Kle ck, W. G.; Bi khol z, L. E.
A icle
Use o eg ession analysis o o ecas cash lows
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: Kle ck, W. G.; Bi khol z, L. E. (1984) : Use o eg ession analysis o o ecas cash
lows, 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. 15, Iss. 3, pp. 135-139,
h ps://doi.o g/10.4102/sajbm. 15i3.1117
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/217862
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Use
o
eg ession
analysis
o
o ecas
cash
lows
W.G.
Kle ck and LE. Bi khol z
School o Business Leade ship, Uni e si y o Sou h A ica, P e o ia
In
his a icle he need o o ecas he cash lows o a co po a-
ion is discussed. Al hough many co po a ions ope a e
on
a
decen alized basis o a g ea e o lesse deg ee he cash
esou ces o he co po a ion a e o en con olled om head o -
ice.
The
sys em is cash eceip s a e emi ed o he head o -
ice easu e
on
a daily, weekly, o mon hly basis and
he
unde akes o make unds a ailable. Owing o he size o many
co po a ions he easu e is a emo ed om ac i i ies a he
b anch le el and i is no unknown o him o expe ience
an
unexpec ed in low o ou low
o
unds. I is also o en aken
o g an ed
by
he ope a ions' accoun an s ha he co po a e
easu e will always ha e su icien unds o place a hei
disposal. This lack
o
communica ion can esul in di icul ies
in
p o iding he ope a ions wi h he equi ed unds. I is
he e o e necessa y ha he easu e o ecas his u u e cash
posi ion
in
o de o ha e adequa e cash esou ces a his
disposal o mee he equi emen s o he ope a ions o e he
sho e m.
In
o de o assis he easu e in making sho
e m
o ecas s a model using eg ession analysis was
de eloped.
S.
A .
J.
Bus. Mgm . 1984,
15:
135-139
In
die a ikel wo d die noodsaaklikheid
om
die kon an -
behoe es
an
'n
maa skappy e oo spel besp eek. Alhoewel
baie
maa skappye gedesen alisee d is, wo d die kon an -
behoe es
an
die maa skappy anui die hoo kan oo beha ig.
Die
s elsel wa ge olg wo d is om behoe es aan kon an
na
die
hoo kan oo esou ie e e wys
en
hy oo sien dan die
nodige ondse.
As
ge olg
an
die g oo e
an
baie onde ne-
mings is die esou ie nie al yd bewus
an
al
die ak iwi ei e in
a delings nie
en
ge olglik onde ind hy dikwels
'n
on e wag e
aag
na
ondse. A delings aan aa ook dikwels da die
esou ie al yd genoeg ondse sal
h~
om
in hul behoe es e
oo sien. Hie die geb ek aan kommunikasie lei daa oe da
p obleme on s aan in die oo siening
an
ondse. Di is
om
die
ede
nodig
om
die oekoms ige kon an behoe es
an
die
maa skappy e oo spel.
Ten
einde hie die oo spelling e
maak
is
'n
model wa geb uik maak
an
eg essie-analise on -
wikkel.
Die
model wo d geb uik
om
die ko e myn-kon an be-
hoe es
an
die maa skappy e oo spel.
S.-A .
Tydsk . Bed y sl. 1984,
15:
135-139
W.G.
Kle ck
and
L.E.
Bi khol z
School
o
Business Leade ship, Uni e si y
o
Sou h A ica,
P.O.
Box
392,
P e o ia 0001, Republk
o
Sou h A ica
Accep ed
Ap il
1984
In oduc ion
Wo king
capi al,
especially
cash
o o e d a
acili ies,
o m
he
basis
a ound
which
a company's a ai s o a e.
S ocks
a e
ans o med
in o
sales
which
become
deb o s
om
which
cash
is
collec ed.
The
cash
is
used
o
pay
he
c edi o s
o
he
goods
o iginally
bough
as
well
as
o
all
he
o he
alue-added
cos s.
