Question

Isabella Publishing's tax rate is 21%, its beta is 1.40, and it currently has no debt. The CFO is considering moving to a capital structure with 25% debt and 75% equity and using the newly raised capital to repurchase shares of the common stock. If the risk-free rate is 4.5% and the market risk premium is 7.0%, by how much would the cost of equity for the levered firm increase, compared to the cost of equity of the unlevered firm? What will be the change in the WACC, if the company can borrow at 6 percent?

Answer 1

unlevered cost of equity:

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 4.5 + 1.4 * (7)

Expected return% = 14.3

Levered cost of equity

Levered Beta = Unlevered Beta x (1 + ((1 – Tax Rate) x (Debt/Equity)))

levered beta = 1.4*(1+((1-0.21)*(0.333333333333333)))

levered beta = 1.77

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 4.5 + 1.77 * (7)

Expected return% = 16.89

where debt/equity = 0.25/0.75 = 0.333333

Change in cost of equity = 16.89-14.3=2.59%

WACC

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 6*(1-0.21)

= 4.74

Weight of equity = 1-D/A

Weight of equity = 1-0.25

W(E)=0.75

Weight of debt = D/A

Weight of debt = 0.25

W(D)=0.25

WACC=after tax cost of debt*W(D)+cost of equity*W(E)

WACC=4.74*0.25+16.89*0.75

WACC% = 13.85

change in WACC = 13.85-14.3= -0.45%