business may be forced to decide which investments will reap the greater benefits and returns for both their own business and that of its investing partners. In this situation capital budgeting is used which is a process of estimating and selecting long-term investment projects which are in alignment with the basic objective of investors.

When completing project investment analysis, Internal Rate of Return (IRR) and Marginal Rate of Return (MIRR) are two capital budgeting techniques which measure an investment attractiveness.

Internal Rate of Return (IRR) is a financial analysis of cash flow and is commonly used as a method for evaluating an investment, capital investment or project proposals. The IRR is defined as a measurement which compares returns to costs by finding the interest rate that produces a zero Net Present Value (NPV) for the investment cash flow stream.

Similar to other cash flow measurements, IRR measurement adopts an investment view of expected financial results which allows it to compare the magnitude and timing of cash flow returns to cash flow costs. The IRR work on the assumption that project cash flows will be reinvested at the project’s own IRR. For an IRR to be accepted the result must be greater then the company’s cost of capital.

Modified Internal Rate of Return is also use as a financial measure for determining an investments attractiveness. As the name suggests, the MIRR is a modified version of the IRR which aims to resolve problems encountered when using the IRR. Unlike the IRR the MIRR allows you to set a different reinvestment rate for cash flows received however this increases the complexity as this requires additional assumptions about what rate the funds will be reinvested at. Most people can easily compare MIRR results with compound interest growth and understand the magnitude of the MIRR differences whereas understanding the meaning of the IRR difference is more problematic.

Key differences:

Some of the key differences between the two is that the IRR is an interest rate at which NPV is equal to zero. Conversely, MIRR is the rate of return at which NPV of terminal inflows is equal to the outflow. Additionally IRR is based on the principle that interim cash flows are reinvested at the project’s IRR unlike the MIRR where cash flows apart from initial cash flows are reinvested at firm’s rate of return. Finally the accuracy of the MIRR is greater than IRR measures as the MIRR measures the true rate of return.

IRR vs MIRR example

MIRR = ( FVCF / PVCF ) ^ ( 1 / t ) -1

where :

FVCF = future value cash flow

PVCF = present value cash flow

Ct = net cash inflow during the period t

Co = total initial investment costs

r = discount rate

t = number of time periods

Assume that a two-year project with an initial investment of $195 and a cost of capital of 12%, will return $121 in year one and $131 in year 2

To calculate the IRR make 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:

$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 value proposition of the initial outlay, which was $195, and find the return for 2 periods.

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

MIRR = ($266.52 / $195) ^ (1 / 2) – 1 = 1.1691 – 1 = 16.91%