This
cycle
is
cons an ly
epea ing
i sel
wi hin
he
business
and
he
la ge
he
co po a ion o
conglome a e,
he
la ge
will
be
he amoun s
in ol ed.
The e
is
a
e y
close
in e dependence
be ween
he
a ious
ac o s
in
he
cycle,
and
cash
in
pa icula , o
he
lack
o
i ,
can
se iously
hampe he
smoo h
ope a ion and
unc ion
o
he
business.
Many
co po a ions ope a e on a
decen alized
basis,
o a
g ea e
o
lesse
deg ee,
wi h
he
esul
ha
nea ly
all
he
ou ine
ansac ions
a e
nego ia ed
a
he
ope a ional
le el.
Howe e ,
one o en
inds
ha he
cash
esou ces
o
he
co po a ion a e
con olled
om
he
cen e.
The
sys em
is
ha
cash
eceip s
a e
emi ed
o
he
head
o ice
easu e
on
a
daily,
weekly,
o mon hly
basis
and
he
unde akes
o
make
unds
a ailable
o
cheques
d awn
agains
he
ope a ion's
bank
accoun
in
he
no mal
cou se
o
e en s.
This
esul s
in
subs an ial amoun s
o
cash
coming
unde
his
con ol.
The
in oduc ion o
elec onic
aids
in o
he
banking
sys em,
including
he
use
o compu e s
o
p ocessing
as
amoun s
o documen a ion
wi hin
a sho
space
o
ime
and
he
use
o
elec onic
da a
ansmission
be ween
cen es,
acili a es
he
cen alizing
o
he
easu e 's
unc ion
o
include
ope a ions
in
dis an
owns
and
ci ies
as
well
as
hose
nea
a hand.
The
banks
hemsel es
ha e
welcomed
his
in
p inciple
as
i
allows
hem
o moni o
mo e
easily
hei o al
exposu e
o
a co po a ion,
and
hey
ha e
aided
he
easu e 's unc ion,
by
consolida ing
he
a ious
accoun s
a co po a ion
uses
h ough
au oma ic
clea ing
o
mon h-end
balances
in o
a
single
bank accoun .
The
easu e 's
dilemma
The easu e o
he
a e age
co po a ion
is,
by
i ue
o he
size
o
he
co po a ion,
a
emo ed
om
he
ac i i ies
a he
ope a ional
and
b anch
le els.
I
is
hus
no
possible
o
him
o
know
wi h
easonable
accu acy
wha
he
co po a e bank
balance
will
be,
o
o
him
alone o
p edic
he
maximum
o
minimum
bank
accoun
balance.
I
is
no
unknown
o
a
ea-
su e
o
expe ience
an
unexpec ed
sudden
in low
o ou low
o
unds
because
he
was
no
imeously
in o med he eo .
I
is
equen ly
aken
o
g an ed
by
he
ope a ions'
accoun-
an s ha he co po a e easu e will
always
ha e
su icien
136
unds o
place
a hei disposal o
mee
wha e e
cheques hey
may
issue
in
he conduc
o
hei nonnal a ai s.
This
lack
o
communica ion
can
esul
in
di icul ies
in
p o iding
he
ope a-
ions
wi h
he equi ed unds.
I
becomes
clea
hen
ha
he
easu e
has
a
need
o
o ecas
his
u u e
cash
posi ion
in
o de o
ha e
adequa e cash
esou ces
o o e d a
acili ies
a
his
disposal o
mee
he
e-
qui emen s
o
he ope a ions on he sho - e m
daily
basis.
The
easu e 's
ole
The easu e 's
ole
in
an o ganiza ion
includes
amongs o he s
he du y o
maximize
he
use
o
he co po a e
cash
esou ces
o al e na i ely o
minimize
he cos
o
bo owings. He
does
his
by
a anging sho - enn c edi s o deposi
acili ies
wi h
he banke s a he
bes
possible
in e es a es. Fo ins ance,
i
he
knows
ha
he
has
a
pa cel
o
cash
ha will no
be
called
upon
o
a numbe
o
weeks,
he
is
hen able o nego ia e a
sligh ly
be e in e es a e
wi h
a banke , on condi ion
he
lays
his
money
ou o a
ixed
e m.
