CHAPTER15

COMPANYANALYSISANDSTOCKVALUATION

AnswerstoQuestions

1.ExamplesofgrowthcompanieswouldincludetechnologyfirmssuchasInteland

Microsoft.Thesefirmshaveexperiencedveryhighratesofreturnontotalassetsand

returnsonequitywhencomparedtomarketvalues.Theyretainhighpercentagesof

earningstofundsuperiorinvestmentprojects.StockissuesofIntelandMicrosofthave

beenconsideredgrowthstockssincetheirP/Eratiosareabovetheindustryaverage.

2.Acyclicalstockwouldbeanystockwithahighbetavalue.Examplesofhighbetastock

wouldincludestocksoftypicalgrowthcompaniesandsomeinvestmentfirms.Asto

whethertheissuingcompanyisacyclicalcompanywilldependonthespecificselection.

3.Thebiotechnologyfirmmaybeconsideredagrowthcompanybecause(1)ithasagrowth

rateof21percentperyearwhichprobablyexceedsthegrowthrateoftheoverall

economy,(2)ithasaveryhighreturnonequityand(3)ithasarelativelyhighretention

rate.However,sinceabiotechnologyfirmreliesheavilyoncontinuousresearchand

development,theabove-averageriskwillrequireahighrateofreturn.Therefore,itis

unlikelythatthestockwouldbeconsideredagrowthstockduetotheextremelyhigh

priceofthestockrelativetoitsearnings.

4.StudentExercise

5.StudentExercise

6.StudentExercise

7.StudentExercise

8.TheDDMassumesthat(1)dividendsgrowataconstantrate,(2)theconstantgrowthrate

willcontinueforaninfiniteperiod,and(3)therequiredrateofreturn(k)isgreaterthan

theinfinitegrowthrate(g).Therefore,theinfiniteperiodDDMcannotbeappliedtothe

valuationofstockforgrowthcompaniesbecausethehighgrowthofearningsforthe

growthcompanyisinconsistentwiththeassumptionsoftheinfiniteperiodconstant

growthDDMmodel.Acompanycannotpermanentlymaintainagrowthratehigherthan

itsrequiredrateofreturn,becausecompetitionwilleventuallyenterthisapparently

lucrativebusiness,whichwillreducethefirm'sprofitmarginsandthereforeitsROEand

growthrate.Therefore,afterafewyearsofexceptionalgrowth(aperiodoftemporary

supernormalgrowth)afirm'sgrowthrateisexpectedtodecline.Eventuallyitsgrowth

rateisexpectedtostabilizeataconstantlevelconsistentwiththeassumptionsofthe

infiniteperiod.

9.Price/BookValue(P/BV)isusedasameasureofrelativevaluebecause,intheory,

marketprice(P)shouldreflectbookvalue(BV).Inpractice,thetwocandiffer

dramatically.SomeresearchershavesuggestedthatfirmswithlowP/BVratiostendto

outperformthosewithhighP/BVratios.

10.AhighP/BVratiosuchas3.0canresultfromalargeamountoffixedassetsbeingcarried

athistoricalcost.Alowratio,suchas0.6,canoccurwhenassetsareworthlessthanbook

value,forinstance,badrealestateloansbybanks.

11.Theprice/cashflowratio(P/CF)hasbecomemorepopularbecauseoftheincreased

emphasisoncashbyvariousanalystsandbecauseoftheincreasedavailabilityofcash

flownumbers.Differencescouldresultfromdifferencesinnetincomeornon-cashitems.

12.Price/salesratiovariesdramaticallybyindustry.Forexample,thesalespersharefor

retailfirmsaretypicallyhigherthansalespersharefortechnologyfirms.Thereasonfor

thisdifferenceisrelatedtothesecondconsideration,theprofitmarginonsales.Theretail

firmshavehighsalespershare,whichwillcausealowP/Sratio,whichisconsidered

gooduntilonerealizesthatthesefirmshavelownetprofitmargins.

13.ThemajorcomponentsofEVAincludethefirm'snetoperatingprofitlessadjustedtaxes

(NOPLAT)anditstotalcostofcapital(indollars)includingthecostofequity.Apositive

EVAimpliesthatNOPLATexceedsthecostofcapitalandthatvaluehasbeenaddedfor

stockholders.

