Simpson Inc.is considering a vertical merger with The Lachey Company.Simpson currently has a required return of 11%,while Lachey's required return is 15%.The market risk premium is 5% and the risk-free rate is 5%.Assume the market is in equilibrium.If Simpson is going to make up 67% of the new firm (and Lachey will comprise the remaining 33%),what will be the beta of the new merged firm? There will be no additional infusion of debt in the merger.
A)1.46
B)1.54
C)1.61
D)1.69
E)1.78

Question

Quizplus · Accepted Answer

The beta of the new merged firm can be calculated using the weighted average of the betas of the two companies. First, calculate the beta for each company using the CAPM formula: Beta = (Required Return - Risk-Free Rate) / Market Risk Premium. For Simpson: Beta = (11% - 5%) / 5% = 1.2. For Lachey: Beta = (15% - 5%) / 5% = 2.0. Then, calculate the weighted average beta: (0.67 * 1.2) + (0.33 * 2.0) = 1.46.