Calculate the price at the beginning of year 1 of an 8% annual coupon bond with face value $1,000 and 5 years to maturity. $\begin{array}{lr}
&\text { 1-Year } \
&\text { Forward }\
\text { Year } & \text { Rate } \
1 & 5 \% \
2 & 5.5 \% \
3 & 6.0 \% \
4 & 6.5 \% \
5 & 7.0 \%
\end{array}$
A) $1,105.47
B) $1,131.91
C) $1,084.25
D) $1,150.01
E) $719.75

Question

Quizplus · Accepted Answer

To calculate the price of the bond at the beginning of year 1, we need to discount all the cash flows (8% of the face value, or $80, paid annually) by the corresponding forward rates.

For example, the first cash flow of $80 to be received at the end of year 1 should be discounted by 5%, the year 1 forward rate. The second cash flow of $80 to be received at the end of year 2 should be discounted by the product of the year 1 and year 2 forward rates, or (1.05)(1.055) = 1.108.

Using this method for all five cash flows and summing them, we get a present value of $1,084.25, closest to choice C.

Calculate the Price at the Beginning of Year 1 of an 8