Mr Know How

Question:

1.Suppose the rate of return on short-term government securities (perceived to be risk-free) is 5%. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is 12%. According to the CAPM:

a) What is the expected rate of return on the market portfolio?

b) What would be the expected rate of return on a stock with β = 0?

c) Suppose you consider buying a stock which does not pay a dividend. The current price is $50, and in one year, you expect the price to be $57.50, giving a rate of return of 15%. The stock has a β which you calculate to be 0.75. Assuming your estimate of the stock’s price in one year is correct, is the stock currently overpriced or underpriced according to the CAPM? Explain thoroughly, using the ideas and formulas we covered in lecture.

2. A firm has common stock with a market price of $25 per share and an expected dividend of $2 per share at the end of the coming year. The growth rate in dividends has been 5 percent. What is the cost of the firm's common stock equity?

Solution:

1.

a. As per CAPM,

Re = Rf + (Rm – Rf)*β

Re = 5% + (12% - 5%)*1

Re = 12%

(Equal to market return, as market beta is equal to 1)

b. Re = 5% + (12% - 5%)*0

Re = 5%

(Equal to risk free return, as its beta is equal to 0)

c. As per CAPM,

Re = Rf + (Rm – Rf)*β

Re = 5% + (12% - 5%)*0.75

Re = 10.25%

Thus, market price today should be = $57.5/(1+0.1025) = $52.15

As the expected return as per CAPM is lower than the return offered by the market, the share today is underpriced.

2. Excel workings:

|1/A |B |C |D |
|2 |Expected dividend |2 |
|3 |Market price | |25 |
|4 |Growth rate