FA2011-Sample_Exam_3_Solutions

# FA2011-Sample_Exam_3_Solutions - 1 Hilton Hotels has a beta...

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1. Hilton Hotels has a beta of 1.1, while Sun Motels has a beta of 0.9. The required rate of return on an index fund that holds the entire stock market is 12%. The risk-free rate is 7%. By how much does Hilton’s required return exceed Sun’s required return? This problem requires the application of CAPM. We are given the rate of return on the risk free assets (7%). The expected return on the market is represented by the return on the index fund (12%) First let’s calculate the expected return for each company: Hilton Er = 0.07 + 1.1*(0.12-0.07) = 0.125 Sun Er = 0.06 +0.9*(0.12-0.07) = 0.115 The difference is 0.125 – 0.115 = 0.01 = 1% 2. Huang Investments must maintain a weighted average cost of capital of 10% to satisfy covenants in the bond indenture. Analysts forecast the after tax cost of debt to be 5% and the cost of equity to be 11%. There are no preferred stocks. What debt-equity ratio must be employed to meet the targeted WACC? WACC = Re*E/V + Rd*D/V 1.1 = 0.11*E/V + 0.05*D/V Remember that E+D=V E/V + D/V = 1 D/V = 1-E/V Let’s call E/V = x 1.1 = 0.11*x + 0.05*(1-x) 1.1 = 0.11x + 0.05 - 0.05x 1.1 = x*(0.11-0.05) + 0.05 1.1 - 0.05 = 0.06x 0.05/0.06 = x x = 0.833 = E/V 1-x = 1-0.8333 = 0.16667 = D/V D/E = (D/V)/(E/V) = 0.16667 / 0.8333 = 0.20 3. A portfolio is invested equally in stock A and a risk free asset. The expected return of stock A is 15% and the beta is 1.3. The expected return on the risk free asset is 5%. What is the beta of the portfolio? Since we know that the portfolio is equally invested in the two assets we know that the weight of each asset equals 50% of the portfolio. Beta is calculated as the weighted average of the betas of each asset. Remember that the risk free asset has a beta of zero. Bp = 0.5*1.3 + 0.5*0 = 0.65

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4. The return of Pilgrim Co. is influenced by the overall state of the economy. In a recessionary economy Pilgrim is likely to lose 5%, in a boom economy, the return is projected at 15%. In a normal economy the return is supposed to be 7%. The probability of a boom is 20%, the probability of a recession is 15%. What is the expected return of this stock? State of the economy Probability Return Return*Probability Boom 20% -0.05 -0.10 Normal 65% 0.07 0.046 Recession 15% 0.2 0.030 Total 100% 0.066 The closest answer is therefore 6.8% Use the following information to answer questions 5-7 Stock A has an expected return of 10% and a variance of 9%. Stock B has an expected return of 15% and a variance of 16%. The beta of stock A is 1.2.
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