Question

Question:Twenty-five-year B-rated bonds of Parker Optical Company were initially issued at a 12 percent yield. After 10 years the bonds have been upgraded to Aa2. Such bonds are currently yielding 10 percent to maturity. Use Table 16-2 to determine the price of the bonds with 15 years remaining to maturity. (You do not need the bond ratings to enter the table; just use the basic facts of the problem.)

Short answer

Answer

The price per bond is computed as $1,153.72

Step-by-step solution

Definition of Coupon rate

The coupon rate is defined as the normal rate paid by the financial instrument. It is the annual coupon payment paid by the issuer of the securities.

Computation of price of the bond

$$\begin{gathered} \mathbf{SemiannualCoupon}\mathbf{=}\left(\frac{\mathbf{CouponRate}}{\mathbf{2}}\right)\mathbf{\times }\mathbf{FaceValue} \\ \mathbf{=}\left(\frac{\mathbf{0}\mathbf{.}\mathbf{12}}{\mathbf{2}}\right)\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{000} \\ \mathbf{=}\mathbf{\$}\mathbf{60} \\ \mathbf{Priceperbond}\mathbf{=}\mathbf{CouponPayment}\mathbf{\times }\mathbf{\left(}\frac{{\displaystyle 1-{\left(1+r\right)}^{-n}}}{{\displaystyle r}}\mathbf{\right)}\mathbf{+}\frac{{\displaystyle \mathbf{FaceValue}}}{{\displaystyle {\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{r}\mathbf{)}}^{\mathbf{n}}}} \\ \mathbf{=}\mathbf{60}\mathbf{\times }\mathbf{\left(}\frac{{\displaystyle 1-{\left(1+0.05\right)}^{-15\times 2}}}{{\displaystyle 0.05}}\mathbf{\right)}\mathbf{+}\frac{{\displaystyle \mathbf{1}\mathbf{,}\mathbf{000}}}{{\displaystyle {\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{05}\mathbf{)}}^{\mathbf{15}\mathbf{\times }\mathbf{2}}}} \\ \mathbf{=}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{153}\mathbf{.}\mathbf{72} \end{gathered}$$