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The gain from exercising a call can be written as:
share price exercise price
Note that when n = the number of shares, share price is:
Firm' s value net of debt
nts can be separated into different securities and a conver tible bond cannot. • Recall that the minimum (floor) value of a convertible is t he maximum of:
Dilution Example
• Imagine that Mr. Armstrong and Mr. LeMond are shareholders i n 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 certifi cates and named the firm uppose that Mr. Armstrong decides to sell Mr. Mercx a call opti on issued on Mr. Armstrong’s share. The call gives Mr. Mercx the option to buy Mr. Armstong’s share for $1,500.
1. Stock price 2. Exercise price 3. Interest rate 4. Volatility in the stock price 5. Expiration date
6. Dividends
+ – + + + –
4
24-4
24.2 The Difference between Warrants a nd Call Options
n
Thus, the gain from exercising a call can be written as:
Firm' s value net of debt exercise price n
11
24-11
Warrant Pricing and the Black-Scholes Model
• In this case, they are often referred to as a Green Shoe Option.
3
24-3
Warrants
• The factors that affect call option value affect warrant value in the same ways.
• Suppose the warrant finishes in-the-money, (gold increased to $350 per ounce). Mr. Mercx will ex ercise. The firm will print up one new share.
7
24-7
Dilution Example
Firm' s value net of debt exercise price#w exercise price ##w
A bit of algebra shows that these equatio#ns
differ by a factor of
##w
So to value a warrant, multiply the value of
$3,000 Total
0 $3,000
8
$3,000
24-8
Dilution Example
Assets
Balance Sheet Before (Market Value) Liabilities and Equity
Gold: Cash:
Total Assets
$3,500 Debt
$1,500 Equity (3 shares)
• If this call finishes in-the-money, Mr. Mercx will exercise, Mr. Ar mstrong will tender his share.
• Nothing will change for the firm except the names of the shareh
olders.
6
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 sh are for $1,500.
Chapter 24
Warrants and Convertibles
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
• Understand how warrants and convertible bonds are similar to call options • Understand how warrants and convertible bonds differ from call options • Understand why corporations would issue either warrants or convertible bonds
2
24-2
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 are worth a bit less than calls due to the dilution.
• To value a warrant, value an otherwise-iden tical call and multiply the call price by:
The gain from exercising a warrant =
share price after warr ant exercise exercise price
Note that when # = the original number of shares and #w = the number of warrants,
share price
after
warrant exercise
Firm'
s
value
net
of
debt exercise ##w
price #w
Thus, the gain from exercising a warrant can be written as:
12
Firm' s value net of debt exercise price#w exercise price
• Warrants tend to have longer maturity periods than exchange t raded options.
• Warrants are generally issued with privately placed bonds as an “equity kicker.”
n
Where
n nw
n = the original number of shares
nw = the number of warrants
10
24-10
Warrant Pricing and the Black-Scholes Model
To see why, compare the gains from exercising a call wit h the gains from exercising a warrant.
• Warrants are also combined with new issues of common stock and preferred stock and/or given to investment bankers as co mpensation for underwriting services.
an otherwise-identical call by
#
13
##w
24-13
24.4 Convertible Bonds
• A convertible bond is similar to a bond with warrants. • The most important difference is that a bond with warra
1
24-1
Chapter Outline
24.1 Warrants 24.2 The Difference between Warrants and Call Options 24.3 Warrant Pricing and the Black-Scholes Model 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
$5,000 Total
0 $5,000
$3,000
Note that Mr. Armstrong’s claim falls in value from $1,750 = $3,500 ÷ 2 to $1,666.67 = $5,000 ÷ 3
9
24-9
24.3 Warrant Pricing and the Black-Scho les Model
• The balance sheet of LegStrong Inc. would change in the following way:
Gold:
Assets
Total Assets
Balance Sheet Before (Book Value) Liabilities and Equity $3,000 Debt Equity (2 shares)
##w
24-12
Warrant Pricing and the Black-Scholes Model
The gain from exercising a call can be written as:
Firm' s value net of debt exercise price #
The gain from exercising a warrant can be written as:
• When a warrant is exercised, a firm must is sue new shares of stock.
• This can have the effect of diluting the clai
ms of existing shareholders.
