Winter 2014 Version A Note for multiplechoice questions Choose the closest answer Growing Dividends Thunder Chargers Printers is expected to pay out dividends as follows A C dividend will be paid today Each subsequent dividend will be paid yearly and grow by 4 per year The final div ID: 460571
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Slide1
Test 2 solution sketches
Winter 2014, Version A
Note for multiple-choice questions: Choose the closest answerSlide2
Growing Dividends
Thunder Chargers Printers is expected to pay out dividends as follows: A $
C
dividend will be paid today. Each subsequent dividend will be paid yearly, and grow by 4% per year. The final dividend will be paid 30 years from today. After the final dividend is paid, the company will go out of business and never pay anything to stock holders again. Find
C
if the effective annual discount rate is 8% and the current stock value is $45 per share.Slide3
Growing Dividends
45 = C + C * 26 * [1 – (0.962963)
30
]
C = 45/18.6197
C = $2.42
Slide4
Geometric Average
In the hypothetical country of
Egonischle
, the annual rate of return for long-term government bonds for the last 6 years was 20%, 15%, –50%, 25%, 30%, and 10%. What is the geometric average rate of return during this period?Slide5
Geometric Average
R
G
= [1.2*1.15*.5*1.25*1.3*1.1]
1/6
– 1RG = [1.233375] 1/6 – 1RG = 0.03558 = 3.56%Slide6
Portfolio Standard Deviation
Two stocks, X and Y, have a covariance of zero. Suppose that you invest in a portfolio of 70% of your money in stock X and 30% of your money in stock Y. what is the standard deviation of this portfolio if the standard deviation of stock X’s return is 15% and the standard deviation of stock Y’s return is 25
%?Slide7
Portfolio Standard Deviation
Portfolio Variance = (.7)
2
(.15)
2
+ 2*(.7)(.3)(0) + (.3)2(.25)2Portfolio Variance = 0.1665Portfolio s.d. = 12.90%Slide8
Bond PV
Joe owns a bond. The bond has three remaining coupon payments of $600 per year, starting later today. It also has a face value payment of $1000 on the date of the last coupon
payment
. If the stated annual discount rate is 8%, compounded monthly, what is the present value of this bond
?Slide9
Bond PV
EAR = (1 + .08/12)
12
– 1 = 0.0830
PV = 600 + 600/1.0830 + 600/1.0830
2 + 1000/1.08302 PV = 1154.02 + 1364.15PV = $2,518.17Slide10
CAPM
Use the following information to answer the next two questions
:
Assume that the risk-free return in the market is currently 5%, and a stock with beta (ß) of 4 has an expected return of 17%.Slide11
CAPM
What is the expected return on the market portfolio (as defined in lecture
)?
.17 = .05 + 4 * (R
M
– .05).12 = 4RM – .2RM = .08What is the risk premium?RM – RF = .08 – .05RM – RF = .03Slide12
Growing Dividends
Yakima Yak Food, Inc. will start paying out dividends 10 years from today. The first dividend 10 years from today will be $8. Each subsequent dividend will be 12% higher than the previous dividend. The effective annual discount rate for this stock is 17%. What is the present value of this stock?Slide13
Growing Dividends
Yakima Yak Food, Inc. will start paying out dividends 10 years from today. The first dividend 10 years from today will be $8. Each subsequent dividend will be 12% higher than the previous dividend. The effective annual discount rate for this stock is 17%. What is the present value of this stock?Slide14
Growing Dividends
PV = 8/(.17-.12) * 1/(1.17)
9
PV = 160 * (1/4.10840)
PV = $38.94Slide15
Confidence Interval
From Jan. 1, 1910, to Jan. 1, 1991, the historical average annual rate of return in the hypothetical county of
Ipaly
was 14%. The annual standard deviation of the rate of return was 27%. What is the
lower
bound of the 95.4% confidence interval for the annual rate of return based on this information?Slide16
Confidence Interval
Hint: You need to be within 2 standard errors of the average to find the upper and lower bounds of the 95.4% confidence interval
.
S.E. = std. dev./(n
1/2
) = .27/(81)1/2 = .03C.I. = R ± 2 * S.E.C.I. = .14 ± 2 * (.03) = [.08, .20]C.I. lower bound = 8%Slide17
Random Walk
Use the following information to answer the next two questions: Charlie Quack Soda stock exhibits price changes that are a random walk. In a given day, the value of the stock goes up by $3 with probability 0.2 and down by $1 with probability 0.8. The stock’s current value is $70
.Slide18
Random Walk
What is the probability that the value of the stock will be more than $76 three days from today
?
Only way to have a price>$76 is up, up, up
Pr
(up, up, up) = (.2)3 = 0.008Slide19
Random Walk
What is the probability that the value of the stock will be the same three days from today
?
No combination will give a price of exactly $70 in three days
Probability = 0Slide20
Cash Cow & Retained Earnings
Phoenix currently owns a share of stock in Mel’s Kitchen Supplies, Inc. Without any re-investment of their earnings, the company will earn $40 per share every year forever. The effective annual discount rate for the company is 14%. Assume that the next dividend payment will be made in 1 year.
Suppose that Mel’s Kitchen Supplies could retain all of its earnings 5 years from today, and earn 25% on these earnings the following year.Slide21
Cash Cow & Retained Earnings
(In other words, no dividend would be paid 5 years from today if Mel’s Kitchen Supplies retains all of its earnings that year, and would continue to act as a cash cow in the other years.)
(a) What is the PV of this stock if it continues to act as a cash cow?
PV = 40/.14 = $285.71Slide22
Cash Cow & Retained Earnings
(b)
Should Mel’s Kitchen Supplies retain its earnings 5 years from today? Why/why
not?
Yes, because the rate of return (25%) is higher than the discount rate (14%).
Alternative answer: show that PV of stock increasesSlide23
Cash Cow & Retained Earnings
(c)
How much does the present value of Mel’s Kitchen Supplies
change
if the company retains its earnings 5 years from today?
NPV of retaining earnings= -40/1.145 + 40(1.25)/1.146= $2.0046Slide24
Bond Face Value
A bond with face value of $
X
pays a $70 coupon twice, 4 months from today and 10 months from today. The bond matures 10 months from today, and the bond currently sells for $650. If the effective annual interest rate for this bond is 11%, then what is
X
?Slide25
Bond Face Value
650 = 70/(1.11)
4/12
+ 70/(1.11)
10/12
+ X/(1.11)10/12650 = 67.61 + 64.17 + X / 1.09086518 = X / 1.09086X = $565.31