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8/9/2019 Brigham Ch9 Stock Edited 97 2003
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Stocks and Their aluation!"e#$ %righa&, '.(., and ).(. Houston. 200*. (unda&entals o#(inancial +anage&ent, th 'd, Harcourt College -ublishers, Ch.
(eatures o# co&&on stock
/eter&ining co&&on stock values
'##icient &arkets
-re#erred stock
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"epresents onership.
1nership i&plies control.
Stockholders elect directors.
/irectors elect &anage&ent.+anage&ents goal$ +a3i&i4e the
stock price.
(acts about Co&&on Stock
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Social5'thical 6uestion
Should &anage&ent be e7uallyconcerned about e&ployees,
custo&ers, suppliers, and 8thepublic,9 or :ust the stockholders;
In an enterprise econo&y,
&anage&ent should ork #orstockholders sub:ect to constraints!environ&ental, #air hiring, etc. andco&petition.
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A #ir& 8goes public9throughan I-1 hen the stock is #irsto##ered to the public.
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Issuer -roceeds #ro& sale
AT=T .0? billion
In#ineon Technologies >2.@2 billion
+etropolitan i#e Ins. Co. >2.B0 billion
TyCo& >2. billion
Denuity >*.* billion
%iggest I-1s o# 2000 in the ESA
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Average Initial "eturns on I-1s in
arious Countries
+alaysia
*00F
@BF
B0F
2BF
%ra4il
-ortu
gal
)apa
n
S0ed
en
Enite
d
States
Cana
da
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*. /ividend groth &odel$
G Constant Droth !Dordon +odel
G Supernor&al !onGconstant Droth Stock
G 'rratic Droth Stock
2. (ree cash #lo ðod
?. Esing the &ultiples o# co¶ble#ir&s
/i##erent Approaches #or aluing
Co&&on Stock
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/e#initions o# Ter&s
/t /ividend the stockholder e3pects toreceive at the end o# Jear t. /0is the&ost recent dividend, hich hasalready been paidK /*is the #irstdividend e3pected, and ill be paid atthe end o# this yearK /2is the dividend
e3pected at the end o# to years, andso #orth. /*represents the #irst cash#lo a ne purchaser o# the stock illreceive. ote that /0, the dividend thathas been paid, is knon ith certainty.
%ut all #uture dividends are e3pectedvalues, so the esti&ate o# /t&ay di##era&ong investors.
-0 Actual &arket price o# the stock today
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-0 '3pected price o# the stock at the end o#Jear t !pronounced 8- hat t9. -0is theintrinsic, or theoretical, value o# the stocktoday as seen by the particular investordoing the analysisK -*is the price
e3pected at the end o# one yearK and so on.ote that -0is the intrinsic value o# the stocktoday based on a particular investors
esti&ate o# the stocks e3pected dividendstrea& and the riskiness o# that strea&.Hence, hereas the &arket price -0is#i3ed and is identical #or all investors, -0could di##er a&ong investors depending on
ho opti&istic they are about theco&pany. The caret, or 8hat9 is used toindicate that -tis an esti&ated value.
contL
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contL
-0, the individual investors esti&ate o# the
intrinsic value today, could be above orbelo -0, the current stock price, but aninvestor ould buy the stock only i#his5her esti&ate o# -0ere e7ual orgreater than -0. Since they are &any
investors in the &arket, there can be &anyvalues #or -0. Hoever, e can think o# an8average9 or 8&arginal9 investors hoseactions actually deter&ine the &arketprice. (or these &arginal investors, -0
&ust -0K otherise a dise7uilibriu&ould e3ist, and buying and selling in the&arket ould change -0, until -0 -0#orthe &arginal investor.
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+arket -rice, -0 the price at hichthe stock sell in the &arket
Intrinsic alue, -0 the value o# anasset that, in the &ind o# a particularinvestor, is :usti#ied by the #actsK -0&ay be di##erent #ro& the assetscurrent &arket price.
Droth "ate, g The e3pected rate o#groth in dividends per share.
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g e3pected groth rate in dividendsas predicted by a &arginal investor.I# dividends are e3pected to gro ata constant rate, g is also e7ual to thee3pected rate o# groth in earnings
and in the stocks price. /i##erentinvestors &ay use di##erent gs toevaluate a #ir&s stock, but the&arket price, -0, is set on the basis
o# the g esti&ated by &arginalinvestors.
