Global Financial Managmnt Valuation of Stocks Copyright 999 by Alon Brav, Stphn Gray, Campbll R Harvy and Ernst Maug. All rights rsrvd. No part of this lctur may b rproducd without th prmission of th authors. Latst Rvision: August 23, 999 3. Introduction This lctur provids an ovrviw of quity scuritis (stocks or shars). Ths scuritis provid an ownrship intrst in th firm whras dbt scuritis (loans, bonds or othr fixd-intrst scuritis) stablish a crditor rlationship with th firm. Aftr a brif ovrviw of som of th institutional dtails of ths scuritis, this modul focuss on valuing quity scuritis by making som simplifying assumptions. This lads us to a discussion of financial ratios that ar widly usd in practic, in particular, dividnd yilds and pric/arnings multipls. Aftr complting this modul, you should b abl to: Undrstand basic transactions involving stocks Dmonstrat why stocks can always b valud as th prsnt valu of futur dividnds. Dtrmin th valu of a stock that pays a constant dividnd Dtrmin th valu of a stock that pays a dividnd that grows at a constant rat. Us th dividnd growth modl to infr th xpctd rturn on quity if you know th xpctd growth rat of a company. Us th dividnd growth modl to infr th xpctd growth rat of futur dividnds for a company whr you know th xpctd rat of rturn on quity. Valu a company using appropriat /E-multipls and undrstand th limitations of this mthodology. Show how th valu of a company can b dcomposd into th valu of growth options and valu of a constant arnings stram.
3. Introduction to Stocks Stocks rprsnt an ownrship intrst in a company and confr thr rights on th ownr of a shar: Vot at company mtings: Sharholdrs vot on mtings on issus ranging from mrgr proposals to changs in th corporat chartr to th lction of corporat dirctors. Collct priodic dividnd paymnts. Unlik intrst paymnts dividnds ar not contractually fixd and can vary. Omission of dividnds dos not triggr bankruptcy. Sll th shar at his or hr discrtion. In som countris this right can b limitd. In this lctur w focus on th valuation of stocks. Thrfor, w ar mainly concrnd with th scond and third point. Howvr, th first point is important for undrstanding th markt for corporat control and corporat govrnanc. Stocks ar first issud to invstors through what is known as th primary or nw issus markt. Typically, companis ar foundd by on or fw ntrprnurs and initially hld by a small numbr of invstors. At som point th company dcids to rais capital by offring shars to th gnral public. This is known as an initial public offring (IO). Th company may dcid to rais mor capital through slling shars in th futur. Ths subsqunt offrings ar calld sasond quity offrings (SEO). IOs and SEOs togthr form th quity primary markt. In most cass companis nlist th hlp of an invstmnt bank for conducting ths offrings. Th bank handls th distribution of shars to invstors. Somtims thy also provid companis with a guarant to sll a crtain numbr of shars in xchang for a f. Invstors purchas stocks for thir rturns. Ths rturns com in th form of: capital gains - th apprciation in valu ovr tim, and 2
dividnds - most companis pay priodic dividnds. Invstors will b rluctant to purchas a stock unlss thr is a mchanism availabl for th spdy rsal of ths stocks. This allows thm to raliz capital gains and to obtain liquidity indpndntly of th payout policy of th company. rovision of a rsal mchanism is th function of th stock xchang (also known as th scondary markt). Invstors ar abl to buy and sll stocks through th stock xchang. Invstors trad btwn thmslvs on ths xchangs. Th company is not a party to th transaction and rcivs no funds as a rsult of ths transactions. Convrsly, invstors can liquidat thir invstmnts for consumption purchass without forcing th company to liquidat invstmnts. This fatur of a scondary markt is crucial for conomic dvlopmnt: companis can plan thir invstmnt policis indpndntly of th consumption pattrns of thir invstors. Various stock indxs ar also maintaind and ar closly watchd by invstors. Whn w think of how th stock markt prformd in a particular priod, w invariably rfr to on of ths indxs. Th following tabls giv th major stock markt indics and thir valus on Novmbr 24, 997. 3
