Transcript No Slide Title

Chapter
20
Financing with Derivatives
Copyright ©2003 South-Western/Thomson Learning
Introduction
• This chapter examines the
characteristics and valuation of
options and option-related financing.
• It explores the concepts necessary to
evaluate the impact that decisions to
issue or purchase these type of
securities have on shareholder
wealth.
Classes of Derivatives: Securities
• Options are one of two important
classes of so-called derivative
securities – that is, securities whose
value is derived from another asset.
• Another important class of derivative
securities is forward-type contracts, such
as futures contracts and forward
contracts.
• Swaps are another important class of
derivative securities.
Options
• Short-Term options
• Convertible fixed-income securities
• Warrants
• Rights offering
Options: Short-Term Options
• Short-term options on common stocks,
stock market indexes (e.g., Standard &
Poor’s 500 index), 30-year Treasury
bonds (e.g., interest rate options), and
foreign currency options (e.g., on the
British pound and Japanese yen). These
options are traded on organized
exchanges, such as the Chicago
Mercantile Exchange and the Chicago
Board Options Exchange.
Options: Convertible Fixed-Income
Securities
• Convertible fixed-income securities,
such as debentures or preferred stocks,
that may be exchanged for the
company’s common stock at the holder’s
option. By giving the fixed-income
security holder an opportunity to share in
any increase in its common stock value,
the firm is able to reduce potential
conflicts between the fixed-income
security holders and stockholders,
resulting in lower agency costs.
Options: Warrants
• Warrants, which are options issued by a
company to purchase shares of the
company’s common stock at a particular
price during a specified period of time.
Warrants are frequently sold to investors
as part of a unit that consists of a fixedincome security with a warrant attached.
As a result, warrants are issued by firms
for similar reasons as convertible
securities.
Options: Rights Offering
• A rights offering occurs when common
stockholders are given an option to
purchase additional shares of the
company’s common stock, in proportion
to the fraction they currently own, at a
price below the market value.
Option Exchanges
• http://www.aantix.com/
• http://www.cboe.com/
• http://www.cbot.com/
• http://www.cme.com/
Options to Buy and Sell
Call
Option to buy
Option
Put
Option to sell
Options to Buy and Sell
• An option is a security that gives its
holder the right, but not the obligation, to
buy or sell an asset at a set price (the
exercise price) during a specified time
period.
• A call is an option to buy a particular
asset.
• A put is an option to sell a particular
asset.
Call Option Valuation
• At expiration = Stock price – Exercise
price
• Prior to expiration > Stock price –
Exercise price
• Maximum value = Stock price
• Minimum value = 0
Call Option Valuation
• Suppose an investor is offered an
opportunity to purchase a call option on
one share of McKean Company stock.
Consider the following possible sets of
conditions (see Figure 20.1):
Call Option Valuation
• The option’s exercise price is $25; the
McKean stock price is $30 a share; and
the option’s expiration date is today.
Under these conditions, the investor is
willing to pay $5 for the option. In other
words, the value of a call option is equal
to the stock price minus the exercise
price, or
Value of a call option at expiration =
Stock price – Exercise price
Call Option Valuation
• The option’s exercise price is $25; the
McKean stock price is $30 a share; and
the option expires in six months. Given
these conditions, the investor is willing to
pay more than $5 for the option because
of the chance that the stock price will
increase, thereby also causing the option
to increase in value. Therefore,
Value of a call option prior to expiration >
Stock price – Exercise price
Call Option Valuation
• The option’s exercise price is $0.01; the
McKean stock price is $30; and the
option expires in six months. Under
these somewhat unusual conditions, the
option investor is willing to pay almost as
much as the stock price. However, under
no conditions should the investor be
willing to pay more than the stock price.
Therefore,
Maximum value of a call option = Stock
price
Call Option Valuation
• The option’s exercise price is $25; the
McKean stock price is $0.01; and the
option expires today. The investor most
likely is willing to pay nothing for the
option given these conditions, but the
investor also is not willing to pay
someone to take the option “off his
hands,” because it is an option and can
be allowed to expire with no addition
cost. Therefore,
Minimum value of a call option = 0
Variables Affecting Value
Exercise price
Stock price
Variables
affecting
the value of
an option
Time to
expiration date
Interest
rates
Expected stock
price volatility
Relationship Between the Exercise
Price and the Stock Price
• For options expiring at the same time,
the call option with a lower exercise
price sell at a higher price than the
option with a higher exercise price
because buyers have to pay more
money to exercise options with higher
exercise prices. Thus, these options
have less value to potential buyers.