Con e sely,
should
he
equi e
a
ce ain
amoun and
is
awa e
a he
ime
ha in e es
a es
a e 'ha dening',
he
may conside
bo owing sho - enn money a a
ixed
a e o a pe iod,
ex-
pec ing
ha a e
his
he
will
be
able o
edeem
he loan om
u u e
expec ed
cash
in lows. I
causes
him a ce ain amoun
o
emba assmen should
he
o ecas a su plus
o
cash
which
he
hen
lays
ou on
ixed
deposi , o
say
150/o
p.a., only o
ind
ha
he
is
sho
o
unds and
has
o empo a ily bo ow
he equi ed amoun s a a
highe
in e es
a e,
o
say
190/o
p.a.
E ec i ely
he
makes
a
loss
(qui e
unnecessa ily)
o
40/o
p.a.
on
hese
ansac ions.
The
p oblem
is
exace ba ed
du ing
imes
when
in e es
a es
a e unning a eco d
le els,
as
cu en ly being expe ienced
in
he
business
wo ld.
I should
be
clea hen ha he easu e
who
is
able o
o ecas
his
cash
esou ces o equi emen s accu a ely can
minimize
he cos
o
sho - e m bo owings. Whe eas
i
may
be
possible
only
in
excep ional
ci cums ances
o
o ecas
u u e
cash
lows
exac ly,
i
is
desi able o ind a echnique ha will
show
g ea e accu acy han ha demons a ed
in
Table
1.
The ques ion
o
he co po a ion's s anding
wi h
i s
bank
Table 1 Mon h-end cash balances
(ROOOs)
Mon h 1 Mon h 2 Mon h 3 Mon h 4 Mon h 5 Mon h 6
Fo ecas
Ac ual
1197
429
75
251
716
196
1649
982
142
916
2236
1810
o banke s
also
comes
in o play in ha i
is
usual o nego ia e
loans o
acili ies
up
o a ce ain maximum
le el,
and should
his
be
exceeded,
i
causes
emba assmen o he co po a ion
especially
i
such
an o e d a
is
unexpec ed and he
easu C.:
is
no
in
a posi ion o ake p io
s eps
o a oid he o e -limi
posi ions.
Thus
i
becomes
clea ha he easu e
needs
o
be
able
o o ecas
his
u u e
cash
posi ion
as
accu a ely
as
possible
in
o de o: '
(a)
P o ide
in
ad ance o he
cash
equi emen s
o
his
ope a ions;
(b)
~
he esou ce,
i.e.
cash
o
which
he
is
espon-
sible
o ,
con e sely,
o
minimize
he cos
o
bo owinac,•
and
··--·
(c)
a oid
possible
emba assmen and
loss
o
s anding wi h
S.-A .
Tydsk . Bed y sl.
1984,
15(3)
his
banke s.
Desc ip ion
o
he
company
The company upon
which
he o ecas ing model
is
based
was
o med a he beginning
o
1980,
as an Ope a ing
Di ision
wi hin a la ge Sou h A ican company quo ed on
he
Johan-
nesbu g S ock Exchange. I
is
one
o
wel e
di isions
wi hin
he co po a ion. Annual u no e
o
he co po a ion
was
in
excess
o
R600
million o he 1981/82 inancial
yea .
Each
o
he Ope a ing Di isions
is
cons i u ed
wi h
a
Chai -
man, Managing Di ec o , and Boa d
o
Di ec o s
who
a e
esponsible o he s a egy
as
well
as
o he unning o
hei
pa icula di isions. The di isions
in
um a e
esponsible
o
he Co po a e Boa d o whom hey submi o app o al
hei
budge s, capi al o es, and s a egies on an annual
basis.
They
epo p og ess agains hese on a mon hly basis.
All
he
di i-
sions
wi hin he co po a ion
use
he
se ices
o
he
Cen aliz.ed
Banking
Se ice
which
is
adminis e ed by he
Co po a e
T easu e .
The pa icula
Di ision
( o company)
wi h
which
we
a e
con-
ce ned
is
in ol ed
in
he con e sion
o
pape and
plas ic
esin
in o
sacks
and bags
o
a ious cons uc ions and
sizes,
o
sale
o indus ial cus ome s o hei packaging
equi emen s.
The di ision
buys
i s
aw ma e ials om
six
main
supplie s.
I hen
con e s
his
in o packaging o sui
indi idual
cus ome 's
equi emen s.
Ve y
ew
s ock
lines
a e ca ied
as
he
cus ome s
all
speci y
di e en equi emen s o
size,
cons uc ion,
p in -
ing,
closu e, e c. and he goods a e only manu ac u ed
once
an o de has been ecei ed.
The cus ome s his di ision deals wi h a e
all
indus ial
con-
ce ns
whose
in ol emen
is
mainly
in
he oods u s
sec o
(i.e.
suga , lou , maize meal, e c.) and
in
he d y
chemical
p o-
duc s sec o (i.e. e ilize , lime, cemen , e c.).
Sales
and ma ke ing a e conduc ed mainly on a
na ional
le el,
h ough a na ional ma ke ing manage and
s a ,
al hough
sales
o local cus ome s a e equen ly nego ia ed
by
he
local
ope a ion. The e a e e y
ew
cash
sales
and
c edi
e ms a e 'paymen wi hin hi y days
o
s a emen '.
As he e
is
a ime
lag
be ween o de and
deli e y
by
sup-
plie s,
aw
ma e ials s ocks app oxima ing wo-mon hs'
supply
a e
held
o ensu e con inued p oduc ion.
By
a angemen wi h he supplie s, paymen o
s ock
is
made hi y days a e he mon h-end. This means ha
he
company mus und he aw ma e ials o an addi ional
hi y
days
be o e hey a e commi ed o manu ac u e.
Manu ac u ing akes place
in
esponse o cus ome s'
o de s
and
because
o
p oduc ion-scheduling equi emen s,
he
inish-
ed
goods
a e
held
in
s ock o en
days
be o e
deli e y,
a
which
poin hey a e sold. A his ans o ma ion poin , he
inished
goods ha e changed in o deb o s
ia
he
sales
ansac ion.
On a e age i akes i een days om he da e
o
sale
o
he da e he s a emen
is
issued a he mon h-end.
Al hough
he c edi e ms o he cus ome s a e hi y days,
expe ience
shows
ha he cus ome s pay hei accoun s
45
days
om
s a e-
men da e -i.e. a day
130
o
he
cycle
depic ed abo e.
This
hen comple es he
cycle
and shows he e
is
a
100-days
cash
cycle
om he ime cash
is
paid ou o aw ma e ials
un il
i
is
ecei ed
back om cus ome s (day
130
minus day
30).
Fo ecas ing
cash
lows
Fo ecas ing
o
u u e
cash
lows
is
done a he ope a ional
le el
by he accoun an o
his
assis an . The aim
is
o a emp
o
o ecas
as
accu a ely
as
possible he ne cash
low
o he
en-
suing mon h,
so
ha he Co po a e T easu e
is
in a posi ion
S.
A . J. Bus. Mgm . 1984, I
5(3)
o
assess
his
immedia e si ua ion and o enable him o plan
he bes s a egy o ei he u ilizing su plus moneys o und-
ing
sho - e m de ici s.
Sales
Sales
o m he link be ween he ope a ion and he cus ome
in
he ading
cycle.
Once a
sale
has
been
concluded and he
goods despa ched, he ope a ion acqui es an addi ional deb
o u u e cash in low. I akes on a e age
60
days o
ecei e
he money a e a sale has aken place. Fo his eason
sales
will be lagged
by
one, wo, o h ee mon hs.
