Chapter 24 – Options and Corporate Finance
Chapter 24
OPTIONS AND CORPORATE FINANCE
CHAPTER WEB SITES
Section Web Address
24.1 www.cboe.com
www.cmegroup.com
www.euronext.com
finance.yahoo.com
24.2 www.financial-guide.ch/ica/derivatives
24.4 www.esopassociation.org
www.nceo.org
CHAPTER ORGANIZATION
24.1 Options: The Basics
Puts and Calls
Stock Options Quotations
Option Payoffs
24.2 Fundamentals of Option Valuation
Value of a Call Option at Expiration
The Upper and Lower Bounds on a Call Option’s Value
A Simple Model: Part I
Four Factors Determining Option Values
24.3 Valuing a Call Option
A Simple Model: Part II
The Fifth Factor
A Closer Look
24.4 Employee Stock Options
ESO Features
ESO Repricing
ESO Backdating
24.5 Equity as a Call Option on the Firm’s Assets
Case I: The Debt is Risk-Free
Case II: The Debt is Risky
24.6 Options and Capital Budgeting
The Investment Timing Decision
Managerial Options
24.7 Options and Corporate Securities
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Chapter 24 – Options and Corporate Finance
Warrants
Convertible Bonds
Other Options
24.8 Summary and Conclusions
ANNOTATED CHAPTER OUTLINE
1. Options: The Basics
Option – a contract that gives the owner the right, but not the obligation, to buy or
sell a specified asset on or before a specified date at a specified price.
Option Terminology:
1. Exercising the option – using the option to buy or sell the underlying asset
2. Strike or exercise price – fixed price at which the underlying asset may be
bought (or sold)
3. Expiration date – the last day that the option can be exercised
4. American option – the option can be exercised any time up to and including the
expiration date
5. European option – the option can only be exercised on the expiration date
A. Puts and Calls
Call option – gives the owner the right, but not the obligation, to
buy the underlying asset at a fixed price before the option expires
Put option – gives the owner the right, but not the obligation, to
sell the underlying asset at a fixed price before the option expires
The person who sold the option is called the option writer and has
an obligation to fulfill the agreement if the option is exercised. In other
words, the writer must sell (buy) the underlying asset if the call (put) is
exercised.
Lecture Tip: You may wish to emphasize the symmetrical nature of
options transactions by contrasting the positions of options buyers and
options writers. For example, call buyers hope that the value of the
underlying asset rises before their option expires. Their potential gain is
unlimited, while their loss is limited to the price paid (the premium) for
the option contract.
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Chapter 24 – Options and Corporate Finance
Call writers, on the other hand, hope that the value of the
underlying asset falls (or, at least, doesn’t rise); their gain is limited to the
premium received, while their potential (opportunity) loss is unlimited.
Writers of covered calls possess the underlying asset at the time the call is
written, so the cost of delivering the underlying asset, should it become
necessary, is known. However, the opportunity cost of having to sell the
asset at a below market price is unknown and unlimited. Writers of naked
calls do not own the underlying asset and must purchase it at the
prevailing market price if the option is exercised. Their actual potential
cost (the amount of cash they have to come up with) is unknown and
unlimited. For this reason, many people view writing naked options as
much riskier than writing covered options.
B. Stock Option Quotations
Chicago Board Options Exchange (CBOE) – the largest organized
stock options exchange. Virtually all listed options are American options.
(Even in Europe, most options are American, not European.) An option is
described as “Firm/Expiration month/ Strike price/Type.”
Contracts are generally for 100 shares (index options provide their
basis in the quote), so a contract will cost 100*price.
Options expire on the third Friday of the expiration month.
Lecture Tip: There has been a great deal of innovation in the
derivatives field over the years. In the options area, a number of
interesting twists on the standard option contract provide interesting class
discussion topics. Consider the growing credit derivatives sector. A couple
of examples are “price/spread” options which are triggered by changes in
the spread between the value of emerging market debt and U.S. Treasuries
and “default puts” where payment occurs upon the default of a third
party.
Lecture Tip: Students are often fascinated by the topics of hedging and
speculation. Options provide an excellent opportunity to introduce the
differences between these terms. Hedging occurs when you use options (or
some other security) to offset a position you already have. For example, if
you own 100 shares of GM stock and the price has risen nicely, you might
want to hedge against a price decline by buying a put option contract.
Speculators do not hold offsetting positions. Instead, they take a stand-
alone derivatives position hoping the price will move in the direction they
want. If you expect the price of GM to decline, you could buy put options
and then profit if you are correct. If you are incorrect, then your loss is
limited to the price that you paid for the options.
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Chapter 24 – Options and Corporate Finance
Both investors bought put options, but for very different reasons. The first
is protecting against a loss, like insurance. The second is hoping to profit
by “guessing” at the direction of the price movement. Corporations are
using options and other derivative securities to hedge much more
frequently than they have done in the past. If done properly, this should
reduce the variability in the firm’s earnings. FASB 133 provides the
accounting guidelines for the use of derivatives and the guidelines are
different depending on whether or not the company is hedging or
speculating.
