Foundations of Finance
Solutions to Homework 3
Prof. Eduardo Davila
Topic 6: Equity Valuation
1. Suppose
that the consensus forecast of security analysts of your favorite company is
that earnings next year will be E1 = $5:00 per share. Suppose that the company
tends to plow back 50% of its earnings and pay the rest as dividends. If the
Chief Financial O cer (CFO) estimates that the company’s growth rate will be 8%
from now onwards, answer the following questions.
(a)
If your estimate of the company’s required rate
of return on its stock is 10%, what is the equilibrium price of the stock?
(b)
Suppose you observe that the stock is selling
for $50.00 per share, and that this is the best estimate of its equilibrium
price. What would you conclude about either (i) your estimate of the stock’s
required rate of return; or (ii) the CFO’s estimate of the company’s future growth
rate?
(c)
Suppose your own 10% estimate of the stock’s
required rate of return is shared by the rest of the market. What does the
market price of $50.00 per share imply about the market’s estimate of the
company’s growth rate?
2. This
question requires data collection. You can nd all numbers on
http://finance.yahoo. com. The questions concern Microsoft (ticker: MSFT). The
answers are for the numbers as of March 21, 2012. Current numbers may be
slightly di erent.
(a)
What is the current price and the current
price-earnings ratio?
(b)
What is the current plow-back ratio?
(c)
What is the growth rate of earnings for the next
5 years according to the analysts?
(d)
What is the beta of MSFT? Hint: look for /Key
Statistics”. If the risk-free rate (Rf ) is
4%
and the market risk premium E[RM Rf ] is 6%, what is the required rate of
return on MSFT according to the CAPM?
(e)Assume that Microsoft will have earnings and dividends
that will grow at the analysts forecasted rate forever after; i.e., the Gordon
growth model (GGM) applies. What is the price-earnings ratio that the GGM
predicts for Microsoft?
(f) What growth rate does the market price-earnings ratio
price in (a) imply?
Topic 6: Arbitrage
3.The stock PolarBear.com trades on both the South Pole
Stock Exchange and the North Pole Stock Exchange.
(a)Suppose the price on the North Pole is $18. What does the
No-Arbitrage Condition say about the price on the South Pole? (Assume no
trading costs.)
(b)Suppose the price on the North Pole is $18 and the price
on the the South Pole is $17? How can you make an arbitrage pro t? (Assume no
trading costs.)
(c)Suppose that the price on the North Pole is $18, that
buying or selling on the North Pole costs $2, and that buying or selling on the
South Pole is free. What does the No-Arbitrage Condition say about the price on
the South Pole?
4. Suppose that there are two securities RAIN and SUN. RAIN
pays $100 in there is any rain during the next world cup soccer nal. SUN pays
$100 in there is no rain. Suppose that the world cup soccer nal is 1 year from
today (although this is not true), and suppose that RAIN is trading at a price
of $23 and SUN is trading at a price of $70.
(a)If you buy 1 share of RAIN and 1 share of SUN, what is
your payo after 1 year, depending on the weather?
(b) What does
the No-Arbitrage Condition imply about the price of a 1-year zero-coupon bond?
(Assume no trading costs.)
(c) Suppose
that a 1-year zero-coupon bond is trading at $90. Show how you would set up a
transaction to earn a riskless arbitrage pro t. (Assume no trading costs.)
(d) Suppose
that trading zero-coupon bonds is costless, but trading RAIN and SUN each cost
$2 per $100 face value. Can you still make an arbitrage pro t?
Topic 8: Fixed Income
Securities
5. Suppose
you buy a ve-year zero-coupon Treasury bond for $800 per $1000 face value.
Answer the following questions:
(a)
What is the yield to maturity (annual
compounding) on the bond?
(b)
Assume the yield to maturity on comparable zeros
increases to 7% immediately after purchasing the bond and remains there.
Calculate your annual return (holding period yield) if you sell the bond after
one year.
(c)
Assume yields to maturity on comparable bonds
remain at 7%, calculate your annual return if you sell the bond after two
years.
(d)
Suppose after 3 years, the yield to maturity on
similar zeros declines to 3%. Calculate the annual return if you sell the bond
at that time.
(e)
If yield remains at 3%, calculate your annual
return after four years
(f)
After ve
years.
(g)
What explains the relationship between annual
returns calculated in (b) through (f) and the yield to maturity in (a)?
6.Assume the government issues a semi-annual pay bond that
matures in 5 years with a face value of $1,000 and a coupon yield of 10
percent.
(a)What price would you be willing to pay for such a bond if
the yield to maturity (semi-annual compounding) on similar 5-year governments
were 8%?
(b) What would
be the price if the yield to maturity (semi-annual compounding) on similar
governments were 12%?
(c) If the
price of the bond is 103 19/32 per $100 of face value, what is the yield to
maturity?
(d) Suppose
you held the bond in (c) for 6 months, at which time you received a coupon
payment and then sold the bond for a price of 102 (per $100 of face value). What
would be the annualized holding period return?
7. Suppose
the yield to maturity on a one-year zero-coupon bond is 8%. The yield to
matu-rity on a two-year zero-coupon bond is 10%. Answer the following questions
(use annual compounding):
(a) According
to the Expectations Hypothesis, what is the expected one-year rate in the
marketplace for year 2?
(b) Consider a
one-year investor who expects the yield to maturity on a one-year bond to equal
6% next year. How should this investor arrange his or her portfolio today?
(c) If all
investors behave like the investor in (b), what will happen to the equilibrium
term structure according to the Expectations Hypothesis?
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