Corporate Finance 第7版 答案Ch015.docx
《Corporate Finance 第7版 答案Ch015.docx》由会员分享,可在线阅读,更多相关《Corporate Finance 第7版 答案Ch015.docx(52页珍藏版)》请在冰豆网上搜索。
CorporateFinance第7版答案Ch015
Chapter15:
CapitalStructure:
BasicConcepts
15.1a.SinceAlphaCorporationisanall-equityfirm,itsvalueisequaltothemarketvalueofitsoutstanding
shares.Alphahas5,000sharesofcommonstockoutstanding,worth$20pershare.
Therefore,thevalueofAlphaCorporationis$100,000(=5,000shares*$20pershare).
b.Modigliani-MillerPropositionIstatesthatintheabsenceoftaxes,thevalueofaleveredfirmequalsthevalueofanotherwiseidenticalunleveredfirm.SinceBetaCorporationisidenticaltoAlphaCorporationineverywayexceptitscapitalstructureandneitherfirmpaystaxes,thevalueofthetwofirmsshouldbeequal.
Modigliani-MillerPropositionI(NoTaxes):
VL=VU
AlphaCorporation,anunleveredfirm,isworth$100,000(VU).
Therefore,thevalueofBetaCorporation(VL)is$100,000.
c.Thevalueofaleveredfirmequalsthemarketvalueofitsdebtplusthemarketvalueofitsequity.
VL=B+S
ThevalueofBetaCorporationis$100,000(VL),andthemarketvalueofthefirm’sdebtis$25,000(B).
ThevalueofBeta’sequityis:
S=VL–B
=$100,000-$25,000
=$75,000
Therefore,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.
Sincetheinvestornowowns20%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
=½
Therefore,Acetate’sDebt-EquityRatiois½.
b.Intheabsenceoftaxes,afirm’sweightedaveragecostofcapital(rwacc)isequalto:
rwacc={B/(B+S)}rB+{S/(B+S)}rS
whereB=themarketvalueofthefirm’sdebt
S=themarketvalueofthefirm’sequity
rB=thepre-taxcostofafirm’sdebt
rS=thecostofafirm’sequity.
Inthisproblem:
B=$10,000,000
S=$20,000,000
rB=14%
TheCapitalAssetPricingModel(CAPM)mustbeusedtocalculatethecostofAcetate’sequity(rS)
AccordingtotheCAPM:
rS=rf+βS{E(rm)–rf}
whererf=therisk-freerateofinterest
E(rm)=theexpectedrateofreturnonthemarketportfolio
βS=thebetaofafirm’sequity
Inthisproblem:
rf=8%
E(rm)=18%
βS=0.9
Therefore,thecostofAcetate’sequityis:
rS=rf+βS{E(rm)–rf}
=0.08+0.9(0.18–0.08)
=0.17
ThecostofAcetate’sequity(rS)is17%.
Acetate’sweightedaveragecostofcapitalequals:
rwacc={B/(B+S)}rB+{S/(B+S)}rS
=($10million/$30million)(0.14)+($20million/$30million)(0.17)
=(1/3)(0.14)+(2/3)(0.17)
=0.16
Therefore,Acetate’sweightedaveragecostofcapitalis16%.
c.AccordingtoModigliani-MillerPropositionII(NoTaxes):
rS=r0+(B/S)(r0–rB)
wherer0=thecostofcapitalforanall-equityfirm
rS=thecostofequityforaleveredfirm
rB=thepre-taxcostofdebt
Inthisproblem:
rS=0.17
rB=0.14
B=$10,000,000
S=$20,000,000
Thus:
0.17=r0+(1/2)(r0–0.14)
Solvingforr0:
r0=0.16
Therefore,thecostofcapitalforanotherwiseidenticalall-equityfirmis16%.
ThisisconsistentwithModigliani-Miller’spropositionthat,intheabsenceoftaxes,thecostofcapitalforanall-equityfirmisequaltotheweightedaveragecostofcapitalofanotherwiseidenticalleveredfirm.
15.3SinceUnleveredisanall-equityfirm,itsvalueisequaltothemarketvalueofitsoutstanding
shares.Unleveredhas10millionsharesofcommonstockoutstanding,worth$80pershare.
