■
va ua ,on
LEARNING OBJECTIVES
After studying this chapter, yo,u sf1ould be able to:
9. 1 describe tt1e four types of secondary rnarkets
9 .2 explain why many financial ar,alysts treat preference shares as a special type of bond rather than an
eqLJity security
9.3 describe how the general dividend valuation n1odel values a share
9.4 discuss the assumptions tl1at are necessa.ry to make the general dividend valuation model easier to use
and be able to use the model to ca.lculate the value of a company's ordinary shares
9.5 explain ho\v valuing preference shares with a stated maturity differs from valuing preference shares with
no maturity date and be able to calculate the price of a preference share under both conditions.
.._
r in lin!! tl1 ;tcluttl
I1ric of a 11 ublic1y tLdlce_l,har
., 1
.
,·
·
~ is ca y. < canJ11~t look it up in tl1ei\11.\trc1lil111 t~i11c111,·i(1/
. 11
le 11 rI cc l< ~ t~l)' l hc ~. 1r1·1,, . h
.
tfran1at1L'i.l . ·
''
• · ar prices L"hanoc all rh tir11e- ~on1ctimc-...
13 t, . 11 2()()5 ar d 2()07 th f"L
l .
-\ l~ r·t 1I "Lil t
. .· ] I ' (All
~ ()C fll't 'k-'t
.
Ord111a11e~ . n( ex , , rdi-) r •achinu a cak or
'/ t c_xrcr~cn cd a bull mnrkct wilh 1hc ASX All
Rt ,,icl,' ()f 011 1llll'.
Lll tfo11~l L' l)L' ·t ti
l
l
I
67 7
J. I P<lint 111 Oc1ol1 ·r 2()()7. 1 Thi~ \.\'~~ followccl by
·1··
,.,
,1·
111g,1 1>\-vof32<)69'111 [·h ·
2.
"
,tl'ad1) 111 1 ~"C( 111 v;.tlt1 "Xe , 111 f'or. r
.
.- ·
c 1uary 2()0~. Since 1J1cn. the All (Jrd\ h:t~
1
11 rL' I p r, (> f
•
.
•
'
• I
d~cl111cd fl) 4 )7( . I 1n c1 t ·I1 1b 'r 20 11
.
c ~, \ It 1 a clo, n\vard tr nd. For cxarnpJe, the 1\11 Orel.
11t1l t<>s-- tu S8985 111
·
·
_O 19 , hc11 tl1e 111clcx r~rovcrccl bact .· ,
~
· ·
l)ruary 2() 15 anti t > 694 7. 9 i11 Nc>vcrnber
.
.
o its 0 ctobcr 2()()7 I . I1 ' .
~ h --11 ~l1ar J rice rt ( r f·tll llt)\V (I .
irg .· Tl1e. e tr n(I arc . ho\\'n in fiourc 9 J
'·
<>111 '\to·
I 1111
c:
· •
,~anc
·111 i'tlm~ttnagcr~ k' 110\V \i t,en Jl
· J· l1fl1C
•
,c ll ''l 11 () tl1c 1·\VOi(·I • l1{)\ l'~ll1 tl1C)' tell I
to tJUY or
.
t. .
.
I I le Illar~ ·t pric
r'
I. . .
.
.
dcrcl< f) as 1,11c- al 1at1 )fl llll>clcl .1111 , .
L
"~ 1,trc 1cf lcct~ 1t
alue? On~ arJproach ,s to
on1p,r·th· '\Li111·t·f
I
.
.
111arket I rrcc 1~ he l<)\V t l1c est j iit ·tt 11 • . .
ct L rc>n l 1• n1< lei I ,v I Lh the rnarkct price. If the
1
'
• ~ ~ 11~u ' 111ay l1c uncJ · l ,1 •
·
t l ll)' tl1c ]1arc. (Of c ur~c. otllrr f·
.
.
. er a ucu. 111 \Vl11 - h ca,c th in\!c tor might (leciclc
d l 1Ol :,. 111 l)' \ C10u) 1 111 lO Lf1 { 111 ] f • •
•
clc,clo1 a11c1 ~11 f)1)' 11 . tre-,aluati )Jl 111 ,. J .
.
~1 c ec,~1(,n tel I uy.) In tl11s chapter, \\C
< ( 1c1" L1·1t cn·,l le • t 0
·1111
•
~i111ilar l< tlll>,e u~t·tl in 11r~tcticc 11.\} l- . ,·.,
c~t a.tc a hare, aJue. The 111oclcl'.\ are very
4u'-;
:1 cra,11 lur111g _()()8 and 2()09. 1 •acl ·
.
·r
1 •
•
•
l
' l
(
l.
111,111 1,1 analyst, .
Thi, cha1,tcr f<>L'. Iscs ,1 et1uil)' " cui't•
.
I I s ,lfl 11 1()\\ Il1c ·uc , I
w
fi. .
.
I r
faLl< r~ tl1al Jclc1111111e ~l liar,·~ ,.
• t·f , . .
~
tt Lieu.
e 11 st c a111111e t 1c undarncntal
11
' u . icn we ll1~ ·u~'-; "'c =>r• I I ..1
,, I
- harc·~1riL·t' .,/1,,,,//hc \\
' .·
e , t auat on111oue .Thc~en1oclc]~tcllu\\.Vhat
'1
•
c.: tan on11 ar' ot1r cst1n
·
.
.
1•1t cs f l(.>111
,
~ucnt 111 ti I~ with
ltc·111t1I 1narkct pr1ccc;;.
•
.
•
.1
'
- - - ----
-
\ii
-
All Ords 14-year trend cha
8000
7000
6000
5000
g
0
4000
►
{/)
3000
2000
1000
0
L.[)
0
I
C
(ii
J
(!)
0
I
C
CTJ
-,
,-
0
0
,I
I
..--I
C
C
C
C
J
J
co
0)
I
I
I
C
C'J
C:
"
0
-,
0
ro
J
ro
J
ro
..--
co
N
co
J
I
..--I
..--
C
C
C
c.o
C'
J
J
J
J
Cf)
,-
·ro
~
ro
l{)
I
ro
,-
ro
,-....
J
,-
'
C
co
co
r-
0)
..--
I
I
C
C
co
-,
ro
J
Year
our : (i_j .,\SX I in1ll d A ~
'JX OOk 62 ➔ <,91. ASX,_()_() 1\II right~ rc~l:rvcd. "l hi, n1aIcrial i, reproduced,, ith the pcrmi ~ion of
,.\ .X . Thi, 111dtcr1al , huuld 1101 bL'. ri:proc.Juccc.J ,tored in .i r ·1ri1.:val '-) 'lt:n1 lf 11 .111,1nillcd in any f rn1 \\'h~ther in,, hol~ r in part
\\ 11ho111 the prior\'- r1llcn pcrrni ion of A \X.
\\ hy arc ~11ar~-\·,1Juati()J1 f orr ulH" i, 1Jt>rt ·1nt r )' (}ll t study in a corporate fina11
cot1r e? Fir~t.
~ <)1npan)1 '~ n1an~1gcrncnt 111ay ,>1anl tt> "-n l\ ' ii th'
111pany· · ' l1ar"s ar · unllcr\-'alr1 d or o,,crvalt1 d.
F<)r t; a11 I Jc. if the . liar ~ a tindcr,,afuccJ. 1na11 ·1<1 11 nt 1n·1)1 \V~111t lt) buy b,t ·k . l1are . to r~i ,Ll i11 the
future r po ' tpoI1c n quily off rin.g uI1til tl1 • ·hare I ri ~ in r a •.
c net, ,t ·
n1 11tioned i11 tl1
chaJJlcr n the, fi11ar1cial 111anag r an J tl1 01n1, ny, tl1 o,, ·rarchin(l goal ,f fir1'111 i l rnc111agc111 nt i to
n1a ' i.n1i~e the current vL I 1c of a · 111p(1ny·\ . h'tr · . To r11 ·1k inv trn nt r finan in° le i i 11 that in rea e
~hareholt.ler v;;J)u.e. you must tJn I r tan I l.h fu11 la111t;Ill I factor tt1at cl'ctern1i11 th 111arkt;t \ alt1 · of th•
Cc)1n1Jany '~ ha r .
We begin tllis chapter \ ith a Ji c t1~ i n f Lh ~ con<.lar)' r11arket, tc1r c1uit
ttriti ,111d th ir
efficiency cxpl in 11 w 1 r a J har 1n rk t JJric Ii ti11g~ i11 th· 11 \VSJ)ap r ar1d 11lin ~. ctn 1 i1 trodu
the type~ of qui Iy . c •uritics tint c mpnnic~ lypi al Iy is~u . h n '' I , I p a gen ·ral valuali n model
and de 111 onstr,:1tc that tll, alti
fa "ll.1·tr~ i~ 1h f)I\~ .. I1l ,a1u" of c1/I C\{) ct ~J tL1tL1r ca h cli\'iclc11c.l~.
CHAP E
Share valuation
271
9.1 The mark -t for shares
ARNI
OB
TIV - 9.1 Describe the four types of secondary markets.
.
..
.
.
.
- .
. y J·,1ui1ic~ Jr the 111cl,t isil)lc '-iec11ri ie, on
l-:lJllll\ '-iCL'l tllll'~ .._Ill' ccrlil1c~1lc'-I tlf <J\ 11cr,h1f) t>I a ClJtllpttn ... "1
.
.
.
.
·
.
·
.
· 11 ., rtrin
~,, I trillllJfl <>f pt1bl1c cq1111y \Cc11riti
1
the l111~111c1.t Lu1d,L.tpL·. ,\t tllL' L'lld llf SLptcrn1) ·r 2()llJ. H>Ic
d ,
. .
"
1·. . .. , •r Iy t r ac k t hc u JJ" ~ n c1<>\\ n " <>f t hc , h r
\\CtL' ()t1t,t~11h.l111u 1111\u,1r.1lia al >11 . l·~\cry dav /\tr"lta 1.tll'-l ldl:!L:
.
L
..
•
•
•
f I . . t. ·, r ·,rkct i" nn 1111p rtant har<>r11cter of 1~1
111~1, "L'l. i\ 1~111\ j'll'l'j)IC I) ·liL'VL' that the f1L'l ll>l 11l~tl1rl' <l t le" ldlC 1
·
·
·
·
- ·
. ii , 1 ,·u,. . nt11nl)er c)f ·pcc)JJlc (37 per cent of the adu t
Lc,u11t1~, L'L'lllH)Jllll' 1,1L·alth. 1\l~cl luc 11 1n e 1111c1c~t ,11c lL . •1 ~~ · 7
f)())'llll. ti(,.n) ,, bl,()\\ 11 cLJllit) "cL·uritie~ ci1h ·r J1rcctly <>r 1nd1rcctl).
l
---·
l
•
ec
RL·\.·atl frl,111 the chapter c 11 the financial en ironrn nf and the level <>f jntcr~c~t rate" th at the ~har~ n1arket
\..' 11,·,t, t)f 1)ri111~1r) anLI ~ccondary 111arkcl~. fn th prin1ar.. n1arkct. C(>1nranic, ell n . . ,, ~hare, ll.> tn\e\tor"
l() rai,c lllt)l1C)'. [11 ~ccondary n1arkct~.
ut tanding ·hare. ~re b<Jught anti ~c>lcl drTiong 111 ' e"l<)r'-i. \\t: \\ ill
Ji,cus~ the 1)rin1ar)' 111arket" for bor1d~ and cqt1it)' ccurities in a later chapter. Our f ocu, her\.· i" on
,econc.Ian'
n1arket "·
•
An~ t1 adc of a ~ecurit)' after it.· prirnar)' off ring is said to he a ec ndar) 111arkct tran"act1on. \lo t
,econdar) n1drket tr, n~·1cti(>ns don >t direct I)' affect the 111pan that ori~inall)' i~<;ucd the ~ecuritie"'-. Fo
c,a111plc. ,, hen an invc tor buys J 00 share in 'vV l\ orth, Lirnit d n the Au tralian Sec·uritic" E:\changc
( ..\SX ). the exchan£!e c)f n1one) is onl) l'l ~t, 'Cn th inv tor buying ar1d sell.ing tJ1e ~c urit ,e~: \VfJOl\, ()rth" ·
ca. h po"ition i1.; ll<ll affc led.
The prc,c nee of a secondary 111arl-..ct docs. ho\ c, er, affect the i ._ ut=r indirectly. Si 111 rl) put. in, c ~tor~ \\ ii I
pa_ a higher pric clr r>rin1, r)' ~c ur iti~s 1hrtt have ar1 n ti scconclar)' n1ark.Lt bcca J~e f)f th 1r1ark.ctJhilil~
that the cc<)nJary n1ark.cl provide .. As a r ·~u lt, 1111 ani \\ ho cs ct1riti ~ trade l)Tl J ecl,nJaf) n1ar~~t
can ,ell their nc,, debt or equity i ,uc. at" ll>\Vcr funLlin_ co. t tl1an c 111J'lanic, ~cl ling ,in1ilar ~ curiue~
that l1a\'e nc> secondary n1arkct.
Secondary markets and their efficiency
111ark. t tran a til1ns ta"c plac l1ll tl1e .\SX. 111 tt=rn1" of total
\()llllllC ()r acti\ ity and lt>l~tl equity value of the C()l1lj)anie. Ii teu. the r\SX i~ the \\l1rl<.l·~ 1-lth lar!!C'\l ~hare
,narl-..ct a, al August 2() 19.' ()f cour~t the \JV<.>rl l's largest cqt1it)' 1 1nrket 11) tll~lrkct \ dlUL 1, the .... L\\ Ytlf~
St< ,c ~ l:xc,ha11gc ( Y SI :,J
The r(>le <>f thc'-ie and ()thcr ~ecc>ndary 1ark.Lts is IL) brine: l1u. er, ~tnll ~cllcr~ to~cther. Idcall,. ,,~ \\ ulJ
likL· \~~·u1 tl) 111arhet" tc, l)c "" L'. rL·i, ·11_1 ~~" P<)~"_ih lc. !\ farket" ,u~ L'lltciL·nt \Vl)L\ 11 th; L·urrL~nt nl~trkct priL·e~ of
,e_c111111e~ 11a<ll'd rL·fl:ct al l ava1lal'll~ 111lor1nat1 _H1 _re levant llJ ithc "L' •urit). lf t1 1j, i~ tlle ·a,c. "·curit)' priL·es
\\ ii~ J 11 e nc,, r <>r. at thc I r t ru L. vaI 11 •• I l 1L' 1n I c L' 11 1c IL 11 t· t he n1'·1r1-.. ct • t he n· 1•l, 1·,, ~ I •tt11~
· l~
· 1{), h ap(JL'rl.
. I hl'r~ _arL~ fc,u_r ty1)e~ (>_I "~C<>ndar)' n1·1r~ "ts. anll ca l1 t) p, lliffer, acCL)rc.lirlg to the anlllUlll ot' price
1nfo1n1alH>Jl a\dll,tl)ll' t() lll\L'S(()f"~.
\\h1ch
In lUlll arf"Cl\ tl11""' ,,t~
,-1,··,
.,,1,·)' 01· 11 lC lll~lfr\.Cl.
-1 .
wL' 1·I~· 'll"". ti'le
.
•
""
"" l'. "1 J . •tl•·t· ·i·t id .
l<)ur tvpe~
of '-lccc>nllary 111arket" - tl1rcct ~l'arch · hroh.er·,~·
·
-·
·
_ .
~u.
• ~ • · · •.1tic 1ton 111 l)rc1er )1 111crl:a u1~
111<.1rl-..ct et f 1c1cncy.
111 Au"tralja, virtual I)' all ~ccc)ndary cquit
1
.
" -
·
)
'
Direct searc
The. secondar)' 111ark t~ furthest fron1 the id al of con1plct,
'l\''tl·l·tb'l ·t
- • .
.
·
' " ' •l 1 )' C) 1 p11cc 1nl rn atL n ar • t 1
l()~l~ ·111
\Vh1ch l)U)'Cf~ an(l "cller 111t1.. t seek. · ach other ut lire riv ln tlie
. ·k
. . .
t·
. t
•
•
•
• •
•
·
J •
e 111 ctr :-. ts. 111 c11 v I lu a l" hL ,u· t hL u11 l t) ~
ol l<>cat1ng anJ ncgc)t1at1n°. an I 1l l'-i tyfJJcally llJO C(>stl)' f r tt1 , 111 l , 1
· ,
I1 ,
. .
