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Williamson, Inc
Williamson, Inc., has a debt−equity ratio of 2.45. The company's weighted average cost of capital is 10 percent, and its pretax cost of debt is 6 percent. The corporate tax rate is 35 percent.
a. What is the company's cost of equity capital? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Cost of equity capital
________________%
b. What is the company's unlevered cost of equity capital? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Unlevered cost of equity __________________%
c. What would the weighted average cost of capital be if the company's debt−equity ratio were .80 and 1.70? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Weighted average
cost of capital
Debt-equity ratio .80 ______________%
Debt-equity ratio 1.70 _______________%
Expert Solution
Computation of Company's Cost of Equity Capital:
Weighted Average Cost of Capital (WACC) = [After Tax Cost of Debt * Weight of Debt] + [Cost of Equity * Weight of Equity]
10.00% = [(6.00% * (1-35%)) * (2.45/3.45)] + [Cost of Equity * (1 / 3.45)]
10.00% = [3.90% * 0.7101] + [Cost of Equity * 0.2899]
10.00% = 2.77% + Cost of Equity * 0.2899
7.23% = Cost of Equity * 0.2899
Cost of Equity = 7.23% / 0.2899
Cost of Equity = 24.95%
Computation of Unlevered Cost of Equity:
Unlevered Cost of Equity = Cost of Equity + Pre-tax Cost of Debt*D/E*(1-Tax Rate))/(1+D/E*(1-Tax Rate))
= 24.95% + 6%*2.45*(1-35%) / (1+2.45*(1-35%))
= 13.31%
Computation of Williamson's Weighted Average Cost of Capital if the debt-to-equity ratio is 0.80:
Weight Average Cost of Capital =D/E*1/(1+D/E)*Pre-tax Cost of Debt*(1-Tax Rate)+(Unlevered Cost+(Unlevered Cost- Pre-tax cost of debt)*D/E*(1-tax rate))*1/(1+D/E)
=0.80/1.80*6%*(1-35%)+(13.31%+(13.31%-6%)*0.80*(1-35%))*1/1.80
= 1.73% + 9.51%
=11.24%
Computation of Williamson's Weighted Average Cost of Capital if the debt-to-equity ratio is 1.70:
Weight Average Cost of Capital =D/E*1/(1+D/E)*Pre-tax Cost of Debt*(1-Tax Rate)+(Unlevered Cost+(Unlevered Cost- Pre-tax cost of debt)*D/E*(1-tax rate))*1/(1+D/E)
=1.70/2.70*6%*(1-35%)+(13.31%+(13.31%-6%)*1.70*(1-35%))*1/2.70
= 2.46% + 7.92%
= 10.38%
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