14.AbsoluteEVAmakesitdifficulttojudgewhetherafirmissucceedingrelativetopast

performanceorifthegrowthratecansupportadditionalcapital.Toovercomethose

shortcomingsandtofacilitatethecomparisonoffirmsofdifferentsize,itispreferableto

computeanEVAreturnoncapitalratio:EVA/CapitaL

15.WhiletheEVAmeasuresafirm'sinternalperformance,theMVAreflectsthemarket's

judgmentofhowwellthefirmperformedintermsofthemarketvalueofdebtandequity

vis-a-visthecapitalinvestedinit.Sincethelattermeasureisaffectedbyexternalfactors

suchasinterestrates,itisnotsurprisingthattheEVAandMVAshareaweak

relationship.

16.Thetwofactorsthatdetermineafirm'sfranchisevalueare(1)thedifferencebetweenthe

expectedreturnonnewopportunitiesandthecurrentcostofequityand(2)thesizeof

thosenewopportunitiesrelativetothefirm'scurrentsize.Intheabsenceofafranchise

value,anequitycostof11%wouldtranslateintoa(base)P/Eratioof9.1(or1/.11).

17.Aboveaverageearningsgrowthisacharacteristicofagrowthcompany.Additionally,a

ratherhighretentionrateof80percentimpliesthatthefirmwillhavetheresourcesto

takeadvantageofhigh-returninvestmentopportunities.Thesefactorslendsupportto

classifyingthefirmasagrowthcompany.However,asaresultofthehighretentionrate,

investorswillcontinuetorequireahighreturnoninvestment.Onlyifthefirmcan

continuetoachievereturnsaboveitscostofcapitalwillthefirmcontinuetobeclassified

asagrowthcompany.

18.Inaperfectlycompetitiveeconomy,ifothercompaniesseeaparticularfirmachieving

returnsconsistentlyaboverisk-basedexpectations,itisexpectedthattheseother

companieswillenterthatparticularindustryormarketandeventuallydrivepricesdown

untilthereturnsareconsistentwiththeinherentrisk.Inotherwords,thecompetition

wouldnotallowthecontinuingexistenceofexcessreturninvestmentsandsocompetition

wouldnegatesuchgrowth.Thecomputerindustryisagoodexampleofincreased

competitionresultinginlowerprofitmargins.Thetheoryimpliesthatintrulycompetitive

environments,atruegrowthcompanyisatemporaryclassification.

19.Becausethedividendmodelassumesaconstantrateofgrowthforaninfinitetimeperiod,

thepointisthatatruegrowthcompanyisearningarateofreturnaboveitscostofcapital

andthisshouldnotbepossibleinacompetitiveenvironment.Therefore,itisimpossible

foratruegrowthfirmtoexistforaninfinitetimeperiodinapurelycompetitive

environment.Changesinnon-competitivefactors,aswellaschangesintechnologywill

tendtocausevariousgrowthpatterns.Therefore,wewillconsiderspecialvaluation

modelsthatallowforfiniteperiodsofabnormalgrowthandforthepossibilityof

differentratesofgrowth.

20.Thegrowthdurationmodelattemptstocomputetheimpliedgrowthdurationforagrowth

firmgivendifferentialpastgrowthratesforthemarketandforthefirmandalso

alternativeP/Eratios.Thesemajorassumptionsofthemodelare:(1)equalriskbetween

thesecuritiescompared;(2)nosignificantdifferencesinthepayoutratioofdifferent

firms;and(3)thestockwiththehigherP/Eratiohasthehighergrowthrate.Whilethe

assumptionofequalriskmaybeacceptablewhencomparingtwolarger,well-established

firmstoeachotherortoamarketproxy,itisprobablynotavalidassumptionwhen

comparingasmallfirmtotheaggregatemarket.Likewise,theassumptionofno

significantdifferencesinpayoutratioscouldpresentaproblem.Forexample,many

growthfirmshavelowinitialpayoutratiosinordertouseretainedearningsforfuture

investmentprojects.Itmightbeinappropriatetocompareawell-establishedcompany

withanewstart-upfirmonthebasisofanequalpayoutratio.Finally,whilethemodel

assumesthatthestockwiththehigherP/Eratioshasthehighergrowthrate,inmany

casesyouwillfindthatthisisnottrue.

