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

Cost of Equity Capital = 25.25%, Cost of Unlevered Equity = 13.33%, WACC = 11.33%, 10.26%.

Given Information

The Debt Equity Ratio is 2.5

The Weight of debt is 2.5/3.5

The Weight of Equity is 1/3.5.

1.  Calculation of Williamson’s cost of equity capital

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%))= (1/3.5 * Cost of Equity Capital)

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

(0.10 - 0.02785714285)*2.5 = Cost of Equity Capital

0.25250000002 = Cost of Equity Capital

Cost of Equity Capital = 25.25%

2. Calculation of Williamson’s Cost of Levered Equity Capital

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 = 0.35 / 2.625

Cost of Unlevered Equity = 0.13333333333

Cost of Unlevered Equity = 13.3333%

3. Calculation of Williamson’s WACC

a. 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%

b. 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)

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

WACC = 10.26%

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