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Instructions:
1.
Please type all your answers into this file. The answer
to each question should follow the question itself.
2.
Please, write short VERBAL conclusion at the end of
each problem summarizing your answer in words. Verbal answers are not substitute
for the quantitative solution.
Question 1
Ms. Maple is considering two securities, A and B, and the
relevant information is given below:
State of the economy
Probability
Return on A(%)
Return on B(%)
Bear
0.4
3
6.5
Bull
0.6
15
6.5
Calculate
expected return and standard deviation of two securities.
Suppose
Miss Maple invested $2,500 in security A and $3,500 in security B.
Calculate the expected return and standard deviation of her portfolio.
Question 2
Suppose that you want to buy a 2-year 5% coupon bond, which
pays semi-annual coupons and costs
$997.
Find the yield to maturity
on this bond (YTM)
Find the effective annual rate of return that you
earn on this bond (EAR)?
Question 3
The current market price
of a security is $40, the security’s expected return is 13%, the riskless rate
of interest is 7%, and the market risk premium is 8%.
a. According to CAPM, what is the current beta of this
security?
b. What will be the beta of this security if the
covariance of its rate of return with the market portfolio doubles?
c. According to CAPM, what is the new expected return
on this security?
d. What is the new price of this security?
e. How is your result consistent with our
understanding that assets with higher systematic risks must pay higher returns
on average?
Question
4
Consider the following risk-free T-bill and coupon bonds available for sale in the
bond market (annual coupons):
Maturity
Price
Coupon
1
942
T-bill (zero coupon bond)
2
995
6.3%
3
998
7.5%
4
985.25
6.75%
a. Construct
the term structure of interest rates for these four years.
b. Your
company plans to issue four-year maturity bonds. You plan to issue bonds priced
at $1010. At what level should you plan to set the coupon on your bond to
justify this price?
Question
5
Two retail corporations, both equity financed with no debt,
are essentially in the same business.
However, whereas one of the corporations has a stable earnings and
dividend record, paying out all its earnings in dividends, the other is a
growth stock increasing its earnings and dividends annually through a different
management strategy. The current
dividend is $5 per share for both corporations.
The stable corporationâs stock trades for $40 per share, whereas the
price of the growth stock is $50.
a.
Estimate the investorsâ required rate of return on
these stocks
b.
Estimate the steady future growth rate of the growing
corporation as perceived by the market.
Question
6
The
common stock of the STABBLES Corporation has been trading in a narrow price
range for the past month, and you are convinced it is going to break far out of
that range in the next three months. You do not know whether it will go up or
down, however. The current price of the stock is $100 per share, and the price
of a three-month call option at an exercise price of $100 is $10.
a.
If the risk-free interest rate is 10% per year, what
must be the price of a 3-month put option on STABLES stock at an exercise price
of $100? The stock pays no dividend.
b.
What would be a simple options strategy to exploit your
conviction about the stock priceâs future movements? How far would it have to
move in either direction for you to make a profit on your initial investment?
(The answer to this question should include a payoff table for your strategy and
a graph to support your argument).
Question 7
You are interested in
purchasing a shoe machine XYZ, especially designed for men’s fashion shoes. The
machine costs $10,000. You expect to recover $6,000 a year in operating cash
flows for only two years because of rapidly changing fashions. You estimate the
salvage value of the machine at the end of two years to be $1,200. Assume that
the tax rate is zero. Assume that the $6,000 per year after tax operating cash
flow is received at the end of each year.
(a) What is the Net Present Value
(NPV) of this project, if cash flows are to be discounted at 20% cost of
capital?
(b) What is the IRR of this
project?
You decide to invest in machine XYZ.
But just before you place an order for the machine you hear about another
machine UVW. This machine costs $15,000 and has operating flows of $18,000
during the first year and, for some unknown reason, only $50 during the second
year, with no salvage value at the end of two years. (Assume all cash flows
occur at the end of the year for the purpose of discounting.)
(c) You know that whether you prefer XYZ or UVW
depends upon your cost of capital. Draw the graph showing how NPVs of these two
machines relate to their cost of capital. Both NPVs should be on the same graph.
(d) At what cost of capital both machines have
the same Net Present Value? (Please do not forget to show the equation you need
to solve with the help of Excel to answer this question).
(e) What is
the IRR of machine UVW?
(f) Without making any further calculations,state
the region(s) of cost of capital that make XYZ preferable to UVW, assuming you
must choose either one of these machines but not both.
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