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Problem Sets Chapter 2
In what ways is preferred stock like long-term debt? In what way is it like equity?
Preferred stock is like long-term debt in that it typically promise a fixed payment each year and it does not
give the holder voting rights in the firm
Preferred stock is like equity in that the firm is under no contractual obligation to make the preferred stock
dividend payments. Failure to make payments does not set off corporate bankruptcy.

Why are money market securities sometimes referred to as "cash equivalents"?
Bc of their great liquidity
The prices of money market securities are very stable
Can be converted to cash on a very short notice and with very low transaction cost

What would you expect to happen to the spread between yields on commercial paper
and Treasury bills if the economy were to enter a steep recession?
The spread will widen. Deterioration of the economy increases credit risk, that is, the likelihood of default.
Investors will demand a greater premium on debt securities subject to default risk

What are the key differences between common stock, preferred stock, and corporate
bonds?

Problem Sets Chapter 2

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Why are high-tax-bracket investors more inclined to invest in municipal bonds than
low-bracket investors?
Bc municipal bonds' interest is tax-exempt. When facing higher marginal tax rates, a high-income investor
would be more inclined to pick tax-exempt securities

Turn back to Figure 2.3 and look at the Treasury bond maturing in November 2041.
a. How much would you have to pay to purchase one of these bonds?
b. What is its coupon rate?
c. What is the yield to maturity of the bond?

a. You would have to pay the asked price of:
111.82% of par = $1118. 2 for the $1000 par value bond
b. Its coupon rate is 3.125% implying coupon payments of $31.25 annually
c. Current yield = Annual coupon income/price = 31.25/1118.2 = 2.8%

Suppose investors can earn a return of 2% per 6 months on a Treasury note with 6
months remaining until maturity. What price would you expect a 6-month maturity

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Treasury bill to sell for?
Face value = Return + Price = 0.02 x Price + Price
Face value = 1.02 x Price
Suppose the face value is $10,000, then the price is $9,803.9

Find the after-tax return to a corporation that buys a share of preferred stock at $40,
sells it at year-end at $40, and receives a $4 year-end dividend. The firm is in the 30%
tax bracket.
Tax laws allow up to 70% of dividends received from preferred shares to be tax-exempt
→ Taxable income: 0.3 x $4 = $1.2
→ Tax: 0.3 x $1.2 = $0.36

→ After-tax income: $4 - $0.36 = $3.64
→ Rate of return: $3.64/$40 = 9.1%

Turn to Figure 2.8 and look at the listing for General Dynamics.
a. How many shares could you buy for $5,000?
b. What would be your annual dividend income from those shares?
c. What must be General Dynamics’ earnings per share?
d. What was the firm’s closing price on the day before the listing?

a. You could buy: $5000/$142.97 = 34.97 shares
b. Annual dividend income from those shares: 34.97 x $3.04 = $106.3088
c. P/E (Price-earnings) ratio = 15.39
General Dynamics' earnings per share (last year): $142.97/15.39 = $9.29
d. The firm's closing price on the day before the listing: $142.97 + $0.47 = $143.44

Problem Sets Chapter 2

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Consider the three stocks in the following table. Pt represents price at time t, and Qt
represents shares outstanding at time t. Stock C splits two for one in the last period.
P0 Q0 P1
Q1 P2 Q2
A 90 100 95
100 95 100
B 50 200 45
200 45 200
C 100 200 110 200 55 400
a. Calculate the rate of return on a price-weighted index of the three stocks for the first

period (t = 0 to t = 1).
b. What must happen to the divisor for the price-weighted index in year 2?
c. Calculate the rate of return for the second period (t = 1 to t = 2).
a. Price-weighted index:
The rate of return: 10/240 = 4.167%
b. The index value before the stock split: 250/3 = 83.33
Because the new divisor must leave the index unchanged after C split, meaning
83.33 = ((95+45+55)/d
→ The new divisor d = (95 + 45 +55)/83.33 = 2.34
→ The rate of return for the second period = 0%