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"e7uired "ate o# "eturn, ks The
&ini&u& rate o# return on a co&&onstock that a stockholder considersacceptable.
ks &ini&u& acceptable, or re7uired,
rate o# return on the stock,considering both its riskiness andthe returns available on otherinvest&ents. Again, this ter&
generally relates to &arginalinvestors. The deter&inants o# ksinclude the real rate o# return,e3pected in#lation, and risk.
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'3pected "ate o# "eturn, ks The rateo# return on a co&&on stock that astockholder e3pects to receive in the#uture.
ks '3pected rate o# return that aninvestor ho buys the stock e3pectsto receive in the #uture. Ms!pronounced 8k hat s9 could be
above or belo ks, but one ouldbuy the stock only i# ksere e7ual orgreater than ks.
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Actual, "eali4ed "ate o# "eturn, ks The rate
o# return on a co&&on stock actuallyreceived by stockholders in so&e pastperiod. Ms &ay be greater, or less than,and5or ks.
ks actual, or reali4ed, after-the factrate o#return !pronounce 8k bar s9. Jou &aye3pect to obtain a return o# ks *BF i# youbuy '33on today, but i# the &arket goes
don, you &ay end up ne3t year ith anactual reali4ed return that is &uch loer,perhaps even negative.
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Capital Dains Jield The capital gainduring a given year divided by thebeginning price.
!-*G-05-0 '3pected capital gainsyield on the stock during the co&ingyear. I# the stock sells #or >*0 today,and i# it is e3pected to rise to >*0.B0at the end o# one year, the e3pectedcapital gain is -*G -0 >0.B0.'3pected capital gain yield >0.B05>*0 BF
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'3pected Total "eturn The su& o#the dividend yield and the e3pectedcapital gains yield.
'3pected total return ks '3pecteddividend yield !/*5-0 N e3pectedcapital gains yield !-*G-05-0. In our
e3a&ple, the e3pected total return is*0F N BF *BF
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( ) ( ) ( ) ( )-
/
k
/
k
/
k
/
ks s s s0
**
22
??
* * * *=
+
+
+
+
+
+ +
+
. . .
A stock hose dividends are e3pected togro #orever at a constant rate, g.
Stock alue - o# /ividends
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(or a Constant Droth Stock
/* /0!* N g*
/2
/0
!* N g2 /*
!*Ng*
/t /0!* N gt
-0
I# g is constant, then$
/0!* N g
ksO g
/*ksO g
P
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t
$t g1%%
tt
t&1
%'(%
)'&,*g+f$
t$ '(%'
>
0.2B
Jears !t0
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Assu&e beta *.2, k"( @F, and k+
*2F.
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/0as >2.00 and g is a constant UF.
(ind the e3pected dividends #or thene3t ? years, and their -s !ks *?F
0 *
2.2V@
2
2.?2
?g UF
>*.@U*
>*.@B
/0 2.00
>*.UB0
*?F2.*2
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2.*2
>2.*2
0.0@>?0.2
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/*ill have been paid, so e3pecteddividends are /2,/?, /Vand so on.
?0.2, /2/*!*Ng>2.*2!*.0U>2.2V@K
Could also #ind -*as #ollos$
ksO g 0.*? O 0.0U-*
2.2V@P
>?2.*0
-* -0!*.0U?0.2!*.0U>?2.*0
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(ind the e3pected dividend yield,capital gains yield, and total return
during the #irst year.
/ividend yld
Cap gains yld
Total return @.0F N U.0F *?.0F
/*
-0-*O-0
-0
P>?0.2
>2.*2
@.0F
>?2.*0O>?0.2>?0.2
U.0F
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"earrange &odel to rate o# return #or&$
-
/
k g
/
- gs0* *
0
=
= +
to k s
Then, ks >2.*25>?0.2 N 0.0U 0.0@ N 0.0U *?F
P
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-0 >*B.?
2.00
0.*?
P
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Can no longer use constant groth&odel.
Hoever, groth beco&es constanta#ter ? years.
I# e have supernor&al groth o# ?0F#or ? years, then a longGrun constant
g UF, hat is -0; ksis still *?F.P
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aluing a Supernor&al5onGconstantDroth Stock
Supernor&al5nonGconstant groth is that
part o# the #ir&s li#e cycle in hich it gros
#aster than the econo&y as a hole.
