Calculation
Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the net present value as a function of the rate of return. A rate of return for which this function is zero is an internal rate of return.
Given the (period, cash flow) pairs (, ) where is a positive integer, the total number of periods, and the net present value, the internal rate of return is given by in:
The period is usually given in years, but the calculation may be made simpler if is calculated using the period in which the majority of the problem is defined (e.g., using months if most of the cash flows occur at monthly intervals) and converted to a yearly period thereafter.
Any fixed time can be used in place of the present (e.g., the end of one interval of an annuity); the value obtained is zero if and only if the NPV is zero.
In the case that the cash flows are random variables, such as in the case of a life annuity, the expected values are put into the above formula.
Often, the value of cannot be found analytically. In this case, numerical methods or graphical methods must be used.
Read more about this topic: Internal Rate Of Return
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