B-257Chapter15:CapitalStructure:BasicConcepts15.1a.SinceAlphaCorporationisanall-equityfirm,itsvalueisequaltothemarketvalueofitsoutstandingshares.Alphahas5,000sharesofcommonstockoutstanding,worth$20pershare.Therefore,thevalueofAlphaCorporationis$100,000(=5,000shares*$20pershare).b.Modigliani-MillerPropositionIstatesthatintheabsenceoftaxes,thevalueofaleveredfirmequalsthevalueofanotherwiseidenticalunleveredfirm.SinceBetaCorporationisidenticaltoAlphaCorporationineverywayexceptitscapitalstructureandneitherfirmpaystaxes,thevalueofthetwofirmsshouldbeequal.Modigliani-MillerPropositionI(NoTaxes):VL=VUAlphaCorporation,anunleveredfirm,isworth$100,000(VU).Therefore,thevalueofBetaCorporation(VL)is$100,000.c.Thevalueofaleveredfirmequalsthemarketvalueofitsdebtplusthemarketvalueofitsequity.VL=B+SThevalueofBetaCorporationis$100,000(VL),andthemarketvalueofthefirm’sdebtis$25,000(B).ThevalueofBeta’sequityis:S=VL–B=$100,000-$25,000=$75,000Therefore,themarketvalueofBetaCorporation’sequity(S)is$75,000.d.SincethemarketvalueofAlphaCorporation’sequityis$100,000,itwillcost$20,000(=0.20*$100,000)topurchase20%ofthefirm’sequity.SincethemarketvalueofBetaCorporation’sequityis$75,000,itwillcost$15,000(=0.20*$75,000)topurchase20%ofthefirm’sequity.e.SinceAlphaCorporationexpectstoearn$350,000thisyearandowesnointerestpayments,thedollarreturntoaninvestorwhoowns20%ofthefirm’sequityisexpectedtobe$70,000(=0.20*$350,000)overthenextyear.WhileBetaCorporationalsoexpectstoearn$350,000beforeinterestthisyear,itmustpay12%interestonitsdebt.SincethemarketvalueofBeta’sdebtatthebeginningoftheyearis$25,000,Betamustpay$3,000(=0.12*$25,000)ininterestattheendoftheyear.Therefore,theamountofthefirm’searningsavailabletoequityholdersis$347,000(=$350,000-$3,000).Thedollarreturntoaninvestorwhoowns20%ofthefirm’sequityis$69,400(=0.20*$347,000).f.Theinitialcostofpurchasing20%ofAlphaCorporation’sequityis$20,000,butthecosttoaninvestorofpurchasing20%ofBetaCorporation’sequityisonly$15,000(seepartd).Inordertopurchase$20,000worthofAlpha’sequityusingonly$15,000ofhisownmoney,theinvestormustborrow$5,000tocoverthedifference.Theinvestormustpay12%interestonhisborrowingsattheendoftheyear.B-258Sincetheinvestornowowns20%ofAlpha’sequity,thedollarreturnonhisequityinvestmentattheendoftheyearis$70,000(=0.20*$350,000).However,sinceheborrowed$5,000at12%perannum,hemustpay$600(=0.12*$5,000)attheendoftheyear.Therefore,thecashflowtotheinvestorattheendoftheyearis$69,400(=$70,000-$600).Noticethatthisamountexactlymatchesthedollarreturntoaninvestorwhopurchases20%ofBeta’sequity.StrategySummary:1.Borrow$5,000at12%.2.Purchase20%ofAlpha’sstockforanetcostof$15,000(=$20,000-$5,000borrowed).g.TheequityofBetaCorporationisriskier.Betamustpayoffitsdebtholdersbeforeitsequityholdersreceiveanyofthefirm’searnings.Ifthefirmdoesnotdoparticularlywell,allofthefirm’searningsmaybeneededtorepayitsdebtholders,andequityholderswillreceivenothing.15.2a.Afirm’sdebt-equityratioisthemarketvalueofthefirm’sdebtdividedbythemarketvalueofafirm’sequity.ThemarketvalueofAcetate’sdebt$10million,andthemarketvalueofAcetate’sequityis$20million.Debt-EquityRatio=MarketValueofDebt/MarketValueofEquity=$10million/$20million=?Therefore,Acetate’sDebt-EquityRatiois?.b.Intheabsenceoftaxes,afirm’sweightedaveragecostofcapital(rwacc)isequalto:rwacc={B/(B+S)}rB+{S/(B+S)}rSwhereB=themarket...
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