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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 year-end at a price of $40

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 year-end at a price of $40. The stock will pay a dividend at year-end of $3.00. Assume that risk-free 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
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.)

(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 year-end 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 year-end.

 

a. What is the rate of return on your investment if the end-of-year 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 (inflation-adjusted) 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?

 

  • No
  • Yes

 

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?

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