Chapter 23
Warrants
• Similar to long-term call options
• Differences:
– Issued by the corporation
– Holders can purchase new shares from the
corporation
• Number of outstanding shares of the corporation
increases when warrants are exercised
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Special types of warrants
• Usually to purchase shares of common
stock of the issuing corporation
• Sometimes for purchase of a commodity
that the issuing corporation produces
– E.g., gold, copper, oil
• Sometimes the exercise price of the warrant
increases over time
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Units
• Warrants are often issued as a package (or
unit) consisting of a
– Bond + warrant or
– Preferred Stock + warrant
• If the unit can be broken and the warrants
can be sold separately, then the warrants are
said to be detachable.
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Other warrant features
• No voting power until exercised and the common
shares are owned
• Protected against stock splits or stock dividends
(as are regular call options)
– by automatically adjusting exercise price and number of
shares that can be purchased
– Example:
• Not protected against cash dividends
– Similar treatment to regular call options
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Valuing Warrants
• Use option pricing models (e.g., Black-Scholes)
but must make adjustments
– Because of longer terms of warrants
• Interest rates are unlikely to be constant over the life of a
warrant (as assumed in basic Black-Scholes model)
• More likely dividends will be paid before warrant expires (an
adjustment to Black-Scholes is needed)
– Also exercising warrants results in more stock issued
and a dilution of the stock price
• An additional adjustment to Black Scholes is needed.
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Convertible Bonds (CB)
• Gives the investor who owns the CB the following
– a bond with regular coupon payments and face value
– plus the option to exchange the bond for a
predetermined number of the corporation’s common
stock.
• If the conversion option is exercised, no cash is
paid, the CB is surrendered to the corporation, and
the corporation gives the investor shares of stock
– New shares are issued, the outstanding stock increases
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Convertible Bonds – Definitions
• Conversion Ratio = number of shares received if
bond is surrendered
• Conversion Price = face value (or par value) of the
bond divided by the conversion ratio
– Conversion ratio and price are adjusted for stock
dividends or splits.
• Conversion Premium = difference between the
conversion price and the current stock price
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Valuing Convertible Bonds
• Consider the values of the components:
– Straight bond value = the price of an equivalent bond
that cannot be converted
• I.e., the present value of the coupons and face value
– Conversion value = the value if the bond had to be
converted immediately
• The current stock price multiplied by the conversion ratio
– Option value = the value of having the option to
convert or not convert immediately
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The Convertible Bond Value
• Is at least the value of the straight bond, or
the conversion value
– Otherwise an arbitrage opportunity exits
– Examples:
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Convertible Bond Value
= max(straight bond value, conversion value) + option value
• Diagram:
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Callable Convertible Bonds
• Almost all convertible bonds are callable
– Callable means the corporation can force CB holders to
return the bonds by paying a specified amount of
money (the call price) to them
– CB holders have time to decide to take the call price or
to convert the CB to the shares of stock
• A rational investor will choose the alternative that results in the
higher value retained
• Usually firms call the CB only when they are sure the investor
will convert – the firm effectively issues new stock and avoids
the necessity for the firm to raise new cash for financing the
call price to be paid
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Convertible Bond Strategies
• How can a firm force conversion?
• When should a firm force conversion? Why?
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Why finance with convertibles?
• Fallacious Argument
• Valid Argument
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Convertible Bond (CB) vs.
Warrant+Bond (WB) packages
• Warrants are usually detachable, conversion feature can’t
be separated from CB.
• WB packages are often issued through private placements,
CBs are usually issued through public offerings.
• Warrants may be issued by themselves (without the bond
part).
• To exercise a warrant, the investor must pay cash to the
firm to get the stock; to convert a CB, the investor just
exchanges the CB for stock – no cash is exchanged.
• Warrants are not callable, most CBs are.
• Corporate tax treatment is different for WBs vs. CBs.
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Convertible Bond Example
• Stangoby Corp has CBs outstanding with
the following features:
–
–
–
–
–
Face value (par value) of $1,000
Conversion price of $20
Callable with a 5% call premium
Maturity in 10 years
Coupon rate of 8% per year, paid semiannually
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Stangoby Corp. CBs
• Currently Stangoby Corp has straight bonds that are priced
to yield 10.25% per year (effective annual rate).
• The current stock price of Stangoby common shares is $22
per share
• What is the straight bond value of Stangoby’s CBs?
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Stangoby Corp. CBs
• What is the conversion ratio of the CBs?
• What is the current conversion value of the
CBs?
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Stangoby Corp. CBs
• Should a rational investor convert the CBs
now if Stangoby does NOT call them?
Explain.
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Stangoby Corp. CBs
• Plot the conversion value of the CBs as a
function of the stock price.
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Stangoby Corp. CBs
• If Stangoby Corp wants to call the CBs,
what is the minimum stock price that will
result in investors converting?
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Stangoby Corp. CBs
• Suppose the current stock price of Stangoby Corp.
is $400 per share. How would you evaluate
Stangoby management if they decided to NOT call
the bonds for the foreseeable future? Explain.
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