博迪投资学第九版 Investment Chap018 习题答案.docx

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博迪投资学第九版 Investment Chap018 习题答案.docx

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博迪投资学第九版 Investment Chap018 习题答案.docx

博迪投资学第九版InvestmentChap018习题答案

CHAPTER18:

EQUITYVALUATIONMODELS

PROBLEMSETS

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

2.Itismostimportanttousemulti-stagedividenddiscountmodelswhenvaluingcompanieswithtemporarilyhighgrowthrates.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:

E01.03（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=20%

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%

b.Thepriceshouldriseby15%peryearuntilyear6:

becausethereisnodividend,theentirereturnmustbeincapitalgains.

c.ThepayoutratiowouldhavenoeffectonintrinsicvaluebecauseROE=k.

15.a.ThesolutionisshownintheExcelspreadsheetbelow:

Inputs

Year

Dividend

Divgrowth

Termvalue

InvestorCF

beta

.90

2008

0.77

mkt_prem

0.08

2009

0.88

0.045

2010

0.99

k_equity

0.117

2011

1.10

plowback

0.74

2012

1.24

0.1262

1.24

roe

0.13

2013

1.39

0.1232

1.39

term_gwth

0.0962

2014

1.56

0.1202

1.56

2015

1.74

0.1172

1.74

2016

1.94

0.1142

1.94

2017

2.16

0.1112

2.16

Valueline

2018

2.39

0.1082

2.39

forecastsof

2019

2.64

0.1052

2.64

annualdividends

2020

2.91

0.1022

2.91

2021

3.20

0.0992

3.20

2022

3.51

0.0962

3.51

Transitionalperiod

2023

3.85

0.0962

202.65

206.50

withslowingdividend

growth

45.71

=PVofCF

Beginningofconstant

E17*（1+F17）/（B5-F17）

growthperiod

NPV（B5,H2:

H17）

b.,c.UsingtheExcelspreadsheet,wefindthattheintrinsicvaluesare$29.71and$17.39,respectively.

16.ThesolutionsderivedfromSpreadsheet18.2areasfollows:

Intrinsicvalue:

FCFF

Intrinsicvalue:

FCFE

Intrinsicvaluepershare:

FCFF

Intrinsicvaluepershare:

FCFE

81,171

68,470

36.01

37.83

59,961

49,185

24.29

27.17

69,813

57,913

29.73

32.00

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=11.2%

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:

In"normalperiods"whenthereisnospecialinformation,

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）31.13=$1.8744

D3=E30.30=$1.87430.30=$0.5623

3.a.Freecashflowtoequity（FCFE）isdefinedas

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