Solutions to Chapter 16 Debt Policy.docx

Solutions to Chapter 16 Debt Policy.docx

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SolutionstoChapter16DebtPolicy

SolutionstoChapter16

DebtPolicy

1.a.True.

b.False.Asfinancialleverageincreases,theexpectedrateofreturnonequityrisesbyjustenoughtocompensateforitshigherrisk.Thevalueofthefirmandstockholders’wealthareunaffected.

c.False.Thesensitivityofequityreturnstobusinessrisk,andthereforethecostofequity,increaseswithleverageevenwithoutachangeintheriskoffinancialdistress.

d.True.

2.Whilethecostofdebtandthecostofequitybothincrease,theweightappliedtodebtinthecostofcapitalformulaalsoincreases.Applyingahigherweighttothelower-costsourceofcapitaloffsetstheincreaseinthecostofdebtandthecostofequity.

3.Theinteresttaxshieldisthereductionincorporateincometaxesduetothefactthatinterestistreatedasanexpensethatreducestaxableincome.Totheextentthatthegovernmentcollectslesstax,thereisabiggerpieofafter-taxincomeavailabletothedebtandequityholders.

Example:

Assumeoperatingincomeis$100,000,theinterestrateondebtis10%,andthetaxrateis35%.Compareincomeforanunleveredfirmversusafirmthatborrows$400,000:

Zero-debtfirm

$400,000ofdebt

Operatingincome

$100,000

$100,000

Interestondebt

0

40,000

Before-taxincome

100,000

60,000

Taxat35%

35,000

21,000

After-taxincome

65,000

39,000

Sumofdebtinterestplus

after-taxincome

$65,000

$79,000

Thecombineddebtinterestplusequityincomeishigherfortheleveredfirm.Thedifferenceequals$14,000,whichisalsothedifferenceintaxespaidbythetwofirms.

4.PV（Taxshield）=

5.a.False.Inliquidation,equityholdersgenerallyreceivenothing.Therefore,theyhavenothingtoloseinareorganization,whichallowsequityholders（andjuniorcreditors）to“playfortime,”hopingforareversaloffortunes.Ifthefirmisultimatelyliquidated,equityholdersmaystillreceivenothing,buttheyhavenotlostanythingeither.

b.True.

c.False.Claimsforpaymentofexpensesincurredafterthebankruptcyfilingreceivefirstpriority,followedbyemployeeclaimsforwagesandbenefits.IRSclaims（alongwithsomeclaimsfordebtsowedtogovernmentagencies）arenextinline.

d.True.

e.False.Ifthefirmisliquidated,tax-losscarry-forwardsdisappear.Inareorganization,thenewentityisentitledtoanytax-losscarry-forwardsoftheoldfirm.

6.Thetradeofftheoryofcapitalstructureholdsthattheoptimaldebtratioisdeterminedbystrikingabalancebetweentheadvantagesanddisadvantagesofdebtfinancing.Theadvantageofdebtfinancingistheinteresttaxshield.Thedisadvantagesarethevariouscostsoffinancialdistress.Asleverageincreases,themarginaltaxshieldfromeachdollarofadditionalborrowingfalls.Thisisaconsequenceoftheincreasingprobabilitythat,withhigherinterestexpense,thefirmwillnothavepositivetaxableincomeandthereforewillnotpaytaxes.Atthesametime,theexpectedcostsoffinancialdistressincreasewithleverage.Asleverageincreases,themarginalcostoffinancialdistresseventuallyoutweighstheinteresttaxshield.Attheoptimaldebtratio,theincreaseinthepresentvalueoftaxsavingsfromadditionalborrowingisexactlyoffsetbyincreasesinthepresentvalueofthecostsoffinancialdistress.

7.Directcostsofbankruptcysuchaslegaloradministrativecosts

Indirectcostsduetotheproblemsencounteredwhenmanagingafirminbankruptcyproceedings（e.g.,interferencebycreditorsordifficultiesbuyingsuppliesoncredit）

Poorinvestmentdecisionsresultingfromconflictsofinterestbetweencreditorsandstockholders.

8.Thepeckingordertheorystatesthatfirmsprefertoraisefundsthroughinternalfinance,andifexternalfinanceisrequired,thattheypreferdebttoequityissues.Thispreference–orpecking–orderresultsfromthefactthatinvestorsmayinterpretsecurityissues–equityissuesinparticular–asasignalthatmanagersthinkthefirmiscurrentlyovervaluedbythemarket;therefore,investorswillreducetheirvaluationofthefirminresponsetonewsofastockissue.

Ifthepeckingordertheoryiscorrect,wewouldexpectfirmswiththehighestdebtratiostobethosewithlowprofits,becauseinternalfinanceislessavailabletothesefirms.

9.Financialslackreferstoafirm’saccesstocash,marketablesecurities,bankfinancing,ordebtfinancing.Financialslackisvaluablebecauseitmeansfinancingwillbequicklyavailabletotakeadvantageofpositive-NPVinvestmentopportunities.

Toomuchfinancialslackcanbedetrimentalifitallowsmanagerstotakeiteasy,toempirebuild,ortouseexcesscashontheirownperquisites.

