Assuming perpetual cash flows in case II - Proposition I what is the value of equity for a firm with following values? EBIT = $50 million, Tax rate = 21%, Debt = $100 million , Cost of debt = 9%, Unlevered cost of capital = 12% using the information from above what is the cost of equity and the WACC?

Computation of the cost of equity:-

Value of unlevered firm = EBIT* (1- Tax rate)/ Unlevered cost of capital

= $50 million * (1 - 21%) / 12%

= $39.50 / 12%

= $329.17 million

Value of levered firm = Value of unlevered firm + (Tax rate * Debt)

= $329.17 + (21% * $100)

= $329.17 + $21

= $350.17 million

Value of equity = Value of firm - Value of debt

 = $350.17 million - $100 million 

= $250.17

Cost of equity = Unlevered cost of capital + (Unlevered cost of capital - Cost of debt)* (D/E)* (1-tax rate))

= 12% + ((12% - 9%) * ($100/$250.17) * (1-21%))

= 12% + (3% * 39.97% * 79%)

= 12% + 0.95%

= 12.95%

Computation of the WACC:-

Weight of debt = Debt / Value of firm

= $100 / $350.17

= 28.56%

Weight of equity = Equity / Value of firm

= $250.17 / $350.17

= 71.44%

WACC = (Weight of debt * Cost of debt * (1 - Tax rate)) + (Weight of equity * Cost of equity)

= (28.56% * 9% * (1 - 21%)) + (71.44% * 12.95%)

= 2.03% + 9.25%

= 11.28%