Corporate finance 7e ross ch24

Chapter Outline24.1 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 Conv

24

Warrants and Convertibles

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?

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?

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

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

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

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

In this case, they are often referred to as a Green Shoe Option.

24.1 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

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.

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.

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.

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

Debt Equity (2 shares)

Gold:

Liabilities and Equity

Assets

Debt Equity (2 shares)

Gold:

Liabilities and Equity

Assets

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)

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

Warrant Pricing and the Black-Scholes

n = the original number of shares

n w = the number of warrants

w

n n n

+

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

exercise price

n

debt of

net value

s Firm'

price

exercise

debt of

net value

s Firm' −

n

The gain from exercising a warrant can be written as:

Warrant Pricing and the Black-Scholes

exercise exercise

ant after warr

price

w

w

n n

debtof

net value

sFirm'exercise

warrant

after

price

share

price

exercise

priceexercise

debtof

net value

The gain from exercising a warrant can be written as:

Warrant Pricing and the Black-Scholes

exercise

debt of

net value

s

Firm' −

n

price

exercise

priceexercise

debtof

net value

s

+

×+

w

w n

n

n

w

n n

n

+

w

n n

n

+

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 valueConversion 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 valueConversion value

The conversion option has value.

24.5 The Value of Convertible Bonds

The value of a convertible bond has three

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?

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

54.385

$)

10.1(

000,

24.5 The Value of Convertible Bonds

= conversion ratio

floor value

floor value

Convertible bond

values

Option value

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

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

Convertible Debt vs Straight Debt

Convertible debt carries a lower coupon rate than does identical straight debt

otherwise-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 identical straight debt

otherwise-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 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

24.7 Why are Warrants and

Convertibles IssuedConvertible 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.

24.8 Conversion Policy

Most convertible bonds are also callable.

When the bond is called, bondholders have about 30 days to

choose between:

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:

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

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.

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.