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1、Executive Summary,This chapter describes the basic features of warrants and convertibles. The important questions are: How can warrants and convertibles be valued? What impact do warrants and convertibles have on firm value? What are the differences between warrants, convertibles and call options? U
2、nder what circumstances are warrants and convertibles converted into common stock?,Chapter Outline,24.1 Warrants 24.2 The Difference between Warrants and Call Options 24.3 Warrant Pricing and the Black-Scholes Model (Advanced) 24.4 Convertible Bonds 24.5 The Value of Convertible Bonds 24.6 Reasons f
3、or Issuing Warrants and Convertibles 24.7 Why are Warrants and Convertibles Issued 24.8 Conversion Policy 24.9 Summary and Conclusions,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 pric
4、e for a given period of time. Warrants tend to have longer maturity periods than exchange traded options. Warrants are generally issued with privately placed bonds as an “equity kicker”. Warrants are also combined with new issues of common stock and preferred stock, given to investment bankers as co
5、mpensation for underwriting services. In this case, they are often referred to as a Green Shoe Option.,24.1 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 + Di
6、vidends ,24.2 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.,Dilution Example,Imagine that Mr. Armstrong and Mr. LeMond are shareholders in a firm whose onl
7、y 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 LegStrong, Inc Suppose that Mr. Armstrong decides to sell Mr. Mercx a call option issued on Mr. Armstrongs share. The
8、 call gives Mr. Mercx the option to buy Mr. Armstongs share for $1,500. If this call finishes in-the-money, Mr. Mercx will exercise, Mr. Armstrong will tender his share. Nothing will change for the firm except the names of the shareholders.,Dilution Example,Suppose that Mr. Armstrong and Mr. LeMond
9、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 share for $1,500. Suppose the warrant finishes in-the-money, (gold increased to $350 per ounce). Mr. Mercx will exercise. The firm will print up one new share
10、.,Dilution Example,The balance sheet of LegStrong Inc. would change in the following way:,Dilution,The balance sheet of LegStrong Inc. would change in the following way:,Dilution,The balance sheet of LegStrong Inc. would change in the following way:,Note that Mr. Armstrongs claim falls in value from
11、 $1,750 = $3,500 2 to $1,666.67 = $5,000 3,Warrant Pricing and the Black-Scholes Model (Advanced),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:,Where n = the original number of shares nw = the numbe
12、r of warrants,Warrant Pricing and the Black-Scholes Model (Advanced),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:,Note that when n = the number of shares, share price is:,Thus, the gain from exercisi
13、ng a call can be written as:,Warrant Pricing and the Black-Scholes Model (Advanced),Note that when n = the original number of shares and nw = the number of warrants,The gain from exercising a warrant can be written as:,Thus, the gain from exercising a warrant can be written as:,Warrant Pricing and t
14、he Black-Scholes Model (Advanced),The gain from exercising a warrant can be written as:,The gain from exercising a call can be written as:,A bit of algebra shows that these equations differ by a factor of,So to value a warrant, multiply the value of an otherwise-identical call by,24.4 Convertible Bo
15、nds,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 Th
16、e conversion option has value.,24.5 The Value of Convertible Bonds,The value of a convertible bond has three components: Straight bond value Conversion value Option value,Convertible Bond Problem,Litespeed, Inc., just issued a zero coupon convertible bond due in 10 years. The conversion ratio is 25 shares. The appropriate interest rate is 10%. The current stock price is $12 per share. Each convertible is trading at $400 in the market. What is the straight bond