Deb o s (Cash in low only)
In he ans o ma ion p ocess,
sales
a e ansla ed in o
deb-
o s. Deb o s o m pa
o
he wo king capi al
o
he ope a-
ions
and a e cons an ly being u ned o e . As deb o s a e pa
o
he ope a ion's in es men , cash in low
is
inc eased
wi h
a educ ion
in
he o e all deb o s'
le el
inc eases. Deb o s
lag
he cash
low
by
one mon h,
in
ha an inc ease o dec ease
in
deb o s'
le els
o e he mon h de e mines whe he he e
has
been
an ou low o an in low
o
cash.
C edi o s (Cash
ou low
only)
This a iable includes all he amoun s due o supplie s
o
aw
ma e ials held mainly
in
s ock.
By
nego ia ion
wi h
he majo
supplie s, hese ou s anding amoun s mus
be
se led
by
he
28 h
o
he succeeding mon h, ailing
which
he
o ganiz.a ion
will
usually be
penaliz.ed
by
ha ing o pay in e es on he
o e -
due balance. Because his a iable
is
paid du ing he
ollow-
ing
mon h
i
is
necessa y o
lag
i
by
one mon h.
T ading days
Expe ience had indica ed ha he cash
low
in
hose mon hs
wi h
mo e ading days
was
no mally highe han
in
hose
mon hs wi h
less
ading days. Fo his eason he numbe
o
ading days
was
included
as
an independen a iable
in
he
model.
Time
I
was
belie ed
ha
as
ime wen
by
he e migh
be
an
inc ease
(o
e en
dec ease)
in
sales
and he e o e also a co esponding
change
in
cash
lows.
Fo his eason ime (mon h numbe )
was
included
in
he model.
Dummy a iables
The na u e
o
he business conduc ed
by
he ope a ions
shows
a dis inc seasonal end. Business ac i i y eaches a
low
poin
du ing he Decembe /Janua y pe iod
when
cus ome s
usual-
ly
close
hei plan s and educe hei
ac i i ies.
F om
his
poin
ac i i y
slowly
imp o es
ill
i
eaches a
peak
in
he July o
No embe
pe iod. In an icipa ion
o
he
inc eased
business
ac-
i i y
he ope a ion usually inc eases
i s
s ock
le els
in
ad ance
o
he peak season and hen allows hese
le els
o
decline
as
he season
goes
h ough
i s
peak. On he o he hand deb o s'
le els
inc ease du ing he
peak
and only educe a e he peak
has
been
eached. Du ing he slow-down pe iod
le els
educe
acco dingly,
bu s ock
le els
a e no
allowed
o
all
below
'sa e'
le els.
These seasonal ends
we e
ca e ed o
by
he in oduc-
ion
o
dummy a iables.
The
da a
Ha ing iden i ied he a iables i
was
hen
necessa y
o
collec
he da a o each
o
he a iables. The da a span a pe iod
o
o y mon hs, om Ma ch
1980
o Augus
1983.
The e a e
137
no da a u he back
as
he di ision o
which
he o ecas ing
is
done
was
only cons i u ed du ing Ma ch
1980.
The las h ee obse a ions
we e
no used
in
selec ing
an ap-
p op ia e eg ession model.
These
obse a ions
we e
used
o
es
he pe o mance
o
he model. Al hough h ee obse a-
ions
a e no
enough
o es he
model,
mo e obse a ions
could
no
be
used,
owing
o a
lack
o
da a.
Selec ing
an
app op ia e
eg ession
model
Since
he e
is
no ' heo y' linking
cash
lows
o a
speci ic
se
o
independen
a iables,
he app oach adop ed
was
neces.wily
an empi ical one, i.e. a iables
likely
o in luence cash
lows
we e
used
o
build
a ious
eg ession
models
and hen o
check
he
models
o adequacy
o
i .
