Holland Auto Parts is considering a merger with Workman Car Parts.Workman's market-determined beta is 0.9, and the firm currently is financed with 20% debt, at an interest rate of 8%, and its tax rate is 25%.If Holland acquires Workman, it will increase the debt to 60%, at an interest rate of 9%, and the tax rate will increase to 35%.The risk-free rate is 6% and the market risk premium is 4%.Using the Compressed APV Model, what will Workman's required rate of return on equity be after it is acquired?
A) 7.4%
B) 8.9%
C) 9.3%
D) 9.6%
E) 9.7%

Question

Quizplus · Accepted Answer

The Compressed Adjusted Present Value (APV) Model incorporates the effects of financing benefits directly into the cost of equity. The formula to adjust the beta for the new capital structure is:$$ \beta_L = \beta_U \times (1 + (1 - T_c) \times D/E) $$Where:- $ \beta_L $ is the levered beta (beta of the firm with debt),- $ \beta_U $ is the unlevered beta (beta of the firm without debt, or equity beta),- $ T_c $ is the corporate tax rate,- $ D/E $ is the debt-to-equity ratio.Given:- $ \beta_U = 0.9 $ (since Workman's current beta is market-determined and reflects its current capital structure),- $ T_c = 35\% $ after the acquisition,- The new debt-to-equity ratio $ D/E = 60\%/40\% = 1.5 $ (since equity would be 100% - 60% = 40%).First, adjust the beta for the new capital structure:$$ \beta_L = 0.9 \times (1 + (1 - 0.35) \times 1.5) = 0.9 \times (1 + 0.65 \times 1.5) = 0.9 \times (1 + 0.975) = 0.9 \times 1.975 = 1.7775 $$Then, calculate the required rate of return on equity after the acquisition using the CAPM formula:$$ r_E = r_f + \beta_L \times (r_m - r_f) $$Where:- $ r_E $ is the required rate of return on equity,- $ r_f $ is the risk-free rate,- $ \beta_L $ is the levered beta,- $ r_m - r_f $ is the market risk premium.$$ r_E = 6\% + 1.7775 \times 4\% = 6\% + 7.11\% = 13.11\% $$It seems there was a mistake in the calculation or interpretation of the given options, as none of the provided choices match the calculated result. Given the inputs and the methodology, the correct calculation should reflect the impact of leveraging on the cost of equity through the adjusted beta. However, the correct answer should be calculated based on the given options and the methodology described. If we reassess the calculation or the interpretation of the question, we might need to consider simplifications or approximations provided in the question or in the options. Given the discrepancy, it's important to closely review the assumptions and calculations.

Holland Auto Parts Is Considering a Merger with Workman Car