Question

Russell Container Corporation has a \(1,000 par value bond outstanding with 30 years to maturity. The bond carries an annual interest payment of \)105 and is currently selling for $880 per bond. Russell Corp. is in a 40 percent tax bracket. The firm wishes to know what the aftertax cost of a new bond issue is likely to be. The yield to maturity on the new issue will be the same as the yield to maturity on the old issue because the risk and maturity date will be similar. a. Compute the yield to maturity on the old issue and use this as the yield for the new issue. b. Make the appropriate tax adjustment to determine the aftertax cost of debt.

Short answer

Yield to maturity is 11.6%.

After tax cost of debt is 6.96%

Step-by-step solution

a. Calculation of yield to maturity

$\begin{array}{rcl}\mathbf{Yield} \mathbf{to} \mathbf{maturity} & \mathbf{=}& \frac{\mathbf{Coupon}\mathbf{+}\frac{\left(\mathbf{FV}\mathbf{-}\mathbf{Price}\right)}{\mathbf{n}}}{\frac{\left(\mathbf{FV}\mathbf{+}\mathbf{Price}\right)}{\mathbf{2}}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \frac{\mathbf{105}\mathbf{+}\frac{\left(\mathbf{1000}\mathbf{-}\mathbf{880}\right)}{\mathbf{30}}}{\frac{\left(\mathbf{1000}\mathbf{+}\mathbf{880}\right)}{\mathbf{2}}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \frac{\mathbf{105}\mathbf{+}\mathbf{4}}{\mathbf{940}}\mathbf{\times }\mathbf{100}\\ & \mathbf{=}& \mathbf{11}\mathbf{.}\mathbf{6}\mathbf{\%}\\ & & \end{array}$

11.6% is the yield to maturity for the bond.

b. Calculation of after tax cost of debt

$$\begin{gathered} \mathbf{\text{Kd}}\left(\text{Cost of debt}\right)\mathbf{\text{=}}\mathbf{ }\mathbf{ }\mathbf{\text{Yield}}\left(\text{1 - Tax Rate}\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{11}\mathbf{.}\mathbf{6}\mathbf{\times }\left(1-40\%\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{11}\mathbf{.}\mathbf{6}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{6} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{96}\mathbf{\%} \end{gathered}$$

The aftertax cost of debt is 6.96%.