Modified Internal Rate of Return (MIRR)

The internal rate of return (IRR) is a break-even cost of capital - i.e. the discount rate at which the NPV of a project is zero.

For most projects the decision rule can be stated as follows:

"Accept project if IRR > cost of capital"

One interpretation of this rule is to see the IRR as a project "return" - similar to an accounting rate of return but incorporating factors such as the time value of money.

However, there are a number of problems with the standard IRR calculation and its interpretation that can be resolved by calculating the modified internal rate of return (MIRR)

Problems with the standard IRR

The decision rule

For conventional projects (those with a cash outflow at time 0 followed by inflows over the life of the project), the decision rule states that projects should be accepted if the IRR exceeds the cost of capital. 

However unconventional projects with different cash flow patterns may have no IRR, more than one IRR, or a single IRR but the project should only be accepted if the cost of capital is greater.

Assumptions

The IRR calculates the discount rate that would cause the project to break-even assuming it:

• is the cost of financing the project
• is the return that can be earned on all the returns earned by the project.

Since, in practice, these rates are likely to be different, the IRR is unreliable

Choosing between mutually exclusive projects

If choosing between mutually exclusive projects one might believe that picking the one with the higher IRR would be optimal since this gives the greatest "return".

However, a project with a high IRR is not necessarily the one offering the highest return in NPV terms at the company's cost of capital and IRR is therefore an unreliable tool for choosing between mutually exclusive projects.

Modified IRR

This measure has been developed to counter the above problems since it:

• is unique
• can deal with different borrowing and reinvestment rates
• is a simple percentage.

It is therefore more popular with non-financially minded managers, as a simple rule can be applied:

The interpretation of MIRR

MIRR measures the economic yield of the investment under the assumption that any cash surpluses are reinvested at the firm's current cost of capital.

Although MIRR, like IRR, cannot replace net present value as the principle evaluation technique it does give a measure of the maximum cost of finance that the firm could sustain and allow the project to remain worthwhile. For this reason it gives a useful insight into the margin of error, or room for negotiation, when considering the financing of particular investment projects.

Calculating the MIRR

Method 1

(1) Find the terminal value of the cash inflows (or "return phase") from the project if invested at the company's reinvestment rate.

(2) Find the present value of the cash outflows (or "investment phase"), discounted at the company's cost of finance.

(3) The MIRR is then found by taking the n^th root of (TV inflows / PV outflows) and subtracting 1(Note that n is the length of the project in years.)

Method 2

To avoid having to calculate the terminal value of the project inflows, there is an alternative way of computing MIRR which only uses present value calculations. This approach is only valid if the cost of capital and reinvestment rate are the same.

where

PV_R = the present value of the "return phase" of the project

PV_I = the present value of the "investment phase" of the project

r_e  = the firm's cost of capital

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