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 the annualized effective compounded return rate which can be earned on the invested capital, i.e. the
yield on the investment.
A project is a good investment proposition if its IRR is greater than the rate of return that could be earned by alternative
investments (investing in other projects, buying bonds, even putting the money in a bank account). Thus, the IRR should be
compared to an alternative cost of capital including an appropriate risk premium.
Mathematically the IRR is defined as any discount rate that results in a
net present value of zero of a series of cash flows.
In general, if the IRR is greater than the project's cost of capital, or hurdle
rate, the project will add value for the company.
Method
To find the internal rate of return, find the IRR that satisfies the following equation:

Example
| Year |
Cash Flow |
| 0 |
-100 |
| 1 |
+30 |
| 2 |
+35 |
| 3 |
+40 |
| 4 |
+45 |
(i = interest rate in percent)
Internal Rate of Return (IRR)
where NPV = 0 = -100 + 30/[(1+i)^1] + 35/[(1+i)^2] + 40/[(1+i)^3] + 45/[(1+i)^4]
IRR = i,
IRR = 17.09%
Net Present Value (NPV)
Thus using IRR = i = 17.09%,
NPV = -100 + 30/[(1+i)^1] + 35/[(1+i)^2] + 40/[(1+i)^3] + 45/[(1+i)^4]
NPV = 0
(This calculation is condensed. See net present value.)
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 initial 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 (assuming no capital
constraints). A method called marginal IRR can be used to adapt the IRR method to this case.
Because IRR makes no assumptions about the reinvestment of the positive cash flow from a projects, projects of different
duration and with a different overall pattern of cash flow also should not use IRR for comparison. Modified Internal Rate of Return (MIRR) provides a better indication of a project's
efficiency in contributing to the firm's discounted cash flow.
The IRR method should not be used in the usual manner for projects that start with an initial positive cash inflow (or in some
projects with large negative cash flows at the end), 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 easier to compare investments of different sizes in terms of percentage rates of return than by dollars of NPV. However, NPV
remains the "more accurate" reflection of value to the business. The best case scenario for IRR is that it will be just as
accurate as NPV, while NPV will always be accurate. Thus, NPV is the correct method to use when making project decisions.
In addition if the NPV of one project is higher than another and the other project has a higher IRR, then the cross over point
method can be used to solve this dispute.
Cross Over Point > RR = Accept project with higher NPV and if the Cross Over Point < RR = Accept project with higher
IRR
See also
External links
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