Lamb ech s, I. J.; Doppegie e , J. J.
A icle
A capi al in es men app oach o p ice o mulae/
de e mina ion
Sou h A ican Jou nal o Business Managemen
P o ided in Coope a ion wi h:
Uni e si y o S ellenbosch Business School (USB), Bell ille, Sou h A ica
Sugges ed Ci a ion: Lamb ech s, I. J.; Doppegie e , J. J. (1985) : A capi al in es men app oach o p ice
o mulae/de e mina ion, Sou h A ican Jou nal o Business Managemen , ISSN 2078-5976, A ican
Online Scien i ic In o ma ion Sys ems (AOSIS), Cape Town, Vol. 16, Iss. 1, pp. 35-39,
h ps://doi.o g/10.4102/sajbm. 16i1.1070
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/217885
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A capi al in es men app oach o p ice o mulae/
de e mina ion
I.J.
Lamb ech s and
J.J.
Doppegie e
Depa men
o
Business Economics, Uni e si y o S ellenbosch
In
an
analysis
o
en widely used p ice-con ol o mulae i
was shown ha he o mulae ook in o conside a ion a
a ie y
o
di e en s ipula ions such
as
he calcula ion
o
unds employed, he de ini ion
o
p o i
and
he p o i abili y
a e allowed. Fu he mo e i is main ained ha he
commonly used in ui i e and/o con en ional me hods o
e alua ion
a e
subjec o a ious sho comings. The e o e, i
can
be
in e ed ha i is i ually impossible o compa e
di e en p ice o mulae
in
isola ion.
To
o e come his
p oblem a simula ion model, based on ce ain assump ions,
has been de eloped. The model compa es
and
e alua es
he adequacy
o
a ious p ice o mulae o e ime
(dynamically) in di e en ways, i.e. se e al a ios
and
c i e ia
a e
calcula ed wi h he in e nal a e
o
e u n being he
p ima y one.
In
he emaining h ee a icles, he simula ion
model will
be
applied o he wo o mulae p esen ed
in
his
a icle.
S.
A .
J.
Bus. Mgm .
1985,
16:
35
-
39
Deu die ien mees algemene o mules i p ysbehee e
analisee , oon die sk ywe s da die o mules 'n
e skeidenheid
an
e skillende bepalings
in
aanme king
neem soos die be ekening
an
o ale ondse, die de inie ing
an
wins en die g aad
an
winsgewendheid oegelaa .
Ve de wo d
di
ges el da die algemene geb uik
an
in ui iewe en/o kon ensionele me odes
an
e aluasie
aan
e skeie eko kominge bloo ges el is. Daa om wo d aan aa
da di bykans onmoon lik is om e skillende p ys o mules
in isolasie e e gelyk. Om hie die p obleem e oo kom, is
'n simulasiemodel, gebasee op e skeie aannames,
on wikkel. Die model e gelyk
en
e aluee die aan aa baa -
heid
an
e skeie p ys o mules oo yd (dinamies) op
e skillende manie e, e we e e skeie e houdings
en
k i e ia wo d be eken -me die klem op die in e ne
endabili ei .
In
d ie a ikels (in op olgende ui gawes)
sal
die
simulasiemodel oegepas wo d op wee
an
die o mules
wa in hie die a ikel besp eek wo d.
S.-A .
Tydsk . Bed y sl.
1985,
16:
35-
39
I.J. Lamb eeh s* and J.J. Doppegie e
Depa men
o
Business Economics, Uni e si y
o
S ellenbosch,
S ellenbosch, 7600 Republic
o
Sou h A ica
*To whom co espondence should
be
add essed
Accep ed Augus
1984
In oduc ion
A p ice o mula/policy can be desc ibed
in
di e en ways.
Some o mulae a e desc ibed
in
simple e ms, e.g. 15% be o e
in e es and ax on capi al employed, while o he o mulae
a e desc ibed
in
a mo e sophis ica ed way
by
speci ic de ini ion
o
he p o i elemen wi h mo e explici de ail
on
capi al
de e mina ion. P ice o mulae a e common
in
p ice-con olled
and non-p ice-con olled indus ies/unde akings. In he la e
case he objec i e
o
a p ice o mula could be ei he o es
he adequacy
o
a p ice
o
o de e mine he selling p ice.