Indx Valu /24/997, 2:56pm EST Dow Jons Industrial Avrag 78.5 S& 5 953.57 NASDAQ Combind Composit Indx 6.36 Toronto Stock Exchang 3 Indx 6746.7 Mxico Bolsa Indx 472.97 Indx Valu /24/997, 2:56pm EST FT-SE Indx 4898.6 CAC 4 Indx 282.48 DAX Indx 383.63 IBEX 35 Indx 667.25 Milan MIB3 Indx 2296. BEL2 Indx 2357.44 Amstrdam Exchangs Indx 875.46 Swiss Markt Indx 5645.7 Indx Valu /24/997, 2:56pm EST Nikki 225 Indx 672.58 Hang Sng Stock Indx 586.36 ASX All Ordinaris Indx 2482. Ths indics giv som kind of avrag rturn for a particular markt. A major diffrnc btwn stock indics is btwn qually wightd and valu-wightd indics. Equally wightd indics giv th sam wight to all stocks, indpndntly of th siz of a particular company. Valu-wightd indics us th markt capitalization (th total valu of all shars outstanding) of ach company. 3.2 Stock Transactions Thr ar thr ways of transacting in stocks: Buy - w bliv that th stock will apprciat in valu ovr tim, or rquir th stock for its risk charactristics as part of our portfolio (W ar xpcting a bullish markt for th stock). It is also said that w ar long in th stock. 4
Sll - w bliv that th stock will dprciat in valu ovr tim or w rquir funds for anothr purpos (liquidity slling). Short Sll - hr w do not own th stock, but w borrow it from anothr invstor, sll it to a third party, and, in thory, rciv th procds. W ar obligatd to pass on to th lndr of th stock any dividnds dclard on th stock and also to pay to th lndr th markt pric of th stock if h himslf should dcid to sll. Whn w short sll, w bliv that th stock will dclin in valu thus nabling us to buy it back at a low pric latr on to mak up our obligations to th lndr. W ar xpcting a barish markt for th stock. It is also said that w ar short in th stock. Whn a short sal is xcutd, th brokrag firm must borrow th shortd scurity from its own invntory or that of anothr institution. Th borrowd scurity is thn dlivrd to th purchasr on th othr sid of th short-sal. Th purchasr thn rcivs dividnds paid out by th corporation. Th short-sllr must pay out any dividnds dclard by th firm to th original ownr from which th scurity was borrowd during th priod in which th short-sal is outstanding. To clos out th short sal, th short sllr must buy th stock in ordr to rturn th scurity originally borrowd. Not that borrowing fs can b significant for hard-to-borrow scuritis bcaus ths scuritis ar in high dmand du to a high lvl of short-slling (.g., Ntscap immdiatly aftr it wnt public). In modling financ problms w oftn assum that th invstor rcivs th full procds of a short sal. Thr ar a numbr of practical mchanics, which limit th invstors' ability to accss ths funds. Th procds from a short sal ar usually hld by an invstor s brokrag firm as 5
collatral. Th invstor usually dos not rciv th intrst from th short sal procds, and will likly hav to mt a margin rquirmnt. In practic, short sals rquir a cash outlay. Thy do not provid a cash inflow. 3.3 Valuation of Stocks In this sction, w dtrmin th valu of a typical stock. Assum that a stock has just paid a dividnd so that th sris of futur priodic dividnds (D t ) can b rprsntd as: riod 2... t Dividnd D D 2... D t W start by looking at a typical shar tradd on th stock xchang and bought and sold onc a yar. Th original buyr at t buys th shar with a viw to sll it at th nd of th first yar at an xpctd pric of. This ntitls th invstor to rciv th first yar's dividnd D. Assum th discount rat ( rquird rat of rturn) for this stock is constant and qual to r. Thn th buyr valus th shar as: D r () But what dtrmins? Simply assum th buyr in on yar's tim dtrmins th pric in just th sam way, and uss th sam discount rat: 2 2 D r (2) Th important assumption hr is that th hypothtical invstors concrnd hr us th sam discount rat. This is not a strong assumption. Th assumption that discount rats ar idntical across priods simplifis th analysis, but is not ssntial. 6
Or, gnrally, for priod T: T T T - D r (3) Substituting quation (2) into quation () givs: D r 2 2 2 D ( r ) (4) Continuing th sam procss: D r D2 ( r ) 2 T T... D T ( r ) (5) Sinc ( r ) T bcoms vry larg as T bcoms vry larg, th xprssion T T ( r ) can b nglctd for a larg tim horizon. 2 Hnc: D r D2 ( r ) 2 D3 ( r ) 3... (6) This shows th first important rsult: Th shar pric quals th prsnt valu of dividnds. 2 Mathmatically, this rquirs that T dos not grow "too fast" in som appropriat sns as T bcoms larg. 7
