The market required rate of return on a bond (kd) is more commonly referred to as the bond's yield to maturity. Yield to maturity (YTM) is the expected rate of return on a bond if bought at its current market price and held to maturity; it is also known as the bond's internal rate of return (IRR). Mathematically, it is the discount rate that equates the present value of all expected interest payments and the payment of principal (face value) at maturity with the bond's current market price. For an example, let's return to, the valuation equation for an interest-bearing bond with a finite maturity.
If we now substitute actual values for I, MV, and P,„ we can solve for kd, which in this case would be the bond's yield to maturity. However, the precise calculation for yield to maturity is rather complex and requires bond value tables, or a sophisticated handheld calculator, or a computer.
Interpolation. If all we have to work with are present value tables, we can still determine an approximation of the yield to maturity by making use of a trial-and-error procedure. To illustrate, consider a $l,000-par-value bond with the following characteristics: a current market price of $761, 12 years until maturity, and an 8 percent coupon rate (with interest paid annually). We want to determine the discount rate that sets the present value of the bond's expected future cash-flow stream equal to the bond's current market price. Suppose that we start with a 10 percent discount rate and calculate the present value of the bond's expected future cash flows. For the appropriate present value interest factors, we make use of Tables II and IV in the Appendix at the end of the book.
A 10 percent discount rate produces a resulting present value for the bond that is greater than the current market price of $761. Therefore we need to try a higher discount rate to handicap the future cash flows further and drive their present value down to $761.
This time the chosen discount rate was too large. The resulting present value is less than the current market price of $761. The rate necessary to discount the bond's expected cash flows to $761 must fall somewhere between 10 and 15 percent.