Question

jackson corporations outstanding bonds have a $1,000 par - value, a 9% annual coupon, 10 years to maturity, and a 12% ytm. what is the bonds price? round your answer to the nearest cent.

Explanation:

Step1: Calculate annual coupon payment

The annual coupon rate is 9% and the par - value ($F$) is $1000$. The annual coupon payment ($C$) is calculated as $C = 0.09\times1000=90$.

Step2: Identify the number of periods and discount rate

The number of years to maturity ($n$) is 10 years, and the yield - to - maturity ($r$) is 12% or 0.12.

Step3: Calculate the present value of the coupon payments

The present value of the coupon payments is an ordinary annuity. The formula for the present value of an ordinary annuity is $PV_{C}=C\times\frac{1-(1 + r)^{-n}}{r}$. Substituting $C = 90$, $r=0.12$, and $n = 10$ into the formula:
\[

$$\begin{align*} PV_{C}&=90\times\frac{1-(1 + 0.12)^{-10}}{0.12}\\ &=90\times\frac{1 - 0.321973}{0.12}\\ &=90\times\frac{0.678027}{0.12}\\ &=90\times5.650223\\ &=508.52 \end{align*}$$

\]

Step4: Calculate the present value of the par value

The formula for the present value of a single future amount is $PV_{F}=F\times(1 + r)^{-n}$. Substituting $F = 1000$, $r = 0.12$, and $n = 10$ into the formula:
\[

$$\begin{align*} PV_{F}&=1000\times(1 + 0.12)^{-10}\\ &=1000\times0.321973\\ &=321.97 \end{align*}$$

\]

Step5: Calculate the bond price

The bond price ($P$) is the sum of the present value of the coupon payments and the present value of the par value, $P=PV_{C}+PV_{F}$.
\[

$$\begin{align*} P&=508.52+321.97\\ &=830.49 \end{align*}$$

\]

Answer:

830.49