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Chapter Twenty Four
Warrants and
Corporate Finance
Ross Westerfield Jaffe
Convertibles


24
Sixth Edition
Prepared by
Gady Jacoby
University of Manitoba
and
Sebouh Aintablian
American University of
Beirut
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Executive Summary
• This chapter describes the basic features of warrants
and convertibles.
• The important questions are:
– How can warrants and convertibles be valued?
– What impact do warrants and convertibles have on firm
value?
– What are the differences between warrants, convertibles,
and call options?
– Under what circumstances are warrants and convertibles
converted into common stock?
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Chapter Outline
24.1 Warrants
24.2 The Difference between Warrants and Call Options
24.3 Warrant Pricing and the Black-Scholes Model
(Advanced)
24.4 Convertible Bonds
24.5 The Value of Convertible Bonds
24.6 Reasons for Issuing Warrants and Convertibles
24.7 Why are Warrants and Convertibles Issued?
24.8 Conversion Policy
24.9 Summary and Conclusions
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24.1 Warrants
• Warrants are call options that give the holder the right, but
not the obligation, to buy shares of common stock directly
from a company at a fixed price for a given period of time.
• Warrants tend to have longer maturity periods than exchange
traded options.
• Warrants are generally issued with privately placed bonds as
an “equity kicker.”
• Warrants are also combined with new issues of common
stock and preferred stock, given to investment bankers as
compensation for underwriting services.
– In this case, they are often referred to as a Green Shoe
Option.
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24.1 Warrants
• The same factors that affect call option value affect
warrant value in the same ways.
1.
2.
3.
4.
5.
6.
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Stock price
Exercise price
Interest rate
Volatility in the stock price
Expiration date
Dividends
+
–
+
+
+
–
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24.2 The Difference Between Warrants
and Call Options
• When a warrant is exercised, a firm must issue new
shares of stock.
• This can have the effect of diluting the claims of
existing shareholders.
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Dilution Example
• Imagine that Mr. Armstrong and Mr. LeMond are
shareholders in a firm whose only asset is 10 ounces of gold.
• When they incorporated, each man contributed five ounces
of gold, then valued at $300 per ounce. They printed up two
stock certificates, and named the firm LegStrong, Inc..
• Suppose that Mr. Armstrong decides to sell Mr. Mercx a call
option issued on Mr. Armstrong’s share. The call gives Mr.
Mercx the option to buy Mr. Armstong’s share for $1,500.
• If this call finishes in-the-money, Mr. Mercx will exercise,
Mr. Armstrong will tender his share.
• Nothing will change for the firm except the names of the
shareholders.
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Dilution Example
• Suppose that Mr. Armstrong and Mr. LeMond meet as the
board of directors of LegStrong. The board decides to sell
Mr. Mercx a warrant. The warrant gives Mr. Mercx the
option to buy one share for $1,500.
• Suppose the warrant finishes in-the-money (gold increased
to $350 per ounce). Mr. Mercx will exercise. The firm will
print up one new share.
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Dilution Example
• The balance sheet of LegStrong, Inc. would change
in the following way:
Balance Sheet Before
(Book Value)
Assets
Liabilities and
Equity
Gold:
$3,000 Debt
0
Equity
$3,000
(2 shares)
Total Assets $3,000
Total
$3,000
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Dilution
• The balance sheet of LegStrong, Inc. would change
in the following way:
Balance Sheet Before
(Market Value)
Assets
Liabilities and
Equity
Gold:
$3,500 Debt
0
Equity
$3,500
(2 shares)
Total Assets $3,500
Total
$3,500
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Dilution
• The balance sheet of LegStrong, Inc. would change
in the following way:
Balance Sheet After
(Market Value)
Assets
Liabilities and
Equity
Gold:
$3,500 Debt
0
Cash:
$1,500 Equity
$5,000
(3 shares)
Total Assets $5,000
Total
$5,000
Note that Mr. Armstrong’s claim falls in value from
$1,750 = $3,500 ÷ 2 to $1,666.67 = $5,000 ÷ 3
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Warrant Pricing and the Black-Scholes Model
(Advanced)
• Warrants are worth a bit less than calls due to the
dilution.
• To value a warrant, value an otherwise-identical call
and multiply the call price by:
n
n  nw
Where
n = the original number of shares
nw = the number of warrants
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Warrant Pricing and the Black-Scholes Model
(Advanced)
To see why, compare the gains from exercising a call
with the gains from exercising a warrant.
The gain from exercising a call can be written as:
share price  exercise price
Note that when n = the number of shares, share price is:
Firm' s value net of debt
n
Thus, the gain from exercising a call can be written as:
Firm' s value net of debt
 exercise price
n
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Warrant Pricing and the Black-Scholes Model
(Advanced)
The gain from exercising a warrant can be written as:
share price after warr ant exercise  exercise price
Note that when n = the original number of shares
and nw = the number of warrants,
 share price 
Firm' s value net of debt  exercise price  nw