.
..
. .
·
e · (<Jl1l Ltct a lh()f't}ll<'h SL'.tr· h ll' localt: t L
l)c,t JJr1cc. Sccur1t 1e~ that , ell in lhrect search 111 . . rk. 'ts are u u· ll 1.
t=•
1
.
..
•
d ) )OUg 1t anLI s 1 Is • i11frec1u ~·nll)' that J~\,
tl11rcl 11art1L'i. '-Ill ha~ IJr<lk rs ancl Jcalcrs. l1nd it profit·tl)I. . 1 h
·
•
·-=_
.
•
•
•
c L n< ug l ser,,e tl1 n1arkc~t. (11 th~~L' n1arkl·t,.
clh~r, ()1tc111el) n ,vo1d-of-111ou1l1 c H11111un1L·~t1c 11 I<) fintl ii 11...... , b
~
II
1
1
.
.
_
· l:tl'.slL(
ll)' ·r~ l t1c ordinar-)' "h·tre~ ()t ,n a
private ct>1n11an 1e~ ar ,, gc>c>ll exnn1pll' l)I a ~Lcurit\' th·tt tr· d . · . .
·
" · ~ ·
1
·
' · d Cs l ll l 11S 11 an 11 r •
272
AR
Valuation of future cash flo\vs and risk
Brokered
\\ hen tra<lin& in~• ~ccurity i~~u, t1 cconic
.. ,· .
.
\ ~u lf1c1 ntly hc·i\y b
· J)rofitahlc l<> <> r·fer ~pcc1a
· 1·,~cc1
"carch ~ervtcc" ll) 111:u1' 'l J)artirii)·1,.11 B ,
"- , rt) k'ers incl rt
' ~- ro"crs I · h
cr, 11 1111i.,. i<111. Tc> J)l'l>\ idc in\'c~lt)r\ \Viti . . · .)Jtng uycr. and ~clJcrs together t earn a fee. called a
, cln inc rll1\·c t I111
.. , I
h
..
is le~ tl1an the - l'~t (ll' a dir 'ct ~c·ii·cli
k .
t 1c11. rokers n1ay charge a c<)rn1n1, ion that
'
. 8 r () CI . l r ' I I . •
•
"el lcr an<l trv lt> llC£<1tiatc •ui •iccci1 t
( . l() J)d"i~I c agenl~ but agurc~,1\cly ~eek C)UI buyer" or
11 c tran,act1(Hl () · , .. f . _• .
.,,
._
' '
a)
. . .__
.
1
in r'a cs 111ark.ct efficicnc)' lJccau~" l .
.
.
ttct.: <ll t 1c r cl1cnt~. Th prc~cncc t>f act1\c lJr kcr~
11
_
, 1 •
•I
k
· ·
I
Jikclv to k11t)\ \\ h·1t
c,>n"ti utc"- ' .1 •, 1l:-. • _. .·CI ~ :1 I c I n I re nu
,, 11 c<Jntact \l tt 1 111ar 'Ct part1c1i)ant~ ·,nc o arc
~
' <.111 pr tee f(lJ 'l s.. . 111
.·
"fl t\
.
.
.
hrokcr n1arkcl.
' · t: cu )'. 1c • .~X 1 hc~t (Iese I bc(J a a CJ uutc-drr ve n
1
Dealer
If th tralltng in a gi cn1~l'curit)' h·t\ '"ti1·1-,L.,· l •111 V() 1UlllC n1ark t ·fl . -.
. .
r .... d .,. I
·'. ·
· '
he ni·irkctJ1 Jact.' t) pr()\·1 1 1 .
·
c c 1c1cnc I\
1in11ro\c
I t 1c1 . is u111eon~
111 t
1lt1nu u~l1idcJi11 ( •1 1111
·
· .,
·
· . . l, I Ir' , , · , LCC(
.
.
· g sc · , g <lt·I)ll)irng)
f<..>r the ~ecur1Iy. Dealer') prov1d th1.
~er\tCl: 1)' 10 ctnL tll\Llltt>11 -· <lf ,ccuiiti '"
.
.
.
_
· , l \\ 111·c11 t 11ey l1\ 11. and th '11 huyinu new ,ccu itic"i and ,ellin(l
1
tro111t1c111,
·nt(1I) lLlcarna11r(lltt. UnJik·b· k,·
. .
. .
_b
_
..
. / .
..
l:
ro er • l 1cttlcr\ have ca1 ital al r,~k. Dealer, earn th Ir JJrc>f1t,
frlH11 l 1lL ,\/JIC(I( l)ll t 1l "l'L'UJ"IlfC~ thev tr·1d'
· Lr1·r1·crcnce hct, en their hid price (the price at ,,-hich
.
.
.,
·
r - l I1c
the\- bu\')
and t11 1r offer (a~k) 1>rice (ti le. J1 r1cl:
-·~, at \Vh1ch
· thC)' e ll). NAS 1\Q i~ the hc\t kn \ n cxa111ple
·
• .
t1f dt alcr 111arkct.
Tl1c ad\ anta2e
• I1 1·o . . I.c I n1·1r k 'l Js
· that. broker
'". . <lf c.1 dealer n1ar1'ct o, l· d
nnot guarantee that an order
to hu\
)f se]] \\ ti] l)c C ' Cllltcd JJI"OlllJltly - r, .
,. . . .
.
. .
. .
.
·
11~ un
I tLunty about the speed of cxc . ut1on create~ price risk.
Dur1n~tl1
t1111--al1r<Jkcr1"tr
inot
, IJ· -., .· ·
·
•
·
c
•
•
. c . c a , cc u1 It)'. 1t~ price rnay change anicl the c It nt could ~u fl er a l<) ~..\ Jcaler 111arket
c It• 1111 nates th nc d fort i1nc- 011
u·111 in t::a arct
a ··air
1· · d· a I becau. e bU),.tng
· an d . c 11 ·1ng
•
·
.
· , ,_
1-c J~o.
taJ...e J lace 1n1r11cJ1atcl) fr 111 the dea]er·~ in 11tor)' of curiti .
Dealer" 111akc 1_1,arkct. in ~cu ri ti '\ u ing co11111uter 11 tvvorks t quote price at \.Vh icl1 they arc v.·il I ing to
hu~ . r_ ,ell a [Jartrcular t:cur,ty. These nct\vork nab1c dealer to electroni ally ur\ e)' th price quoted
b~ Jilt eren t dealers t lie lp c,tabl i l1 their ensc of a t ,i r price and to trad .
'
'
,"I
L
•
l '
l
1
Au,ctio
In an aucti n 111arkct. bu)·er and seller~ confro11t each other dir ctly and baroain v r price. The
pL1rtic...ipant" can · n1 n1unicat \erl1ally if they ar 1 cated in tl1e am place or th , infor1nation c, n be
tran-..111ittcd eJcctr nicall)'. Th . . ASX did ori 0 in, lly IJerate ·1 an 'op n outcry' 111ark 't but th trading
noor" ,,er pha cd ut ·n l 90 foll \\ ing the intr duction f tl1
t
k E:\change Aut 111:itic Trading
S~ "tcn1 , S -..\TS) in 1987. 9 The l1e~t-kno\ n xa111ple < fan at1ction 111arket i. lhe YSE. ,, her th aucci n
for a "ecurit)' take~ place at a ~pccjfic I cati1 n 11 th· fl r f th
·cl1ang all tl post. (11 thi
the auctI<H1 r i" a pel·ittli. t. \ ho i~ dc~ignatcd by th exchange t r pr nl ord r placed b)' public
cu"t<HnCr"i. ~ pcciali t<; a~ the narn~ in {Jlics. h· ndl a ,nail t f
uritic , and arc al ' t) allo\ved to act
a~ Jcalcr'-.. Thu~. in real if)' the NYSE i~ an aucti n n1ark t that al o l1a . 111 ~ aturc of a clealcr r11arkct.
rfht: ~YSE Jll()\'Cd tO\\afd"i clcct1r)n ,ic trading in 197 \Vith th ' D TL)'· ten1 (DOT :tand ' for ·ct ~ignated
<>r<lcr turnarc,un<J" J. \\l11ch al') >wed orders to b tran ini.tt cl I -·tr ni all t ~peciali t~. fh el~ tronic
"Y~tc1nha~l1ecnuJ)grauc(J , . raltin1·~ . inc th nandin .... 01( th
YS urgradetltheUni\erL
'alTrading
Pla1for1n (UTI ) t<> th
YSI.., Pil.lar. an integrated traclin~ t chn log)' 1Jlatfor111 that ~11ab-les aL: , t . , 11
equiti ·tn I opti , n~ 111arkct\ u,ing a ~inglc \f)Ccifi ati 11 (N'l'
_l)llJ).
1
Rea ing the share
arket listings
The Ai,.\tr(i/ic, 11 Fi,,n,,(·icil J<e, ieit' and otll r nc,v,1)aJJt:rs pro\ i<.lc hare Ii ling, for tl1"' S X a~\\ 11 a~ ther
ccuri ty niar t inf rrTiali 11 . TJ1i~ inf r111ati ,n is al~o a\ailabl
r1 th \
\ b ,it . Fi 0 ur 9.2 ~ ho\\'~
rnarker data for cv ral co111pa11ie. Ji~t "d . n th ASX.
ln th fi<,ure. oo t tli.c entr)' for B _ga Che ·c (Bega).\ hich i ~ l1ighlight 'd. Bega is ~111 At1 tralian tlair)'
C(>lllJ)any f~a~ cl' in B b·t. N
outh W·1l'"'s. 0Jun1n~_1 an I 2 sh_ \ th. higl1e. t {Jri~ ( 6._125) ,LnJ t~e
l<)\\'C~t JJrice ($3 .550) 0
r 111 JJast 5 2 \\ e~ks. Colt1111 n . ho\\' that B--~a !a t al JJr~- L b tor . th da) .~
clo~j 11 g was ·3.835, wliile c -1ui11 n 6 ~h \V~ t'h h( ngc 111 th :) urr nt pr1c~ tr 111 tl1at t th" pre\ 1ot1s tla) ~
cl(J~e in nts olu111n 7 indjc, t "tl1 vo lun1 (Jf ~hare~ traclc t.
~l
·,
B 0 , l" 1·dcnd vi"elcl \ hicl i~ 2 87 11cr ·et t. 'fh.c (.li\ idcnd ) i~I I i~ calLulat d b,
()
UITIJ1
~110\1/S
c a (JI
...
,
· ·
·
·
.
. .
.
.;
C
8
. · 1·
I
d' 'd 1 y )Lil tJ)' th la~t ~a le 1)rice (>f th.c sl1ar ~- It ' C)ll s an tht: lt\'1tl.cn(I ,·,cld .
d I\')(
, Ill£ LlC a1111ua I · !VI
J)( J)a C
·
'
•
•
•
••
• •
•
•1 ·1
·
·1
·11· f ll Au ,-.111· 11 in lu tri·il co1111)an1 . ~ ,n the 11st par 1 1t,·1lle11cl,. l·or c H11p~u11t:,
/(>ll
~ 1 not1c t 1at a
1c
, ~1 , ,
. ·
'
\
· t. d
d' 'd
·
• -. ·, 11 \\ ill in,, to r1ur ·ht1s ~hares 111 thll~e · n1pan1c a"' Ion£! a" the
1 lat <>tlOlJJ~1ya 1v1 11 -1,1 11 s 1<JI ~,11. :,., 1 . · . . . . .. , •· .• ·
~
_
...
·
I
. · 11 .. .... · • 1·1 1·Ll " tlcl"i ·111d/ r a I 1ghcr shllIL price 111 lhL futu1c.
11 1vc~tor l1el i _ rhat t 1ey , r
1.v
L
1
1
1
1
l
'"
E
Share valuation
27
ASX industria l shares
52
wk high
6.600
88 316
6.1,25,
13.136
11 .57
227.39
19 56
4.75
53.63
7.744
49·.1-1
4.667
37 73
1.595
3.40
7.28
74.12
30.13
3.978
7.98
17.19
(3)
(2)
(1)
10
52
-
Company name
wk low
5 850
56.750
3 550
9.576
7 846
155 .22
14.18
2.598
35.295
5.314
37.59
2.925
20.30
0.69
2.29
5.185
52.71
21 .26
2.663
5.94
9.98
(4)
(5)
ASX
code
Last
sale
1300 Srniles
ASX
Bega Cheese
Brarnbles
Coca-Cola An1atll
Cochlear
Computershare
CSR
Domino's Pizza
Elders
Flight Centre Travel
Harvey Norrnan
JB H1-F1
Mortgage Choice
Non, B
Qantas
Ramsay 'Health Care
ONT
ASX
BGA
BXB
CCL
COH
CPU
CSR
DMP
ELD
FLT
HVN
JBH
MOC
NBL
QAN
RHC
6.260
80.300
3.835
12.495
11.305
224.50
16.98
4.69
52.46
6.63
42.63
4.29
36 31
1.35
2.68
7.28
73.26
Sonic Healthcare
Telstra Corp
TPG Telecom
Webjet
SHL
TLS
T,PM
29.85
3.63
6.61
12.40
WEB
(7)
(8)
(9)
Daily vol
Div
yld %
P/E
ratio (x)
4
2.83
2.87
2.34
4.11
1.4 7
2.58
4.9
2 69
3.72
7. 71
3.9
4.41
19.0S
31 75
67.19
9.42
27.87
46 88
15 63
19.54
38.67
11. 74
16 220
12.33
16.74
12.36
(6)
+79
4 080
11' 8 508
146 641
1 726 505
1 280 716
69 718
375 869
906996
168 914
201 695
148 703
760 417
287 346
104 329
178104
14061037
413 040
+8
+7
-1
+42
663 913
19 042 078
394 386
1099043
+1
-38
+0.5
+12 5
-13.5
-34
-8
0
+6
-6
+19
+1
-9
-1
+11
+14
2.2
5.64
30.6
3.5
2.09
13 08
27.36
2.82
2.81
06
1.84
24.3
19.67
35.4
25.49
Source: Q \SX 1_1111itcd .\BN 9 008 6-4 691. A X. 1()19. II right r~,cr,cd. Thi, rnatL·rial i, reproduced \\1th the p~rm" 10n
'
.\SX. fhi-.; 111.1teri,al ,houIJ 1101 bL· reproduced. ~tored in a rl?tri~, ·ti ,y,tc1n or tran,rnillL'd in an) forrn \\ hL·thcr in \\'holt: or in r1
\\ ithout thL' prior\\ irten pcrn1i , 1 not.\ X.
final])'. colt1n1n 9 indicat B ga 's price-earnings (P/E) rati . whi 11 is tl1 curr---nt J)ric per ~hare di, idcd
l ~ it..., car11ing per . . hare. F<Jr Bega. the PIE r,ttio i. 67 .19 tin1e . rfhi" t II u · that irl\t: l()f..., ,u·~ ,, illin!! to
pd)' a JJricc per hare 67.19 tin1 , th~ t;arnin~ r er. hare f r B ga·s. hares. cga·s .P/E r4 ,ti<, i~ \'ef\., hiQh.
... To
ju~tify a higher I:> - ratio. in . tor. n1u t belie\' th, t rh e ·on1pan has good pre). pl: t for future cltrnin~"
gr \vth. \Ve\\ ill have 111 r to ay abc)u t the PIE ratio in later chapter .
~
~
BEFORE YOU GO ON
1. Hov✓ do dealers differ from brokers?
2. What does the price earnings ratio tell us?
9.2 Ordinary and preference shares
LEARNI G OBJECTIVE 9.2 Explain why many financial anal t t
.
b ond rather than an equity security.
ys s reat preference shares as a special type of
1
Equity \L'CUritie l't"-l'. ~ vcral f()f[ll\. rfhc lll()S( ·0111111
t
·
·
01
Ordinar)' hare rcrJresent the ba~ic ()\ ncrshii . , • . llll ype
'(}till) s • t1r1t., i~ ordi11ary hare~
1
. .
L d ll .1 'n a c n1 pan y On • of t t
b . . h
1· I
.1
l<) \ ote on al I i n1pc)rtant n1attcr~ that •lf feet ti I' f--- i· tt·
.