This formula is intrsting in its own right bcaus it shows that vn though invstors may turn ovr thir portfolios vry frquntly, this dos not hav any impact on th valu of th stock: short trm invstmnt horizons do not translat into a short trmist valuation of shars. Howvr, in ordr to mak us of xprssion (6), w hav to mak som assumptions about futur dividnds. Bfor w turn to this topic, it is usful to turn to quation () onc mor and xprss it in trms of rturns. W solv for r to find: r D - (7) Th first part on th right hand sid is commonly known as th dividnd yild. This is a financial ratio widly usd by practitionrs. Howvr, not that in practic w do not know D sinc it is an xpctd valu about a futur dividnd paymnt. ractitionrs commonly rfr to th dividnd yild as D /. This diffrnc is important and w shall thrfor rfr to D / as th historic or trailing dividnd yild, and to D / as th prospctiv dividnd yild. Th scond part on th right hand sid of (7) is th capital gain, xprssd as a prcntag of th currnt stock pric. Thn w can xprss (7) as: Rturn on quity rospctiv Dividnd Yild Expctd Capital Gain 3.4 Th "Constant Growth" Formula Th simplst assumption about dividnds is that thy stay constant ovr tim, so that D D 2 D 3.. D. Thn xprssion (6) simplifis to: 8
D r DY (8) r D whr DY dnots th dividnd yild. Hnc, w hav two important conclusions:. If th dividnd is xpctd to stay constant ovr tim, shars can b valud lik prptual bonds as D/r. 2. If th dividnd is xpctd to stay constant, th xpctd rturn on quity is qual to th dividnd yild. Unfortunatly, constancy of dividnds is a vry spcific assumption with littl ralism, and thrfor fw applications. A mor gnral assumption is that dividnds grow at a constant rat. Hnc, assum that dividnds grow at a constant rat g forvr: D D ( g) 2 D D ( g) D ( g ) 3 2 2 D D ( g) D ( g ) 4 3 3... D D ( g) D ( g ) T T - T - Substituting ths xprssions into (6) givs: D r D ( g) 2 ( r ) T -... D ( g ) T ( r )... (9) 9
Assum that g is smallr than r. 3 Thn th gnral formula for adding this sris is (s th appndix for a drivation): D r - g () Not that () rducs to (8) if g, hnc th constant dividnd cas is covrd as a spcial cas. From this w can s immdiatly: r D g () This givs th third important rsult: Expctd Rturn on Equity rospctiv Dividnd Yild Growth Rat Using (7) togthr with () givs also: g ( ) g (2) 3 T It turns out that g<r is prcisly th condition notd abov to conclud that ( r ) T bcoms small as T T bcoms larg. If g<r, thn would bcom infinitly larg, hnc w would hav to conclud ( ) T r that is infinitly larg, hardly a plausibl conclusion.
Hnc, if w assum that th company is in a stady stat whr dividnds ar xpctd to grow at a constant rat g, w also xpct that th stock pric grows at th sam rat constant rat g. Th strongst assumption w mad in driving () is th constancy of th growth rat, that is, w assum th firm is in a "stady stat". This is a strong assumption for any firm, but if w viw 2.5 2..5..5. Grow th ath Analyst Forcast 3 5 7 9 3 5 g as som kind of avrag w can sacrific som gnrality for simplicity. Howvr, for firms which ar clarly not in a stady stat (considr firms whr th currnt dividnd and is zro, so in th first yar in which thy pay a dividnd th dividnd growth will b infinity!), this procdur is ntirly inappropriat. In this cas w hav to xtnd th constant growth modl and dfin subpriods with diffrnt growth rats. Altrnativly, w could formulat a modl whr th dividnd growth modl holds for all priods aftr 3-5 yars, and w us analysts dividnd forcasts for th first fw yars. This is illustratd in th following graph: Th graph illustrats xponntial dividnd growth, starting at a dividnd of $. in yar. Th squar-shapd points illustrat xponntial growth (i.., growth at a constant rat). Th triangl shapd points illustrat analyst s forcast basd on dtaild projctions for th first 5 yars.
3.5. Valuation of Gnral Motors: an xampl In ordr to s how ths formula may b applid, considr th cas of Gnral Motors. Th trailing (historic) dividnd of GM in Dcmbr 96 was $.6 pr shar. Othr data ar: Numbr of shars outstanding: 856,695, Markt capitalization: $ 46.3bn Th markt capitalization of a company is always dfind as: MCANumbr of shars outstanding*shar pric Hnc, w can us th apparatus w hav built so far ithr on a pr shar basis (divid total arnings, dividnds and MCA by th numbr of shars), or for th company as a whol. Suppos you forcast that until th nd of 997 GM s dividnd will b $.75 pr shar, and thn grow at a constant rat forvr aftr. What valuation for GM do you obtain for altrnativ combinations of th growth rat and th discount rat? Th following tabl shows th typ of rsults you obtain: Tabl Rturn/ 3% 4% 4.5% 5% 6% 7% Growth 7% 37.48 49.97 59.97 74.96 49.92-8% 29.98 37.48 42.83 49.97 74.96 49.92 9% 24.99 29.98 33.32 37.48 49.97 74.96 % 2.42 24.99 27.26 29.98 37.48 49.97 % 8.74 2.42 23.6 24.99 29.98 37.48 2% 6.66 8.74 9.99 2.42 24.99 29.98 In ordr to s how you obtain ths rsults, considr th cas of a 5% annual growth rat and 9% rturn. (th boxd ntry in th tabl). Our dividnd pr shar forcast was $.75. Multiplying this with th numbr of shars outstanding givs a total xpctd dividnd for GM for 998 of $.499bn, or a prospctiv dividnd yild of 3.78%. Thn w hav: 2
