金融学讲义大纲及课后习题答案详解-十六章

CHAPTER16

Outline

16.1InternalversusExternalFinancing

16.2EquityFinancing

Intherealworldthereareanumberoffrictionsthatcan

Byreducingtaxcostsorthecostsofburdensomeregulations.

Byreducingpotentialconflictsofinterestamongvarious

stakeholdersinthefirm.

Byprovidingstakeholderswithfinancialassetsnototherwise

availabletothem.

Therearethreealternativemethodsusedinestimatingthenet

presentvalueofaninvestmentprojecttotakeaccountof

financialleverage:theadjustedpresentvaluemethod,the

flowstoequitymethod,andtheweightedaveragecostof

capitalmethod

SolutionstoProblemsatEndofChapter

Debt-EquityMix

1.DividoCorporationisanall-equityfinancedfirmwithatotal

marketvalueof$100million.Thecompanyholds$10millionin

cash-equivalentsandhas$90millioninotherassets.Thereare

1,000,000sharesofDividocommonstockoutstanding,eachwitha

marketpriceof$100.DividoCorporationhasdecidedtoissue$20

millionofbondsandtorepurchase$20millionworthofitsstock.

Whatwillbetheimpactonthepriceofitssharesandonthe

a.

wealthofitsshareholders?Why?

AssumethatDivido’sEBIThasanequalprobabilityofbeing

b.

$20million,or$12million,or$4million.Showtheimpactof

thefinancialrestructuringontheprobabilitydistributionof

earningspershareintheabsenceoftaxes.Whydoesthefact

thattheequitybecomesriskiernotnecessarilyaffect

shareholderwealth?

SOLUTION:

InanM&Mfrictionlessenvironment,wheretherearenotaxes

a.

andcontractsarecostlesstomakeandenforce,thewealthof

shareholdersisthesamenomatterwhatcapitalstructurethe

firmadopts.Insuchanenvironment,neitherthestockprice

norshareholders’wealthwouldbeaffected.Intherealworld

Divido’smanagementmightbeabletocreateshareholdervalue

byissuingdebtandrepurchasingsharesintwoways:

Byreducingtaxcosts

Byreducingthefreecashflowavailabletomanagementand

exposingitselftogreatermarketdiscipline.

TheformulaforEPSwithoutdebtis:

b.

EPS

=EBIT

1,000,000shares

allequity

Theinterestpaymentswillbe$1.2millionperyear(.06x$20

million)regardlessoftherealizedvalueofEBIT.Thenumber

ofsharesoutstandingafterexchangingdebtforequitywillbe

800,000.EPSwithdebtistherefore:

EPS

withdebt

=NetEarnings=EBIT–$1.2million

800,000shares800,000shares

EBIT

ProbabilityDistributionofDivido’sand

EPS

Stateof

the

Economy

EBITAllequityWith$20millionofdebt

financing

EPS

Net

EPS

(1millionEarnings

shares)

(800,000

shares)

Bad$4million

$4pershare$2.8$3.50per

million

10.8

business

Normal

share

13.50

12

20

12

12

20

business

Good

18.8

10.8

23.50

13.50

$8.16

business

Mean

12

Standard

deviation

$6.53

Althoughthesharesofstockbecomeriskierwithdebtfinancing,

theexpectedearningspersharegoup.Inafrictionless

financialenvironment,theneteffectistoleavethepriceof

thestockunaffected.

Leasing

2.PlentileaseandNoleasearevirtuallyidenticalcorporations.

TheonlydifferencebetweenthemisthatPlentileaseleasesmost

ofitsplantandequipmentwhereasNoleasebuysitsplantand

equipmentandfinancesitbyborrowing.Compareandcontrast

theirmarket-valuebalancesheets.

SOLUTION:

Market-ValueBalanceSheetsofNoleaseandPlentilease

Corporations

NoleaseCorporation

a.

Assets

Liabilities

and

Shareholders’

Equity

Plantand

Bonds

equipment

Otherassets

Total

Equity

Total

PlentileaseCorporation

b.