21.Theprojectedgrowthrateforthecompany(15%)isabovethatofthemarket(8%);

however,thegrowthcompanyalsohasalowerP/Eratiothantheaggregatemarket.This

impliesthatthestockofthegrowthcompanymightbeundervalued.Itwouldbe

necessarytoinvestigatethecompanyfurthertodetermineifthefirm'sstockisagrowth

stock.ItisstillnecessarytoestimatetheaveragepayoutratioandtheROEandits

componentsforboththefirmandtheaggregatemarketinordertomakeaproper

comparisonofthegrowthcompanytotheaggregatemarket.Thisshouldhelpyou

determineifitiscurrentlyatruegrowthcompanyandifthisperformancecanbe

sustained.

22.Walgreenseemstoillustrate“simplelong-rungrowth^^sincer>kandb>0.Itsfailureto

observeaconstantretentionrateprecludes“dynamicgrowth^^.

23.GMislikelyanexampleof“expansion“sincer=kandb>0.

24.CFAExaminationI(1993)

Thecomputationofbookvalueis:(assets-liabilities)/#ofshares

Accountingconventionscanaffectthiscomputationbyincreasingordecreasinganyof

thethreecomponents:assets,liabilities,ornumberofshares.

IncreasingorDecreasingAssets

?Accountants9useofhistoriccostdoesnotrecognizethereplacementvalueofassets

andis,therefore,notanaccuratemeasurementofanassefsvalue.Thisis

particularlytrueofrealestateassets.

?Severalassetswithrealeconomicvalueareignoredbyaccountants.Internally

developedgoodwill,managementexpertise,marketshare,andtechnological

innovationarejustafewoftheassetsignoredbyaccountants.

?Someassetsthatareonthebalancesheetshouldnotberecognized.Purchased

goodwillisanaccountingconventionthatisoftenplacedonorstaysonthebalance

sheetwhenthereisnoeconomicreasonfbrittoexist.

?Assetscanchangevaluefbranyofthefollowingreasons:

?Differentestimatesresultindifferentvalues(estimatesofdifferentassetlives

canaffectdepreciationcalculationsandthenthebookvalueofanasset)

?Differentaccountingstandardscanresultinchangesinbalancesheetvalues

(thedecisiontoadoptSFAS106immediatelyorover20years)

?Adoptionofdifferentaccountingchoicescanaffectassetvalues

?LIFO/FIFOinventory

?Straightline/accelerateddepreciation

?Short-term/long-termmarketablesecurities

?Purchase/poolingacquisitions

?Cost/equityrecognition

?Lowerofcostormarket

?Capitalizationofcosts

?Pensionoptions

?Deferraloftaxes

?Foreigncurrencytranslations

?Revenuerecognitionchoices

IncreasingorDecreasingLiabilities

?Off-balance-sheetliabilitieswillchangebookvalue.Contingentliabilitiesand

off-balance-sheetfinancingaretwosuchliabilitiesthatsometimesarenotincluded

onthebalancesheetthatshouldbeincluded.

?Changesinthevalueofexistingliabilitiescanaffectbookvalue.Wheninterestrates

changelong-termdebtwhichisonthebalancesheetdoesnotchangeeventhough

theeconomicvalueoftheseliabilitiesdochange.

IncreasingorDecreasing#ofShares

?Theexistenceofwarrantsoroptionscanincreasethenumberofsharesdepending

uponthedecisiontoincludetheminthecomputationofbookvalueornot.

?Thepurchaseorsaleofsharesatavaluedifferentfrombookvaluewillchangebook

value.

25.CFAExaminationII(1995)

25(a).Someargumentsforahighdividendpayoutpolicyare:

1.Limitedinvestmentopportunities.Ifafirmhascashflowsgreaterthanthoseneeded

tofundprojectswithpositivenetpresentvalues,itshouldreturnthecapitalto

shareholdersashigherdividends.

2.Clienteleeffect.Someinvestorsrequiresomeincomefrominvestments.Thehigher

thedividend,thegreatertheproportionofinvestorswhowillbesatisfiedwiththeincome

ofagiveninvestment.

3.Certaintyofdividendsversuscapitalgains.The"birdinhand^^argumentsaysthat(a)

cashdividendsareadefinitereturnwhereascapitalappreciationislesscertain,or(b)

investorsshouldapplyalowerdiscountratetocashdividendsversuscapitalappreciation

becausedividendsaremorecertain.