P ice con ol was i s in oduced
in
Sou h A ica du ing
he Second Wo ld Wa when ci cums ances we e a ou able
o indus y and comme ce o cha ge unjus i iably high p ices
o a ailable goods. A e he wa , p ice con ol was e ained
o ce ain commodi ies. In
1963
he p ices
o
only abou
18
commodi ies we e s ill subjec o p ice con ol bu since
1964
p ice con ol has been ex ended o a ious o he commodi ies.
In
1964
The P ice Con ol Ac , No.
25
o
1964
was passed
by Pa liamen . This Ac was amended
in
1967.
The Ac
p o ides in e
alia
o he appoin men
o
a P ice Con olle
who
is
empowe ed o
ix
maximum p ices
o
cha ges.
P esc ibed p ices a e no only de e mined in e ms
o
he
P ice Con ol Ac . Examples
o
p esc ibed p ices
in
e ms
o
o he Ac s a e elec ici y a i s (The Elec ici y Ac
o
1958),
ailway a i s (The Republic
o
Sou h A ica Cons i u ion
Ac , No.
32
o
1961)
and ce ain ag icul u al p oduc s (in
e ms
o
di e en Ac s) ma ke ed h ough Con ol Boa ds.
In analysing he me hods
o
p ice calcula ions applied in
e ms
o
he di e en Ac s e e ed o abo e,
i
is
e iden ha
he applied o mulae di e o i ually
e e y
p oduc /se ice.
E en he o mulae applied
in
e ms
o
he P ice Con ol Ac
di e subs an ially om one ano he .
I
appea s as i he o iginal o mula could ha e been he
same bu ha concessions/changes we e implemen ed o e
ime o accommoda e eques s subsequen ly made by di e en
indus ies and companies.
The objec i e
o
his a icle
is
i s { o compa e ce ain
p icing o mulae. Secondly, a e he di e ences be ween he
o mulae ha e been poin ed ou , an a emp
will
be made o
de elop an app oach o quan i y he di e ences
in
e ms
o
a single denomina o . I should be s essed ha he unde lying
sen imen
o
his a icle
is
no he con inua ion
o
p ice
con ol. The au ho s a e ully awa e
o
he unde aking
o
he P ime Minis e a he Ca l on and he Good Hope
Con e ences ha ma ke o ces
will
be allowed o ac as a
g ea e egula o
o
economic ac i i ies han in he pas . In
ac , qui e a numbe
o
p oduc s/indus ies ha e been
exemp ed om p ice con ol since hese con e ences. The
36
app oach de eloped in his a icle is, howe e , applicable o
all p icing o mulae/policies.
I
could
be
applied o example
in espec
o
he pa as a als, e.g. Escom, Sou h A ican
T anspo Se ices, he Pos O ice,
and
he Ag icul u al
Con ol Boa ds whe e p ice con ol
is
s ill applicable, as
well
as in he case
o
p i a e companies whe e de ini e p icing
o mulae/policies a e spelled ou .
The capi al in es men app oach o p ice o mulae/de e mi-
na ion will
be
discussed in a se ies
o
ou a icles. In his
i s a icle
an
ou line
is
gi en
o
di e en o mulae, he
gene al app oach
is
analysed and he o mulae o be used as
illus a ion a e desc ibed. In he
second
a icle h ee inancial
aspec s
o
indus ies/companies whe e p ice con ol applies
o
whe e p ice o mulae a e applicable
will
be e alua ed, i.e.
p o i abili y, p o ision o in la ion, and inancial s uc u e.
The hi d a icle deals wi h a quan i ica ion
o
he speci ic
di e ences be ween p icing o mulae in e ms
o
he in e nal
a e
o
e u n. In he ou h a icle he sensi i i y
o
appa en ly
impo an ex e nal pa ame e s (inpu s)
is
es ed.