5
24-5
share price exercise price
Note that when n = the number of shares, share price is:
Firm' s value net of debt
nts can be separated into different securities and a conver tible bond cannot. • Recall that the minimum (floor) value of a convertible is t he maximum of:
Dilution Example
• Imagine that Mr. Armstrong and Mr. LeMond are shareholders i n 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 certifi cates and named the firm uppose that Mr. Armstrong decides to sell Mr. Mercx a call opti on issued on Mr. Armstrong’s share. The call gives Mr. Mercx the option to buy Mr. Armstong’s share for $1,500.
1. Stock price 2. Exercise price 3. Interest rate 4. Volatility in the stock price 5. Expiration date
6. Dividends
+ – + + + –
4
24-4
24.2 The Difference between Warrants a nd Call Options
n
Thus, the gain from exercising a call can be written as:
Firm' s value net of debt exercise price n
11
24-11
Warrant Pricing and the Black-Scholes Model
• In this case, they are often referred to as a Green Shoe Option.
3
24-3
Warrants
• The factors that affect call option value affect warrant value in the same ways.
• Suppose the warrant finishes in-the-money, (gold increased to $350 per ounce). Mr. Mercx will ex ercise. The firm will print up one new share.
7
24-7
Dilution Example
Firm' s value net of debt exercise price#w exercise price ##w
A bit of algebra shows that these equatio#ns
differ by a factor of
##w
So to value a warrant, multiply the value of
$3,000 Total
0 $3,000
8
$3,000
24-8
Dilution Example
Assets
Balance Sheet Before (Market Value) Liabilities and Equity
Gold: Cash:
Total Assets
$3,500 Debt
$1,500 Equity (3 shares)
• If this call finishes in-the-money, Mr. Mercx will exercise, Mr. Ar mstrong will tender his share.
• Nothing will change for the firm except the names of the shareh
olders.
6
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 sh are for $1,500.
Chapter 24
Warrants and Convertibles
McGraw-Hill/Irwin
Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills
• Understand how warrants and convertible bonds are similar to call options • Understand how warrants and convertible bonds differ from call options • Understand why corporations would issue either warrants or convertible bonds
2
24-2
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 are worth a bit less than calls due to the dilution.
• To value a warrant, value an otherwise-iden tical call and multiply the call price by:
The gain from exercising a warrant =
share price after warr ant exercise exercise price
Note that when # = the original number of shares and #w = the number of warrants,
share price
after
warrant exercise
Firm'
s
value
net
of
debt exercise ##w
price #w
Thus, the gain from exercising a warrant can be written as:
12
Firm' s value net of debt exercise price#w exercise price
• Warrants tend to have longer maturity periods than exchange t raded options.
• Warrants are generally issued with privately placed bonds as an “equity kicker.”
n
Where
n nw
n = the original number of shares
nw = the number of warrants
10
24-10
Warrant Pricing and the Black-Scholes Model
To see why, compare the gains from exercising a call wit h the gains from exercising a warrant.
• Warrants are also combined with new issues of common stock and preferred stock and/or given to investment bankers as co mpensation for underwriting services.
an otherwise-identical call by
#
13
##w
24-13
24.4 Convertible Bonds
• A convertible bond is similar to a bond with warrants. • The most important difference is that a bond with warra
1
24-1
Chapter Outline
24.1 Warrants 24.2 The Difference between Warrants and Call Options 24.3 Warrant Pricing and the Black-Scholes Model 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
$5,000 Total
0 $5,000
$3,000
Note that Mr. Armstrong’s claim falls in value from $1,750 = $3,500 ÷ 2 to $1,666.67 = $5,000 ÷ 3
9
24-9
24.3 Warrant Pricing and the Black-Scho les Model
• The balance sheet of LegStrong Inc. would change in the following way:
Gold:
Assets
Total Assets
Balance Sheet Before (Book Value) Liabilities and Equity $3,000 Debt Equity (2 shares)
##w
24-12
Warrant Pricing and the Black-Scholes Model
The gain from exercising a call can be written as:
Firm' s value net of debt exercise price #
The gain from exercising a warrant can be written as:
• When a warrant is exercised, a firm must is sue new shares of stock.
• This can have the effect of diluting the clai
ms of existing shareholders.
5
24-5