collectthewholesurplusfrombargainingandshareholdersrealizetheiroutside - PDF document

collectthewholesurplusfrombargainingandshareholdersrealizetheiroutsideoption,whichisequaltozero.Sincethisequalstheirpayofrombankruptcy,theoptiontorenegotiateisworthexactlythevalueoftheoptiontogobankrupt.Asaconsequence,themagnitudesofthewealthtransferwithandwithouttheoptiontorenegotiatearethesameandsoaretheexpansionpolicies.Asitisknownfromtheliterature,thepresenceoftheoptiontorenegotiatedependsonthestructureofdebt.Inparticular,renegotiationisexpectedtobefeasibleifthenumberofthe“rmscreditorsislow(seeBoltonandScharfstein(1996),andHegeandMella-Barral(2005)).Thelimitingcaseofasingleissueofprivatedebt(abankloan)isassociatedwiththeleastcostlyrenegotiation.Ontheoppositesideofthespectrumliesdiuselyheldpublicdebt,whichcanmakerenegotiationprohibitivelyexpensive(Hackbarth,Hennessy,andLeland(2007)).Thisisduetotheco-ordinationamongthecreditorsbeinghardlyfeasibleasaresultofafree-riderproblemand,possibly,ofdierentseniorityclasses(HegeandMella-Barral(2005)).Suchaviewissupportedbytheexistingempiricalevidence.Theratioofpublictoprivatedebtandthenumberofbondissuesareshowntoreducetheprobabilityofsuccessfulout-of-courtdebtrestructuring(AsquithandScharfstein(1994))andtobenegativelycorrelatedwiththedeviationsfromtheabsolutepriorityrule(APR)(FranksandTorous(1994)).Theoutcomeofrenegotiationisdeterminedbythedistributionofbargainingpowerbetweenthe“rmsownersanditscreditors.Usually,thebargainingpowerofthe“rmvis-`a-visitsbankwouldbelimitedwhenthe“rmisrelativelyyoungandsmallandwhenitusesaportfolioofthebanksservices.Consequently,theshareoftherenegotiationsurplusreceivedbythebankissubstantial.Theoppositeholdsforlargecorporations,especiallythosewithlegaldepartmentsspecializedindebtrestructuring.Higherbargainingpoweroftheshareholdersisalsoexpectedifthemanagementownsalargefractionofthe“rmsequity.Insuchasituation,thealignmentofmanagerialinterestswithshareholdersobjectivesishigherandsoistheeortexertedintherenegotiationprocess(DavydenkoandStrebulaev(2007)).Finally,whencorporatedebtisheldbymultiplecreditors,theirbargainingpowermayberelativelysmall,again,duetoarisingcoordinationproblems(seeHegeandMella-Barral(2005)).Subsequently,Ianalyzetheeectofthe“rmsgrowthoptiononitsoptimaldebtrestructuringpolicy.I“ndthatthepresenceofapositiveNPVproject,incombinationwithhighdebtorsbargainingpower,islikelytoresultinanearliertimingofdebtrenegotiation.Finally,Ishowthatthepossibilityofrenegotiatingthedebtcontractcanreduce debtrestructuringtobeabinaryvariableanddonotlimititsduration(seeHackbarthetal.(2002)andFran¸coisandMorellec(2004)fortherelevantextensions).Theremainderofthepaperisorganizedasfollows.InSection2themodelofthe“rmisdescribed.NumericalresultsandcomparativestaticsarepresentedinSection3.ThesummaryandconclusionsareprovidedinSection4.ProofsofpropositionsarerelegatedtotheAppendix.2ModelofaLeveredFirmAsastartingpoint,Iprovidebasiccharacteristicsofthe“rmandofthestochasticenvironmentinwhichitoperates.Subsequently,Idevelopadynamicvaluationmodelofthe“rmfollowingtheexerciseofthegrowthoption.Usingthismodel,Icalculatethevaluesoftheclaimswrittenonthe“rmscash”owsandderivetheoptimaldebtrestructuringandliquidationpolicies.Theseareusedtoderiveresultsconcerningtheexpansionpolicyofthe“rm.Considera“rmthatisrunbyadeep-pocketowner-manager(equityholders)max-imizingthevalueofequity.The“rmgeneratesinstantaneouscash”ow.The“rmhasanoptiontoexpandbyincurringsunkcost.Afterspending,the“rmisentitledtocash”ow,with1.Letindicatorbeequalto0ifthegrowthoptionhasnotyetbeenexercised,andto1intheoppositecase.Theliquidationvalueofthe“rmisequaltoAllpartiesinthemodelareassumedtoberisk-neutralandistheinstantaneousrisklessinterestrate.Theimpactofeconomicuncertaintyonthe“rmscash”owiscapturedbylettingfollowageometricBrownianmotion debt“nancingontheexercisepolicyofagrowthoption.However,neitherofthepapersallowsforthe“rmtobeactivepriortotheoptionexercise.Asaconsequence,thereisnoinitialdebtoutstandingandthedebtoverhangproblem,whichisthefocusofthecurrentpaper,doesnotexist.AfarfromcompletelistofreferencesincludesVercammen(2000),analyzinghowbankruptcy,triggeredbytheassetsvaluefallingbelowthefacevalueofthedebt,in”uencesinvestment,LelandandToft(1996),consideringa“nitematuritydebtwithastationarystructure,AndersonandSundaresan(1996),Mella-Barral(1999),Acharyaetal.(2006),andHackbarthetal.(2002,2007),analyzingtheimpactofdebtrenegotiability.ArelatedworkpresentedbyFischeretal.