Chapter 17THE INTERNAL RATE OF RETURN

A well-deserved return

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.

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 CALCULATING YIELD TO MATURITY

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

italic upper N upper P upper V equals sigma-summation Underscript n minus 1 Overscript upper N Endscripts StartFraction upper F Subscript n Baseline Over left-parenthesis 1 plus r right-parenthesis Superscript n Baseline EndFraction minus upper V 0

To use the same example from Section 16.4:

StartFraction 0.8 Over left-parenthesis 1 plus r right-parenthesis EndFraction plus StartFraction 0.8 Over left-parenthesis 1 plus r right-parenthesis squared EndFraction plus ellipsis plus StartFraction 0.8 Over left-parenthesis 1 plus r right-parenthesis Superscript 5 Baseline EndFraction equals 2

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

In our illustration, the IRR is about 28.6% (see figure in Section 16.4).

Section 17.2 YIELD TO MATURITY AS AN INVESTMENT CRITERION

The yield to maturity is frequently used in financial markets because it represents for the investor the return to be expected for a given level of risk, which they can then compare to their required ...

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