An unlevered company (just common stock, no preferred) with a cost of equity of 16% generates $2 million in earnings before interest and taxes (EBIT) each year. The decides to alter its capital structure to include debt by adding $6 million in debt with a pre-tax cost of 4% to its capital structure and using the proceeds to reduce equity by a like amount as to keep total invested capital unchanged. The firm pays a tax rate of 28%. Assuming that the company's EBIT stream can be earned into perpetuity and that the debt can be perpetually issued (or rolled), what is the firm's new weighted average cost of capital?
Value of unlevered firm = EBIT*(1-tax rate)/cost of equity
=2*(1-0.28)/0.16=9 m
Value of levered firm = Value of unlevered firm + debt*tax rate
=9+6*0.28=10.68
D/E = debt/(Value of levered firm-debt)
=6/(10.68-6)=1.282
Levered cost of equity = Unlevered cost of equity+D/E*( Unlevered cost of equity-cost of debt)*(1-tax rate) |
Levered cost of equity = 16+1.282*(16-4)*(1-0.28) |
Levered cost of equity = 27.08 |
D/A = D/(E+D) |
D/A = 1.282/(1+1.282) |
=0.5618 |
Weight of equity = 1-D/A |
Weight of equity = 1-0.5618 |
W(E)=0.4382 |
Weight of debt = D/A |
Weight of debt = 0.5618 |
W(D)=0.5618 |
After tax cost of debt = cost of debt*(1-tax rate) |
After tax cost of debt = 4*(1-0.28) |
= 2.88 |
WACC=after tax cost of debt*W(D)+cost of equity*W(E) |
WACC=2.88*0.5618+27.08*0.4382 |
WACC =13.48% |
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