11(i)
Top hedge fund manager Sally Buffit believes that a stock with the same market risk as the S&P 500 will sell at yearend at a price of $40. The stock will pay a dividend at yearend of $3.00. Assume that riskfree Treasury securities currently offer an interest rate of 1.5%.
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 
Average Premium (Extra return 

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.)
(ii)
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 $57.
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 yearend stock price after the dividend is paid is $43. What are the dividend yield and percentage capital gain in this case?
(iii)
You purchase 100 shares of stock for $60 a share. The stock pays a $3 per share dividend at yearend.
a. What is the rate of return on your investment if the endofyear stock price is (i) $57; (ii) $60; (iii) $66? (Leave no cells blank  be certain to enter "0" wherever required. Enter your answers as a whole percent.)
Stock Price Rate of Return
57 
60 
66 
b. What is your real (inflationadjusted) rate of return if the inflation rate is 4%? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Negative amounts should be indicated by a minus sign.)
Stock price Rate of Return
57 
60 
66 
(iiii)
Consider the following scenario analysis:


Rate of Return 

Scenario 
Probability 
Stocks 
Bonds 

Recession 
0.20 
−5 
% 
19 
% 
Normal economy 
0.60 
20 
% 
10 
% 
Boom 
0.20 
27 
% 
4 
% 

a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?
b. Calculate the expected rate of return and standard deviation for each investment. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.)
Expected RoR Standard Deviation
Stocks:
Bonds:
c. Which investment would you prefer?
Stocks or Bonds?