教育成本（PPT44页)

TOPIC6:CAPITALSTRUCTUREANDTHEMARKETFORCORPORATECONTROL1.Introduction2.ThefreeriderproblemInaclassicalpaper,GrossmanandHart(BellJ.,1980),showthatthereisafundamentalproblemwithtakeovers.Ifeachoftheexistingshareholdersholdsasmallamountofsharesthennotakeoverwillevertakeplace.GrossmanandHartrefertothisasthefree-riderproblem.Tounderstandthenatureofthefreeriderproblem,considerafirmwhosecurrentvalueisX.Ifwenormalizethenumberofoutstandingsharesto1,Xalsorepresentsthemarketvalueofeachoutstandingshare.Nowsupposethataridercomesalongandwantstotakeoverthefirm.Iftheriderissuccessfulandbuysenoughshares(saymorethanhalfoftheoutstandingshares),hegainscontroloverthefirmandcanenhanceitsvaluebyR,sothevalueofthefirmbecomesX+R.Inordertobuyshares,theriderneedstomakeatenderoffertothecurrentshareholdersthatspecifiesapricethattheywouldgetforeachsharetheytender.Forsimplicity,supposethattheofferisconditionalonbeingsuccessful:thatistheraiderwillbuysharesatthespecifiedpriceprovidedthatenoughsharesaretenderedtoensurethathecantakeoverthefirm.Otherwisetheraiderbuysnosharesandpaysnothing.ObviouslythepricethattheraideroffersshouldbeatleastXotherwisenoshareholderwillevertenderhisshares.SupposethenthatthepriceisX+PwherePisthepremiumoneachshareaboveitscurrentvalue.HowbigshouldPbeinordertoinduceshareholderstotendertheirshares?Toanswerthisquestion,consideranindividualshareholderwhoholdsafractionαofthefirm’s2equity.Iftheshareholderdoesnottenderhisshares,hisexpectedpayoffiswhereγ1istheprobabilitythatthetakeoversucceedsgiventhattheshareholderdidnottenderhisshares.(1)Thatis,withprobabilityγ1thetakeoversucceedsandthevalueofthesharesisX+Randwithprobability1-γ1thetakeoverfailsandthevalueofthesharesisX.Iftheshareholdertendershisshares,hisexpectedpayoffiswhereγ2istheprobabilitythatthetakeoversucceedsgiventhattheshareholdertendershisshares.1(2)Obviously,γ2γ1sinceiftheshareholdertendershissharethereisahigherlikelihoodthattheraiderwillbeabletobuyenoughsharestogaincontroloverthefirm.Comparingtheexpectedpayoffsoftheshareholderwhenhedoesnottenderhisshareandwhenhedoes,itisclearthattenderingsharesisanoptimalstrategyifandonlyif:Howeverifeachshareholderholdsanegligibleamountofshares,thedifferencebetweenγ2andγ1isalso(3)negligiblesothetakeovercanbesuccessfulifandonlyifP≥R.Thismeansthattheraidershouldpaythewholeincreaseinfirmvaluetoshareholder,implyinginturnthathispayoffis0sincehenowownssharesworthX+ReachbutpaysforeachshareX+R.Soifthetakeoverinvolvessometransactioncostsofrequiresaneffortonthepartoftheraider,hispayofffromtakingoverthefirmisnegativeandhenceheisbetteroffnotmakingthetenderofferinthefirstplace.Theproblemisreferredtoasthefree-riderproblemsinceeachshareholdersisbetter-offnottenderinghisownsharesunlessP≥Rbecausehefailstotakeintoaccounthisownimpactonthelikelihoodofatakeoverandinsteadfreeridesonthe1Notethatabsenttheassumptionthatthetenderofferisconditionalonbeingsuccessful,thepayoffofatenderingshareholderwouldhavebeenαPregardlessofwhetherthetakeoverissuccessfulornot.3willingnessofothershareholderstosubmitsharesandenabletheraidertotakeoverthefirm.Inotherwords,solongas0PR,eachshareholderwantsothershareholderstotendertheirsharestoensurethatthetakeoverissuccessfulbutwishestoholdontohisownshareandobtainthefullincreaseinfirmvalue.2.1DilutionasasolutiontothefreeriderproblemApossiblesolutiontothefree-riderproblem,offeredbyGrossmanandHart(1980),istowriteacorporatecharterthatallowstheraider,oncehetakesoverthefirm,todilutethesharevalueofthenon-tenderingshareholders.Thiscanbeachievedbyeitherallowingtheraidertopayhimselfexcessivesalary,orissuetohimselfnewsharesatbelowtheirvalue,orsellassetsoroutputatbelowtheircosttoanotherfirmownedbytheraider.Inanyevent,whateverformittakes,thedilutionmakeitundesirableforsmallshareholderstoholdontotheirsharesastheyarenotgoingtoenjoythefullincreaseinfirmvalueduetothetakeover.Toseehowdilutionworks,supposethatthecorporatecharterallowstheraidertodilutethevalueofthefirmafterhetakesitoverbyφ.GivenapremiumP,ashareholderwhotendershissharesgetsthesameexpectedpayoffasinequation(2),i.e.,α(X+γ2P).Iftheshareholderdoesnottender,hisexpectedpayoffisα(X+γ1(R-φ)).Thispayoffissimilartothatinequation(1)exceptthatRisreplacedbyR-φ.Assumingasbeforethatindividualshareholdersaresmallandhavenoinfluenceonthelikelihoodthatthetakeoverwillsucceed(i.e.,γ1=γ2),itfollowsthattenderingsharesisanoptimalstrategyifandonlyifThisinequalityimpliesthattheoptimalstrategyfortheraider’sistoofferaprice,(4)4ItshouldbenotedthatP*couldbelessthanXinwhichcasetheequilibriumissupportedbythe(5)pessimisticbeliefofeachshareholderthatothershareholdersaregoingtotendertheirsharesandhenceitisbettertotenderandgetX+PthannottotenderandgetX+R-φ.Althoughthereisanother(arguablymorereasonable)equilibriuminwhichshareholdersbelievethatotherswillnottenderifPXandhencenottenderingisabest-responsegiventhisbelief,Ichoosetoconsiderthepessimisticbeliefscasesincethissimplifiestheexposition(otherwiseP*=Max{R-φ,X}).NowletCbethecostthattheraiderneedstoincurinordertoinitiateatakeover.SincethepremiumP*ensuresthatallshare