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Test 2 solution sketches
Winter 2014, Version A
Note for multiple-choice 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 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.
Growing Dividends




45 = 𝐶 +
𝐶 ∗ 1.04
∗
.08 − .04
1 −
1.04 30
1.08
45 = C + C * 26 * [1 – (0.962963)30]
C = 45/18.6197
C = $2.42
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?
Geometric Average



RG = [1.2*1.15*.5*1.25*1.3*1.1]1/6 – 1
RG = [1.233375] 1/6 – 1
RG = 0.03558 = 3.56%
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%?
Portfolio Standard Deviation



Portfolio Variance = (.7)2(.15)2 +
2*(.7)(.3)(0) + (.3)2(.25)2
Portfolio Variance = 0.1665
Portfolio s.d. = 12.90%
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?
Bond PV




EAR = (1 + .08/12)12 – 1 = 0.0830
PV = 600 + 600/1.0830 + 600/1.08302
+ 1000/1.08302
PV = 1154.02 + 1364.15
PV = $2,518.17
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%.
CAPM

What is the expected return on the
market portfolio (as defined in lecture)?




.17 = .05 + 4 * (RM – .05)
.12 = 4RM – .2
RM = .08
What is the risk premium?


RM – RF = .08 – .05
RM – RF = .03
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?
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?
Growing Dividends



PV = 8/(.17-.12) * 1/(1.17)9
PV = 160 * (1/4.10840)
PV = $38.94
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?
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./(n1/2) = .27/(81)1/2 = .03
C.I. = R ± 2 * S.E.
C.I. = .14 ± 2 * (.03) = [.08, .20]
C.I. lower bound = 8%
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.
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 = 0.008
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 = 0
Cash Cow & Retained Earnings

Phoenix currently owns a share of stock in
Mel’s Kitchen Supplies, Inc. Without any reinvestment 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.
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 = $285.71
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
increases
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
= $2.0046
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?
Bond Face Value

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650 = 70/(1.11)4/12 + 70/(1.11)10/12 +
X/(1.11)10/12
650 = 67.61 + 64.17 + X / 1.09086
518 = X / 1.09086
X = $565.31