(1989),MauerandTriantis(1994),andDanglandZechner(2004),focusesontheoptimalrecapitalizationpolicy.Alternatively,onecouldimposeanassumptionthatthepayoutfromtheprojectisspannedbyaportfoliooftradedassets. Thedivergencebetweenthevalueofthe“rmmanagedbyshareholdersanditsvalueinthehandsofcreditorsimpliesthatthereisscopefordebtrenegotiation.Rene-gotiationallowsforavoidingthefollowingthreecomponentsofthecostof“nancialdistress.First,theinvestmentopportunityispreservedunderrenegotiationbutnotuponbankruptcy.Second,theineciencyresultingfromcreditorsmanagingthe“rm(andgeneratingreducedcash”ow)isavoided.Finally,thetaxshieldondebtisnotirreversiblylostbutonlytemporarilysuspended.TherenegotiationprocessisformalizedasNashbargaininginwhichbargainingpowerissplitbetweenthetwogroupsofthe“rmsstakeholders(FanandSundaresan(2000),Christensenetal.(2002)).Thedistributionofbargainingpoweriscapturedbyy,1].Ahigh(low)valueofisassociatedwithhighbargainingpowerofequityholders(creditors).Highbargainingpowerofequityholdersisexpectedforlargecorporations,whicharelikelytobeaggressiveinnegotiationsandhavespecializedlegaldepartments.Incontrast,smallandyoung“rmsthatuseaportfolioofthebanksservicesarelikelytohaveamuchweakerbargainingposition.Inaddition,DavydenkoandStrebulaev(2007)arguethattheequityholdersincentivestoexerteortinrenegotiationincreasewithinsiderownership.TheirnotionissupportedbytheempiricalobservationthatdeviationsfromtheAPRinChapter11aresigni“cantlyhigherwhenmanagershaveanequitystakeinthe“rm(Betker(1995),LoPuckiandWhitford(1990)).Finally,shareholdersareexpectedtobemoretoughifinstitutionalshareholdingsarerelativelyhigh.Thisisduetothefactthatcoordinatedandmoresophisticatedinvestorscanbargainmoreeectively.Take-itorleave-itoersmadebyshareholdersorbycreditors,asinMella-BarralandPerraudin(1997),arelimitingcasesoftheNashbargainingsolution.Theycorrespondtosituationswhere=1and=0,respectively.Asdebtrenegotiationhasaformofastrategicdebtservice,itisassociatedwithalowerthancontractualcouponpayment.IfollowMella-BarralandPerraudin(1997)andFanandSundaresan(2000)inassumingthatthecouponisafunctionofthecurrentcash”ow.Moreover,IimposetheassumptionmadebyFanandSundaresan(2000)thatduringtherenegotiationprocessthetaxshieldistemporarilysuspended.Assoon tore”ectthecoordinationproblemsamongcreditors),withaspecialcasemeaningthatthegrowthoptionexpiresunexercised,()debtholderswillrunthe“rmlesseciently,sothatthecash”owgeneratedbythe“rmintheirhandsequalswhere1).Thisapproachallowsforavoidingpath-dependencyleadingtoanalyticalintractability.HegeandMella-Barral(2000)makeanalternativeassumptionthataonce-reducedcouponcannotbeincreased. outsideoptionequalsthevalueofthe“rm(=1),shareholdersreceivenothing.Theassociatedstreamofcouponpaymentsisexactlyequaltofraction(1ofthenetcash”owintherenegotiationregionoroutsidethatregion: r li , )xx bx�x The“rstregimeofthestrategicdebtservicecorrespondstotheearningslevelremainingbetweenthe“rmsoptimalliquidationtrigger, ,andcreditorsliquidationtrigger, .Inthiscase,creditorsreceiveaweightedaverageofcash”owfromholdingthe,andfromoperatingthe“rmeciently,).Thesestreamsareweightedwithshareholdersbargainingpowercoecient,.Fortheearningslevelabove ,butstillintherenegotiationregion,creditorsreceiveaweightedaverageofcash”owfromoperatingthecompanyontheirown,),andfromservingasfullyecientmanagers,).Outsidetherenegotiationregion,thecontractualcoupon,,ispaid.Notethatfor=0and,thecouponschedulecorrespondstotheoutcomeofthetake-itorleave-itoersinMella-BarralandPerraudin(1997),whereassettingtozeroreducesthesolutiontothepaymentschemeofFanandSundaresan(2000).Furthermore,thepresenceofthegrowthopportunitydoesnotchangethecoupon”owtothecreditorswithinanyofthethreeregimes.Thisresultsfromthefactthattheinvestmentopportunity,whichconstitutesapartofthe“rmsvalue,isnotassociatedwithanypaymentstream.Todierentiatebetweentheclaimsvaluesandpolicytriggersintheabsenceandinthepresenceofrenegotiation,Iintroduceindicatorthatassumesthevalueof1ifrenegotiationoccursupondefaultand0otherwise.Fornotationalconvenience,Iassumethat0implies=1(whenrenegotiationisnotallowedfor,thedistributionofbargainingpowerisirrelevantanyway).Byobservingthatequityholdersmaximizethevalueoftheirclaimwhenselectingthedebtrestructuringpolicyandthattheliquidationpolicymaximizesthe(remain-ing)valueofthe“rmandbysolvingthesystemofcorrespondingvalue-matchingandsmooth-pastingconditions,onecanformulatethefollowingproposition. Attheoptimalequityholdersrenegotiationtrigger,thevalueofallclaimsremaindierentiable.Fortheequityitistheresultofthesmooth-pastingconditionthatguaranteesoptimalityofthetrigger. .Followingdebtrestructuring,thevaluesofequityanddebtareequaltothecorrespondingfractionsofthe“rmvalueobtainedaccordingtotheAPRincaseofbankruptcyupondefaultandtotheoptimalsharingrule(2)whenrenegotiationisallowedfor.Thevalueofdebtcanbesimplycalculatedasthedierencebetweenthevalueofthe“rmandofitsequity.Thevalueoftaxshieldisaproductofitspresentvalueifoperatedperpetually,b/r,andtheprobabilityweighteddiscountedtimeofitsoperation(thevalueofwhichdependsonthetypeofdebtrestructuringupondefault).Finally,thevalueofthe“rmwhenmanagedbycreditors,),isequivalenttowithbankruptcyhavingalreadyoccurred.From(4)itfollowsthattaxesin”uencethedebtrestructuringtriggeronlywhenrenegotiationisallowedforandshareholdershaveatleastsomebargainingpower(i.e.,when0).Shareholderspreferanearlierdebtrestructuringwhenthetaxrateincreasessincetheyobtainafractionofthepresentvalueofthe“rmstaxWhencreditorshavetheentirebargainingpower,optimalrenegotiationthresholdequalsthebankruptcytrigger.Ingeneral,theoptimalrenegotiationtrig-gerdoesnotdependonliquidationvalue.Thisresultsfromthefactthatthechangeoftheinstantaneouspayowhentherenegotiationcommencesisnotin”uencedbytheEquation(5)impliesthat,intheabsenceoftaxes,theoptimalliquidationtrigger, ,reducestotheexitthresholdofanotherwiseidenticalall-equity“nanced“rm.For islowerthantheall-equitythresholdasthestrictlypositivepresentvalueoftaxshieldincreasestheopportunitycostofliquidation.Consequently,inthepresenceoftaxestheliquidationoptionisexercisedlaterwhenthe“rmispartially“nancedwithdebtandrenegotiationispossible.Intheabsenceofrenegotiation,the“rmisliquidatedbycreditorsatahigherlevelof(cf.(5)with=0).Havingderivedthevaluesofdebtandequityafterinvestment,Iamabletode-terminetheoptimalpoliciesandcalculatetheclaimsvaluesbeforetheexpansionis InFanandSundaresan(2000),theunderlyingvariableistheafter-taxvalue(seealsoLeland(1994)).Consequently,theoptimalrenegotiationtriggerintheirpaperdecreaseswithtaxessinceonlytheeectoftheincreasingtaxshieldistakenintoaccount.washighenoughsothat,thentherenegotiationtriggerwoulddependonHowever,thisisruledoutbyassumption.ThisresultalsoisduetothespecialstructureofoptimalstoppingproblemsthatalsounderliesthemainconclusionsofLeahy(1993)andBaldurssonandKaratzas(1997),accordingtowhichaninvestor,whomusttakeintoaccountsubsequentinvestmentsofthecompetitors,employsthesameinvestmentpolicyasamonopolistwhoisnotthreatenedbysuchfutureevents. debt(netofthetaxshield)andaugmentedbytheoptionstoexpandandtorenegotiatethedebtcontract.Intherenegotiationregion,thevalueofequityequals,again,thefractionofthe“rmvaluederivedaccordingtothesharingrule(2).Thevalueofdebtequalsthedierencebetweenthetotalvalueofthe“rmandthevalueofequity.FromProposition2itfollowsthatinvestment,debtrestructuringandliquidationtriggersareaectedbythethegrowthandbankruptcyoptionsbeinginterrelated.The“rstcomponentoftheexpansiontrigger(6)issimplyequaltotheoptimalinvestmentthresholdofanall-equity“rm(withnooptiontoexit).Thesecondcomponentre”ectsthechangeinthevalueofthedebtrestructuringoptionupontheexpansion( x2ŠB0 ).Aslongasisdierentfrom,thelattercomponentisdierentfromzeroandtheexpansionpolicyofadebt“nancedcompanydiersfromthepolicyofanotherwiseidenticalall-equity“nanced“rm.Theoptimaldebtrestructuringtriggerofthe“rmisgivenby(7).Its“rstcompo-nentequalsthedefaulttriggerofanotherwiseidentical“rmbutwithoutthegrowthoption(cf.(4)).Itssecondcomponentre”ectstheimpactofthegrowthoptiononthetimingofdebtrestructuring.Asimilardecompositioncanbemadefortheliquidationtrigger(8).Inthiscase,theintuitionisverysimple:theopportunitycostofliquidationishigherwhenthegrowthoptionispresent.Proposition3RiskydebtÞnancingleadstounderinvestmentinthesenseoftheshareholdersexhibitingexcessivewaiting.Proposition3isadirectimplicationofthedebtrestructuringoptionbeingworthlessafterthegrowthoptionisexercisedthanbeforethe“rmsexpansion.Inotherwords,equityholdersnotonlyincurthecostofexpansionbutalsofaceareductionofthevalueoftheirdebtrestructuringoption(cf.Myers(1977)).Themechanismofthereductionintheoptionvaluetorestructuredebtcanbeexplainedusingthefollowingoptionsanalogy.Priortoinvestment,thedebtrestructuringoptionisequivalent(ignoringtheinteractionbetweenoptions)toaputonthepresentvalueofperpetualcash”owthefraction(1)thereofwhenrenegotiationispossible)withastrikepriceequalto.Afterinvestment,thestrikeremainsthesamebuttheputiswrittenonthepresentvalueof(oritscorrespondingfraction)receivedinperpetuity.Obviously,thevalueofthelatterputoptionislower. Infact,thetwooptionsdieronlywithrespecttotheinitialpriceoftheunderlyingandthelatteroptionismoreout-of-the-money.Theratiooftheoptionvalues(ignoringtheinteractionoftheformerwiththegrowthoption)isthereforeequaltothediscountedprobabilityofcash”owfallingfrom