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1、CorporateFinance(AutumnTerm)NorvaldInstefjordOctober7,2011Modigliani-MillerCapitalStructureIrrelevanceICapitalstructureirrelevancedealswiththeliabilityside:itdoesn'tmatterhowmoneyisraised(inthesensethatthevalueoftheliabilitiesremainsthesameregardless).IThe`proof':IUn-doingborrowingIhome-
2、madeleverageIAlternativeproof:arbitrage-freepricing(theexistenceofstate-pricesorapricingkernel)andput-callparityfromoptionpricingIWhendoesitnotwork?Frictionsofvarioustypes:incompletemarkets,cash
owsdependenton nancing,informationalasymmetries,taxesdependenton nancingIA rmhasacash
owofX~,
3、andadebtliabilityofD.Thepayo todebtholdersisX~D=min(X~;D)andthepayo toequityholdersisX~E=X~ X~D.Supposethe rmhasdebt(D>0)buttheinvestorsbelievethe rmwouldbeworthmorewithoutthedebt,i.e.thevalueofX~isgreaterthanthesumofthevaluesofX~EandX~D:V(X~)>V(X~E)+V(X~D)IThenthedebtholderscould`undo't
4、he rm'sborrowingfreeofcostbybuyingdebtandequitytogether,i.e.bybuyingafractionofdebtandofequity,whichhasapayo X~E+X~D=(X~ X~D+X~D)=X~and,therefore,hasvalueV(X~)=V(X~).ITheinvestorcanthenbuyV(X~E)+V(X~D)andsellV(X~)tomakearbitragepro ts.Sincethis`undoing'operationisfreeofcost,itmustbetheca
5、sethatV(X~)V(X~E)+V(X~D)INext,supposethe rmhasnotborrowed(D=0)buttheinvestorsbelievethe rmwouldbeworthmorewithdebt:V(X~E)+V(X~D)>V(X~)IThentheinvestorcouldbuytheunleveredequityandsellaportfoliointhestockmarketthatexactlymimicsacorporatedebtcontract,i.e.aclaimwithpayo min(X~;D)atavalueV(
6、X~D).ThenetpositionisaclaimworthV(X~E).TheinvestorcansellV(X~E)+V(X~D)andbuyV(X~)tomakearbitragepro ts.Sincethis`home-made'borrowingoperationisfreeofcost,therefore,itmustbethecasethatV(X~E)+V(X~D)V(X~)IPuttingbothtogetherwegetcapitalstructureirrelevanceV(X~E)+V(X~D)=V(X~)IThecapitalstru
7、ctureirrelevancetheoremtellsus,essentially,thatassetpricingtheoryhasnothingtocontributetocorporate nanceapartfrommanagingtheinvestmentpolicyofthe rm(bychoosingpositiveNPVprojects-weneedassetpricingtheorytoworkoutNPVs)ITheusefulnessofthistheoremis,however,thatwecansystemat
