IFM10 Ch16 Solutions Manual文档格式.docx

IFM10 Ch16 Solutions Manual文档格式.docx

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PartII

ANSWERSTOBEGINNING-OF-CHAPTERQUESTIONS

16-1Arbitrageisgenerallythoughtofastheprocessofbuyinganiteminonemarketandsimultaneouslysellingitatahigherpriceinanothermarketandthusearningarisklessprofit.MMbroadenedthisconcept.Theyshow,underasetofassumptions,thatpersonaldebtcanbeusedtocausetheriskoftwodifferentstockstobethesamebutthereturnsonthestockscanbedifferent.Then,onecouldbuythecheaperstockandsimultaneouslysellthemoreexpensiveoneandendupearningarisklessprofit.Usingthisarbitrageconcept,theydemonstratedthatifanunleveredfirmhadahighervaluethanaleveragedfirm,theninvestorscoulduse“homemade”leveragetoearnarisklessprofitbysellingtheleveragedfirm’sstockandborrowingtobuystockintheunleveredfirm’sstock.So,investorswouldgettothesamedebtpositionandhavethesamerisk,butearnahigherprofit.

TheMMconclusionswerebasedonanumberofassumptions,andintherealworld,thoseassumptionsarenotcorrect.Investorscannotnecessarilyborrowatthesamerateascorporations,interestratesincreasewiththeamountborrowed,bankruptcycostsdoexist,andsoon.Moreover,inbadtimescorporationsaremorelikelytousecashflowstoservicetheirowndebtthantheyaretopaydividendstoenablestockholderstoservice“homemade”leveragedebts,whichcouldresultinadditionalrisktothepersonallyleveragedinvestor.

ItshouldbenotedthatmanyoftheargumentsagainsttheMMassumptionsarevalidifonethinksaboutindividualinvestorslikecollegeprofessorsbutlessvalidifthe“investor”isaninstitutionalinvestorlikeapensionfundthathasreadyaccesstocapitalandmaynothavetopaytaxes.Then,taxesandbrokeragecostsmayreallybeimmaterial,borrowingcostsmaybethesamefortheinvestorandthecompany,theinvestorandthefirmmayhavethesameinformation,andtheinvestormayhaveenoughclouttoforcethecompanytoprovidecashtoservicetheinvestor’sdebt.Asaresult,arbitrageundoubtedlyworksbetterforcertainlargeinvestorsthanforsmallinvestors.TheuseofdebtincorporateAmericaincreasedafterMMpublishedtheirwork,andwebelievethatMM’sworkcontributedtothisdevelopment.

16-2MilleraddedpersonalincometaxestotheMMequation.Heargued

（1）thatthepersonaltaxratewashighoninterestincomeanddividendsbutmuchloweroncapitalgainsincome,and

（2）thatindividualscouldusevarioustaxshields,includingdeath,toavoidcapitalgainstaxes,whilecorporationscouldretainearnings,usestockbuy-backprograms,andsoontohelpstockholdersminimizepersonaltaxesonincomefromstock.Miller’sconclusionwasthatinvestorscouldessentiallyavoidtaxesonstockincome,hencetheyhadamuchlowerrisk-adjustedrequiredrateofreturnonstocksthanonbonds,andthatthisadvantagelargelyoffsetthetaxadvantagetocorporatedebt.

HereisMiller’sformulaforthegainfromleverage:

Gainfromleverage=

D

Notethatifallthetaxrateswerezero,thegainfromleveragewouldreducetozero,andwewouldbebackattheoriginalMMposition.Millerpersonallythoughtthatthiswasthemostlikelysituation.NotealsothatifTs=Td,i.e.,thetaxratesonstockanddebtincomeareequal,thenthegainfromleverageisequaltoTcD,whichistheMMwithcorporatetaxesposition.

MostsubsequentresearchersconcludedthatMillerhadagoodpoint,butthepersonaltaxadvantageofstockonlypartially,notcompletely,offsettheadvantageofcorporatedebt,becauseTd>

Ts.Forexample,supposethatTc=35%,Td=28%,andTs=10%,thentheterminbracketswillbe1-（1-.35）（1-.10）/（1-.28）=0.1875versus.35undertheMMwith-taxesmodel.Thegainfromleveragewithothertaxratesisshowninthemodeloutput.

TheMillerModelleadsustotheconclusionthatthe“PureMM”lineinthevaluegraphsshouldhavealesssteepslopethatTD,andthat,inturn,leadstotheconclusionthattheoptimalcapitalstructureinthetrade-offmodelshouldincludesomewhatlessdebt.

16-3UndertheMMandMillerassumptions,firmsdonotgrowandthedebttaxshieldisdiscountedatthecostofdebt.UndertheseassumptionsthevalueoftheunleveredfirmisVL=VU+TDandtheleveredcostofequityisrsL=rsU+（rsU–rd）（1-T）（D/S）.ThisexpressionfortheleveredcostofequityalsomeansthattheWACCdecreasesasthelevelofdebtincreases.