only1.4).Now,thefollowingpropositioncanbeformulated.Proposition4StrategicdebtrestructuringunderÞnancialdistressexacerbatestheunderinvestmentprobleminthesenseoftheexpansionoptionbeingexercisedlaterthaninthepresenceofbankruptcyoccurringupondefault.Inasituationwhereshareholderscanrenegotiatethedebtcontract,underinvestmentismoreseverethanuponbankruptcyoccurringupondefault.Thisisaresultofthefactthattheoptiontostrategicallyrenegotiatedebtgenerallyhasahighervaluethanananalogousoptiontogobankrupt.Sincethevalueoftheoptiontorestructuredebt(i.e.,eithertorenegotiateortogobankrupt)decreasesuponthe“rmsexpansion,andtheproportionalreductionissimilaracrossthetwotypesofoptions(andisoftheorderof),theabsolutereductioninthevalueoftherenegotiationoptionmustbehigherthanintheoptionvaluetogobankrupt(infact,thisdierenceisoftheorderof(1)oftheinitialvalueofthebankruptcyoption).Tosummarize,thehighermagnitudeofunderinvestmentwithrenegotiabledebtisdrivenbyagreaterabsolutelossintheoptionvaluetorestructuredebtoccurringuponthe“rmsexpansion.ImpactofGrowthOpportunitiesonLiquidationandStrategicDefaultThegrowthoptionaects,throughitsimpactonthevalueofequityandthe“rmasawhole,theoptimalliquidationanddebtrestructuringpolicies.Asfarasitsimpactonthetimingofliquidationisconcerned,itholdsthat l0 x l1 ,(9)withtheequalityholdingfor=0(thegrowthoptionislostuponbankruptcysoitdoesnotaecttheliquidationpolicyevenwithnoexpansionhavingbeenmade).For=1,thepresenceofthegrowthoptionraisestheopportunitycostofliquidatingthe“rm.Asaconsequence,the“rmisliquidatedoptimallyatacash”owlevellowerthan Therelationshipbetween andthedebtrestructuringtriggerofanotherwiseidentical“rmbutwithoutthegrowthoption, ,is,ingeneral,ambiguous.Beforeexpansion,thevalueofequitycontainsanadditionalcomponentre”ectingthevalueofthegrowthoption.Otherthingsbeingequal,thismakesdebtrestructuringless 3NumericalResultsThissectionpresentsnumericalresultsandcomparativestaticsconcerningthe“rmsoptimalpolicies,thevaluesofitsclaims,agencycosts,capitalstructuredecisionsandthe“rst-passagetimeprobabilities.Thesetofinputparametersusedisasfollows:risk-freerate=5%,returnshortfall=4%,volatilityofearnings=20%,taxrate=35%,instantaneouscoupon5,eciencyofcreditorsastheusersofthe“rmsassets=50%,shareholdersbargainingpowerparameter5,liquidationvaluebeforeexpansion=1,liquidationvalueafterexpansion=2,investmentcost=10,expansionscaleparameter=2.Unlessstatedotherwise,thoseparametervalueswillbeusedinallnumericalexamples.OptimalPoliciesThemajor“ndingconcerningtheimpactoftherenegotiabilityofdebtontheexpansionpolicyisthattheoptiontorestructuredebtexacerbatesMyers(1977)underinvestmentproblem.Alargermagnitudeofunderinvestmentmeansinourcontextthatthegrowthoptionisexercisedlaterthanintheabsenceoftheoptiontorenegotiatethedebtcontract(seeFigure2,PanelsA…D).Thisisduetothefactthat,uponundertakingtheexpansionproject,shareholdersofthe“rmnotonlyincurtheinvestmentcostbuttheyalsoreducethevalueoftheoptiontorenegotiatedebt.[PleaseinsertFigure2abouthere.]Recallthatthisadditionaldelayinexercisingthegrowthoptionresultsfromthefactthatthereductioninthevalueoftheoptiontorenegotiateexceedsthecorrespondingreductioninthevalueofthebankruptcyoption.Thecomparativestaticsfortheoptimalinvestment,debtrestructuring,andliqui-dationpoliciesaredepictedinTable1.Someoftheresultsareconsistentwiththoseknownfromtherealoptionsliterature(DixitandPindyck(1994),Ch.6),structuralvaluationofcorporatedebtpricing(Leland(1994,1998),Mella-BarralandPerraudin(1997),FanandSundaresan(2000)),andoninvestmentunderdebt“nancing(MauerandOtt(2000),TitmanandTsyplakov(2003),andMoyen(2007)).Therefore,intheremainderofthesection,Ifocusonthoseresultsthatarenoveltothispaper.[PleaseinsertTable1abouthere.] negativelyin”uencestheequityholderswillingnesstoengageindebtrenegotia-tion.However,ifshareholdersexpecttoextractahighfractionofthebargainingproceeds(high),theycommencerenegotiationearliersincethegrowthoptionenhancesthevalueofthe“rmasthebargainingobject.Recallthatunderall-equity“nancingtheinvestmentthresholdisincreasingwithrisk-lessrate(DixitandPindyck(1994),Ch.6).Debt“nancingintroducesanothereect,whichworksintheoppositedirection:givencoupon,ahigherisassociatedwithalowerdebtvalue,andthuswithalowermagnitudeofunderinvestment.Thelattereectcanbeadominantoneifbothcash”owuncertaintyandinterestratearelow(Figure2,PanelD).ValuationofSecuritiesAslongasshareholdersbargainingpowerparameterisstrictlypositive,theoptiontorenegotiateenhancesthevalueofequity.Thisisduetothefactthatshareholderscandointheprocessofrenegotiationatleastaswellasinthecaseofbankruptcyoccurringupon“nancialdistress.Equityholdersoptiontorenegotiatemayadverselyaectthevalueofdebt.Thisoc-curswhentherenegotiationtriggerisconsiderablyhigherthanthebankruptcythresh-oldofanotherwiseidentical“rmbut“nancedwithnon-renegotiabledebtandthe“nancialpositionofthe“rm(measuredby)issound.Ontheotherhand,forcloseenoughtothebankruptcytrigger,allowingforrenegotiationincreasesthevalueofdebtsincecreditorsshareofthe“rmreceiveduponrenegotiationisworthmorethantheirclaimuponbankruptcy.Table2depictsthedirectionoftheeectsofmodelparametersonthevaluationofequity,debtandthe“rmasawhole.