Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch16.docx

Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch16.docx

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FundamentalsofCorporateFinance3rdedJonathanBerkCh16

Chapter16

CapitalStructure

Note:

AllproblemsinthischapterareavailableinMyFinanceLab.Anasterisk（*）indicatesproblemswithahigherlevelofdifficulty.

1.Plan:

InordertocalculatetheNPVoftheproject,wemustfirstcomputethefreecashflowsforthatyearbycalculatingtheaverageofthetwolikelyscenariosforcashflowsthatyear.WecanthencomputetheNPVusingtheNPVformula.Knowingthefreecashflows,thediscountrate,andtheinitialinvestment,wecancomputetheNPVaswellastheequityvalue.Finally,wecancomputethecashflowsoftheleveredequitybycomputingtherisk-freerateofthedebtpaymentsandsubtractingthatfromthetwolikelyscenariosforthecashflowsusedinpart（a）.Finally,theinitialvalueoftheprojectcanbefoundbysubtractingthedebtpaymentsoftheprojectfromtheequityvalue.

Execute:

a.

b.Equityvalue

c.Debtpayments=100,000,equityreceives20,000or70,000

Initialvalue,byMM,is

Evaluate:

TheNPVrulestatestoacceptaprojectwithpositiveNPV,suchasthisproject;thereforeallelsebeingequal,thecompanyshouldundertaketheproject.

2.Plan:

Wecanfindthetotalmarketvalueofthefirmwithoutleveragebycomputingthetotalvalueofequityknowingthe$2millionininitialcapitalandthe$2millionneededtofundyourresearch.Wecancomputethefractionofthefirm’sequityyouwillneedtoselltoraisetheadditional$1millionyouneedusingthetotalvalueofthefirmandthenewvalueofequityafterborrowingtogetthepercentageofequitythatmustbesold.Finally,wecancomputethefirm’svalueofequityinbothcases,knowingthefractionofthefirm’sequityyouwillneedtosellinbothcases.

Execute:

a.Totalvalueofequity

b.MMsaysthetotalvalueoffirmisstill$4million.$1millionofdebtimpliesthetotalvalueofequityis$3million.Therefore,33%ofequitymustbesoldtoraise$1million.

c.In（a）,50%⨯$4M=$2M.In（b）,2/3⨯$3M=$2M.Thus,inaperfectmarket,thechoiceofcapitalstructuredoesnotaffectthevaluetotheentrepreneur.

Evaluate:

Inthiscase,changingthecapitalstructuredoesnotaffectthevaluetotheownerofthefirm,andthereforetheownershavemoreflexibilitywiththeircapitalstructure.

3.Plan:

WecanuseEq.16.1tocomputethecurrentmarketvalueofAcort’sequity.Todetermineitsexpectedreturn,wewillcomputethecashflowstoequity.Thecashflowstoequityarethecashflowsofthefirmnetofthecashflowstodebt（repaymentofprincipalplusinterest）.

Execute:

a.E[Valuein1year]

b.D=

Therefore,

c.Withoutleverage,

withleverage,

d.Withoutleverage,

withleverage,

Evaluate:

ThecurrentmarketvalueofAcort’sequitywhenunleveredisnearlydoublethecurrentmarketvalueofAcort’sequitywhenlevered.Theexpectedreturnisgreaterwithdebtthanwithout,yetthelowestpossiblerealizedreturnofAcort’sequityislesswhenunleveredasopposedtolevered.

*4.Plan:

Wecancomputethedebtpaymentsandequitydividendsforeachfirmusingthecapitalstructureofeachfirm.WecanuseEq.16.1tocomputetheunleveredequityandleveredequityofbothfirms.

Execute:

a.

ABC

XYZ

FCF

DebtPayments

EquityDividends

DebtPayments

EquityDividends

$800

0

800

500

300

$1000

0

1,000

500

500

b.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）.

Evaluate:

MMPropositionIstatesthatinaperfectcapitalmarket,thetotalvalueofafirmisequaltothemarketvalueofthefreecashflowsgeneratedbyitsassetsandisnotaffectedbyitschoiceofcapitalstructure.Byaddingleverage,thereturnsoftheunleveredfirmareeffectivelysplitbetweenlow-riskdebtandmuchhigherriskleveredequity.Returnsofleveredequityfalltwiceasfastasthoseofunleveredequityifthecashflowsdecline.Leverageincreasestheriskofequityevenwhenthereisnoriskthatthefirmwilldefault.

5.Plan:

WecanuseEq.16.3tocomputetheexpectedreturnofequityinbothcases.

Execute:

a.re=ru+d/e（ru-rd）=12%+0.50（12%-6%）=15%

b.re=12%+1.50（12%-8%）=18%

c.Returnsarehigherbecauseriskishigher—thereturnfairlycompensatesfortherisk.Thereisnofreelunch.

Evaluate:

Withnodebt,theWACCisequaltotheunleveredequitycostofcapital.Asthefirmborrowsatthelowcostofcapitalfordebt,itsequitycostofcapitalrisesaccordingtoEq.16.3.Theneteffectisthatthefirm’sWACCisunchanged.Astheamountofdebtincreases,thedebtbecomesmoreriskybecausethereisachancethefirmwilldefault;asaresult,thedebtcostofcapitalalsorises.

6.Plan:

WecanuseEq.16.3tocomputethecostofequityusingthecostofdebt,using95%equity（E）and5%debt（D）.Itsunleveredcostofequity,rU,is9.2%.

