“Buy when everyone else is selling and hold until everyone else is buying. That’s not just a catchy slogan. It’s the very essence of successful investing.”
– J. Paul Getty
Valuation and Rates of Return (part C)
by
Charles Lamson
 |
Time to Maturity  Table 1 Impact of time to maturity on bond prices The impact of a change in yield to maturity on valuation is also affected by the remaining time to maturity. The effect of a bond paying 2 percentage points more or less than the going rate of interest is quite different for a 20-year bond than it is for a 1-year bond. In the latter case, the investor will only be gaining or giving up $20 for one year. That is certainly not the same as having this $20 differential for an extended period. Let's once again return to the 10 percent interest rate bond and show the impact of a 2 percentage point decrease or increase in yield to maturity for varying times to maturity. The values are shown in Table 1 above and graphed in Figure 1 below. The upper part of Figure 1 shows how the amount (premium) above par value is reduced as the number of years to maturity becomes smaller and smaller. Figure 1 should be read from left to right. The lower part of the figure shows how the amount (discount) below par value is reduced with progressively fewer years to maturity. Clearly, the longer the maturity, the greater the impact of changes in yield. Figure 1  Determining Yield to Maturity from the Bond Price Until now, in the previous posts of this analysis, we have used yield to maturity as well as other factors, such as the interest rate on the bond and the number of years to maturity, to compute the price of the bond. We shall now assume we know the price of the bond, the interest rate on the bond, and the years to maturity, and we wish to determine the yield to maturity. Once we have computed this value, we have determined the rate of return that investors are demanding in the marketplace to provide for inflation, risk, and other factors. Let's once again present Formula 1 from Part 31 of this analysis.   Assume a 15 year bond pays $110 per year (11 percent) in interest and $1,000 after 15 years in principal repayment. The current rate of the bond is $932.21. We wish to compute the yield to maturity, or discount rate, that equates future flows with the current price. In this trial-and-error process, the first step is to choose an initial percentage in the tables to try as the discount rate. Since the bond is trading below the par value of $1,000, we can assume the yield to maturity discount rate must be above the quoted interest rate of 11 percent. Let's begin the trial-and-error process. A 13 Percent Discount Rate As a first approximation, we might try 13 percent and compute the present value of the bond as follows: Present Value of Interest Payments---  *Again, note that the IF in the subscript indicates we are dealing the interest factor from the tables, and the A in the subscript indicates we are using the annuity table rather than a single amount. Present Value of Principal Payment at Maturity---  Total Present Value---  The answer of $870.82 is below the current bond price of $932.21 as stated on previously. This indicates we have used too high a discount rate in creating too low of value.
A 12 Percent Discount Rate As a next step in the trial and error process we will try 12 percent. Present Value of Interest Payments---  Present Value of Principal Payment at Maturity---  Total Present Value  The answer precisely matches the bond price of $932.21 that we are evaluating. That indicates the correct yield to maturity for the bond is 12 percent. If the computed value were slightly different from the price of the bond, we could use interpolation (a type of estimation) to arrive at the correct answer. An example of interpolating to derive yield to maturity is presented below. The Bond Yield to Maturity Using Interpolation We will use a numerical example to demonstrate this process. Assume a 20-year bond pays $118 per year (11.8 percent) in interest and $1,000 after 20 years in principal repayment. The current price of the bond is $1,085. We wish to determine the yield to maturity or discount rate that equates the future flows with the current price.
Since the bond is trading above par value at $1,085, we can assume the yield to maturity must be below the quoted interest rate of 11.8 percent (the yield to maturity would be the full 11.8 percent at a bond price of $1,000). As a first approximation, we will try 10 percent. Annual analysis is used. Present Value of Interest Payments---  Present Value of Principal Payment at Maturity---  Total Present Value---  The discount rate of 10 percent gives us too high a present value in comparison to the current bond price of $1,085. Let's try a higher discount rate to get a lower price. We will use 11 percent. Present Value of Interest Payments---  Present value of principal payment at maturity---  Total Present Value  The discount rate of 11 percent gives us a value slightly lower than the bond price of $1,085. The rate for the bond must fall between 10 and 11 percent. using linear interpolation, the answer is 10.76 percent.   *MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 275-277, 299-300* end |
No comments:
Post a Comment