4.Taxeffects.Corporateandtaxexemptinvestorsinsometaxjurisdictionspayno

incometaxondividends.

5.Informationalcontent.Managementusesthedividendpayoutpolicytocommunicate

thelong-termprospectsofthecorporation.

Someargumentsagainstahighdividendpayoutpolicyare:

1.Noeffectonvalue.Afirm'sinvestmentdecisionsdetermineitsprofitability.Dividend

policydoesnotaffectinvestmentdecisions,butitdoesaffecttheamountofoutside

financingneededbyafirm.

2.Lesscashavailableforinvestments.Payinghighdividendsreducesthecash

availabletofinanceprofitableinvestmentprojects.Withlessinternalfinancing,afirm

mayresorttoexternalfinancingtofinanceprojects,whichmayreduceearningspershare

becauseofgreaterinterestexpenseormoresharesoutstanding.

3.Taxes.Investorscandefertaxesoncapitalappreciationuntilrealizedbutpaytaxeson

dividends(excepttax-exemptinvestors)evenifdividendsarereinvested.Also,double

taxationexistsoncorporateprofitsanddividendspaidtoinvestors.

4.Violationofanindenture.Highdividendpayoutsmayviolatebondindenturesor

loancovenants.

5.Financialdistress.Payinghighdividendswhilefinancinginvestmentprojectsmay

forcethefirmtoincreaseitsleverageratiosandleadtoahigherlevelofrisk.Thiscould

eventuallyleadtofinancialdistress.

25(b).Theconstantgrowthdividenddiscountmodel,Po=Di/(k-g),impliesthatastock's

value,Po,willbegreater

1.thelargeritsexpecteddividendpershare,Di；

2.thelowerthemarketcapitalizationrate,k,(alsocalledtherequiredrateofreturn);

3.thehighertheexpectedgrowthrateofdividends,g.

Thedirectorhasignoredthedenominatorusedtoconvertthedividendtoapresentvalue.

Thedenominatorconsistsoftwovariables,bothofwhichdividendpolicycould

influence.Onevariableisthemarketcapitalizationrate,k,whichriskaffects.Investors

mayviewahigherdividendpayoutasincreasingriskbecauseahigherpayoutmaylead

toanincreaseinafirm'sleverageratios.Theothervariableistheexpectedgrowthrate

ofdividends,g,whichislikelytobeloweriffirmspayhigherdividendsintheshortrun.

Insummary,ahigherdividendpayoutmayincreasekandlowerg.Therefore,the

statementbythedirectorthattheuseofdividenddiscountmodelsbyinvestorsis

“proof*'that"thehigherthedividend,thehigherthestockprice^^ispotentially

misleadingandpossiblyinaccurate.

25(c).(i)Internal(implied,normalized,orsustainable)growthrate

Theinternal-growthrateofdividends,g,iscalculatedas:

g=ROExb

where:ROE=returnonequity

b=plowbackorearningsretentionratio(1-dividendpayoutratio).

Asthedividendpayoutratioincreases,theexpectedgrowthrateindividendsdecreases.

Ifthefirmpaysoutallearningsasdividends,theexpectedgrowthrateindividends

wouldbezero.Valuationwouldalsodecreasetothedegreeinvestorswouldpayalower

ratioofpricetoearningsforthelowergrowthratecalculatedinthismanner.

(ii)Growthinbookvalue

Ahigherdividendpayoutratiowouldslowtheincreaseinbookvalue(allotherfactors

beingequal)becausetheretainedearningsincludedinstockholders9equitywould

increaseataslowerrate(reflectingthehigherdividendpayout).

26.CFAExamination11(1997)

26(a).PossibleValuationDecrease

Theconstant-growth-rateversionoftheDDMisoftenexpressedas

DiDo(1+g)

P=andalsoP=inthatDi=Do(l+g)

K-gK-g

inwhichD\isnextyear'sdividendpershare,kistherequiredrateofreturn(sometimes

calledtheinternalrateofreturn),andgisthedividendgrowthrate.

