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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 $½À»
½
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$À/ (¼½Î - ÂÎ) Ó $¼»»
(d) What is the fair price of the stock given the probabilities above?
$¼»» *
Ҁ
Ï $½À» *
⅓
Ó $ ¼À»
(e) What is the expected growth rate for the stock? Given your calculations, which
security is more valuable for an investor: the stock with a ÃÎ growth rate
for
sure
or the stock described in part (c) with an uncertain growth rate.
¼» *
⅓
Ï ÂÎ *
Ҁ
Ó ÃÎ
For investors, the stock in part c has a higher value since the uncertainty give a
higher current price despite having the same expected return.
¾.
Excel Question. (2 points)
This question requires data collection.
You can use
http://finance.yahoo.com
to find the numbers. Please note the date on
which you downloaded the data. (date: ¿.¼Â at Àpm)
The questions are about CVS Health Corporation (ticker: CVS).
(a) What is the current price and the current price-earnings ratio?
The current price is ÂÀ.û and EPS is ¾.¼¿.
Price-earnings ratio is $ÂÀ.û/¾.¼¿ Ó ½¿.¼¿
(b) What is the current plow-back ratio?
Plow-back ratio Ó ¼ - Payout Ratio Ó ¼ - ».»ÁÎ Ó ½Ä.Ä¿Î
(c) What is the growth rate of earnings for the next À years according to the
analysts? Hint: look for annual growth rates under “Analysis”. What is the growth
rate of earnings for the next year according to analysts?
The growth estimate is ¿.ÄÃÎ for the next À years. The growth rate for the next
year is ¾.¾»Î.
(d) What is the CAPM beta of CVS? Hint: look for “Statistics.” If the risk-free rate
R
f
is
¿Î and the market risk premium E[
R
M
]
−
R
f
is ÄÎ, what is the required rate of
return on CVS according to the CAPM?
Beta is ».Á». The return under CAPM is Ó ».»¿Ï ».Á»*».»Ä Ó Ä.¿Î
(e) Suppose the earnings and dividends of CVS will grow at a rate equal to the À year
forecast from part (c) forever, meaning the Gordon Growth Model (GGM) applies.
What is the price-earnings ratio according to the GGM?
¾
P»/E» Ó (¼-b)(¼Ïg)/ (R-g) Ó (¼-».¾»)(¼Ï».»¿ÄÃ)/(».»Ä¿-».»¿ÄÃ) Ó ¼Á.Á¾
(f)
What growth rate does the current market price-earnings ratio imply, under our
numerical assumptions regarding the value of the risk-free rate and the market
risk premium.
P»/E» Ó (¼-b)(¼Ïg)/ (R-g)
½¿.¼¿/(¼-».¾»)Ó (¼Ïg)/(R-g)
¾¿.¿Ä Ó (¼Ïg)/(R-g)
¾¿.¿ÄG-¾¿.¿ÄR Ó ¼Ïg
g Ó (¾¿.¿Ä*».»Ä¿ - ¼)/ (¼ Ï ¾¿.¿Ä) Ó ».»Á¾½
The trailing P/E ratio is ½¿.¼¿, which implies that current market earning
growth rate is Á.¾½Î, which is much higher than the company earning growth
rate ¾.¾» Î.
Fixed Income Securities
¿.
(1.À points)
Today is
t
Ó ». You have just bought a five-year zero-coupon Treasury
bond with
$
¼»» face value. You paid
$
û.
(a) What is the annually compounded yield to maturity on the bond?
¼»» Ó Ã»/(¼ Ïy)^À, y Ó (¼»»/û) ^
⅕
- ¼ Ó ».»¿ÀÁ¿ Ó ¿.ÀÁÎ
(b) Suppose that yields at all maturities decrease to ½Î immediately after you have
purchased the bond. Calculate the annualized holding period return if you sell
the bond one year after you have purchased it, at
t
Ó ¼.
