HW3 Jimmy
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Foundations of Finance
Prof. Toomas Laarits
Spring 2023
Homework Cover Sheet
Print your name:
Class section:
FINC-UB.0002.004, 9:30am
FINC-UB.0002.005, 2:00pm
FINC-UB.0002.006, 3:30pm
Homework number:
Students in your homework group:
“I pledge my honor that I have not violated the NYU Stern Student Code of Conduct in the
completion of this exam/problem set.”
Signed:
1
Jimmy Li
Jimmy Li
HW 3
Charlie Ma
Foundations of Finance
Prof. Toomas Laarits
Spring ½»½¾
HW # ¾
Due: ¿/¼Ã before class on the course website.
Note ¼: You are encouraged to work in groups, but everyone must submit their own work.
Feel free to write up the homework any way you want. In particular, you can type it, or you
can write it on paper and scan.
Note ½: Please use the “Homework Cover Sheet” available on the course website as the first
page of your submission.
Note ¾: One of the problems is the designated “Excel problem”. You can also use other
statistical software. Note too that many of the other problems are easier to solve with Excel,
as they ask you to apply the same formula using multiple different inputs.
No Arbitrage
¼.
(2 points)
Consider the following three securities: SNOW, RAIN and SUN. SNOW pays
$
¼»» if it snows on NYU graduation day. RAIN pays
$
¼»» if it rains, but doesn’t snow
on NYU graduation day. SUN pays
$
¼»» if there is neither rain nor snow on graduation
day. Suppose that SNOW is currently trading at
$
¼, RAIN is currently trading at
$
¿¼
and SUN is trading at a price of
$
À½.
(a) If you buy ¼ share of SNOW, ¼ share of RAIN and ¼ share of SUN, what is the
payoff you guarantee on NYU graduation day?
Since one of the three must happen on the Graduation day, the payoff is $¼»» -
$¼ - $¿¼ - $À½ Ó $Á
(b) According to the No Arbitrage Condition, what must be the price of a $¼»» face
value zero-coupon bond that matures on NYU graduation day?
The face value is ¼»»-Á Ó $Ä¿
(c) Suppose that this zero-coupon bond is trading at
$
Ä». How would you set up a
transaction to earn a riskless arbitrage profit? Assume no trading costs.
¼
im
I can buy a zero-coupon bond today at a price of $Ä» and sell ¼ share of rain, one
share of sun, and one share of snow today at a price of Ä¿$ which will guarantee
a $¼»» payment on the graudation day. This will guarantee a $¿ profit.
(d) Suppose that trading zero-coupon bonds and RAIN is costless, but shorting SUN
costs
$
¾ per
$
¼»» face value and shorting SNOW costs
$
¼ per
$
¼»» face value.
Can you still make an arbitrage profit?
Since we are shorting RAIN and SUN in the previous arbitrage, the shorirng cost
will increase our cosrt by ¼ Ͼ Ó $¿ which is equal to our arbitrage profit. The
short cost will eliminate the arbitrage profit.
Equity Valuation
½.
(¾ points)
Suppose that the consensus forecast of security analysts of NoWork Inc. is
that earnings
next year
will be
E
¼
Ó $¼»
.
»» per share. The company tends to plow back
À»Î of its earnings and pay the rest as dividends. The CFO estimates that the
company’s growth rate will be ÃÎ from now on.
(a) If your estimate of the company’s required rate of return is ¼½Î, what is the
equilibrium price of the stock?
P Ó V» Ó $¼» * ».À/ (¼½Î - ÃÎ) Ó $¼½À
(b) You observe that the stock is selling for
$
¼½».»» per share. Suppose you believe
that the market price is right. What must you conclude about either (
i
) your
estimate of the stock’s required rate of return, (
ii
) the CFO’s estimate of the
company’s future growth rate, or (
iii
) the forecast of earnings from the analysts?
If the market price is correct, my estimated price is higher than the current fair
market price. Then: (i) I might have underestimate the required rate of return.
(ii) The CFO might overestimate the growth rate. (iii) The future earning might
be overestimated.
(c) Suppose there is uncertainty about the stock’s dividend growth rate. With
probability
the growth rate will be ¼»Î, with probability
it will be ÂÎ. What
are the respective market values under the two different growth rates?
$À/ (¼½Î - ¼»Î) Ó $½À»
½
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A newspaper editor starts a retirement savings plan in which $225 per month is deposited at the beginning of each month into an account that earns an annual interest rate of 6.4% compounded monthly.
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Which of the deposits are used by business people in majority?
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