· c
· le a · 1c r1 ° t l) t 1c ()\Vn~r~ ~
... '
e I L () ic cc)n1pany, such ·1 I
t· l b . . 1· . . .
:Jo
•
•
ot· . 1. .
' e e ll<)n o t 1e oa, cl of lfl l H~
t:
"
1c tlldf)' har ~ 'tr
..
and ha c the ll)\ e~t pri ril)' clain1 11 the ct 111 p.. . , . ._ '. ·
not gnara11l --ct ~lll)' 11\'1 lcnc.1 ~)~ . n1cnt,
.
dllY s d:...\ t I 11 th C 11 t t· .
1
1·
har hc1lder. cnJOV li111ite{/ lir1/,il,1, .. that is t'l' .1·1. 1
. .
() ltls
;\11c '· Legall,,. orl 1n.1f)
•
.,
•
• •
• • .me.:
ssC'iar-- 1
, 1111lt It 0. I
~
·.
. . ..... :
,
1
111 the C<Jn1pan)' and t he1 r fJcr~o-nal a 1..,ets cann t h-.., t · k
.
t <H 1g u1a 1a111 n n t oJ th Ir 1n\ e-..l 1nc nl
.
c dent
at1~fvth· bl'1 ·
· II
ordinary "'hare. arc JJer1,e111i1ie.\ jn the ~en c that the)' 11 , n ·. ., .· c ll ~at1011~ uf th con11)all)'. F111~1 ~1
111
if n1anage111l:nl blt)' then1 in the O(J n niarkct fi
. ~
l
~\!ur 11 ) · 01\i1n,11·)' l1ur "S l.'a11 b-- rctirl·d onl~
111 1nve,ttlr, r 1t 1
1
it,[l sct,arcS<)ld.a~dt:~ ribetlinth--- 11 xt~c ti
ticc
n1pan)
i
li}tlidate(l.in,,hichl'~
'
ll.
a11tl prlJposcd 111
rocr
r acqu1~ 1t 1on~. o,vn ·r
I
-274
PAR
- ----
Valuation of future cash flows and nsk
Like ordi 1,try l1~trcs. r r · \i•en ·c sliai·
~
r
~,1re e11t ·u1 o 11 I · ·
i1nrili s. JJrc 1er nc hare receive JJr f . . .
(
'
r 11 1 tercst ir1 tl1e c 1111 ,t11y but, as tJ1c r 'ln
e1 i1t1·tl tr'·tt1n 1 t 0
"liar 11 Icier · tak 11rcccdc11 , l cr(lrdi ,iar, . . '
~
'
rd i11,1ry har . Sp i 1c,tlJy. preference
1
~tc<JJJ()l"~ltta s~t~I11t1
. l c 'tlt flii id t· ) s1l11el1(>ldcr
' in tl1
c P<tym
.
1· j"1v.1
. I d
d.111f1I c1stri
1· 'b L1f1. 11
.
11to
cen
s·11
1
1 1 • 11 l I kc l l1c i ,1t re t
.
r
•
b d
·
)l)lig,tll'Otl .. Ir ,er 11ce ~liar, (li,,iLlcnd,. ~ d
s p[ty111 r1t or1 011 s. wh1ct1 arc c<lntra {LJal
.
.
.
.
.
s
,ti
clarccl
by
11 1 b
d
f d·
oar · 1rector~ a11d if it lividend i. 1101 JJ,1id,
111 l,1 k of I l1yn1 11l 1. 11,ot lega l ly vie\\,t;L1•c.ls 1' I.at11t
[)reft'rc11 ·' sl1ar s ar legally ~1 f l'lll f , .
·
.
\\1it l1 ~1ftcr-t~1 ~ o 1l~trs.
ri J,ctt h . .. qLll ty. hu · JJre1er 11 c &l1arc clivicl nds arc p,1icl l1y tl1c isst1cr
. .
.
.
o
.Pl C1Cl CllCC h,1rcs ar • ,
·
. ·
.
. .
1
)rt 11 Q t1nlt:, s tl1e 11rct r · Ile'..\ sliri. . .
.
.
ctn cq 1ty , ecL1r1ty, tl1e
11e1. ,h~l en
voting
J.
~
..
. - , i,rc is o11, crt, I le 111t
. ·J. .
. ..
. -.
.
1
1I1
\ IC\\ Cd a~ JJ r11ett11 1 b cnLt
tli 1 , .
. an
ary share. Piefer n e l1are . are gene1a11y
..
l c.l\ - 11
fllt- t llD l)' ]-f ·
·
. " .,. .
.
. .~
L'rpctLt 1l1c~ l1eca tl
tl.1c 1. r ~11,1r . e)'
t•
.
· · we CI, 111o~t pref crc11ce . t1,irc. are not true
P
. ' e l: c) 11 J. a ts . f l c n . 11 t . i·1
l I 1 1. 1.
.
1ro\1isi n~.. l1icl1 reqt1ire 111 a11 ~1(Tet _ tlt ; rt tir . . <1 · 1 _ca · J rc) s 11s. tt11d can c c 11 ir1cJt1d .,·i11ki11g fit,1(/
1
1 · ·
0
1 Lert,.1 111 pcrcc11t,tgc c>f ,fhc ~11arc i ~l1·e ar1n1J,til\1 :unti) the
· . ·. . d..
1 11 1
L
3
-
.
L
<..;
r
•
.
°
1
e11t1rc I st1' 1
-
L,
.
.J
0
h,1tcs i11 111"111· c i~· \ llclll t;.,.r i)r ter
r
11c sl1arc. ,tre debt or ecJtt ity. A str no case ca11
he.. 111ad
t}1Jt 1Jr1..:terc11c
l1~1res
arc ·1 p, .. ·.1 t
fI
.. u
. .
.
,
·
.
- _ s
cr,i , YJ e o
)11 I. Tl1e ~1rgt1 1n 11t b l1incl thi~ ca e is a follow .
F11,t. ;Jc_ula1 (no11-cll11, 1t1l1le) J)rctcrc11 •e t1 1r
•onf 1.
r·
.·
I
s
d
c
h
.,,. · . - d d' •ct . d
"
· n< ,,o 1ng 11,g 1t . econ , preierence ~ areho]ders
tl:CCJ\e ,l 1,1xe
1, 1 c11 • r' 0 ~1rdlt:ss ftl1e c 111
.
• ·
d··
· · ·
·
~
·
·
P'- tl)'
. • 1.111I1g , an 1l tf1e om1 any 1~ l1qu1clated they receive
a t,1teo \'~1lt1e
( .u~t1all~., p,1r) a11d r1ot a t·c • 1·d Lia·I ,1.'lu . 1·111r· d. • preference
·
·hare'" fite,1 ·l1ave ·credit
· · rat1nQ.
·
.
.
011c of the 011goi112 LI
.
l
T
tl 1a~ rt: imi]ar in ~ature lo tl, e i ued t bot1d . Fourtl1 preference llar ,lf . 111 times co11 crtiblc ir1to
<)rd,iiar_ liarc · F 111 ~1IJ_,. in l I re} r"n e . l1are i ue re n t tr L1 perp tuitie ,. F r t'l1e " rea 011~, n1.a,n y
i11\ c~tor
011 ider I fer nc
l1are to be a special type of debt ratl1er than quity.
't
Jn earlier chapter~ \\C empl1a i ed tl1at the \1a]t1e of a11y a~~ et i tl1 pr ent alue of it ft1tttre ca 11 flow .
Tl1c lcp"' in , I uing an " et arl: c.1 fol Iow :
J. ,ti mate the future ca h flo\\ ~2. Deterrn i11e tl1e rcquj red rate <)f r torn. r cli ot111t rate, , l1i 11 dep -ncl 0 11 t11 ri kir1 of th futt1re
Ca\ll flO\\' .
3. c~1Jcu.lat tt1c J)re cnt ,·a uc of tt1c f utL1re ca. 11 flo\v t deter111 in \Nha.t tl1 a. ti wortl1.
It i"' r J~tti\ely lraichl C>f\\ard to aJ)f>1y thee te1J in · alu il1g ab 11d beca11 --e tl1e a.. t1 flo, ar tatcd
a\ pan of the bond conLracl ,1nd tl1e required rat o1~ r turn, r di -int rat . i .ju l th · ield to 111aturity 011
l1ond, \\ ith cornparabl · ri\k ch,1ract ri~tic . l <>We er rdina r)r har al11ati 11 i m r difft 'Ltlt for several
rl:a on'.'). ir t, \J l1iJe 1l1e t!,xpcctcd c,1~11 now for b 1 cl ar w 11 d L11n 11t d a11d
)' t cleter111ir1 .. rdinaf)'
~11c1r div1dend" arc mucl Jc ~ crt,1in. ivjcJe11cl ar de lar d by tl1 b ·1rd o·f dir . tor and ab ard n1ay
or n1a 11ot dee ide to pay ,t c,1sh (Ii vi dc11 I at ,J JJ,trti. Lt lar t j m . T.l1LI, , tl1 · i a11d 111 tim i11 0 of di icl nd
ca"J1 no\~1~ arc both Jc~~ ccrt~1i11. Second. ordir1,1ry liar ar tru p rp tt1iti in tl1,1t tt1ey 11,1, c n fi,1,11
111atL1rity dat . Tl,u , con r,, ni .. ~ 11 vcr ]1,t e to rcdee111 rl1 m. In 11 tra t, b 11ds l1a\ a ft .nit n1atu1ity.
Finally uiilik tJ,e rat of r tur11, cJr yielcl, n or1ds. th· rat· of r t1rn 11 ordint1ry J1arc i 11ot tlir · lly
c)b~er\a.b le.Tl.1u .grourJingordinary l1are intorL.kcJa se i rn r lirfi 11lt tl1,111~r 11pi11gb nd "' .Kc'.l>pin ....
tl1e~e tnplexities ·n n iiid. \VC r1ow tur11 to a di ti. sio11 of rtli11ary sl1ar ,1ltu1ti n.
1
A one- eriod mo el
Let·~ as uine th·tt you h'l a!! 111 e wh
11 tel1 Lhe futt1r , ith perfe l . ertainty. L1ppo . y LI [lr tl1i11ki11g
ahout 'buy irl a . h r 11ct. ellin it after year. Tl1e O 11ic , lL111t er~ that in I y ar yolr \Vill b able t ~ell
tl1e share for $10 (Pi) allCl it wi ll p y an 8 divi I 11d. (0 1) at th er1.l oflh )'e,tr. The ci111 line for lhc
tr,111saction i. :
1
Year
0
S8 + $100
Buy share
.
.
l . . 'J It·,~-. 'l 1
' lf you ·11.1 l t l1 otJ1 r 11 V 0 1~ I ~
\\ l1at IJri e \ ou J. y u b wil lin l r~Y for 'ti
-
..
p r c J t r l llfll 011 in,·c~lll\ Ill~ 111 \CCtlr1t1e
.
I
~l1arc I (.1l,t) '!
S ar val a o
27
= $90
tlic '·"""·t1(·1rc • ycJu w i 11 ha vc • a I -year ho Id in br,
. . tJ . ·1~ · <- O I f• ,o LI I.J a)' 9(1 1'or
,
Tl1L1s. tl1 ,llt1c <1f tl1c sl1,ll t<l ,iy · · )
.
.
i ·t ·tirr I l v·ilue elf the ~h·1rc f<>r u
· rett1rn of· exactly 20 11 ·r c ·nt.
·f ·· • II)'• tl1·t1111cl111·an<
11 c
~
(
r
JJer1od
IL: \)I 111,1
·
011e-I1cri<.lU 1110Llcl l'an 11 ·a" . l1<)\\ 11:
,
.
1
0
Year
,,·l1crc:
P 0 = tl1e cu1 · _nt, alue. or price, of th , har ·
0 1 = tl1e di,·id nd paid ,tt tl1e 11d f tl1 period
P 1 = t l1e price of tl1e ~11,u·c at the e11d of tl1e period
R = tl1c requir d r turI1 n ordinary ·l1are. , or di C<)ltnt rr1te, in a particular ri k cla
· ote that P0 denote ti111 zero, , Iii h i t day~ P 1 i tl1e pri ·e 011 period l atcr: P 2 i~ t \\ fl p~ri od" in the
f uturc a11d o 011.
tc I tl1c1t wl1 11 w peak f tl1 pri (P) in this 11t xt. \ e n1 an the, aluc - ,, hat
,, e l1a, c detcr111i11 d tl1c pric hr,ulrl I c. gi 11 ur 1nod 1 - not th a ·tu,1I 111~tr"'l:t pri e. Ot1r cln -pt:riod
,node I pr()vidc an c timate of what the 111ark -t pri ·e sh tild be.
·()\\' , l1at if at tl1,c bcgi11ning of y ar 2 \V '- re a 0 ,1in a. keel to det r111i1 th . pri ~ of ar1 orJin,tr)· ~l1are
\\ itl1 the a111c di iclend pattern and , 1-ycar .l1oldin p ·riod. As in t1r fir. t ~1]ct1l~1ti 11. the urr nt price
P 1 ) c>f tl1e har i~ tl1e PY f tl1 _ diviclc11d a11d tl1c ~11arl.:·_. sale price. l1otl1 re t·i,·ed at tl1c ci1d of tht:) ~ r
( P2 ). Spcci fi call y. ur ti 111 Ii I ancl th "l1arc-prici ng f or111t1 Ia arc:
L
1
2
Year
P,
) _ D2 + I 2
l 1l+R
lf ,vc repeat the pr(>cc~~ again at the hcgin11ino <1f yc·tr 1 tli. .
'
· •
· • .
1
IL:~ll t 1~ s1n11l~1r:
D3 + P3
P-, -- ----=..
l+R
A11d at tl1e begi1111ing of year 4:
D4 + P4
P1 -- -----=J
+R
ret~:r~.h ingle-p riod mod I di ount. lhe di id nd and ~ale pril: at the nd of th p ·rio I b) th, re 1uir.:d
t
odel
nfortunatcl). alth ugl1 our on -J)cr 1·,>,f
.
.
.
.
\. \. lll()l1l'. 1 , ~ C<>rrc ·t . .
.
. .
.
111
f< rn1ula i(>r I cr11ctu1ty n t r r ()ll"' <>r 1
. ·
c · ' 11<)1 very 1cal1<;;,t1c. We nccu a ~hare-valuation
. .
'
\V() (1C l()tl ~ r lo,
· .
·
·
·
~hare 11r1c1nu tll()del~ tt> a11ive 'll 'l "" ll · .,
:·
eve,.' c ca, "itr111° together a ~cr,c <>f c>nc-pcr1<Jd
' "" ,.., .. 11 c (Jer J>ctu, ty
I I 1I .
rir:-il. \\ C Oll~tru l a l\VO-() rioo cJ1· . , I .
lllO. ( C ·
er IS h(>W \ Car g<)ill~ l() do il .
. . , cllC-\ct ll~ltH)ll lll d ] 'fl
.
.
<J e . 1c ltlllt; l1n fc)r th two-period 111c>clcl i\:
0
1
J
Po
2
I
II(
I
(D 1 + P1 )
P,
To co11struc1 ot1r l\\O-r>cric)tl 111<)<lcl
\\l' ~t·
11 '
•
· d
Period
II(
(D2 + P2)
•11
•• • •
•
•
t 1 <>Lil 111111<11 '°1111glc-J)Crt<>d aluaLj<Jn f<>1111ula:
I o-
DI
+ f>I
I+R
N \\ \ e ub. tilulc into lhi~ c4ua1io11 the ·,pre sion derived c,,rlicr (or P = (0 + P )!(1 + R):
1
2
2
Po == D, + [ (D2 + P2 ) / ( I + R) J
l+R
Sol, ing tt1i, equati n re ult"' in a share- alt1ati n rnodel for two period :
D1
D2
P2
Po = - - + - - - + - - 1+ R
( I + R)2
( I + R)2
Final!~.' t; or11bine tJ,1e seconu-JJeriod ter111 . re. 11ltincr in this l\J a-period , I1are alu . . tion equation:
Thi, equation 110\.\" t h,1t the price of a hare ~ r t, o IJeriod i the PV of th clivid 11d in period I ( D 1)
plu~ t}1e P of the di\·idcnd and ~ale price in J)eriod 2 (D_ a11d P2 ).