[PleaseinsertTable2abouthere.])Theinteractionbetweentheoptionstoinvestandtorenegotiatecanin”uencethevalueofdebtinbothdirections.Iftheequityholdersbargainingpowerissohighthatrenegotiationcommencesearlierwhenthegrowthoptionispresent(seeProposition5),thenthegrowthoptioncanreducethevalueofdebt.Nevertheless,formostparametercon“gurations,thevalueofdebtisaugmentedbythepresenceofthegrowthoption,duetoalowerprobabilityofstrategicdefault. proportionofdebt.Moreover,changesincouponratehaveasimilar“rst-ordereectontheagencycostofbothrenegotiableandnon-renegotiabledebt.Shareholdersbargainingpowercoecientin”uencestheagencycostofrenego-tiabledebtthroughitspositiveimpactontherenegotiationtrigger.Consequently,theagencycostofdebtduetounderinvestmentincreasessinceequityholdersbecomemorereluctanttoforegoafractionofthe(higher)optionvaluetorenegotiate.Withnon-renegotiabledebt,thebargainingpowercoecientdoesnotplayanyrolesinceitdoesnotaecttheoptimalinvestmenttrigger.Creditorsabilitytomanagethe“rmsassets,,reducestheagencycostofbothkindsofdebt.Fornon-renegotiabledebt,higherreducesthepresentvalueofinef-“cienciesarisingwhenthe“rmbecomesmanagedbythecreditors.Forrenegotiabledebt,inaddition,anincreaseinnegativelyin”uencestheprobabilityofstrategicdefault.Therefore,thereductionintheagencycostswhichresultsfromhighergreaterforrenegotiabledebt.Themoneynessofgrowthoptions,measuredbybothandtheinverseof,exac-erbatestheagencycostofdebt.Thisisduetolargerdierencesinthepresentvaluesofcash”owsbeforeandafterinvestmentunder“rst-andsecond-bestpolicies.Thiseectisstrongerforrenegotiabledebtsince()thegrowthoptioncontainsnotonlytherighttoacquirehighercash”owsbutalsoarighttoreducethepossibilityofdebtrestructuring,and()forstrategicdefault,thelatterpossibilityhasamuchhighervalue.Iuseourbasicsetofparametervaluestoillustratethepotentialmagnitudeoftheagencycostofdebtthatcanbeattributedtounderinvestment.Ishowthattherene-gotiabilityofthedebtcontractcansubstantiallyincreasethiscost.Figure3illustratestheagencycostofrenegotiableandnon-renegotiabledebtasafunctionofthecash”owvariable01(PanelA)and06(PanelB).[PleaseinsertFigure3abouthere.]Theagencycostofdebtinducedbytheunderinvestmentproblemhighlydepend Inaddition,theagencycostofdebtdecreaseswithcash”owvolatilityasaresultoftheinvestmentthresholdbeinghigher(whichisassociatedwithalowerdiscountedprobabilityofinvestment)forbothkindsofdebt.Furthermore,theagencycostofdebtduetounderinvestmentispositivelyrelatedtothereturnshortfall,,andnegativelyrelatedtotherisklessrate,.Thisisduetothefactthattheprobabilityofdebtrestructuringincreaseswith(decreaseswith)sotimelyinvestmentbecomesmore(less)importantforreducingtheexpectedcostofdefault.Thepresenceoftherenegotiationoptiongenerallyincreasesthesensitivityoftheagencycoststothechangesofthethreeparameters. Barclayetal.(2006))islowerthanthedebtcapacityofassetsinplace.Consequently,marketleverageofthe“rmwiththegrowthoptionislowerthantheoptimalleverageofitscounterpartwiththeassets-in-placeonly.Introducingtheoptiontorenegotiatethedebtcontractampli“esthenegativeimpactofthegrowthoptionontheoptimalleveragelevel(seeTable4).[PleaseinsertTable4abouthere.]SimilarlyasinLeland(1994),FanandSundaresan(2000),andMauerandOtt(2000),theoptimalleverageincreaseswiththecurrentvalueoftheproject,,therisklessrate,,thetaxrate,,andthecreditorseciencyparameter,.Moreover,itdecreaseswithcash”owvolatility,.AsinAndersonandSundaresan(1996),leverageincreaseswithshortfallwhenequityholdersbargainingpowerissucientlyhigh.Moreover,marketleveragedecreaseswithequityholdersbargainingpowerparameterIntroducingthegrowthoptionreducestheleveragemostdramaticallyforhighlevelsofearnings,highinterestrate,andlowlevelsoftaxes.Theinteractionbetweenthegrowthanddebtrenegotiationoptionsappearstobethemaindrivingforceofaloweroptimalleveragewhenequityholdersbargainingpowerishigh.Incontrast,whencreditorshavemuchsayinthedebtrestructuringprocess(low),