The c i e ion
o
model-building
in
eg ession
is
pa simony,
i.e. a model
is
de eloped
which
includes he
ewes
numbe
o
independen a iables ha pe mi an adequa e in e p e a-
ion
o
he
cash
lows.
Mul iple
eg ession
models ha ha e
ewe
independen
a iables
a e
easie
o
analyse
and in e p e .
In his s udy he mos app op ia e
eg ession
model
was
iden i ied
by
e alua ing
all
possible
eg ession
models. In he
examina ion o
all
possible
eg ession
models
wo selec ion
p ocedu es
we e
used:
(a)
The R2p c i e ion (coe icien
o
de e mina ion); and
(b)
Mallows
Cp,
whe e
p e e s o he numbe
o
independen a iables
conside ed.
The R2p C i e ion
The R2p c i e ion
in ol es
he compa ison
o
he coe icien s
o
de e mina ion o
all
possible
eg ession
models.
Since
R2p
canno
dec ease
as
addi ional independen a iables a e
in-
oduced, he
highes
R2p
alue
will
occu
when
all
possible
independen a iables a e included
in
he model. The
goal
in
u ilizing
R2p
is
o compa e al e na i e
models
so
ha
i
can
be
de e mined
when
he in oduc ion
o
addi ional indepen-
den a iables
does
no p oduce a commensu a e inc ease
in
R2p.
The
Cp
C i e ion
The Cp c i e ion de eloped
by
Mallows
(see
Daniel & Wood,
1971)
measu es he o al squa ed e o
o
a eg ession model
wi h
p pa ame e s. The o al squa ed e o consis s
o
a bias
componen and a andom e o componen . The bias com-
ponen ep esen s he di e ence
in
he p edic ed Y
alues
ob-
ained om he i ed
eg ession
model and he ' ue'
eg es-
sion
model.
The andom e o componen
ep esen s
he
a ia-
bili y
a ound he i ed
line
o
eg ession. When a eg ession
equa ion
wi h
p independen a iables
does
no con ain any
bias componen , he a e age
alue
o
Cp
is
p,
he numbe
o
pa ame e s. The goal
is
he e o e o iden i y hose eg ession
models
o
which
Cp
is
close
o p.
The model o cash in low
The independen a iables used
in
de eloping he model o
cash
in low
we e:
XI -
sales
lagged
I mon h
X2
-
sales
lagged
2 mon hs
X3
-numbe
o
adding days
X4 - he ime a iable (mon h numbe )
X5
-deb o s
X6 o
Xl6
-dummy a iables o each mon h
o
he
yea .
The
i s
un on he compu e e ealed ha obse a ions
138
numbe 6 9 and
24
we e ou lie s i.e. he s anda dized esidual
o hese ~bse a ions exceeded
2.
As ou lie s end
~o
ha e a
signi ican e ec
on
he eg ession esul s, hese pom s we e
igno ed in he de elopmen
o
a model. .
In Table 2 he alues o Mallows Cp
and
he coe ie en
o
de e mina ion R2p a e shown o selec ed combina ions
o
he independen a iables.
Only hose combina ions o which Mallows Cp a e he
Table 2 Cp
and
R2p alues o selec ed eg ession
models
Numbe
o
Independen a iables included pa ame e s
in
eg ession model p
Rzp
Cp
X2 2 0,578 94,18
X2,
Xl3
3 0,683 65,37
XI,
X2,
Xl3
4 0,764 43,54
XI,
X2, X3,
XII
5 0,853
19,38
XI,
X2, X3,
XII,
Xl3
6 0,898 8,12
XI,
X2, X3,
Xll,Xl2,Xl3,
7 0,912 5,75
XI,
X2, X3,
Xll,Xl2,Xl3,Xl6
8 0,920 5,44
XI,
X2, X3, X4,
Xll,Xl2,Xl3,Xl6
9 0,927
5,59
XI,
X2, X3, X4, X9,
XlJ,Xl2,Xl3,
X16
10
0,930 6,59
XI,
X2, X3, X4, X9,
Xll,Xl3,Xl4,Xl6
II 0,932
8,14
smalles a e shown. Because Cp
is
a measu e
o
o al squa ed
e o ,
an
a emp was made o ind he
se
o
independen
a iables ha leads o he smalles Cp alue while a he same
ime minimizing he bias componen (see Daniel & Wood).
