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Williamson, Inc., has a debt-equity ratio of 1.7. The firm's weighted average cost of capital is 8.4%, and its pretax cost of debt is 5.3%. The corporate tax rate is 21%.
a) What is the company's cost of equity?
b) What is the company's unlevered cost of equity?
c) What would the company's weighted average cost of capital be if the firm's debt-equity ratio were 0.6?
a) Computation of Company's Cost of Equity:
Weighted Average Cost of Capital = Weight of Debt * Cost of Debt * (1 - Tax Rate) + Weight of Equity * Cost of Equity
8.4% = (1.7/(1+1.7)) * 5.3% * (1 - 21%) + (1/(1+1.7)) * Cost of Equity
8.4% = 2.64% + (1/2.7) * Cost of Equity
8.4% - 2.64% = (1/2.7) * Cost of Equity
Cost of Equity = 5.76%*2.7/1
Cost of Equity = 15.56%
b) Computation of Company's Levered Cost of Equity:
Using Modigillani Miller formula,
rL = rU + D/E ( rU - rD) * ( 1 - Tax Rate)
15.56% = rU + 1.7 * (rU - 5.3%)* (1 -0.21)
15.56% = ru * 1.343 * ( rU - 5.3%)
15.56% + 7.12% = 2.343 * rU
Unlevered Cost of Equity = rU = 9.68%
c) Computation of Company's weighted average cost of capital be if the firm's debt-equity ratio were 0.6:
Levered Cost of Equity = 9.68% + 0.6 * (9.8% - 5.3%) * ( 1 - 0.21) = 11.76%
Weighted Average Cost of Capital = (0.6/1.6) * 5.3% * (1 - 21%) + (1/1.6) * 11.76% = 1.87 + 8.54 = 8.92%