1. a. You expect that company A will pay its first dividend of $2 per share 3 ye

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% for ever. 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. 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% for ever. 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. 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% for ever. 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. In this question we are to find the expected return on equity by CAPM formula.

But beta is not given, let us first find Beta of the stock

Beta = Cov(Rs,Rm)/Var(Rm)

Cov(Rs,Rm) = 0.10

Variance(Rm) = Standard Deviation(Rm)^2 = 0.20^2 = 0.04

Beta = 0.10/0.04 = 2.5

Required return = Rf+Rf(Market Premium) = 6% + 2.5(10%-6%) = 0.06 + 2.5(0.04) = 0.06+0.10 = 0.16 or 16%

Fair Value of the stock = Next year's dividend/(discount rate - growth rate) = D1/(r-g) = 2(1+0.05)/0.16-0.05 = 2.1/0.11 = $19.090909

Value of stock at the end of three years = $19.090909

Current Value = 19.090909/(1+0.16)^3 = $12.23 (Answer)

2. If the actual price of the stock is less than the fair value as calculated in (a), it means that the stock is undervalued, it doesnt reflect the true value on the stock price, and it is expected to rise in value in the future, the stock should be given buy recommendation, because it may give better return than earlier predicted.

3. if the stock return falls on SML, the price of the stock must increase in near future, the current price is slow, and is expected to make a price change, which will increase the price of the stock. Thus making it an attractive investment option for thee potential investors. The increase in price would lead to fall in the return of the stock, till it falls on the SML

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