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10.4 TAXES
325
4.05%=
(1−τ
marginal
)
.
5.38% ⇔τ
marginal
= 1−
4.05%
5.38%
≈24.7%
r
aftertax
=(1−τ
marginal
)
.
r
beforetax
⇔τ
marginal
=1−
r
aftertax
r
beforetax
Anyinvestorwithamarginalincometaxrateabove24.7%(suchasahigh-income
retail investor)should prefer thetax-exempt bond. Anyinvestorwitha marginal
incometaxratebelow24.7%(suchasatax-exemptpensionfund)shouldpreferthe
taxablebond.Wheneconomiststhinkmoregenerallyabouthowassetsarepriced,
theyalsousethistaxrateastheeffectiveeconomy-wideone.
solvenow!
Q10.18 Ifyourtaxrateis20%,whatinterestratedoyouearninafter-taxterms
ifthebefore-taxinterestrateis6%?
Q10.19 Ifthemarginalinvestor’staxrateis30%andtaxablebondsofferarate
ofreturnof6%,whatrateofreturndoequivalentmunibondsoffer?
Q10.20 OnMarch28,2008,tax-exemptAAA-rated5-yearmunibondstraded
atayieldof3.04%.Corporate5-yearAAAbondstradedat4.14%.What
wasthemarginalinvestor’staxrate?
10.4C TAXESINNETPRESENTVALUES
Again,aswithtransactioncosts,youshouldtakecaretoworkonlywithcashinthe
Youshouldonlycareabout
yourownafter-taxcashflows.
sameunits—here,thismeanscashthatyoucanuseforconsumption.Again,itshould
notmatterwhetheryoureceive$100thathastobetaxedat50%orwhetheryou
receive$50thatdoesnothavetobetaxed.AsfarasNPVisconcerned,youshould
computeeverythinginafter-taxdollars.Thisincludesallcashflows,whetherthey
occurtodayortomorrow,andwhethertheyareinflowsoroutflows.
IMPORTANT: DoallNPVcalculationsinafter-taxmoney.Thisappliesbothtothe
expectedcashflowsandtotheopportunitycostofcapital.
Unfortunately,youcannotsimplydiscountbefore-taxcashflowswiththebefore-
Youmustcomputetheafter-
taxopportunitycostof
capital.
taxcostofcapital(wrong!)andexpecttocomeupwiththesameresultaswhenyou
discountafter-taxcashflowswithafter-taxcostsofcapital(right!).
Forexample,consideraprojectthatcosts$10,000andreturns$13,000nextyear.
Youropportunitycostofcapital
dependsonyourowntaxrate.
Yourtaxrateis40%,and1-yearequivalentlyriskybondsreturn25%iftheirincome
istaxableand10%iftheirincomeisnottaxable.First,youmustdecidewhatyour
opportunity cost ofcapital is. Section10.4B showed that ifyouinvest$100into
taxables,youwillreceive$125buttheIRSwillconfiscate($125−$100)
.
40%=
$10.Youwillthusown$115inafter-taxwealth.Tax-exemptsgrowonlyto$110,so
youpreferthetaxablebond—itisthetaxableequallyriskybondthatdeterminesyour
opportunitycostofcapital.Yourequivalentafter-taxrateofreturnistherefore15%.
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326
CHAPTER10
MARKETIMPERFECTIONS
This15%isyourafter-tax“opportunity”costofcapital—itisyourbestalternativeuse
ofcapitalelsewhere.
Returntoyour$10,000projectnow.Youknowthatyourtaxableprojectreturns
Youmustdiscountyourafter-
taxexpectedcashflowswith
yourafter-taxopportunitycost
ofcapital.
30%taxable($3,000),whiletaxablebondsreturn25%($2,500),soNPVshouldtell
youtotakethisproject.UncleSamwillconfiscate40%
.