Assets

Liabilities

and

Shareholders’

Equity

Plantand

equipment

Otherassets

Total

Lease

Equity

Total

Themaindifferencebetweenthebondsandtheleaseasaform

ofdebtfinancingiswhobearstheriskassociatedwiththe

residualmarketvalueoftheleasedassetattheendofthe

termofthelease.SinceNoleaseCorporationhasboughtits

equipment,itbearsthisrisk.InPlentilease’scase,however,

itisthelessorthatbearsthisresidual-valuerisk.

PensionLiabilities

3.EuropensandAsiapensarevirtuallyidenticalcorporations.

TheonlydifferencebetweenthemisthatEuropenshasa

completelyunfundedpensionplan,andAsiapenshasafullyfunded

pensionplan.Compareandcontrasttheirmarket-valuebalance

sheets.Whatdifferencedoesthefundingstatusofthepension

planmaketothestakeholdersofthesetwocorporations?

SOLUTION:

BalanceSheetsofAsiapensandEuropensCorporations

AsiapensBalanceSheet

a.

Assets

Liabilities

and

Shareholders’

Equity

Operating

assets:Plant,

equipment,

etc.

Bonds

Pension

liability

Shareholders’

Equity

Pension

assets:

stocks,bonds,

etc.

Total

Total

EuropensBalanceSheet

b.

Assets

Liabilities

and

Shareholders’

Equity

Operating

Pension

assets:Plant,

liability

equipment,

etc.

Shareholders’

Equity

Total

Total

Asiapenshasfundeditspensionplanbyissuingbondsand

investingthefundsraisedinasegregatedpoolofpensionfund

assets.Thesepensionassetstaketheformofadiversified

portfolioofstocksandbondsissuedbyothercompaniesand

serveascollateralforthepensionbenefitspromisedby

Asiapenstoitsemployees.InthecaseofEuropens,thereisno

segregatedpoolofpensionassets.Thepensionpromisesof

Europensarebackedbytheassetsofthecompanyitself.

Therefore,theemployeesofAsiapensaremoresecureabout

receivingtheirpromisedpensionbenefits,sincethebenefits

arecollateralizedbyamorediversifiedportfolioofassets.

Inthecaseofbothcompanies,however,anyunfundedpension

liabilityreducesshareholdersequity.

4.ComfortShoeCompanyofEnglandhasdecidedtospinoffits

TangoDanceShoeDivisionasaseparatecorporationintheUnited

States.TheassetsoftheTangoDanceShoeDivisionhavethesame

operatingriskcharacteristicsasthoseofComfort.Thecapital

structureofComforthasbeen40%debtand60%equityintermsof

marketingvalues,andisconsideredbymanagementtobeoptimal.

TherequiredreturnonComfort’sassets(ifunlevered)is16%

peryear,andtheinterestratethatthefirm(andthedivision)

mustcurrentlypayontheirdebtis10%peryear.

SalesrevenuefortheTangoShoeDivisionisexpectedtoremain

indefinitelyatlastyear’slevelof$10million.Variablecosts

are55%ofsales.Annualdepreciationis$1million,whichis

exactlymatchedeachyearbynewinvestments.Thecorporatetax

rateis40%.

a.HowmuchistheTangoShoeDivisionworthinunleveredform?

b.IftheTangoShoeDivisionisspunoffwith$5millionindebt,

howmuchwoulditbeworth?

c.WhatrateofreturnwilltheshareholdersoftheTangoShoe

Divisionrequire?

d.Showthatthemarketvalueoftheequityofthenewfirmwould

bejustifiedbytheearningstotheshareholders.

SOLUTION:

TheunleveredfreecashflowfortheTangoShoeDivisionwould

a.

be(in$millions):

Sales:

$10.0

Var.Cost:

5.5

1.0

Depreciation

TaxableIncome

Taxes(@40%)

After-TaxIncome

Depreciation

Investment1.0

FreeCashFlow

$3.5

1.4

$2.1

1.0

$2.1million

Unlevered,Tangoisworth:$2.1million/0.16=$13.125

million

IfTangohad$5millionofdebt,itstotalvaluewouldbe:

MarketValuewithDebt=MarketValuewithoutDebt+PVof

InterestTaxShield

b.

x

V=V+TB

L

U

x

=$13.125+(.45)=$15.125million

TangoEquity=$15.125$5=$10.125million

Tango’scostofequitycapitalwouldbe.1778

k=k+(1-T)(k-r)D/E=.16+(1-.4)(.16-.10)x5/10.125

e

=.1778

c.

d.