MCA D g $.499bn.9.5 998 GM r $37. 48 GM GM bn (3) Hnc, w can us th dividnd growth modl in ordr to valu th quity of a company by using th following stps:. Forcast th nd of yar dividnd of th company 2. Estimat th growth rat of dividnds and th rquird rat of rturn on capital 3. Us formula () Convrsly, w can also us th formula in th othr vrsions discussd abov in ordr to: Infr th growth rat of dividnds: If you know th xpctd rturn on quity and th currnt valu, you can infr th growth rat (rarrang () or ()) xpctd by th markt. On way of stimating xpctd rturns is using anothr modl for prdicting rquird rturns. W will discuss on such modl, th Capital Asst ricing Modl, in a subsqunt lctur. Infr xpctd rturns. If you know th growth rat of dividnds (. g., from industry forcasts), you can infr th cost of quity capital usd by th markt. 3.6 Earnings yilds and /E ratios Th most widly usd ratio ar pric arnings multipls, or short /E multipls. Dnot arnings pr shar by E. Thn th arnings yild is dfind as E /. It is thrfor th rciprocal of th /E-ratio dfind as / E. Not that ths ar prospctiv /E-ratios and arnings yilds, 3
and that financial analysts rfr oftn to historic or trailing valus, dfind as E / and / E rspctivly. Dividnds and arnings ar rlatd via th company s payout policy. This can b summarizd in th payout ratio d dfind as th ratio of dividnds pr shar and arnings pr shar: d D E (4) Thn th dividnd can b writtn as D de which can b substitutd into () to giv: r E *d g (5) which rlats to rquird rturn on quity to th arnings yild. Rarranging onc mor givs: E d r g (6) This shows th rsult that: If two companis hav th sam payout policy, th sam cost of quity capital and th sam growth rat, thn thy should also hav th sam /E ratio. Th problm with using th abov masurs is that thy rfr to prospctiv dividnd and arnings yilds, whras th financial prss oftn rports historic yilds. Howvr, it is asy to s that thy can b rlatd in a similar way by assuming that dividnds and arnings grow at th constant rat g from now on, i.. that D (g)d. If d is constant ovr tim, this implis also that E (g)e. Thn () and (5) and (6) bcom: 4
E r g ( g) ( g) E D ( g) d r g (7) W shall work through on xampl on infrring th growth rat from publicly availabl data using (7). Considr th big thr Amrican car manufacturrs. Th main data ar givn in th following tabl: Tabl 2 Chryslr Ford GM MCA ($billion) 3.92 4.7 46.3 No. of shars (in s) 72,5,87, 856,695 Shar ric $44. $34.3 $54.6 Dividnd pr shar $.35 $.43 $.6 Dividnd Yild 3.7% 4.7% 2.96% ES $5.3 $3.72 $6.6 /E ratio 8.75 9.22 8.92 Thn rarranging (7) givs: g r D D (8) whr D / is th historical dividnd yild rfrrd to in tabl II. Thn w obtain th following implid growth rats (dpnding on th discount rats in th lft-hand column). 5
Rturns Implid growth rats Chryslr Ford GM 9% 5.76% 4.64% 5.87% % 6.73% 5.6% 6.84% % 7.7% 6.56% 7.8% 2% 8.67% 7.52% 8.78% 3% 9.64% 8.48% 9.75% 4%.6% 9.44%.72% 5%.58%.4%.69% So, if w know (. g. from analysis driving from th capital asst pricing modl, s th lctur on th capital asst pricing modl) that th rquird rat of rturn on quity is 2%, thn w can driv th xpctd growth rat for Ford (historic dividnd yild 4.7%) as: g Ford.2.47.47.752 which givs th rsult of 7.52% statd in th tabl. 3.7 (How) Should you us /E ratios? Analysts oftn rfr to companis with a low /E multipl as bing undrvalud, or as ovrvalud if th /E ratio is high. (.g. if thy say that hilip Morris has a modst /E ). Th /E ratio bcoms thn lik a pric tag in a suprmarkt: th industry avrag says that $m of rtail arnings or arnings from computr manufacturing tc. sll for a crtain pric or multipl, say 28. If you can thn buy $m of arnings in computr manufacturing for 4, you strik a bargain, bcaus you ar ntitld to th sam arnings, hnc dividnd stram, for a lowr pric. 6
