Modified internal rate of return

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. 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.

Problems with the IRR

While there are several problems with the IRR, MIRR resolves two of them.

First, 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 judging the projects more fairly, the weighted average cost of capital should be used for reinvesting the interim cash flows.

Second, more than one IRRs can be found for projects with alternating positive and negative cash flows, which leads to confusion.

Calculation

MIRR is calculated as follows:

${\mbox{MIRR}}={\sqrt[{n-1}]{\frac {-FV({\text{positive cash flows, reinvestment rate}})}{PV({\text{negative cash flows, finance rate}})}}}-1$,

where n is the number of equal periods in which the cash flows occur, PV is present value (at the beginning of the first period), 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, adds up the positive cash flows after factoring in the proceeds of reinvestment at the final period, then works out what rate of return would equate the discounted negative cash flows at time zero to the future value of the positive cash flows at the final time period.

Spreadsheet applications, such as Microsoft Excel, have inbuilt functions to calculate the MIRR. In Microsoft Excel this function is "=MIRR".

Example

If an investment project is described by the sequence of cash flows:

Year ($n$)	Cash Flow ($C_{n}$)
0	-1000
1	-4000
2	5000
3	2000

then the IRR $r$ is given by

${\mbox{NPV}}=-1000+{\frac {-4000}{(1+r)^{1}}}+{\frac {5000}{(1+r)^{2}}}+{\frac {2000}{(1+r)^{3}}}=0$.

In this case, the answer is 25.48% (the other solutions to this equation are -593.16% and -132.32%, but they will not be considered meaningful answers).

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):

$PV({\text{negative cash flows, finance rate}})=-1000+{\frac {-4000}{(1+10\%)^{1}}}=-4636.36$.

Second, we calculate the future value of the positive cash flows (reinvested a the reinvestment rate):

$FV({\text{positive cash flows, reinvestment rate}})=5000*(1+12\%)^{1}+2000=7600$.

Third, we find the MIRR:

${\mbox{MIRR}}={\sqrt[{3}]{\frac {-7600}{-4636.36}}}-1=17.91\%$.

The calculated MIRR (17.91%) is significantly different from the IRR (25.48%).