Kelly Tubes is considering a merger with Reilly Tires.Reilly'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 Kelly acquires Reilly,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%.What will Reilly's required rate of return on equity be after it is acquired?
A)7.4%
B)8.9%
C)9.3%
D)9.7%

Question

Quizplus · Accepted Answer

To find Reilly's required rate of return on equity after being acquired by Kelly, we use the levered beta formula to adjust for the new capital structure, and then apply the Capital Asset Pricing Model (CAPM) to find the new required return on equity.First, calculate the unlevered beta (βu) using Reilly's current beta (βL) and capital structure before the acquisition:$$ \beta_u = \beta_L / [1 + (1 - Tax Rate) * (Debt/Equity)] $$Given βL = 0.9, Debt = 20%, Equity = 80% (since Debt + Equity = 100%), and Tax Rate = 25%:$$ \beta_u = 0.9 / [1 + (1 - 0.25) * (0.2/0.8)] = 0.9 / [1 + 0.75 * 0.25] = 0.9 / 1.1875 = 0.758 $$Next, calculate the new levered beta (βL') using the new capital structure after the acquisition:$$ \beta_L' = \beta_u * [1 + (1 - New Tax Rate) * (New Debt/New Equity)] $$With the new Debt = 60%, New Equity = 40%, and New Tax Rate = 35%:$$ \beta_L' = 0.758 * [1 + (1 - 0.35) * (0.6/0.4)] = 0.758 * [1 + 0.65 * 1.5] = 0.758 * [1 + 0.975] = 0.758 * 1.975 = 1.497 $$Finally, apply the CAPM to find the new required return on equity (Re'):$$ Re' = Risk-Free Rate + βL' * Market Risk Premium $$Given Risk-Free Rate = 6% and Market Risk Premium = 4%:$$ Re' = 6% + 1.497 * 4% = 6% + 5.988% = 11.988% $$It appears there was a mistake in my calculations as none of the provided options match the result. Let's correct the approach:The correct approach involves directly calculating the cost of equity after the acquisition using the Modigliani-Miller proposition II with taxes, which adjusts for the change in leverage. However, given the provided options and the initial setup, it seems there was a computational error in my explanation. The correct calculation should directly relate to how the increased debt and interest rate affect the cost of equity through the leveraged beta or directly through the weighted average cost of capital (WACC) formula, adjusting for the new capital structure and tax shield. However, without the explicit formula or numbers leading to the options given, it's clear my detailed calculation does not directly lead to the correct choice based on the options provided. The correct answer should reflect the impact of increased leverage and the associated tax shield on the required rate of return on equity, considering the higher debt level and tax rate post-acquisition.

Kelly Tubes Is Considering a Merger with Reilly Tires