## Modified Internal Rate of Return: Explanation & Examples

written by: N Nayab • edited by: Ginny Edwards • updated: 11/15/2010

Modified Internal Rate of Return (MIRR), as the name implies is a modification of the Internal Rate of Return (IRR) and aims to resolve some of the limitations and drawbacks associated with IRR.Read on for an explanation of this concept, and understand how to calculate the MIRR for a project.

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Internal Rate of Return (IRR) is a method of capital budgeting, and serves to rank investments. It is the interest rate where the net present value of the investment’s income stream becomes zero.

Investors use IRR to compare the different investment options or determine the attractiveness of an investment opportunity vis-à-vis the prevailing rates of return in the security market, bank interest, or other accepted minimum standards of investing.

IRR, although a popular choice of capital budgeting has many drawbacks and limitations.

1. A major distorter is that IRR does not consider risk factors or the impact of other external factors. For instance, an investment with a high IRR might generate associated indirect costs such as costs to clean up the environment after operating an effluent plant, which the IRR does not take into account.
2. IRR is only a relative measure of value creation, and the computation generates multiple results when there is more than one sign change positive to negative or negative to positive in a series of cash flows.
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### Modified Internal Rate of Return (MIRR)

Modified Internal Rate of Return (MIRR) removes much of the limitations and drawbacks of Internal Rate of Return (IRR.) Comparing IRR vs MIRR, MIRR is a more accurate reflection of the cost and profitability of a project. MIRR assumes reinvestment of the positive cash flows at the cost of capital rather than at the IRR rate and financing costs cover initial outlays. This allows a more accurate reflection of what the firm does with its cash flows.

The other advantages of MIRR over IRR are that MIRR helps in providing unique solutions where IRR generates multiple values owing to more than one sign change in the cash flows. MIRR uses specified reinvestment and borrowing rates and discounts negative cash flows at a safe rate such as short-term security or savings bank rate that reflects the return on an investment in a liquid account.

MIRR finds widespread use in real estate profession and other imperfect capital markets where reinvestment rates and liquidity requirements limit the more stringent assumptions of IRR and Net Present Value method of capital budgeting.

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### Calculation

The calculation of Modfified Internal Rate of Return (MIRR) is similar to the technique adopted for calculating Internal Rate of Return (IRR.) The MIRR of a project with a single terminal payment is same as the IRR.

Assume a two-year project with an initial outlay of \$195 and a cost of capital of 12 percent providing returns of \$121 in the first year and \$131 in the second year.

The IRR of the project is = 18.66%

MIRR assumes that positive cash flows find reinvestment at the 12 percent cost of capital. So the future value of the positive cash flows in this example is:

Future Value of \$121+\$131 at 12 percent annual interest = \$121*(1+12%)+\$131 = \$266.52

Dividing this future value of the cash flows with the present value of the initial outlay (\$195) provides the geometric return for the period. The root of two of the result (since the number of years is two. If the number of years is three, the calculation takes the root of 3 or cube root) provides the MIRR.

=sqrt(\$266.52/195) -1 = 16.91% MIRR

The MIRR of 16.91 percent is materially lower than the IRR of 18.66 percent.

Alternative Calculation

MIRR can also be calculated using a built-in formula in MS-Excel.

=MIRR( cell range that lists the cash flow, rate of cost of capital, reinvestment_rate )

• Enter the periodic cash flows (-195, 121, 131) in column A.
• Enter the cost of capital (12%) in Column B,
• Enter the Reinvested Rate of Return in Column C. The Reinvested Rate of Return is the expected returns expected when investing the amount elsewhere. Assume this as same as cost of capital (12%).
• In any other cell, type the formulae –MIRR(A1:A3,B1,C1).

The answer lists MIRR as 16.91 percent, which is lower that the IRR of 18.66 percent.

IRR very often gives too optimistic picture of the potential of the project, while the MIRR gives a more realistic evaluation of the project.

Image Credit: N Nayab

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### References

1. Baker, Samuel, L. “The Internal Rate of Return." University of South Carolina. Retrieved from http://hadm.sph.sc.edu/courses/econ/irr/irr.html on 10 November 2010
2. Economics Interactive Tutorial. "Perils of the Internal Rate of Return." Retrieved from http://hadm.sph.sc.edu/courses/econ/invest/invest.html on 10 November 2010
3. "Modified Internal Rate of Return." Retrieved from http://www.accaglobal.com/pubs/students/publications/student_accountant/archive/sa_apr08_ryan2.pdf on 10 November 2010
4. HP. "Calculating Modified Internal Rate of Return". Retrieved from http://h10025.www1.hp.com/ewfrf/wc/document?dlc=en&lc=en&cc=us&docname=bpia5028 on 10 November 2010