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chap018ise
CHAPTER18:
EQUITYVALUATIONMODELS
1.IandII
2.a.k=D1/P0+g
0.16=$2/$50+gg=0.12=12%
b.P0=D1/(k–g)=$2/(0.16–0.05)=$18.18
Thepricefallsinresponsetothemorepessimisticdividendforecast.Theforecastforcurrentyearearnings,however,isunchanged.Therefore,theP/Eratiofalls.ThelowerP/Eratioisevidenceofthediminishedoptimismconcerningthefirm'sgrowthprospects.
3.a.g=ROE⨯b=16%⨯0.4=6.4%
D1=SFr2(1–b)=SFr2(1–0.4)=SFr1.20
P0=D1/(k–g)=SFr1.20/(0.12–0.064)=SFr21.43
b.P3=P0(1+g)3=SFr21.43(1.064)3=SFr25.81
4.P0=D1/(k–g)=€2.10/(0.09–0)=€23.33
5.a.Thisdirectorisconfused.Inthecontextoftheconstantgrowthmodel
[i.e.,P0=D1/(k–g)],itistruethatpriceishigherwhendividendsarehigherholdingeverythingelseincludingdividendgrowthconstant.Buteverythingelsewillnotbeconstant.Ifthefirmincreasesthedividendpayoutrate,thegrowthrategwillfall,andstockpricewillnotnecessarilyrise.Infact,ifROE>k,pricewillfall.
b.(i)Anincreaseindividendpayoutwillreducethesustainablegrowthrateaslessfundsarereinvestedinthefirm.Thesustainablegrowthrate
(i.e.,ROE⨯plowback)willfallasplowbackratiofalls.
(ii)Theincreaseddividendpayoutratewillreducethegrowthrateofbookvalueforthesamereason--lessfundsarereinvestedinthefirm.
6.Sincebeta=1.0,thenk=marketreturn=15%
Therefore:
15%=D1/P0+g=4%+gg=11%
7.a.k=rf+β[E(rM)–rf]=6%+1.25(14%–6%)=16%
g=2/3⨯9%=6%
D1=E0(1+g)(1–b)=€6(1.06)(1/3)=€2.12
=€21.20
b.LeadingP0/E1=€21.20/€6.36=3.33
TrailingP0/E0=€21.20/€6.00=3.53
c.
−€18.55
ThelowP/EratiosandnegativePVGOareduetoapoorROE(9%)thatislessthanthemarketcapitalizationrate(16%).
d.Now,yourevisebto1/3,gto1/3⨯9%=3%,andD1to:
E01.03⨯(2/3)=€4.12
Thus:
V0=€4.12/(0.16–0.03)=€31.69
V0increasesbecausethefirmpaysoutmoreearningsinsteadofreinvestingatapoorROE.Thisinformationisnotyetknowntotherestofthemarket.
8.a.
¥16,000
b.Thedividendpayoutratiois¥800/¥1,200=2/3,sotheplowbackratiois
b=1/3.TheimpliedvalueofROEonfutureinvestmentsisfoundbysolving:
g=b⨯ROEwithg=5%andb=1/3ROE=15%
c.AssumingROE=k,priceisequalto:
¥12,000
Therefore,themarketispaying¥4,000pershare(¥16,000–¥12,000)forgrowthopportunities.
9.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
10.a.Freecashflowtoequity(FCFE)isdefinedasthecashflowremainingaftermeetingallfinancialobligations(includingdebtpayment)andaftercoveringcapitalexpenditureandworkingcapitalneeds.TheFCFEisameasureofhowmuchthefirmcanaffordtopayoutasdividends,butinagivenyearmaybemoreorlessthantheamountactuallypaidout.
Sundanci'sFCFEfortheyear2000iscomputedasfollows:
FCFE=
Earningsaftertax+DepreciationexpenseCapitalexpendituresIncreaseinNWC
=$80million+$23million$38million$41million=$24million
FCFEpershare=FCFE/numberofsharesoutstanding
=$24million/84millionshares=$0.286
Atthegivendividendpayoutratio,Sundanci'sFCFEpershareequalsdividendspershare.
b.
TheFCFEmodelrequiresforecastsofFCFEforthehighgrowthyears(2001and2002)plusaforecastforthefirstyearofstablegrowth(2003)inordertoallowforanestimateoftheterminalvaluein2002basedonperpetualgrowth.BecauseallofthecomponentsofFCFEareexpectedtogrowatthesamerate,thevaluescanbeobtainedbyprojectingtheFCFEatthecommonrate.(Alternatively,thecomponentsofFCFEcanbeprojectedandaggregatedforeachyear.)
ThefollowingtableshowstheprocessforestimatingSundanci'scurrentvalueonapersharebasis.