However,iffirmsareallowedtogrow,thentwodifferencesemerge.First,thepresentvalueofagrowingtaxshieldislargerthanthepresentvalueofaconstanttaxshield,sothecontributiontovaluethatthedebttaxshieldmakesislarger.Second,thevalueofthegrowingtaxshielddoesn’tmakeanysenseifthediscountrateisthecostofdebt,becauseusingsuchalowdiscountrateallowsthevalueofthegrowingtaxshieldtodominatethevalueofoperations,whichmakesnoeconomicsense.Rather,thediscountrateforthetaxshieldmustbetheunleveredcostofequity,whichislargerthanthecostofdebt.Usingahigherdiscountratemakesthetaxshield’scontributiontovaluesmallerthanifthecostofdebthadbeenusedtodiscountit.ThesetwooppositeeffectsleadtotheresultthatthepresentvalueofthegrowingtaxshieldswhendiscountedattheunleveredcostofequityisVL=VU+（rdTD/（rsU–g）.TheleveredcostofequityundertheseassumptionsisrsL=rsU+（rsU–rd）（D/S）;

boththetaxrateandthegrowthratedropoutoftheexpressionanditlookslikeMM’sresult,butwithouttaxes.Thismeansthateverythingelseequal,MM’scalculationoftheleveredrequiredrateofreturnissmallerthanitwouldbeifgrowthwereaccountedfor.ThisalsomeansthatthecalculationofWACCunderMMwillbesmallerthanthecalculationofWACCundertheextension.Theendresultisthatwhengrowthiscorrectlyincludedinthemodel,thebenefitsduetothetaxshieldareactuallylowerthanwhatMM’smodelsuggests.

ThemodelforthesequestionsgraphstheWACCbasedonMMandtheWACCbasedontheextensiontoMM.

16-4IfcorporatedebtisactuallyriskyratherthanrisklessasMMassumed,thenmanagersreallyhavetheoptiontodefaultifthevalueofthecompanyisn’tenoughtomakeitworthwhiletopaytheinterestorprincipalonthedebt.Inthesimplecaseofaleveredcompanywithzerocoupondebt,theequityinthefirmlooksalotlikeacalloptiononthevalueoftheentirefirm,withastrikepriceequaltothefacevalueofthedebt.Viewingequityinthiswaycanleadtosomedangerousbehavioronthepartoffirmmanagement.Forexample,optionsareworthmorewhentheunderlyingstockismoreriskier.Thesameistruewiththeequityinaleveredfirm.Ifmanagementtakesthemoneythatitborrowsandinvestsitinriskierprojectsthanoriginallyintended,thenitmakesthefirmriskier,anditmakestheoptionvalue（theequityvalue）greater.Thiswouldbegoodnewsfortheshareholders—thevalueoftheirstockincreases.Anditwouldbebadnewsforthebondholders.Ifmanagementisn’tinvestinginhighernpvprojects,onlyriskierones,thentheincreaseintheshareholders’positionisexactlyoffsetbyadecreaseinthebondholders’position.Sotheshareholderswouldbeexpropriatingwealthfromthebondholdersbyusinga“baitandswitch”strategy.Ofcoursebondholderswouldwanttoavoidthisifpossible,sotheywouldputrestrictionsonhowthemoneythattheylendcanbeused,ortheymightchargeahigherinterestratebecausetheyknowthismighthappen,ortheymightrefusetodealwiththefirmagainifithappens.

ANSWERSTOEND-OF-CHAPTERQUESTIONS

16-1a.MMPropositionIstatestherelationshipbetweenleverageandfirmvalue.PropositionIwithouttaxesisV=EBIT/rsU.SincebothEBITandrsUareconstant,firmvalueisalsoconstantandcapitalstructureisirrelevant.Withcorporatetaxes,PropositionIbecomesV=Vu+TD.Thus,firmvalueincreaseswithleverageandtheoptimalcapitalstructureisvirtuallyalldebt.

b.MMPropositionIIstatestherelationshipbetweenleverageandthecostofequity.Withouttaxes,PropositionIIisrsL=rsU+（rsU–rd）（D/S）.Thus,rsincreasesinaprecisewayasleverageincreases.Infact,thisincreaseisjustsufficienttooffsettheincreaseduseoflowercostdebt.Whencorporatetaxesareadded,PropositionIIbecomesrsL=rsU+（rsU–rd）（1–T）（D/S）.Heretheincreaseinequitycostsislessthanthezero-taxcase,andtheincreasinguseoflowercostdebtcausesthefirm’scostofcapitaltodecrease,andagain,theoptimalcapitalstructureisvirtuallyalldebt.

c.TheMillermodelintroducespersonaltaxes.Theeffectofpersonaltaxesis,essentially,toreducetheadvantageofcorporatedebtfinancing.

d.Financialdistresscostsareincurredwhenaleveragedfirmfacingadeclineinearningsisforcedtotakeactionstoavoidbankruptcy.Thesecostsmaybetheresultofdelaysintheliquidationofassets,legalfees,theeffectsonproductqualityfromcuttingcosts,andevasiveactionsbysuppliersandcustomers.

e.Agencycostsarisefromlostefficiencyandtheexpenseofmonitoringmanagementtoensurethatdebtholders’rightsareprotected.

f.TheadditionoffinancialdistressandagencycoststoeithertheMMtaxmodelortheMillermodelresultsinatrade-offmodelofcapitalstructure.Inthismodel,theoptimalcapitalstructurecanbevisualizedasatrade-offbetweenthebenefitofdebt（theinteresttaxshelter）andthecostsofdebt（financialdistressandagencycosts）.

g.Thevalueofthedebttaxshieldisthepresentvalueofthetaxsavingsfromtheinterestpayments.IntheMMmodelwithtax