after


n  nw
 warrant exercise 
Thus, the gain from exercising a warrant can be written as:
Firm' s value net of debt  exercise price  nw
 exercise price
n  nw
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Warrant Pricing and the Black-Scholes Model
(Advanced)
The gain from exercising a call can be written as:
Firm' s value net of debt
 exercise price
n
The gain from exercising a warrant can be written as:
Firm' s value net of debt  exercise price  nw
 exercise price
n  nw
A bit of algebra shows that these
equations differ by a factor of
n
n  nw
So to value a warrant, multiply the value
n
of an otherwise-identical call by
n  nw
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24.4 Convertible Bonds
• A convertible bond is similar to a bond with warrants.
• The most important difference is that a bond with warrants
can be separated into different securities and a convertible
bond cannot.
• Recall that the minimum (floor) value of convertible:
– Straight or “intrinsic” bond value
– Conversion value
• The conversion option has value.
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24.5 The Value of Convertible Bonds
The value of a convertible bond has three components:
1. Straight bond value
2. Conversion value
3. Option value
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Convertible Bond Problem
• Litespeed, Inc., just issued a zero coupon
convertible bond due in 10 years.
• The conversion ratio is 25 shares.
• The appropriate interest rate is 10%.
• The current stock price is $12 per share.
• Each convertible is trading at $400 in the market.
– What is the straight bond value?
– What is the conversion value?
– What is the option value of the bond?
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Convertible Bond Problem (continued)
– What is the straight bond value?
SBV 
$1,000
 $385.54
10
(1.10)
– What is the conversion value?
25 shares × $12/share = $300
– What is the option value of the bond?
$400 – 385.54 = $14.46
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24.5 The Value of Convertible Bonds
Convertible
Bond Value
Convertible bond
values
Conversion
Value
floor value
Straight bond
value
floor
value
= conversion ratio
Option
value
Stock
Price
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24.6 Reasons for Issuing Warrants and
Convertibles
• A reasonable place to start is to compare a hybrid like
convertible debt to both straight debt and straight equity.
• Convertible debt carries a lower coupon rate than does
otherwise-identical straight debt.
• Since convertible debt is originally issued with an out-ofthe-money call option, one can argue that convertible debt
allows the firm to sell equity at a higher price than is
available at the time of issuance. However, the same
argument can be used to say that it forces the firm to sell
equity at a lower price than is available at the time of
exercise.
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Convertible Debt vs. Straight Debt
• Convertible debt carries a lower coupon rate than does
otherwise-identical straight debt.
• If the company subsequently does poorly, it will turn out
that the conversion option finishes out-of-the-money.
• But if the stock price does well, the firm would have been
better off issuing straight debt.
• In an efficient financial market, convertible bonds will be
neither cheaper nor more expensive than other financial
instruments.
• At the time of issuance, investors pay the firm for the fair
value of the conversion option.
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Convertible Debt vs. Straight Equity
• If the company subsequently does poorly, it will turn out
that the conversion option finishes out-of-the-money, but
the firm would have been even better off selling equity
when the price was high.
• But if the stock price does well, the firm is better off issuing
convertible debt rather than equity.
• In an efficient financial market, convertible bonds will be
neither cheaper nor more expensive than other financial
instruments.
• At the time of issuance, investors pay the firm for the fair
value of the conversion option
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24.7 Why are Warrants and Convertibles
Issued?
• Convertible bonds reduce agency costs, by aligning the
incentives of stockholders and bondholders.
• Convertible bonds also allow young firms to delay expensive
interest costs until they can afford them.
• Support for these assertions is found in the fact that firms
that issue convertible bonds are different from other firms:
– The bond ratings of firms using convertibles are lower.
– Convertibles tend to be used by smaller firms with high
growth rates and more financial leverage.
– Convertibles are usually subordinated and unsecured.
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Why are Convertibles Issued?: Example
• In August 2001, Nortel Networks issued $1.5 billion U.S. of
convertible debt.
• The bonds were convertible to common shares.
• Convertible debt made sense for Nortel because:
– it faced high financing costs (matching cash flows),
– high uncertainty in the tech sector at that time (risk
synergy), and
– Nortel’s stock price fell by over 90% over the last year
(convertibles as back-door equity).
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24.8 Conversion Policy
•
•
•
•
Most convertible bonds are also callable.
When the bond is called, bondholders have about 30 days to
choose between:
1. Converting the bond to common stock at the conversion
ratios.
2. Surrendering the bond and receiving the call price in
cash.
From the shareholder’s perspective, the optimal call policy
is to call the bond when its value is equal to the call price.
In the real world, most firms wait to call until the bond
value is substantially above the call price. Perhaps the firm
is afraid of the risk of a sharp drop in stock prices during
the 30-day window.
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24.9 Summary and Conclusions
• Convertible bonds and warrants are like call options.
• However, there are important differences:
– Warrants are issued by the firm.
– Warrants and convertible bonds have different effects on
corporate cash flow and capital structure.
– Warrants and convertibles cause dilution to existing
shareholder’s claims.
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