Capital Structure

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Re = Rf + βe (Rm – Rf)

Re = Ra + (D/E)(Ra – Rd)

Ra = (D/V)Rd + (E/V)Re

βE = βA + (D/E)(βA – βD)

Re = Rf + βe (Rm – Rf) → Re = 10% + 1.5(18%-10%) = 22%

Re = 22%

D/V = 0.5 → E/V = 0.5 → D/E = 1.0

Ra = (D/V)Rd + (E/V)Re → 0.5*12% + 0.5*22% = 17%

Ra = 17%

Ra = Rf + βa (Rm – Rf) → 17% = 10% + βa (18%-10%) → βa = (17% - 10%)/8% = 0.875

βa = 0.875

βE = βA + (D/E)(βA – βD) → 1.5 = 0.875 + (1)(0.875 – βD) → βD = 0.875 – 1.5 + 0.875 = 0.25

βD = 0.25

4. BG has a beta of equity of 0.9 and a leverage ratio of 50%. It rebalances its debt to keep a constant leverage ratio. Assume that the debt of BG is risk-free and that BG 2 has a marginal tax rate of 25%. The risk-free rate is 2% and the market risk premium is 5%. a. What is BG’s after-tax WACC? b. What is the after-tax WACC if the leverage ratio increases to 0.7 and the beta of debt is 0.1?

Re = Rf + βe (Rm – Rf) = 2% + 0.9 *5% = 6.5%

WACC = (1-t) (D/V) Rd + (E/V) Re = (1-25%)(50%)(2%)+(50%)(6.5%) = 4.0%

Ra = WACC = 4.0%

Rd = Rf + βd (Rm – Rf) → Rd = 2% + 0.1*5% = 2.5%

Ra = (D/V)Rd + (E/V)Re → 4.0% = 0.7*2.5% + 0.3*Re → Re = (4.0% - 0.7*2.5%) / 0.3 = 7.5%

WACC = (1-25%)(70%)(2.5%) + (30%)(7.5%) = 3.6%