Executive Summary

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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.

• 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. Armstrongs
  share. The call gives Mr. Mercx the option to buy
  Mr. Armstongs 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

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Dilution

• The balance sheet of LegStrong, Inc. would change
  in the following way

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Dilution

• The balance sheet of LegStrong, Inc. would change
  in the following way

Note that Mr. Armstrongs 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

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

Note that when n the number of shares, share
price is
Thus, the gain from exercising a call can be
written as
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Warrant Pricing and the Black-Scholes Model
(Advanced)

• The gain from exercising a warrant can be written
  as

Note that when n the original number of shares
and nw the number of warrants,
Thus, the gain from exercising a warrant can be
written as
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Warrant Pricing and the Black-Scholes Model
(Advanced)
The gain from exercising a call can be written as

• The gain from exercising a warrant 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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24.4 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
• Straight bond value
• Conversion value
• 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?
• 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
Conversion 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-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.

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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
• Nortels 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
• Converting the bond to common stock at the
  conversion ratios.
• Surrendering the bond and receiving the call
  price in cash.
• From the shareholders 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 shareholders claims.