In p esen ing his se ies
on
p ice de e mina ion he au ho s
end o sol e he p oblems in e alua ing p ice o mulae. These
sho comings ollow mainly om he di icul y in compa ing
di e en o mulae, di e ences in applying he accoun ing a e
o
e u n, he a bi a y de ini ion
o
p o i
and
capi al
employed and he absence
o
a meaning ul app oach
o
e alua e echniques (based
on
cash low) combined wi h a
compu e simula ion model. The adequacy
o
o mulae could
he e o e be e alua ed in e ms
o
cash low, business
and
inancial isk, in la iona y e ec s, g ow h equi emen s,
and
inancial s a egies
and
policies.
Compa ison
o
p ice
con ol
onnulae
P ice con ol
in
e ms
o
he P ice Con ol Ac was mainly
exe cised by con olling he p o i abili y
o
an indus y
o
company. The c ucial componen s in de e mining p o i abili y
a e he calcula ion
o
unds
employed, he de ini ion
o
p o i ,
he
p o i abili y a e allowed,
he
accoun ing
pe iod
used o
p ice de e mina ion and he di iso o de e mine he p ice
adjus men pe uni
o
p oduc . The main p oblem unde lying
a compa ison
o
he o mulae
is
he combina ion
o
di e en
p ac ices/app oaches in espec
o
each
o
hese c ucial
componen s. These di e ences
will
now be discussed b ie ly.
In o al en di e en p icing o mulae ha e been analysed.
The di e ences in he o mulae a e clea om he ollowing
summa y which shows he di e en p ac ices unde each
a iable:
Funds employed
(i) A e age unds employed
and
yea -end balances.
(ii) Dep ecia ed ixed asse s a book alue, conse a i e
ma ke alue
and
dep ecia ed ixed asse s a eplacemen
alue.
(iii) Wo k unde cons uc ion included and wo k unde con-
s uc ion excluded.
(i ) Cash balances allowed
and
disallowed.
( ) T ade c edi o s no deduc ed om unds employed and
ade c edi o s
and
o he in e es - ee loans deduc ed.
( i) Ac ual cu en asse s employed allowed and no mal
(acco ding
o
o mulae) cu en asse s allowed.
De ini ion o p o i
(i) P o i be o e deduc ing in e es
and
ax bu excluding
in es men income
and
non- ecu ing income and expen-
di u e;
and
p o i be o e in e es bu a e ax excluding
in es men income
and
non- ecu ing income
and
S.-A . Tydsk . Bed y sl.
198S,
16(1)
expendi u e.
(ii) Addi ional dep ecia ion allowed ully and addi ional
dep ecia ion only allowed pa ially.
(iii) Addi ional dep ecia ion calcula ed
on
di e en
alues,
i.e.
-Ac ual eplacemen alues.
-Re alua ions, adjus ed wi h he p oduc ion
p ice
index.
-Insu ance alua ions.
-Subjec i e alua ions.
(i ) In some cases he ac
ha
addi ional dep ecia ion
is
no
deduc ible o ax pu poses
is
aken in o accoun and
he
amoun
allowed
is
inc eased
o
p o ide o his.
( ) S ock p o i s deduc ed
and
s ock p o i s included.
P o i abili y allowed
The p o i abili y allowed luc ua es widely, mos ly be ween
8,5 and
170/o.
The magni ude
o
hese pe cen ages
is,
howe e ,
i ele an because
o
he di e ences ega ding unds employed
and
p o i le els. In ce ain cases a highe p o i abili y
le el
is
allowed p o ided he inc eases a e he esul
o
p oduc i i y
imp o emen s. In o he cases p oduc i i y
is
no aken in o
accoun explici ly. Some imes he allowed p o i abili y
is
exp essed
on
a be o e- ax basis
and
in o he cases
on
an a e -
ax basis.
Accoun ing pe iod
His o ical igu es a e used as a basis o p ice con ol as
well
as es ima ed igu es. Combina ions a e also used, e.g. nine
mon hs ac ual plus h ee mon hs budge ed igu es. Audi ed
s a emen s a e equi ed in ce ain ins ances.
