McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-0
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?
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-1
Chapter Outline
Warrants
The Difference between Warrants and Call Options
Warrant Pricing and the Black-Scholes Model
(Advanced)
Convertible Bonds
The Value of Convertible Bonds
Reasons for Issuing Warrants and Convertibles
Why are Warrants and Convertibles Issued
Conversion Policy
Summary and Conclusions
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-2
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.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-3
Warrants
• The same factors that affect call option value affect
warrant value in the same ways.
1. Stock price +
2. Exercise price –
3. Interest rate +
4. Volatility in the stock price +
5. Expiration date +
6. Dividends –
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24-4 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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24-5
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 5 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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24-6
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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24-7
Dilution Example
• The balance sheet of LegStrong Inc. would change
in the following way:
Balance Sheet Before
(Book Value)
0
$3,000
$3,000
Total $3,000Total Assets $3,000
Debt
Equity
(2 shares)
Gold:
Liabilities and
Equity
Assets
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24-8
Dilution
• The balance sheet of LegStrong Inc. would change
in the following way:
Balance Sheet Before
(Market Value)
0
$3,500
$3,500
Total $3,500Total Assets $3,500
Debt
Equity
(2 shares)
Gold:
Liabilities and
Equity
Assets
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-9
Dilution
• The balance sheet of LegStrong Inc. would change
in the following way:
Balance Sheet After
(Market Value)
0
$5,000
$3,500
$1,500
Total $5,000Total Assets $5,000
Debt
Equity
(3 shares)
Gold:
Cash:
Liabilities and
Equity
Assets
Note that Mr. Armstrong’s claim falls in value from
$1,750 = $3,500 ÷ 2 to $1, = $5,000 ÷ 3
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-10 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:
Where
n = the original number of shares
nw = the number of warrants
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-11 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:
Note that when n = the number of shares, share price is:
Thus, the gain from exercising a call can be written as:
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-12 Warrant Pricing and the Black-Scholes Model
(Advanced)
Note that when n = the original number of shares
and nw = the number of warrants,
The gain from exercising a warrant can be written as:
Thus, the gain from exercising a warrant can be written as:
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-13 Warrant Pricing and the Black-Scholes Model
(Advanced)
The gain from exercising a warrant can be written as:
The gain from exercising a call can be written as:
A bit of algebra shows that these
equations differ by a factor of
So to value a warrant, multiply the value
of an otherwise-identical call by
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24-14
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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24-15
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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24-16
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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24-17
Convertible Bond Problem (continued)
– What is the straight bond value?
– What is the conversion value?
25 shares × $12/share = $300
– What is the option value of the bond?
$400 – = $
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24-18
The Value of Convertible Bonds
Convertible
Bond Value
Stock
Price
Straight bond
value
Conversion
Value
= conversion ratio
floor value
floor
value
Convertible bond
values
Option
value
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-19 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-of-
the-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.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-20
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 or more expensive than other financial
instruments.
• At the time of issuance, investors pay the firm for the fair
value of the conversion option.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-21
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 or 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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24-22
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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24-23
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.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
24-24
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.