Our analysis has two implications for this typ of argumnt. On th positiv sid, w hav shown that a simpl dividnd discount modl can rationaliz th /E ratio. Thn a /E ratio can b usd for company valuation using th following stps:. Forcast th company s nd of priod arnings (. g. us forcasts of sals and margins tc.). 2. Estimat growth and th rquird rat of rturn (us industry forcasts, asst-pricing thory). 3. Estimat which proportion of arnings nds to b rtaind so that invstmnt is sufficint to gnrat th growth w hav assumd in stp 2. Th rtntion ratio of arnings is thn -d in our notation. 4. Us formula (6) to valu th shar as d E r g. Howvr, /E ratios ar almost nvr usd this way. Th whol point of using financial ratios is to avoid th stimations involvd in stps -3. Instad, practitionrs us th following two-stp approach:. Find a sampl of companis in th sam industry, which ar similar to th company you wish to valu and dtrmin th avrag (historical or trailing) /E ratio of this sampl. 2. Valu th company by using th approximation: V / E * E Company Avrag Company (9) 7
This advantag of th scond procdur is that it uss markt stimats of th ratio r d g. Sinc masuring and stimating ach of th componnts is fraught with rrors driving from th rspctiv forcasting modls for rquird rturns, growth rats tc., using a markt masurmnt may avoid this. Th disadvantag of this procdur is that it maks it asy to ovrlook th assumptions that go into th analysis:. Constant growth, th company is in a stady stat. 2. Th company is comparabl to th industry sampl with rspct to xpctd rturns on quity(r ), growth prospcts (g), and rtntion ratio(-d). Assumption 2 is th mor rstrictiv on. Not in particular that two companis can hav th sam tchnological structur and markts, and thrfor th sam growth prospcts, but still diffr with rspct to xpctd rturns on quity,. g. bcaus thy hav diffrnt lvrag and diffrnt dbt policis. W discuss this at a latr stag whn w analyz capital structur and borrowing. Many tims practitionrs fl unasy about th constant growth assumption. This is a much lss srious problm. In most cass, vn a fully spcifid discountd cash flow analysis (s th lcturs on projct appraisal) will procd in two stps: () stimat th V of nt cash flows for 5- yars into th futur, and (2) stimat a horizon valu or trminal valu by using som variant of a constant growth scnario. Typically, mor than 75% of a company s valu coms from th horizon valu, and th (implicit) assumptions about futur growth. Hnc, vn though th constant growth assumption may b a strong on, it will b part of most valuation procdurs in on way or anothr. 8
Hnc, /E ratios can provid usful information for company valuation, but thy nd to b handld with car. Th apparnt simplicity of just using on financial ratio can b problmatic if th strong assumptions bhind it ar ovrlookd. Howvr, if you us it, mak sur that th company you wish to valu is always comparabl with rspct to th cofficints that dtrmin th multipl. This rquirs, among othr things, to compar companis with broadly similar lvrag and oprating charactristics. 3.8 Financial ratios in practic This sction lists a numbr of typical applications, whr financial commntators rfr to pric/ arnings or othr multipls for valuation purposs: (A) Company valuation On Dcmbr 3 996 Linda Sandlr, Staff Rportr of th WSJ wrot in th Hard on th Strt column: Invstors pay clos attntion to Mr. Bufftt s oracular pronouncmnts about invstmnts, particularly his notion of ral or intrinsic, valu. ( ) Th asy part is putting a multipl on Brkshir s arnings or cash flow from its wholly ownd insuranc and manufacturing businsss. ( ) Th hard part is dciding on a fair valu for Brkshir s invstmnt portfolio ( ). Brkshir s big stak in Coca-Cola cost around $.3 billion. ( ) Cok stock is up 45% this yar; it now slls for narly 4 tims arnings in th past 2 months. Gilltt is Brkshir s scond biggst holding, valud at $3.5 billion at Sptmbr 3. That stock is up 37% this yar and its trailing pric-arnings multipl is 35. Hnc, th articl argus that a portfolio (Bufft s Brkshir Hathaway) may b fully valud (or vn ovrvalud), bcaus som of th major individual assts of this portfolio () trad at high pric arnings multipls and (2) th stocks hav risn a lot rcntly. W s from (6) that /E- 9