Relationship Between the Exercise
Price and the Stock Price
• The higher the exercise price, given the
stock price, the lower the call option
value, all other things being equal.
• Because an option’s value (payoff) is
dependent, or contingent, on the value of
another security (in this case, the
underlying stock), an option is said to be
a contingent claim.
Time Remaining Until Expiration
Date
• An option with the longer time to
expiration has a higher value than an
option with the shorter time to expiration
because investors realize that the
underlying stock of the former has a
greater chance to increase in value with
the more time before expiration.
Time Remaining Until Expiration
Date
• The longer the time remaining before the
option expires, the higher the option
value, all other things being equal.
Because of this, an option is sometimes
referred to as a “wasting asset.”
Interest Rates
• The buyer of common stock incurs either
interest expense (explicit cost) if the
purchase funds are borrowed or lost
interest income (implicit cost) if existing
funds are used for purchase. In either
case, an interest cost is incurred.
Interest Rates
• Buying a call option is an alternative to
buying stock, and by buying an option,
the interest cost associated with holding
stock is avoided. Because options are
an alternative to ownership, option
values are affected by the stock
ownership interest costs. As a result, the
higher the level of interest rates (and,
hence, the interest cost of stock
ownership), the higher the call option’s
value, all other things being equal.
Expected Stock Price Volatility
• Suppose an investor has a choice of
buying a call option on either stock S or
stock V. Both stocks currently sell at $50
a share, and the exercise price of both
options is $50. Stock S is expected to be
the more stable of the two – its value at
the time the option expires has a 50
percent chance of being $45 and a 50
percent chance of being $55 a share.
Expected Stock Price Volatility
• In valuing the call option on stock S, the
investor considers only the $55 price and
its probability because if the stock goes
to $45 a share, the call option with a $50
exercise price becomes worthless.
Expected Stock Price Volatility
• Stock V is expected to be more volatile –
its expected value at the time of option
expiration has a 50 percent probability of
being $30 and a 50 percent probability of
being $70 a share. Similarly, in valuing
the call option on stock V, the investor
considers only the $70 price and its
probability.
Expected Stock Price Volatility
• The investor now has sufficient
information to conclude that the call
option on stock V is more valuable than
the call option on stock S because a
greater return can be earned by
investing in an option that has a 50
percent chance of being worth $20
(stock price – exercise price = $70 – $50
= $20) at expiration than an option that
has a 50 percent probability of being
worth $5 (stock price – exercise price =
$55 – $50 = $5) at expiration.
Expected Stock Price Volatility
• Therefore, the greater the expected
stock price volatility, the higher the call
option value, all other things being equal.
The Foundations of Option
Valuation
• The valuation of a call of option was
determined to be a function of the
following variables:
– The current price of the asset underlying the
option. In the case of stock options this is
the price of the common stock on which the
option has been written.
– The exercise price of the option.
The Foundations of Option
Valuation
– The time remaining until the option expires.
– The risk-free rate of interest.
– The probability of the underlying asset, e.g.,
the share of stock on which the option was
written.
The Foundations of Option
Valuation
• The Black-Scholes model was
developed from the premise that a
strategy of borrowing to buy stock can
exactly equal the risk associated with the
purchase of a call option. Because the
price of a common stock is readily
observable, as is the borrowing rate,
they showed that it is possible to derive
the theoretically correct value for a call
option.
The Foundations of Option
Valuation
• The Black-Scholes model is based on
the following assumptions:
– The stock pays no dividends during the life
of the option. Although this might seem like
a serious limitation of the model, other
models have been developed that take
dividends into account. A common way of
adjusting the Black-Scholes model for the
effect of dividends is to subtract the present
value of expected dividend payments during
the life of the option from the stock price
variable in the model.
The Foundations of Option
Valuation
– The call option is a European option.
European options can only be exercised at
expiration, whereas American options can
be exercised at any time up until the
expiration date. This assumption is not
important because few options are
exercised prior to expiration.
The Foundations of Option
Valuation
When an option is exercised prior to
expiration, the option holder loses the value
of any premium (the difference between the
market value of the option and option’s
intrinsic value, which is defined as the
difference between the stock price and the
exercise price) that is contained in the
option price.
