Question 8.A.3: The Price of a Bond PROBLEM: An investor is considering buy...
The Price of a Bond
PROBLEM: An investor is considering buying a U.S. corporate bond with an eight-year maturity and a coupon rate of 6 percent. Similar bonds in the marketplace yield 14 percent. How much should the investor be willing to pay for the bond? Using Equation 8.1 (or 8.2), set up the equation to be solved, and then solve the problem using your financial calculator. Note that the discount rate used in the problem is the 14 percent market yield on similar bonds (bonds of similar risk), which is the investor’s opportunity cost.
P_B=\frac{C_1}{1+i}+\frac{C_2}{(1+i)^2}+…+\frac{C_n+F_n}{(1+i)^n} 8.1
P_B=\frac{C/m}{1+i/m}+\frac{C/m}{(1+i/m)^2}+\frac{C/m}{(1+i/m)^3}+…+\frac{C/m+F_{mn}}{(1+i/m)^{mn}} 8.2
APPROACH: Since U.S. corporate bonds pay coupon interest semiannually, we first need to convert all of the bond data to reflect semiannual compounding: (1) the annual coupon payment is $60 per year (6 percent × $1,000 = $60) and the semiannual payment is $30 per period ($60/2 = $30); (2) the appropriate semiannual yield is 7 percent (14 percent/2 = 7 percent); and (3) the total number of compounding periods is 16 (2 periods per year × 8 years = 16 periods). The time line for the semiannual cash flows is as follows:
Using Equation 8.1 (or 8.2), the setup is as follows:
P_B=\frac{\$30}{1.07}+\frac{\$30}{(1.07)^2}+…+\frac{\$1,030}{(1.07)^{16}}To solve the problem using a fi nancial calculator, we enter the appropriate values and solve for PV:
The investor should be willing to pay $622.13 because the bond’s yield at this price would be exactly 14 percent, which is the current market yield on similar bonds. If the bond price was more than $622.13, the investment would yield a return of less than 14 percent. In this situation an investor would be better off buying the similar bonds in the market that yield 14 percent. Of course, if the investor can buy the bond for less than $622.13, the price is a bargain, and the return on investment will be greater than the market yield