$3,000=$1,200,leaving
youwith$11,800.Therefore,theNPVofyourprojectis
NPV=−$10,000+
$11,800
1+15%
≈$260.87
after-taxcashflows
after-taxcostofcapital
NPV=
C
0
+
E(
C
1
)
1+E(˜r
1
)
Itmakesintuitivesense:Ifyouhadinvestedmoneyintothebonds,youwould
Hereareincorrectshortcut
attempts,workingwith
before-taxcashflowsand/or
before-taxcostsofcapital.
haveendedupwith$11,500.Instead,youwillendupwith$11,800,the$300differ-
enceoccurringnextyear.Discounted,the$261seemsintuitivelycorrect.Ofcourse,
thereareaninfinitenumberofwaysofgettingincorrectsolutions,butrecognizethat
noneofthefollowingcalculationsthatusethebefore-taxexpectedcashflows(andtry
differentdiscountrates)givethesamecorrectresult:
NPV=−$10,000+
$13,000
1+25%
=
$400
taxablecashflows
taxablebondcostofcapital
NPV=−$10,000+
$13,000
1+15%
≈$1,304.35
taxablecashflows
after-taxcostofcapital
NPV=−$10,000+
$13,000
1+10%
≈$1,818.18
taxablecashflows
municostofcapital
Youhavenochoice:Youcannot workwithbefore-taxexpectedcashflows.Instead,
youneedtogothroughtheexerciseofcarefullycomputingafter-taxcashflowsand
discountingwithyourafter-taxopportunitycostofcapital.
Youknowthatcomputingafter-taxcashflowsisapain.Canyouatleastcompare
Insome,butnotall,situations,
youcancomparetwoprojects
basedontheirbefore-tax
NPVs.
twoequallytaxableprojectsintermsoftheirbefore-taxNPV?Ifoneprojectisbetter
thantheotherinbefore-taxterms,isitalsobetterinafter-taxterms?Ifyes,thenyou
couldatleastdorelativecapitalbudgetingwithbefore-taxprojectcashflows.This
mayormaynotwork,andhereiswhy.CompareprojectSAFE,whichcosts$1,000and
willprovide$1,500thisevening;andprojectUNSAFE,whichcosts$1,000andwill
provideeither$500or$2,500thiseveningwithequalprobability.Theexpectedpayout
isthesame,andthecostofcapitalispractically0%for1day.Ifyouareinthe20%
marginaltaxbracket,projectSAFEwillleaveyouwith$500intaxableearnings.The
IRSwillcollect20%
.
($1,500−$1,000)=$100,leavingyouwith+$400inafter-tax
netreturn.ProjectUNSAFEwilleithergiveyou$1,500or−$500intaxableearnings.
.
Iftheprojectsucceeds, youwouldsend$1,500
.
20%=$300totheIRS.Ifthe
projectfails,andifyoucanusethelossestooffsetgainsfromprojectselsewhere,
youwouldsend$500
.
20%=$100lesstotheIRS(becauseyourtaxableprofits
elsewherewouldbereduced).Inthiscase,projectsSAFEandUNSAFEwouldhave
thesameexpectedtaxcostsandafter-taxcashflows:1/2
.
$300+1/2
.
(−$100)=
$100.
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10.4 TAXES
327
.
Ifyoudropintoadifferenttaxbracket,say,25%,whenyour(additional)netincome
is$1,000higher,thenprojectUNSAFEbecomeslessdesirablethanprojectSAFE.For
the$1,500income,thefirst$500wouldstillcostyou$100intax,buttheremaining
$1,000wouldcostyou$250.Thus,yourproject’smarginaltaxobligationwouldbe
either$350or−$100,foranexpectedtaxburdenof$125.(Thesamelogicapplies
ifyourlosseswouldmakeyoufallintoalowertaxbracket—theUNSAFEproject
wouldbecomelessdesirable,becausethetaxreductionwouldbeworthless.)
.
IfyouhavenocapitalgainselsewherethatyoucanreducewiththeUNSAFEproject
capitalloss,thentheUNSAFEprojectwouldagainbeworthless.Corporationscan
askforataxrefundonoldgains,sotheunrealizedtaxlossfactorislessbindingthan
itisforindividuals,whomayhavetocarrythecapitallossforwarduntiltheyhave
sufficientincomeagaintouseit—ifever.
