投资学10版习题答案CH18.docx

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投资学10版习题答案CH18.docx

投资学10版习题答案CH18

CHAPTER18:

EQUITYVALUATIONMODELS

PROBLEMSETS

1.Theoretically,dividenddiscountmodelscanbeusedtovaluethestockofrapidlygrowingcompaniesthatdonotcurrentlypaydividends;inthisscenario,wewouldbevaluingexpecteddividendsintherelativelymoredistantfuture.However,asapracticalmatter,suchestimatesofpaymentstobemadeinthemoredistantfuturearenotoriouslyinaccurate,renderingdividenddiscountmodelsproblematicforvaluationofsuchcompanies;freecashflowmodelsaremorelikelytobeappropriate.Attheotherextreme,onewouldbemorelikelytochooseadividenddiscountmodeltovalueamaturefirmpayingarelativelystabledividend.

2.Itismostimportanttousemultistagedividenddiscountmodelswhenvaluingcompanieswithtemporarilyhighgrowthrates.Thesecompaniestendtobecompaniesintheearlyphasesoftheirlifecycles,whentheyhavenumerousopportunitiesforreinvestment,resultinginrelativelyrapidgrowthandrelativelylowdividends（or,inmanycases,nodividendsatall）.Asthesefirmsmature,attractiveinvestmentopportunitiesarelessnumeroussothatgrowthratesslow.

3.Theintrinsicvalueofashareofstockistheindividualinvestor’sassessmentofthetrueworthofthestock.Themarketcapitalizationrateisthemarketconsensusfortherequiredrateofreturnforthestock.Iftheintrinsicvalueofthestockisequaltoitsprice,thenthemarketcapitalizationrateisequaltotheexpectedrateofreturn.Ontheotherhand,iftheindividualinvestorbelievesthestockisunderpriced（i.e.,intrinsicvalue>price）,thenthatinvestor’sexpectedrateofreturnisgreaterthanthemarketcapitalizationrate.

4.Firstestimatetheamountofeachofthenexttwodividendsandtheterminalvalue.Thecurrentvalueisthesumofthepresentvalueofthesecashflows,discountedat8.5%.

5.Therequiredreturnis9%.

6.TheGordonDDMusesthedividendforperiod（t+1）whichwouldbe1.05.

7.ThePVGOis$0.56:

8.a.

Thepricefallsinresponsetothemorepessimisticdividendforecast.Theforecastforcurrentyearearnings,however,isunchanged.Therefore,theP/Eratiofalls.ThelowerP/Eratioisevidenceofthediminishedoptimismconcerningthefirm'sgrowthprospects.

9.a.g=ROEb=16%0.5=8%

D1=$2（1–b）=$2（1–0.5）=$1

b.P3=P0（1+g）3=$25（1.08）3=$31.49

10.a.

b.LeadingP0/E1=$10.60/$3.18=3.33

TrailingP0/E0=$10.60/$3.00=3.53

ThelowP/EratiosandnegativePVGOareduetoapoorROE（9%）thatislessthanthemarketcapitalizationrate（16%）.

d.Now,yourevisebto1/3,gto1/39%=3%,andD1to:

E0（1+g）（2/3）

$31.03（2/3）=$2.06

Thus:

V0=$2.06/（0.16–0.03）=$15.85

V0increasesbecausethefirmpaysoutmoreearningsinsteadofreinvestingapoorROE.Thisinformationisnotyetknowntotherestofthemarket.

11.a.

b.Thedividendpayoutratiois8/12=2/3,sotheplowbackratioisb=1/3.TheimpliedvalueofROEonfutureinvestmentsisfoundbysolving:

g=bROEwithg=5%andb=1/3ROE=15%

c.AssumingROE=k,priceisequalto:

Therefore,themarketispaying$40pershare（$160–$120）forgrowthopportunities.

12.a.k=D1/P0+g

D1=0.5$2=$1

g=bROE=0.50.20=0.10

Therefore:

k=（$1/$10）+0.10=0.20,or20%

b.Sincek=ROE,theNPVoffutureinvestmentopportunitiesiszero:

c.Sincek=ROE,thestockpricewouldbeunaffectedbycuttingthedividendandinvestingtheadditionalearnings.

13.a.k=rf+β[E（rM）–rf]=8%+1.2（15%–8%）=16.4%

g=bROE=0.620%=12%

b.P1=V1=V0（1+g）=$101.821.12=$114.04

14.

Time:

$10.000

$12.000

$24.883

$27.123

$0.000

$10.849

1.00

0.60

20.0%

9.0%

Theyear-6earningsestimateisbasedongrowthrateof0.15×（1-.0.40）=0.09.

b.Thepriceshouldriseby15%peryearuntilyear6:

becausethereisnodividend,theentirereturnmustbeincapitalgains.

c.ThepayoutratiowouldhavenoeffectonintrinsicvaluebecauseROE=k.

15.a.ThesolutionisshownintheExcelspreadsheetbelow:

b.,c.UsingtheExcelspreadsheet,wefindthattheintrinsicvaluesare$33.80and$32.80,respectively.

16.ThesolutionsderivedfromSpreadsheet18.2areasfollows:

IntrinsicValue:

FCFF

IntrinsicValue:

FCFE

IntrinsicValueperShare:

FCFF

IntrinsicValueperShare:

FCFE

100,000

75,128

38.89

41.74

109,422

81,795

44.12

45.44

89,693

66,014

33.16

36.67

17.

