Gabriella has a perpetual annual cash flow of $55 million, and the market value

Question

Gabriella has a perpetual annual cash flow of $55 million, and the market value of its all-equity financed securities is $500 million. The asset beta is 1.0 and the stock price is $100. The firm decides to raise $150 million in debt and then retire an equal amount of equity. The debt has a beta of 0.2, while the interest rate on debt is 5%. There are no personal or corporate taxes, or any other market imperfections.
What is the weighted average cost of capital after the issue of debt and retirement of equity? What is the beta of Gabriella’s equity after the issue of debt?
(all the information given in the text).

Explanation / Answer

cost of equity=55/500=11%

cost of debt=5%

D=150

E=500-150=350

D/E=150/350=3/7

pd=D/(D+E)=0.3

pe=E/(D=E)=0.7

t=0 as no taxes

WACC=pd*(1-t)cost of debt+pe*cost of equity

hence, WACC=0.3*5+0.7*11=9.2%

Unlevered beta=1

Levered Beta=Unlevered beta*(1+(1-t)*D/E)-beta of debt*(1-t)*D/E

Hence, levered beta=1*(1+D/E)-0.2*D/E=9.4/7=1.3428

This is beta of the firm

Beta of equity*E/(D+E)+Beta of debt*D/(D+E)=1.3428

hence, beta of equity=(1.3428*500-0.2*150)/350=1.8325

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