Risk-free Treasury securities

1. Top hedge fund manager Sally Buffit believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $46. The stock will pay a dividend at year-end of $3.00. Assume that risk-free Treasury securities currently offer an interest rate of 2.4%.

 

Average rates of return on Treasury bills, government bonds, and common stocks, 1900–2017 (figures in percent per year) are as follows.

 

Portfolio Average Annual Rate of Return (%) Average Premium (Extra return versus Treasury bills) (%)
Treasury bills   3.8        
Treasury bonds   5.3     1.5  
Common stocks   11.5     7.7  
 

 

a. What is the discount rate on the stock? (Enter your answer as a percent rounded to 2 decimal places.)

 

 

b. What price should she be willing to pay for the stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

 

 

2. Assume these are the stock market and Treasury bill returns for a 5-year period:

 

Year   Stock Market Return (%) T-Bill Return (%)
2013     33.30     0.12  
2014     13.20     0.12  
2015     −3.50     0.12  
2016     14.50     0.07  
2017     23.80     0.09  
 

 

Required:

a. What was the risk premium on common stock in each year?

 
 
Year Risk Premium
2013   %
2014   %
2015   %
2016   %
2017   %

 

·

 

b. What was the average risk premium?

 
 
Average risk premium   %

 

 

c. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.)

 

 
 
Standard deviation   %

 

 

 

 

3. A stock is selling today for $50 per share. At the end of the year, it pays a dividend of $2 per share and sells for $59.

 

Required:

a. What is the total rate of return on the stock?

 
   

 

b. What are the dividend yield and percentage capital gain?

 

 

c. Now suppose the year-end stock price after the dividend is paid is $44. What are the dividend yield and percentage capital gain in this case?

 

 

 
   

 

 

4.

You purchase 100 shares of stock for $40 a share. The stock pays a $2 per share dividend at year-end.

 

a. What is the rate of return on your investment if the end-of-year stock price is (i) $38; (ii) $40; (iii) $46? (Leave no cells blank – be certain to enter “0” wherever required. Enter your answers as a whole percent.)

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