Chapter-14-Capital-Structure-in-a-Perfect-Market

©2011PearsonEducation,Inc.PublishingasPrenticeHallChapter14CapitalStructureinaPerfectMarket14-1.Consideraprojectwithfreecashflowsinoneyearof$130,000or$180,000,witheachoutcomebeingequallylikely.Theinitialinvestmentrequiredfortheprojectis$100,000,andtheproject’scostofcapitalis20%.Therisk-freeinterestrateis10%.a.WhatistheNPVofthisproject?b.Supposethattoraisethefundsfortheinitialinvestment,theprojectissoldtoinvestorsasanall-equityfirm.Theequityholderswillreceivethecashflowsoftheprojectinoneyear.Howmuchmoneycanberaisedinthisway—thatis,whatistheinitialmarketvalueoftheunleveredequity?c.Supposetheinitial$100,000isinsteadraisedbyborrowingattherisk-freeinterestrate.Whatarethecashflowsoftheleveredequity,andwhatisitsinitialvalueaccordingtoMM?a.()()11130,000180,000155,000,2155,000100,000129,167100,000$29,1671.20ECNPV=+=⎡⎤⎣⎦=−=−=b.()()155,000Equityvalue1129,1671.20PVC===c.Debtpayments100,000,=equityreceives20,000or70,000.Initialvalue,byMM,is129,167100,000$29,167−=.14-2.Youareanentrepreneurstartingabiotechnologyfirm.Ifyourresearchissuccessful,thetechnologycanbesoldfor$30million.Ifyourresearchisunsuccessful,itwillbeworthnothing.Tofundyourresearch,youneedtoraise$2million.Investorsarewillingtoprovideyouwith$2millionininitialcapitalinexchangefor50%oftheunleveredequityinthefirm.a.Whatisthetotalmarketvalueofthefirmwithoutleverage?b.Supposeyouborrow$1million.AccordingtoMM,whatfractionofthefirm’sequitywillyouneedtoselltoraisetheadditional$1millionyouneed?c.Whatisthevalueofyourshareofthefirm’sequityincases(a)and(b)?a.Totalvalueofequity2$2m$4m=×=b.MMsaystotalvalueoffirmisstill$4million.$1millionofdebtimpliestotalvalueofequityis$3million.Therefore,33%ofequitymustbesoldtoraise$1million.c.In(a),50%×$4m=$2m.In(b),2/3×$3m=$2m.Thus,inaperfectmarketthechoiceofcapitalstructuredoesnotaffectthevaluetotheentrepreneur.Berk/DeMarzo•CorporateFinance,SecondEdition185©2011PearsonEducation,Inc.PublishingasPrenticeHall14-3.AcortIndustriesownsassetsthatwillhavean80%probabilityofhavingamarketvalueof$50millioninoneyear.Thereisa20%chancethattheassetswillbeworthonly$20million.Thecurrentrisk-freerateis5%,andAcort’sassetshaveacostofcapitalof10%.a.IfAcortisunlevered,whatisthecurrentmarketvalueofitsequity?b.SupposeinsteadthatAcorthasdebtwithafacevalueof$20milliondueinoneyear.AccordingtoMM,whatisthevalueofAcort’sequityinthiscase?c.WhatistheexpectedreturnofAcort’sequitywithoutleverage?WhatistheexpectedreturnofAcort’sequitywithleverage?d.WhatisthelowestpossiblerealizedreturnofAcort’sequitywithandwithoutleverage?a.E[Valueinoneyear]()()0.8500.22044=+=.44E$40m.1.10==b.D=2019.0481.05=.Therefore,4019.048$20.952m.E=−=c.Withoutleverage,r=44110%40−=,withleverage,r=4420114.55%.20.952−−=d.Withoutleverage,r=20150%40−=−,withleverage,r=01100%.20.952−=−14-4.WolfrumTechnology(WT)hasnodebt.Itsassetswillbeworth$450millioninoneyeariftheeconomyisstrong,butonly$200millioninoneyeariftheeconomyisweak.Botheventsareequallylikely.Themarketvaluetodayofitsassetsis$250million.a.WhatistheexpectedreturnofWTstockwithoutleverage?b.Supposetherisk-freeinterestrateis5%.IfWTborrows$100milliontodayatthisrateandusestheproceedstopayanimmediatecashdividend,whatwillbethemarketvalueofitsequityjustafterthedividendispaid,accordingtoMM?c.WhatistheexpectedreturnofMMstockafterthedividendispaidinpart(b)?a.(.5×450+.5×200)/250=1.30=30%b.E+D=250,D=100=E=150c.(.5×(450-105)+.5×(200-105))/150=1.4667=46.67%14-5.Supposetherearenotaxes.FirmABChasnodebt,andfirmXYZhasdebtof$5000onwhichitpaysinterestof10%eachyear.Bothcompanieshaveidenticalprojectsthatgeneratefreecashflowsof$800or$1000eachyear.Afterpayinganyinterestondebt,bothcompaniesuseallremainingfreecashflowstopaydividendseachyear.a.Fillinthetablebelowshowingthepaymentsdebtandequityholdersofeachfirmwillreceivegiveneachofthetwopossiblelevelsoffreecashflows.b.Supposeyouhold10%oftheequityofABC.Whatisanotherportfolioyoucouldholdthatwouldprovidethesamecashflows?186Berk/DeMarzo•CorporateFinance,SecondEdition©2011PearsonEducation,Inc.PublishingasPrenticeHallc.Supposeyouhold10%oftheequityofXYZ.Ifyoucanborrowat10%,whatisanalternativestrategythatwouldprovidethesamecashflows?a.ABCXYZFCFDebtPaymentsEquityDividendsDebtPaymentsEquityDividends$8000800500300$1,00001000500500b.UnleveredEquity=Debt+LeveredEquity.Buy10%ofXYZdebtand10%ofXYZEquity,get50+(30,50)=(80,100)c.LeveredEquity=UnleveredEquity+Borrowing.Borrow$500,buy10%ofABC,receive(80,100)–50=(30,50)14-6.SupposeAlphaIndustriesandOmegaTechnologyhaveidenticalassetsthatgenerateidenticalcashflows.AlphaIndustriesisanall-equityfirm,with10millionsharesoutstandingthattradeforapriceof$22pershare.OmegaTechnologyhas20millionsharesoutstandingaswellasdebtof$60million.a.AccordingtoMMPropositionI,whatisthestockpriceforOmegaTechnology?b.SupposeOmegaTechnologystockcurrentlytradesfor$11pershare.Whatarbitrageopportunityisavailable?Whatassumptionsarenecessarytoexploitthisopportunity?a.V(alpha)=10×22=220m=V(omega)=D+E⇒E=220–60=160m⇒p=$8pershare.b.Omegaisoverpriced.Sell20Omega,buy10alpha,andborrow60.Initial=220–220+60=60.Assumeswecantradesharesatc