Internal rate of return
From Free net encyclopedia
The internal rate of return (IRR) is defined as the discount rate that gives a net present value (NPV) of zero. The NPV is calculated from an annualized cash flow by discounting all future amounts to the present.
Example: Year Cash flow 0 -100 1 +120
Calculation of NPV: i = interest rate in percent NPV = -100 +120/[(1+i/100)^1] (This calculation is condensed, see the definition of net present value for the full story.)
Calculation of IRR (in percent): NPV = 0 -100 +120/[(1+IRR/100)^1] = 0 IRR = 20
As an investment decision tool, the calculated IRR is used to rate alternative investments. The investment alternative with the highest IRR is preferred. Note that placing the initial investment amount in the bank is always an alternative. Thus, any investments that do not match the bank's going deposit rate will not be realized.
It should also be noted that zeros of NPV as a function of IRR may lack existence or uniqueness if there is some alternation of positive and negative cash flow. The IRR exists and is unique if one or more years of net investment (negative cash flow) are followed by years of net revenues.
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 new measure called Modified Internal Rate of Return (MIRR) is used.
In spite of 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.
See also
es:Tasa interna de retorno fr:Taux de rentabilité interne pl:IRR pt:Taxa interna de retorno ru:Ставка внутренней доходности