Corporate Finance 第7版 答案Ch015Word文件下载.docx

Corporate Finance 第7版 答案Ch015Word文件下载.docx

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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:

=（$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

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.

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