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, S.A.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

To find the maximum beta coefficient for the new division, we need to use the Capital Asset Pricing Model (CAPM):

CAPM = Rf + (Rm – Rf) × Beta

Where: 
Rf = risk-free rate = 7%
Rm = market risk premium = 5%
Beta = beta coefficient of the new division

First, let’s calculate the required rate of return for Sun State Mining Inc. with its current 100% equity structure:

Required Rate of Return = Rf + (Rm – Rf) × Beta 
18% = 7% + (5%) × Beta

Solving for Beta:
Beta = (18% - 7%) / 5% 
Beta = 2.2

Therefore, the current beta coefficient for Sun State Mining Inc. is 2.2.

Next, we need to calculate the new beta coefficient that would result in a required rate of return of 16% for the firm. Since we know that the new division will increase the assets of the firm by 50%, we can use the following equation to calculate the new beta coefficient:

Beta_new = (1 + 0.5) × Beta_old / (1 + 0.5 × Beta_old)

Where: 
Beta_old = current beta coefficient = 2.2

Plugging in the numbers, we get:

Beta_new = (1 + 0.5) × 2.2 / (1 + 0.5 × 2.2) 
Beta_new = 1.0

Therefore, the maximum beta coefficient the new division could have is 1.0, which is answer choice B.