Thus,whetheryoucancompareprojectsonabefore-taxbasisdependsonwhether
youhaveperfectsymmetryintheapplicablemarginaltaxratesacrossprojects.Ifyou
do,thentheprojectthatismoreprofitableinafter-taxtermsisalsomoreprofitable
inbefore-taxterms.Thiswouldallowyoutosimplycompareprojectsbytheirbefore-
taxNPVs.Ifgainsandlossesfacedifferenttaxation—eitherbecauseoftaxbracket
changesorbecauseofyourinabilitytousethetaxlosseselsewhere—thenyoucannot
simplychoosetheprojectwiththehigherbefore-taxNPV.Youwillhavetogothrough
theentireafter-taxNPVcalculationsandcomparethem.
IMPORTANT: Youcanonlycompareprojectsonabefore-taxNPVbasisifthetax
treatmentisabsolutelysymmetric.Thisrequiresconsiderationofyouroverall
taxsituation.
Younowknowhowtodiscountprojectsinthepresenceofincometaxes.However,
Twomoretax-adjusting
corporatevaluationmethods,
WACCandAPV,unfortunately
havetowait.
youdonotyetknowhowtocomputetheproperdiscountrateforprojectsthatare
financedbydebtandequity,becausedebtandequityfacedifferenttaxconsequences.
Unfortunately,youwillhavetowaituntilChapter17beforewecandoagoodjob
discussingthetwosuitablemethods—calledAPVandWACC—tohandledifferential
taxationfordifferentcorporatesecurities.
solvenow!
Q10.21 Youhaveaprojectthatcosts$50,000andwillreturn$80,000in3years.
Yourmarginalcapitalgainstaxrateonthe$30,000gainwillbe37.5%.
Treasuriespayarateofreturnof8%peryear;munispayarateofreturn
of3%peryear.WhatistheNPVofyourproject?
Q10.22 Youareinthe33.3%taxbracket.Aprojectwillreturn$14,000in1
yearfora$12,000investment—a$2,000netreturn.Theequivalenttax-
exemptbondyields15%,andtheequivalenttaxablebondyields20%.
WhatistheNPVofthisproject?
Q10.23 It isnotuncommonfor individualsto forgetabouttaxes, especially
wheninvestmentsaresmallandpayoffsarelargebutrare.Sayyouare
inthe30%taxbracket.IstheNPVofa$1lotteryticketthatpaysoff
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328
CHAPTER10
MARKETIMPERFECTIONS
taxablewinningsof$10millionwithachanceof1in9millionpositive
ornegative?Howwoulditchangeifyoucouldpurchasethelotteryticket
withbefore-taxmoney?
10.4D TAXTIMING
Inmanysituations, theIRSdoesnotallowreinvestmentoffundsgeneratedbya
Itisoftenbetterifyouare
taxedonlyattheveryend,
ratherthanintheinterim.
projectwithoutaninterimtaxpenalty.Thiscanbeimportantwhenyoucompareone
long-terminvestmenttomultipleshort-terminvestmentsthatareotherwiseidentical.
Forexample,considerafarmerinthe40%taxbracketwhopurchasesgrain(seed)that
costs$300andthattriplesitsvalueeveryyear.
.
IftheIRSconsidersthisfarmtobeonelong-term2-yearproject,thefarmercanuse
thefirstharvesttoreseed,so$300seedturnsinto$900in1yearandthenintoa
$2,700harvestin2years.UncleSamconsiderstheprofittobe$2,400andsocollects
taxesof$960.Thefarmerisleftwithanafter-taxcashflowof$2,700−$960=
$1,740.
.
IftheIRSconsidersthisproductiontobetwoconsecutive1-yearprojects,thenthe
farmer’safter-taxprofitsarelower.Heendsupwith$900attheendofthefirst
year. UncleSamcollects40%
.
($900−$300)=$240, leaving thefarmer with
$660.Replanted,the$660growsto$1,980,ofwhichtheIRScollectsanother40%
.
($1,980−$660)=$528.Thefarmerisleftwithanafter-taxcashflowof$1,980−
$528=$1,452.
Thediscrepancybetween$1,740and$1,452isduetothefactthatthelong-term
projectcanavoidtheinterimtaxation.Similarissuesarisewheneveranexpensecan
bereclassifiedfrom“reinvestedprofits”(taxed,ifnotwithsomecreditatreinvestment
time)into“necessarymaintenance.”
solvenow!
