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Modified Internal Rate of Return

From Wikipedia, the free encyclopedia

Modified Internal Rate of Return (MIRR) is a financialmeasure used to determine theattractiveness of an investment. It is generally used as part of a capital budgeting process torank various alternative choices. As the name implies, MIRR is a modification of the financialmeasure Internal Rate of Return (IRR). The main difference is that rather than ignoring theinvestment rate of the positive cash flow, MIRR makes an explicit assumption about the rateof return of investment of those flows.

The modified internal rate of return assumes all positive cash flows are re-invested (usually attheWACC) to the terminal year of the project. All negative cash flows are discounted andincluded in the initial investment outlay. MIRR ranks project efficiency consistent with the

present worth ratio (variant of NPV/Discounted Negative Cash Flow), considered the gold

standard in many finance textbooks. (Principles of Corporate Finance, Brealey, Myers, andAllen; or Economic Evaluation and Investment Decision Methods, Stermole and Stermole)

Problems with IRR

There are a few misconceptions about the IRR calculation. The major one is that IRRautomatically assumes that all cash outflows from an investment are reinvested at the IRRrate. IRR is the "internal rate of return" with "internal" meaning each dollar in an investment.It makes no assumptions about what an investor does with money coming out of aninvestment. Whether the investor gives it away or puts it in a coffee can, the IRR stays the

same. The IRR does, however, reflect reinvestment at the IRR.

It does however have a few drawbacks. First, IRR is not made to calculate negative cashflows after the initial investment. If an investment has an outflow of $1,000 in year three andan IRR of 30%, the $1,000 is discounted at 30% per year back to a present value. You wouldhave to put this PV amount in an investment earning 30% per year for the IRR to reflect thetrue yield.

Also, IRR ignores the reinvestment potential of positive cash flows. Since most capitalinvestments have intermediate (non-terminal) positive cash flows, the firm will reinvest thesecash flows. Unless a better number is known, the firm's cost of capital is a reasonable proxyfor the return to be expected. Investments with large or early positive cash flows will tend tolook far better with IRR than with MIRR for this reason.

To illustrate: a firm has investment options with returns that are generally moderate. Anunusually attractive investment opportunity comes up with much higher return. The cash spunoff from this latter investment will probably be reinvested at the moderate rate of return ratherthan in another unusually high-return investment. In this case, IRR will overstate the value ofthe investment, while MIRR will not.

Formula

MIRR is calculated as follows:

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http://en.wikipedia.org/wiki/Financehttp://en.wikipedia.org/wiki/Financehttp://en.wikipedia.org/wiki/Capital_(economics)http://en.wikipedia.org/wiki/Internal_rate_of_returnhttp://en.wikipedia.org/wiki/WACChttp://en.wikipedia.org/wiki/WACChttp://en.wikipedia.org/wiki/Present_valuehttp://en.wikipedia.org/wiki/Financehttp://en.wikipedia.org/wiki/Capital_(economics)http://en.wikipedia.org/wiki/Internal_rate_of_returnhttp://en.wikipedia.org/wiki/WACChttp://en.wikipedia.org/wiki/Present_value

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where n = i +j

External links

Internal Rate of Return: A Cautionary Tale

Retrieved from "http://en.wikipedia.org/wiki/Modified_Internal_Rate_of_Return "Categories:Mathematical finance

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