第二十四章认股权证和可转换债券

ExecutiveSummary,Thischapterdescribesthebasicfeaturesofwarrantsandconvertibles.Theimportantquestionsare:Howcanwarrantsandconvertiblesbevalued?Whatimpactdowarrantsandconvertibleshaveonfirmvalue?Whatarethedifferencesbetweenwarrants,convertiblesandcalloptions?Underwhatcircumstancesarewarrantsandconvertiblesconvertedintocommonstock?,ChapterOutline,24.1Warrants24.2TheDifferencebetweenWarrantsandCallOptions24.3WarrantPricingandtheBlack-ScholesModel(Advanced)24.4ConvertibleBonds24.5TheValueofConvertibleBonds24.6ReasonsforIssuingWarrantsandConvertibles24.7WhyareWarrantsandConvertiblesIssued24.8ConversionPolicy24.9SummaryandConclusions,24.1Warrants,Warrantsarecalloptionsthatgivetheholdertheright,butnottheobligation,tobuysharesofcommonstockdirectlyfromacompanyatafixedpriceforagivenperiodoftime.Warrantstendtohavelongermaturityperiodsthanexchangetradedoptions.Warrantsaregenerallyissuedwithprivatelyplacedbondsasan“equitykicker”.Warrantsarealsocombinedwithnewissuesofcommonstockandpreferredstock,giventoinvestmentbankersascompensationforunderwritingservices.Inthiscase,theyareoftenreferredtoasaGreenShoeOption.,24.1Warrants,Thesamefactorsthataffectcalloptionvalueaffectwarrantvalueinthesameways.,Stockprice+ExercisepriceInterestrate+Volatilityinthestockprice+Expirationdate+Dividends,24.2TheDifferenceBetweenWarrantsandCallOptions,Whenawarrantisexercised,afirmmustissuenewsharesofstock.Thiscanhavetheeffectofdilutingtheclaimsofexistingshareholders.,DilutionExample,ImaginethatMr.ArmstrongandMr.LeMondareshareholdersinafirmwhoseonlyassetis10ouncesofgold.Whentheyincorporated,eachmancontributed5ouncesofgold,thenvaluedat$300perounce.Theyprinteduptwostockcertificates,andnamedthefirmLegStrong,Inc.SupposethatMr.ArmstrongdecidestosellMr.MercxacalloptionissuedonMr.Armstrongsshare.ThecallgivesMr.MercxtheoptiontobuyMr.Armstongssharefor$1,500.Ifthiscallfinishesin-the-money,Mr.Mercxwillexercise,Mr.Armstrongwilltenderhisshare.Nothingwillchangeforthefirmexceptthenamesoftheshareholders.,DilutionExample,SupposethatMr.ArmstrongandMr.LeMondmeetastheboardofdirectorsofLegStrong.TheboarddecidestosellMr.Mercxawarrant.ThewarrantgivesMr.Mercxtheoptiontobuyonesharefor$1,500.Supposethewarrantfinishesin-the-money,(goldincreasedto$350perounce).Mr.Mercxwillexercise.Thefirmwillprintuponenewshare.,DilutionExample,ThebalancesheetofLegStrongInc.wouldchangeinthefollowingway:,Dilution,ThebalancesheetofLegStrongInc.wouldchangeinthefollowingway:,Dilution,ThebalancesheetofLegStrongInc.wouldchangeinthefollowingway:,NotethatMr.Armstrongsclaimfallsinvaluefrom$1,750=$3,5002to$1,666.67=$5,0003,WarrantPricingandtheBlack-ScholesModel(Advanced),Warrantsareworthabitlessthancallsduetothedilution.Tovalueawarrant,valueanotherwise-identicalcallandmultiplythecallpriceby:,Wheren=theoriginalnumberofsharesnw=thenumberofwarrants,WarrantPricingandtheBlack-ScholesModel(Advanced),Toseewhy,comparethegainsfromexercisingacallwiththegainsfromexercisingawarrant.Thegainfromexercisingacallcanbewrittenas:,Notethatwhenn=thenumberofshares,sharepriceis:,Thus,thegainfromexercisingacallcanbewrittenas:,WarrantPricingandtheBlack-ScholesModel(Advanced),Notethatwhenn=theoriginalnumberofsharesandnw=thenumberofwarrants,Thegainfromexercisingawarrantcanbewrittenas:,Thus,thegainfromexercisingawarrantcanbewrittenas:,WarrantPricingandtheBlack-ScholesModel(Advanced),Thegainfromexercisingawarrantcanbewrittenas:,Thegainfromexercisingacallcanbewrittenas:,Abitofalgebrashowsthattheseequationsdifferbyafactorof,Sotovalueawarrant,multiplythevalueofanotherwise-identicalcallby,24.4ConvertibleBonds,Aconvertiblebondissimilartoabondwithwarrants.Themostimportantdifferenceisthatabondwithwarrantscanbeseparatedintodifferentsecuritiesandaconvertiblebondcannot.Recallthattheminimum(floor)valueofconvertible:Straightor“intrinsic”bondvalueConversionvalueTheconversionoptionhasvalue.,24.5TheValueofConvertibleBonds,Thevalueofaconvertiblebondhasthreecomponents:StraightbondvalueConversionvalueOptionvalue,ConvertibleBondProblem,Litespeed,Inc.,justissuedazerocouponconvertiblebondduein10years.Theconversionratiois25shares.Theappropriateinterestrateis10%.Thecurrentstockpriceis$12pershare.Eachconvertibleistradingat$400inthemarket.Whatisthestraightbondvalue?Whatistheconversionvalue?Whatistheoptionvalueofthebond?,ConvertibleBondProblem(continued),Whatisthestraightbondvalue?Whatistheconversionvalue?25shares$12/share=$300Whatistheoptionvalueofthebond?$400385.54=$14.46,24.5TheValueofConvertibleBonds,ConvertibleBondValue,StockPrice,ConversionValue,24.6ReasonsforIssuingWarrantsandConvertibles,Areasonableplacetostartistocompareahybridlikeconvertibledebttobothstraightdebtandstraightequity.Convertibledebtcarriesalowercouponratethandoesotherwise-identicalstraightdebt.Sinceconvertibledebtisoriginallyissuedwithanout-of-the-moneycalloption,onecanarguethatconvertibledebtallowsthefirmtosellequityatahigherpricethanisavailableatthetimeofissuance.However,thesameargumentcanbeusedtosaythatitforcesthefirmtosellequityatalowerpricethanisavailableatthetimeofexercise.,ConvertibleDebtvs.StraightDebt,Convertibledebtcarriesalowercouponratethandoesotherwise-identicalstraightdebt.Ifthecompanysubsequentlydoespoorly,itwillturnoutthattheconversionoptionfinishesout-of-the-money.Butifthestockpricedoeswell,thefirmwouldhavebeenbetteroffissuingstraightdebt.Inanefficientfinancialmarket,convertiblebondswillbeneithercheaperormoreexpensivethanotherfinancialinstruments.Atthetimeofissuance,investorspaythefirmforthefairvalueoftheconversionoption.,ConvertibleDebtvs.StraightEquity,Ifthecompanysubsequentlydoespoorly,itwillturnoutthattheconversionoptionfinishesout-of-the-money,butthefirmwouldhavebeenevenbetteroffsellingequitywhenthepricewashigh.Butifthestockpricedoeswell,thefirmisbetteroffissuingconvertibledebtratherthanequityInanefficientfinancialmarket,convertiblebondswillbeneithercheaperormoreexpensivethanotherfinancialinstruments.Atthetimeofissuance,investorspaythefirmforthefairvalueoftheconversionoption,24.7WhyareWarrantsandConvertiblesIssued,Convertiblebondsreduceagencycosts,byaligningtheincentivesofstockholdersandbondholders.Convertiblebondsalsoallowyoungfirmstodelayexpensiveinterestcostsuntiltheycanaffordthem.Supportfortheseassertionsisfoundinthefactthatfirmsthatissueconvertiblebondsaredifferentfromotherfirms:Thebondratingsoffirmsusingconvertiblesarelower.Convertiblestendtobeusedbysmallerfirmswithhighgrowthratesandmorefinancialleverage.Convertiblesareusuallysubordinatedandunsecured.,24.8ConversionPolicy,Mostconvertiblebondsarealsocalla