Q10.24 Assumeyourmarginaltaxrateis25%.AssumethattheIRSwouldtax
paymentsonlywhenmade.(Sorry,inreallife,theIRSnowadaysdoes
taxzero-bondsevenwhentheydonotyetpayoutanything.)
(a)Whatisthefuturevalueofa10-yearzero-bondpricedataYTMof
10%?HowmuchdoestheIRSgettokeep?
(b)What isthefuturevalueofa10-yearannuallevel-couponbond
pricedataYTMof10%,assumingthatcouponsareimmediately
reinvestedatthesame10%?
(c)Whatwoulditbeworthtoyoutodaytobetaxedonlyattheend
(viathezero-bond)andnotintheinterim(viathecouponbond)?
Whichisbetter?
10.5 ENTREPRENEURIALFINANCE
Nowthatyouunderstandhowtoworkwithmarketimperfections,forwhattypes
Forlargecompanies,aperfect
marketassumptionwithequal
borrowingandlendingratesis
reasonable.
offirmsdotheymattermost?Marketimperfectionsareprobablyjustmildforlarge,
publiclytradedcorporations.Thesetypesoffirmstypicallyfaceonlymodestinterest
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10.5 ENTREPRENEURIALFINANCE
329
rate spreadsbetweentheir (risky)borrowing g and lending rates.Of course, their
promisedborrowinginterestratesarealittlehigherthanwhattheycanreceivein-
vestingtheirmoneyinTreasurybonds.Yet,giventhattheystillhavesomepossibility
ofgoingbankrupt,largefirms’requiredexpectedborrowingcostsofcapitalareproba-
blyfairlyclosetotheexpectedratesofreturntheycouldearniftheyinvestedinbonds
withcharacteristicssimilartothebondsthattheythemselveshaveissued.Thus,large
publiccorporationscanoftenpretendtoliveinareasonablyperfectmarket.Thisalso
meansthattheyhavetheluxuryofseparatingtheirprojectchoicesfromtheirfinancial
needs.
➤
Altmanstudyofbond
defaultrates,Section6.2D,
p.148
Intheworldofindividuals,entrepreneurs,andsmallcompanies,however,itis
Forentrepreneurs,aperfect
marketassumptionis
problematic.
quiteplausiblethatthecostsofcapitalareoftenhigherthanequivalentexpectedsav-
ingsinterestrates.Infact,themostimportantdifferencebetween“ordinarycorporate
finance”and“entrepreneurialfinance”arethedegreetowhichtheircapitalmarkets
areperfect.Almostallentrepreneursfinditverydifficulttoconveycrediblytheirin-
tentandabilitytopaybackloans.Andanycreditthatentrepreneursreceiveisusually
alsoveryilliquid:Lenderscannoteasilyconvertitintocash,shouldtheneedarise.
Therefore,theydemandahighliquidityspread,too.Manyentrepreneursevenend
uphavingtoresorttofinancingprojectswithcreditcards,whichmaycharge1,000
basispointsormoreaboveTreasury.
Insum,smallfirmsoftenfaceextraordinarilyhighdifferentialsbetweenexpected
Theexpectedcostsofcapital
areoftenveryhighfor
entrepreneursneedingcapital.
borrowingandlendingrates.Entrepreneurs’highborrowingcostscanthusprevent
themfromtakingmanyprojectsthattheywouldhaveundertakeniftheyhadthe
moneyalreadyonhand.Cash-on-handcanbecomeaprimedeterminantofalltheir
decisions.Moreestablishedfirmsorwealthierentrepreneursshouldoptimallytake
moreprojectsthanpoorerentrepreneurs.Yes,theworldisnotfair.
