Question

You are considering purchasing shares of GreenGro, a supplier of fresh produce. The stock just paid a dividend of $1.42 and dividends are expected to grow after that at an annual rate of 2%, forever. The stock has a correlation with the overall market of 0.70. The standard deviation of the stock’s returns is 0.60 and the standard deviation of the overall market’s returns is 0.375. The yield on T- Bills is 3%, and the return on the market portfolio is expected to be 11.5%.

a) What should be the price of the stock assuming that the Capital Asset Pricing model is true?

b) Suppose the stock is selling in the market at a price of $14.10, is it over-valued or under-valued? Explain what should happen to the stock price if the market is efficient.

Answer 1

a)

Using CAPM model;

we need to calculate s (beta of stock) to find the required rate of return of stock

CAPM rs = rf + beta of stock * (rm - rf)

rf = 3%

rm = 11.5%

beta of stock = [(correlation with the overall market) * (standard deviation of the stock’s returns)] / standard deviation of the overall market’s returns

= 0.7 * 0.6 / 0.375 = 1.12

rs = rf + beta of stock * (rm - rf)

= 0.03 + 1.12(0.115-0.03)

= 0.1252 = 12.52%

we can find stock price using the constant growth rate

price of the stock P0 = D1/(rs - g)

D1 = D0(1+g)

rs = 12.52%

g = 2%

D0 = 1.42

D1 = 1.42(1+0.02) = 1.4484

P0 = D1/(rs - g) = 1.4484/(0.1252 - 0.02) = $ 13.76

b)

Dividend growth model suggests that the stock price must be $ 13.76 but it is trading at $14.10 hence it is overvalued.

Market efficiency does not mean prices to be equal to fair value all the time. Prices may change but they eventually revert back to their fair values. In our case, for the market to be efficient the price must reduce back to its fair value of $ 13.76