Corporate-income-taxes-and-the-cost-of-capital：-A-

AmericanEconomicAssociationCorporateIncomeTaxesandtheCostofCapital:ACorrectionAuthor(s):FrancoModiglianiandMertonH.MillerSource:TheAmericanEconomicReview,Vol.53,No.3(Jun.,1963),pp.433-443Publishedby:AmericanEconomicAssociationStableURL::26/05/201011:11YouruseoftheJSTORarchiveindicatesyouracceptanceofJSTOR'sTermsandConditionsofUse,availableat://=aea.EachcopyofanypartofaJSTORtransmissionmustcontainthesamecopyrightnoticethatappearsonthescreenorprintedpageofsuchtransmission.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,[e-mail]ioniscollaboratingwithJSTORtodigitize,preserveandextendaccesstoTheAmericanEconomicReview.[6,pp.5-7and9-12].IV.ConiclusionThemostnoteworthyconclusiontobedrawnfromthisanalysisisthatthesuccessfuloperationofamultiplekey-currencysystemwouldrequirebothexchangeguaranteesandcontinuingcooperationbetweencentralbankersofatypethatwouldeffectivelylimittheirchoiceastotheforminwhichtheyholdtheirreserves.Yetthesearetwooftheconditionswhoseundesirabilityhasfrequentlybeenheldtobeanobstacletoimplementationofthealterlna-tiveproposaltocreateaworldcentralbank.Themultiplekey-currencypro-posalrepresentsanattempttoavoidtheimpracticalitysupposedlyassociatedwithaworldcentralbank,butifbothproposalsinfactdependonthefulfill-mentofsimilarconditions,itisdifficulttoconvinceoneselfthatthesacrificeoftheadditionalliquiditythatanalmostclosedsystemwouldpermitisworthwhile.Unless,ofcourse,theobjectoftheexerciseistoreinforcedisciplineratherthantoexpandliquidity.JOHNWILLIAMSON**TheauthorisinstructorineconomicsatPrincetonUniversity.HeacknowledgesthehelpfulcommentsofFritzMachlup.Viewsexpressedarethoseoftheauthoralone.REFERENCES1.R.Z.ALIBER,ForeignExchangeGuaranteesandtheDollar:Comment,Am.Econ.Rev.,Dec.1962,52,1112-16.2.S.T.1E3ZAANDG.PATTERSON,ForeignExchangeGuaranteesandtheDol-lar,Am.Econ.Rev.,June1961,51,381-85.3.AND,ForeignExchangeGuaranteesandtheDollar:Reply,Amn.Econ.Rev.,Dec.1962,52,1117-18.4.F.A.LUTZ,TheProblemofInternationalEquilibrium.Amsterdam1962.5.R.NURKSE,InternationalCurrencyExperience.Geneva1944.6.R.V.RooSA,AssuringtheFreeWorld'sLiquidity,BusinessReviewSupplement,FederalReserveBankofPhiladelphia,Sept.1962.CorporateIncomeTaxesandtheCostofCapital:ACorrectionThepurposeofthiscommunicationistocorrectanerrorinourpaperTheCostofCapital,CorporationFinanceandtheTheoryofInvestment(thisReview,June1958).Inourdiscussionoftheeffectsofthepresentmethodoftaxingcorporationsonthevaluationoffirms,wesaid(p.272):Thedeductionofinterestincomputingtaxablecorporateprofitswillpreventthearbitrageprocessfrommakingthevalueofallfirmsinagivenclassproportionaltotheexpectedreturnsgeneratedbytheir434THEAMERICANECONOMICREVIEWphysicalassets.Instead,itcanbeshown(bythesametypeofproofusedfortheoriginalversionofPropositionI)thatthemarketvaluesoffirmsineachclassmustbeproportionalinequilibriumtotheirex-pectedreturnsnetoftaxes(thatis,tothesumoftheinterestpaidandexpectednetstockholderincome).(Italicsadded.)Thestatementinitalics,unfortunately,iswrong.Foreventhoughonefirmmayhaveanexpectedreturnaftertaxes(ourXr)twicethatofanotherfirminthesamerisk-equivalentclass,itwillnotbethecasethattheactualreturnaftertaxes(ourX7)ofthefirstfirmwillalwaysbetwicethatofthesecond,ifthetwofirmshavedifferentdegreesofleverage.'Andsincethedistributionofreturnsaftertaxesofthetwofirmswillnotbeproportional,therecanbenoarbitrageprocesswhichforcestheirvaluestobepropor-tionaltotheirexpectedafter-taxreturns.2Infact,itcanbeshown-andthistimeitreallywillbeshown-thatarbitragewillmakevalueswithinanyclassafunctionnotonlyofexpectedafter-taxreturns,butofthetaxrateandthedegreeofleverage.Thismeans,amongotherthings,thatthetaxadvantagesofdebtfinancingaresomewhatgreaterthanweoriginallysuggestedand,tothisextent,thequantitativedifferencebetweenthevalu-ationsimpliedbyourpositionandbythetraditionalviewisnarrowed.Itstillremainstrue,however,thatunderouranalysisthetaxadvantagesofdebtaretheonlypermanentadvantagessothatthegulfbetweenthetwoviewsinmattersofinter