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%.

1. What is the beta of the stock?
2. What is the cost of equity? [Hint: Use the CAPM]
3. What is the rate of growth in dividends?
4. What is the stock price? [Note: the answer from part (b) would be your discount rate]
5. How useful (or limited) is this method in valuing stocks? [1-2 sentences]

Answer 1

a, Beta =Correlation*Standard Deviation of Stock/Standard Deviation of Market =0.6*50%/25% =1.2
b. Cost of equity =Risk free rate+Beta*Market Risk Premium =2%+1.2*7% =10.40%
c.growth =ROE*(1-Dividend payout ratio) =15%*(1-75%) =3.75%
d . Stock Price =Dividend share*(1+growth)/(Required Rate -growth) =2.50*(1+3.75%)/(10.40%-3.75%) =39.00