No\v let· construct a thrCl:-period 111odel. The ti111 lin f r tl1 thr e-p rio(i 111 (.lcl i ·
0
1
2
3
Period
(D 1 + P 1)
P1 ~ - - - - (02 + P2)
P2 ~ - - - - (D3 + P3)
Jf \\'e ub~titutc th cqu'1tion fc)r P2 int<> Lile I\ <>-11eri()<I \<1Juati n 111(> lei ·t10, n aho,,e. \\ e l1a, a tl1reeperiod rnodel ,L~ sl1own i,n tl1c fc>llo,ving cc1ualions. R call LJ1al P,, =(DJ+ P3)l(l + R). Thi. n1odcl ,,, .
de, eloped in JJreci cl y the ~a,11 \Vay a" ur I, <)-pcri<>d lll<)Clc I:
Sha e alJ ~ on
277
cvclc ,1" 1c,ur-11cric>cl 11H>clel. a fivc-JJCrir>cl 111 odcl ,
(
l
l3 y 11t ,v. it ~11 til<l l1c clc·u· tlJat , e coul d 0 r,n c> c ,
JJ
•
• d
•
·
•
. J · 11 , f. 11 <JV i 11 , c q, ,~l I Ir> n:
~ 1x- 11c rit>cl lllt>clt l an l ~
>11 . Th Ltlt1111atc re. u l J. l
<>
v
D,
J,
0
1
I I
.,
P---+
- 2+
o- 1+I
. .
D1
- ~+ ... + ( I + R.)1 + ( I + R)1
( I + J{ )
( I + R )·
.
.
. 1
f1 • 0-:1ri·y 11 unih r fr< rr1 n · I<> in 1ni y ( oo).
Ir ere.
the 11t111l1cr <>f 11111" I cr1c>cls. 111c 1 can 1.:
. •
,
•
• •
•
•
·
,
· ti ·· , tlic 'tluc I J) 1 c. (>I c1 shc1 r I (f<-LV ( J) ) 1.. th
l 11 ~u111111ary. \ c h·t . c etc, lc>pccJ a 11100 I s1ll>V IJ1° ld, .
'
,
.
, . . ., . . . - _o , e
l)V r>f ·ill f Ltlur diviclc11ds an I Lll ,liar '~ \al pric in the f ,tur · Alth<>Ugli l_hcoicl~lctll y. ou nd · tlii\ n1c>d •I
· ·
·
1· 1· · 1 d ·<>lll.d
l
i11 1111t. It 1s unlikely th 'lt \\e.,
1~ tl<. t rract1ral t ap1 I)' l) cau~e the nu111l) r o c 1vtt en
·
C<tn
·c 1· 11 f
.
.
1·
1· LI1·V I·o, 1·1cl tJ·1y111,·11l·1.
c,1-- .., ~11ar ·', ~<1I~ JJr1c.:c fc.tr into th fttlLtr,1.:.
·Sllc . ~s 11 y oreca,t ,1t1 111 1n1Le nun11 r
., .
'"' , · u •
I'"
1
•
•
(.
\Vl1at, e 11 ell atL' . ()Ill r 'alislic· si111J)lifying a"-Slllllf)lion s.
1. Why are preference shares often v1 wed RS a special type of n bond rather than a share?
general dividend valuation model
9.3 T
LEAR I G O JECTIVE 9.3 Describe how the general dividend valuation model values a share.
111 th 11rcccdi11g eqt1ati 11. 1101.i that tl1 fi'nL l t rn1. ~t. ir1 th , rli er · aluati n motlcls. i" al, ,1y~ the ale
pric' of the "l1Jrc in 11criod , (P 1 ) a11d th·Lt 1 an be a11y nurnb r, incJudir1g i1 finity. Th' -r11odcl a ~un1c that
''~can foreca~l th e ale price of tl1 · ~harl; f r in.to th futLtr wl1ich doe n t ee r11 \·ery Jj1' ly i11 real life.
H \\ c\·cr. a. a f)ractical r11att r. a P 1 m , s fi1rtl1er out j11 t.im tov ard. infinity, tf1 [tl uc o,f P, ,1pproachc
z "ro. \Vl1)''! ro I,11att r }10, large tl1e ale pri e of the .-,11ar ·. tl1 P
f P , , ill a ppr ach ~ ero becat1~e tht:
di count f'"tct r app roacl1e~ ro. Tl1er fore, if\ g out to infinit)' w a11 ignore th P 1/(J+R) 1 tern1,1nJ
\\ rite uur fi11al cc1t1atio11 a, :
J
D1
D,
D,
D,
D-
D
P,)=--+
- +
·
+--.,.- +---+···+---:,
oo
1 + R ( ·1 + R) 2 ( l + R )1 ( 1 + R) 4 ( 1 + R) 5
( f + R) :o
00
==
L
9.1
(1 ~IR)'
I= J
\\ here:
P0 = tl1e curr 11t alue. or JJricc. t>f t.h · ~.har •
D1 = rl1c clivi(fcnc.J recci eel in 11cri It. where t = 1,2....... 00
R = the rcciuired retur1 un rdinary ~11ares or disco int r~llc
. EqLra.tit>n 9. I .i, a gc11. ral
. XJJr ~si(>ll f<>r tl1 · aJ 1· •
of rill xpcctcd futur .. dr 1d nds:
r '-1 ·sli·i·
. r· , · It ~ays l1liJl tJ1 I ri . . of a . hare is th PY
Share pric ·• = PV(All futltre di,,id 110~)
Tl1ci 1111uJadoc~11otassu n ·a11 . pccificpatt r11fl>rfuttir r '°d
.·
.
1
does it n1akc 'lI1Y a su1np. ti n alJ ut whc, 1· 1·he 11. . • • .
c I\ er1ct • SLl h [ls ,t 011 t,1nt grl)\ tl1 rate. 01
di 1so111 . t bold"111 l
- ..
1
. ays that to calculate a har ·. curr nt valu .
_ t . lutm . u1 th r'.n?r . th mo?~I
11 c I t J re a .
j_ a daunting ta. k at l1 ,t.
t an rnft 11 11 nL11nb r of d1 1cle11d~. \\ h1ch
-
I
.
Equatior1 9. J J)fO icle
111 in ioht int \\'hy ll"'.
.· s Hr" ·h· :T.
e
, u l e prt
•
certain time. , pri change~ an be dramatic. Equ· ti
. . r · c <1ng1110- 111 th' ltm an I ,, h_. • 1
11 9 1
i~ dct r111incd by the 111arket' · p ct'ttion
f ti . . · ltnp I tll,tt th UI1d rlyi11e- \',tlt1 of(• ~h, re·
,,e 1utur Cc. 11 flo (f 1 . . . . .... .
. ·111
C(>t11pa 11)' car1 gc11cral . fn "ffi i 11t 111arkets st·11•11.,~
~· .
h '
. \Vs r .11 d1 1(i 11d ·) tl1ac th '""U t•
•
•
·•
c. ""J1lt(e
Cano~
, .
.
.
,.
;iv~11lab l and 1. 111corrJorar - dint() the con 11 .1ny's 111 .. ·k . .
C<)nSlcttltl)' as n _ 1nforn1~tt1 11 b ~collll'
.
.
(.
. . di
t pr1 , • F .
l 11· .
j in u nJat J w1 lh fa t~ and run1c)urs. ~lt h as , h • .
· (>t Pll) ·l Y tracl. d . n p'tni "· tl1 111arJ...e
11
.
.
.
·
c1 tJn111 a11)1 f- tiJs t
CF 0
re~'fO'n~ r)r 1~ rr d, t)r u c: lc1 s-ac trr>n t1it. i~ Iii . I ·t o q'
~.
-111 t s<tle 11r ,j, ·ti n~. tllL'
.._
, b u I r1 s l t) 11
o t ' t s J) . I .
.
1
· IO(Ltct . . Son1 c, 11t 111,l l1a\ elittl•lH
1
l
1
s
e p icing p ra ox
i11 t re ting isst1 l't)l1Cc ning orov th sl. _, .·
.
•
•
• ,.,
. •, 1 d ,.
. .. .
· · ldlt:S arise OLtl (>f tl1 lact tl1n1 th <:,)1arc-,aluatJ<>n cc1uc1t1011
1
. . .,
.
.
.
.
1, l)il u 011 l 11 lu 11 Id) 111c11ts, Gr<>\rfll I
. .
.
.
. .
'l(IJf.\ di
tyJ11c~Llly cf ·l111cd as th '.> hares of ·01npantcs wJ10. c
1
car11111e: aI gt(1\\ 111g at al1c)vc-averanc 1d
•• ,t
. .i
, ..
.
.
.
. .
.
~
dl1l art: ex11cctcd tel c JnL1nu • "l'O\ Ir12 f<>r on1
li111e.
1
\ C lll[)all)' oft ll. tr J t' l) f )C\lll)' J)a) S litl ll' ()I,' no cJivi(lc11cl" ( fl it. ~hare\ 11 cat~ C 111a1~1 TC.I ll nf belie es
that tJ1r co11111a11y l1a ~ nut 1l1cr ()I l1it,J 1- • 1 . · . •
. . .
•
.
•
• .
·e- le uin lll\c t111t·11t ()J)J1<>rtun1t1 ·s anll tl1ar l1c>tl·1 the c<>rnpanv anll 1t
•t '" . ,·
, , 1 ,
.
.
•
•
.,
1n,c~t . r \\1Jl l l1c l) . ttcr t)I it carnin""
. . ·o
I 1.c111vt ~tco ctllhcr than J)at I out as d1 1tlcncJs.
1 1th , ·11ui n
To 1llt1stralc' tl1 . 1, 1rc)hl
t
111
,,
11 .... c 1•(l\\· t l 1·1 ~ I1a1\~,. I ·t •~ ~u1111os ti al tl1 • earn ·ing of Ac111 · Ltd Jrc
.
'
cir l)\\'j 11 ....~ at :J.11 C cc JJ t 1l) n ,JI l \' hi u h r •1t L' 11 1 ..
,
•
.
:::- :::- ' ·
~ ron11 1 l-111)' ~ ~ 1
.1arc~ J)a 11<> tl1. Jt1end
ancl. 1 1ana2.en1 nt tl re"
that there> ar n pla11s ll1. J)~1\ a11\'-1 Lli,,;lf,,
,fs B·i ~ .,.(I l n l ur ~ I1arc-va 1uar,· n cc11at1c· 11. \ h"' 1st
· hc \ ,1 I,trc o f
·
~ 11
/.\cn1c ' " 11 ,1 re ·7
Ol1vi
t: ~111 l l1c LI i\' it.il'Jlll , ~1 lt1c~ arc' 1erl>. the · aJu of
Ir gr<>V.'l h l1ar • is zcr() !
1\n
l
1
~ - •
1
l
p _ 0 .
0
0
o---+---+---+···-0
l + R ( I + l< )2
( l + R)3
H()\\' ·a11 tl1e , ~1lt1c l fa grc1,vtl1 "l1arc be . r ? What i o in 2 n. h re?
The problen1 i" tl1at <.)Ur clefiniti n of gro,vth , l1ar s v.a le, , than pre ·i c. Our appii·catio11 o,f cqttati n
9.1 a~"u111t" tl1l1t Al'111 ,,·ii) 11 \er I ay a tii id nd. Tf Ac111 l1ad an arti le of a ociati n that tatcd it wou ld
ncrer pa~ di, iJe11(I" ~111d ,,·ould 11c1·er liquidate itself (unle, it b a1ne in I ent), tl1 · valu of it shares
\\ uld indeed be ero. Ec.1t1ati 11 9.1 r>re<l1ct anci cc 1nn1 11 en says tl1at if u wn hare in a · 111pan)'
that,, ill nc, er J)a~ ~ LI an~' ca~l1. 111 n1arket alu <lf th.o e ·hare i ab olut ly nothin . A . )' OtJ m y recall.
th i, i" p int ,, c c 111pha i cd ·11 t 11 chapter n tl1e fin·111cial ma11ag "r a11d th · co1npa11)'.
\\rl1at ,, ~ ,l1lluld l1a, e "aid i" tl1at a grtl\Vll1 . I1ar i a hare i11 a ompaI1y tl1at ·i1rre11rl_r ha~ e ceptional
in,c~tmcnt opp(1rtu,nit1c, ancf tht1s i~ n t l'Ltrrc·,11/_v payincr di,1id nd b cat1 cit i r in, ting ,ir11ing~. At
on1e 1i111L in tl1c f uturc. gro," th l1ar
11111anie. , ill [JJ)' di i.(le11d . r will liquic.Jar tl1en1~ 1,·e (for
t.:\t 111plc. l1) ,clli 1g . ut to ot]1cr
mpani . ) and 11ay a in le L. rg ·ca h cli id rid,. P ·opl . \\·(10 bu)'
_;rel\\ .th ~11are~ e pc t a pill f)ftCL aJJpreciati 11 l1ccause 111 nage111ent r in. t th c·:i h no,· fr 111 arning
intcrn,111) in i11\ e"tn1 nt rr(>·~cl~ h licvc I to }1· · e hi.gl1 rate fr turn. If th ir1ternal ir1 t1n.c 11t t1 cced.
the ~11arc:·'-> pri c ~11 uld go up ~j~nifica11t l)' ·111cl in, l r an , ell tl1 ir har " at a pric _ tl1at is l1igl1er th, 11
the price tllC) paid.
1. What 1s the general formula used to calculate the price of a share? WJ1at does it mean?
2. What are growth shares and why do· they typically pay little or no d ividends?
9.4 Share valuation: some simplifying assumptions
LEARNI G OBJECTIVE 9.4 Discuss the assumptions that are necessary to make the gen,eral dividend
valuation model easier to use and be able to use the model to calculate the value of a company's
ordin.a ry shares.
. d' 'd d model· (eq u ·iti· 11 9 I ) i · 11. ist 11t \\ ith tl1 11 tio11 thl t tl1 altt of an a s t
C011ceptt a 11 )', ur 1v1 11 · ,
'
· · ·
i~ the di cotll led alu of futur ca h fl \i\· • nfortunat I)'. at a practical level tl1 111 d ~1 js not a )'
t<) u e becati , of th diffi till)' f _stir11atin o futur
li vid nd. o ~- :1 lo11g p ·riocl_ of ti1n . \\c can.
..
k
·
i·r · .1 su,npti 11 ~ abot1t th 11att rn f. d1 ·1 I ncJ s th., t ,,·ill 111akc th 111 dLI
I1C)\\Cvcr n1·t e
11 ·
11np1 y111
ll c ea ' tl lllJ)t i Jns cl , l)' re ·c111l1l tl1 \VH)' t11'111
n1pan1es 1
, nanagc their
n1<1r 111ar1agc,1 b] . o rtL111<1l I y, 1 .
· ·
~
,1· ·d
d
,1 r I
. J ·cc
'••ni n o thr LltJf r ~nt <1s un111t1 r1 . ( I D1, ttl r1ti I ..1~ 111 111~ 1 n1a1n
1
U J\f J
I)
I a)1 (nent . VY la . e ,l , } )'
u .
.
,
.
, •
,
·,
. , , ,
.
, ,
.
.
I
. l
I,
crr(>\Vlll r · t( L; t 7e l ). (_)
(\ 1dt:11cJ 11,l\ C: cl ( n"tcllll grO\\ tl1 fdlt:.
con~tan t 0,1,e r 1111 c: l 1,JL , s, t,1 ,y 1 ' . • b
·
.. .
.
.
.
.
t
r )'ea r (3 , 1, i I ·n I b.av-· a 1111 CLI gr()\\ 111 ratL l)~ttlern: that '"·
1
f or eAar plc. tllC)' (1 ro at 3 11 1 cen I
' · ~
.
.
. •
.
. .
, 1 l th •11 ~\ it ·l t · a11 •tl1 r. ext. \\C' cl1~ct1-.,." a ha \lit 111)11111 turn.
d 1,,1d nd~ have ( n J)·1yrn nl J) tl " n uJ
·
1
i
..
·
·
·
L
I
.
·
•
•
.
•
•
•
)
•
,
·
•
--.