Execute:

Atacostofdebtof6%:

Evaluate:

Withnodebt,theWACCisequaltotheunleveredequitycostofcapital.Asthefirmborrowsatthelowcostofcapitalfordebt,itsequitycostofcapitalrisesaccordingtoEq.16.3.Theneteffectisthatthefirm’sWACCisunchanged.Astheamountofdebtincreases,thedebtbecomesmoreriskybecausethereisachancethatthefirmwilldefault;asaresult,thedebtcostofcapitalalsorises.

7.Plan:

WecanfindthenetincomeofthefirmusingtheEBIT,interestexpense,andthecorporatetaxrate.WecancomputetheinteresttaxshieldusingEq.16.4.

Execute:

a.Netincome

b.Netincome+Interest=120+125=$245million

c.Netincome

Thisis245-195=$50 millionlowerthanpart（b）.

d.Interesttaxshield=125⨯40%=$50million

Evaluate:

Thegaintoinvestorsfromthetaxdeductibilityofinterestpaymentsisreferredtoastheinteresttaxshield.Theinteresttaxshieldistheadditionalamountthatafirmwouldhavepaidintaxesifitdidnothaveleveragebutcaninsteadpaytoinvestors.

8.Plan:

WecanfindthenetincomeofthefirmusingtheEBIT,interestexpense,andthecorporatetaxrate.

Execute:

a.Netincomewillfallbytheafter-taxinterestexpenseto$20.750-1⨯（1-0.35）=

$20.10million.

b.Freecashflowisnotaffectedbyinterestexpenses.

Evaluate:

Leveragemerelychangestheallocationofcashflowsbetweendebtandequity,withoutalteringthetotalcashflowsofthefirminaperfectcapitalmarket.Inaperfectcapitalmarket,thetotalvalueofafirmisequaltothemarketvalueofthefreecashflowsgeneratedbyitsassetsandisnotaffectedbyitschoiceofcapitalstructure.

9.BraxtonEnterprisescurrentlyhasdebtoutstandingof$35millionandaninterestrateof8%.Braxtonplanstoreduceitsdebtbyrepaying$7millioninprincipalattheendofeachyearforthenextfiveyears.IfBraxton’smarginalcorporatetaxrateis40%,whatistheinteresttaxshieldfromBraxton’sdebtineachofthenextfiveyears?

Year

0

1

2

3

4

5

Debt

35

28

21

14

7

0

Interest

2.8

2.24

1.68

1.12

0.56

TaxShield

1.12

0.896

0.672

0.448

0.224

10.Plan:

WecanuseEq.16.5tocomputethepresentvalueofthetaxshield.

Execute:

Evaluate:

Weknowthatinperfectcapitalmarkets,financingtransactionshaveanNPVofzero.However,theinteresttaxdeductibilitymakesthisapositive-NPVtransactionforthefirm.Thetotalvalueoftheleveredfirmexceedsthevalueofthefirmwithoutleverageduetothepresentvalueofthetaxsavingsfromdebt.Thereisanimportanttaxadvantagetotheuseofdebtfinancing.

11.Plan:

WecanuseEq.16.3tocomputethevalueofthefirm’sequityanddebt.Wecanuseouranswersinparts（b）and（c）tocomputethepercentageofthevalueofdebt.

Execute:

a.Netincome=1000⨯（1-40%）=$600.Thus,equityholdersreceivedividendsof$600peryearwithnorisk.

b.Netincome

Debtholdersreceiveinterestof$500peryear⇒D=$10,000.

c.Withleverage=6,000+10,000=$16,000

Withoutleverage=$12,000

Difference=16,000-12,000=$4,000

d.

corporatetaxrate

Evaluate:

MMPropositionIstatesthatinaperfectcapitalmarket,thetotalvalueofafirmisequaltothemarketvalueofthefreecashflowsgeneratedbyitsassetsandisnotaffectedbyitschoiceofcapitalstructure.Byaddingleverage,thereturnsoftheunleveredfirmareeffectivelysplitbetweenlow-riskdebtandmuchhigherriskleveredequity.Returnsofleveredequityfalltwiceasfastasthoseofunleveredequityifthecashflowsdecline.Leverageincreasestheriskofequityevenwhenthereisnoriskthatthefirmwilldefault.

12.Plan:

Wemustcomputethevalueofthetaxshieldineachyearandthencomputethepresentvalueofthetaxshields.

Execute:

Year

0

1

2

3

4

5

Debt

100

75

50

25

0

0

Interest

10

7.5

5

2.5

0

TaxShield

4

3

2

1

0

PV

$8.30

Evaluate:

Thepresentvalueoftheannualtaxshieldsis$8.30million.

13.Plan:

WecanuseEq.16.4tocomputetheinteresttaxshield.WecanuseEq.16.5tocomputethepresentvalueoftheinteresttaxshield.

Execute:

a.Interesttaxshield

b.PV（Interesttaxshield）

c.Interesttaxshield=$10⨯5%⨯35%=$0.175million.

Evaluate:

Weknowthatinperfectcapitalmarkets,financingtransactionshaveanNPVofzero.However,theinteresttaxdeductibilitymakesthisapositive-NPVtransactionforthefirm.Thetotalvalueoftheleveredfirmexceedsthevalueofthefirmwithoutleverageduetothepresentvalueofthetaxsavingsfromdebt.Thereisanimportanttax