ratios dpnd dirctly on th growth rat, hnc growth stocks hav highr /E-ratios. Hnc, th argumnt abov could b right in arguing that 4 tims arnings is too high a pric for Cok if Cok is in a matur markt wr th growth potntial is limitd. (B) Mrgrs and Acquisitions Stvn Lipin, Grg Jaff and Bnjamin A. Holdn, wrot in th WSJ on Dcmbr 9 on in an articl ntitld Wstrn Rsourcs Bids To Acquir Rst of ADT Th bid for ADT as a multipl of rvnu appars to b valud at lss than th $368 million Wstrn agrd to pay for Wstinghous Elctric Corp. s alarm businss. Wstrn paid a pric quivalnt to about 4.8 tims th Wstinghous scurity systms stimatd annual rcurring rvnu for 996, says Edward Wojachowski, an analyst with Strong Capital Managmnt, which owns about 62, ADT shars. Th Wstrn bid is about 4.5 tims ADT s projctd annual rcurring rvnu for 996, h said. Bcaus ADT s dominant position in th markt, it should b abl to gt at last fiv tims annual rcurring rvnu ( ) Mrgrs and acquisitions always rquir a carful valuation of th asst to b bought. Th articl shows how financial analysts us a multipl - hr rvnu multipl - in ordr to compar this transaction with a similar transaction in th sam industry and assss whthr th pric is fair. Not that rvnus and arnings ar rlatd (arnings bfor intrst and taxs dividd by rvnus quals th sals margin). Hr th analyst argus that a low multipl is indicativ of a low transaction pric. Th mrit of this argumnt dpnds critically on whthr th "dominant position" translats into mor growth than that of othr comptitors: you can only grow at a highr rat than your comptitors if you incras your markt shar. 2
(C) ublic stock offrings On Dcmbr 2 996 Bakr Li (A - Dow Jons Nws Srvic) wrot th following in th Dow Jons Businss Nws in an articl on Asian IO Focus/Taiwan: Ultima Elctronics Sn A Bargain (quotd according to Wall Strt Journal Intractiv Edition): Half of th plannd IO shars wr sold through a public offring compltd Dcmbr 7 with a winning pric of $36. (Taiwan) pr shar ( ) Ultima is posd to rach around NT$ 44. in th first thr days upon listing, forcasts Hsih Chih-mo, an lctronics analyst with Top Soon ortfolio Corporation. ( ). Kvin Chan, an lctronics analyst with Cor acific Scuritis Corp., is mor cautious, saying NT$38 is a rasonabl xpctation for th stock s dbut. H taks into account his company s forcast 997 arnings pr shar (ES) of NT$3.6 for Ultimat which givs a consrvativ pric/arnings ratio (/E) of 4 tims, wll blow th industry s avrag of 28 tims. Annual growth rat of global scannr output is xpctd (at) 4% in th following two yars says Sancy Wang, company chairman and chif xcutiv officr. 4 ublic stock offrings (IOs) ar gnrally offrd at prics to invstors that ar blow th prics thy trad subsquntly on th stock xchang. In som sns, IOs ar offrd at a discount. This phnomnon has bn widly obsrvd and is rfrrd to as IO undrpricing. IOs ar notoriously difficult to pric, sinc it is not always clar what a "comparabl" company is. 4 Thr may b an rror hr, ithr in th sourc or in th copy. ES of NT$3.6 multiplid by /E of 4 givs NT$5.4, not $38. 2
3.9 rsnt Valu of Growth Opportunitis You oftn har th buzz words growth firm. W will xplor what this mans in th contxt of our stock valuation modl. From th formulas alrady dvlopd, w can sparat th pric of a company s stock into two componnts: a no growth componnt and a growth componnt. Bfor w work out th dtails, w could writ th pric of th shar as: E r VGO (2) whr VGO quals th prsnt valu of growth opportunitis. Th first trm is th prsnt valu of an arnings flow if all arnings in th futur wr constant and qual to E. If th firm wr not xpctd to grow, all arnings would b paid in dividnds (D t E t ) and th valu of th stock would b th prsnt valu of th dividnd annuity givn abov. It is unlikly that th firm will not hav any growth opportunitis. Th mor ralistic scnario is that som of th arnings ar plowd back into th firm s oprations and thr is an additional trm that rprsnts th prsnt valu of growth opportunitis. In trms of th formula abov, you can considr th VGO to b a rmaindr trm. W can dtrmin th valu of th no growth portion of th stock pric. If th stock pric is availabl, thn th diffrnc must b th prsnt valu of th growth opportunitis. Th splitting of th valu of th stock into a growth and a no growth componnt is an insightful xrcis. It is now tim to rconcil our dividnd growth formula with this split. Rcall that d is th fraction of arnings distributd as dividnds, hnc (-d), rprsnts that fraction of arnings that ar plowd back into th firm. 22