The Foundations of Option
Valuation
– Stock prices are assumed to follow a
random walk. Investors are assumed not to
be able to predict the direction of the overall
market or of any particular stock.
– There are no transaction costs in the buying
and selling of options. This assumption is
violated in reality, but transaction costs are
low enough that this assumption is not a
serious limitation of the model.
– The probability distribution of stock returns
is normally distributed.
The Foundations of Option
Valuation
– Short-term, risk-free interest rates are
assumed to be known and constant over
the life of the option contract. The discount
rate on 30-day U.S. government Treasury
bills is often used as the risk-free rate in the
Black-Scholes model.
– The variance of returns on the underlying
stock is assumed to be constant and known
to investors over the option’s life.
The Foundations of Option
Valuation
• With these assumptions, the “correct”
market value of an option can be
determined. If the price of an option
differs from this theoretically “correct’
value, it is possible for investors to set
up a risk-free arbitrage position and earn
a rate of return is excess of the risk-free
rate. Hence, it can be said that there are
powerful market forces at work to keep
actual market values of options
consistent with their theoretical values.
The Black-Scholes Option Pricing
Model
• The Black-Scholes model defines the
equilibrium value of a call option to buy
one share of a company’s common stock
as:
E
C  Ps N(d1 )  rt N(d 2 )
e
where:
Ps = current stock value
t = time in years until the expiration of
the option
The Black-Scholes Option Pricing
Model
E = exercise price of the call option
r = short-term annual, continuously
compounded, risk-free rate of interest
N(d) = the value of a cumulative normal
density function; the probability
that a standardized, normally
distributed random variable will
be less than or equal to the value
d
e = the exponential value (2.71828)
The Black-Scholes Option Pricing
Model
Ps

ln( )  ( r 
)t
E
2
d1 
 t
2
d 2  d1  
t
σ = the standard deviation per year in
the continuous return on the stock
In = natural logarithm
Applying the Black-Scholes
• Consider the case of Queen
Pharmaceuticals, Inc. Based on an
analysis of past return for Queen’s
common stock, the standard deviation of
its stock returns has been estimated to
be 0.3 or 30 percent. As of January 14,
Queen’s stock price was Ps = $30. The
exercise price of its call options was E =
$29.
Applying the Black-Scholes
the short-term annual, continuously
compounded interest rate was r = 0.06,
and the time to expiration of the call
option was t = 0.5 or one-half year. With
this information, we can now compute
the equilibrium value of these call
options.
Applying the Black-Scholes
• Step 1: Compute the values for d1 and
d2.
Ps
2
d1 
ln(
E
)  (r 
 t
2
)t
30
(0.3) 2
ln( )  (0.06 
)0.5
29
2

 0.4074
0.3 0.5
d 2  d1   t
 0.4074  0.3 0.5  0.1953
Applying the Black-Scholes
• Step 2: Compute N(d1) and N(d2).
Recall that the values in Table V are the
probabilities of having a value greater
than z (for positive standard normalized
values such as d1 or d2 in this example)
or less than z (for negative standard
normalized values).
Applying the Black-Scholes
Because d1 and d2 are both positive, we
can find the probability of a value greater
than d1 or d2 directly from Table V and
then subtract this probability from 1.0 to
get the probability of a value less than d1
or d2 , as is required in the BlackScholes model.
Applying the Black-Scholes
From Table V, the probability of a value
greater than d1 (rounded to 0.41) is
0.3409. Hence the value for N(d1) will be
1.0 – 0.3409 or 0.6591. Similarly the
probability of a value greater than d2
(rounded to 0.20) is 0.4207. Hence the
value for N(d2), that is, the probability of
a value less than d2, will be 1.0 – 0.4207
= 0.5793.
Applying the Black-Scholes
• Step 3: Calculate the value of C, the call
option for Queen Pharmaceuticals stock.
E
C  Ps N(d1 )  rt N(d 2 )
e
$29
 $30(0.6591)  (0.06)(0.5) (0.5793)
e
 $3.47
Applying the Black-Scholes
• Therefore, the Black-Scholes model
indicates that an option to purchase one
share of Queen Pharmaceuticals stock
is worth approximately $3.47, given the
assumptions presented above. Option
values are especially sensitive to the
estimates of stock return volatility that
are input in the model.