Di iso o de e mine he p ice adjus men pe uni
Sales olume
o
p e ious yea s
o
he highe
o
he p e ious
yea 's sales
and
expec ed sales subjec
o
a no mal capaci y,
minimum ac ual p oduc ion igu e
o
p e ious yea and he
a e age
o
he p oduc ion igu e o he p e ious yea and
o he ollowing yea .
F om
he abo e summa y
i
is
clea ha a e y la ge
numbe
o
p ice o mulae a e possible, consis ing
o
an
i em
unde each
o
he abo e i e headings.
The
ollowing
is
an
example
o
such a o mula (combina ion):
150/o
o
unds
employed (a e age
o
o al unds including cu en liabili ies
and
wo k unde cons uc ion based
on
dep ecia ed book
alues).
The
p o i
is
be o e in e es
and
ax, a e addi ional
dep ecia ion
and
excluding s ock adjus men s. The o ecas
pe iod
is
used as a basis as well as he es ima ed sales olume.
I
is
clea ha he wide a ia ion in p ice o mulae makes
i
i ually impossible o compa e he inal esul
o
each. Such
a compa ison
is
essen ial
o
judge he adequacy
o
he o mula
applicable o each indus y/unde aking in he ligh
o
i s
inhe en business
and
inancial isk.
An
app oach o judge
speci ic o mulae will be discussed
and
illus a ed in he nex
sec ion by using he o mulae as discussed in he nex sec ion
( o mulae A
and
8).
Fo mula A will be discussed in de ail
and
o mula B b ie ly by poin ing
ou
he di e ences be ween
o mulae A
and
B.
App oach
o
e alua e
a
p ice
onnula
P ice o mula A
Funds
employed
The amoun
o
unds employed
is
equal
o
a e age unds,
wi h ixed asse s
a
dep ecia ed
book
alue including wo k
unde cons uc ion, plus addi ional cash
and
including ac ual
cu en asse s ( he s ock e alua ion me hod applied by he
s.
A .
J.
Bus. Mgm . 1985,
16(1)
indus y
is
he e o e accep ed). T ade in es men s and good-
will
a e excluded. The amoun
o
ade c edi o s
is
no
deduc ed om unds employed.
P o i
le els
The p o i igu es used o de e mine p ices consis
o
p o i
be o e in e es and ax bu excluding in es men income and
non- ecu ing income
and
expendi u e. Addi ional dep ecia-
ion based on e alued asse s
is
allowed ully and no p o ision
is
made o compensa e o he non-deduc ibili y
o
addi ional
dep ecia ion o ax pu poses.
P o i abili y
A pe cen age (be o e in e es and ax)
is
based on unds
employed wi h p oduc i i y no aken in o accoun explici ly.
Accoun ing pe iod
The p esen yea 's igu es a e used; in he case
o
unds
employed he a e age igu e
o
he p esen and pas yea
is
used.
Di iso
No di iso
is
used in he capi al in es men app oach because
o
he assump ion ha no ime lag exis s and ha he allowed
p o i abili y
is
ully a ained. In he ac ual si ua ion di e en
di iso s a e used depending on u iliza ion/sales olume and
he allowed p o i abili y
is
usually no a ained.
P ice o mula B
The mos impo an di e ences be ween p ice o mula A and
p ice o mula B a e he ollowing:
(i)
Fixed asse s a e alued a dep ecia ed eplacemen cos
and wo k unde cons uc ion
is
excluded.
(ii)
No p o i om addi ional cash
is
included in he p o i
de ini ion.
(iii)
P o ision
is
made o compensa e o he non-deduc -
abili y
o
addi ional dep ecia ion o ax pu poses.
(i )
A p o i abili y a e be o e in e es bu a e ax
is
used
o
calcula e he allowed p o i le els.
Gene al assump ions
Se e al assump ions a e made, he mos impo an being:
(i)
The amoun
o
o iginal
ixed
asse s
is
equal o he o iginal
cos p ice he eo .
(ii)
Replacemen
o
ixed asse s
is
on a con inuous basis.
(iii) Full capaci y u iliza ion exis s a he beginning. Expansion
occu s con inuously wi h inc easing olumes.