Since Cp
is
lowes o he
Xl,
X2, X3,
Xll,
Xl2,
X13, X16
model (C7 = 5,44)
and
he
Xl,
X2, X3, X4,
XI
1,
Xl2,
X13,
X16 model (C8 = 5,59)
i
would appea ha one
o
hese wo
models should be selec ed.
The
Xl,
X2, X3,
XI
I,
Xl2,
X13, X16 model was selec ed
since i s Cp alue
is
sligh ly lowe and
i
appea s
o
con ain
less bias (in
ac
i s Cp alue
is
e en
less
han p, he a e age
o al squa ed e o when no bias exis s). The coe icien s
o
de e mina ion o he wo bes models
do
no di e much and
he e o e he abo e choice seems easonable.
The comple e ou pu ob ained om he abo e model
is
gi en
in Table
3.
The F- alue o he eg ession
is
42,96
and
his
is
signi i-
can
a
he
950/o
con idence le el. Thus he independen
a iables as a whole p o ide a s a is ically signi ican causal
ela ionship. The R2s e m shows a easonably close i wi h
920/o
o
he a ia ion in cash in lows being explained by he
independen a iables.
The - alues indica e ha
all
he eg ession coe icien s wi h
he excep ion
o
Xl6
di e signi ican ly om e o.
The
assump ions o eg ession analysis
The
ou basic assump ions no mally made in eg ession
analysis mus be me be o e a eg ession model can be used.
These assump ions a e:
(a) Linea i y
(b) Independence
o
esiduals
(c)
Homoscedas ici y
(d) No mali y
o
1esiduals
Linea i y
Linea eg ession assumes ha he independen a iables a e
linea ly ela ed wi h he dependen a iable.
The
easonably
S.-A . Tydsk . Bed y sl.
1984,
15(3)
Table 3 Reg ession equa ion o cash in low
Reg ession Es ima ed
Independen a iables coe icien s anda d e o
- aluc
In e cep
-4,62089
0,85388 -5,41
Sales Lagged I Mon h
(XI) 0,000373 0,00009
4,33
Sales Lagged 2 Mon hs
(X2) 0,000732 0,00009
8,08
Days (X3) 0,20469 0,03544
5,78
Dummy Va iable No. 6
(XII)
-1,52675
0,35013
-4,36
Dummy Va iable No. 7
(X12) 0,67773 0,27981
2,42
Dummy Va iable No. 8
(Xl3)
-1,01780
0,29714 -3,43
Dummy Va iable No. II
(Xl6) 0,43415 0,27130
1,60
R28 = 0,920
F = 42,96
S anda d E o
o
Es ima e = 0,4139
Du bin-Wa son 1,6655
high alue
o
R2p
and
he signi ican F- alue indica ed ha
he e seemed
o
be
a linea ela ionship be ween he
depen-
den
and
independen a iables.
Independence o esiduals
To
es ablish whe he he esiduals a e independen a
commonly
used plo , namely
ha
o
he s anda dized esiduals
a~ns
he i ed alues, was u ilized (see o example Cha e Jee &
P ice,
1977).
The
plo e ealed
ha
he s anda dized esi~u~
all ended o all be ween 2
and
- 2
and
we e andomly
dis n-
bu ed abou ze o. I he e o e seemed
ha
he esiduals
we e
independen ly dis ibu ed. Fu he mo e, he Du bin-Wa son
s a is ic lay wi hin he ange
1,
10
o
2,90, indica ing ha he e
seemed o be e y li le
o
no
au oco ela ion.
