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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?Chapter Outline24.1 Warrants24.2 The Difference between Warrants and Call Options24.3 Warrant Pricing and the Black-Scholes Model (Advanced)24.4 Convertible Bonds24.5 The Value of Convertible Bonds24.6 Reasons for Issuing Warrants and Convertibles24.7 Why are Warrants and Convertibles Issued24.8 Conversion Policy24.9 Summary and Conclusions24.1 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 Warrants The same factors that affect call option value affect warrant value in the same ways.1.Stock price+2.Exercise price3.Interest rate+4.Volatility in the stock price+5.Expiration date+6.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$3,000Total$3,000Total Assets$3,000Debt Equity(2 shares)Gold:Liabilities and EquityAssetsDilution The balance sheet of LegStrong Inc.would change in the following way:Balance Sheet Before(Market Value)0$3,500$3,500Total$3,500Total Assets$3,500Debt Equity(2 shares)Gold:Liabilities and EquityAssetsDilution The balance sheet of LegStrong Inc.would change in the following way:Balance Sheet After(Market Value)0$5,000$3,500$1,500Total$5,000Total Assets$5,000Debt Equity(3 shares)Gold:Cash:Liabilities and EquityAssetsNote that Mr.Armstrongs claim falls in value from$1,750=$3,500 2 to$1,666.67=$5,000 3Warrant 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:wnnnWhere n=the original number of sharesnw=the number of warrantsWarrant 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:price exerciseprice sharendebt ofnet valuesFirmNote that when n=the number of shares,share price is:price exercisedebt ofnet valuesFirmnThus,the gain from exercising a call can be written as:Warrant Pricing and the Black-Scholes Model(Advanced)price exerciseprice exercisedebt ofnet valuesFirmwwnnnNote that when n=the original number of shares and nw=the number of warrants,The gain from exercising a warrant can be written as:price exerciseexerciseant after warr price shareThus,the gain from exercising a warrant can be written as:wwnnnprice exercisedebt ofnet valuesFirmexercisewarrant afterprice shareWarrant Pricing and the Black-Scholes Model(Advanced)price exerciseprice exercisedebt ofnet valuesFirmwwnnnThe gain from exercising a warrant can be written as:price exercisedebt ofnet valuesFirmnThe gain from exercising a call can be written as:A bit of algebra shows that these equations differ by a factor ofwnnnSo to value a warrant,multiply the value of an otherwise-identical call by wnnn24.4 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 convertible:Straight or“intrinsic”bond value Conversion value The conversion option has value.24.5 The Value of Convertible BondsThe value of a convertible bond has three components:1.Straight bond value2.Conversion value3.Option valueConvertible 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 value?What is the conversion value?What is the option value of the bond?Convertible Bond Problem(continued)What is the straight bond value?What is the conversion value?25 shares$12/share=$300 What is the option value of the bond?$400 385.54=$14.4654.385$)10.1(000,1$10SBV24.5 The Value of Convertible BondsConvertible Bond ValueStock Price Straight bond valueConversion Value=conversion ratiofloor valuefloor valueConvertible bond valuesOption value24.6 Reasons for Issuing Warrants and Convertibles A reasonable place to start is to compare a hybrid like convertible debt to both straight debt and straight equity.Convertible debt carries a lower coupon rate than does otherwise-identical straight debt.Since convertible debt is originally issued with an out-of-the-money call option,one can argue that convertible debt allows the firm to sell equity at a higher price than is available at the time of issuance.However,the same argument can be used to say that it forces the firm to sell equity at a lower price than is available at the time of exercise.Convertible Debt vs.Straight Debt Convertible debt carries a lower coupon rate than does otherwise-identical straight debt.If the company subsequently does poorly,it will turn out that the conversion option finishes out-of-the-money.But if the stock price does well,the firm would have been better off issuing straight debt.In an efficient financial market,convertible bonds will be neither cheaper or more expensive than other financial instruments.At the time of issuance,investors pay the firm for the fair value of the conversion option.Convertible Debt vs.Straight Equity If the company subsequently does poorly,it will turn out that the conversion option finishes out-of-the-money,but the firm would have been even better off selling equity when the price was high.But if the stock price does well,the firm is better off issuing convertible debt rather than equity In an efficient financial market,convertible bonds will be neither cheaper or more expensive than other financial instruments.At the time of issuance,investors pay the firm for the fair value of the conversion option24.7 Why are Warrants and Convertibles Issued Convertible bonds reduce agency costs,by aligning the incentives of stockholders and bondholders.Convertible bonds also allow young firms to delay expensive interest costs until they can afford them.Support for these assertions is found in the fact that firms that issue convertible bonds are different from other firms:The bond ratings of firms using convertibles are lower.Convertibles tend to be used by smaller firms with high growth rates and more financial leverage.Convertibles are usually subordinated and unsecured.24.8 Conversion PolicyMost convertible bonds are also callable.When the bond is called,bondholders have about 30 days to choose between:1.Converting the bond to common stock at the conversion ratios.2.Surrendering the bond and receiving the call price in cash.From the shareholders perspective,the optimal call policy is to call the bond when its value is equal to the call price.In the real world,most firms wait to call until the bond value is substantially above the call price.Perhaps the firm is afraid of the risk of a sharp drop in stock prices during the 30-day window.24.9 Summary and Conclusions Convertible bonds and warrants are like call options.However,there are important differences:Warrants are issued by the firm.Warrants and convertible bonds have different effects on corporate cash flow and capital structure.Warrants and convertibles cause dilution to existing shareholders claims.
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