Rarranging (5) w obtain: E r VGO g r ( d ) g r ( d ) E E (2) Not that th constant stram of arnings, E, is pulld out of th VGO to avoid doubl counting. Equation (2) has a simpl intrprtation: g is th xpctd apprciation in th stock pric ovr th nxt priod ( g d E ) is ). Th scond trm in th numrator ( ( ) simply th amount of invstmnt ncssary to gnrat this apprciation in pric. Hnc, th numrator is th nt incras in sharholdr valu pr priod: sharholdrs "buy" th apprciation in stock pric g through a rducd distribution of dividnds ((-d)e ). Th prsnt valu of growth opportunitis is th capitalizd valu of all futur incrmnts of sharholdr valu. To illustrat som of ths points, it is usful to go through a fw xampls. Suppos that TECHCO, Inc. will hav arnings pr shar nxt yar of US $4. Th company will plow back 6% of its arnings into continuing oprations. Th rquird rat of rturn for th firm, r, is 6%, th xpctd growth rat of futur arnings is 2%. Calculat: ) th stock pric, 2) th E ratio, 3) th VGO, and 4) th amounts of invstmnt that produc th VGO. Th first stp of this xrcis is to carfully map ths data into th paramtrs of our modl: 23
g 2% r 6% E $4. -d 6% Th stock pric calculation is straightforward. W know th nxt priod s arnings, so th dividnd will b: D de (.4)(4.) $.6 W can dduc what th growth in arnings is going to b. Th company is going to plow back 6% of its arnings to b usd in projcts that ar xpctd to arn 2% pr yar. Now w can plug dirctly into th constant dividnd growth modl: D $.6.6.2 r g $4. Th E ratio is also fairly lmntary. W know that: E $4 $4 Sinc arnings will b growing at 2%, w can calculat th trailing E-ratio: E E / ( g) $4 $4. /.2.2 W can us our formula for th VGO to calculat this quantity: VGO E $4. $4.6 r $5. 24
So, $25 of th stock pric is rlatd to th prsnt valu of arnings without growth opportunitis, and $5 of th stock pric is rlatd to th growth opportunitis of th firm. Now th hardst part of th problm is to show th amounts of invstmnt that produc th VGO. Lt s tak it in stps. In th first yar, th firm plows back (.6)(4.), or $2.4 of thir arnings back into th firms oprations. Hnc, sharholdrs' distribution of dividnds is rducd by xactly this amount. This gnrats an incras in stock pric of $4.*.2$4.8, i.., w xpct th stock pric to incras from $4. to $44.8. Hnc, sharholdrs' nt gain is $4.8- $2.4$2.4. Th valu of this in prptuity is: VGO$2.4 /.6 $5. A VGO of $5 is th sam rsult that w arrivd at arlir. 3. Th Dividnd Discount Modl - A Usr s Guid Th numbr of diffrnt quations of th form &#) *? w hav drivd and discussd abov is somtims bwildring and confusing. This sction attmpts to provid som guidanc as to how ths quations ar rlatd and whn to us which on. Th fundamntal and gnral quation that is at th basis of all othrs is: 5 D r D2 ( r ) 2 D3 ( r ) 3... (6) 5 S th formula on slid of th class nots. 25
which is rpatd hr for convninc. This xprsss th currnt pric as a function of all futur dividnds. Hnc, in ordr to mak us of (6) you nd a complt forcasting modl that xtnds into all priods into th futur. If you hav such a forcast, simply us th forcast valus for D, D 2,,D and obtain a valuation. You ar rarly - if vr - in a privilgd situation whr you hav such a forcast, so you nd to gnrat a forcast. All othr quations for th dividnd discount modl ar about gnrating forcasts. Considr th cas is whr you only hav a dividnd forcast for a finit tim horizon T, say yars, so you know D, D 2,,D T. Thn you can us a finit horizon vrsion of th modl, whr you us th xplicit forcasts for th first T priods, and th constant growth formula for th horizon valu T. This givs us: 6 i T i i ( r ) ( r ) ( r ) ( g) DT T ( r ) ( r g) i T Di T T Di (22) i Hr w hav substitutd T ( g) DT DT for th dividnds aftr priod T, for which w r g r g hav no othr forcast, so w us constant growth as a first approximation to gnrat such a forcast. If w can only forcast dividnds on priod into th futur, thn w us a spcial vrsion of (22) for T, and in this cas w obtain th standard quation for th dividnd growth modl: 7 6 S slid 22 of th class nots. 7 S slid 4 of th class nots. 26
D r - g () Finally, if w do not vn obtain a forcast for this yar s dividnd, thn th only valu w may hav is th historic dividnd D. Thn w us our forcasting modl for on priod, so that ( ) D g D. As a rsult th valuation quation bcoms: 8 ( g) D r - g (23) which only rlis on th known historic dividnd and our stimats for th constant growth rat and th cost of quity capital. W can summariz our discussion in th following flow chart. In this chart "know.." rfrs to having a forcast xcpt constant growth. 8 S slids 2, 28 of th class nots. 27
Figur Know all futur dividnds to infinity? YES Us (6) NO Know dividnds until yar T? YES Us (22) NO Know dividnds for currnt yar? YES Us () NO Us formula (23). 3. Summary and rviw Th ky rsults of this lctur ar: Stocks can b valud as prsnt discountd valus of futur dividnds or as dividnds plus xpctd capital gains. 28