(i )
The maximum pe iod
o
e alua ing he o mula
is
equal
o he a e age li e ime
o
ixed asse s.
( )
No ime lag exis s wi h he esul ha a sho all
o
he
allowed p o i abili y
is
ully eco e ed he nex yea .
Desc ip ion
o
model
In oduc ion
Ou app oach
is
based
on
he de elopmen
o
a compu e
model, which simula es he balance shee (asse s and
liabili ies)
and he ele an i ems
o
he income s a emen . On he basis
o
easonable assump ions, basic ela ionships be ween he
inancial a iables a e exp essed algeb aically. The assump-
ions a e based pa ly on he abo e-men ioned gene al assump-
ions and pa ly on p edic ions
o
ce ain ex e nal ac o s. The
algeb aic ela ionships a e cons uc ed in such a
way
ha la e
expe imen a ion will be possible. In his way e iciency and
lexibili y
is
p ese ed
and
he model he eby enables he
analys in e
alia
o
es he sensi i i y
o
each speci ic
37
pa ame e .
The main classi ica ion
o
i ems included in he model
is
as
ollows:
• Asse i ems
• P o i i ems
• Capi al i ems
• Analysis sec ion.
The e
is
an in e ela ionship be ween he abo e-men ioned
i ems, e.g. he o al asse s o m he basis o he p o i i ems
which subsequen ly in luence he capi al i ems ( ia undis i-
bu ed p o i s). All hese i ems ha e an e ec on he analysis
sec ion.
A& e
i ems
FIXed
asse s.
Fixed asse s o m an ideal complex
wi h
he esul
ha con inuous eplacemen akes place and no p o ision o
unde - eco e y
o
dep ecia ion
is
necessa y. The ideal complex
is
no dis o ed
as
a esul
o
echnological imp o emen s and,
because expansion
o
ixed asse s akes place con inuously,
he e
is
a
ai ly
cons an u iliza ion
o
capaci y.
All
ixed
asse s
a e dep ecia ed on a s aigh -line basis. The a io
o
ixed
asse s o o al asse s
is
supplied
as
an ex e nal inpu which
o ms he basis o he calcula ion
o
he ini ial alues
o
ixed
and cu en asse s. The amoun o ixed asse s o he sub-
sequen yea s
is
calcula ed
as
ollows:
Fixed asse s
o
p e ious yea + expansion in es men +
eplacemen in es men -dep ecia ion.
Expansion
in es men
is
ela ed o he g ow h in sales and
speci ic inc eases
o
capi al expendi u e. Replacemen
in es men
is
also in luenced by nominal g ow h (p ice
inc eases)
as
well
as
he a e age li e ime
o
ixed asse s, which
is
an ex e nal inpu .
The ixed asse s a e dep ecia ed on a s aigh -line basis,
based on he ixed asse s
o
he p e ious yea plus
500Jo
o
he expansion and eplacemen in es men
o
he speci ic yea .
Cu"en
asse s.
The ini ial alue
o
cu en asse s
is
an ex e nal
inpu . The alues o he subsequen yea s a e a unc ion
o
eal and nominal g ow h (speci ic p ice inc eases).
P o i
i ems
The p o i i ems a e calcula ed p io o he capi al i ems
because he amoun
o
undis ibu ed p o i s has an in luence
on capi al equi emen s. The i s p o i i em
is
p o i be o e
in e es and ax ( o o mula A and a e ax o o mula B)
which
is
ob ained
by
mul iplying he allowed a es
o
p o i abili y (an ex e nal inpu ) wi h ei he a e age
o
o al
asse s
(an ex e nal inpu
is
equi ed o indica e whe he a e age
o o al asse s should be used).
Addi ional dep ecia ion
is
calcula ed a e e aluing ixed
asse s
by
using speci ic p ice inc ease a es which a e supplied
as
ex e nal inpu s. The addi ional dep ecia ion
is
he di e ence
be ween eplacemen and his o ical cos dep ecia ion. This
addi ional dep ecia ion
is
be o e ax and
as
a esul
is
subjec
o ax.
luc ua ing cash
le els
which di e om yea -end le els),
is
a
e y
di icul i em o de ine, and
is
ela i ely small in
magni ude. I
is
exp essed as a pe cen age ( ixed)
o
p o i
be o e in e es and ax.
