1. a. You expect that company A will pay its first dividend of $2 per share 3 ye
ID: 2785372 • Letter: 1
Question
1. a. You expect that company A will pay its first dividend of $2 per share 3 years from today. After that, the dividend is expected to grow at an annual rate of 5% forever. The risk-free rate is 6%, and the expected rate of return on the market is 10%. Also, the covariance between stock A and the market is 0.10, and standard deviation of the market portfolio is 20%. What is the fair value of the stock today?
b. Assume that the actual price is less than what you have calculated in part a. What does this say about its actual return compared to what is predicted by the security market line?
c. If it is true that properly priced securities fall on the security market line, what would you expect to happen to the price of stock A given that it is currently less than your calculation from part a? Explain why you believe that a price change would occur.
Explanation / Answer
1.a Beta of the stock = covariance between A and market/ Variance of market portfolio =0.1/0.2^2 = 0.1/0.04 = 2.5
Expected return on Stock A as per CAPM = Rf + beta*(Rm-Rf) = 6 + 2.5*(10-6) = 16%
Expected return on stock A (r) = 16% =0.16
Dividend growth rate = 5% = 0.05
Dividend 3 years from today = D3 = $2
As per dividend distribution model, P2 = D3/(r-g) = $2/(0.16-0.05) =$18.18
Price 2 years from now is 18.18
Price today = 18.18/(1+0.16)^2 = 13.51
Price today = $13.51
(b) If the actual price is less than what is calculated in part (a), it means that the stock is undervalued and it is recommened to buy the stock.
(c) The price of Stock A is currenlyt below the SML and will increase to the intrinsic value calculated in part(a)
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