Question

Question:Cox Media Corporation pays an 11 percent coupon rate on debentures that are due in 10 years. The current yield to maturity on bonds of similar risk is 8 percent. The bonds are currently callable at $1,110. The theoretical value of the bonds will be equal to the present value of the expected cash flow from the bonds.

a. Find the market value of the bonds using semiannual analysis.

b. Do you think the bonds will sell for the price you arrived at in part a? Why?

Short answer

Answer

(a) The price per bond is computed as $1,203.85.

(b) Bonds should not be sold at this price, as call price is low.

Step-by-step solution

Computation of price of the bond

$\begin{array}{rcl}\mathbf{SemiannualCoupon}& \mathbf{=}& \left(\frac{\mathbf{CouponRate}}{\mathbf{2}}\right)\mathbf{\times }\mathbf{FaceValue}\\ & \mathbf{=}& \left(\frac{\mathbf{0}\mathbf{.}\mathbf{11}}{\mathbf{2}}\right)\mathbf{\times }\mathbf{1}\mathbf{,}\mathbf{000}\\ & \mathbf{=}& \mathbf{\$}\mathbf{55}\\ \mathbf{Priceperbond}& \mathbf{=}& \mathbf{CouponPayment}\mathbf{\times }\left(\frac{\mathbf{1}\mathbf{-}{\left(\mathbf{1}\mathbf{+}\mathbf{r}\right)}^{\mathbf{-}\mathbf{n}}}{\mathbf{r}}\right)\mathbf{+}\frac{\mathbf{FaceValue}}{{\left(\mathbf{1}\mathbf{+}\mathbf{r}\right)}^{\mathbf{n}}}\\ & \mathbf{=}& \mathbf{55}\mathbf{\times }\left(\frac{\mathbf{1}\mathbf{-}{\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{04}\right)}^{\mathbf{-}\mathbf{10}\mathbf{\times }\mathbf{2}}}{\mathbf{0}\mathbf{.}\mathbf{04}}\right)\mathbf{+}\frac{\mathbf{1}\mathbf{,}\mathbf{000}}{{\left(\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{04}\right)}^{\mathbf{10}\mathbf{\times }\mathbf{2}}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{203}\mathbf{.}\mathbf{85}\\ & & \end{array}$

Bonds will sell or not

The current call price of the bond is $1,110 which indicates that the price of the bond computed in part a is less than the current call price. Therefore, the bond shouldn’t be sold at $1,203.85