'.
r
I
'
:. •
•
el
•
IVI . e
w
, 'l
Tl1c '-ii111r1lL'~l a~. t1111.ptirH1 is tl1al Ii iclen(l~ \,\'i JI lia
11atl ·rn rr111ai11'-i · ,11sta11t ,·er ti111 :
or<>Wtll rate <>f ,ere>. ']'l1u~, tl1c tli, iclcncl tJa) nient
-~ -··•=loo
-
.., -
-
111 tl1i" ca~ tl1c Ji, ill nu li~COlllll lllOC.lc] ( quati( 11 9.1) t, C()ll)CS:
Pn =
D
l +R
+
D
., +
( I + l~ )-
I.
( I + R)
D
D
+---+···+
~ + -(l_+_l~-)4
(I + R)s
(I+ R)oo
•
·
.
,
.
.
·ri
·tuity
,,
ith
a
·c>Jl 1a11l ca~h f l(J\ . You n1ay recall thdt
1
l1is l'a'-;h. n )\ 11alt rn e~,cllll<l 11 (--~er,)
1
s ,l J)C
.
.
.
~
, · · I , .I . tc r n I is <l U tl t ccl c {l ~ h f1 (> w ~ a 11d \·a1ua t I n.
,, c dc,·cll)J ctJ a11 Cl1uat1(lll ltH' su ·h a f) ·r1) tu1ty 111 1.1 t: ld(1
•
, .
•
· \\ ·it I1 a .<>11~ t·,Hl t t:,"I s h .I <) · ,~ I·/, \ her CF I the con tanL
Equalit.>11 6.?, ait1 that th· P (ll • a J)Crf)Ctu1ty
11 <lth.=I. , c Cc.tn 11rcscnt tl1c an1c
c a l1 11 ( , v a nLI ,• 1· s thc ·I n t c r •s t I a tL' • 1·11 t L' 1.111, <1 1· <>u1. ' 11, ,-11·c ..·du·lf1<)'1l
' ·
r ·lati 11~l1ip as:
'
1)
Po= R
9.2
\\ l1crc:
P0 = tl1e ct1r1e11t \ alu . or JJrice. of the l1 t1rc
D=tl1eco11 tant a~hdi\,idendr c jveciin achti r11~r,eri d
R = tl1c rc4uired rctur11 11 rdi11ary . har , or di. unt rat
Thi
111oc.Jel fit" tl1e di\ id nd pall rn f r ordinary ~l1arc. of a 0111pan
t'hat i~ 11ot gro\\'ing a11d t1a, little
r fc.1r prefere11ce )har . \ hich wL (Ji cu ~ i11 tl1 n ·t ccti 11.
F r exan1plc. Great Sot1th rn Print & l)py i, a ~n al l I rin ti11 c, coI11pan th'- t f\ c~ Alban)·. \\e"t rn
A ti tra] ia. The lO\\ n' .. econ 111 ic ba c t1a · r n1a in LI C()n t·1nt , er th )·c,1r a11d Gr r1t Oll tl1 'rn ·" ale"' and
ear, i11g ren ct tl1i trend. Tl1c c 1111Ja11y (JH " a $5 divid 11d p r year a11d tl1c board of dire tor ha~ n
plan~ t change th divitlcnd. The c 111pany·s i11 st rs ,1re 111 tl)1 lo 'tl bu~i n ~. peopl \\"}10 xpcct a _o
per l.ent return n their in "tm 111. Wl1at h Ltld be th pric f tl1c · 111r),tll)' ·~ sl1arc,'!
Since tl1c a h di\'id "11d f)a)IJ 1 nt <-1re con"t·111t.,
~111 us quation ·- lo fi11d 1l1e 11ril'C of tl1 ~ ,t1arc":
gro\\'tl1 potential
5
I o -- -R -- Q. ( -- S2S
,. ~ f)•"t·
~ .sl1·t1·"
" I.;
.- )
•
T e val e of a mall business
ro e
For the past 15 years, a family has operated the gift
shop in a luxury hotel in Cairns, Queensland. The hotel
management wants to sell the 91ft shop to the f am,ily
members rather than paying them to operate It. The
family's accountant will incorporate the new business
and estimates that it will generate an annual cash dividend of $150 000 for the shareholders. The hotel will
provide the family with an infinite guarantee for the space
and a ge,nerous buyout plan in the event that the ho,t el
closes _its doors. Th~ account~nt estimates that a 20 per
cent discount rate Is appropriate. What is the value of
the shares?
280
p RT 2 Valuation of future cash flows and risk
. . - - ----------------------~-------------jjjjjiiiiiii--~~------------Assuming that the busir1ess will operate ind f .
t~ie zero growth. discount model ca b
e in,tely arid that its growth is constrained by its circumstances,
number of shares outstanding is no~ k~oused to value_the .s~ares. Thus we can use equation 9.2. Since !he
ordinary shares.
wn, we can simply interpret P0 as the total value of the outstanding
olu o
I
= _ = , l 50 ()00
11
R
-
7.-(). 00()
Llncler tl1c ,1 xt di\·iJc11ll a~su11111tio1.1. ca~h di, idcncJs lltJ ll<ll r'111ai11 ·c ll~tanl l)Ul in ~tcacJ grow "Lt 'iOmc
a,cragc rate 'tro 111 llll I ~ri()tl ll lit~ next f r~ver. · llt.: atl' <>f r , tl1 . ·a .11 I) 11<l\iti e <lr negative. ;\11J.
~~ it turn~ lllt. a on st ant grl)\\'ll1 ratl' i~ ll()t a l)all, ppro, .~111~1ti<111 t,r the ~1ctual Ii iLI "nu pattc n lur so1nc
cc)n1pa11ie'i. C<Jn~t~ll1 t di\ itle,.icl ~r '' tl1 is an apprc>J ri ·,tc as~ un11 tic n fc,r n1atur c- rn11anie" \Vith " hi'-itory
<)I ~tal1le gr \\' ltl.
You 111, ~' lic.1,·c t'l)tl '"rn al1l)lll t t1 as~u11111tit)t1 of tltl infi11itc ti,11 hl>riLon. Ir pr,tcticc. th·c ugh. thi~ tl<1es
nc)l 11rc enl a prc)hle111. lt '" true tl1al tlll t
111i1ani d n t g
11 for er. W k110\\i\ hc>\Vever. that the
furtl1tr in tl1c futttrc ~t l'a"l1 fl · ,, ,, i11 llCcur. tl1e s1na l] r it~ P'V. J1u.~. far-di . tant diviclend ~ ha a ~rnall PY
,1nll cc ntribull~ ,·er~ little tl) tl1c ~11are 11ric '. For cxatn()l ,. a }10\v11 in figL1r · 9.3, v. it11 con tanl dividend~
an<l a I: per L~llt di,LL,unt r·1tc. Ji,,idcnd~ paid du i110 tl1c fir. t l · )'ears a count f r ,nor tl ·an 75 per cent
Llf tl1c,, luc of u l1arc. ,, l1il . . Ji, t(ie11d~ I aid aft r tl1e 20t11 year c 11tribute le s tha11 6 p r c nt of the aluc .
1
EIGURE 9.3
1
Impact on share prices of near and distant future dividends
0 1 dends expected ar in the future have a smaller present value than dividends expected in the
next fe · y ears and so they have less effect on the share price. As you can see in the figure, with
constan d ·v dends more tt1an 75 per cent of the current price of a share comes from expected
d t dends 1n the first 1O years.
S2 50
$2.00
t/'J
'O
"1ore
75% of the present
_g $1.50
>
·"C
valu of
har come
C:
rom e1
e IS
'O
c d dividends 1n
Q. year .
QJ
4J
(.)
QJ
~ $1 .00
QJ
About 20% of the p1resent
value comes frem years 11-20.
0
>
a.
$0.50
Less than 6% comes
from all other years.
$0.00
0
5
20
25
30
10
15
.
. , 0 f J5 JJCr cent and con~tant div1dcnd".
35
40
45
50
Year
,\'nt<': ('alculation c1r~ ha,ed on a cl,~count r.ilt.:
-
i~ f< irl)' ~tr,tightf r\,,ar l. Fir,t.
·011 . tn11t -gro\vtl1
Ii i l 11d mo lel
lde11tif i11g ~ n(l ,ip11lyinb th ~
fr 'tny 11111 pl:ri cl. \ · \viii
th ,,aluc of di itl t1ti I '- yn~ ,ts
\\ c ne d a 111odel to c,dcu]at
)l C p rioJ l{) lll
)l xt r r \er.
a~. uI11
tl1at the ca h. d ivicJ cn J
gro\V ,· t a cor1 l ·tnt ra t~ .~ Ir 1
H PTE
Share valuation
2 .1
Tl1is ~ituat1011 is a 11 ~lJJI li cati 1, 0 r t 11
Oil tl1c Li111
. cl 1ll e
tt1 rrilc r rJllLll,1 Cl!U cttic 11 5.5 developed i 11 tl1c ch·ipt
. 1 l J) u11 d g I Ow I
er
.
C,I
rm I1ey:
V II = PYX (1 + g
·
. •
.
.
•
(
,,)
b
.
er·
of
c<Jt
J Lindi ng JJcr i od .. We c<,n appJ \' th•
11
\V I1crc ,it 15 tl1e co1nr10L1nd cro tl1 rat a11<.l ,, lS t 11 11ltI
·
. . .
.
.
_
. .J
I~
f nn ila t our di idend p· yin nl..
. not ,hat D is the curr nl div dcnd . ~)al~ a~ llm I - 0, and I grow1
. •
J
·d al , 1·111 t - 1 is 0 1 v J 1ch 1. JU~t the current di idcnd
,at tt c nstat1 t grov,: tl rate g.
l1 11 t cj1v1c 1c11c , p,11 •
· - , ·
·
· .
(Do) n1t1lt'pl i d by the growth fact r ( l + g). hu . . D 1 == Do X ( 1 + o-). The general formula for dividend
\ alll s over ti111 i :
9.3
D, = 1l1 di, itlc11cl {Ji~l. ' I17. 11l i11 p riod t, \ 11 r 1 = I ,2.3 .... oo
D 0 = tl1e di\ ide 11d 11aiu ir1 tl1 u11·~11t p riod. t = 0
c :..... tl1e c 11 ta11t ....g_r \ tl1 rt1t f r di id r1d
1
EqL1~tio11 9.3 all \\' L1s l cJl ulat tl1e di id 11d pa)11ne11t or any time period.
>Joti c tl1at to calcttlate tl1, di idend for , n.y period, w 111ultiply D0 by th growtl1 rate factor to s me
po,, er, l ut \~ a/1,·a · start vl itl1 D .
\ e Ct 11 110\, de,,elop tl1e coI1st int growtl1 divide11d 111odcJ. whicl1 i ea y to do becau it j ju t
aI1 c ·i, n i 11 <.1f equati 11 6. fror11 tl1e cl1apt r on di ·c LI11t cl ca~l1 flo\ and .aluation. Eqt1atio11 6.3 a,
tt1at tl1e pr cnt alu of a I r1J tuity (PVP) i the ca ti fl \J ·· alu (C 1) from peri d I di,·id d b)' the
di cou I1t rate ( i):
CF 1
PVP=•
l
. We c n ~ ,
te11d thi r la.ti n hip to i11 lt1de o-ro in <1 h fl w . Th · PVP of a gro\\·in;:, perp tuity
1 the gro,~'1ng ca 11 fl \ valLte (CF 1) fr 111 I eri d 1 di · id d b)1 tl1 difi r n
n th ·.
Lint r" te ( i
and tl1e rat of gro\vtl1 (g) of tl1 ca~l1 flow (CF 1), , , foll w :
PVP ==
CF
~l
•
1-g
\ e an re pre er, t thj s sa1nc rel,ttj on. 111 p a :
9.4
wl1ere:
P O = the curr 11l alue, r price, f tl1 liar
D l = the .di\1idend paid in tl1c n l p riod (1 = I)
g = the 011. ta11t gro\v lh rate for di id nd.
R = th reqt1jr d return n ord111ary share. or di c ur.1 t r t
I11 otl1er words. tl1e con tant growth di id _11d r11odcl tell
t·l th
.
· r 1 c betw en tli . di .,.......LI .. ,at.
per1· d ct·1v1·d. e11d d'1 1·ct ect.· by the d1ft
1
.
f a h ar · 1· tl1e 11 ,xt
, PVP · th
·
1
·
. .
uiit iate a11 l tl1 di 1·ct 1·1d o · ti ·· ·t"' ()te
t l,at
1. .
cur nt a Ll r IJr1c of th ~1,.- li·ti· (P0 ) , . h'LC h 1. th
. p
·f .
c, IO\ 1 1(.1 L. ·
·
·
0
1·11e growing JJerpett1ity m clel is v,1lid 011 ]\t a 1 11 0 ,, tl 0 ~ .
th · di 1cl nd · a 11 fl \\ - .
•
.
~
.1
· o ,t'"
1e 10 \\,tl1 rat 1: l
l
·
r
re.quired rate of r turn. In t r11 f eq uati n 9 4 ·t·h n I
e. • ·
'
· . t 1,1n tl1 d1 , · lllll r,Lt .
I
~
.
.
.
.
.
·· · ,
. , 1 \' a ti
f
b
.
It rhe equall n u e<l 111 . 1tuaLJon wher R i.. qua! to r le , t g m~ t I s than th alu f R (g < ~).
h 1n a11inglc .
han .i; (R:.:; i). th al uht ·I r suit~ will
tLrr
. nt
· pr1
C,
·t
Fi11ally. noti c tJ1·tt if 1!? = 0 tl1 r i.- i
di\,jd 11cl or \\'th , 1 ._. .
. .d d
. ' l , d' ,,i l -nd pa)'
t
.
t
110-growt h d 1\:1 - r1 tr rim a11d eqL1" li o 1 9.-l bccoi 1 s p _
. r1 11 pctt r11bec 111 _ , 0n,tan
1
1~ quati n i pr ci I_ th sam-: :i
,cc1L1ati(>r1 c .2, v. }1icl1 is ur, ro growth livicl 11 1 11100
T.
l
/R.
!'h
1· lll~ cq,tl 'lll 1 " · ·
1 .!. l Jll ta ~1 ·i~1l c·1 • . f , luat1on
9.4 wl1e re g = 0.
·· · '
T 2 Valuation of future cash flows and risk
-
►
Lct·~,,ork tl1ro 1gh :..111c., a1111 1c 1~ii,, h,.
· . . .
.
gl ·
c1n autt)111c)t 1,, 1 at t\ ~LIJ1} ltcr t,a~ccl iil , "' l
tI1 ,1• ·, 1
•
.
'
ul\ tu ncf 111 clcl. Ju • Oval Motor \\Ir ·ckcr~ 1
.
cc t 11c. Victor·. J\ I1
,
.
.
th . Cl_.0 a1111 tine ~ tl1nt tl11 yc,11.\. d' .
._ · _ Jll. t t co111pany ~ yea -end sharehlJlclcrs 111 • 11112
I1. tan l o ro
•"
1'' 1t 1.. nd ,
l
-
i 11 t , $-· 4
,
•
... -•
di, idencJ p<)IIC)'. v\1l11cl1 t~ livitl Jlcl l'r
) · .8] · fhc an11 u11c 11 1 nt cc>nft,1111s to Blue o,,aJ '~
.
o O\· l 1
1 at a 4 I r c •11 t '\
., I
. . .
l}'IJe~ <1f ·011111a111 ·~ c., pect l< e·, rn l r l
f 'nnuct rate. 111 e~tor. , 110 o,vn ~l1are~ ,n ~,n,,tar
urn f) 1 P r c 11t \VI 1 · I
l ◄irst. we 11eed to l'al til·itc the c·,~ll d' .. ,
·
at 1st 1 alu · <)f th,.. co111.p~1ny's ~hares?
' . 1v Luc nd 11 ay 11 11 t f <>·r nc t ar D 1). A 11 p I)' ., ng c1 uat 1.c n 9.')~, for
, = I y1.. ~ l t I t·1l t: ·f-o11o, 1.11n :
•
•
..
l
D I = Do X ( I + (~) = $➔. c I X ( I + 0. () ) = $ .8] X ] .()
e ·t. ,, a1 ply qLtati( ,1 (J.4 to find tl1c alu, ( r the c
.
= S5 .()0
I
111pany s ~ 1Hre~. \ J1ich i~ SJ.5.71 per hare:
(). l 8 - ().()4
$5. 0
.14
= 35. 71
I
a
e
~
lem
Using the information given in the text, calculate
the value of Blue Oval's shares if dividends gro-w
at 12 per cent rather than 4 per cent. Explain why
the ansvJer makes sense.