Therefore,thevalueofUnleveredis$800million(=10millionshares*$80pershare).
Modigliani-MillerPropositionIstatesthat,intheabsenceoftaxes,thevalueofaleveredfirmequalsthevalueofanotherwiseidenticalunleveredfirm.SinceLeveredisidenticaltoUnleveredineverywayexceptitscapitalstructureandneitherfirmpaystaxes,thevalueofthetwofirmsshouldbeequal.
Modigliani-MillerPropositionI(NoTaxes):
VL=VU
Therefore,themarketvalueofLevered,Inc.,shouldbe$800millionalso.
SinceLeveredhas4.5millionoutstandingshares,worth$100pershare,themarketvalueofLevered’sequityis$450million.ThemarketvalueofLevered’sdebtis$275million.
Thevalueofaleveredfirmequalsthemarketvalueofitsdebtplusthemarketvalueofitsequity.
Therefore,thecurrentmarketvalueofLevered,Inc.is:
VL=B+S
=$275million+$450million
=$725million
ThemarketvalueofLevered’sequityneedstobe$525million,$75millionhigherthanitscurrentmarketvalueof$450million,forMMPropositionItohold.
SinceLevered’smarketvalueislessthanUnlevered’smarketvalue,Leveredisrelativelyunderpricedandaninvestorshouldbuysharesofthefirm’sstock.
15.4a.SincethemarketvalueofKnight’sequityis$1,714,000,5%ofthefirm’sequitycosts$85,700(=0.05*$1,714,000).
SincethemarketvalueofVeblen’sequityis$2,400,000,5%ofthefirm’sequitycosts$120,000(=0.05*$2,400,000).Inordertocomparedollarreturns,theinitialnetcostofbothpositionsshouldbethesame.Therefore,theinvestorwillborrow$34,300(=$120,000-$87,500)at6%perannumwhenpurchasing$120,000ofVeblen’sequityforanetcostof$85,700(=$120,000-$34,300).
Aninvestorwhoowns5%ofKnight’sequitywillbeentitledto5%ofthefirm’searningsavailabletocommonstockholdersattheendofeachyear.WhileKnight’sexpectedoperatingincomeis$300,000,itmustpay$60,000todebtholdersbeforedistributinganyofitsearningstostockholders.Knight’sexpectedearningsavailabletostockholdersis$240,000(=$300,000-$60,000).
Therefore,aninvestorwhoowns5%ofKnight’sstockexpectstoreceiveadollarreturnof$12,000(=0.05*$240,000)attheendofeachyearbasedonaninitialnetcostof$85,700.
Aninvestorwhoowns5%ofVeblen’sequitywillbeentitledto5%ofthefirm’searningsattheendofeachyear.SinceVeblenisanall-equityfirm,itowesnoneofitsmoneytodebtholdersandcandistributeall$300,000ofitsearningstostockholders.Aninvestorwhoowns5%ofVeblen’sequitywillexpecttoreceiveadollarreturnof$15,000attheendofeachyear.However,sincethisinvestorborrowed$34,300at6%perannuminordertofundhisequitypurchase,heowes$2,058(=0.06*$34,300)ininterestpaymentsattheendofeachyear.Thisreduceshisexpectednetdollarreturnto$12,942(=$15,000-$2,058).
Therefore,aninvestorwhoborrows$34,300at6%peranunminordertopurchase5%ofVeblen’sstockwillexpecttoreceiveadollarreturnof$12,942attheendoftheyearforaninitialnetcostof$85,700.
Foranetcostof$85,700,purchasing5%ofVeblen’sequityyieldsahigherexpecteddollarreturnthanpurchasing5%ofKnight’sequity.
b.Bothoftheabovetwostrategiescost$85,700.SincethedollarreturntotheinvestmentinVeblenishigher,allinvestorswillchoosetoinvestinVeblenoverKnight.
TheprocessofinvestorspurchasingVeblen’sequityratherthanKnight’swillcausethemarketvalueofVeblen’sequitytoriseandthemarketvalueofKnight’sequitytofall.Anydifferencesinthedollarreturnstothetwostrategieswillbeeliminated,andtheprocesswillceasewhenthetotalmarketvaluesofthetwofirmsareequal.
15.5BeforetherestructuringthemarketvalueofGrimsley’sequitywas$5,000