FreeCashFlowtoEquity
BaseAssumptions
Sharesoutstanding:
84million
Requiredreturnonequity(r):
14%
Actual
2000
Projected
2001
Projected
2002
Projected
2003
Growthrate(g)
27%
27%
13%
Total
Pershare
Earningsaftertax
$80
$0.952
$1.2090
$1.5355
$1.7351
Plus:
Depreciationexpense
$23
$0.274
$0.3480
$0.4419
$0.4994
Less:
Capitalexpenditures
$38
$0.452
$0.5740
$0.7290
$0.8238
Less:
Increaseinnetworkingcapital
$41
$0.488
$0.6198
$0.7871
$0.8894
Equals:
FCFE
$24
$0.286
$0.3632
$0.4613
$0.5213
Terminalvalue
$52.1300*
Totalcashflowstoequity
$0.3632
$52.5913**
Discountedvalue
$0.3186***
$40.4673***
Currentvaluepershare
$40.7859****
*Projected2002Terminalvalue=(Projected2003FCFE)/(rg)
**Projected2002Totalcashflowstoequity=
Projected2002FCFE+Projected2002Terminalvalue
***Discountedvaluesobtainedusingr=14%
****Currentvaluepershare=
SumofDiscountedProjected2001and2002Totalcashflowstoequity
c.i.TheDDMusesastrictdefinitionofcashflowstoequity,i.e.theexpecteddividendsonthecommonstock.Infact,takentoitsextreme,theDDMcannotbeusedtoestimatethevalueofastockthatpaysnodividends.TheFCFEmodelexpandsthedefinitionofcashflowstoincludethebalanceofresidualcashflowsafterallfinancialobligationsandinvestmentneedshavebeenmet.ThustheFCFEmodelexplicitlyrecognizesthefirm’sinvestmentandfinancingpoliciesaswellasitsdividendpolicy.Ininstancesofachangeofcorporatecontrol,andthereforethepossibilityofchangingdividendpolicy,theFCFEmodelprovidesabetterestimateofvalue.TheDDMisbiasedtowardfindinglowP/Eratiostockswithhighdividendyieldstobeundervaluedandconversely,highP/Eratiostockswithlowdividendyieldstobeovervalued.Itisconsideredaconservativemodelinthatittendstoidentifyfewerundervaluedfirmsasmarketpricesriserelativetofundamentals.TheDDMdoesnotallowforthepotentialtaxdisadvantageofhighdividendsrelativetothecapitalgainsachievablefromretentionofearnings.
ii.Bothtwo-stagevaluationmodelsallowfortwodistinctphasesofgrowth,aninitialfiniteperiodwherethegrowthrateisabnormal,followedbyastablegrowthperiodthatisexpectedtolastindefinitely.Thesetwo-stagemodelssharethesamelimitationswithrespecttothegrowthassumptions.First,thereisthedifficultyofdefiningthedurationoftheextraordinarygrowthperiod.Forexample,alongerperiodofhighgrowthwillleadtoahighervaluation,andthereisthetemptationtoassumeanunrealisticallylongperiodofextraordinarygrowth.Second,theassumptionofasuddenshiftformhighgrowthtolower,stablegrowthisunrealistic.Thetransformationismorelikelytooccurgradually,overaperiodoftime.Giventhattheassumedtotalhorizondoesnotshift(i.e.,isinfinite),thetimingoftheshiftformhightostablegrowthisacriticaldeterminantofthevaluationestimate.Third,becausethevalueisquitesensitivetothesteady-stategrowthassumption,over-orunder-estimatingthisratecanleadtolargeerrorsinvalue.Thetwomodelsshareotherlimitationsaswell,notablydifficultiesinaccuratelyforecastingrequiredratesofreturn,indealingwiththedistortionsthatresultfromsubstantialand/orvolatiledebtratios,andinaccuratelyvaluingassetsthatdonotgenerateanycashflows.
11.a.Theformulaforcalculatingapriceearningsratio(P/E)forastablegrowthfirmisthedividendpayoutratiodividedbythedifferencebetweentherequiredrateofreturnandthegrowthrateofdividends.IftheP/Eiscalculatedbasedontrailingearnings(year0),thepayoutratioisincreasedbythegrowthrate.IftheP/Eiscalculatedbasedonnextyear’searnings(year1),thenumeratoristhepayoutratio.
P/Eontrailingearnings:
P/E=[payoutratio(1+g)]/(rg)=[0.301.13]/(0.140.13)=33.9
P/Eonnextyear'searnings:
P/E=payoutratio/(rg)=0.30/(0.140.13)=30.0
b.TheP/Eratioisadecreasingfunctionofriskiness;asriskincreasestheP/Eratiodecreases.IncreasesintheriskinessofSundancistockwouldbeexpectedtolowertheP/Eratio.
TheP/Eratioisanincreasingfunctionofthegrowthrateofthefirm;thehighertheexpectedgrowththehighertheP/Eratio.SundanciwouldcommandahigherP/Eifanalystsincreasetheexpectedgrowthrate.
TheP/Eratioisadecreasingfunctionofthemarketriskpremium.Anincreasedmarketriskpremiumwouldincreasetherequiredrateofreturn,loweringthepriceofastockrelativetoitsearnings.AhighermarketriskpremiumwouldbeexpectedtolowerSundanci'sP/Eratio.
12.a.Thesustainablegrowthrateisequalto:
plowbackratio×returnonequity=b×ROE
where
b=[NetIncome–(Dividendpershare×sharesoutstanding)]/NetIncome
ROE=NetIncome/Beginningofyearequity
In2000:
b=[208–(0.80×100)]/208=0.6154
ROE=208/1380=0.1507
Sustainablegrowthrate=0.6154×0.1507=9.3%
In2003:
b=[275–(0.80×100)]/275=0.7091
ROE=275/1836=0.1498
Sustainablegrowthrate=0.7091×0.1498=10.6%
b.i.Theincreasedretentionratioincreasedthesustainablegrowthrate.
Retentionratio=[NetIncome–(Dividendpershare×sharesoutstanding)]/NetIncome
Retentionratioincreasedfrom0.6154in2000to0.7091in2003.
Thisincreaseintheretention
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