Steps to alue Supernor&al Droth Stock$
*. Co&pute the e3pected #uture cash
dividendscontL.
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2. Co&pute the stocks price at a
#uture point in ti&e, using constantgroth &odel -t /tN*5!rGg. !Jou&ust pick a point a#ter the dividendgroth rate has beco&e constant
?. Co&pute the - o# the e3pected#uture sale price and add that to the- o# all the e3pected cashdividends beteen no and then.
(Source: Emery, D.R., J.D. Finnerty andJ.D. Stowe.1998. rinci!le" of Financial#ana$ement. rentice %all, !! 1&'-1&)
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onconstant groth #olloed by
constant groth$0
2.?0*
2.UV@
?.0VB
VU.**V
* 2 ? Vks *?F
BV.*0@ -0
g ?0F g ?0F g ?0F g UF...
/0 2.00 2.U00 ?.?0 V.?V V.UB
.
. .>UU.BV-?
V.UB
*? 0 0U0
...
P
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2.U0>BV.**
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/uring nonconstant groth,dividend yield !/5- and capitalgains yield are not constant, and
capital gains yield is not e7ual to g.A#ter t ?, g constant UF
capital gains yieldK ks *?FK so /5-
*?FUF @F.
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2B.@2
Suppose g 0F #or t * to ?, and theng is a constant UF.
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I# g GUF, ould anyone buy the
stock; I# so, at hat price;
(ir& still has earnings and still pays
dividends, so -0Q 0$( )
-/
k g
/ g
k gs s0
* 0 *
+
>2.00!0.V >*.
0.*? O !G0.0U 0.* >..
O O
N
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(urther '3a&ple o# Supernor&al DrothStock
etscape is operating in a ne industry that hasrecently caught on ith the public. Sales aregroing at 0F per year. This high sales groth is
e3pected to translate into a 2BF groth rate in cashdividends #or each o# the ne3t V years. A#ter that, thedividend groth rate is e3pected to be BF #orever.Annual dividend paid yesterday is >0.@B. The stocksre7uired return is 22F.
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i Co&pute the e3pected #uture cash dividends$
Ti&e 0 * 2 ? V B U ... /iv!> 0.@B 0.? *.*@2 *.VUB *.?* *.2? 2.0* L
g!F 2BF 2BF 2BF 2BF BF BF BF L
ii (ind the stock price at a #uture ti&e, a point a#ter hich the dividend groth rate has
beco&e constant #orever. That point is at year B, thus$
-B /U5!rGg >2.0*5!0.22G0.0B >**.@U
iii Co&pute the -s o# all the #uture e3pected cash dividends #ound in step !i
and add to the - o# the e3pected #uture sale price !-B calculated in step !ii$
-0 0.?5*.22*N *.*@25*.222 *.VUB5*.22?
N *.?*5*.22VN *.2?5*.22BN **.@U5*.22B
>!0.@U N 0.@@ N 0.0@ N 0.2@ N 0.@** N V.?V
>.2B
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'3a&ple$
ovells dividend as >* last year and is to be >* #or
each o# the ne3t ? years. A#ter its pro:ects have beendeveloped, earnings are e3pected to gro at a high rate#or 2 years as sales resulting #ro& ne pro:ects arereali4ed. The higher earnings are e3pected to result inV0F increase in dividends #or 2 years. A#ter these 2e3traordinary increases in dividends, the dividend
groth rate is e3pected to be ?F per year #orever.ovells re7uired rate o# return is *2F. *.00 *.00 *.00 *.00 *.V0 *.U 2.0* 2.0@ L
Droth 0F 0F 0F V0F V0F ?F ?F ?FL.
contL
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!ii /Bis here the groth rate in dividends is e3pected tobeco&e constant #orever and is the earliest point thatsatis#ies the constantGgroth assu&ption. *.U,
g?F, and r *2F,
-0/*5! *Nr* N /25!*Nr2NL/n5!*NrnN !*Ng/n5W!*Nrn!rGgZ
-0 *.005*.*2*
N *.005*.*22
N *.005*.*2?
N*.V05*.*2V
N *.U5*.*2B
N !*N0.0?*.U5W!*.*2B!0.*2G0.0?Z
>*@.*?
