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Explanation & Answer

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1.
Assume these are the stock market and Treasury bill returns for a 5-year
period:
Year Stock Market Return (%)T-Bill Return (%)
2013
32.10
0.05
2014
11.30
0.05
2015
−2.00
0.05
2016
13.40
0.23
2017
21.70
0.25
Required:
a. What was the risk premium on common stock in each year?
Market risk premium
Risk premium (2013)
Risk premium (2014)
Risk premium (2015)
Risk premium (2016)
Risk premium (2017)
= Expected Return on Market - Risk free rate
=
32.1% - 0.05%
=
32.05%
=
11.3% - 0.05%
=
11.25%
=
-2.0% - 0.05%
=
-2.05%
=
13.4% - 0.23%
=
13.17%
=
21.7% - 0.25%
=
21.45%
b. What was the average risk premium?
Average Risk premium
=
=
(32.05%+11.25%-2.05%+1317%+21.45%) / 5
15.17%
c. What was the standard deviation of the risk premium? (Ignore that the
estimation is from a sample of data.)
Standard Deviation (Risk premium) = [((32.05% - 15.17%)2 + (11.25% - 15.17%)2 + (-2.05%15.17%)2+(13.17%-15.17%)2+(21.45%-15.17%)2)/5]1/2
=
0.01281/2
=
11.32%
2.
A stock is selling today for $75 per share. At the end of the year, it pays a
dividend of $3 per share and sells for $84.
Required:
a. What is the total rate of return on the stock?
Rate of return
=
=
=
=
(P1 + D- P0) / P0
(84 + 3 - 75) / 75
12 / 75
16%
b. What are the dividend yield and percentage capital gain?
Dividend yield%
Capital gains yield %
=
=
D / P0
(P1 - P0) / P0
=
3 / 75
= (84 - 75) / 75
=
=
4%
12%
c. Now suppose the year-end stock price after the dividend is paid is $69.
What are the dividend yield and percentage capital gain in this case?
Dividend yield%
Capital gains yield%
= 3 / 75
= (69 - 75) / 75
= 4%
= -8%
3.
You purchase 100 shares of stock for $50 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) $47; (ii) $50; (iii) $53? (Leave no cells blank - be certain to enter "0"
wherever required. Enter your answers as a whole percent.)
Rate of return
=
(P1 + D- P0) / P0
i)
Price $47: Rate of return
=
(47 + 3 - 50) / 50
ii)
Price $50: Rate of return
=
(50 + 3 - 50) / 50
iii) Price $53: Rate of return
=
(53 + 3 - 50) / 50
=
=
=
0
6%
12%
b. What is your real (inflation-adjusted) rate of return if the inflation rate is
5%? (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.)
Real Rate of return
i)
ii)
=
((1 + Nominal Rate) / (1+ Inflation Rate)) - 1
Price $47: Real Rate of return =
=
Price $50: Real Rate of return =
((1+0%) / (1+5%)) - 1
-4.76%
((1+6%) / (1+5%)) - 1
iii)
=
Price $53: Real Rate of return =
=
0.95%
((1+12%) / (1+5%)) - 1
6.67%
4.
Consider the following scenario analysis:
Rate of Return
Scenario
Probability Stocks Bonds
Recession
0.30
−4%
16%
Normal economy
0.50
17%
10%
Boom
0.20
28%
9%
a. Is it reasonable to assume that Treasury bonds will provide higher returns in
recessions than in booms?
•
No
•
Yes
Yes, it is 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 rate of return
=
Sum of (Probability * Rate of Return)
Expected rate of return (Stocks)
=
=
(-4%*0.30) + (17%*0.50) + (28%*0.20)
12.9%
Expected rate of return (Bonds)
=
=
(16%*0.30) + (10%*0.50) + (9%*0.20)
11.6%...