Lecture Tip: You might want to point out that the strike prices in
listed options are standardized. The various exchanges offer contracts in
$2.50 and $5.00 increments for individual stocks. Cheap stocks have
$2.50 increments, and higher priced stocks traded in $5 increments.
Indexes can trade with varying strike price increments depending on the
“size” of the contract.
C. Option Payoffs
Calls: An option is in-the-money when the stock price is higher
than the strike price (profitable to exercise), at-the-money when the stock
price and the strike price are the same, and out-of-the-money when the
stock price is less than the strike price.
Puts: An option is in-the-money when the stock price is less than
the strike price, at-the-money when they are the same, and out-of-the-
money when the stock price is greater than the strike price.
Options are a zero-sum game (ignoring transaction costs). This is
because one person gains and one person loses by the same amount. The
transaction occurs because you don’t know which you will be ex ante.
Lecture Tip: Although the concepts are similar for puts and calls,
students generally have more difficulty working with puts. An example
showing what happens to the intrinsic value of both a put and a call when
the stock price changes may be helpful.
At expiration, the call value will be equal to Max(0, S – E). If the
strike price is greater than the stock price, the option will not be exercised
and the value is zero. If the stock price is greater than the strike price,
then the option will be exercised and the owner will gain the difference
between the two.
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Chapter 24 – Options and Corporate Finance
At expiration, the put value will be equal to Max(0, E – S). If the
strike price is less than the stock price, the option will not be exercised
(you could sell it for more in the market) and the option value is zero. If
the stock price is less than the strike price, then the owner will exercise
the option and the gain will be the difference between the two.
Example: Consider options with a strike price of $30.
Strike Price Stock Price Call Value Put Value
30 20 0 10
30 25 0 5
30 30 0 0
30 35 5 0
30 40 10 0
2. Fundamentals of Option Valuation
A. Value of a Call Option at Expiration
Notation:
S1 = stock price at expiration
S0 = stock price today
C1 = value of call at expiration
C0 = call premium today
E = exercise price
If S1 E, then C1 = 0
If S1 E, then C1 = S1 – E
B. The Upper and Lower Bounds on a Call Option’s Value
Upper bound: C0 S0. A call option can never sell for more than
the stock.
Lower bound: 0 or S0 – E, whichever is larger. To prevent
arbitrage, the value of a call must be greater than the stock price minus the
exercise price. Otherwise, buy the option, pay the exercise price, and get
the stock for less than it sells for in the market.
Intrinsic value = Max(0, S0 – E), i.e., option value just before
expiration.
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Chapter 24 – Options and Corporate Finance
Lecture Tip: You may want to discuss the importance of arbitrage
in the valuation of options. The classic definition of arbitrage is trading in
more than one market simultaneously to earn a riskless profit. It is
designed to exploit price discrepancies between markets. Risk arbitrage,
on the other hand, is used to exploit the apparent mispricing of stocks
involved in a takeover. The “risk arbitrageur” buys the stock of the firm
being acquired and shorts the stock of the acquiring firm. The goal is to
profit from the tendency of target firm prices to increase and acquiring
firm prices to decrease. The difference here is that there is risk involved
because there is no guarantee that the prices will move “normally.”
Lecture Tip: The phrase “intrinsic value” is important in the field
of finance, but it has more than one meaning. In this context, it refers to
the lower bound on options. In the investments area, however, it is used by
fundamental analysts to refer to the “true” value of a financial asset.
C. A Simple Model: Part I
One way to illustrate option pricing is to show equivalent cash
flows with different sets of securities.
Suppose a stock currently sells for $62, and its price will be either
$70 or $90 in one period. Assume there is a call option with a strike price
of $65. The risk-free rate for one period is 10%.
Portfolio 1: Buy the stock
Portfolio 2: Buy the call and lend 59.09 for one period (PV(E))
In one period the stock (portfolio 1) will be worth either $70 or $90. The
value of portfolio 2 will equal the value of the call + $65 (proceeds from
the loan).
Stock = $70; Portfolio 2 = 70 – 65 + 65 = 70
Stock = $90; Portfolio 2 = 90 – 65 + 65 = 90
Since portfolio 1 and portfolio 2 will have equal values at the end,
they must have equal values today. Otherwise, you would buy the “cheap”
one and sell the “expensive” one and make a risk-less profit.
Therefore, S0 = C0 + PV(E)
C0 = S0 – PV(E) = 62 – 59.09 = 2.91
This can be extended to any stock price where the option finishes
in-the-money.
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Chapter 24 – Options and Corporate Finance
D. Four Factors Determining Option Values
Current stock price – the higher the stock price, the more valuable
the call
Strike price – the lower the strike price, the more valuable the call
Time to expiration – the longer the time to expiration, the more
valuable the call
Risk-free rate – the greater the risk-free rate, the more valuable the
call
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