However, becareful inthereal worldbeforeyoubelievetheclaimsofentre-
Becareful:Don’tbelieve
entrepreneurialclaims!Often,
highborrowingratesarejust
promised,notexpected.
preneurs.Entrepreneursalsotendtohavenotoriouslyoveroptimisticviewsoftheir
prospects. Evenventurecapitalists, , the e financing g vehiclefor manyhigh-tech en-
trepreneurialventures, which advertiserates ofreturnof30%per yearor more,
seemtohavemanagedtoreturnonlyacoupleofpercentagepointsabovetherisk-
freerateoverthelast30years.Adjustingforthecorrectdefaultratesmayactually
meanthatentrepreneursfaceonlyhighpromisedborrowingcosts,nothighexpected
borrowing costs. Thus, , thelarge e quoted spread betweenentrepreneurs’ borrow-
ingandlending rates, whichisreallyall that youcaneasily observe, likely hasa
largecomponentthatisduenottoinformationdisagreementsbutsimplytocredit
risk.
Thisissueofhowtodealwithmarketimperfectionsforsmallfirmsalsoarises
Thecourtsapplyanadhoc
discounttothevaluesof
entrepreneurialcompanies
basedontheirlimitedaccess
tocapital.
frequentlyinthecourts,whereacost-of-capitalestimateisnecessarytocomputethe
valueforanentrepreneurialenterprise—forexample,forpurposesofassessingthein-
heritancetaxorresolvingdisputesamongformerbusinesspartners.(Suchvaluation
servicesareanimportantrevenuebusinessformanyfinanceprofessorsandconsult-
ingfirms.)Ithasbecomecustomaryandlegallyacceptabletocomputefirstthevalue
ofanequivalentpubliclytradedbusinessorcompanyasifitfacedaperfectmarket,
andthentoapplya“privatediscount”ofaround10%to30%offirmvalueinorder
toreflectthelimitedaccesstocapital.Theamountofthisdiscountisadhoc,butitis
betterthannoattemptatall.
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330
CHAPTER10
MARKETIMPERFECTIONS
solvenow!
Q10.25 What arethetwo possiblereasonswhy entrepreneursoftenhaveto
financetheirprojectswithcreditcards,whichcanchargeinterestrates
ashighas1,000basispointsaboveTreasury?
10.6 DECONSTRUCTINGQUOTEDRATESOF
RETURN—LIQUIDITYANDTAXPREMIUMS
InSections6.2Cand9.3A,youlearnedthatyoucoulddecomposequotedratesof
➤
Section6.2C,
“DeconstructingQuoted
RatesofReturn—Timeand
DefaultPremiums,”p.147
➤
Section9.3A,
“DeconstructingQuoted
RatesofReturn—Risk
Premiums,”p.254
returnintoatimepremium,adefaultpremium,andariskpremium.Marketimper-
fectionscancreateadditionalpremiums.
PromisedRateofReturn=TimePremium+DefaultPremium
+RiskPremium+ImperfectMarketPremiums
ExpectedRateofReturn=TimePremium+RiskPremium

providedbytheCAPM
+ImperfectMarketPremiums
Quantifyingimperfectmarketpremiumsisnoteasy,butwewilltryanyway.Un-
fortunately,thereisnotmuchthatcanbesaidaboutoneoftheimperfectmarket
premiums—thepremiumcompensatingfordifferencesinopinions.Thenatureof
informationdisagreementsisthattheyareidiosyncratic.Thisdoesnotmeanthat
theyareunimportant.Asnotedearliertheycanbesolarge,eveninfinancialmar-
kets,thattheymaydestroyafinancialmarket’sviability.Fortunately,theotherthree
imperfections—taxes,transactioncosts,andshallowmarkets—createpremiumsthat
areoftenalittleeasiertoquantifythanthepremiumassociatedwithinformationdis-
agreements.
Taxdifferencesareoftenmodestacrossassetsinthesameclass.However,when
Taxpremiumsareusually
“investmentclass”similar.
thereareassetsthataretreateddifferentlyfromataxperspective,theonewiththe
worsetreatmenthastoofferahigherrateofreturn.Forexample,municipalbonds
areexcludedfromfederaltaxation.Therefore, non-municipalbondshavetooffer
ahigherrateofreturnrelativetothesetax-exemptbonds.Similarly,unlikefederal
Treasurybonds,theholdersofcorporatebondsaresubjecttostateincometaxes.
ThismeansthatcorporatebondsneedtopayapremiumrelativetoTreasuries—a
taxpremium.
