warrants

Jacoby, Stangeland and Wajeeh, 2000

1

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

Chapter 23


2

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


3

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.


4

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


5

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.


6

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


7

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


8

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


9

The Convertible Bond Value

• Is at least the value of the straight bond, or the conversion value– Otherwise an arbitrage opportunity exits– Examples:


10

Convertible Bond Value

= max(straight bond value, conversion value) + option value

• Diagram:


11

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


12

Convertible Bond Strategies

• How can a firm force conversion?

• When should a firm force conversion? Why?


13

Why finance with convertibles?

• Fallacious Argument

• Valid Argument


14

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.


15

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


16

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?


17

Stangoby Corp. CBs

• What is the conversion ratio of the CBs?

• What is the current conversion value of the CBs?


18

Stangoby Corp. CBs

• Should a rational investor convert the CBs now if Stangoby does NOT call them? Explain.


19

Stangoby Corp. CBs

• Plot the conversion value of the CBs as a function of the stock price.


20

Stangoby Corp. CBs

• If Stangoby Corp wants to call the CBs, what is the minimum stock price that will result in investors converting?


21

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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