CHAPTER 24
WARRANTS AND CONVERTIBLES
SLIDES
CHAPTER ORGANIZATION
24.1 Warrants
24.2 The Difference between Warrants and Call Options
How the Firm Can Hurt Warrant Holders
24.3 Warrant Pricing and the Black-Scholes Model
24.4 Convertible Bonds
24.5 The Value of Convertible Bonds
24.1 Key Concepts and Skills
24.2 Chapter Outline
24.3 Warrants
24.4 Warrants
24.5 The Difference between Warrants and Call Options
24.6 Dilution Example
24.7 Dilution Example
24.8 Dilution Example
24.9 Dilution Example
24.10 Warrant Pricing and the Black-Scholes Model
24.11 Warrant Pricing and the Black-Scholes Model
24.12 Warrant Pricing and the Black-Scholes Model
24.13 Warrant Pricing and the Black-Scholes Model
24.14 Convertible Bonds
24.15 The Value of Convertible Bonds
24.16 Convertible Bond Example
24.17 Convertible Bond Example
24.18 The Value of Convertible Bonds
24.19 Reasons for Issuing Warrants and Convertibles
24.20 Convertible Debt vs. Straight Debt
24.21 Convertible Debt vs. Straight Equity
24.22 Why Are Warrants and Convertibles Issued?
24.23 Conversion Policy
24.24 Quick Quiz
Straight Bond Value
Conversion Value
Option Value
24.6 Reasons for Issuing Warrants and Convertibles
Convertible Debt versus Straight Debt
Convertible Debt versus Common Stock
The “Free Lunch” Story
The “Expensive Lunch” Story
A Reconciliation
24.7 Why Are Warrants and Convertibles Issued?
Matching Cash Flows
Risk Synergy
Agency Costs
Backdoor Equity
24.8 Conversion Policy
ANNOTATED CHAPTER OUTLINE
Slide 24.0 Chapter 24 Title Slide
Slide 24.1 Key Concepts and Skills
Slide 24.2 Chapter Outline
24.1. Warrants
Slide 24.3 –
Slide 24.4 Warrants
Warrant – security issued by firms that gives the holder the right,
but not the obligation, to purchase the common stock directly from
the company at a fixed price for a given period.
May be used as sweeteners or equity kickers – warrants issued in
combination with privately placed loans or bonds, public issues of
bonds, and new stock issues.
Similarities between warrants and options:
1. Both give the right to purchase the equity of the firm.
2. Both are usually protected against stock dividends and stock
splits.
3. Neither is protected against cash dividends.
4. The values of both are affected in the same way from changes in
stock price, exercise price, etc.
Lecture Tip: Although warrants are typically issued as options to
buy common stock, they have also been issued on preferred stock
and bonds. In theory, they could be issued on any asset. For
instance, in June 1986, Saloman Brothers offered 1,000 warrants
to buy up to $250 million of mortgage-backed 8% GNMAs with an
expiration date of June 1987. These warrants are simply call
options on the underlying security.
24.2. The Difference between Warrants and Call Options
Slide 24.5 The Difference between Warrants and Call Options
Differences between warrants and options:
1. Exercise period of a warrant is usually several years.
2. Warrants are issued by the firm. Options are issued by
individuals.
3. When a warrant is exercised the firm receives the exercise price
from the investor, and the firm simultaneously issues new shares.
The last two differences are important because a warrant is a
contract between the firm and a warrant-holder, while an option is
a contract between individuals.
Slide 24.6 –
Slide 24.9 Dilution Example
Further, the exercise of warrants causes an increase in the number
of outstanding shares, whereas the exercise of “normal” calls does
not. When the number of shares increases, the EPS will decrease,
all else equal. Because of the dilution impact of warrants, firms
with a large number of warrants or convertible securities
outstanding report earnings on a diluted basis.
.A How the Firm Can Hurt Warrant Holders
To reduce the firm value, existing owners could liquidate assets
and pay out dividends, thereby keeping warrants out of the money.
24.3. Warrant Pricing and the Black-Scholes Model
Slide 24.10 –
Slide 24.13 Warrant Pricing and the Black-Scholes Model
As warrants are exercised, dilution occurs because the firm’s assets
and profits are spread over a larger number of shares.
As share price rises above the exercise price, warrants will be
converted into common stock, thus diluting the proportional
ownership of each share in the company. Therefore, outstanding
warrants have a dampening effect on stock price appreciation.
The Black-Scholes Option Pricing Model must be restated for use
with warrants. In general, the gain from a warrant is always less
than the gain from an otherwise-identical option, and the
relationship is:
Gain from exercising a warrant = # / (# + #W) × Gain from
exercising a call option
where # is the number of shares outstanding before the warrants
are exercised and #W is the number of shares issued when the
warrants are exercised.
