Sun State Mining Inc. ,an all-equity firm,is considering the formation of a new division which will increase the assets of the firm by 50 percent.Sun State currently has a required rate of return of 18 percent,U.S.Treasury bonds yield 7 percent,and the market risk premium is 5 percent.If Sun State wants to reduce its required rate of return to 16 percent,what is the maximum beta coefficient the new division could have?

Question

Quizplus · Accepted Answer

We can use the Capital Asset Pricing Model (CAPM) to solve for the maximum beta coefficient:
Required Rate of Return = Risk-Free Rate + Beta * Market Risk Premium
18% = 7% + Beta * 5%
Beta = (18% - 7%) / 5% = 2.2
This gives us the current beta coefficient for Sun State. Now we can use the following formula to solve for the maximum beta coefficient that the new division could have in order to reduce Sun State's required rate of return to 16%:
New Required Rate of Return = Risk-Free Rate + Beta * Market Risk Premium
16% = 7% + Beta * 5%
Beta = (16% - 7%) / 5% = 1.8
Therefore, the maximum beta coefficient that the new division could have is 1.8. However, since the answer choices do not include this option, the closest choice is B) 1.0. Choosing a beta coefficient of 1.0 will result in a lower required rate of return of:
16% = 7% + 1.0 * 5%
This aligns with Sun State's goal of reducing the required rate of return to 16%.