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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,24-,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Warrants and Convertibles,Chapter 24,Copyright 2021 by the McGraw-Hill Companies,Inc.All rights reserved.,McGraw-Hill/Irwin,Key Concepts and Skills,Understand how warrants and convertible bonds are similar to call options,Understand how warrants and convertible bonds differ from call options,Understand why corporations would issue either warrants or convertible bonds,Chapter Outline,24.1 Warrants,24.2 The Difference between Warrants and Call Options,24.3 Warrant Pricing and the Black-Scholes Model,24.4 Convertible Bonds,24.5 The Value of Convertible Bonds,24.6 Reasons for Issuing Warrants and Convertibles,24.7 Why are Warrants and Convertibles Issued?,24.8 Conversion Policy,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 price 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 and/or given to investment bankers as compensation for underwriting services.,In this case,they are often referred to as a Green Shoe Option.,Warrants,The 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,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 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 LegStrong,Inc.,Suppose that Mr.Armstrong decides to sell Mr.Mercx a call option issued on Mr.Armstrongs share.The 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 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.,Dilution Example,The balance sheet of LegStrong 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 Example,Note that Mr.Armstrongs claim falls in value from$1,750=$3,500,2 to$1,666.67=$5,000,3,Balance Sheet Before,(Market Value),0,$5,000,$3,500,$1,500,Total$3,000,Total Assets$5,000,Debt,Equity(3 shares),Gold:,Cash:,Liabilities and Equity,Assets,24.3 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:,Where,n,=the original number of shares,n,w,=the number of warrants,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:,Note that when,n,=the number of shares,share price is:,Thus,the gain from exercising a call can be written as:,Warrant Pricing and the Black-Scholes Model,Note that when,#,=the original number of shares and,#,w,=the number of warrants,The gain from exercising a warrant=,Thus,the gain from exercising a warrant can be written as:,Warrant Pricing and the Black-Scholes Model,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 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 a convertible is the maximum of:,Straight or“intrinsic bond value,Conversion value,The 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 Example,Litespeed,Inc.,just issued a zero coupon convertible bond due in 10
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