LeCompte Learning Solutions is considering making a change to its capital structure in hopes of increasing its value.The company's capital structure consists of debt and common stock.In order to estimate the cost of debt,the company has produced the following table: $\begin{array}{ccccc}\begin{array}{c}\text { Percent financed } \\\text { with debt }\left(\mathrm{w}_{\mathrm{d}}\right) \end{array} & \begin{array}{c}\text { Percent financed } \\\text { with equity }\left(\mathrm{w}_{\mathrm{c}}\right) \end{array} & \begin{array}{c}\text { Debt-to-equity } \\\text { ratio }(\mathrm{D} / \mathrm{S}) \end{array} & \begin{array}{c}\text { Bond } \\\text { Rating }\end{array} & \begin{array}{c}\text { Before-tax } \\\text { cost of debt }\end{array} \\\hline 0.10 & 0.90 & 0.10 / 0.90=0.11 & \text { AAA } & 7.0 \% \\0.20 & 0.80 & 0.20 / 0.80=0.25 & \text { AA } & 7.2 \\0.30 & 0.70 & 0.30 / 0.70=0.43 & \text { A } & 8.0 \\0.40 & 0.60 & 0.40 / 0.60=0.67 & \mathrm{BBB} & 8.8 \\0.50 & 0.50 & 0.50 / 0.50=1.00 & \mathrm{BB} & 9.6\end{array}$
The company uses the CAPM to estimate its cost of common equity,r_s.The risk-free rate is 5% and the market risk premium is 6%.LeCompte estimates that if it had no debt its beta would be 1.0.(Its "unlevered beta," b_U,equals 1.0.) The company's tax rate,T,is 40%.
On the basis of this information,what is LeCompte's optimal capital structure,and what is the firm's cost of capital at this optimal capital structure?

Question

LeCompte Learning Solutions is considering making a change to its capital structure in hopes of increasing its value.The company's capital structure consists of debt and common stock.In order to estimate the cost of debt,the company has produced the following table:

\begin{array}{ccccc}\begin{array}{c}\text { Percent financed } \\\text { with debt }\left(\mathrm{w}_{\mathrm{d}}\right) \end{array} & \begin{array}{c}\text { Percent financed } \\\text { with equity }\left(\mathrm{w}_{\mathrm{c}}\right) \end{array} & \begin{array}{c}\text { Debt-to-equity } \\\text { ratio }(\mathrm{D} / \mathrm{S}) \end{array} & \begin{array}{c}\text { Bond } \\\text { Rating }\end{array} & \begin{array}{c}\text { Before-tax } \\\text { cost of debt }\end{array} \\\hline 0.10 & 0.90 & 0.10 / 0.90=0.11 & \text { AAA } & 7.0 \% \\0.20 & 0.80 & 0.20 / 0.80=0.25 & \text { AA } & 7.2 \\0.30 & 0.70 & 0.30 / 0.70=0.43 & \text { A } & 8.0 \\0.40 & 0.60 & 0.40 / 0.60=0.67 & \mathrm{BBB} & 8.8 \\0.50 & 0.50 & 0.50 / 0.50=1.00 & \mathrm{BB} & 9.6\end{array}

The company uses the CAPM to estimate its cost of common equity,r_s.The risk-free rate is 5% and the market risk premium is 6%.LeCompte estimates that if it had no debt its beta would be 1.0.(Its "unlevered beta," b_U,equals 1.0.) The company's tax rate,T,is 40%.
On the basis of this information,what is LeCompte's optimal capital structure,and what is the firm's cost of capital at this optimal capital structure?

Quizplus · Accepted Answer

r_RF = 5%; r_M F1F1F1S1F1F1F10 r_RF = 6%.r_s = r_RF + (r_M F1F1F1S1F1F1F10 r_RF)b.WACC = r_d F1F1F1S1F1F1F10 w_d F1F1F1S1F1F1F10 (1 F1F1F1S1F1F1F10 T)+ r_s F1F1F1S1F1F1F10 w_c.You need to use the D/E ratio given for each capital structure to find the levered beta using the Hamada equation.Then,use each of these betas with the CAPM to find the r_s for that capital structure.Use this r_s and r_d for each capital structure to find the WACC.The optimal capital structure is the one that minimizes the WACC. $$\begin{array} { c c c c c c c } ( \mathrm { D } / \mathrm { E } ) & \mathrm { b } = \mathrm { b } _ { \mathrm { U } } [ 1 + ( 1 - \mathrm { T } ) ( \mathrm { D } / \mathrm { E } ) ] & \mathrm { r } _ { \mathrm { s } } = \mathrm { r } _ { \mathrm { RF } } + \left( \mathrm { r } _ { \mathrm { M } } - \mathrm { r } _ { \mathrm { RF } } \right) \mathrm { b } & w _ { \mathrm { r } } & r _ { \mathrm { d } } & w _ { \mathrm { d } } & \mathrm { WACC } \ \hline \mathrm { 0.11 } & 1.0667 & 11.4005 \% & 0.9 & 7.0 \% & 0.1 & 10.68 \% \ 0 .25 & 1.1500 & 11.9000 & 0.8 & 7.2 & 0.2 & 10.38 \ 0.43 & 1.2571 & 12.5429 & 0.7 & 8.0 & 0.3 & 10.22 \ 0.67 & 1.4000 & 13.4000 & 0.6 & \mathbf { 8. 8 } & 0.4 & 10.15 \ 1.00 & 1.6000 & 14.6000 & 0.5 & 9.6 & 0.5 & 10.18 \end{array}$$ Far exmmple, if the D/E is $0.11$ : $$\begin{array} { l } \mathrm { b } = 1 . 0 [ 1 + ( 1 - \mathrm { T } ) ( \mathrm { D } / \mathrm { E } ) ] = 1 . 0 [ 1 + ( 1 - 0 .4 ) ( 0.1111 ) \ = 1 . 0667 . \ \mathrm { r } _ { s } = \mathrm { r } _ { \mathrm { RF } } + \left( \mathrm { r }_ { \mathrm { M } } - \mathrm { r } _ { \mathrm { RF } } \right) \mathrm { b } = 5 \% / 6 \% ( 1.0667 ) = 11.4 0\% \end{array}$$ The weights are given at 0.9 and 0.1 for equity and debt,respectively,and the r_d for that capital structure is given as 7%. $$\begin{array}{l} \text { WACB } = r _ { \mathrm { d } } \times W _ { \mathrm { d } } \times ( 1 - T ) + I _ { 5 } \times W _ { \mathrm { c } }\ = 7 \% \times 0 .1 \times ( 1 -0 .4 ) + 11.40\% \times 0 .9 = 10.68\% \end{array}$$ Do the same calculation for each of the capital structures and find each WACC.The optimal capital structure is the one that minimizes the WACC,which is 10.15%.Therefore,the optimal capital structure is 40% debt and 60% equity.

LeCompte Learning Solutions Is Considering Making a Change to Its