Answer:
Hello your question is incomplete below is the complete 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 with debt (wd) 0.10, 0.20, 0.30, 0.40, 0.50) ; (Percent financed with equity (wc) 0.90, 0.80, 0.70, 0.60, 0.50) ; (Debt-to-equity ratio (D/S) 0.11, 0.25, 0.43, 0.67, 1.00) ; (Bond Rating AAA, AA, A, BBB, BB) ; (Before-tax cost of debt 7.0%, 7.2, 8.0, 8.8, 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? 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%
Answer : wc = 0.6; wd = 0.4; WACC = 10.15% ( D )
Explanation:
Given data :
company's tax rate = 40% = 0.4
attached below is the tabular solution to the problem above
The formula for calculating ( Beta, Return and WACC on the table for each given D/E )
for Beta :
= 1 [ 1 + ( 1 - T ) (d/e) ]
d/e = debit to equity ratio
T = tax rate
for Return :
( risk free rate + market risk premium ) * beta
where risk free rate = 5%
market risk premium = 6%
for WACC:
Rd * Wd * ( 1 - company tax rate ) + return * WC
for D/E = 0.11
beta = 1[1 + (1-0.4)(0.11) ]
= 1.0667
return = (5% + 6%) (1.0667) = 11.40%
WACC = 7% * 0.1 * (1-0.4) + 11.40% * 0.9 = 10.68%
The option with the lowest WACC is the most suitable option hence we choose D