10.Numberofshares=75,000

Pricepershare=$10

Marketvalueofshares=$750,000

Marketvalueofdebt=$250,000

StateoftheEconomy

Slump

Normal

Boom

Operatingincome

$75,000

$125,000

$175,000

Interest

$25,000

$25,000

$25,000

Equityearnings

$50,000

$100,000

$150,000

Earningspershare

$0.667

$1.333

$2.000

Returnonshares

6.67%

13.33%

20.00%

11.Theinvestorcansellone-fourthofherholdingsinthefirm,andtheninvesttheproceedsindebt.Supposeshehas$10,000currentlyinvestedinthefirm.Shecouldsell$2,500worthofshares,usingtheproceedstobuybondsyielding10%.Thereturnonherportfolioinanyeconomicscenariois:

StateoftheEconomy

Slump

Normal

Boom

ReturnonShares

6.67%

13.33%

20.00%

ReturnonDebt

10.00%

10.00%

10.00%

PortfolioReturn*

7.50%

12.50%

17.50%

*PortfolioReturn=（0.25returnondebt）+（0.75returnonshares）

Theportfolioreturnispreciselythesameasitwaswhenthe$10,000wasinvestedintheunleveredfirm.

12.Shareprice=$10

Withnoleverage,thereare100,000sharesoutstanding:

Expectedearningspershare=

P/E=$10/$1.25=8

Withleverage,thereare75,000sharesoutstanding:

Expectedearningspershare=

P/E=$10/$1.333=7.5

P/Edecreasesbecausetheequityisnowriskier.Althoughearningspershareareexpectedtorisefrom$1.25to$1.333,thevalueofeachshareofequityisnohigher.Theincreaseinriskoffsetstheincreaseinexpectedearnings.

13.After-taxincomeforall-equityfirm:

StateoftheEconomy

Slump

Normal

Boom

Operatingincome

$75,000

$125,000

$175,000

Taxat35%

$26,250

$43,750

$61,250

After-taxincome

$48,750

$81,250

$113,750

After-taxincomeassuming$250,000ofdebtfinancing:

StateoftheEconomy

Slump

Normal

Boom

Operatingincome

$75,000

$125,000

$175,000

Debtinterestat10%

25,000

25,000

25,000

Before-taxincome

50,000

100,000

150,000

Taxat35%

17,500

35,000

52,500

After-taxincome

32,500

65,000

97,500

Combineddebt&equityincome

（debtinterest+after-taxincome）

57,500

90,000

122,500

After-taxincome（all-equitycase）

$48,750

$81,250

$113,750

Differenceinincome

$8,750

$8,750

$8,750

Inallstatesoftheeconomy,thedifferenceintotalincometoallsecurityholdersis$8,750.Thisisexactlyequaltothetaxshieldfromdebt:

TcInterestexpense=0.35$25,000=$8,750

14.Expectedreturnonassetsis:

rassets=（0.0830/100）+（0.1670/100）=0.136=13.6%

Thenewreturnonequityis:

requity=rassets+[D/E（rassets–rdebt）]

=0.136+[20/80（0.136–0.08）]=0.15=15%

15.a.Marketvalueoffirmis:

$10010,000=$1,000,000

Withthelow-debtplan,equityfallsby$200,000,so:

D/E=$200,000/$800,000=0.25

8,000sharesremainoutstanding.

Withthehigh-debtplan,equityfallsby$400,000,so:

D/E=$400,000/$600,000=0.67

6,000sharesremainoutstanding.

b.Low-debtplan

EBIT$90,000$130,000

Interest20,00020,000

EquityEarnings70,000110,000

EPS[Earnings/8,000]$8.75$13.75

ExpectedEPS=（$8.75+$13.75）/2=$11.25

High-debtplan

EBIT$90,000$130,000

Interest40,00040,000

EquityEarnings50,00090,000

EPS[Earnings/6000]$8.33$15.00

ExpectedEPS=（$8.33+$15）/2=$11.67

Althoughthehigh-debtplanresultsinhigherexpectedEPS,itisnotnecessarilypreferablebecauseitalsoentailsgreaterrisk.ThehigherriskshowsupinthefactthatEPSforthehigh-debtplanislowerthanEPSforthelow-debtplanwhenEBITislow,butEPSforthehigh-debtplanishigherwhenEBITishigher.

c.Low-debtplanHigh-debtplan

EBIT$100,000$100,000

Interest20,00040,000

EquityEarnings80,00060,000

EPS$10.00$10.00

EPSisthesameforbothplansbecauseEBITis10%ofassetswhichisequaltotheratethefirmpaysonitsdebt.Whenrassets=rdebt,EPSisunaffectedbyleverage.

16.Currently,withnooutstandingdebt:

equity=1.0

Therefore:

assets=1.0

Also:

requity=10%rassets=10%

Finally:

rdebt=5%

Thefirmplanstorefinance,resultinginadebt-to-equityratioof1.0,anddebt-to-valueratio:

debt/（debt+equity）=0.5

a.（equity0.5）+（debt0.5）=assets=1

（equity0.5）+0=1equity=1/0.5=2.0

b.requity=rassets=10%

riskpremium=requity–rdebt=10%–5%=5%

（Notethatthedebtisrisk-free.）

c.requity=rassets+[D/E（rassets–rdebt）]=10%+[1（10%–5%）]=15%

riskpremium=requity–rdebt=15%–5%=10%

d.5%

e.rassets=（0.5requity）+（0.5rdebt）=（0.515%）+（0.55%）=10%

Thisisunchanged.

f.Supposetotalequitybeforetherefinancingwas$1,000.Thenexpectedearningswere10%of$1000,or$100.Aftertherefinancing,therewillbe$500ofdebtand$500ofequity,sointerestexpensewillbe$25.Therefore,earningsfallfrom$100to$75,butthenumberofsharesisnowonlyhalfaslarge.Therefore,EPSincreasesby50%:

g