Warrants and ConvertiblesCHAPTER 2469524.1 WarrantsWarrants are securities that give holders the right, but not the obligation, to buy shares of common stock directly from a company at a fixed price for a given period. Each warrant specifies the number of shares of stock that the holder can buy, the exercise price, and the expiration date.From the preceding description of warrants, it is clear that they are similar to call options. The differences in contractual features between warrants and the call options that trade on the Chicago Board Options Exchange are small. For example, warrants have longer maturity periods.1 Some warrants are actually perpetual, meaning that they never expire.Warrants are referred to as equity kickers because they are usually issued in combination with privately placed bonds.2 In most cases, warrants are attached to the bonds when issued. The loan agreement will state whether the warrants are detachable from the bond—that is, whether they can be sold separately. Usually, the warrant can be detached immediately.For example, during a reorganization, famed banana company Chiquita Brands Inter- national issued warrants. Each warrant gave the holder the right to purchase one share of stock at an exercise price of $19.32. The warrants expire on March 19, 2009. On March 1, 2006, Chiquita Brands stock closed at $17.57, and the price of a warrant was $4.05.In February 2006, biotech giant Amgen announced the pricing on two new bond issues. The company sold $2.5 billion worth of zero coupon bonds due in 2011, with another $2.5 billion in zero coupon bonds due in 2013. What might surprise you is that the yields to maturity on the bonds when they were issued were 0.125 percent and 0.375 percent, respectively. At the same time, U.S. Treasury bonds with five years to maturity had a yield of about 4.6 percent. So how was Amgen able to issue bonds with a lower yield than U.S Treasuries?The answer is that Amgen’s bonds were convertible into shares of common stock in the company. The bonds maturing in 2011 could be converted into 12.52 shares for every $1,000 in par value, and the bonds maturing in 2013 could be converted into 12.58 shares for every $1,000 in par value. The conversion of the bonds into shares of stock is at the discretion of the bondholder. So, in essence, these convertible bonds are zero coupon bonds with an attached call option on the company stock.How do we value a financial instrument that is a combination of a bond and a call option? This chapter explores this and other issues.1Warrants are usually protected against stock splits and dividends in the same way that call options are.2Warrants are also issued with publicly distributed bonds and new issues of common stock.ros05902_ch24.indd 695ros05902_ch24.indd 6959/26/06 2:38:53 PM9/26/06 2:38:53 PM696 Part VI Options, Futures, and Corporate FinanceFigure 24.1Chiquita Warrants on March 1, 2006Value of warrantValue of a share of common stockUpper limit on warrant valueActual warrant value curveLower limit on warrant valueActual stock price = $17.57Exercise price = $19.32Price of warrant = $4.05The relationship between the value of Chiquita’s warrants and its stock price can be viewed as similar to the relationship between a call option and the stock price, described in a previous chapter. Figure 24.1 depicts the relationship for Chiquita’s warrants. The lower limit on the value of the warrants is zero if Chiquita’s stock price is below $19.32 per share. If the price of Chiquita’s stock rises above $19.32 per share, the lower limit is the stock price minus $19.32. The upper limit is the price of Chiquita’s stock. A warrant to buy one share of stock cannot sell at a price above the price of the underlying stock.The price of Chiquita’s warrants on March 1, 2006, was higher than the lower limit. The height of the warrant price above the lower limit will depend on the following:1. The variance of Chiquita’s stock returns.2. The time to expiration date.3. The risk-free rate of interest.4. The stock price of Chiquita.5. The exercise price.These are the same factors that determine the value of a call option.Warrants can also have unusual features. For example, the Montana Mills Bread Com- pany, Inc., has warrants that expire in 2007 with an exercise price of $7.58. Each warrant can be used to purchase 0.15 shares of stock in Krispy Kreme Doughnuts. To purchase one share of Krispy Kreme stock, a holder must give up 6.66 warrants and $50.48. This means the exercise price on the stock is $50.48, not the $7.58 exercise price listed on the warrant. 24.2 The Difference between Warrants and Call OptionsFrom the holder’s point of view, warrants are similar to call options on common stock. A warrant, like a call option, gives its holder the right to buy common stock at a specified price. Warrants usually have an expiration date, though in most cases they are issued with longer lives than call option。