Common Stock in an Options
Framework
• Any firm with debt can be analyzed in an
options framework. Suppose a start-up
firm raises equity capital and also borrow
$7 million, due two years from now.
Then, suppose further that the firm
undertakes a risky project to develop
new computer parts. In two years, the
firm must decide whether or not to
default on its debt repayment obligation.
Common Stock in an Options
Framework
• Consider this example in an options
context. The stockholders can be viewed
as having sold this firm to the debt
holders for $7 million when they
borrowed the $7 million. But the
stockholders retained an option to buy
back the firm. The stockholders have the
right to exercise their option by paying
off the debt claim at maturity.
Common Stock in an Options
Framework
• Whether they do depends on the value
of the firm at the time the debt is due. If
the value of the firm is greater than the
debt claim, the stockholders will exercise
their option by paying off the debt. But if
the value of the firm is less than the debt
claim, the stockholders will let their
option expire by not repaying the debt.
Common Stock in an Options
Framework
• This simplified example has interesting
implications. Earlier in the options
discussion, we showed that the greater
the expected stock price volatility, the
higher the call option value will be.
Therefore, if the stockholders choose
high-risk projects with a chance of very
large payoffs, they increase the value of
their option. But, at the same time, they
also increase the likelihood of defaulting
on the debt, thereby decreasing its
value.
Common Stock in an Options
Framework
• Thus it is easy to see how potential
conflicts between stockholders and debt
holders can occur. These potential
conflicts are discussed further in the next
section on convertible securities. In fact,
we shall see that giving the bondholders
an equity stake in the firm decreases the
potential for conflicts between
stockholders and debt holders.
Option Valuation Calculator
• Check out the option valuation calculator
at this Web site:
http://www.numa.com/
Convertible Securities
• Both debentures and preferred stock can
have convertibility or conversion
features. When a company issues
convertible securities, its usual intention
is the future issuance of common stock.
Convertible Securities
• To illustrate, suppose the Beloit
Corporation issues two million shares of
convertible preferred stock at a price of
$50 a share. After the sale, the company
receives gross proceeds of $100 million.
Because of the convertibility feature, the
company can expect to issue shares of
common stock in exchange for the
redemption of the convertible preferred
stock over some future time period. As a
result, convertibles are sometimes
described as a deferred equity offering.
Convertible Securities
In the case of Beloit’s convertible
preferred, each $50 preferred share can
be exchanged for two shares of common
stock; that is, the holder has a call option
to buy two shares of the company’s
common stock at an exercise of $25 a
share.
Convertible Securities
Therefore, if all the preferred shares are
converted, the company in effect will
have issued four million new common
shares, and the preferred shares will no
longer appear on Beloit’s balance sheet.
No additional funds are raised by the
company at the time of conversion.
Features of Convertible Securities
• As an introduction to the terminology and
features of convertible securities,
consider the $115 million, 25-year issue
of 6.125 percent convertible
subordinated debentures sold by
Advanced Research, Inc. (ARI), a
computer software company.
Convertible securities are exchanged
for common stock at a stated
conversion price.
Features of Convertible Securities
In the case of the ARI issue, the
conversion price at the time of issue was
$84. This means that each $1,000
debenture was convertible into common
stock at $84 a share.
Features of Convertible Securities
• The number of common shares that can
be obtained when a convertible security
is exchanged is determined by the
conversion ratio, which is calculated as
follows:
Par value of security
Conversion ratio 
Conversion price
Features of Convertible Securities
• In the case of ARI’s convertible
subordinated debentures, the conversion
ratio at the time of issue was the
following:
Conversion ratio = ($1,000)/($84) = 11.9
Features of Convertible Securities
Thus, each $1,000 ARI debenture could
be exchanged for 11.9 shares of
common stock. Although the conversion
ratio may change one or more times
during the life of the conversion option
(as it did for the ARI bonds), it is more
common for it to remain constant.
Features of Convertible Securities
• Normally, the conversion price is set
about 15 to 30 percent above the
common stock’s market price prevailing
at the time of issue. For example, at the
time ARI issued its convertible
debentures, the market price of its
common stock was about $65 a share.
The $19 (=$84 – $65) difference
between the conversion price and the
market price represents a 29 percent
premium.
