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[QUESTION] [Problem 15.8] Acosta Sugar Company has estimated that the overall return for the S&P 500 Index will be 15 percent over the next 10 years. The company also feels that the interest rate on Treasury securities will average 10 percent over this interval. The company is thinking of expanding into a new product line – almonds. It has no experience in this line but has been able to obtain information on various companies involved in producing and processing nuts. Although no company examined produces only almonds, Acosta’s management feels that the beta for such a company\ would be 1.10, once the almond operation was ongoing. There is some uncertainty about the beta that will actually prevail. (Assume that Acosta and all proxy firms are all-equityfinanced.) Management has attached the following probabilities to possible outcomes: a. What is the required rate of return for the project using the mode-average beta of 1.10? b. What is the range of required rates of return? c. What is the expected value of required rate of return? [ANSWER] a. Required Return = 0.10 + (0.15 – 0.10)(1.10) = 15.5 percent b. Minimum Required Return = 0.10 + (0.15 – 0.10)(1.00) = 15 percent Maximum Required Return = 0.10 + (0.15 – 0.10)(1.40) = 17 percent c. Required Return for beta of 1.20 = 0.10 + (0.15 – 0.10)(1.20) = 16 percent Required Return for beta of 1.30 = 0.10 + (0.15 – 0.10)(1.30) = 16.5 percent Expected value of required rate of return
= (0.2)(0.15) + (0.3)(0.155) + (0.2)(0.16) + (0.2)(0.165) + (0.1)(.17) = 15.85 percent
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