Using the data in the previous problem, calculate the first-period rates of return on the
following indexes of the three stocks:
a. A market-value-weighted index.
b. An equally weighted index.
a. Market-value-weighted index:
The rate of return = (-1000 + 500 + 2000)/(9000 + 10000 + 20000) = 3.85%
b. Equally weighted index:
The return on each stock is as follows:
rA = 95/90 -1 = 0.0556
rB = -5/50 = -0.1
rC = 10/100 = 0.1
→ The equally weighted average is: [(0.0556 - 0.1 + 0.1)]/3 = 1.85%

An investor is in a 30% tax bracket. If corporate bonds offer 9% yields, what must
municipals offer for the investor to prefer them to corporate bonds?
The after-tax yield on the corporation bonds is: 0.09 x (1 - 0.3) = 6.30%
→ Municipals must offer at least 6.3% yield

Find the equivalent taxable yield of a short-term municipal bond currently offering

yields of 4% for tax brackets of (a) zero, (b) 10%, (c) 20%, and (d) 30%.
r(taxable) (1 - t) = r(muni) → r(taxable) = r(muni)/(1 - t)

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a. r(taxable) = 4%
b. r(taxable) = 4.44%
c. r(taxable) = 5%
d. r(taxable) = 5.714%

What problems would confront a mutual fund trying to create an index fund tied to an
equally weighted index of a broad stock market?
In equally weighted index fund, each stock is given equal weight regardless of its market cap. Smaller cap stocks
will have the same weight as larger cap stocks.
→ The challenges are as follows:
Given equal weights placed to smaller cap and larger cap, equal-weighted indices (EWI) will tend to be more
volatile than their market-capitalization counterparts
It follows that EWIs are not good reflectors of the broad market which they represent; EWIs underplay the
economic importance of large companies
Turnover rates will tend to be higher, as an EWI must be rebalance back to its original target. By design,
many of the transactions would be among the smaller, less-liquid stocks

Which security should sell at a greater price?
a. A 10-year Treasury bond with a 4% coupon rate versus a 10-year T-bond with a 5%
coupon.
b. A 3-month expiration call option with an exercise price of $40 versus a 3-month call
on the same stock with an exercise price of $35.

c. A put option on a stock selling at $50, or a put option on another stock selling at $60
(all other relevant features of the stocks and options may be assumed to be identical).
a. The higher coupon bond
b. The call with the lower exercise price
c. The put with the higher priced stock

Look at the futures listings for the corn contract in Table 2.8. Suppose you buy one
contract for March 2017 delivery. If the contract closes in March at a level of 4.06, what
will your profit be?

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You buy the contract at a price of $3.96, and the contract closes in March at a price of $4.06. The contract
multiplier is 5000.
→ The gain will be: 5000 x ($4.06 - $3.96) = $500

Turn back to Table 2.7 and look at the IBM options. Suppose you buy a June 2016
expiration call option with exercise price $150.
a. Suppose the stock price in June is $152. Will you exercise your call? What is the profit
on your position?
b. What if you had bought the June call with exercise price $145?
c. What if you had bought a June put with exercise price $155?

a. Each contract is for the purchase of 100 shares.
The profit on my position: 100 x ($152 - $150 - $3.31) = -$131 (loss)
b. Profit: 100 x ($152 - $145 - $6.6) = $40
c. Profit: 100 x ($152 - $155 - $1.27) = -$427


. Why do call options with exercise prices greater than the price of the underlying stock
sell for positive prices?

Problem Sets Chapter 2

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There is always a possibility that the option will be in-the-money at some time prior to expiration. Investors will
pay something for this possibility of a positive payoff

Both a call and a put currently are traded on stock XYZ; both have strike prices of $50
and expirations of 6 months. What will be the profit to an investor who buys the call for
$4 in the following scenarios for stock prices in 6 months? What will be the profit in
each scenario to an investor who buys the put for $6?
a. $40
b. $45
c. $50
d. $55
e. $60
The profits to an investor who buys the call for $4:
-$16 ; -$11 ; -$4 ; $1 ; $6

Explain the difference between a put option and a short position in a futures contract.
A put option conveys the right to sell the underlying asset at the exercise price
A short position in a futures contract carries an obligation to sell the underlying asset at the futures price

Explain the difference between a call option and a long position in a futures contract.
A call option conveys the right to buy the underlying asset at the exercise price

A long position in a futures contract carries an obligation to buy the underlying asset at the futures price

Problem Sets Chapter 2

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