Question

Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. a. Calculate each stock’s coefficient of variation. b. Which stock is riskier for a diversified investor? c. Calculate each stock’s required rate of return. d. On the basis of the two stocks’ expected and required returns, which stock would be more attractive to a diversified investor? e. Calculate the required return of a portfolio that has $7,500 invested in Stock X and$2,500 invested in Stock Y. f. If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

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In this exercise, we will calculate the coefficient of variation of each stock.

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Here is the condensed 2016 balance sheet for Skye Computer Company (in thousands of dollars):

 2016Current assets$ 2.000Net fixed assets3.000Total assets$ 5.000Accounts payable and accruals$ 900Short-term debt100Long-term debt1.110Preferred stock (10.000 shares)250Common stock (50.000 shares)1.300Retained earnings1.350Total common equity$ 2.650Total liabilities and equity$ 5.000\begin{matrix} \text{ } & \text{2016}\\ \text{Current assets} & \text{\$ 2.000}\\ \text{Net fixed assets} & \text{3.000}\\ \text{Total assets} & \text{\$ 5.000}\\ \text{Accounts payable and accruals} & \text{\$ 900}\\ \text{Short-term debt} & \text{100}\\ \text{Long-term debt} & \text{1.110}\\ \text{Preferred stock (10.000 shares)} & \text{250}\\ \text{Common stock (50.000 shares)} & \text{1.300}\\ \text{Retained earnings} & \text{1.350}\\ \text{Total common equity} & \text{\$ 2.650}\\ \text{Total liabilities and equity} & \text{\$ 5.000}\\ \end{matrix}

Skye’s earnings per share last year were $3.20. The common stock sells for$55.00, last year’s dividend $\left(\mathrm{D}_{0}\right)$ was $2.10, and a flotation cost of 10% would be required to sell new common stock. Security analysts are projecting that the common dividend will grow at an annual rate of 9%. Skye’s preferred stock pays a dividend of$3.30 per share, and its preferred stock sells for $30.00 per share. The firm’s before-tax cost of debt is 10%, and its marginal tax rate is 35%. The firm’s currently outstanding 10% annual coupon rate, long-term debt sells at par value. The market risk premium is 5%, the risk-free rate is 6%, and Skye’s beta is 1.516. The firm’s total debt, which is the sum of the company’s short-term debt and long-term debt, equals$1.2 million. a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock, the cost of equity from retained earnings, and the cost of newly issued common stock. Use the DCF method to find the cost of common equity. b. Now calculate the cost of common equity from retained earnings, using the CAPM method. c. What is the cost of new common stock based on the CAPM? d. If Skye continues to use the same market-value capital structure, what is the firm’s WACC assuming that (1) it uses only retained earnings for equity? (2) If it expands so rapidly that it must issue new common stock?