Arizona Rock,an all-equity firm,currently has a beta of 1.25,and r_RF = 7 percent and r_M = 14 percent.Suppose the firm sells 10 percent of its assets (beta = 1.25)and purchases the same proportion of new assets with a beta of 1.1.What will be the firm's new overall required rate of return,and what rate of return must the new assets produce in order to leave the stock price unchanged?

Question

Quizplus · Accepted Answer

First, we need to find the new beta of the firm after the asset sale and purchase:

New Beta = (0.9 x 1.25) + (0.1 x 1.1) = 1.2225

Next, we can use the Capital Asset Pricing Model (CAPM) to find the new overall required rate of return:

rS1U1B1 = rS1U1B1RFS1U1B0 + (rS1U1B1MS1U1B0 - rS1U1B1RFS1U1B0) x Beta
rS1U1B1 = 7% + (14% - 7%) x 1.2225
rS1U1B1 = 15.645%

Finally, we can use the following formula to find the rate of return the new assets must produce in order to leave the stock price unchanged:

(rS1U1B1 - rS1U1B1RFS1U1B0) / (Beta - 1) = (rNewAssets - rS1U1B1RFS1U1B0) / (1.1 - 1)

Simplifying this equation, we get:

(rNewAssets - 7%) / 0.1 = (15.645% - 7%) / 0.2225

Solving for rNewAssets, we get:

rNewAssets = 14.7%

Therefore, the answer is choice C: 15.645%;14.7%.

Arizona Rock,an All-Equity Firm,currently Has a Beta of 1