Chapter 24
Warrants and Convertibles
Warrants
The Difference between Warrants and Call
Options
Warrant Pricing and the Black-Scholes Model
Convertible Bonds
The Value of Convertible Bonds
Reasons for Issuing Warrants and Convertibles
Why are Warrants and Convertibles Issued
Conversion Policy
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.
•
Tend to have longer maturity periods
•
Generally issued with privately placed bonds as an
“equity kicker”.
•
Also combined with new issues of common 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
•
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
–
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.
Warrant Pricing
Stetson Inc. stock is currently selling for $15 per share.
You own warrants that give you the right to purchase
.25 shares of new common stock for $5.00 per
warrant. The price of the warrants are currently $1.00.
Dilution Example
•Imagine that Mr. X and Mr. Y 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 XY, Inc.
•Suppose that Mr. X decides to sell Ms. Z a call option issued on Mr. X’s share. The call gives Ms. Z the option to buy Mr. X’s share for $1,500.
•If this call finishes in-the-money, Ms. Z will exercise, Mr. X will tender his share.
•Nothing will change for the firm except the names of the shareholders.
Dilution Example
•
Suppose that Mr. X and Mr. Y meet as the board
of directors of XY. The board decides to sell Ms.
Z a warrant. The warrant gives Ms. Z the option to
buy one share for $1,500.
•
Suppose the warrant finishes in-the-money, (gold
increased to $350 per ounce). Ms. Z will exercise.
The firm will print up one new share.
Dilution Example
•
The balance sheet of XY Inc. would change in the
following way:
Balance Sheet Before (Book Value) 0 $3,000 $3,000 Total $3,000 Total Assets $3,000 Debt Equity (2 shares) Gold: Liabilities and Equity Assets
Dilution
•
The balance sheet of XY Inc. would change in the
following way:
Balance Sheet Before Warrant (after price change) (Market Value)
0 $3,500 $3,500 Total $3,500 Total Assets $3,500 Debt Equity (2 shares) Gold: Liabilities and Equity Assets
Dilution
•
The balance sheet of XY Inc. would change in the
following way:
Balance Sheet After Warrant (Market Value) 0 $5,000 $3,500 $1,500 Total $5,000 Total Assets $5,000 Debt Equity (3 shares) Gold: Cash: Liabilities and Equity Assets
Warrant Pricing and the Black-Scholes Model
•
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
n
n
+
Where
n
= the original number of shares
Warrant Pricing and the Black-Scholes Model
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:
(
S
-
E
)
price
exercise
price
share
−
n
debt
-value
Firm
Note that when
n
= the number of shares, share price
is:
Warrant Pricing and the Black-Scholes Model
price exercise price exercise debt -value s Firm' − + × + w w n n nNote that when n= the original number of shares and nw= the
number of warrants,
The gain from exercising a warrant can be written as:
price
exercise
exercise
warrant
after
price
share
−
Thus, the gain from exercising a warrantcan be written as: w w n n n + × + = price exercise debt -value s Firm' exercise warrant after price share
Warrant Pricing and the Black-Scholes Model
price exercise price exercise debt -value Firm − + × + w w n n n
Gain from exercising a single warrantcan be written as (from previous slide): price exercise debt -value Firm − n
The gain from exercising a callcan be written as (from previous slide):
This shows that these equations differ by a factor of
w n n
n +
So to value a warrant, multiply the value of an otherwise-identical call by w n n n + − × + Exercise price debt -value Firm n n n n w
Gain from exercising a single warrantcan be written as:
[Gain from a call option with no warrants (above)]
Pricing Warrants using the Ratio
•Stetson Inc. has assets of $100 million and debt of $25 million. They have 1.9 million shares outstanding and they will be issuing 150,000 warrants. Each warrant has the option to buy 4 shares of common for one year. The exercise price is $35. Call options on the firm’s stock are selling for $6.50. What is the value of their warrants? What is the gain from the call and warrant?
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.
The Value of Convertible Bonds
The value of a convertible bond has three
components:
1.
Straight bond value
2.
Conversion value
3.
Option value
Convertible Bonds Terms
1.
Conversion value = # shares x common price2.
Conversion ratio = # shares received for each bond3.
Conversion price = bond face value / conversion ratio = $1,000 / # shares receivedConvertible Bond Problem
•
Litespeed, Inc., just issued a zero coupon convertible
bond due in 10 years.
•
The conversion ratio is 35 shares.
•
The appropriate interest rate is 11%.
•
The current stock price is $10 per share.
•
Each convertible is trading at $390 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?
•
What is the option value of the bond?
Maturity = 10 years, conversion ratio = 35 shares, stock price = $10 per share, convertible is trading at $390, rate = 11%
The Value of Convertible Bonds
Convertible
Bond Value
Stock
Price
Straight bond
value
Conversion
Value
= conversion ratio
floor value
floor
value
Convertible bond
values
Option
value
Reasons for Issuing Warrants and Convertibles
•Start by comparing 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. But, 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.
Case for and Against Convertible Bonds (CB)
CB’s provide cheap CB’s provide
Compared to:
CB’s provide expensive financing because bonds are converted, which dilutes existing equity CB’s provide cheap financing because coupon is lower Compared to: Straight Bonds Conversion because of high stock price No conversion
because of low stock price
Convertible Bonds (CB)
If Stock Does Well (after issued) If Stock Does Poorly
(after issued)
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.
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
Why are Warrants and Convertibles Issued
•CB’s reduce agency costs, by aligning the incentives of stockholders and bondholders.
•CB’s 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.
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. • Bondholders will convert if conversion value is above call
price.
• Bondholders prefer the bonds be called if bond’s market value is below the call price.
• 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