The income de i ed om in es men s
is
ele an only i
su plus cash esul s a e
all
inancing equi emen s ha e been
sa is ied ( he in es men a e
o
su plus cash
is
an ex e nal
inpu ).
38
The in e es paid
is
calcula ed by mul iplying he a e age
in e es a e (an ex e nal inpu ) wi h he a e age in e es -
bea ing loan capi al o a speci ic yea . The
le el
o
he in e es
expense has an e ec
on
he amoun
o
a e age in e es -
bea ing loan capi al.
Taxa ion
is
calcula ed a e aking in o accoun in es men
and ini ial allowances (ex e nal inpu s)
on
all ixed asse s in
he i s yea and new in es men s a e wa ds. The e ec
o
ini ial allowances on he dep ecia ion allowed o ax pu poses
is
ully accoun ed o .
I
he e
is
an accumula ed ax loss i
should i s be elimina ed be o e ax
is
payable.
Since he di idend policy
o
a company
o
an indus y
is
de e mined by a ious ac o s, an equa ion
is
cons uc ed
which p ese es lexibili y and can be changed acco ding o
he speci ic si ua ion. The maximum amoun
o
di idends
is
limi ed o he p o i a e ax. P o ision
is
made o di e en
di idend o mulae which can be es ed o sensi i i y
on
he
inal esul s.
Capi al i ems
The ini ial s uc u e
is
supplied as an ex e nal inpu consis ing
o
equi y capi al and loan capi al, whe e a di e en ia ion
is
made be ween long- and sho - e m in e es -bea ing capi al
as
well
as sho - e m non-in e es -bea ing loan capi al. In
subsequen yea s he amoun
o
o al asse s
is
compa ed o
he equi y capi al
o
he p e ious yea plus undis ibu ed p o i
o he speci ic yea wi h long- e m loans
o
he p e ious yea s
being educed o p o ide o edemp ion based
on
an a e age
edemp ion pe iod.
I
he e
is
a sho all in unds
i
is
aised
in he ollowing assumed sequence:
(i)
New
equi y capi al
is
aised equal o a pe cen age (ex e nal
inpu )
o
new expansion in es men s ( ixed asse s plus he
inc ease in cu en asse s).
(ii)
I
he e
is
s ill a sho all in unds, addi ional loan capi al
is
aised. The di e en ypes
o
loan capi al a e in he
same a io as in he ini ial capi al s uc u e.
I
he e
is
a su plus
o
unds
i
esul s
in
su plus cash wi h in es men
income, which also has an e ec
on
in e es payable.
Analysis
o
model
and
desc ip ion o capi al in es -
men s app oach o p ice o mulae
The esul
o
a speci ic p ice o mula on a company/indus y
can
be e alua ed by means
o
(amongs o he s) a p o i abili y
analysis, an e alua ion
o
he su iciency
o
in la ion
allowances g an ed and an analysis
o
he inancial s uc u e.
These aspec s
will
now be discussed in mo e de ail.
P o i abili y
analysis
The p o i abili y a e used in a p ice o mula does no gi e
an indica ion
o
he ac ual (e ec i e) p o i abili y ea ned by
an indus y e en i
i
is
assumed ha no ime-lag exis s.
Di e ences be ween he ac ual (e ec i e) p o i abili y and he
allowed (planned) p o i abili y a e esul because
o
ce ain
'allowances', e.g. addi ional dep ecia ion, p o i om
addi ional cash, and o he di e ences in he o mulae, such
as he de ini ion
o
p o i s (be o e ax
o
a e ax; based on
his o ical
o
eplacemen cos s) and unds employed (c edi o s
deduc ed
o
no , based
on
his o ical
o
eplacemen cos s).
O he ac o s which esul in impo an di e ences a e he
es ing pe iod and whe he
o
no he p ice
is
calcula ed
on
his o ical esul s wi h ce ain adjus men s on p ojec ed igu es.
The di e ences in p ice o mulae c ea e he need o a
uni o m a iable o e alua e he su iciency
o
a speci ic
o mula.
