You are provided the following information of a firm\'s stocks and bonds along w
ID: 2756437 • Letter: Y
Question
You are provided the following information of a firm's stocks and bonds along with other pertinent information.
The stocks have a standard deviation of 50% and a correlation of 0.6 with the market index.
The risk-free rate is 2%, and the market risk premium is 7%. The standard deviation of the market is 25%.
The firm just paid dividends of $2.50 per share. Assume that the firm pays dividends annually and that the firm adjusts its dividends to maintain a constant dividend payout ratio of 75%. The ROE of the firm is 15%.
What is the beta of the stock?
What is the cost of equity? [Hint: Use the CAPM]
What is the rate of growth in dividends?What is the stock price? [Note: the answer from part (a) would be your discount rate]
How useful (or limited) is this method in valuing stocks? [1-2 sentences]
Explanation / Answer
Variance of market portfolio = 0.252
= 0.0625
Coefficient of correlation = Covariance / (SD of Stock x SD of Market)
0.60 = Covariance / (0.50 x 0.25)
Covariance = 0.075
Beta = Covariance / Variance of market portfolio
= 0.075 / 0.0625
= 1.2
Cost of equity = Risk free rate + [Beta x Market Risk Premium]
= 2 + [1.2 x 7]
= 10.4%
Growth = Retention ratio x ROE
= .25 x .15
= 0.0375
Stock Price = 2.5(1.0375) / (0.104 - 0.0375)
= $39
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