Question 4 (25 marks / Risk & Return and Equity Valuation)

(a) Donald is considering the merits of two securities. He is interested in the common shares of A Co. and B Inc. The expected monthly rate of return of securities is shown below:

State of Affair Probability

Boom 0.1 Normal 0.5 Recession 0.4

Stock A Stock B

40% -20% 20% 8% -10% 15%

At the time of purchase, the market value is $70/share for A and $50/share for B. Donald plans to invest 10,000 shares of Stock A and 6,000 shares in Stock B.

1. (i) Compute the portfolio weights of Stock A and Stock B. (3 marks)

2. (ii) Compute the expected returns of Stock A and Stock B. (3 marks)

3. (iii) Assume that the covariance between Stock A and Stock B is -28%2 (0.0028). Compute the expected rate of return and variance of rate of return of Donalds portfolio.

   (9 marks)

4. (iv) If the risk-free rate is 2%, the market risk premium is 18% and the beta of Stock A is 0.75, estimate the required and expected rates of return of Stock A. Should Donald invest in Stock A? Show the calculations. (4 marks)

(b) Assume that Stock X is fairly priced today. Stock X just distributed a per share dividend of $1. It is expected that the company will increase its dividend by 20% in the coming year, 15% in the second year, 10% in the third year, and 5% in the fourth year. Starting from the fifth year, the company will maintain the dividend growth rate to be 5% per year forever. How much is Stock X worth today if its equity cost of capital is 10%? (6 marks)