Problem SetLeverage and Capital Structure学习资料Word下载.docx
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Problem SetLeverage and Capital Structure学习资料Word下载.docx
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schoiceofcapitalstructureisirrelevant.
3.ABCCo.andXYZCo.areidenticalfirmsinallrespectsexceptfortheircapitalstructure.ABCisall-equityfinancedwith$600,000instock.XYZusesbothstockandperpetualdebt;
itsstockisworth$300,000andtheinterestrateonitsdebtis10percent.BothfirmsexpectEBITtobe$73,000.Ignoretaxes.
a.Ricoowns$30,000worthofXYZ'
sstock.Whatrateofreturnissheexpecting?
b.ShowhowRicocouldgenerateexactlythesamecashflowsandrateofreturnbyinvestinginABCandusinghomemadeleverage.
c.WhatisthecostofequityforABC?
WhatisitforXYZ?
CapitalStructure
4.MoonBeamIndustrieshasadebt-equityratioof1.5.ItsWACCis12percent,anditscostofdebtis12percent.Thecorporatetaxrateis35percent.
a.WhatisMoonBeam'
scostofequitycapital?
b.WhatisMoonBeam'
sunleveredcostofequitycapital?
c.Whatwouldthecostofequitybeifthedebt-equityratiowere2?
Whatifitwere1.0?
Whatifitwerezero?
5.Bruce&
Co.expectsitsEBITtobe$95,000everyyearforever.Thefirmcanborrowat11percent.Brucecurrentlyhasnodebt,anditscostofequityis22percent.Ifthetaxrateis35percent,whatisthevalueofthefirm?
WhatwillthevaluebeifBruceborrows$60,000andusestheproceedstorepurchaseshares?
6.ToolManufacturinghasanexpectedEBITof$35,000inperpetuityandataxrateof35percent.Thefirmhas$70,000inoutstandingdebtataninterestrateof9percent,anditsunleveredcostofcapitalis14percent.WhatisthevalueofthefirmaccordingtoM&
MPropositionIwithtaxes?
ShouldToolchangeitsdebt-equityratioifthegoalistomaximizethevalueofthefirm?
Explain.
7.OldSchoolCorporationexpectsanEBITof$9,000everyyearforever.OldSchoolcurrentlyhasnodebt,anditscostofequityis17percent.Thefirmcanborrowat10percent.Ifthecorporatetaxrateis35percent,whatisthevalueofthefirm?
WhatwillthevaluebeifOldSchoolconvertsto50percentdebt?
To100percentdebt?
Solutions
1.a.Sincethecompanyhasamarket-to-bookratioof1.0,thetotalequityofthefirmisequaltothemarketvalueofequity.UsingtheequationforROE:
ROE=NI/$150,000
TheROEforeachstateoftheeconomyunderthecurrentcapitalstructureandnotaxesis:
Recession
Normal
Expansion
ROE
.0373
.0933
.1213
%∆ROE
–60
–––
+30
ThesecondrowshowsthepercentagechangeinROEfromthenormaleconomy.
b.Ifthecompanyundertakestheproposedrecapitalization,thenewequityvaluewillbe:
Equity=$150,000–60,000
Equity=$90,000
So,theROEforeachstateoftheeconomyis:
ROE=NI/$90,000
.0222
.1156
.1622
–76.36
+38.18
c.Iftherearecorporatetaxesandthecompanymaintainsitscurrentcapitalstructure,theROEis:
.0243
.0607
.0789
Ifthecompanyundertakestheproposedrecapitalization,andtherearecorporatetaxes,theROEforeachstateoftheeconomyis:
.0144
.0751
.1054
NoticethatthepercentagechangeinROEisthesameasthepercentagechangeinEPS.ThepercentagechangeinROEisalsothesamewithorwithouttaxes.