Valuation of Convertible Securities
• Because convertible securities possess
certain characteristics of both common
stock and fixed-income securities, their
valuation is more complex than that of
ordinary nonconvertible securities. The
actual market value of a convertible
security depends on both the common
stock value, or conversion value, and the
value of a fixed-income security, or
straight-bond or investment value.
Features of Convertible Securities:
Conversion Value
• The conversion value, or stock value,
of a convertible bond is defined as the
conversion ratio times the common
stock’s market price:
Conversion value
= Conversion ratio*Stock price
Features of Convertible Securities:
Conversion Value
• To illustrate, assume that a firm offers a
convertible bond that can be exchanged
for 40 shares of common stock. If the
market price of the firm’s common stock
is $20 per share, the conversion value is
$800. In the case of ARI’s convertible
bonds, the conversion value was
11.9*$65 (the price per common share at
the time of issue), or $774.
Features of Convertible Securities:
Straight-Bond Value
• The straight-bond value, or investment
value, of a convertible debt issue is the
value it would have if it did not possess
the conversion feature (option). Thus, it
is equal to the sum of the present value
of the interest annuity plus the present
value of the expected principal
repayment:
Features of Convertible Securities:
Straight-Bond Value
n
Interest Principal
Straight-bond value  

t
n
(1+
k
)
(1

k
)
t 1
d
d
where kd is the current yield to maturity
for nonconvertible debt issues of similar
quality and maturity; t, the number of
years; and n, the time to maturity.
Features of Convertible Securities:
Straight-Bond Value
• Considering again ARI’s 6.125 percent,
25-year convertible debentures, the
bond value at the time of issue is
calculated as follows, assuming that 9
percent is the appropriate discount rate
(and that interest is paid annually):
25
$61.25 $1,000
Straight-bond value  

t
25
(1.09)
(1.09)
t1
 $61.25(PVIFA0.09, 25 )  $1,000(PVIF0.09, 25
 $61.25(9.823)  $1,000(0.116)  $718
Features of Convertible Securities:
Market Value
• The market value of a convertible debt
issue is usually somewhat above the
higher of the conversion or the straightbond value; this is illustrated in Figure
20.2.
• The difference between the market value
and the higher of the conversion or the
straight-bond value is the conversion
premium for which the issue sells.
Features of Convertible Securities:
Market Value
• This premium tends to be largest when
the conversion value and the straightbond value are nearly identical. This set
of circumstances allows investors to
participate in any common stock
appreciation while having some degree
of downside protection because the
straight-bond value can represent a
“floor” below which the market value will
not fall.
Features of Convertible Securities:
Market Value
• The ARI convertible debentures
described in this section were offered to
the public at $1,000 per bond and
quickly were bought up by investors. In
this case, investors were willing to pay
$1,000 for an issue having a conversion
value of approximately $774 and a bond
value of about $718. The $1,000 market
value contained a premium of $226 over
the conversion value (which was higher
than the bond value).
Features of Convertible Securities:
Market Value
• This premium can be thought of as the
value of the implicit call option on a firm’s
common stock associated with this
convertible security. In practice,
convertible securities are valued by
adding the straight-bond value to the
value of the conversion options to buy
common stock. These conversion
options can be valued using a variation
of the Black-Scholes option pricing
model.
Converting Convertible Securities
Voluntary
Prior to expiration
Conversion
Forced
Call privilege
Converting Convertible Securities
• Conversion can occur in one of two
ways:
– It may be voluntary on the part of the
investor.
– It can be effectively forced by the issuing
company.
Whereas voluntary conversions can occur
at any time prior to the expiration of a
conversion feature, forced conversions
occur at specific points in time.
Converting Convertible Securities
The method most commonly used by
companies to force conversion is the
exercise of the call privilege on the
convertible security.
Another way in which a company can
encourage conversion is by raising its
dividend on common stock to a high enough
level that holders of convertible securities
are better off converting them and receiving
the higher dividend.
Convertible Securities and Earnings
Dilution
• If a convertible security (or warrant)
issue is ultimately exchanged for
common stock, the number of common
shares will increase and earnings per
share will reduced (i.e., diluted), all other
things being equal. Companies are
required (by Accounting Principles Board
Opinion 15) to disclose this potential
dilution by reporting both primary and
fully diluted earnings per shares.
Convertible Securities and Earnings
Dilution
• Primary earnings per share are
calculated based on the number of
common shares outstanding plus
common stock equivalents. A common
equivalent must meet certain tests, but it
basically includes any convertible
security that derives its value primarily
from the common stock into which it can
be converted.