thegrowthoptiondoesnotseemtoreducemarketleverageintheoptimum.Ingeneral,anincreaseintheoptionmoneyness(lowerorhigher)reducesmoresigni“cantlytheoptimalleveragerenegotiableTheresultsofthissectionprovidethereforeacomplementaryexplanationtotheexistingcapitalstructurepuzzleastheyhelptoreconcilethewedgebetweenhightheoreticallevelsofoptimalleverageandmuchlowerlevelsofcorporateindebtnessobservedempirically.Oneofthedeterminantsoflowmarketleverageistheinteractionofthegrowthoptionwiththedebtrenegotiationoption.Theleverageofgrowth“rmswithrenegotiabledebtisshowntobelowerthanasimplesuperpositionoftheeectsofthegrowthoptionanddebtrenegotiabilitywouldindicate.Inotherwords,leverageisexpectedtobepositivelycorrelatedwiththeinteractiontermofaproxyforgrowthopportunities(suchasTobins)andrenegotiationfrictions.Thepresenceoftheinvestmentoptionresultsinahigherfacevalueofdebt,attheoptimalleveragelevel.Theincrementofafacevalueofdebtduetothegrowthoptionisgenerallylowerwhendebtisrenegotiable.Again,theadverseeectofthe conditionalonnothittingtheliquidationtrigger, .Byexaminingtheseprobabilities,itispossibletoconcludeinwhichsituationsa“rmis,afterall,morelikelytoinvestifitusesrenegotiabledebt,despiteahighermagnitudeoftheunderinvestmentproblem.Thepresenceofthegrowthoptionaectstheprobabilityofstrategicdebtrestruc-turing.Inmostcases,renegotiationislesslikelywhenthegrowthoptionispresentduetothehigheropportunitycostofstrategicdefault.Nevertheless,inthepresenceofapositiveNPVproject,theprobabilityofdebtrenegotiationcanbethanwithouttheinvestmentoption.Thissituationcanoccurwhenshareholdersbargainingpowerishighsotheactualrenegotiationtrigger exceedstheanalogoustrig-gerintheabsenceoftheinvestmentopportunity(seeProposition5)andthecurrentcash”owisnotexcessivelyhigh.Thiseectisampli“edforlowlevelsofuncertainty(highuncertaintyincreasestheshareholdersvalueoftheinvestmentoptionwhichmakesrenegotiationlesslikely).Therelationshipbetweentheequityholdersbargain-ingpowerparameterandtheratiooftheprobabilitiesofrenegotiation(withinyears)intheabsenceandpresenceofthegrowthoptionisillustratedinFigure4,Panel[PleaseinsertFigure4abouthere.]Debtrenegotiabilityaectstheprobabilityofexpansionintwooppositeways.First,itraisestheoptimalinvestmentthreshold.Second,itallowspreservationoftheinvest-mentopportunityforthelevelsofcash”owlowerthanthebankruptcytrigger.PanelBofFigure4illustrateshowtheratiooftheprobabilitiesofinvestmentwithandwith-outarenegotiationoptionchangeswithshareholdersbargainingpower(again,=5).Whentheratioislargerthanone,theeectofapreservedinvestmentopportunity(be-tween l0 )morethanosetstheimpactofdelayedinvestment.Forlowvalues,bothinvestmentthresholdsareclosetoeachothersothattheonlysigni“cantfactoraectingtheprobabilitiesofinvestmentisthepresenceofthedown-and-outbar-rierassociatedwithbankruptcy.Forhighershareholdersbargainingpower,notonlydoeshittingtheliquidationtrigger, ,becomemorelikelybutalsothedivergenceofinvestmentthresholdsstartsplayinganimportantrole.Therefore,forsucientlyhigh,theratioofprobabilitiesbecomesstrictlylowerthanone. Thederivationoftherelevantprobabilities,basedonanexplicit“nitedierencemethod,isavailablefromtheauthoruponrequest.Sincebankruptcytrigger isalwayslowerthan ,thepresenceoftheinvestmentopportunityalwaysreducesthedefaultprobabilitywhenthereisnooptiontorenegotiate.Recallthatwithrenegotiabledebtthegrowthoptionislostonlyupontheliquidationofthe“rm. operations.ThisimpliesthatahighermagnitudeofMyers(1977)underinvestmentmakesinvestmentlesslikelytobetriggeredbyanincrementalcash”owincreaseforanyinitialcash”owlevel.Asaconsequence,thepresenceoftherenegotiationoptioncombinedwithhighshareholdersbargainingpower,whichresultsinhigherunder-investment,islikelytoreducethesensitivityofinvestmenttothe“rmscash”ow.Therefore,mymodelprovidesanalternativeexplanationoftheempiricalevidencethatsmallandyoung“rms(thatis,thosewithlowbargainingpower)aswellascompanies“nancedwithmarketdebt,exhibitrelativelyhigherinvestment-cash”owsensitivity(seeHubbard(1998)andBoyleandGuthrie(2003)).Theriskinessofdebtre”ectedbyitscreditspreadishighlyin”uencedbythepres-enceofbothaninvestmentandarenegotiationoption.Mella-BarralandPerraudin(1997)showthatallowingforthepossibilityofstrategicdebtservicecansigni“cantlyincreasespreads.Mymodelimpliesthatthepresenceofinvestmentopportunitieswillleadtoabiggerreductioninacreditspreadofdebtforwhichrenegotiationfrictionsareinsigni“cant.Conversely,withouttherenegotiationoption(i.e.,inacaseofawidelyhelddebtandalargenumberofissues),theimpactoftheinvestmentopportunityoncreditspreadsisexpectedtobethesmallest.Theresultsofthemodelyieldtestableimplicationsfortheoptimalcapitalstructure.Thepresenceofthegrowthoptionreducestheoptimalleveragetoalargerextentifdebtisrenegotiableandthebargainingpoweroftheshareholdersishigh.Theresultprovidethereforeacomplementaryexplanationofthecapitalstructurepuzzlefollowingfromtheobservedlevelsofleveragebeinggenerallylowerthantheoreticallypredicted.Empirically,thecoecientoftheinteractiontermoftherenegotiationfrictionsproxywithTobinsisexpectedtohaveapositivesignintheleverageregression.Finally,themodelgeneratestestableimplicationsfortheoptimal“nancingofgrowthoptions.Whenthe“rmis“nancedwithprivate,thatisrenegotiable,debt,theoptimal“nancingstructureofanewprojectwillentailahigherparticipationofthecreditors.Thisisduetothefactthatahigherleverageratioofthenewprojectisrequiredtoreduceanotherwiselargerineciencyoftheshareholdersinvestmentpolicy. Inthissimplesetup,theendogenousinvestmentvariablewouldbebinary. Since(x and(A.8)itholdsthatTheonlyremainingunknownconstantsareNow,oneneedstoconsidertwocases.Ifrenegotiationisnotallowed(=0),asthetaxshieldisirreversiblylostupondefault.Then,iscalculatedbyapplyingthevalue-matchingcondition )=lim whichgives x Ifrenegotiationisallowedfor(=1),thereisnorestrictionon,anditisdeter-minedsimultaneouslywithusingvalue-matchingcondition(A.10)andthefollowingsmooth-pastingconditionTS xx TS xx Thisresultsin Š2 1Š2x and(A.13) Š1 1Š2x Theoptimalliquidationtriggercanbefoundbyapplyingthefollowingvalue-matchingandsmooth-pastingconditionstothevalueofthe“rm: l1) +x l1Šx l1+L1x 2l1=1,) +1 x l1x l1Š(x) x=x l1+2L1x Constantcanbedirectlycalculatedfrom(A.15).Multiplyingbothsidesofcon-dition(A.15)by andsubtractingitfrom(A.16)yieldstheimplicitformulafor Thesmooth-pastingconditionre”ectsthefactthatrenegotiationtrigger isareversibleswitchpointanddoesentailanyoptimization.Continuityofthe“rstderivativeofthevaluefunctionat isthenrequiredfornoarbitrage(fordetailsseeDumas(1991)). isthestoppingtimeatrealizationofprocess(1).Consequently, x,x x) x , ))isthepresentvalueof$1receiveduponprocesshittingupperbarrier (lowerbarrier )conditionalonnothitting ( )beforeandstartingfromlevel(seeGemanandYor(1996)).Theexpressionsinsquarebracketsin(A.26)arenetpayosassociatedwithhittingthecorrespondingthresholds.For=0,thevalueofthegrowthoptioniscalculatedusingthefactthatinvestmentopportunityislostuponbankruptcyat .Therefore,thisvaluefor canbedecomposedas,where:=( x,x r0)×(Š ) +( x)Š( x)Š( x( x)ŠI+L1 and(A.29)isobtainedbysolvingvalue-matchingcondition(A.17)withanauxiliaryvalue-matchingconditionensuringthecontinuityofthe“rmvalueat .Now,thefollowingsimpli“cationcanbemade: x Constantiscalculatedanalogouslyasin(A.15)asthereisnogrowthoptionafterbankruptcy.Finally,constantsre”ectingtheequityholdersvalueofthegrowthanddebtrestructuringoptions,respectively,arecalculatedfrom(A.18)and(A.20):=( x,x 0)×(Š ) + V1x r1ŠR1x r1 1) +b) r x r12ŠI V0x r0ŠR0x r0 x x r02Šx r0) +b) Theimplicitformulaefortheoptimalinvestmentthreshold, ,optimaldebtrestruc-turingtrigger, ,andliquidationtrigger, ,areobtainedbypairwiserearrangingequations(A.18)…(A.19),(A.20)…(A.21),and(A.22)…(A.23). ProofofProposition3.Underinvestmentoccursaslongas,sinceinthiscasetheoptimalinvestmentthreshold, ,ishigherthanacorrespondingthreshold Theoption-likecomponentsofequitycanalsobeexpressedalongthelinesof(A.26). shareholderscanmaketake-itorleave-itoers(=1).Then,Iusethefactthatnodierenceoccurswhencreditorsholdtheentirebargainingpower(=0).(Recallthat,for=0,cf.(A.6)and(A.31).)Finally,IshowthatincreaseswithbargainingpowerparameterConsider“rstthevalueofanoptiontorestructuredebtintheabsenceoftheinvestmentoption,.(Obviously,.)Aftersubstituting(7)for (A.33)andobservingthatisobtainedanalogously,itfollowsthat 22r2Š1 kix2 Withrenegotiation,therelevantdierenceequalsls (1Š)x]2,whichislargerthantheanalogousdierencefornon-renegotiabledebt,t,(Š)x]2(2isnegative).Therefore,whentheeectofthegrowthoptionisdisregarded,thedierenceintheoptionvaluestorestructuredebtfortheoriginalandtheexpanded“rmislargerwhendebtisrenegotiable.Now,observethat,i.e.,theoptiontogobankrupt,mustbeworthlessthan(A.37)evaluatedfor=0,astheexpansionoptionincreasestheopportunitycostofbankruptcy(cf.