New yield Ó½Î
Price ¼ Ó ¼»»/(¼Ï½Î)^¿ Ó $Ľ.¾Ã
HPRa Ó (Ľ.¾Ã - û) / û Ó ».¼À¿Â Ó ¼À.ÀÎ
(c) What is the annually compounded yield to maturity on the bond at
t
Ó ¼?
($¼»»/$Ľ.¾Ã)^Ë - ¼ Ó ».»½»»¼¾ Ó ½Î
À.
(1.À points)
Suppose the yield to maturity on a one-year zero-coupon bond is ÀÎ.
The yield to maturity on a two-year zero-coupon bond is ¾Î.
¿
(a) According to the Expectations Hypothesis, what is the expected one-year rate in
the marketplace for year ½?
(¼Ï».»¾)^½ Ó (¼Ï».»À) Ï (¼ÏE(r½))
E(r½) Ó ¼.»¾ÃÎ
(b) Consider an investor who is absolutely convinced that interest rates will not
change so that the yield on a one-year bond will still be ÀÎ this time next year.
Which of these two bonds, the one-year zero coupon bond, or the two-year zero
coupon bond, should this investor buy to maximize their
one year
return (under
their strongly-held belief about future rates)?
P Ó $¼»»/(¼Ï».»À) Ó$ ÄÀ.½¿
Pirce of two year bond Ó $¼»»/(¼Ï».»¾)^½ Ó$ Ä¿.½Á
One year return Ó ($ÄÀ.½¿-$Ä¿.½Á)/$Ä¿.½Á Ó ¼.»¾ÃÎ
The investor should purchase the one-year coupon bond to maximize return
since it has a higher return ÀÎ while the two-year bond only has ¼.»¾ÃÎ.
À
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The monthly principal and interest payment is $
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1: Monthly Principal and Interest Payment per $1000 of Mortgage
Number of Years
Rate %
10
15
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4.0
$10.12451
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No. R-7539
Panorama Products
INVOICE DATE
June 16, 20XX
486 5th Avenue
CUSTOMER'S
ORDER NO.
14155
Eureka, CA 95501
FOl dIHS
SAME
J.M. Hardware Supply
2051 West Adams Blvd.
Lansing, MI 48901
SALESMAN
SHIPPED VIA
Marshall Trucking
TERMS
Net 30 Days
Effingham, IL
H. Gilbert
QTY. ORDERED
QTY. SHIPPED
DESCRIPTION
LINO
17 cases
Masking Tape 1/2" Standard
$21.70
11cases
Masking Tape 1 1/2" Standard
2" Reflective Tape
saxoq 97
37case
37case
Sandpaper Assorted
INVOICE SUBTOTAL
SHIPPING CHARGES
Insurance
66
INVOICE TOTAL
Type here to search
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ins
prt sc
144
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Case Study # 4 Excel Submission – Capital Budgeting Comprehensive Problem
Pinnacle Custom Home Builders purchased a 40 foot articulating boom lift three years ago for
$50,000. The equipment has been depreciated under the 5-year MACRS schedule (20%, 32%,
19%, 12%, 12% & 5%). The old equipment can be sold for $33,000.
Pinnacle is considering the purchase of a new 60 foot articulating boom lift that would allow
the company to complete nearly all of its construction projects without the need for costly rental
lifts. The new lift could be purchased for $105,000 and would also fall under the 5-year MACRS
depreciation schedule.
Assume the old and new equipment would provide the following operating gains (or losses)
over the next six years.…
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Home > MAT106A OSA Fall 21 > Assessment
Problem Set 1: Finance
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Question 17
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You want to buy a $228,000 home. You plan to pay 5% as a down payment, and take out a 30 year loan for the
rest.
a) How much is the loan amount going to be?
b) What will your monthly payments be if the interest rate is 6%?
c) What will your monthly payments be if the interest rate is 7%?
Question Help: D Video 1 D Video 2
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