SoftCorporation'sacquisitionofaslower-growthcompetitormightdecreaseitsvaluation

basedonaconstant-growthDDMbecause

?SC's$300millioninnewlong-termdebtandrelatedinterestcostsdecreasesthe

likelihoodthatthedividendwillbeincreasednextyear(￡)/);

?theacquisitionofaslower-growthcompanyreducestheacquirer'slong-termgrowth

ratefordividends;

?thehigherfinancialleverageresultingfromtheacquisitionwillincreasetheperceived

riskinessofSC,raisinginvestors9requiredrateofreturn(%);

?everythingelsebeingequal,thesefactors(lowerdividendgrowthrateandhigher

requiredrateofreturn)couldinteracttoincreasethedenominatoranddecreasethe

numeratoroftheDDM.

26(b).PossibleIncreaseinP/EMultiple

TheacquisitionmightincreasetheP/EmultipleinvestorswillbewillingtopayforSC

forthefollowingreasons:

?Theacquisitioncouldprovideinternalsourcesofgrowth.Synergies(theopportunity

forcostcutting,economiesofscale,etc.)fromthecombinationmightwellemergein

time,whichwouldincreasetheearningsgrowthrateintheintermediateterm.

Investorsmightanticipatethisimprovedgrowthrate,whichwouldenhancetheP/E

multiple.

?Theacquisitioncouldprovideexternalsourcesofgrowth.Particularlyiftheacquired

companyisanimportantdirectcompetitor,investors9perceptionsofreduced

competitionandimprovedpricinginthefuturecouldleadtoahighermultipleonthe

stockoncurrentearnings.

?Theacquisitionwilladdvalueifreturnsexceedcosts.Theuseofdebttofinancethe

acquisitionwillenhancetheROEofSCzftheincrementalprofitabilityexceedsthe

after-taxcostofdebtcapital.IfinvestorsperceivethishigherROEtobesustainable,

theirexpectationsforgrowthand,consequently,themultipletheyarewillingtopay

forthestockarelikelytoincrease.

?Investorsmaydecidethattheexternalsourcesofgrowth(seeabove)justifyviewing

theriskinessofthecombinedentityaslessthanthatofSCalone,whichwouldjustify

ahigherP/Emultiple.

?Short-termEPSmaydropbecauseoftheexpensesrelatedtotheacquisition,but

investorslookingbeyondthisshort-termdropmaybelievethatlonger-termearnings

growthprospectshaveimproved.Themultipleoncurrentearningsmayriseasa

resultofthisexpectation.

?IfSCiscurrentlyunderleveraged,thedebtloadtakenoninthisacquisitionmay

actuallyoptimizeSC'sleverage,whichwouldproducealoweroverallcostofcapital

andjustifyahigherP/Emultiple.

27.CFAExamination11(1999)

1Lifeoftheasset(N).Typically,bondshaveastatedmaturity.Bondinvestorswill

bepaidcouponsandrepaidprincipalatorbeforethatmaturity.Thelifeofthebondis

contractuallydeterminedandcreatesanobligationtohonorthepromisedpayments.

Thereisnomaturityforcommonstocks;indeedthelifeofthecorporationisassumedto

beinfinite.

2.Contractualnatureofthecashflows(CF).Thecontractualnatureofbond

paymentscreatesanobligation,whichmakestheestimationofthesepaymentsafairly

routinetaskespeciallyforhighqualitybonds.Dividendpaymentsoncommonstocks,on

theotherhand,aremuchmoredifficulttoestimatebecausedividendsarediscretionaryor

indeterminatebasedonfactorssuchasprofitability,financialstructure,capital

expenditures,managementdiscretion,etc.

3.Appropriatediscountrate(k).Thediscountrate,orrequiredrateofreturn,reflects

theriskoftheasset.Therequiredrateofreturnonabondisobservableandtypically

determinedbycomparisonwithotherbondsofsimilarmaturity(asgivenbytheyield

curve)andtheissuercreditrisk(asgivenbythebondrating).Theestimationofthe

requiredrateofreturnforacommonstockismoresubjective,oftenrelyingonan

estimatedriskproxysuchasbetaorsimilarmeasuresofriskiness.

