0. Warrants and Convertibles
CHAPTER 24
Warrants and Convertibles

1. 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?

2. 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

3. 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.
Warrants are usually protected against stock splits and dividends in the same way that exchange traded call options are.
The Green Shoe Company, a St. Louis Missouri-based manufacturer of shoes (presumably in all colors) was the first company to offer this warrant to their investment banker.

4. 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 –

5. 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.

6. 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.

7. 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.

8. Dilution Example
The balance sheet of LegStrong Inc. would change in the following way:
Balance Sheet Before
(Book Value)
$3,000
Total $3,000
Total Assets $3,000
Debt Equity
(2 shares)
Gold:
Liabilities and
Equity
Assets

9. Dilution
The balance sheet of LegStrong Inc. would change in the following way:
Balance Sheet Before
(Market Value)
$3,500
Total $3,500
Total Assets $3,500
Debt Equity
(2 shares)
Gold:
Liabilities and
Equity
Assets

10. Dilution
The balance sheet of LegStrong Inc. would change in the following way:
Balance Sheet After
(Market Value)
$5,000
$3,500
$1,500
Total $5,000
Total 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

11. 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: w n +
Where
n = the original number of shares
nw = the number of warrants

12. 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:
price
exercise
share -
Note that when n = the number of shares, share price is: n
debt of
net
value s
Firm'
Thus, the gain from exercising a call can be written as:
price
exercise
debt of
net
value s
Firm' - n

13. Warrant Pricing and the Black-Scholes Model (Advanced)
The gain from exercising a warrant can be written as:
price
exercise
ant
after warr
share -
Note that when n = the original number of shares and nw = the number of warrants, w n + = ú û ù ê ë é
price
exercise
debt of
net
value s
Firm'
warrant
after
share
Thus, the gain from exercising a warrant can be written as:
price
exercise
debt of
net
value s
Firm' - + w n

14. Warrant Pricing and the Black-Scholes Model (Advanced)
The gain from exercising a warrant can be written as:
price
exercise
debt of
net
value s
Firm' - n
price
exercise
debt of
net
value s
Firm' - + w n w n +
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 w n +

15. 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.

16. 24.5 The Value of Convertible Bonds
The value of a convertible bond has three components:
Straight bond value
Conversion value
Option value

17. 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?

18. Convertible Bond Problem (continued)
What is the straight bond value? 54 .
385 $ ) 10 1 (
000 , =
SBV
What is the conversion value?
25 shares × $12/share = $300
What is the option value of the bond?
$400 – = $14.46

19. 24.5 The Value of Convertible Bonds
Convertible Bond Value
Convertible bond values
Conversion Value
floor value
Option value
Straight bond value
= conversion ratio
Stock Price

20. 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.

21. 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.

22. 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

23. 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.

24. 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 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.

25. 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.
Many arguments, both plausible and implausible, are given for issuing convertible securities.
Convertible bonds give lends the chance to benefit from risks and reduces the conflicts between bondholders and stockholders concerning risk.