24-1

Warrants and Convertibles

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.

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.

24-3

Warrants

The same factors that affect call option value affect warrant value in the same ways.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 +

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.

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.

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.

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.

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.

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.

24-7

Dilution Example

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

24-8

Dilution

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

24-9

Dilution

The balance sheet of LegStrong Inc. would change in the following way: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 $1,666.67 = $5,000 ÷ 3

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:

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

wnn

n

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:

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:

price exerciseprice share

n

debt ofnet valuesFirm'

price exercisedebt ofnet valuesFirm'

n

24-12

The gain from exercising a warrant can be written as:

The gain from exercising a warrant can be written as:

Warrant Pricing and the Black-Scholes Model (Advanced)

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:

price exerciseexerciseant after warr price share

w

w

nn

n

price exercisedebt ofnet valuesFirm'

exercisewarrant

after

price share

price exerciseprice exercisedebt ofnet valuesFirm'

w

w

nn

n

24-13

The gain from exercising a warrant can be written as:

The gain from exercising a warrant can be written as:

Warrant Pricing and the Black-Scholes Model (Advanced)

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

price exercisedebt ofnet valuesFirm'

n

price exerciseprice exercisedebt ofnet valuesFirm'

w

w

nnn

wnnn

wnnn

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.

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.

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

The value of a convertible bond has three components:1. Straight bond value

2. Conversion value

3. Option value

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?

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?

24-17

Convertible Bond Problem (continued)

What is the straight bond value?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

54.385$)10.1(

000,1$10

SBV

24-18

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.

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.

24-19

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.

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.

24-20

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

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

24-21

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.

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.

24-22

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.

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.