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Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,McGraw-Hill/Irwin,Copyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.,Click here for title,24-,0,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?,Under what circumstances are warrants and convertibles converted into common stock?,Executive SummaryThis chapter,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 for Issuing Warrants and Convertibles,24.7 Why are Warrants and Convertibles Issued,24.8 Conversion Policy,24.9 Summary and Conclusions,Chapter Outline24.1 Warrants,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,given to investment bankers as compensation for underwriting services.,In this case,they are often referred to as a,Green Shoe Option.,24.1 WarrantsWarrants are call,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+,Dividends,24.1 WarrantsThe same factors,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.,24.2 The Difference Between Wa,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 ExampleImagine that M,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 ExampleSuppose that M,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 ExampleThe balance sh,Dilution,The balance sheet of LegStrong Inc.would change in the following way:,Balance Sheet Before,(Market Value),0,$3,500,$3,500,Total$3,500,Total Assets$3,500,Debt Equity,(2 shares),Gold:,Liabilities and,Equity,Assets,DilutionThe balance sheet of L,Dilution,The balance sheet of LegStrong Inc.would change in the following way:,Balance Sheet After,(Market Value),0,$5,000,$3,500,$1,500,Total$5,000,Total Assets$5,000,Debt Equity,(3 shares),Gold:,Cash:,Liabilities and,Equity,Assets,Note that Mr.Armstrongs claim falls in value from$1,750=$3,500 2 to$1,666.67=$5,000 3,DilutionThe balance sheet of L,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,n,w,=the number of warrants,Warrant Pricing and the Black-,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 exercising a call can be written as:,Warrant Pricing and the Black-,Warrant Pricing and the Black-Scholes Model(Advanced),Note that when,n,=the original number of shares and,n,w,=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 the Black-,Warrant Pricing and the Black-Scholes Model(Advanced),The gain from exercising a warrant can be written as:,The gain from exercising a call can be writt
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