The
con en ional
p o i abili y
(accoun ing
a e
o
e u n)
S.-A . Tydsk . Bed y sl.
1985,
16(1)
based
on
annual inancial s a emen s
is
subjec o ce ain
sho comings
o
which he mos impo an a e:
I
igno es
he
ime alue
o
money and he e o e
i
is
di icul o compa e
di e en al e na i es; as applied in mos
o
he o mulae
i
is
only a one-yea measu e; and i s alue
is
o a la ge ex en
he esul
o
accoun ing igu es which end o a y acco ding
o he assump ions made (Lamb ech s,
1979).
To
o e come hese p oblems a mo e meaning ul c i e ion
has been de eloped, namely he in e nal a e
o
e u n
(dis-
coun ed cash- low a e
o
e u n) which akes in o accoun
he ime alue
o
money; p o ides o he au oma ic
eco e y
o
in es men s made; akes in o accoun he ull pe iod
which
is
analysed; and
is
based
on
cash lows compa ed o p o i s
and asse alues which
do
no a y acco ding o he
assump ions
o
accoun ing me hods applied.
I
enables he
analys o make meaning ul compa isons be ween p ice
o mulae because
i
is
a common denomina o .
The in e nal a e
o
e u n
is,
howe e , also subjec o
ce ain sho comings. Owing o he na u e
o
he simula ion
model some
o
hese sho comings do howe e no apply. The
possibili y
o
no in e nal a e
o
e u n
o
mul iple in e nal
a es
o
e u n does no exis because he simula ion model
desc ibes a con en ional low
o
unds, i.e. an ini ial
in es men ollowed by in lows which exceed subsequen
in es men s. The e o e no p oblem a ises wi h compa isons
be ween di e en p icing o mulae because
o
equal ini ial
in es men s and pe iods o e which he o mulae a e
e alua ed. The implici assump ion ha all cash in lows a e
e-in es ed a a a e which equals he calcula ed in e nal a e
is
howe e s ill applicable. This
is
he only heo e ical sho -
coming he analys should be awa e
o
(Lamb ech s,
1979).
The in e nal a e
o
e u n
is
calcula ed by sol ing o
in he ollowing equa ion:
I:
-1
-'--
I:_£__
, = o
(I
+ )' , = o
(I
+ )'
~=0
(I+
)'
whe e n = li e ime o e which he o mulae
is
e alua ed;
I, = in es men amoun
in
pe iod , which consis s
o
o al
asse s in pe iod nil, expansion in es men s, eplacemen s
in es men s and inc eases in cu en asse s;
C,
= cash in low
in pe iod , which consis s
o
p o i a e ax plus in e es
paid
x
(I
-e ec i e ax a e) plus dep ecia ion; and
Rn
= esidual
alue consis ing
o
o al asse s and su plus cash a he end
o
he e alua ion pe iod.
Please no e ha , in he calcula ion
o
C,.
in e es (on an
a e - ax basis)
is
added o p o i a e ax because he e ec
o
he in e es (also a e ax)
is
included in he cos
o
capi al
wi h which he in e nal a e
o
e u n
is
compa ed.
The in e nal a e
o
e u n can be used in di e en
ways.
Fi s ly, i can be used o e alua e he adequacy
o
a
p ice
o mula. I
i
exceeds he c i ical a e
o
e u n (cos
o
capi al)
o
he speci ic indus y, a sa is ac o y a e
o
e u n
is
ea ned.
I should be emembe ed ha he calcula ed in e nal a e o
e u n
is
a eal e u n because p o ision
is
ully made
o
highe eplacemen cos s, and i should consequen ly
be
compa ed wi h he eal cos
o
capi al. Secondly,
i
can
be
used o compa e di e en p ice o mulae. The in e nal a e
o
e u n
is
he e o e a c i e ion which ends o poin ou
di e ences be ween p ice o mulae.
