A firm is currently financed with $300 of debt and $700 of equity. The expected return on the debt is 9%. The market beta of the firm's equity is 1.50; the risk-free rate is 4%; and the equity premium is 6%. The firm pays taxes at the marginal rate of 35%.
-Refer to the information above. The firm is considering increasing its debt to $400 and using the funds to repurchase some of its stock. This is likely to increase the expected return on debt
To 10%. All else equal, what will the new market beta of the firm's equity be? Round your
Answer to the nearest tenth.

Question

Quizplus · Accepted Answer

Increasing the debt-to-equity ratio will increase the financial leverage of the firm, which will lead to an increase in the firm's equity beta. The new equity beta can be calculated as:
New equity beta = Current equity beta * [1 + (1 - Tax rate) * (Debt increase / Equity)]
New equity beta = 1.50 * [1 + (1 - 0.35) * (400 / 700)]
New equity beta = 1.6
Therefore, the correct choice is (A). When a firm increases its debt, the financial risk of the firm increases. This leads to an increase in the market beta of the firm's equity. The formula for the levered beta is:
Levered Beta = Unlevered Beta x (1 + (1 - Tax Rate) x (Debt/Equity))
The initial unlevered beta can be calculated using the CAPM formula:
rE = rf + betaE x (rm - rf)
rE = 4% + 1.50 x 6% = 13%
Unlevered Beta = Levered Beta / (1 + (1 - Tax Rate) x (Debt/Equity))
Initial Unlevered Beta = 1.50 / (1 + (1 - 35%) x (300/700)) = 0.967
With the new debt level of $400, the levered beta can be calculated:
New Levered Beta = 0.967 x (1 + (1 - 35%) x (400/700)) = 1.69
Therefore, the new market beta of the firm's equity will be approximately 1.6 after the increase in debt.

A Firm Is Currently Financed with $300 of Debt and $700