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Modified IRR
The MIRR is a financial measure of an investment's attractiveness; it is used to rank alternative investments of equal size.
Learning Objective

Calculate a project's modified internal rate of return
Key Points

MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.

More than one IRR can be found for projects with alternating positive and negative cash flows, which leads to confusion and ambiguity. MIRR finds only one value.

MIRR = {[FV(positive cash flows, reinvestment rate)/PV(negative cash flows, finance rate)]^(1/n)}1.
Terms

reinvestment rate
The annual yield at which cash flows from an investment can be reinvested.

cost of capital
the rate of return that capital could be expected to earn in an alternative investment of equivalent risk
Full Text
The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.
While there are several problems with the IRR, MIRR resolves two of them. Firstly, IRR assumes that interim positive cash flows are reinvested at the same rate of return as that of the project that generated them. This is usually an unrealistic scenario and a more likely situation is that the funds will be reinvested at a rate closer to the firm's cost of capital. The IRR therefore often gives an unduly optimistic picture of the projects under study. Generally, for comparing projects more fairly, the weighted average cost of capital should be used for reinvesting the interim cash flows. Secondly, more than one IRR can be found for projects with alternating positive and negative cash flows, which leads to confusion and ambiguity. MIRR finds only one value.
MIRR is calculated as follows:
Where n is the number of equal periods at the end of which the cash flows occur (not the number of cash flows), PV is present value (at the beginning of the first period), and FV is future value (at the end of the last period).
The formula adds up the negative cash flows after discounting them to time zero using the external cost of capital, adds up the positive cash flows including the proceeds of reinvestment at the external reinvestment rate to the final period, and then works out what rate of return would cause the magnitude of the discounted negative cash flows at time zero to be equivalent to the future value of the positive cash flows at the final time period.
Let take a look at one example. If an investment project is described by the sequence of cash flows: Year 0: 1000, year 1: 4000, year 2: 5000, year 3: 2000. Then the IRR is given by: NPV = 1000  4000 * (1+r)^{1} + 5000*(1+r)^{2} + 2000*(1+r)^{3} = 0. IRR can be 25.48%, 593.16% or 132.32%.
To calculate the MIRR, we will assume a finance rate of 10% and a reinvestment rate of 12%. First, we calculate the present value of the negative cash flows (discounted at the finance rate): PV(negative cash flows, finance rate) = 1000  4000 *(1+10%)^{1} = 4636.36.
Second, we calculate the future value of the positive cash flows (reinvested at the reinvestment rate): FV (positive cash flows, reinvestment rate) = 5000*(1+12%) +2000 = 7600.
Third, we find the MIRR: MIRR = (7600/4636.36)^{(1/3)}  1 = 17.91%.
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Key Term Reference
 Future Value
 Appears in this related concepts: SinglePeriod Investment, Future Value of Annuity, and Calculating Values for Different Durations of Compounding Periods
 capital
 Appears in this related concepts: Types of Businesses, Issuing Stock, and Architecture
 capital budgeting
 Appears in this related concepts: Advantages of the IRR Method, Replacement Projects, and Defining Risks in Capital Budgeting
 cash flow
 Appears in this related concepts: Defining the Cash Flow Cycle, The Imperative of Liquidity, and Interpreting Overall Cash Flow
 discounting
 Appears in this related concepts: The Discount Rate, The Relationship Between Present and Future Value, and Why is it Important?
 finance
 Appears in this related concepts: Committees, Personal Financial Management, and Constraint on Managers
 interim
 Appears in this related concepts: Reinvestment Risk, Disadvantages of the IRR Method, and Method of Payment
 investment
 Appears in this related concepts: Functions of Corporate Finance, Defining Finance, and Agencies
 period
 Appears in this related concepts: Atomic Size, SinglePeriod Investment, and Frequency of Sound Waves
 present value
 Appears in this related concepts: Calculating Values for Fractional Time Periods, Capital Leases versus Operating Leases, and Present Value and the Time Value of Money
 return
 Appears in this related concepts: Dollar Returns, Finance, Economics, and Accounting: Differences and Commonalities, and Disadvantages of the Payback Method
 scenario
 Appears in this related concepts: Applying the Decision Tree, Forecasting, and Scenario Analysis
 weighted average
 Appears in this related concepts: Expected Value, Calculating Expected Portfolio Returns, and Calculating Diluted Earnings per Share
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Cite This Source
Source: Boundless. “Modified IRR.” Boundless Finance. Boundless, 14 Nov. 2014. Retrieved 20 Mar. 2015 from https://www.boundless.com/finance/textbooks/boundlessfinancetextbook/capitalbudgeting11/internalrateofreturn93/modifiedirr4064850/