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
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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.
b.
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
c.
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:
0
1
5
6
Et
$10.000
$12.000
$24.883
$27.123
Dt
$0.000
$0.000
$0.000
$10.849
b
1.00
1.00
1.00
0.60
g
20.0%
20.0%
20.0%
9.0%
Theyear-6earningsestimateisbasedongrowthrateof0.15×(1-.0.40)=0.09.
a.
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
a.
100,000
75,128
38.89
41.74
b.
109,422
81,795
44.12
45.44
c.
89,693
66,014
33.16
36.67
17.
Time:
0
1
2
3
Dt
$1.0000
$1.2500
$1.5625
$1.953
g
25.0%
25.0%
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:
0
1
4
5
Et
$5.000
$6.000
$10.368
$10.368
Dt
$0.000
$0.000
$0.000
$10.368
Dividends=0forthenextfouryears,sob=1.0(100%plowbackratio).
a.
(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%
b.
Time
EPS
Dividend
Comment
0
$1.0000
$0.5000
1
1.1000
0.5500
g=10%,plowback=0.50
2
1.2100
0.7260
EPShasgrownby10%basedonlastyear’searningsplowbackandROE;thisyear’searningsplowbackrationowfallsto0.40andpayoutratio=0.60
3
$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
1
2
3
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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