0
C
First calculate the cash dividend p,ayment for next
year (0 1 using the 12 per cent growth rate. Then
apply equ·ation 9.4 to solve for the company's
share price.
olut·on
D 1 = ~4.81 x I. 2 = S5.39
Po = _'>_5_.3_9_ - ~5.39 = 89.83
.18-().12
{J.(J6
The higher share value of $89.93 is no surprise because dividends are now growing at a rate of
12 per cent rather than 4 per cent. Hence, value from cash payments to investors (dividends) 1s expected
to be larger.
Calculating future share prices
The con t<.tnt ro .ti, div·c1e1 1d m I J ( q· ti 119.4) a11 b 111 dificd t d t r111i11 · th v(lt1 . r price. of ~1
0
~hare at r111y J) int in ri m _. In o n ra,I. th pri · fa har P , can b exprc. ed int rms of th di,·iden I i,1
the ne :l 1eri-od ( r+I ), g ancl R \Vl1 n th dividend fr 111 D ,+1 f r\v·1rd ar ✓ p cted to grO\\ ,it a 011stanl
1
rate. Thus, tl1e I rice of a "t1ar t tin1 / is:
95
C
Share valu t1on
28
0
1
2
3
I
I
I
I
Dividend· $2 .50
Share price : P0
o,
4
03
D;,
5
I
I
D .i
05
Ps
Year
n ", t -vear:
'",, S() X I .()5 = ~2.(125
L1 1 = 1)0 X (I+.~ ) -- ,n_,_
.
hLn \\l' L\tll ll"-l' cLJll"tlt()ll
9.--l t0 f-1n d l Il L" Pr1 L·c ()f th' ~hare lcluay:
$2 .(125
l>2.(llS = ~26.25
= l). I 5 - (). () 5 - 0. 10
D1
1--,() --
-
l~
_. ,. ·
Nt)\\ ,,c find the ,aluc of the ~hare .in)_ year~. [n Lht. 'i s1tuatto11
e CJU 'L lio11 9.5 j~ cxpre'-l"CU cl
\\c need tc, calculate D<, and ,,e do o by u ing equati n 9.3:
D(, = D0 x ( 1 + ,) 6 = 2.50 x ( 1.05) 6 = 2.50 x 1.34 == S3.35
Thcr .. forc. rhe JJrice lf th ~hare in 5) ar 1• s:
_
Ps ·
$3 .3.0. I S - 0 .l) 5
~J.JS = _r-33,_50
0. 10
5
J i 1al I)'. note that $33.5()/( 1.05 ) = $26.25. ,,,hi ch i~ tl1e
o e ' cur ent
are
nlu tc1Jay .
•
rice
Suppose that the current cash dividend on David Jones Pty Limited's ordinary shares is $0.27. F1nanc1al
analysts expect the d1v1dends to grow at a constant rate of 6 per cent per year and investors require a 12
per cent return on this class of shares. What should be the current share price of David Jones?
0
C
In this scenario, D 0 = 50.27, R = 0.12 and g = 0.06. We first find
the value of a share using equation 9.4.
o, using equation 9 _3 and then calculate
So
().2862
() 12 - 0.06 -
284
ART
Valuation of future cash flows and nsk
0.2862
().06
== \➔. 77
f
Da d o
IC
p
ContInuIng
the
exarnple
in
demo ns t ration
problem 9.3. \Vhat should David Jones' st1are price
be 7 years from now (P 7 )?
Thts ,s an appl1cat1on of equat,on 9.5 We first n ed
to calculat~ David Jones' d1v1dend
period 8
using equation 9.3 Th n \Ve can apply quat,on ~-~~
~o calculate the estIn1ated price of tt, share 7 ear
In the future
Y
ir,
D v,dend In period a·
I)
= l)( X
n , y ar
Pnce of a sh
p- =
-
....'
n
"()
~
S().4J
I{ - , - -()-.1-,--t,-_ll-(1 -
Alte na
t).(16
= ~ 7. I 7
el · ou could calculate the price of a share In 7 years by using equation 5.5
Value o a h re n e r O
r =
--
.I I
. -, ea s:
P ce o a s
➔. 77 X
X
-
I.( ) = S ➔. 77 X I .S()36 = ~ 7.17
The e a ons ip between R and g
pr i u I_
r ti ncd th ' t ti .IL" di, idl!nd grt>'-\'th n1cldcl pr<)\ itle"' , alid , luti n, l1nly ,, ht=tl ~ < R.
5tt11 ·nt r I ntl
hat ll~q1pl:11'-i tc, ·c1uatit,11, 9.4 and lJ.5 if thi, L'C)tH.litiln UL)~~ 11 t l1c)lll (if t: >
I< , ~l 'ith
If_. ;1 , , pprc,achc, I{ the '>hdr' J)ricl! hcco111 , larger and larg r anti ,, l1en ~t: = R th~
a 11L , tf •
t· i int111.1fc \\ hich i\ IH>ll'-IL"ll\C. \\/h~n lh · gr \\ th 1alc (,t:) i, larg 'r tl1an tllL (li,L'<1Ulll rate
f{,. thl (>JJ tar1t 'fi , rli tli,i<len<l 111t><ILI tell\ ll'-1 that th~ ,aluL t)f thL ~har· i\ ll'~ati\l'.
llr,\\C\~r. thi, i,
.....
1H1t p )', il1lc:. t c · u · ,1 ~ '-ih, re can n \Cr l1 • 11cgati,c.
f·11>111 a 11 ii 1ic,tl
r~11 · ti\ , 111 • g, )\\ th 1, t~ i1 the ct>ll'-il·tnt grt)\.\'lh Ii, illl'11tl 111l,(l ·l l.'a11n(ll he ~rLalcr
thJn the ,L11n c,t th\: ]<JIJI tt:r111 r~IIL' ,,t 1nllati,,11 an<l fill' hu1g-te1n1 real g.rc)\\tl1 ratL' l)f thl: CL'llllL'lll\.
- incc
thi'-1111<,cJ<.:f a" trill<.: that ,1 t(111q),lll)' ,, ill e,c,\\ al ,t Cl)ll'-it,1nt talc flH\~\L'r. an~, grt)\\ th r.1tc tl1at i~ gr ·atL~r than
tl1i\ \llJll \\ ,ultJ i1111 ]~ tli,tt th. l'()lllr:an) \\ ill . e11tually t!ll-..L· ()\L"r the entirl' L(l)lll)lll~. I 'l)llr L. \\'kill\\
thi'-1 i\ nc,t p<>'-i'-iihle \1nL the ~u,11 c,f ,1i._,, lc,11(' -t ·rn1 ratL: 1)l 1nllatitu1 ~,ntl tl1c l,)ng-t~1 n1 tL',tl grt)\\ tl1 rat~ l1a,
hi,tt,ricall) l1cL·11 Jc~ tlla11 7 re, X f)L'r ce11l. th· gt<>\\th 1~1tL· (t:) i, vi1tuall~ ,tl,\a), le~, than till: tli . . ct)llnt ratL'
(I{) f<)r lhL: ..,.J1arc\ thur, L" \\Oul J \\ant l<l u~L" thl' l'l)ll'-ita11t gr(>\\lh clivitlcnll llll)tlL·l tt) ,alu .
ft i~ po~"il1 lc I r ccJil f)a11ic\ t<, gr(>\\' la,tL·t tl1<111 the l<lng-tL·r1111atc l)i 1ntl,1tit n l)lu, Ll1c real ~I(), th 1atL'
<)I the eccln ,11) -ju"'l r1c>l Jt,rc,er. A c<)I pan) that i\ t!r<)\Ving ,lt ,ul'l\ a hie-h ralc i'-i ,a1ll l<l he grll\\ ing at
a \LI/Jcr1,r>ii,,c,I gr()\\tli rail'. \l L" 111u~t ll"L. a differ ·11t Jlll>LILI lll \alul tl1c "'harl', l)I a L' n1pan~ lik.e lhi, \\'L•
L'
r
~
Ji"<.·u,, ()11~ "'uch rll()dcl nc t.
Mixed (supernormal) growth dividen model
I <lr 111an) c<linpanie,. if i~ 11 >t apfJl<>[Jrialt= t · a'>,t1111 thal cl,vicJ ~ntl, \Viii grl)\\ al a L't)n,t~u1L 1at~. l'l 111pltniL·,
l) l)icall) O(> 11 rouoh /i[t_, '')'<·le., anLI. a, a rL",ult. exl1il1it (lt11c1 ·11l li\'1LIL ncl pdltL·111, ()\ c, ti111L·.
1
t:'
t:::•
•
During lht ca,ly l)arl <lf Lllcjr Jive,,. uccl',\llll cc)11111~u11c~ L"xp ·r1~~1~cl' a ,ur1crlll'lll1al ,ate t) · ~Ll)\\tll
111 l\trniug~. Thc,c l.
01
,panic, t ·ml 1 > JXI) lm1 ·1 di1 id 'ml, 111 n J d111dc1HI, at all h~T.1lhl' many .,,od
- - - - - - - - - - - - - - - - - - - -ft-~,-. - R
St r v IL o
2 5
Dividend growth rate patterns
.
from supernormal growth of 25 per cent for
The graph shovJs several dividend growth curves
ye~rs to a negative 10 per cent growth rate .
$60-.---- - - -- -- -- - -- -- -- -7
Sup rnormal 25% growth
Normal 5 °'o gro\~th
Normal 5% growth
S5 o
S4 o
~
- - Zero growth
Declining -10% growth
D1v1dends exhibr a
super-normal growth
rate of 25% for A years
and then a more norma
growth rate of 5 /,: .
(fl
~
C:
,:, S3 0
Dividends exh1b1t a
0
of 5% .
·->
S2 .0
D1v1dends exh1b1t zero
growth.
$1 .0
so.a o--- - ---r-,- - - - . 2 - - - - , 3 - - - - - - - r 4 - - - - , s - - - - - 1 6
D1v1dends exhibit a
negative growth rate
of 10%
Year
A, ,ncntrc>nc<l earlier. "uc(C!'\~ful co,n1panie~ oft n exp· i nee :--.t1pernorn1al gr<.)\\ th l'arl) in thLir Ille
C) clc,. Dur1n_ 2() 18. fur c ample. on1rJanie" "'ucl1 as Yer~cnt. Al 111 Re~<.. u1cc~, an'-1 ,I ri111l: Q e\1)er1~n1..~u
11
,upcrnc)r11 al bf '"·th. 0J<lcr <)1111 ·tni "'th, l r"in ent thcn1'-i~I C!-i ,, ilh 11L ,, 11r0Juct"' ( r ~tratL·gie" 1t1a al )
xp1.,r1cnLc perimh of wpc non ~I gnl\\lh.B ·tv. ·en the rclUrn of Sieve J11lh to th helm ol Appl.: in 199 ~
an(l h1, death 111 2() I I . h(>lh arn I ngs gro,, th and "har h l,ler IL l urn~ t: \cccdcLI J() per en t JJt: r . nn u111. 1
"J()t I< n~ a,~ Ii111 Ct)()~ l()()k )\l!f cl\ c1..:o, A11p)c anll()llllCCd that lll:l f)r()fit hall, in~rca~ctl b~· 85 J)t:r ·cnt
in the t111Jncial )CJr ending 27 ScJ)l n1l)cr 2()1 I. It, annual n ·t J1t'l) ,t gr()\\l11 l1a" ,aricll c lll'-liUL'tabl~
~incc ~()1 l nuctuating t1ct,\ '·11 -14.➔ f)er rent (i11 ~()15) anLI (l().9l ))l'f cent (in _01~). 111 tl1 Jun 20Il)
c.ruartL:r. \pplc p(>,tcd d n~t pr< ftl (lcclin · <>f 12.8 J)L'r CL'nt: tht LlccrL\l'-lt: in gro,,·tl1 ha~ bcL:n attributlJ to
1
J dcCrL"t\C in iPh<>n ,ale". ~ Apt)lc·" ~l lCk. J)ricl'. ha" 1 i"L'll 13(l.() per r "'Ill Juri11~ tllL la,t 5 y ars ending
_8 Oclt>l1er
19. l.t It ha, ,ince return d 1...c)n1 (>fit" profits le> !'\harch >l lcr" i11 the rr11 of li, itle11d~ anJ
hare buybar ~. \\.ht:rL'a"' in th r>a'-it lob, prcrL~rrc(I t > retain A11plc', earning~ for ltirthcr in, ~t111cnt i11
profital)lc project~.
_o
r
T(> , a Iu a '-I hare tor a c rnr)any " it h su I er11 rn1a I cli, idcnJ gro,, th pat terns. , c It) 11 t 11 cd lt) ll~\ '-'ll)P
an) nc\V cquati n . l11~tcaJ. ' c an ltpply 1uatit1 n 9.1. our <• llLral divic.lcnd 111uc.lel. a11cl l: 1uati()ll 9 5.
,vhit:h gi,,c~ u~ th prr c of a hare, ith cc)n tant diviclt:nd gro,vth at an)' poi tit in tinic.
We \\ j J l i II u~ trate ,vi th ~ n c ·an11 1 · · upp<l,c a ron11Jany ·" · pcctctl di, ictcnd I alt ·rn ft>r 3 ) c dr. 1' ~l'
ftJllu,v~: D 1 = l. D~ =$2. D1 = 1. After 3 years. lhc Ii, iclcnd, are t:\J) ct ll ltl ~f()\\ at a con,tanl 1.tl~ ")t
6 per cenr a )L'H1. \Vl1at ,hould th c currl'nt ~hare pric (l'o) he if the rcquirctl rate l)f rl'tu111 c.l('111anJeu h)
i11ve'-llt)r, i"' 15 per cent?
\Ve h.:grn by dra\\ ing a Iii l li_nc, a, ,hm, n ii'. ligu,c 9.5. \Ve rec mmen I that ) ou prL·parc: a iimc: line
\\hcne\er )'<1U '-lt)lve d p1oblc1n ,v1th a C<Jlllf)IL'\ d1vH.IL'nc.l pattL·rn ~ll that\ u L'an be ,urL the ca,h Ill)\\' di'-'
placed in rho.: proper 1imc pc ind~. The c1 itical _du11cnh in" or!-ing th.:~~: problem, arc Cllt r.:cll) id.:111if~
\\ hc::ri the ·c,1 ~tant gr<J\ th '-lta1 t~ and ll) , alu'" 1t p1c>perl)
286
111
Valuation of future cash flows and risk
◄
Time lino fo n n-constant div, .
The figure shows a t1n1e I
f
dend patt rn
ine or rl non
t
easy to ee that vve have tw d ff
-cons ant growth d1v1dend patt rn. The time line makes 1t
0 1 erent d1v·d
d
I
grow at a non-constant r t
f
en patterns. For 3 years, the d1v1dends ar expected to
t
e; a ter that th
, ey are expected to grow nt constant rate of 6 pe cent
Non-constant growth
Tirr1e
0
1
Dividends
1.00
Key variables p
o,
grov,th at 6 it
•I
Const
2
3
4
5
2. 00
~3 00
3.1R
37
n
[)
y
r
[)
t\cLI di, ilh~nll grLl\\ thJ + PV(C n~tant di id nd gr<>\vth)
Co111t1inin
h "
r' l L' ll \'JlUl:, ~ il:ld, ti) ft)IIO\ in~ fL~U.)l:
~
p
D
D,
D,
---+ . . - + - -' 1
( 1 + R)
( l + R )~
( I + R)
+
PV of rni '\ed er \\ Ll1
"'
di,,idenJ fJa) 111ent,
Val u , of con tant
gro,vt h
._
di,, ich:ncl I a y 111cn l:--.
