Question

# A firm has a debt to equity ratio of 2/3. Its cost of equity is 15.2%,...

A firm has a debt to equity ratio of 2/3. Its cost of equity is 15.2%, cost of debt is 4%, and tax rate is 35%. Assume that the risk-free rate is 4%, and market risk premium is 8%.

Suppose the firm repurchases stock and finances the repurchase with debt, causing its debt to equity ratio to change to 3/2:

• What is the firm’s WACC before and after the change in capital structure?
• Compute the firm’s new equity beta and new cost of equity?

WACC at debt to equity ratio of 2/3 = Weight of Equity * Cost of equity + weight of Debt* Cost of Debt*(1-Tax Rate)
=3/5*15.2%+2/5*4%*(1-35%) = 10.16%

Beta unlevered = Beta Levered/(1+(1-Tax Rate)*Debt /Equity) = 1.4/(1+(1-35%)*2/3) =0.976744

Beta levered at 3/2 debt equity ratio = Beta unlevered *(1+(1-Tax Rate)*Debt /Equity) =0.976744*(1+(1-35%)*3/2) = 1.929 or 1.93

Cost of New Equity = Risk Free + Beta * Market Risk Premium = 4% + 1.929 *8% = 19.43%

New WACC =Weight of Equity * Cost of equity + weight of Debt* Cost of Debt*(1-Tax Rate)
=2/5*19.43%+3/5*4%*(1-35%) = 9.33%

Please Discuss in case of Doubt

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