Convertible Securities and Earnings
Dilution
• Fully diluted earnings per share are
calculated based on the assumption that
all dilutive securities are converted into
common shares. In calculating primary
or fully diluted earnings per share,
earnings must be adjusted for the
interest or preferred dividends saved as
the result of conversion.
Reasons for Issuing Convertibles
• Make security more attractive
• Sell common stock in the future at higher
price
• Allow time for investments to pay
benefits
• Small, risky companies
• Lessen agency conflict
Warrants
• A warrant is a company-issued option to
purchase a specific number of shares of
the issuing company’s common stock at
a particular price during a specific time
period. Warrants are frequently issued in
conjunction with an offering of
debentures or preferred stock. In these
instances, like convertibles, warrants
tend to lower agency costs.
Features of Warrants
• Warrants are usually issued with other
securities.
• The exercise price of a warrant is the
price at which the holder can purchase
common stock of the issuing company.
– The exercise price is usually between 10
and 35 percent above the market price of
the common stock prevailing at the time of
issue.
Features of Warrants
– The exercise price normally remains
constant over the life of the warrant. One
exception is the case of a stock split. When
this occurs, the exercise price of the warrant
is adjusted to reflect the new number of
shares and share price.
– Typically, the life of a warrant is between 5
and 10 years, although on occasion the life
can be longer or even perpetual.
Features of Warrants
• With convertible securities such as
convertible bonds or preferred stock, the
company does not receive additional
funds at the time of conversion.
Features of Warrants
• If a warrant is issued as part of a “unit”
with a fixed-income security, the warrant
is usually detachable from the debenture
or preferred stock; this means that
purchasers of the units have the option
of selling the warrants separately and
continuing to hold the debenture or
preferred stock. As a result, other
investors can purchase and trade
warrants.
Features of Warrants
• Holders of warrants do not have the
rights of common stockholders, such as
the right to vote for directors or receive
dividends, until they exercise their
warrants.
Reasons for Issuing Warrants
• Lower agency costs
• Sell common stock in the future at higher
price
• Sell common stock in the future without
incurring significant costs at the time of
sale
Valuation of Warrants
• The value of a warrant depends upon
the same variables that affect call option
valuation. Because a warrant’s value
depends upon the price of the issuing
company’s stock, it is a contingent claim,
just like an option. In this connection, the
formula value of a warrant (also called
“the value at expiration”) is defined by
the following equation:
Valuation of Warrants
Formula value of a warrant = Max{$0;
(Common stock market price per share –
Exercise price per share)*(number of
shares obtainable with each warrant)}
Note that the market value of the warrant
may not be equal to its formula value.
Valuation of Warrants
• At the time of issue, a warrant’s exercise
price is normally greater than the
common stock price. Even though the
calculated formula value may be
negative, it is considered to be zero
because securities cannot sell for
negative amounts.
Valuation of Warrants
• For example, at the time of issue, the
Fannie Mae warrants had an exercise
price of $44.25 and the firm’s common
stock price was $33 per share. Each
warrant entitled the holder to one share,
and the formula value was zero:
Formula value
= Max {$0; ($33 – $44.25)(1)}
=0
Valuation of Warrants
• Once the stock price rises above the
exercise price of the warrant, the formula
value will be greater than zero.
• For example, on February 24, 1989,
Fannie Mae’s stock price was $59 and
the warrant price was $19.375. At this
point, the formula value of the warrant
was
Formula value
= Max {$0; ($59 – $44.25)(1)}
= $14.75
Valuation of Warrants
• On the expiration date of a warrant, the
market price of the warrant should be
equal to the formula value.
• For the Fannie Mae warrants on the
expiration date, the market price of the
stock (after the 3-for-1 stock split) was
$45.375, and the market price of the
warrants was $30.625. Note that the
exercise price of the warrants was
lowered from $44.25 to $14.75 as a
result of the 3-for-1 stock split.
Valuation of Warrants
• As we see, the market price of the
warrants was equal to the formula value:
• Formula value
= Max {$0; ($45.375 – $14.75)(1)}
= $30.625
Comparison of Warrants and
Convertible Securities
• Assume that the warrants are issued as
part of a fixed-income security offering.
The similarities include the following:
– Both warrants and convertibles tend to
lessen potential conflicts between fixedincome security holders and stockholders,
thereby reducing agency costs.