2.a.Theearningspershareare:
EPS=$16,000/2,000shares
EPS=$8.00
So,thecashflowforthecompanyis:
Cashflow=$8.00(100shares)
Cashflow=$800
b.Todeterminethecashflowtotheshareholder,weneedtodeterminetheEPSofthefirmundertheproposedcapitalstructure.Themarketvalueofthefirmis:
V=$70(2,000)
V=$140,000
Undertheproposedcapitalstructure,thefirmwillraisenewdebtintheamountof:
D=0.40($140,000)
D=$56,000
indebt.Thismeansthenumberofsharesrepurchasedwillbe:
Sharesrepurchased=$56,000/$70
Sharesrepurchased=800
Underthenewcapitalstructure,thecompanywillhavetomakeaninterestpaymentonthenewdebt.Thenetincomewiththeinterestpaymentwillbe:
NI=$16,000–.08($56,000)
NI=$11,520
ThismeanstheEPSunderthenewcapitalstructurewillbe:
EPS=$11,520/1,200shares
EPS=$9.60
Sinceallearningsarepaidasdividends,theshareholderwillreceive:
Shareholdercashflow=$9.60(100shares)
Shareholdercashflow=$960
c.Toreplicatetheproposedcapitalstructure,theshareholdershouldsell40percentoftheirshares,or40shares,andlendtheproceedsat8percent.Theshareholderwillhaveaninterestcashflowof:
Interestcashflow=40($70)(.08)
Interestcashflow=$224
Theshareholderwillreceivedividendpaymentsontheremaining60shares,sothedividendsreceivedwillbe:
Dividendsreceived=$9.60(60shares)
Dividendsreceived=$576
Thetotalcashflowfortheshareholderundertheseassumptionswillbe:
Totalcashflow=$224+576
Totalcashflow=$800
Thisisthesamecashflowwecalculatedinparta.
d.Thecapitalstructureisirrelevantbecauseshareholderscancreatetheirownleverageorunleverthestocktocreatethepayofftheydesire,regardlessofthecapitalstructurethefirmactuallychooses.
3.a.Therateofreturnearnedwillbethedividendyield.Thecompanyhasdebt,soitmustmakeaninterestpayment.Thenetincomeforthecompanyis:
NI=$73,000–.10($300,000)
NI=$43,000
Theinvestorwillreceivedividendsinproportiontothepercentageofthecompany’ssharetheyown.Thetotaldividendsreceivedbytheshareholderwillbe:
Dividendsreceived=$43,000($30,000/$300,000)
Dividendsreceived=$4,300
Sothereturntheshareholderexpectsis:
R=$4,300/$30,000
R=.1433or14.33%
b.Togenerateexactlythesamecashflowsintheothercompany,theshareholderneedstomatchthecapitalstructureofABC.TheshareholdershouldsellallsharesinXYZ.Thiswillnet$30,000.Theshareholdershouldthenborrow$30,000.Thiswillcreateaninterestcashflowof:
Interestcashflow=.10($30,000)
Interestcashflow=–$3,000
TheinvestorshouldthenusetheproceedsofthestocksaleandtheloantobuysharesinABC.Theinvestorwillreceivedividendsinproportiontothepercentageofthecompany’ssharetheyown.Thetotaldividendsreceivedbytheshareholderwillbe:
Dividendsreceived=$73,000($60,000/$600,000)
Dividendsreceived=$7,300
Thetotalcashflowfortheshareholderwillbe:
Totalcashflow=$7,300–3,000
Totalcashflow=$4,300
Theshareholdersreturninthiscasewillbe:
c.ABCisanallequitycompany,so:
RE=RA=$73,000/$600,000
RE=.1217or12.17%
TofindthecostofequityforXYZweneedtouseM&
MPropositionII,so:
RE=RA+(RA–
RD)(D/E)(1–tC)
RE=.1217+(.1217–.10)
(1)
(1)
RE=.1433or14.33%
d.TofindtheWACCforeachcompanyweneedtousetheWACCequation:
WACC=(E/V)RE+(D/V)RD(1–tC)
So,forABC,theWACCis:
WACC=
(1)(.1217)+(0)(.10)
WACC=.1217or12.17%
AndforXYZ,theWACCis:
WACC=(1/2)(.1433)+(1/2)(.10)
WACC=.1217or12.17%
Whentherearenocorporatetaxes,thecostofcapitalforthefirmisunaffectedbythecapitalstructure;
thisisM&
MPropositionIwithouttaxes.
4.a.Withtheinformationprovided,wecanusetheequationforcalculatingWACCtofindthecostofequity.TheequationforWACCis:
WACC=(E/V)RE+(D/V)RD(1–tC)
Thecompanyhasadebt-equityratioof1.5,whichimpliestheweightofdebtis1.5/2.5,andtheweightofequityis1/2.5,so
WACC=.12=(1/2.5)RE+(1.5/2.5)(.12)(1–.35)
RE=.1830or18.30%
b.Tofindtheunleveredcostof
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