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

cost of capital
the rate of return that capital could be expected to earn in an alternative investment of equivalent risk

reinvestment rate
The annual yield at which cash flows from an investment can be reinvested.
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:
MIRR
The formula for calculating MIRR.
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%.
Key Term Reference
 Future Value
 Appears in these related concepts: Calculating Values for Different Durations of Compounding Periods, The Valuation of Stocks, and Future Value of Annuity
 capital
 Appears in these related concepts: Temple Architecture in the Greek Orientalizing Period, Minoan Architecture, and The Acropolis
 capital budgeting
 Appears in these related concepts: Advantages of the IRR Method, Replacement Projects, and Risks Involved in Capital Budgeting
 cash flow
 Appears in these related concepts: Calculating the NPV, Interpreting the NPV, and Defining the Cash Flow Cycle
 discounting
 Appears in these related concepts: The Discount Rate, The Relationship Between Present and Future Value, and Importance of the Time Value of Money
 finance
 Appears in these related concepts: Personal Financial Management, Three examples, and Financial Instruments
 interim
 Appears in these related concepts: Reinvestment Risk, Disadvantages of the IRR Method, and Methods of Paying Dividends
 investment
 Appears in these related concepts: Functions of Corporate Finance, The Role of the Financial System, and GDP Equation in Depth (C+I+G+X)
 period
 Appears in these related concepts: Frequency of Sound Waves, Sine and Cosine as Functions, and Tangent as a Function
 present value
 Appears in these related concepts: Capital Leases vs. Operating Leases, Present Value and the Time Value of Money, and Chapter Questions
 return
 Appears in these related concepts: Dollar Returns, Comparing the Fields of Finance, Economics, and Accounting, and Disadvantages of the Payback Method
 scenario
 Appears in these related concepts: Applying the Decision Tree, Forecasting, and Scenario Analysis
 weighted average
 Appears in these related concepts: Average Cost Method, Market Reporting, and Expected Value
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