– The intention is the deferred issuance of
common stock at a price higher than that
prevailing at the time of the convertible or
warrant issue.
Comparison of Warrants and
Convertible Securities
– Both the attachment of warrants and the
convertibility option result in interest
expense or preferred dividend savings for
the issuing company, thereby easing
potential cash flow problems.
Comparison of Warrants and
Convertible Securities
• Some of the differences include the
following:
– The company receives additional funds at
the time warrants are exercised, whereas
no additional funds are received at the time
convertibles are converted.
– The fixed-income security remains on the
company’s books after the exercise of
warrants; in the case of convertibles, the
fixed-income security is exchanged for
common stock and taken off the company’s
books.
Comparison of Warrants and
Convertible Securities
– Because of the call feature, convertible
securities potentially give the company
more control than warrants over when the
common stock is issued.
Warrants (W) and Convertible
Securities (C)
Characteristic
W
C
Lessen Agency Conflicts


Deferred Issuance of C/S


Savings of Interest or Dividends

Company Receives Additional
Funds
Two Securities on Books
More Control


x

x
x

Analysis of Rights Offerings
• In a rights offering the firm’s existing
stockholders are given an option to
purchase a fraction of the new shares
equal to the fraction they currently own,
thereby maintaining their original
ownership percentage.
Analysis of Rights Offerings
• Hence, rights offerings are used in equity
financing by companies whose charters
contain the preemptive right. In addition,
rights offerings may be used as a means
of selling common stock in companies in
which preemptive rights do not exist. The
number of rights offerings has gradually
declined over the years.
Analysis of Rights Offerings
• The following example illustrates what a
rights offering involves. The Miller
Company has 10 million shares
outstanding and plans to sell an
additional 1 million shares via a rights
offering. In this case, each right entitles
the holder to purchase 0.1 share, and it
takes 10 rights to purchase one share.
(The rights themselves really are the
documents describing the offer. Each
stockholder receives one right for each
share currently held.)
Analysis of Rights Offerings
The company has to decide on a
subscription price, which is price the
right holder will have to pay per new
share. The subscription price has to be
less than the market price, or right
holders will have no incentive to
subscribe to the new issue. As a general
rule, subscription prices are 5 to 20
percent below market prices. If the Miller
Company’s stock is selling at $40 per
share, a reasonable subscription price
might be $35 per share.
Valuation of Rights
• Because a right represents an
opportunity to purchase stock below its
current market value, the right itself has
a certain value, which is calculated
under two sets of circumstances:
– The rights-on case
– The ex-rights case
Valuation of Rights
• A stock is said to “trade with rights-on”
when the purchasers receive the rights
along with the shares they purchase.
• In contrast, a stock is said to “trade exrights” when the stock purchasers no
longer receive the rights.
Valuation of Rights
• For example, suppose the Miller
Company announced on May 15 that
shareholders of record as of Friday, June
20, will receive the rights. This means
that anyone who purchased stock on or
before Wednesday, June 18, will receive
the rights, and anyone who purchased
stock on or later than June 19 will not. (A
stock purchaser become a “shareholder
of record” two trading days after
purchase.)
Valuation of Rights
The stock trades with rights-on up to and
including June 18 and goes ex-rights on
June 19, the ex-rights date. On that date,
the stock’s market value falls by the
value of the right, all other things being
equal.
Valuation of Rights
• The theoretical value of a right for the
rights-on case can be calculated using
the following equation:
M0  S
R
N 1
where R is the theoretical value for the
right; M0, the rights-on market value of
the stock; S, the subscription price of the
right; and N, the number of rights
necessary to purchase one new share.
Valuation of Rights
• In the Miller Company example, the
right’s theoretical value is
$40  $35
R
 $0.455
10  1
Valuation of Rights
• The theoretical value of a right when the
stock is trading ex-rights can be
calculated by using the following
equation:
Me  S
R
N
where Me is the ex-rights market price of
the stock; S, the subscription price of the
right; and N, the number of rights
necessary to purchase one new share.
Valuation of Rights
• If the Miller stock were trading ex-rights,
the theoretical value of a right would be
as follows:
$39.545  $35
R
 $0.455
10
• Note that Me is lower than M0 by the
amount of the right; that is, $40 versus
$39.545.