(A.32)).Inotherwords,isalwaysmoreout-of-the-money(orlessin-the-money)than.Therefore,Now,Ishowthatfor=1,.Again,letbethevalueofthedebtrestructuringoptionexercised(possiblynotoptimally)atanexogenouslygiventrigger.Therenegotiationoption,=1isthengivenby rŠ) +B10(y)ŠB11 x2 y x1 Aftersubstituting ,(A.38)canbeexpressedas 1x2=B10x2+B10 1ŠB11x2 1 Furthermore,bysubtractingtheproductof(A.33)andfrom(A.38)(with oneobtainsthat .Thisinequalityisequivalentto Inturn,thelatterimpliesthat,asisaconstantcorrespondingtotheoptionwithanunconstrainedexercisepolicyand,andsuch,cannotbesmallerthan .Therefore,referringbacktoequation(6),thepossibilityofrenegotiationoccurringupondefaultcombinedwithequityholdersmakingtake-itorleave-itoers ReferencesAcharya,ViralV.,andJenniferN.Carpenter,2002,Corporatebondvaluationandhedgingwithstochasticinterestratesandendogenousbankruptcy,ReviewofFinan-cialStudies15,1355…1383.Acharya,ViralV.,JingzhiHuang,MartiG.Subrahmanyam,andRangarajanK.Sun-daram,2006,Whendoesstrategicdebtservicematter?,EconomicTheory29,363…Anderson,Ronald,andSureshSundaresan,1996,Designandvaluationofdebtcon-tracts,ReviewofFinancialStudies9,37…68.Asquith,Paul,RobertGertner,andDavidScharfstein,1994,Anatomyof“nancialdistress:Anexaminationofjunkbondissuers,QuarterlyJournalofEconomicsBaldursson,Fridrik,andIoannisKaratzas,1997,IrreversibleinvestmentandindustryFinanceandStochastics1,69…89.Barclay,MichaelJ.,ErwanMorellec,andCliordW.Smith,2006,Onthedebtcapacityofgrowthoptions,JournalofBusiness79,37…60.Betker,BrianL.,1995,Managementsincentives,equitybargainingpower,anddevi-ationsfromtheabsolutepriorityinChapter11bankruptcies,JournalofBusiness68,161…183.Bolton,Patrick,andDavidS.Scharfstein,1996,Optimaldebtstructureandthenum-berofcreditors,JournalofPoliticalEconomy104,1…25.Boyle,GlennW.,andGraemeA.Guthrie,2003,Investment,uncertainty,andliquidity,JournalofFinance58,2143…2166.Christensen,PeterOve,ChristianRiisFlor,DavidLando,andKristianR.Miltersen,2002,Dynamiccapitalstructurewithcallabledebtanddebtrenegotiations,WorkingPaper,UniversityofSouthernDenmark.Dangl,Thomas,andJosefZechner,2004,Creditriskanddynamiccapitalstructurechoice,JournalofFinancialIntermediation13,183…204. 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OptimalInvestment,LiquidationandDebtRestructuringPolicies CouponBargainingCreditorsVolatilityReturnInterestGrowthratepowereciencyshortfallrateoptionsb r I Investmentthreshold, )+++Renegotiationthreshold, Bankruptcythreshold, +00Liquidationthreshold, l0+Š+Š Table1:Comparativestaticsconcerningtheoptimalinvestment, ,renegotiation, ,bankruptcy, ,andliquidation, thresholds.Ž+Ž,Ž0Ž,andŽŽdenoteapositive,zero,andnegative,respectively,sensitivitywithrespecttothechangesinagivenparameter,andŽ+Žindicatesanambiguoussignoftherelationship.Thenumbersinbracketsrefertotheexplanatorynotesinthetext.Thenegativeeectofthedecreasingvalueofdebt(with)onunderinvestmentcandominateforlowDespitetheindirecteectofthevalueoftheinvestmentopportunitygenerallydecreasingwith AgencyCostsofDebt CouponBargainingCreditorsVolatilityReturnInterestGrowthratepowereciencyshortfallrateoptionsb rI Agencycostsw/renegotiation,Agencycostsnorenegotiation,Agencycostsratio, ŠŠŠ Table3:Comparativestaticsconcerningimpactoftheoptiontorenegotiateontheagencycostofdebt.Ž+Ž,Ž0ŽandŽdenoteapositive,zero,andnegative,respectively,sensitivitywithrespecttothechangesinagivenparameter. ProbabilitiesofDebtRestructuringandInvestment CouponBargainingCreditorsVolatilityReturnInterestGrowthratepowereciencyshortfallrateoptionsb rI Probabilityofinvestment, Probabilityofrenegotiation, Probabilityofbankruptcy, +00 Table5:Comparativestaticsconcerningthe“rst-passagetimeprobabilitiesassociatedwithinvestment, ,debtrenegotiation, ,andbankruptcy, .+Ž,0ŽandŽdenoteapositive,zero,andnegative,respectively,sensitivitywithrespecttothechangesinagivenparameter,and+Žindicatesanambiguoussignoftherelationship.Thenumbersinbracketsrefertotheexplanatorynotesinthetext.SeeProposition5. Equityholders’OptimalInvestmentThresholds 0.5 0.75 1.3 1.4 1.5 1.6  C 1x0xex 0.02 0.04 0.06 0.08 1.4 1.6 1.8 x D 1hx0lx1lx0h 0.5 0.75 1 1.2 1.3 1.4 1.5 1.6  A 1x0xex 0.25 0.5 0.75 1.3 1.4 1.5 1.6 B Figure2:Optimalinvestmentthresholdasafunctionofcouponrate,equityholdersbargainingpower,creditorseciency,andinterestrate x1 the“rmandtheequityvalue-maximizingthreshold,respectively,inthepresenceofrenegotiationoption; 0 denotethe“rmandtheequityvalue-maximizingthreshold,respectively,fornon-renegotiabledebt. istheall-equity“rminvestmentthreshold.Highandlowvolatilityregimes(PanelD)correspondto2and1,respectively. ProbabilitiesofDebtRestructuringandInvestment 0.4 0.6 0.8 0.6 0.7 0.8 0.9  B 0 0 0 0.2 0.4 0.6 0.8 0.4 0.6 0.8  A Figure4:Theratioofprobabilitiesofdebtrenegotiationwithandwithoutthegrowthoption(PanelA)andofinvestmentwithrenegotiableandnon-renegotiabledebt(PanelB)within=5yearsasafunctionofshareholdersbargainingpowerfordierentstartingvaluesofthecash”owprocess,