Transcript Document

Corporate Finance
Introduction to
Financial Math
Hannes Wagner
Felix Suntheim
Arie E. Gozluklu
15 September 2010
Contact Information
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Email:
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[email protected]
[email protected]
Office Hours: Thursday 6-7pm.
Current Office: Grafton Building, 2-C3-02
New office: Grafton Building, 2-E2-fm03
Q1) BMA Chp. 2, PQ 19(Page 33)
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a)
b)
c)
For an outlay of $8 million you can purchase a tanker load of bucolic acid delivered in
Rotterdam one year hence. Unfortunately the net cash flow from selling the tanker load will be
very sensitive to the growth rate of the world economy:
Slump
Normal
Boom
$8million
$12million
$16million
What is the expected cash flow? Assume the three outcomes for the economy are equally
likely.
What is the expected rate of return on the investment in the project?
One share of stock Z is selling for $10.The stock has the following payoffs after one year
Slump
Normal
Boom
$8
$12
$16
Calculate the expected rate of return offered by stock Z. Explain why this is the opportunity cost of
capital for your bucolic acid project.
d)
Calculate the project’s NPV. Is the project a good investment? Explain why.
Q2) BMA Chp. 2, CQ 20(Page 34)
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In real life the future health of the economy cannot be reduced to three equally
probable states like slump, normal, and boom. But we’ll keep that simplification for one
more example.
Your company has identified two more projects, B and C.
Each will require a $5 outlay immediately. The possible payoffs at year 1, are in
millions:
Slump
Normal
Boom
Project B
$4
$6
$8
Project C
5
5,5
6
You have identified the possible payoffs to investors in three stocks X, Y, and Z:
Current Price
Payoff at Year 1
per Share
Slump
Normal
Boom
X
$95,65
$80
$110
$140
Y
40
40
44
48
Z
10
8
12
16
Q2) BMA Chp. 2, CQ 20(Page 34)
a)
b)
c)
d)
e)
What are the expected cash inflows of project B and C?
What are the expected rates of return offered by stocks X,Y, and Z?
What are the opportunity costs of capital for projects B and C? (Hint:
Calculate the percentage differences, slump versus normal and
boom versus normal, for stocks X,Y, and Z. Match up to the
percentage differences in B’s and C’s payoffs.)
What are the NPVs of projects B and C?
Suppose B and C are launched and $5 million are invested in each.
How much will they add to the market value of your company’s
shares?
Q3) BMA Chp. 3, PQ 19(Page 56)
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a)
b)
c)
d)
e)
As winner of a breakfast cereal competition, you can choose one of
the following prizes:
$100.000 now.
$180.000 at the end of five years.
$11.400 forever.
$ 19000 each of 10 years.
$6.500 next year and increasing thereafter by 5% a year forever.
If the interest rate is 12%, which is the most valuable price?
Q4) BMA Chp. 3, CQ 38(Page 58)
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You own a pipeline which generate a $2 million cash return over the
coming year. The pipeline’s operating costs are negligible, and it is
expected to last for a very long time. Unfortunately, the volume of oil
shipped is declining, and cash flows are expected to decline by 4%
per year. The discount rate is 10%.
a)
What is the present value (PV) of the pipeline’s cash flows if its cash
flows are assumed to last forever?
What is the PV of the cash flows if the pipeline is scrapped after 20
years?
b)
Q5) BMA Chp. 4, PQ 7(Page 81)
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The following table shows the prices of a sample of U.S Treasury strips in
August 2006. Each strip makes a single payment of 1000 at maturity.
a)
b)
c)
d)
Maturity
Price(%)
August 2007
95,53
August 2008
91,07
August 2009
86,2
August 2010
81,08
Calculate the annually compounded, spot interest rate for each year.
Is the term structure upward- or downward-sloping or flat?
Would you expect the yield on a coupon bond maturing in August 2010 to
be higher or lower than the yield on the 2010 strip?
Calculate the annually compounded, one year forward rate of interest for
August 2008. Now do the same for August 2009.
Q6) BMA Chp. 4, CQ 35(Page 84)
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What spot and forward rates are embedded in the following Treasury bonds?
The price of one-year (zero-coupon) Treasury bill is 93,46%. Assume for
simplicity that bonds make only annual payments. Hint: Can you devise a
mixture of long and short positions in these bonds that gives a cash payoff only
in year 2? In year 3?
Coupon(%)
Maturity
Price(%)
4
2
94,92
8
3
103,64
A- three year bond with a 4% coupon is selling at 95%. Is there a profit
opportunity here? If so, how would you take advantage of it?
01/31/2010
03/31/2009
05/31/2008
07/31/2007
09/30/2006
11/30/2005
01/31/2005
03/31/2004
05/31/2003
07/31/2002
09/30/2001
11/30/2000
01/31/2000
Long Term Yields
Long Term Bond Yields
12
10
8
6
Greece
US
4
2
0