Transactioncostsanddeep marketsalsoplayimportantroles.Theresulting
Letmeexpandtheimperfect
marketpremiumintoits
componentpremiums.
premiumsareoftenlumpedunderthegeneralterm“liquiditypremiums.”Theidea
isthat,givenachoicebetweenaveryliquidsecuritythatyoucanresellinaninstant
tomanydifferentinvestorsincaseyouneedmoneyandaveryilliquidsecurity,you
willdemandanextrarateofreturntobuythelessliquidone.Wecanthusextendour
earlierpremiumsanalysistothefollowing:
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10.6 DECONSTRUCTINGQUOTEDRATESOFRETURN—LIQUIDITYANDTAXPREMIUMS
331
PromisedRateofReturn=TimePremium+DefaultPremium+RiskPremium
+LiquidityPremium+TaxPremium
ActualEarnedRate=TimePremium+DefaultRealization+RiskPremium
+LiquidityPremium+TaxPremium
ExpectedRateofReturn=TimePremium+ExpectedRiskPremium
+LiquidityPremium+TaxPremium
Again, therecouldbeotherpremiumsthatshould go intothisformula, such as
informationpremiumsorbondcontract featurepremiums.Iomitthembecause
Idon’thaveempiricalevidencetoshowyou.Inaddition, ourconceptofaclean
decompositionisalittleproblematicinitself,becausethesepremiumsoverlap.For
example,itisquitepossiblethattherearecovariance-riskaspectstoliquidity.(Inother
words,itcouldbethatliquidityspreadsincreasewhenthemarketgoesdown,which
wouldmeanthattheyhaveapositivemarketbeta.)Thus,apartofthequotedspread
couldbeconsideredeitherasariskpremiumorasaliquiditypremium.Nevertheless,
thebasicdecompositionintheaboveformulasisuseful.
Let’sgobacktocorporatebonds.YoualreadylearnedinSection6.2Dthatmany
Corporatebonds:CAPM-type
marketcovarianceriskmay
matterforjunkbonds,butit
wouldbetrivialforAAA-grade
bonds.
➤
Section6.2D,“Credit
RatingsandDefaultRates,”
p.148
corporatebondshavesignificantdefaultrisk,whichmeansthattheyhavetoofferade-
faultpremium(relativetoTreasuries,ofcourse).Letmenowtellyouthat,depending
oncreditrating,theyhavemarketbetasbetweenabout0.1(investment-gradebonds)
and0.5(junkbonds).Thismeansthatjunkbondsmayhavetoofferameaning-
fullylargepremiumtocompensateinvestorsformarketrisk,butforinvestment-grade
bonds,anybetapremiumwouldbetrivial.
However,manycorporatebondsaredifficulttoresellquickly—mosthavetobe
Liquiditypremiumscouldbe
highforalltypesofrisky
bonds.Taxpremiumsare
probablysimilaramongall
taxablebonds.
tradedover-the-counter,andnotonanorganizedexchange.Therefore,theyhaveto
offertheirbuyersaliquiditypremium.Finally,corporatebondsaresubjecttostate
incometaxes.Thismeansthattheyhavetoofferataxpremium.
IntheEdAltmanstudyyoufirstsawinSection6.2D,thehistoricalaveragerates
Differencesinexpectedrates
ofreturnbycreditrating
suggestthatriskierandless
liquidbondsearnmorethan
saferbonds—butnotasmuch
moreastheyseemtopromise.
ofreturnoncorporatebondsfrom1971to2003wereasfollows:
Thetypicalinvestment-gradebondpromisedabout200basispointsabovetheequiv-
alentTreasurybond.However,investorsendedupwithonlyabout20–40basis
pointsabovetheTreasury.Thus,about170basispointswasthedefaultpremium.
Thetypicaljunkbondpromisedaspreadofabout500basispointsperannumabove
the10-yearTreasurybond.However,investorsendedupwithaspreadof“only”
about220basispoints.Thedefaultpremiumwasthereforeabout280basispoints.
Thissuggeststhatthedefaultpremiumisthemostimportantpremiuminstated
corporatebondyields.Onlyabout20–40basispointsforinvestment-gradeandabout
220basispointsforjunkbondsstillremaintobeexplainedbythesumoftherisk,
liquidity,andotherpremiums.
