LeCompte Learning Solutions is considering making a change to its capital struct

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:

Percent financed Percent financed Debt-to-equity                Bond                Before-tax

with debt (wd)                with equity (ws)   ratio      (D/S)                           Rating               cost of debt

0.10                              0.90                              0.10/0.90 = 0.11 AAA              7.0%

0.20                              0.80                              0.20/0.80 = 0.25 AA                   7.2

0.30                              0.70                              0.30/0.70 = 0.43 A                     8.0

0.40                              0.60                              0.40/0.60 = 0.67 BBB                 8.8

0.50                              0.50                              0.50/0.50 = 1.00 BB                   9.6

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%. 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? (the lowest WACC)

Explanation / Answer

Formula for calculation of levered Beta =Unlevered Beta*(1+((1-Tax rate)*Debt/Equity)))

Optimal capital structure is one where the weighted average cost of capital is low i.e., 10.18%. Therefore, optimal capital structure is 50% debt and 50% equity.

% of debt (A) % of equity (B) Debt to Equity ratio (C ) Before tax cost of debt (D) Levered Beta=Unlevered beta i.e.(E)=1*(1+(1-.40)*(C )) Risk free rate (F) Market risk premium (G) Cost of equity (H)=(F)+[(E )*(G)] After tax cost of debt (I)=(1-.40)*(D) Weighted cost of capital (J)=(A)*(I)+(B)*(H) 0.1 0.9 0.11 7% 1.07 5% 6% 11.400% 4.20% 10.68% 0.2 0.8 0.25 7.20% 1.15 5% 6% 11.900% 4.32% 10.38% 0.3 0.7 0.43 8% 1.26 5% 6% 12.543% 4.80% 10.22% 0.4 0.6 0.67 8.80% 1.40 5% 6% 13.400% 5.28% 10.15% 0.5 0.5 1.00 9.60% 1.60 5% 6% 14.600% 5.76% 10.18%

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