CHAPTER15

AnswerstoProblems

1.StudentExercise

2.StudentExercise

3(a).RH=.07+1.75(.15-.07)=.07+.14=.21or21%

3(b).RH=.07+1.75(.10-.07)=.07+.0525=.1225or12.25%

4.StudentExercise

5.241+.14+.02

In—=Tln-----------------

161+.06+.04

In(1.5())=Tin(1.16/1.10)

In(1.50)=Tin(1.05455)

T=In(1.50)/ln(1.05455)

T=0.40547/0.05311

T=7.635years

6(a).In(x)=10In(1.18/1.08)

In(x)=1()In(1.09259)

In(x)=10(0.08855)

In(x)=().8855

x=2.424

Thus,theP/Eratiowouldbe33.94x(2.424x14).

6(b).In(x)=5ln(1.18/l.()8)

In(x)=5In(1.09259)

In(x)=5(0.08855)

In(x)=0.44275

x=1.55698

Thus,theP/Eratiowouldbe21.80x(1.55698x14).

7(a).CompanyA

301+.18+.00

In—=Tln-----------------

181+.07+.02

In(1.6667)=Tin(1.18/1.09)

In(1.6667)=Tin(1.08257)

T=In(1.667)/ln(1.08257)

T=.51083/.07934

T=6.44years

CompanyB

271+.15+.01

In—=TIn-----------------

181+.07+.02

In(1.50)=Tin(1.16/1.09)

In(1.50)=Tin(1.06422)

T=In(1.50)/ln(1.06422)

T=.40547/.06224

T=6.51years

7(b).

301+.18+.00

In—=TIn-----------------

271+.15+.01

ln(l.ll)=Tln(1.18/1.16)

In(1.11)=Tin(1.01724)

T=In(1.1l)/ln(1.01724)

T=.10536/.01709

T=6.16years

7(c).Aftercomputingtheimpliedgrowthdurations,theanalystmustdecidewhetherthe

projectedgrowthratescanbesustainedovertheperiodsimpliedinthemodel.Ifthe

impliedgrowthdurationisgreaterthanyoubelieveisreasonable,youwouldlikely

adviseagainstbuyingtherespectivestock.

8.CFAExamination11(1981)

8(a).Threefactorsthatmustbeestimatedforanyvaluationmodelare:

Theexpectedstreamofreturns-whichisspecifiedforbondsintermsofinterest(coupon)

andprincipalpayments,butisuncertainforcommonstocksasdividendsarenot

contractualorpreciselypredictable.

Thetimepatternofexpectedreturns-specifiedforbonds,intermsofsemi-annual

interestpaymentsandprincipalpaymentsannually(sinkingfund)oratmaturity,butis

uncertainforcommonstocksbecausealthoughdividendsmaybepaidannually,astockis

ineffect“perpetual."Maturityvalueofabondisknown,whilethesalepriceforstock

involvesanestimateofearningsinthatyearandP/Ethatwillthenprevail,theconceptof

aterminalP/Eisused.

Therequiredrateofreturnontheinvestmentadjustedforrisksisuncertainforboth

stocksandbonds.Forbonds,thisgenerallydependsupontheprevailingrisk-freerate.

Forcommonstocks,giventhesecuritymarketlineprevailingatapointintime,andthe

estimateofthestock'sbetawiththemarketportfolioofriskyassets,itispossibleto

derivethereturnthatshouldberequiredfbrtheinvestment.

8(b).Theprobleminusingadividendvaluationmodelisthatgrowthisachanging

phenomenonandcannotbeprojectedtoinfinity,asindicatedineachofthefollowing

threetypesofcompanies:

1.Constantgrowthindividendsisunrealisticforacorporationthatissubjectto

cyclicalswingsinitsbusiness.

2.Maturingcompaniesmightbeexperiencingaslowingintherateofgrowthof

dividends,althoughsomesuchcompaniesmaintaindividendgrowthbyincreasing

thepayoutratio,butthisisashort-termphenomenon.

3.Small,rapidlygrowingcompaniesarenotabletosustainaboveaverageratesof

growthindefinitely.

9.CFAExaminationI(1985)

Theanalystwouldrecommendinvestingintheleaseobligationsince,foreachdollar

invested,thepresentvalueofthefuturecashflowsgeneratedbytheleaseisgreater

thanthepresentvalueofthecashflowthatwillberealizedwhenthestockissold.

PresentValueofCommonStock

YearCashFlowPVm10%$PV

1$0.909$0

2$0.8260

3$100,000x(l.l)3=$133,100.751$100,000

$100,000

PresenlValueofLeaseCashFlow

YearCashFlowPV?10%$PV

1