Valuation of Rights
• Some shareholders may decide not use
their rights because of lack of funds or
some other reason. These stockholders
can sell their rights to other investors
who wish to purchase them. Thus, a
market exists for the rights, and a market
price is established for them.
Valuation of Rights
• Generally, the market price is higher
than the theoretical value until the time
of expiration. The same factors
discussed previously, which determine
the value of a call option, also determine
the value of a right, since a right is
simply a short-term call option on the
stock.
Valuation of Rights
• As with call options, investors can earn a
higher return by purchasing the rights
than by purchasing the stock because of
the leverage rights provide. In general,
the premium of market value over
theoretical value decreases as the rights
expiration date approaches. A right is
worthless after its expiration date.
Valuation of Rights
• One can demonstrate that there is no net
gain or loss to shareholders either from
exercising the right or from selling the
right at the theoretical formula value.
Valuation of Rights
• For example, suppose an investor owns
100 shares of the Miller Company
common stock discussed earlier. The
investor is entitled to purchase 10
(0.1*100) additional shares at $35 per
share. Prior to the rights offerings, the
100 shares of Miller Company are
valued at $4,000 (100 shares*$40 per
share).
Valuation of Rights
Exercise of the rights will give the
investor 10 additional shares at a cost of
$35 per share, or a total cost of $350.
These 110 shares will be valued at
$4,350 (110*$39.545). Deducting the
cost of these additional shares ($350)
from the total value of the shares
($4,350), one obtains the same value
($4,000) as before the rights offering.
Valuation of Rights
Sale of the rights will yield $45.50
(100*$0.455) to the investor. Combining
this value with the $3,954.50
(100*$39.545) value of the 100 shares
still owned, one also obtains the same
value ($4,000) as before the rights
offering.
Interest Rate Swaps
• A financial swap is a contractual
agreement between two parties
(financial institutions or businesses) to
make periodic payments to each other.
• There are two major types of swaps:
interest rate swaps and currency swaps.
This section will focus on interest rate
swaps.
Interest Rate Swaps
• Interest rate swaps can be used to
protect financial institutions and
businesses against fluctuations in
interest rates. Like futures contracts,
swaps can be used to hedge against
interest rate risk. Even though futures
contracts are more effective in hedging
against short-term risks (less than one
year), swaps are more effective in
hedging against longer-term risks (up to
10 years or more).
Interest Rate Swaps
• Of the many and various types of
interest rate swaps, the most basic is
one in which a party is seeking to
exchange floating rate interest payments
for fixed rate interest payments, or vice
versa.
Interest Rate Swaps
• Consider the case of a finance company
(e.g., Ford Credit) with floating rate debt
(e.g., floating rate bonds) and fixed rate
loans (e.g., automobile installment loans)
that wants to protect itself against an
increase in interest rates.
Interest Rate Swaps
• The finance company can enter into a
swap contract with another party who
agrees to pay the interest costs in
excess of a specific rate (e.g., 7.5
percent) for a given period of time (e.g.,
three years). Should interest rates
increase in the future, the finance
company will receive rising payments
from the other party to the swap
agreement to cover its losses.
Interest Rate Swaps
• The other party to the swap agreement
could be a bank, which borrows at fixed
interest rates (e.g., certificates of
deposit) and lends money to
corporations at floating rates. The bank
may desire t protect itself against a
decline in interest rates. Should interest
rates decline in the future, the bank will
continue receiving fixed interest
payments from the other party to the
swap agreement.
Interest Rate Swaps
• This swap is illustrated in Figure 20.3. In
most interest rate swaps, the floating
rate used in computing the payments
between the parties to the swap is tied to
the London Interbank Offer Rate
(LIBOR). (LIBOR is discussed in
Chapter 2.) In this example it is 2.5
percentage points above LIBOR.
Generally, in a swap agreement, the
parties exchange only the interest
differential, not the principal or actual
interest payments.
Interest Rate Swaps
• Many financial institutions, such as
investment banks, commercial banks,
and non-financial companies, act as
intermediaries in arranging swaps. Some
intermediaries act as brokers and
receive commissions for finding parties
with matching needs. Other
intermediaries act as dealers or market
makers by offering themselves as a
party to the swap until such time as they
can arrange a match with another party.
Information on Swaps
• Check out the Chicago Board of Trade
Web site as a source of information on
swaps.
http://www.cbt.com/