Question

12. Protekter and Gambler (PKGR) currently has debt equity ratio of approximately 0.22. The current beta of its stock is 0.55. The expectation of the market premium is 9.5%. PKGR can borrow at 4.5%, just 20 basis points over the risk free rate of 4.3%

12.1) What is the weighted average cost of capital with the current capital structure?

12.2) If PKGR wants to increase its debt-to-equity ratio to 0.55 through a leveraged recap, what is the beta of PKGR after this transaction?

12.3) What is the weighted average cost of capital after transaction?

Answer 1

12.1)

Expected return of the stock=Rf+Beta*Rmp

Rf=Risk Free rate=4.3%

Beta=0.55

Rmp=Market Premium=9.5%

Expected stock return=4.3+0.55*9.5=9.525%

Cost of Equity=9.525%

Cost of Debt=4.5%

Income tax rate is not mentioned. Hence it is ignored

Debt Equity ratio=0.22

D/E=0.22

D=0.22E

D+E=1.22E

Weight of debt in total capital=0.22E/1.22E=0.180328

Weight of equity in total capital=1/1.22=0.819672

Weighted Average Cost of Capital(WACC)= 0.180328*4.5+0.819672*9.525=8.62%

12.2)Debt Equity Ratio increased to 0.55:

Beta Unlevered=(Beta Levered)/(1+(1-TC)*D/E)

TC=Tax rate

In this problem tax rate is not mentioned, hence ignored

Existing D/E=0.22

Beta Unlevered=0.55/(1+0.22)

Beta Unlevered=0.45082

If D/E is increased to 0.55,

Beta Levered=Beta Unlevered*(1+D/E)

Beta Levered=0.45082*(1+0.55)= 0.69877

12.3 WACC after the transaction:

Expected stock return=Rf+Beta*Rmp

Expected stock return=4.3+0.69877*9.5=10.94%

D/E=0.55

D=0.55E

D+E=1.55E

Weight of Debt=0.55/1.55=0.354839

Weight of Equity=1/1.55=0.645161

Weighted Average Cost of Capital=0.354839*4.5+0.645161*10.94=8.65%