Logic – the study of arguments
• "the tool for distinguishing between the true and
the false;“
• "the Science, as well as the Art, of reasoning”
• inductive reasoning: drawing general conclusions
from specific examples/ analysis : from object to
its components
• deductive reasoning: drawing logical conclusions
from definitions and axioms/ synthesis: how parts
can be combined to form a whole.
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Chapter 25
OPTIONS AND CORPORATE
SECURITIES
Chapter Outline
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Options: The Basics
Option Payoffs
Employee Stock Options
Equity as a Call Option on the Firm’s Assets
Warrants
Convertible Bonds
Reasons For Issuing Warrants and Convertibles
Other Options
2
Options: The Basics
Option – a contract that gives its owner
the right to buy or sell some asset at a
fixed price on or before a given date
Put option – the right to sell some asset
 Call option – the right to buy some asset
 American vs. European options
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3
Option Payoffs – Calls
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The value of the call
at expiration is the
intrinsic value
◦ C1 = Max(0, S1 - E)
◦ If S1<E, then the payoff
is 0
◦ If S1>E, then the payoff
is S1 – E
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Assume that the
exercise price is $35
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Option Payoffs - Puts
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The value of a put at
expiration is the
intrinsic value
◦ P1 = Max (0, K – S1)
◦ If S1<K, then the
payoff is K-S1
◦ If S1>E, then the payoff
is 0
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Assume that the
strike price is $35
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Employee Stock Options
Options that are given to employees as
part of their benefits package
 Often used as a bonus or incentive
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◦ Designed to align employee interests with
stockholder interests and reduce agency
problems
◦ Empirical evidence suggests that they don’t
work as well as anticipated due to the lack of
diversification introduced into the employees’
portfolios
◦ The stock just isn’t worth as much to the
employee as it is to an outside investor
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Equity: a Call Option
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Equity can be viewed as a call option on the
company’s assets when the firm is leveraged
The exercise price is the value of the debt
If the assets are worth more than the debt
when it comes due, the option will be
exercised and the stockholders retain
ownership
If the assets are worth less than the debt,
the stockholders will let the option expire
and the assets will belong to the
bondholders
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Warrants
A security that gives the holder the right
to purchase shares of stock at a fixed
price over a given period of time
 It is a call option issued by corporations
in conjunction with other securities to
reduce the yield
 Usually included with a new debt or
preferred shares issue as a sweetener or
equity kicker
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Differences between warrants and
traditional call options
Warrants are generally very long term
 They are written by the company and
exercise results in additional shares
outstanding
 The exercise price is paid to the company
and generates cash for the firm
 Warrants can be detached from the
original securities and sold separately
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Convertibles
Convertible bonds (or preferred stock) may be
converted into a specified number of common
shares at the option of the security holder
 The conversion price is the effective price paid
for the stock
 The conversion ratio is the number of shares
received when the bond is converted
 Convertible bonds will be worth at least as
much as the straight bond value or the
conversion value, whichever is greater
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Minimum value of a convertible bond
versus the value of the stock for a given
interest rate
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Valuing Convertibles
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Suppose you have a 10% bond that pays semiannual coupons and will mature in 15 years. The
face value is $1,000 and the yield to maturity on
similar bonds is 9%. The bond is also convertible
with a conversion price of $100. The stock is
currently selling for $110. What is the minimum
price of the bond?
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Straight bond value
Conversion ratio
Conversion value
Minimum price
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Reasons for Issuing Warrants and
Convertibles
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They allow companies to issue cheap
bonds by attaching sweeteners to the
new bond issue. Coupon rates can then
be set at below market rate for straight
bonds
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They give companies the chance to issue
common stock in the future at a premium
over current prices
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The case for and against convertibles
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Other Options
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Call provision on a bond
◦ Allows the company to repurchase the bond
prior to maturity at a specified price that is
generally higher than the face value
◦ Increases the required yield on the bond –
this is effectively how the company pays for
the option
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Put bond
◦ Gives the bondholder the right to require the
company to repurchase the bond prior to
maturity at a fixed price
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Other Options continued
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Over allotment option
◦ Underwriters have the right to purchase
additional shares from a firm in an IPO
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Insurance and Loan Guarantees
◦ These are essentially put options
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Managerial options
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