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: $\begin{array}{ccccc}
\begin{array}{c}
\text { Percent financed } \
\text { with debt }\left(\mathrm{w}_{\mathrm{d}}\right)
\end{array} & \begin{array}{c}
\text { Percent financed } \
\text { with equity }\left(\mathrm{w}_{\mathrm{C}}\right)
\end{array} & \begin{array}{c}
\text { Debt-to-equity } \
\text { ratio }(\mathrm{D} / \mathrm{S})
\end{array} & \begin{array}{c}
\text { Bond } \
\text { Rating }
\end{array} & \begin{array}{c}
\text { Before-tax } \
\text { cost of debt }
\end{array} \
\hline 0.10 & 0.90 & 0.10 / 0.90=0.11 & \mathrm{AAA} & 7.0 \% \
0.20 & 0.80 & 0.20 / 0.80=0.25 & \mathrm{AA} & 7.2 \
0.30 & 0.70 & 0.30 / 0.70=0.43 & \mathrm{~A} & 8.0 \
0.40 & 0.60 & 0.40 / 0.60=0.67 & \mathrm{BBB} & 8.8 \
0.50 & 0.50 & 0.50 / 0.50=1.00 & \mathrm{BB} & 9.6
\end{array}$
The company uses the CAPM to estimate its cost of common equity, rs. 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," bU, equals 1.0.) The company's tax rate, T, is 40%.σσOn 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?
A) wc = 0.9; wd = 0.1; wacc = 14.96%
B) wc = 0.8; wd = 0.2; wacc = 10.96%
C) wc = 0.7; wd = 0.3; wacc = 7.83%
D) wc = 0.6; wd = 0.4; wacc = 10.15%
E) wc = 0.5; wd = 0.5; wacc = 10.18%

Question

Quizplus · Accepted Answer

rRF = 5%; rM σ rRF = 6%. rs = rRF + (rM σ rRF)b. WACC = rd × wd × (1 σ T) + rs × wc. 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 rs for that capital structure. Use this rs and rd for each capital structure to find the WACC. The optimal capital structure is the one that minimizes the WACC.
 $\begin{array}{ccccccc}
(D / E) & b=b U[1+(1-T)(D / E)] & r_{S}=r_{R F}+\left(r_{M}-\right. \left.r_{R F}\right) b& W_{C} & r_{d} & W_{d} & \text { WACC } \
\hline 0.11 & 1.0667 & 11.4005 \% & 0.9 & 7.0 \% & 0.1 & 10.68 \% \
0.25 & 1.1500 & 11.9000 & 0.8 & 7.2 & 0.2 & 10.38 \
0.43 & 1.2571 & 12.5429 & 0.7 & 8.0 & 0.3 & 10.22 \
0.67 & 1.4000 & 13.4000 & 0.6 & 8.8 & 0.4 & 10.15 \
1.00 & 1.6000 & 14.6000 & 0.5 & 9.6 & 0.5 & 10.18
\end{array}$ 
 $\begin{aligned}
\text { For example, if the D/E is 0.11: } \quad & b=1.0[1+(1-\mathrm{T})(\mathrm{D} / \mathrm{E})]=1.0[1+(1-0.4)(0.1111)] \
&=1.0667 \
& r_{S}=r \mathrm{RF}+(r \mathrm{M}-r \mathrm{RF}) \mathrm{b}=5 \%+6 \%(1.0667)=11.40 \%
\end{aligned}$ 
The weights are given at 0.9 and 0.1 for equity and debt, respectively, and the rd for that capital structure is given as 7%.
 $\begin{aligned}
W_{A C C} &=r_{d} \times W_{d} \times(1-T)+r_{\mathrm{S}} \times W_{\mathrm{C}} \
&=7 \% \times 0.1 \times(1-0.4)+11.40 \% \times 0.9=10.68 \%
\end{aligned}$ 
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