FrankdeJong,aprofessorattheUniversityofAmsterdam,producedasimilar
Figure10.1decomposes
expectedratesofreturn
intomarketrisk,liquidity
premiums,andtaxpremiums.
studyonbondsfrom1985to2003.UnlikeAltman,hedecomposedtheaverage(ex-
pected)ratesofreturnintoaliquidityriskpremium,amarketriskpremium,anda
taxpremium.Figure10.1showsthatabout40basispointsforAAAand250basis
332
CHAPTER10
MARKETIMPERFECTIONS
AAA
AA
A
Investment grade
Speculative grade
BBB
BB
B
CCC
300
250
200
150
100
50
0
Basis points above Treasury
Tax premium
Liquidity premium
To find the quoted yield:
For AAA/AA, add 
about 40 basis points 
in default premium.
To find the quoted yield: For 
B/CCC, add about 2,500 basis 
points in default premium.
Risk premium
These are estimates ofexpected yield premiums for long-termcorporate bonds. For highly rated bonds, the
liquidity and tax premiums are muchlarger than the risk premium.For very low-ratedbonds, the liquidity
premiumbecomesrelativelymoreimportant,followedbytheriskpremiumandthen thetax premium.
To obtain stated (quoted) bondyields,you would haveto add thedefaultpremium.The timepremiumhas
beentakenoutbecauseallspreadsarerelativetotheprevailing time-equivalentTreasuryyield.Forexample,the
averageAAA bondwouldhavequoted7.2%whentheaverageTreasury bondyielded6%.Thedefaultpremium
wouldhaveaddedabout40basispoints,withtheremaining80basispointshaving beencompensationfor risk,
liquidity,andtaxes.Source:DeJongand Driessen,2005.Reprinted withpermissionoftheauthors.
FIGURE 10.1 1 TheComponentsofExpectedRatesofReturninCorporateBonds,1985–2003
points for CCC bonds were pure default premiums that you would not have earned
on average. With betas of around 0.1, the market risk premium was negligibly small
for AAA and AA bonds, but then was higherfor CCC-rated bonds, accounting foras
muchas1%yieldperyear.Theliquidity premium wasabout 50basispointsforhighly
rated bonds,and100–150basispointsforjunkbonds.Incidentally,manyinstitutional
investors are only allowed to hold investment-grade bonds. Thus, dropping from in-
vestment grade to speculative grade incurs a large liquidity penalty. You can see this
in the sudden and unusually steep rise in yield for BB and B bonds. Finally, the state
income tax premium was about 20–30 basis pointsfor all bonds, except for the CCC
bonds(which may simply be a data glitch).
solve now!
Q10.26 Howimportantarethevariouspremiumsforinvestment-gradebonds
and junkbonds? (Omitthetimepremium.)
10.7 MULTIPLE EFFECTS: HOW TO WORK NOVEL
PROBLEMS
Of course, in the messy real world, you can suffer many problems (such as inflation,
Life istough—it does not
alwaysoffersimplesolutions.
➤
Inflation,Section5.2,p.97
transaction costs,disagreements,solepotential buyers, and taxes) all at once, not just
in isolation. In fact, there are so many possible real-world problems that no one can
possiblygive you a formula for each one. Thus, it isimportant that you approach the
real world keeping amultitudeofissues in mind.
10.7 MULTIPLE EFFECTS: HOW TOWORK NOVEL PROBLEMS
333
1. Ask yourself in a given situation whether the assumption of a perfect market is
If you get lucky, you
mayget good estimates
ignoringmarketinefficiencies
altogether.Adjust a little
maybejustintuitively.
reasonablyappropriate. For example,in the case oflargeand possiblytax-exempt
companies, you may consider it reasonable to get away with assuming a perfect
market, and justworkout the“perfectmarket”answer—asimpleNPV,for exam-
ple. Then think about the direction in which market imperfections would push
you, judge the magnitude, and make an intuitive adjustment. You can thereby
often work out a good answer without the enormous complicationsthat the per-
fectly correct answer would require.
2. If you concludethat you area long way from home (i.e., from a perfect market),
Youmustlearnhow to think
foryourself.I cannow only
teachyouthemethod,notthe
solution.
then you must first determine which market imperfections are most important.
