Question 8.A.4: A Bond’s Yield to Maturity PROBLEM: You can purchase a U.S. ...
A Bond’s Yield to Maturity
PROBLEM: You can purchase a U.S. corporate bond from your broker for $1,099.50. The bond has six years to maturity, and an annual coupon rate of 5 percent. Another broker offers you a dollar Eurobond (a dollar-denominated bond sold overseas) with a yield of 3.17 percent, which is denominated in U.S. dollars and has the same maturity and credit rating as the U.S. corporate bond. Which bond should you buy?
APPROACH: Solving this problem involves two steps. First, we must compute the U.S. bond’s yield to maturity. The bond pays coupon interest semiannually, so we have to convert the bond data to semiannual periods: (1) the number of compounding periods is 12 (6 years × 2 periods per year = 12 periods) and (2) the semiannual coupon payment is $25 [($1,000 × 0.05)/2 = $50/2 = $25]. Second, we must annualize the yield for the U.S. bond so that we can compare its yield with that of the Eurobond.
We can solve for the yield to maturity using a financial calculator:
The answer, 1.5831 percent, is the semiannual yield. Since the Eurobond’s yield, 3.17 percent, is an annualized yield because of that bond’s yearly compounding, we must annualize the yield on the U.S. bond in order to compare the two.² We annualize the yield on the U.S. bond by computing its effective annual yield:
\begin{matrix} EAY &=& \left(1+\frac{Quoted \ interest \ rate}{m}\right) ^m -1 \\ &=& \left(1+\frac{0.031661}{2}\right) ^2 -1 \\ &=& \left(1.015831\right)^2 -1=0.03191, \ or \ 3.191\% \end{matrix}The U.S. corporate bond is a better deal because of its higher EAY (3.191 percent 3.170 percent). Notice that if we had just annualized the yield on the U.S. bond by multiplying the semiannual yield by 2 (1.5831 percent × 2 = 3.1661 percent) and compared the simple yields for the Eurobond and the U.S. bond (3.170 percent 3.1661 percent), we would have selected the Eurobond. This would have been the wrong economic decision.
²Notice that, for annual compounding, the yield to maturity equals the EAY; for the Eurobond, the yield to maturity = 3.17 percent and EAY = (1 + Quoted interest rate/m)^m – 1 = (1 + 0.0317/1) – 1 = (1 + 0.0317) – 1 = 0.0317, or 3.17 percent.