' lu · tt ·cl tant 'fCJ\ th dividend ,tr~a1n i., .P ~., hich 1\ the \alu . or J)ric . at t1111c r = 3. l\lore
11.,. J) i lL" ' " lu ,, the fut ire c,1\h di, iden<ls di <)unt d t<) tin1 pcrit)cl r = 3. \.Vitl1 a re 1uirecl
r te (Jf t:t rn ()l 5 r · ·r I, thL: , alu~ <>f Lhc~e di, 1ucnll~ i calculatctl a~:
Th
IJ
I,
= I) x ( 1 + ") = 3. 00 x I .()6 = ~ 3. I 8
J
-
I J.t
R-~
3. I 8
- (). I) - ().()()
\3. l 8
- ().()'J
= ~ ~5.33
L: 1u.11i< 11 'J 5. \ I ich ,illL>\V" u, t<> calculate ,harL: I 1iL·(', in the future fl)I
,hare!,\\ ith C n,Lallt Jj, id ·11d gr<)\\ th N<>tl' tl1~1t the l'(jllat1<>1) ~,j\i.,;, ll'-1 lhL' \ allll:', a, l)r) ear 3. (Jr a Cull tanL
gro,, Ll1 p~rJJClLtil) Lh,tl 11 •gin~ in) 'tr ➔. I hi, l(JJ 111ula al\\ ~I)~ ~,i,c, u~ the valt1c d, L>f lHl · ()cril)U bcftlrt: th·
\\e find the \alu • <>f fJ
u"in
l1r-.,t ca~h t IO\\.
()\\. incc J i, at tilllL' JJcr ic>ll / = 3. v..1c 111u,t cli" ·c)t111t 1l l1ack tu the pre cnt (t - ()). Thi, J"- a'-'L'C)n1I li'-ll1cd
3
h) di, iding J> 3 I))' tl1c a11prupriatc..; cli, ·clUllt act<>r - ( I + l{) •
Pluu~in~ tlic \<-tlu ., for th Ji,iLlcnd,. P, ancl
int() tl1 aht1\ • n1i\Cll gro,\th ~tiuatic)n t\~,ult, ·11 thl-...... ~
--
\.,.
!()II l)\,\ 'i n e:
~
I .0() + $2.0()
P0 = - 1.15
.
,
(115)-
+ $3.()(J + ~J5.J3
(1.15)
1
(1.15)
,
= \().87 + I.~ I +. 1.97 + ~23.23
'h27 .5X
IL t
2 7
•
,
. 1 t'r<l\ lit ,\ itt1ati<Hl. ,, here Ii ill~11<l\ gr<)\ 1,r,l at a
\\ c L'~111 \\, tll' a !!l'11c1 al ~qu;ltH>ll lllr tile ~llf)L l lllll tllll e
.
Il<H1-ccH1\tanl rate until I l't i<lll t ~u1d lhcn at a c 11,t,lnl r~llC. a,:
I>
1
+ ... + -(
1-+-1{-)1
I
+
fJ
( l
t
.6
I< )1
+
O
·t l lll'' \lt~1c1 t1l)rt11ld ~r )\\ 1h f)Crt<>d
· cnll, an(I J1v1
· ·c.1 Clll I') ~1 <>\\ d, t 'l c·<>11,L·u1t
rate
then P , i<., calc1ilatccl fr <Hn
'
,., •
l
c ll u at 1<>n lJ •5 a " :
f)t1 I
J>
=
( I< - .t:
Tl1c l\\ () 111ccc-tlint?, c 1ul ltl)ll:-. L·an al,<l 11 apr)lied, hen ,Ii, idenJ, ar · C<Hl~ldnl <)\ ·r t1t11c. \tncc \\C ~110\\
th~1t .~ = l) ..... ju, t a 'l:)L'Ci~l ca~l' ()r lhL (.'()11\l:lnl gr()\ 111 divi<lcnl1 t 1udt:I (,~ > ()).
] .e ( " J (1 ) k l l a ll ) l I1L' r ~ Xa 111 p}C • I Il j , l i 111 U\ l 11 g ' ]lJ a l j () t1 LJ . (1. S II r1 p<>SC ( ha l J\ LL '-I J ~ j <) t CC h L l cl j \ a h j ' htccl1 111--lfi "al Lie, iL·c l·r11111, tl)' 1LlCatcd in ~lcll1uu nc. The c< 1111)ar y i~ 3 yl:ar, c)ld a11d l1a c\pericn ed
~,,L·ct~, ·ul tr gr ,, th ,,nee it~ incc1)ticHl. You ar · a 1nan ial ana lyst for a '-lh~1rc hr(>h.cr(1gc co111pan) anll ha, c
j t ,t 1 LI ll t llL J frc.H11 a 2-da)' \' i ~it tl) l he C( )Jll [)any. You JcarnccJ that Au, Bi ()lcL·h r la n ~ l(J pa., no di, idcnd\
l)r the ne. t) ~ear~. In ~'c~1r (J. n1anagen1 nt plan t<J !Jay a large ~p cial ca~h (Ii, icl 11d. \\ hich ;()LI ti mate
ll) be \25 p~·1 ,hare. Then. bcginninc in year 7 In~u1tIg I11ent JJlan~ to pa) a c 11,t<1nt ar1nu~d di,1llcnu of
"6 11 ~ ,hare fLH. the fc)rc,cc, bl,. ft1tt1re. The ap1)rOJJriate discount ra.te f<Jr tl1e ~l1are i~ 12 per cent and the
cttrrt: 1t 11l rkc-t f)ricc i" S,25 per ~hare. Your hoss lloe n·t think tl1 sl1are ·tre ,,·orth tl'l price. Y >LJ 1hink
th-~ are J hargain and )l)U ,hould reco111n1cnd th 111 toy ur 111pany'~ cli nts. Who i~ rigt1t'!
Our fir,t ~tep in an~," ring thi~ qu tion i. lo la)r out ( n a ti111c tin the e,pL:cted di, idend pa)·n1~nr~:
1
l
0
~
o d v d ends
I
.
hrough y ear t = 5
Po
5
6
7
8
9
I
I
I
I
I
$25
$6
Constant dividend forever
(D5 + P5)
D7
Constant after year 7
Year
>
l 11· ,1tu·1ti(Jll i\ a d1rl!ct aJ)plicati nor c(Jllati n :J.(1. ,vhich i~ lhc .111i,cc.l di\ itlcr 1tl Ill(JJcl. That i . th~re
a _L.: t\\ cli
t di\illend ca~h ~trca111,: ( J) the 111i,c.=d cli, iclcn(ls. \ hicl1 ltl tl1 i~ ca~L L' )lllpri,l' a "in~h.:
,den pat~ 111) ar 6 <cqL~l Lt n 9._l J. unu (2) the C<)J1st~u1t tli itlc11cl ~lrcan1 Ct:= l)) ()f. (1 per~ ~ttr forc,er
( (j t at 1 >n 9 ) ). Th t.: a I c <J f t hc (1 rd I nary ~ha r~ ~ can h c a Ic uIa t ecI a~ :
r:
u,,
J>,, = JJV' 1ix~u di, i lt:11d gr<)\Vth) + ()V (
n~tnnt
Ii\ i IL'ntl~ ,vith nl . gr{)\\ th)
CjU~ ti<>11 (J.6 I<> the ca".ih Ill>'\~ J)f ·,cntL'U 111 the prt)l11c 111 \ tL'ltl~·
•
Note 1hat the first le 1n in tl1e ~econll line ralrulate~ the py O f h , .
. _ .• .
. .
111 the ,econd t r1n P is tl1e di~count ( vt.1lu. r l
l c lcugc 2:-, Ll1, 1clencl plt1ll 1n ~cai b.
0
6
•
)
l,;
t le con~tant ~6 cli, i(l 11· 1
· ·
·1
,alued t JJCricJd t = 6. 1"o calc late the py of p
ct· . . '
c 11a)·111 ·11l 111a l 111 pcr~1ctut ~Cl '' e 1\ l llc , t h)· th . . .1 1
·
· ()lllll tacl()I. ,, 11,~·
· I1 ·1"
( I + J )6.
c l 1Jropr1at
lh~
i\~ t. w~ 11lug the data giv n edrliL"r inl() the ab<>\L' cc.iuatioil:
2 88
T
V luat1on of future cast1 flo~w
~ s;. ~a~n:d~r:,s:k_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
, _ \, 5 + ~ S()
I I) -
(1.11)(1
75
--- - - 1.97JR
= S38.l)l)
Tl1~ ,11,, . . ,.:ti ....... , l 111~ k.ct pri ·c i, ~-5 a11cf if y ur •. ti111ate~ of di\'ide11d p,1y1ncnt~ ,ire· correc t. t C
,hare·" , J lt1
p
I1 I ~ . f Il 1, S LI ...~ ~ t' \ l ~ l hat Lh C l1are is a bargain at1<J )Ottr ho~~ i~ inc<lrrecr .
'-'
1.
2. E pla n
d' ere models are used to val,u e shares based on different dividend patterns?
e ro h ra e g must a 1\vays be less than the rate of return R.
ng
reference shares
EAR, I G OBJECT VE 9.
1
alu1ng preference share.... 11
both cond ons.
1
Explain how valu1r1g preference shares with a stated maturity differs from
no maturity date and be able to calculate the price of a preference share under
~111 r i 11 tli c ct uptt.::r, 11r JL 11cc ~hares ~ire hyl1rid ~ccurilie. fallir1g . 0111"\\'l1crc bct,\cc11
h,11101... ~,nd orcl,naf) ~liar~ . I ,r x,1rilJ)lc:. pre l;ren 'L' "il1a1e, ar H lrigl1cr J)rioril) cl;1i111 ()11 tl1e co111JJ~111y·
,1...,\et, tl1an <>rd,, tr)' J1:11
hut a l<>\'.L'r J1Ji(>rity c:l,1i1 1 ll1a,1 th ccln1pan)1 ·~ crcLlitor" i11 lllL" t'\L"t1t of de Jltlt.
In calcula1 1ng 1l1c \~tllll: (1 pref It:1 ·e "11,1 c • 110,,c,·cr. tl1c critical i,stlL'
11 tl1 r tl1L' 11rl'f(•re11 e "t1~1res
ha\e di c fccti\L' ·m·,turit) ·. J1 ti L. IJrL"f ·1 ·11L·e ,J1~1r • cc,1111:1 ·t ha~ a sin~i11g fu11 l ll1at L'all" fl)r tl1" r11~t11d~1tory
r ct1r~n1cr1 t c)f the ,l1~1re, c \ r a ~c]1cd11lccl 11c i<Hl <>f ti111c:. fillanciltl a11al ~t, \\ ill t ·11d l<) Ir ··~•t the l1~1rc, ,1
11 thL·~ \\ere a hc)ttd ,..,itl1 ,1 rX~(J 111a1u11l)'.
1 he 1n(1\t ~igr1i 1ca11t dif.lcr nee l)ct,v ·c.:r1 a jltct ·, n ·c ~t1arc ,,,itl1 a 11\Cll 111atL1ril)' LlllLI ~1 bo11d i" tl1c ri,k.
11! dcfat1lt.
11 ) C<>ttp 11 pit 111 nl~ arc· a J ·g~tl < l1ligatic,n ()I tl1 C<)lllJ1a11)' c1ncl failttre lC) p~t~' the111 fl:~Ult,
11 delault. '-1. l1t:rca~ pref rcnce ,l1are <livicle11d"' ar' ucclarecl h)1 th l1oaru ()f clircct<)rs ~111 I r~1ilt1rc t pay
di\ idend~ doe~ 11 tr u]t in default. : cI1 th()ttgl it i n l ~1 le al default. tl1c f,1ilL1r to pa) a (Jrcf~rc11 -e
hare <.Ii\ idend a\ pro I11 iscd i~ 11 l a tri\ ial c\ L'llt. It i~ a li11a11cial bre~1cl ll1at can "i('Y11~1l lC) tl1c 111~1rkL''l lh . t
1hl'. C<)111pat1)' i in cri u fi.na11 ial Ii 1culty. As a re ult. n1a11t1gcr" 111,tkc C\cry ffl)rt to 11,1y prcfercn ~
"hare <livid nu, a~ pror i~ed.
\" 111~ntic,n
i,,
1
Pref re nee shares w ith a fixed ma urity
l~~l·i.lu"e [)I~fc·rt:t) ~ ~lia cs
ith all erf ctl\'C 11l1lt111t) arc Lon,i<ILrc I ~i111ilar l() l1l)11cl'-. \\L' c, 11 ti ~ tht' 1,-) ,r1tl
,ll uatiun 1110 ctc,1dcvcl<)flC I in the c;l 1a 11 t~r ,, 11 l1on I, ,tluati<>11 un I 1t1 · "1ru~turL· (lr ii1t ~r~~l, ,llL, lll Jctc1 1 111 1c
It j)1ic~. <lr ,altte. AJ j)lyino equ~ition x..1 ic(Jlli ~ nnl) that ,,r 1 "Cllgt11,e lht1t L'(lllJ1,rn 11 ..1~111t>11t, C, llL:
1H>\, cl1viciend f)ayntLnl, (I Jan I rl e rL·fr 1 1 cc "har
Ii, i lcn(J" all' 11ai(I" ·n1i~u1nt1~t1l~. ,. hu, 'lftt..11 L) 1 ~
1 11
l. ~lll l)e re,tatc(I a~ I 11
fJric \ ol a 111
•re,
CllL'C 'lllLtr~ ( I So):
S
I
V
LJ
ll
28
97
PS 0 -
I )/111
--
i/1 II
I
P,1111
I - ---11111
( + i/111)
+ ( I + ,·t,,z )""'
\\'llt'l ·:
l) = tllL' ~11111t1t1l 11rc c1,c11cc ,l1a1t' lli, iLil"ntl I ay111cnl
r = tl1e ~,~lll'(I (11~1r) '\ allll' ()r !Ill' I rL~fcrl~n C ,har,
i = LI1e ~ iclJ l<l 111·1t 1rit) tlf the 1)1clt ll nee "-ha1 . .
111 = the Jlllflll1cr llf lllllC'i lli, i<l~n<i rt1yEllClll\ ~Ir' 111a(ll' l'acli)
11 = the 1lt1111l1cr (lf ) ' L'~ll~ Ill 111aluril)'
ar
Ft1r prt: rcrcn ·c ,l1art'\ \\ ith ~c111ia11ntm~d (!ividL'll I 11t1yn1cnt"-, ,,, ~4uals 2.
Con,idcr an c~a111J1l~ ()r h,o,v tl1i~ c<.Jt1~1tic n is u ed. Su11pl>~c that ,rin encrg)' on1pan) ~ preference ~hare\
11 ..1, c ~111 .1n11ual cti,·iLle11u 11a) 111 nt ur . O(}Jaid sc 11iannuaJly). a ~lated (par) \alue >f SlOO anc.l an effe ·ti e
111~1turit) <)f 2l) )car" ,,,ing to a ,i11J...i110 [ur1J rcl1uire1ncnt. lf sin1ilar prefer n c "-har t'-i'-.UC" ha,e n1ar~et
) ielJ, ()r ~ 11er cc11t. ,, hat i~ 1l1c, ,1lt1 =- c>f tl1 preference l1arL:,?
Fir,t. \\t 1..:011,ert tl1c LlatL t s 111i;.i1111ual co.n1pouncJing a~ fo]lc)\v~: (I) th 1arket yielcl i~ 4 per cent
~~11,ia· 11t1all~ (\ per ~11tperyear/2).(2)tfr1·di, ide11dpayn1en.t i~55serniannuall)' (SJOp ryear/2 and(3 )
l1c tot~tl nu 11ber · f di, id nd pay111 nt.: i 40 (2 p r .ear x 20 year ,). Plt1g2in° the <lata intc> ec1uation 6 3.
\\ 1..: fi11d that tl1c, :llu
o·f the pref~rc11ce , h'arc~ i~:
1
1
PSn ==
,5
0.04
l _
1
( J .04 ).JO
+
SI 00
40
( 1.04 )
= (125 X 0. 791 7) + S l OO
== 9 ,.96 + 2(). 3
--l.80 1
=$119.79
\Ve ca11. of ·uur"-c, al"o ')(ll L: thi. JJf{)l)l • 111 n a ftn£111c1··tl c·:, 1I ·u l('tl f ~l {'O ll
;\'S.
ion
Enter cash flow data
4 [1/Y]
4 => 1/Y
4 00
40 [N]
40 => N
0.00
100 [FV]
100 - > FV
5 [PMT]
100.00
5 => PMT
5 00
Calculate PV
[COMP] [PV]
PV =
-119. 79
are
r
AGL Energy has a preference share issue outstand
h
by the company in 15 years and which pays a $ ,ndg ~ at has a st ated va. ILJe of $100 which will be retire
4 · , vIdend each 6
. .
