Question

A dividend on the common stock of Baker Company in the amount of $4.77 was just paid. Dividends are expected to grow at a rate of 3%, forever. The stock has a correlation with the overall market of .6. The standard deviation of the stock’s returns is 0.45 and the standard deviation of the overall market’s returns is 0.4. If the yield on Treasury Bills is 2%, and the expected return on the market is 8%.

1. What is the beta of the stock?
2. According to CAPM, what is the required return on the stock?
3. What would you be willing to pay for the stock today?
4. d) If you buy the stock at the current market price of $175, are you earning more or less than the required return? Briefly explain.

Answer 1

(a)          
Beta of stock formula =Correlation * Standard devi of stock /standard deviation of market          
0.6*0.45/0.4=   0.675      
So beta of stock is    0.675      
          
(b)          
Required Return as per CAPM (ke) = Risk free rate + (Beta*(market Return - risk Free rate)          
2% +(0.675*(8%-2%))          
6.05%          

(c) Dividend just paid (D0)=   4.77      
Growth rate=   3%   D1 = 4.77*(1+3%)=   4.9131
Stock price today(Present value of stock) = D1/(ke-g)          
4.9131/(6.05%-3%)          
161.0852459          
So we should we willing to pay    $161.09      
          
(c) Stock price today is $175. So it is more than Present value of stock.           
It means we are earning less than required Return.          
As we calculate Expected Return as per Dividend Discount model          
expected return = D1/P0+g          
(4.9131/175)+3%          
5.81%          
So we are earning only 5.81%. that is less than required Return. So we should not buy it           
          

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