Time:

$1.0000

$1.2500

$1.5625

$1.953

25.0%

5.0%

a.Thedividendtobepaidattheendofyear3isthefirstinstallmentofadividendstreamthatwillincreaseindefinitelyattheconstantgrowthrateof5%.Therefore,wecanusetheconstantgrowthmodelasoftheendofyear2inordertocalculateintrinsicvaluebyaddingthepresentvalueofthefirsttwodividendsplusthepresentvalueofthepriceofthestockattheendofyear2.

Theexpectedprice2yearsfromnowis:

P2=D3/（k–g）=$1.953125/（0.20–0.05）=$13.02

ThePVofthisexpectedpriceis$13.02/1.202=$9.04

ThePVofexpecteddividendsinyears1and2is

Thusthecurrentpriceshouldbe:

$9.04+$2.13=$11.17

b.Expecteddividendyield=D1/P0=$1.25/$11.17=0.112,or11.2%

c.TheexpectedpriceoneyearfromnowisthePVatthattimeofP2andD2:

P1=（D2+P2）/1.20=（$1.5625+$13.02）/1.20=$12.15

Theimpliedcapitalgainis

（P1–P0）/P0=（$12.15–$11.17）/$11.17=0.088=8.8%

Thesumoftheimpliedcapitalgainsyieldandtheexpecteddividendyieldisequaltothemarketcapitalizationrate.ThisisconsistentwiththeDDM.

18.

Time:

$5.000

$6.000

$10.368

$0.000

$10.368

Dividends=0forthenextfouryears,sob=1.0（100%plowbackratio）.

（Sincek=ROE,knowingtheplowbackrateisunnecessary）

b.Priceshouldincreaseatarateof15%overthenextyear,sothattheHPRwillequalk.

19.Before-taxcashflowfromoperations$2,100,000

Depreciation210,000

TaxableIncome1,890,000

Taxes（@35%）661,500

After-taxunleveragedincome1,228,500

After-taxcashflowfromoperations

（After-taxunleveragedincome+depreciation）1,438,500

Newinvestment（20%ofcashflowfromoperations）420,000

Freecashflow

（After-taxcashflowfromoperations–newinvestment）$1,018,500

Thevalueofthefirm（i.e.,debtplusequity）is:

Sincethevalueofthedebtis$4million,thevalueoftheequityis$10,550,000.

20.a.g=ROEb=20%0.5=10%

Time

EPS

Dividend

Comment

$1.0000

$0.5000

1.1000

0.5500

g=10%,plowback=0.50

1.2100

0.7260

EPShasgrownby10%basedonlastyear’searningsplowbackandROE;thisyear’searningsplowbackrationowfallsto0.40andpayoutratio=0.60

$1.2826

$0.7696

EPSgrowsby（0.4）（15%）=6%andpayoutratio=0.60

Attime2:

Attime0:

c.P0=$11andP1=P0（1+g）=$12.10

（Becausethemarketisunawareofthechangedcompetitivesituation,itbelievesthestockpriceshouldgrowat10%peryear.）

P2=$8.551afterthemarketbecomesawareofthechangedcompetitivesituation.

P3=$8.5511.06=$9.064（Thenewgrowthrateis6%.）

Year

Return

Moral:

Innormalperiodswhenthereisnospecialinformation,thestockreturn=k=15%.Whenspecialinformationarrives,alltheabnormalreturnaccruesinthatperiod,asonewouldexpectinanefficientmarket.

CFAPROBLEMS

1.a.Thisdirectorisconfused.Inthecontextoftheconstantgrowthmodel

[i.e.,P0=D1/k–g）],itistruethatpriceishigherwhendividendsarehigherholdingeverythingelseincludingdividendgrowthconstant.Buteverythingelsewillnotbeconstant.Ifthefirmincreasesthedividendpayoutrate,thegrowthrategwillfall,andstockpricewillnotnecessarilyrise.Infact,ifROE>k,pricewillfall.

b.（i）Anincreaseindividendpayoutwillreducethesustainablegrowthrateaslessfundsarereinvestedinthefirm.Thesustainablegrowthrate

（i.e.ROEplowback）willfallasplowbackratiofalls.

（ii）Theincreaseddividendpayoutratewillreducethegrowthrateofbookvalueforthesamereason--lessfundsarereinvestedinthefirm.

2.Usingatwo-stagedividenddiscountmodel,thecurrentvalueofashareofSundanciiscalculatedasfollows.

where:

E0=$0.952

D0=$0.286

E1=E0（1.32）1=$0.9521.32=$1.2566

D1=E10.30=$1.25660.30=$0.3770

E2=E0（1.32）2=$0.952（1.32）2=$1.6588

D2=E20.30=$1.65880.30=$0.4976

E3=E0（1.32）21.13=$0.952（1.32）21.13=$1.8744

D3=E30.30=$1.87430.30=$0.5623

3.a.Freecashflowtoequity（FCFE）isdefinedasthecashflowremainingaftermeetingallfinancialobligations（includingdebtpayment）andaftercoveringcapitalexpenditureandworkingcapitalneeds.TheFCFEisameasureofhowmuchthefirmcanaffordtopayoutasdividendsbut,inagivenyear,maybemoreorlessthantheamountactuallypaidout.

Sundanci'sFCFEfortheyear2008iscomputedasfollows:

FCFE=Earnings+DepreciationCapitalexpendituresIncreaseinNWC

=$80million+$23million$38million$41million=$24million

FCFEpershare=

Atthispayoutratio,Sundanci'sFCFEpershareequalsdividendspershare.

b.TheFCFEmodelrequiresforecastsofFCFEforthehighgrowthyears（2012and2013）plusaforecastforthefirstyearofstablegrowth（2014）inordertoallowforanestimateoftheterminalvaluein2013basedonperpetualgrowth.Becauseallofthecomponentso

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