# Chapter 17

# THE INTERNAL RATE OF RETURN

*A whimsical “nugget”*

If net present value (NPV) is inversely proportional to the discounting rate, then there must exist a discounting rate that makes NPV equal to zero.

The discounting rate that makes net present value equal to zero is called the “internal rate of return (IRR)” or “yield to maturity”.

To apply this concept to capital expenditure, simply replace “yield to maturity” by “IRR”, as the two terms mean the same thing. It is just that one is applied to financial securities (yield to maturity) and the other to capital expenditure (IRR).

**Section 17.1**

## HOW IS INTERNAL RATE OF RETURN DETERMINED?

To calculate IRR, make *r* the unknown and simply use the NPV formula again. The rate *r* is determined as follows:

To use the same example from the previous chapter:

In other words, an investment's internal rate of return is the rate at which its market value is equal to the present value of the investment's future cash flows.

It is possible to use trial-and-error to determine IRR. This will result in an interest rate that gives a negative net present value and another that gives a positive net present value. These negative and positive values constitute a range of values which can be narrowed until the yield to maturity is found; in this case ...

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