Thenyou mustworkouta good solution byyourself.Ifyouhad hopedfortheone
magicbulletthat tells you how tosolveeverydifferentkind of problem you might
encounter, I have to disappoint you.Therearejust toomany possibilities, and the
taskisoften hard.Probablythebestwaytoanswersuchnewandthorny questions
is to internalizethemethod of “thinking by numerical example.” You really need
to become able to workout formulasfor yourself when you need them.
10.7A SOLVING A PROBLEM WITH INFLATION AND TAXES
For example, let’s see how you could approach a situation with both taxes and in-
Now workanexampleofhow
bothtaxesandinflationcould
interact.
flation. Always start by making up some numbers you find easy to work with. Let’s
say you are considering an investment of $100. Further, assume you will earn a 10%
rate of return on your $100 investment and Uncle Sam will take τ = 40% (or $4 on
your $10 return). Therefore, you get $110 before taxes but end up with only $106 in
nominal terms. What you havejust calculated is
$100
.
[1 + 10%
.
(1 − 40%)]
=$106
C
0
.
1+ r
nominal,before tax
.
(1 − τ)
= C
1
Now you need to determine what your $106 is really worth, so you must introduce
inflation. Picksome round number, say, arate of π = 5% perannum. Consequently,
in purchasing power, the$106 isworth:
$106
1+ 5%
≈$100.95
C
1
1+ π
=
P
0
Your after-tax, post-inflation, real rate of return is $100.95/$100 − 1 = 0.95%.
Knowing the numerical result, you need to translate your numbers into a formula.
You computed
334
CHAPTER 10
MARKET IMPERFECTIONS
r
after tax, real
=
$100.95 − $100
$100
=
$100
.
[
1+10%
.
(1−40%)
]
1+5%
−$100
$100
=
10%
.
(1 − 40%) − 5%
1+ 5%
≈
0.95%
r
after tax, real
=
P
0
−C
0
C
0
=
C
0
.
[
1+r
nominal,beforetax
.
(1−τ)
]
1+π
−C
0
C
0
=
r
nominal,before tax
.
(1 − τ) − π
1+ π
(10.1)
This is, of course, not a formula that anyone remembers. However, it is a useful
illustration of how you should approach and simplifycomplex questions—numerical
examplefirst, formulasecond.
Taxes on Nominal Returns?
Hereisan interesting question: Ifthereal rateofreturn remainsconstant, doesit help
If therealinterest ratestays
constant,doesinflation hurt
an investor? Yes, because
taxesareassessedonnominal
returns.
or hurt an investor if inflation goes up? Let’s assume that the real rate of return is a
constant 20%. If inflation is 50%, then the nominal rate of return is 80% (because
(1 + 50%)
.
(1 + 20%) = 1 + 80%): You get $180 for a $100 investment. Now add
income taxes to the tune of 40%. The IRS sees $80 in interest, taxes $32, and leaves
you with $48. Your $148 will thus be worth $148/(1 + 50%) ≈ $98.67 in real value.
Instead of a 20% increase in real purchasing power when you save money, you now
suffer a $98.67/$100 − 1 ≈ −1.3% change in real purchasing power. Despite a high
real interest rate, Uncle Sam ended up with more, and you ended up with less pur-
chasing powerthan you startedwith.Thereason isthatalthough UncleSam claimsto
tax onlyinterest gains,you can actuallylosein real termsbecausetheinterest taxison
nominal interest payments. Contrast this with the samescenario withoutinflation.In
this case, if the real rate of return were still 20%, you would have earned $20, Uncle
Sam would havetaxed you $8, and you could havekept $112 in real value.
IMPORTANT: Ifrealbefore-taxinterestratesremainconstant,becausetheIRStaxes
nominal returns, not real returns, you get the following results:
.
Higher inflation and interest rates hurt taxable savers.
.
Higher inflation and interest rates help taxable borrowers.
(Economic forces of demand and supply for capital may therefore have to
adjust, so that real rates of return increase when inflation increases.)
Formuch of postwar U.S. history, real rates of return on short-term government
bondshaveindeed been negative fortaxed investors.
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