A similar relationship exists between the price of a warrant and the
price of a call option:
Price of a warrant = # / (# + #W) × Price of a call option
24.4. Convertible Bonds
Slide 24.14 Convertible Bonds
Convertible bond – a bond that may be converted into a fixed
number of shares of common stock on or before the maturity date.
Thus, it is similar to a bond with warrants.
The biggest difference between warrants and convertibles is that
when warrants are exercised, investors pay additional capital into
the firm. Convertibles simply change the capital structure without
any additional capital. Convertibles are also usually callable so that
the firm can force conversion.
Terminology
Conversion ratio – number of shares per $1000 bond received if
converted
Conversion price – bond’s (or preferred’s) par value divided by
conversion ratio
Conversion premium – difference between the conversion price
and the current stock price divided by the current stock price
Straight bond value – what the bond would sell for if it did not
have a conversion feature, i.e., the discounted coupons and face
value at maturity
Conversion value – what a convertible bond would be worth if
converted now
Floor value – max(straight-bond value, conversion value)
Option value – the value of the bond over and above the floor
value. The conversion option is essentially a call option on the
company’s stock with the strike price equal to the face value of the
bond.
24.5. The Value of Convertible Bonds
Slide 24.15 The Value of Convertible Bonds
The value of a convertible bond can be decomposed into three
elements. The first is the value of a straight bond. The second is the
conversion value. If the conversion value is greater than the
straight bond, the bondholder will likely exercise the option to
convert into stock. The third component is the value of this call
option. Since the value of a call option is greater than zero before
the expiration date, the value of a convertible must be greater than
that of a straight bond and the conversion value.
Lecture Tip: Option pricing models have been successfully applied
to convertible securities. For instance, Brennan and Schwartz
[1980] present a solution involving a system of partial differential
equations solved by numerical methods on a computer. Brennan
and Schwartz’ work incorporates the impact of bankruptcy risk,
call provisions, and the relationship between stock price and
convertible bond value near expiration.
.A Straight Bond Value
.B Conversion Value
Calculated as the conversion ratio times the market price per share
of the stock to be received.
.C Option Value
Value of convertible bond = max(straight bond value, conversion
value) + option value
Slide 24.16 –
Slide 24.17 Convertible Bond Example
Slide 24.18 The Value of Convertible Bonds
24.6. Reasons for Issuing Warrants and Convertibles
Slide 24.19 Reasons for Issuing Warrants and Convertibles
The Case for and against Convertible Debt Bonds:
Table 24.2 from the text compares convertible bonds to straight
bonds and to common stock.
.A Convertible Debt versus Straight Debt
Convertible debt will pay a lower interest rate, but if the stock
price does well, equity is lost.
.B Convertible Debt versus Common Stock
Slide 24.20 Convertible Debt vs. Straight Debt
Slide 24.21 Convertible Debt vs. Straight Equity
When compared to common stock:
The firm is better off with convertible bonds if the underlying
stock subsequently does well.
The firm is worse off with convertible bonds if the underlying
stock subsequently does poorly.
We reach the exact opposite conclusions when compared to
straight bonds.
.C The “Free Lunch” Story
There is no “free lunch,” and issuing convertible bonds has no
better or worse expected outcome than issuing other securities.
.D The “Expensive Lunch” Story
.E A Reconciliation
In an efficient market, warrants and convertibles would be
correctly priced. From the perspective of the financial manager,
creating the call option with warrants and convertibles should be a
zero NPV transaction.
24.7. Why Are Warrants and Convertibles Issued?
Slide 24.22 Why Are Warrants and Convertibles Issued?
Most firms that issue convertibles are smaller, higher growth, and
highly leveraged. Some potential benefits follow:
.A Matching Cash Flows
Young, risky firms cannot afford high interest payments. If equity
rises in value and warrants or convertibles are exercised, the firm
will probably be in a better position to afford the dilution in equity.
.B Risk Synergy
When it is costly to assess the risk of the issuing firm, the straight
bond value forms a floor price.
.C Agency Costs
Warrants and convertibles are debt-equity hybrids and may reduce
the conflict between debt and equity securities.
.D Backdoor Equity
24.8. Conversion Policy
Slide 24.23 Conversion Policy
From the shareholder’s perspective, the optimal call policy is to call the bond
when its value is equal to the call price.
Curiously, however, firms generally do not force conversion with
the call provision until the conversion value is significantly above
the call price.
Slide 24.24 Quick Quiz