,
currently selling for $95, what 1s the share,'s yield t
.
months. If the preference shares e
o n1atur1ty?
290
'A
-·~~ - -
2 Valuation of future cash flows and risk~ - - - - - - - - - - - - - - - - - - -- - -
share ,n actfy th sam way w c /cul te th y,eld
, maturity on a bond. W air ady know tl1a t l1e
to iannual divid nd rate is $4 but we must consem
.
d
1
·
1
"
.
f
ve the number of p r,o s o · ow ,o _. . m,annu
compounding. The total numl er of compoun Ing
,,ods is 30 (2 per year 1 y ar ). Us,n qu t10
:~ we can enter the dat , nd find i th I I r
eld to maturity ti rough rial and r,or. It rnai:ely, we can solve th pro I m t1a~11y on finan il I
ca culator.
Sol tion
; n 9. 7:
I
l /111
I
1
I/Ill
_ __I__
/
l~l/1/
+---} + /Ill/
)II/II
1/111 Ill/I
l
=J---•
I
( 1 +i lO
, 100
+--( I + I) v
, anciar catcula or steps are as follows.
En er cash flow da a
[+/-] 95 {P\/j
(-95) => PV
-9500
30 [NJ
30-> N
3000
100 [FVJ
100 => FV
100.00
4 [PMT]
4-> PMT
4.00
Ca culate J/Y
[COMP] [1/Y}
IIY=
4.30
r ference share's yield is 4.30 per cent per half-year and the annual yield is 8.60 per cent
4.30 er c n / 2J.
The
Perpetuity preference shares
, omc pr lcrcr1 ~ hare j sues ha~'e n > 111'1lL1rity. TJ1c. ,e ·uritic. /1:l\ ' df,,f<.J. nd th;.1t ar 011 tunt o, r
tin1c ( r: = 0) and tl1 fi d divide1ld payn er?l o ,111 ~ ri \' r. hu,. tl1 ·~ pr1.:li r ·n :J1ar c~1n b ,,·1Jued
a, p rp luiti . ing cquution .2:
I
r,, = R
\\iJ1 re D i
c n tant ca h di idcncJ tincl R i t/1 • inter ,t r,tt . r rt.: Juir ,<.J rat f 1· ci1m .
L l u,r,rk an ampl ... uppo~e Iha 0 'anta\ 11 va : Li111i[ d }Ja
p rp lll,ll pr [t;ren . ~ h, r; i, u
that pay a di i,d nd of 5 p r ear. [11v ror. r quir ,ln 1 p r 111 retu111 n ·ii h an ill\ 1111 nt. ~Vhat
houJd be tl1 alu o th pr ere11ce hart;? pp/ ing cqu,ltion 9...... \\ find tl1at th \',i lt1 i :
p = Q = 5. 00 = 2 7. 7
o R
0. 18
l !EFORE YOU GO ON
I
I
1• Why can skipping payment of a preference share dividend be a bad signal?
/ 2· How is a preference share with a fixed maturity valued?
9 Share valuation 29 t
UMMARY
. 1 Describ
,
~1
I 4
four types of secondary markets.
·
.. , . ,. ·h (2) l)f()"cr. (3) Llc;tlcr ttnc ( J <llllltc>11. In uire(.t
l hL' t (1 LI r l ) 11 l' " ( ) r "l' (.' ( ) 11 ( Ia r)' 11 l ~
.11 " Cl ~ ~ II L' : ( 1) I II L l l s I l .
h k
I
t '11 ~ ' r I .
h
.
I
I
t clirccll\1 In f() rcr rn;1rl\L "· l ()
1r1ng ll)'t:r\
,c~11l·h 111arkct,. l)U\L'r~ ~111(1 ,l'ller, :-ice" cac 1 <ll 1cr <lll
·
. , •.. ,
.
~ ,
.
• •
•
..,.
, .
,, .I
O 1 tl 1(()llllh (I ~~tier,.\\ h(> f1t1y SCClll lllC"i d( <)nc r111c,
an(l ~l'llct~ t<llll'thcr l<>r ~, fee. 1r~H.Jc, 111 llcah.:r llltllr--Cl~ cc
b
•
. ,._
c
~
.
• ,
l 11.· c , ~ c (>lt Ill ll c c I 111 • \ 111 1e l 11c y o \ n I 11c cc u r It 1~
1
<lllll ,ell lit l1 ht1!hcr 1111cc. The clc~dcr~ ra :c lhc 11," t 1t1 P c.
.
•
~
. I ·11 ·r~ C(>nfr<)llt each <>tl1c1 dtrcctl) ,111d harcr·,,n
1
Au ·tt<lll 111~1r"ct, ha\c t1 f1,cLI l<)l'i.llHlll \vhctc 1uycr~ ,till ~ ~
(
C"
n
<..1\Cr the tr ..u1,actic n 1111cc.
9.2 Explain why many financial a1,alysts treat preference shares as a special type of bo nd rather
tt,an n equity security.
.
.
~
.
.
. I , 1,t itl • Lhc O\Vll r"' l<l cl1v1c.lcnd"'. \ l11ch Inu,t
Prctcrc11cc ,h~11c, IL'J1re,L'llt c1\\'11crshq) 111 ii L'<lll J1dll)' .inc LI
l
.
· -1 I1c-lllfC ( 1·1, ·1<. IL'll( I~ 1.lll' 11~11l
· I I<) <lr< I111:1ry "ldlC
I • ·ll<ll<l'••r'"
Si111ib11 · <J l1,H1tl,. I rclcrc11cc ".iharc '" LH?\
v
l1c J 1.lll1
· lltttng~.
·
·
11
• 1· • · 11·11· ,, ·111(1 :·ire <Jlll'l1 caJlat
le.. Unlike <1\\ner'",
all' \(lllll'lll11 '~ (()ll\l'l'll 1 l' I<) lll( lllcll)' ~ ' c '
.
Ild\ 'L'll'lllt
<...1f ortli11~11\ ,harL·~. ()\\ llL'r:--. <lf nt1n-c<...111,·crtil1lc 111\~lcren c ,hate" cl<) ll(lt h~i\c vr)lJng right, and de) not
11~ntici11l tc- in the L'lllllfJany·~ p,tllfit~ l1c)t1n<...l the rxcll tlividcnfJ, they tcccivc. Becau~c ,~r. their \trong
,i111il.1rit, t 1 l1<1nll~. 111an Jinancial anal\~t"' trc~1( 11rcfcr nee ~h~1r "that t.1rL' O(>I tru · J1 crpctuttie~ a~ a~ >rn1
.
"l,
()I
,
u~l-.t rather tha11 etJUit~.
9.3 Describe how tt1e general dividend valuation model values a share.
Tl1' ~en 1<11 Ji, illenll \:Lluati >n n1 dc l value. a ~hare a" th· present alu <)fall future ca~h di idLnd
-pa~ 111cnt,., here the di, id nd JJa) 111ents ar di L·ounlc l u ing th rat of rettll n rcc1,uircd h) 1n '-lOr~ lor a
r• r icular ri," cla,"'.
9.4 Discuss the assumptions that are necessary to make the general dividend valuation model easier
to use and be able to, use the model to calculate the value of a company's ordinary shares.
The r rl1hlen1, \\ ith the general dividend \ aluJtion 111 ciel r that the a t di,count rate that houlu he
,e J j"' un"Jl(.)\\ n. Ji\ iclend"' ar Clft 11 uncertain ancJ ~on1 . n1pani ~ <l n t JJay di\ icle11d, at all. Tl) n1ak..e
the 11, de! ca,ier to~ ppI~,. \\C n.1ake <L~ .. ump,t ion, ahoul tl1c tli, icl ·nd p<1)'Ill nt pattern~ of bu,ine,,c"' Thi:...,e
, i111 pJ f ~ i ng a "',u n1ptiu11, al lo\, th de\ cl<)pn1cnr of 111 r 1nanagcablc n1oclc I" and the) a I o c<1n forn1 \\ ith
t 1-? Jt.:lu 11 Ji\ i<lcnd polici~~ <)f, 1c1ny con1panie\. Dividcncl patt rn in ltt le th follC)\Vin.:-: (I) di\ iJenJ"
arc C()fl'-lt,1nt <zcrc, gro\\ll1). a cal ulated in clcrr1on,trati n JJrol1lc111 9.1: (2) cli,illend~ ha\l' a (()Tl,tJnt
~r(>\ th JJatter11 (the) gro\\ furcvL'r at a · n tant rate~). a calculated in lcnl()ll~trati 11 prob] 111 9 ...,: and (3
1\ jdcn J, gr<..J\\ fir"'t at an n-t.:()11 t<1nt rate th n al a c .n stant fdle, a calculat d ir1 the Att"' iotc ·h e,an1plc
at thL' end )t ,e(ti . n CJ.4.
1
9.5 Explain how valuing preference shares with a stated maturity differs fro,m valuing preference
shares, with no maturity date and be able to calcu late the price of a prefere,n ce share u.nder both
conditions.
\\ hen J prcfl'rLn c ,hare lir1"' a 111'lturi1y dat . financial a, :1ly~,~ ,~dttL' il a" the) ,aluc ~t 11 , ()lhcr li,tJ
c>hli 'ati,, - that i~. like a t1<)ntl. ']<> vn lu' '-llll'h ;1 f)t\:fLr ·nc • ,harl'. \VL' can ll~L' tllL' })(Jllll \'al~J~tti( 111 nl<)J~l
Jrc)n the cli<.1ptcr <H1 h<Hl(I \aluati<111 and th' st,u tur-> l)r i11lcr ·~1 rl tc,. l t:fl1t\~ u~i 11 ~ the t1l()del. ,,c lltCd to
rcc<)gni,e that\ c \-\ ill h~ u,i~1g JiviJend, in the pla · C)I cc up(Hl pa_ r111..·nt~ an.ti tliat tltL par, aluL ()f th .. hare
\\:ill rl'1JlaLc the ~ar al~1 · <>f th h<111d. tlditic~, al ly, in ustralia l1t1itlt t1()lltf t:ou .,()l1"i an.ll r.,rcfercn c "hare
1
di_ 1denll"' ~•r~ pa1J \~n11a1!1111ally. When a prl'fe1cncl' ,ha e ha~ nc) ~1tall'll 111 atut ,it)· ill CCC)llll'~ a pcrpetuit~.
\\ 1th the (Ii\ J(lenu hec<Hn1ng. the · Hl~t~I11t
tJa nh.:nt that el'( c" 011 t <)r ., er·.
ti
·t
I ritt.()n
.
L u"'e 1 pcr11---tt11, v va u,,
111c)dcl rcpre'-i~llted h) cc1uat1<.)0 Y.2 t<, f)rtcc ,tH.:h "'h~11~~ ThL~ c·tlcul·itioi,"' 'lJ)
.
·ll)ll
- pro bl 111
(1 ar ·111 d eI11111~trat
9.5 ancl the Qanta"' e,~.u nplc at thl' encl c)f "L' ·t1<.lll <J.5.
'
•
•
l
4
,
KEY TERMS
flid price 111e priced rcurities cleat 'r will JJa)' f()f a gi,,cn hare.
di~idend )'iel~ A sh,1re·~ <lividcn~ payout di, ided by it~ current pric .
ofter (a k) pr1c fhe J)rt cat ,,h1ch a "ccuriti ~ de, lcr ~c~k t· .11 ,
.
.
.
· t · o "c d 1 c n ~ 11 a re
ordanar~ ~J1ares A typ · (Jf e(1u1ty ,hare th~ tr 1-,r ~ent" th. b· ,.·.
~ .
. ·.
,
·
""'c c1-,vn 1,1111) cl·1111 tn ·1 c· l1111)·1n\ · thl'
111( ,t (H·dinary tyJ)e t)1 c 1uity \Cl'ttrity.
I.
A '-tpccific j()Cati<)Jl Oil the
,a~r plac ·.
f)()St
'
'-
I.
-
•
no I (>Id \CClltiliL·~' ., ch·1r
I
.
.
' lgc \\' l IC aUL'llt)l1'-1 t()f a 11arti ·ttl . 11 :--il'L'lll ll)
----292 P
'
V luatron of future casl1 flows and nsk
1
..._
9.1
The general
dividend
valuation model
11 1
I)
J)~
I
I R + --=--+
+
"'+
( I + R) -(l_R_)_1 (- 1-+ I
I)o-
o,
-
92
9.3
D
o=
Value of a
d idend at time
t 1n a constant
gro\vth scenario
9
Cons
gro
, ide
oder
rr
Value of a sha re
me
en
d1 dends gro ~, a
9. 5
-·
P, -
o,
R-g
D,+1
'
-
.~
a co stant ra te
9.6
o
h
val a ion
al
gro
97
D
1+R
D,
P,
+···+---+--1
( I + . J2
( 1 + R)
(I + R)'
o e
Value of a
preference share
,ith fixed
maturJ y
l)/111
PS, 1 = -
1/111
I
1 - - --- - 1111
( I + i/111 )'
+
P,,,n
( I + i/111) 1""
SELF-STUDY PROBLEMS
Ry1.1n
cVic,1r h:..t\ j,1,r b(>Ught ()rtli11ary ~hare\ in a '(fllitric Mccfi. Ltcl. Tf1e ~on1pany c pect~ to
gro\ at tl1 fo]Jo in 6 r,tf ~ cJr tl1c ne I 3 year\: 2." JJCr c nl. ~() JJer c ~nt ~111d IO J)~r c~nt. La t )'e,tr
tl1c co111ran)' JJaid r1 divicJend o 'r,2.2(). A~\u111e d rcc1uirccJ r~lc of return of pe·r ·e11.l. Cal u1,tte rhc
expected cli icJ ncl~ or tJ1c Ill: I .1 year~ and al~<) th· prc~c11r \ alue of the. c li\ icler1cf .
9.2 Ccntrogcn ~ 11uf:1c1uring Ply Lld l1a~ hccn gro\vi11g at a rate of 6 fJ ·r ·ent tor tl1e pa,t ~ )'e,tr~ and rl1
CEO e fJects Lh cc,mpany t conti11u · g,owing al thi~ raft• f r the nc ·t · \'CJ\ 1 )'C,trs. Th con1pan~
paid a di,,jd 11 I of 51.20 last )'ear. lf yotrr r qtiirccf rale tlfr turn ,,vas l-l 1 ~rce11t. \\ h,tl i, tl1" n1a\i111l1r11
price Lf1at y u woL1ld be willing to pay for this compan)1 ·~ .~l1arcs?
9.3 [deal leclric,1I f'lly Ltd l1a~ b n s 11 ing electrical sup11lic" f )I' tl1 pa . l ..,() ~'e,1r . 1.,hc con1pan) ·
fJrod ct line r,a. ~ er1 \' Cty little cl1c1nge in tl1e fJa r 6 year~ ar1 l j1 dc)CS n )l t'XfJ~ct co ,t(fcl :U1)' JJe,,, itcn1,
in tl1e forc~c alJlc futur . L(t~l ye,tr 111 • CfJrTIJJHll)' pni I a <.li\'i<.f ncJ <>I 2.25 LC) its orcfi11:1r) ,harchoJJe ·,.
ll is not cxpt=ClLd tc, err , it~ It.: enu ~forth JlCXt ~l:Vcral yc~tr~. If )'our reqt1irecl ratl: (> r c ,l ur 1 · r
,uth c.:<ln1panie~ j 9 per ccnl, \ hat i~ tl1e curr nt \alu · elf thi~ c<H1111a11)' , ,l1 ~1rl',?
9.4 c~oopcr <Jriiniunication"i Pty L. 1 Ji~ a J;i~l-i!fO\.\ in2 co111n1u11ic'tticJ11, C(1n1pan). Ir Lli I rt<.)l f)'" ~ a <.f l \ iLll· r LI
la,t year and;~ 11 L c JJCclcd to lo ~o fcH· the ne\t 2 year\ f~a,l )t'ar chc.: C<1lllJ).lll) ·, gro\ lf1 ( L-L·clt·r IL·J
Jr1u it exr ecl" lo gr \.Val a I at t>I 35 per cent for th , ext) )•ea,, l1~f l)l'L' ~I,>\\ ing tl()\\' l1 ll> 111()fL' , tab f
1
9.1
Sh e v Ju tron