Internal rate of return

The internal rate of return (IRR) is a capital budgeting method used by firms to decide whether they should make long term investments. The IRR is defined as any discount rate that results in a net present value of zero, and is usually interpreted as the expected return generated by the investment. In general, if the IRR is greater than the project's cost of capital or hurdle rate, the project should be accepted, though there are occasional problems in using this rule.

To find the internal rate of return, find the IRR that satisfies the following equation

$\mbox{Initial Investment} = \sum_{t=1}^N \frac{C_t}{(1+IRR)^t}$

Example: Year Cash flow 0 -100 1 +120

Calculation of NPV: i = interest rate in percent NPV = -100 +120/^* (This calculation is condensed, see net present value.)

Calculation of IRR: NPV = 0 -100 +120/^* = 0 IRR = 20%

Problems with using IRR

As an investment decision tool, the calculated IRR should not be used to rate mutually exclusive projects, but only to decide whether a single project is worth investing in. In cases where one project has a higher intial investment than a second mutually exclusive project, the first project may have a lower IRR (expected return), but a higher NPV (increase in shareholders' wealth) and should thus be accepted over the second project. A method called marginal IRR can be used to adapt the IRR methodology to this case.

The IRR method should not be used in the usual manner for projects that start with an intial positive cash inflow, for example where a customer makes a deposit before a specific machine is built, resulting in a single positive cash flow followed by a series of negative cash flows (+ - - - -). In this case the usual IRR decision rule needs to be reversed.

If there are multiple sign changes in the series of cash flows, e.g. (- + - + -), there may be multiple IRRs for a single project, so that the IRR decision rule may be impossible to implement. Examples of this type of project are strip mines and nuclear power plants, where there is usually a large cash outflow at the end of the project.

In general, the IRR can be calculated by solving a polynomial. Sturm's Theorem can be used to determine if that polynomial has a unique real solution. Importantly, the IRR equation cannot be solved analytically (i.e. in its general form) but only via iterations.

A critical shortcoming of the IRR method is that it is commonly misunderstood to convey the actual annual profitability of an investment. However, this is not the case because intermediate cash flows are almost never reinvested at the project's IRR; and, therefore, the actual rate of return (akin to the one that would have been yielded by stocks or bank deposits) is almost certainly going to be lower. Accordingly, a measure called Modified Internal Rate of Return (MIRR) is used, which has an assumed reinvestment rate, usually equal to the project's cost of capital..

Despite a strong academic preference for NPV, surveys indicate that executives prefer IRR over NPV. Apparently, managers find it intuitively more appealing to evaluate investments in terms of percentage rates of return than dollars of NPV.

External links

Capital Budgeting, audio lecture with slideshow

Mathematical finance

Gourt Home::Gourt :: Internal rate of return

Problems with using IRR

See also

External links