Question

Williamson, Inc. has a debt-equity ration of 2.5. The firm’s weighted average cost of capital is 10% and its pre-tax cost of debt is 6%. Williamson faces a corporate tax rate of 35%. 1. What is Williamson’s cost of equity capital? 2. What is Williamson’s unlevered cost of equity capital? 3. What would Williamson’s WACC be if the firm’s debt-equity ratio were 0.75? What is it were 1.5?

Answer 1

Answer:

Debt Equity Ratio =2.5

Weight of debt =2.5/3.5

Weight of Equity =1/3.5

a. WACC =Weight of Equity*Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)

10% = 1/3.5*Cost of Equity Capital+2.5/3.5*6%*(1-35%)

(10%-2.5/3.5*6%*(1-35%))*3.5 = Cost of Equity Capital

Cost of Equity Capital = 25.25%

b) Cost of Levered Equity Capital=Cost of Unlevered Equity Capital+Debt*(1-Tax Rate)/Equity*(Cost of Unlevered Equity Capital-Cost of Debt)

25.25% = Cost of Unlevered Equity Capital+2.5*(1-35%)*(Cost of Unlevered Equity Capital-6%)

Cost of Unlevered equity *(1+2.5*0.65)=(25.25%+2.5*0.65*6%)

Cost of Unlevered Equity =(25.25%+2.5*0.65*6%) / (1+2.5*0.65)

Cost of Unlevered Equity = 13.3333%

c) At debt Equity ratio of 0.75

Cost of Levered Equity Capital = Cost of Unlevered Equity Capital+Debt*(1-Tax Rate)/Equity*(Cost of Unlevered Equity Capital-Cost of Debt)

Cost of Levered Equity Capital= 13.3333% + (13.3333%-6%)*0.75*(1-35%)

Cost of Levered Equity Capital =16.9083%

WACC = Weight of Equity*Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)

WACC = 1/(0.75+1)*16.9083%+0.75/(1+0.75)*6%*(1-35%)

WACC = 11.33%

At debt Equity ratio of 1.50

Cost of Levered Equity Capital=Cost of Unlevered Equity Capital+Debt*(1-Tax Rate)/Equity*(Cost of Unlevered Equity Capital-Cost of Debt)

Cost of Levered Equity = 13.3333% + (13.3333%-6%)*1.50*(1-35%)

Cost of Levered Equity = 18.5333%

WACC =Weight of Equity*Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)

=1/(1+1.30)*18.5333%+1.30/(1+1.30)*6%*(1-35%)

=10.26%