I
is
a common
denomina o which elimina es all di e ences be ween
p ice
o mulae. I should howe e be aken in o accoun ha
he
magni ude
o
he in e nal a e
o
e u n o di e en
p ice
o mulae only gi es
an
indica ion
o
hei 'a ac i eness',
Thi dly, a sensi i i y analysis
can
be done
on
he a ious
ex e nal a iables (inpu s) o es hei e ec
on
he in e nal

s.
A .
J.
Bus. Mgm . 1985,
16(1)
a e
o
e u n,
and
o
es ablish hei ela i e impo ance.
Toe analysis sec ion also makes p o ision o he calcula ion
o
he accoun ing p o i abili y
a e
ax
(based
on
a e age
capi al). This enables
he
analys
o
compa e
he magni ude
o
he allowed p o i abili y
a e
(which is also
an
accoun ing
p o i abili y) wi h
he
accoun ing
p o i abili y achie ed pe
pe iod,
and
he
end
he eo .
Fu he mo e,
he ela ionship
be ween
he accoun ing p o i abili y, he in e nal a e
o
e u n
and he e ec
o
changes in a iable inpu s
on
his ela ionship
can
also be de e mined.
E alua ion
o
in la ion
allowances
To
analyse he ex en
o
he in la ion compensa ion p o ided
o in a p ice
o mula,
he
a io
o
dep ecia ion allowed
o
eplacemen in es men s is calcula ed.
I
dep ecia ion is based
on
eplacemen alues,
wo
componen s
a e
included, i.e.
no mal dep ecia ion which is ne
a e
ax
and
he
addi ional
dep ecia ion which is
no
ax
deduc able.
The
cash low om
he addi ional dep ecia ion is, he e o e, equal
o
addi ional
dep ecia ion mul iplied by
(1
-e ec i e ax a e).
The
a io
o
dep ecia ion allowed
o
eplacemen in es men s
is
calcula ed
on
an
annual
basis
and
a cumula i e basis.
I
his
a io equals
o
exceeds
one,
adequa e
p o ision is
made
o
eplacemen
o
ixed asse s.
P o ision
should
howe e also
be
made
o
ha
po ion
o
eplacemen in es men s inanced by means
o
loan capi al.
Financial
s uc u e
I
a p ice
o mula
is sa is ac o y
o
an
indus y/company
i
should no esul in a d as ic de e io a ion
o
he equi y capi al
o
loan capi al a io, especially
i
he assump ion
is
made ha
39
no
new sha e capi al
is
aised. Ano he me hod
o
es he
inancial isk
o
a capi al s uc u e is
o
calcula e he in e es -
co e age a io
based
on
p o i
and
cash low. I his a io
de e io a es o e ime he eason should
be
in he o mula ion
o
he p ice o mula.
The
co e age
a io
based
on
p o i
is
p o i be o e in e es
and
ax
o
in e es paid.
Based
on
cash
low he a io
is
p o i be o e in e es and ax
plus
dep ecia ion
plus/minus changes in wo king capi al (excluding in e es
bea ing loan capi al)
o
in e es paid.
Summa y
In
an
analysis
o
en widely used p ice-con ol o mulae i
was shown ha he o mulae ook in o conside a ion a a ie y
o
di e en s ipula ions such
as
he calcula ion
o
unds
employed, he de ini ion
o
p o i ,
and
he p o i abili y a e
allowed. Fu he mo e
i
is
main ained ha he commonly
used
in ui i e
and/o
con en ional me hods
o
e alua ion a e
subjec
o
a ious sho comings. The e o e,
i
can
be in e ed
ha i
is
i ually impossible
o
compa e di e en p ice
o mulae in isola ion.
To
o e come his p oblem a simula ion model, based
on
ce ain assump ions,
has
been
de eloped. The model compa es
and
e alua es he adequacy
o
a ious p ice o mulae o e
ime (dynamically) in di e en ways, i.e. se e al a ios
and
c i e ia a e calcula ed wi h he in e nal a e
o
e u n being
he p ima y one.
In he emaining h ee a icles, he simula ion model will
be applied
o
he wo o mulae p esen ed in his a icle.
Re e ence
La nb ech s,
I.J.
1979.
Die
ln es e ingsbeslui .
P e o ia: HAUM,
pp.107-
IOCJ.