rojcting growing dividnds into th futur lads to th dividnd growth modl. This modl implis that th xpctd rturn on quity quals th prospctiv dividnds plus xpctd capital gains. /E ratios ar dtrmind by thr ky paramtrs: () th growth rat of futur dividnds, (2) th xpctd rturn on quitis, and (3) th payout ratio. A valuation using /E ratio is simpl, but rquirs that comparabl companis ar carfully slctd. Stock prics can b dcomposd into on componnt that rflcts th prsnt valu of futur arnings gnratd by assts in plac, and anothr componnt that rflcts th prsnt valu of growth opportunitis. Th analysis prsntd hr is simpl. This has th advantag of gnrating powrful rsults, but implis also som limitations. Th dividnd growth modl allows us to dtrmin a rlationship btwn th constant growth rat and th xpctd rturn on quity, but w nd to know on in ordr to dtrmin th othr. Constant growth is a limiting assumption sinc som companis ar not in a stady stat. Financial ratios ar widly usd in practic bcaus thy ar simpl, but thir applicability dpnds on a numbr of assumptions. W nd to dvlop mor robust mthods to conduct company valuation. 29
3 Appndix Drivation of quation (): Rconsidr quation (9) abov. W can rwrit this as: ( ) r g x whr x x x r D... 3 2 (A ) Sinc g<r by assumption, w hav x<. Thn w can us a standard algbraic rsult: ( )( ) g r r x x x x x x x x x x x x......... 3 2 3 2 2 3 2 (A 2) Insrting (A 2) into (A ) w obtain: g r D g r r r D (A 3) which rproducs (). Drivation of quation (2): Us (6) and obsrv th following squnc: ( ) E d g E r de g r g r de (A 4) Thn divid th last quation by r.
Furthr Exampls Exampl A company has just paid a dividnd of US $2 pr shar. Th dividnd is xpctd to grow at a rat of prcnt pr yar indfinitly. What is th stock pric if th rquird rat of rturn is 2 prcnt? Hr w apply th constant growth rat formula. W not that sinc th currnt dividnd D 2, th priod dividnd, D, will b D (g). Thus: D D ( g) 2(.) r g r g.2. $ Exampl 2 Suppos th company in th prvious xampl has a nw managmnt. It is now xpctd that th rat of growth in dividnds will b 5 prcnt pr yar for 3 yars and thn prcnt pr yar thraftr. What is th nw stock pric if th rquird rturn rmains at 2 prcnt? Sinc th stock pays dividnds at a constant rat indfinitly aftr yar 3, find th pric of th stock at th nd of yar 3 using th constant growth formula: D 3.346.2. 4 3 r g 67.3 Finally, comput th currnt stock pric by taking th prsnt valu of ach of th first thr dividnds and th prsnt valu of th stock pric in yar 3: 2.3 2.645 342 67.3 2 3 3.2.2.2.2 $25.4 3
Exampl 3 You r intrstd in buying th stock of company WWWFinanc. Analysts xpct arnings, and consquntly dividnds, to incras at a rat of % pr yar. Th nxt dividnd payout is xpctd to b 85 yn. Your rquird rat of rturn is 5%. What should th stock pric b? 85.5. 3,7 b) Assum that you hav paid th pric from a) for company WWWFinanc stock. Suddnly, analysts rvis thir futur arnings stimats for th company upwards to %. What is th nw stock pric? What absolut (prcntag) gain hav you ralizd on your invstmnt? divgr % Gain Gain Absolut rcnt 85*. 5,33.75 Yn.5. 5,33.75 37,433.75,433.75 38.75% 3,7 Exampl 4 A company has a rquird rturn on quity of % and a prospctiv dividnd yild of 4%. What is th xpctd growth? How much would th constant growth rat hav to dcras so that th stock pric falls by 2%? What is th dividnd yild aftr th xpctd growth rat has falln? g % 4% 6% Aftr th fall th stock pric drops from to '. W hav: 32
33 5% 5% % 5%.8.4.4.8 D r g D D D D Hnc, a % drop in th constant growth rat from 6% to 5% would caus a drop in th stock pric of 2% and an incras in th dividnd yild from 4% to 5%.
Important Trminology Initial public offring 2 Sasond quity offrings 2 Constant growth formula 9 Dividnd discount modl Usr s guid 25 Dividnd yild historic 8 prospctiv 8 trailing 8 Earnings yilds 4 Equity scuritis qually wightd 4 valu-wightd 4 markt capitalization 4, 2 Nw issus markt 2 /E ratio 4 us of 6 rsnt Valu of Growth Opportunitis 2 rimary Markt 2 Scondary markt 3 Short sal 5 growth firm 2 Stock markt indx 3 34
Important Formula Equation (6), (), (6): D r D2 ( r ) 2 D3 ( r ) 3... (6) D r - g () E d r g (6) Thr ar many quations in this lctur, but if you rmmbr (), th dfinition of th payout ratio dd/e, th dfinition of th growth rat g, thn you can driv all of thm from (). 35