Thevalueoftheequityshouldbethepresentvalueofthe

expectednetincomediscountedattherequiredrateofreturn

onequity.Theexpectednetincomewillbetheunleveredcash

flowlesstheafter-taxcostoftheinterestofthedebt:

$2.1-(.6)(.1x$5)=$2.1-$.3=$1.8millionperyear

S=$1.8million/.1778=$10.125million

5.Basedontheaboveproblem,SupposethatFoxtrotDanceShoes

makescustomdesigneddanceshoesandisacompetitorofTango

DanceShoes.Foxtrothassimilarrisksandcharacteristicsas

Tangoexceptthatitiscompletelyunlevered.FearfulthatTango

DanceShoesmaytrytotakeoverFoxtrotinordertocontrol

theirnicheinthemarket,Foxtrotdecidestoleverthefirmto

buybackstock.

Iftherearecurrently500,000sharesoutstanding,whatisthe

a.

valueofFoxtrot’sstock?

HowmanysharescanFoxtrotbuybackandatwhatvalueifit

b.

iswillingtoborrow30%ofthevalueofthefirm?

Whatifitiswillingtoborrow40%ofthevalueofthefirm?

c.

ShouldFoxtrotborrowmore?

d.

SOLUTION:

Currentpricepershare:$13.125million/.5millionshares=

a.

$26.25pershare

@30%debt

b.

Amounttoborrow:30%of13.125million=$3.9375million

PVofTaxShield=.4x$3.9375million=$1.575million

Valueofleveredfirm=$13.125+$1.575=$14.7million

Valueofequityinleveredfirm=$14.7million$3.9375

million=$10.7625million

TocomputethenumberofsharesFoxtrotcanrepurchase,weneed

toknowthepricepershare.

IfFoxtrotcanrepurchasesharesattheexistingpriceof

$26.25thenthenumberofsharesretiredwillbe

$3.9375million/$26.25pershare=.15millionshares.This

willleave.35millionsharesoutstanding,andthepriceof

eachsharewillbe$10.7625million/.35million=$30.75.

IfthePVofthetaxshieldgetsincorporatedinthepriceof

thesharesbeforetherepurchase,thenthepriceoftheshares

willincreaseby$1.575million/.5million=$3.15.Sothe

priceoftherepurchasedshareswillbe

$26.25+$3.15=$29.40.

Thenthenumberofsharesretiredwillbe$3.9375

million/$29.40pershare=133,929shares.Thiswillleave

366,071sharesoutstandingeachwithapriceof$29.40.

@40%debt

c.

Amounttoborrow:40%of$13.125million=$5.25million

PVofTaxShield=.4x$5.25million=$2.1million

Valueofleveredfirm=$13.125+$2.1=$15.225million

Valueofequityinleveredfirm=$15.225million$5.25

million=$9.975million

IfFoxtrotcanrepurchasesharesattheexistingpriceof

$26.25thenthenumberofsharesretiredwillbe

$5.25million/$26.25pershare=.2millionshares.Thiswill

leave.3millionsharesoutstanding,andthepriceofeach

sharewillbe$9.975million/.3million=$33.25.

IfthePVofthetaxshieldgetsincorporatedinthepriceof

thesharesbeforetherepurchase,thenthepriceoftheshares

willincreaseby$2.1million/.5million=$4.20.Sotheprice

oftherepurchasedshareswillbe

$26.25+$4.20=$30.45.

Thenthenumberofsharesretiredwillbe$5.25million/$30.45

pershare=172,414shares.Thiswillleave327,586shares

outstandingeachwithapriceof$30.45.

d.Foxtrot’smanagementmusttradeoffthetaxsavingsdueto

additionaldebtfinancingagainstthecostsoffinancial

distressthatrisewiththedegreeofdebtfinancing.

6.Hanna-CharlesCompanyneedstoaddanewfleetofvehiclesfor

theirsalesforce.Thepurchasingmanagerhasbeenworkingwitha

localcardealershiptogetthebestvalueforthecompanydollar.

