The US Government has a 3-year 5% coupon bond with a face value of $1,000. The bond pays annual coupons and the first coupon is due in one year. Using the data on zero coupon US Government bond yields in the table, below, what is the price of the coupon bond? $$\begin{array} { | c | c | }
\hline \text { Term } & \text { Yield } \
\hline t = 1 & 8.11 \% \
\hline t = 2 & 5.41 \% \
\hline t = 3 & 4.55 \% \
\hline
\end{array}$$

Question

The US Government has a 3-year 5% coupon bond with a face value of $1,000. The bond pays annual coupons and the first coupon is due in one year. Using the data on zero coupon US Government bond yields in the table, below, what is the price of the coupon bond? $$\begin{array} { | c | c | } 
\hline \text { Term } & \text { Yield } \
\hline t = 1 & 8.11 \% \
\hline t = 2 & 5.41 \% \
\hline t = 3 & 4.55 \% \
\hline
\end{array}$$

Quizplus · Accepted Answer

The price of the coupon bond is the present value of the future cash flows. The future cash flows are the annual coupons and the face value at maturity. The present value of the future cash flows is calculated using the zero coupon bond yields. The present value of the first coupon is $1,000 * 0.0811 = $81.10. The present value of the second coupon is $1,000 * 0.0541 = $54.10. The present value of the third coupon is $1,000 * 0.0455 = $45.50. The present value of the face value at maturity is $1,000 * 0.9545 = $954.50. The price of the coupon bond is the sum of the present values of the future cash flows, which is $81.10 + $54.10 + $45.50 + $954.50 = $1,135.20.

The US Government Has a 3-Year 5% Coupon Bond with a Face