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(ree Cash (lo +ethod5Total Co&pany orCorporate aluation +odel
The #ree cash #lo ðod suggeststhat the value o# the entire #ir&e7uals the present value o# the #ir&s
#ree cash #los !calculated on ana#terGta3 basis.
"ecall that the #ree cash #lo in any
given year can be calculated as$1-AT O et capital invest&ent
!1-AT et operating pro#it a#ter ta3es
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The Corporate aluation +odel !Te3t,pg ?0U
+arket alueco&pany - o# e3pected #uture (reecash #los o# co&pany
(C(*5!*Nr* N(C(25!*Nr2NL(C(n5!*Nrn
(C( !'%IT!*GT N /ep N A&ort G !Cap '3p N Change in 1
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1nce the value o# the #ir& is esti&ated,an esti&ate o# the stock price can be
#ound as #ollos$+ o# co&&on stock !&arket
capitali4ation + o# #ir& O + o#
debt and pre#erred stock.- + o# co&&on stock5[ o# shares.
Esing the (ree Cash (lo +ethod
P
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(ree cash #lo ðod is o#ten
pre#erred to the dividend groth&odel GG particularly #or the largenu&ber o# co&panies that dont paya dividend, or #or ho& it is hard to
#orecast dividends.
Issues "egarding the (ree Cash (lo
+ethod
Cont..
9 - 5$
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Si&ilar to the dividend groth &odel,the #ree cash #lo ðod generally
assu&es that at so&e point in ti&e,the groth rate in #ree cash #lo illbeco&e constant.
Ter&inal value represents the value o#the #ir& at the point in hich grothbeco&es constant.
(C( +ethod Issues !continued
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>V*U.V2
(C( esti&ates #or the ne3t ? years areG>B, >*0, and >20 &illion, a#ter hich the (C( ise3pected to gro at UF. The overall #ir& cost o#
capital is *0F.
!rGg 0.*0G0.0U 0.0V
0
GV.BVB.2UV
*B.02U?.*@
* 2 ? Vk *0F
g UF
GB *0 20 2*.20
2*.200.0V
...
\T?represents the ter&inal value o#the #ir&, at t ?
>B?0 \T?
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I# the #ir& has >V0 &illion in debt andhas *0 &illion shares o# stock, hat is
the price per share;
alue o# e7uity Total value O alue o# debt
>V*U.VO>V0
>[email protected] &illion
-rice per share alue o# e7uity5[ o# shares >[email protected]*0
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Analysts o#ten use the #olloing &ultiples tovalue stocks$
-5'-5C(-5Sales-5Custo&er
'3a&ple$ %ased on co¶ble #ir&s,esti&ate the appropriate -5'. +ultiply this bye3pected earnings to back out an esti&ate o#the stock price.
Esing the +ultiples o# Co¶ble
(ir&s to 'sti&ate Stock -rice
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'3pected returns are obtained by esti&atingdividends and e3pected capital gains !hichcan be #ound using any o# the threeco&&on stock valuation approaches.P
Ms !/*5-0 N g
"e7uired returns are obtained #ro& the
CA-+$ks k"(N !k+O k"(#ir&
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Ho is e7uilibriu& established;
I# ks N g Q ks!CA-+ then
-0is 8too lo9 !a bargain.
%uy orders Q sell ordersK
-0bid upK /*5-0#alls until
!/*5-0 N g ks ks
P
P
/*-0
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*.
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2. Se&istrongG#or& '+H$
All publicly availablein#or&ation is re#lected instock prices, so doesnt pay to
pore over annual reportslooking #or undervaluedstocks. argely true, but
superior analysts can stillpro#it by #inding and using nein#or&ation.
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?. StrongG#or& '+H$All in#or&ation, even insidein#or&ation, is e&bedded instock prices. ot trueGGinsiders
can gain by trading on the basiso# insider in#or&ation, but thatsillegal.
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*. *B,000 or so trained analystsK +%As,
C(As, Technical -h/s.2.
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-re#erred Stock
Hybrid security.
Si&ilar to bonds in that pre#erred
stockholders receive a #i3ed dividend that&ust be paid be#ore dividends can be paidon co&&on stock.
Hoever, unlike interest pay&ents on
bonds, co&panies can o&it dividendpay&ents on pre#erred stock ithout #earo# pushing the #ir& into bankruptcy.
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B0 and
annual dividend >B;
.kB>B0>p
p
F.0.*0*0.0B0>B>kS p