Aftersomenegotiations,alocaldealerhasofferedHanna-Charles

twooptions:1)athreeyearleaseonthefleetofcarsor2)15%

offthetoptopurchaseoutright.Option2wouldcostHanna-

Charlescompanyabout5%lessthantheleaseoptionintermsof

presentvalue.

Whataretheadvantagesanddisadvantagesofleasing?

a.

WhichoptionshouldthepurchasingmanageratHanna-Charles

b.

pursueandwhy?

SOLUTION:

Advantages:

a.

Thelessorbearsalltheresidual-valuerisk

TaxBenefits

Nodisposalconcerns(orresale)whenlifeofequipmentis

expended.

Disadvantages:

Noownershipwhilemaintainingmaintenanceresponsibility

LeaseorBuy:

b.

Hanna-Charlescompanyshouldlease.Althoughtheymayspend

morewiththelease,theydonotbeartheresidual-valuerisk.

7.HavemandNeedemcompaniesareexactlythesamedifferingonly

intheircapitalstructures.Havemisanunleveredfirmissuing

onlystockswhereasNeedemissuesstocksandbonds.Neitherfirm

payscorporatetaxes.Havempaysoutallofitsyearlyearnings

intheformofdividendsandhas1millionsharesoutstanding.

Itsmarketcapitalizationrateis11%andthefirmiscurrently

valuedat$180million.Needemisidenticalexceptthat40%of

itsvalueisinbondsandhas500,000sharesoutstanding.

Needem’sbondsareriskfreeandpayacouponof9%peryearand

arerolledovereveryyear.

WhatisthevalueofNeedem’sshares?

a.

Asaninvestorforecastingtheupcomingyear,youexamine

b.

HavemandNeedemusingthreepossiblestatesoftheeconomy

thatareallequallylikely:normal,bad,andexceptional.

Assumingtheearningswillbethesame,onehalf,andoneand

ahalfrespectively,produceatablethatshowstheearnings

andtheearningspershareforbothHavemandNeedeminall

threescenarios.

SOLUTION:

Needemhas$72millionindebtand$108millioninequity.

a.

Sincethereare500,000shares,thevalueofeachshareis$216.

ExpectedEBIT=$180millionx11%=$19.8millionperyear

b.

InterestexpenseforNeedem=$72millionx.09=$6.48

millionperyear

Stateof

EBIT

Havem

Needem

theEconomy

EPS

Net

EPS

(1millionEarningsb

shares)

(500,000

shares)

Bad

$9.9

19.8

29.7

$9.90/share$3.42millio$6.84/share

Normal

Exceptional

Mean

19.80

29.70

19.80

13.32

23.22

26.64

46.44

26.64

Std.Dev.

8.08

16.17

EBIT–InterestExpense

b

8.Usingtheforegoingexample,letusnowassumethatHavemand

Needemmustpaytaxesattherateof40%annually.Giventhesame

distributionofpossibleoutcomesaspreviously:

Whatarethepossibleafter-taxcashflowsforHavemand

a.

Needem?

Whatarethevaluesoftheshares?

b.

Ifonewasnotriskaverse,whichcompanywouldthatperson

c.

investin?

SOLUTION:

After-taxCF=(1TaxRate)EBIT=Netincome

a.

Havem

Netincome

=(1TaxRate)(EBITInt.Pmt.)

Needem

CF=(1TaxRate)(EBIT)+TaxRatexInt.Pmt

Needem

CF

(bad)=(.60)$9.9+(.40)x6.48=$8.532million

Needem

CF(normal)=(.60)$19.8+(.40)x6.48=$14.472million

Needem

CF

(except.)=(.60)$29.7+(.40)x6.48=$20.412million

Needem

Stateofthe

Economy

Havem

Needem

After-TaxCashTaxShieldonAfter-TaxCash

Flow

Debt

Flow

Bad

Normal

Exceptional

$5.94million$2.592million$8.532million

11.88million$2.592million$14.472million

17.82million$2.592million$20.412million

TheequityofHavemwillbeworth$11.88million/.11=$108

millionor$108pershare

b.

ThetotalvalueofNeedem’sdebt+equitywillbe$108,000,000

+.4x$72,000,000=$136.8