Homoscedas ici y
A plo
o
he s anda dized esiduals agains ime e ealed ha
he e o e m
had
a cons an a iance
and
he e o e he
e-
qui emen
o
homoscedas ici y was me .
No mali y o esiduals
A no mal p obabili y plo
o
he esiduals e ealed ha he
esiduals we e app oxima ely no mally dis ibu ed. .
I would hus appea
ha
he mul iple linea
eg ess1?n
model gi en abo e is
an
app op ia e model o he cash 10-
Table 4 Reg ession equa ion o cash ou low
Independen a iables
Ince cep
Sales lagged 2 mon hs
(X2)
No.
o
ading days (X3)
Dummy Va iable No. 5
(XII)
R24 = 0,68
F = 21,68
Reg ession
coe icien
-5,95423
0,000749
0,299313
-0,96651
S anda d E o
o
Es ima e = 0,879
Du bin-Wa son = 1,86
Es ima ed
s anda d e o - alue
1,40697
-4,23
0,00012
6,09
0,06072
4,93
0,53150
-1,82

S.
A . J. Bus. Mgm . 1984,
15(3)
139
Table 5 Tes esul s o he eg ession models
Cash In (000') Cash Ou (000')
Ne
Cash Flow
Ac ual P edic ed E o Ac ual P edic ed E o Ac ual P edic ed E o
5,374
6,752
5,643
5,341
0,033 4,392
6,318 0,434 5,836
6,184
-0,541
3,833
low p oblem.
One
ad an age
o
he abo e model
is
ha he
independen a iables a e all known wi h ce ain y
and
need
no
be o ecas .
The
model o cash ou low
A simila
app oach
was adop ed in de eloping a model o
he cash ou low.
The
independen a iables used we e:
XI
sales lagged I
mon h
X2
sales lagged 2 mon hs
X3
sales lagged 3 mon hs
X4
numbe
o
ading days
X5 he ime a iable
X6
c edi o s
X7
-
XI
7 -
dummy
a iables
P elimina y in es iga ions e ealed ha obse a ions numbe
6, 7,
and
16
we e ou lie s
and
we e consequen ly omi ed om
he analysis.
The
esul s
o
he analysis a e con ained in Table
4.
The
mos app op ia e eg ession model (in e ms
o
Cp
and
R2
p)
con ained he a iables X2, X4, X5,
and
XI
I.
The
F- alue o his model
is
signi ican a he
950/o
con-
idence le el.
The
coe icien
o
de e mina ion
is
680/o,
which
is
less
han ha ob ained om he p e ious model. The /- alues
again indica e
ha
all he eg ession coe icien s excep dum-
my
a iable
numbe
5
a e
signi ican .
The
abo e model does
no
seem
o
iola e any
one
o
he
ou assump ions men ioned p e iously
and
can he e o e
be
accep ed.
Tes ing
he
model
The
p edic i e abili y
o
eg ession models
is
usually de e mined
by selec ing a se
o
da a
no used in de eloping he model
and
using hese
da a
o
e alua e he pe o mance
o
he model.
Owing
o
a lack
o
da a
(only 40 obse a ions we e a ailable)
i was no possible
o
e alua e he pe o mance
o
he model
adequa ely.
In
o de
o
ob ain
some idea
o
he p edic i e abili y
o
he
3,930 0,462 0,982
1,411
-0,429
5,487 0,349 0,916
0,831
0,085
3,954
-0,121
1,810 2,230 - 0,420
model he las h ee obse a ions we e no used in de eloping
he model
and
we e consequen ly used
o
es he model.
The
esul s
o
he es a e gi en in Table 5.
The
pe cen age
e o s o he cash in low model a e 0,60/o,
640/o,
and
9,60/o.
Fo
he cash ou low model hey a e
10,50/o,
6,00Jo,
and
30/o.
The
pe cen age e o s in he o ecas
o
he ne cash low
a e
430/o,
9,30/o,
and
23,30/o.
The
p esen o ecas ing sys em gi es
he ollowing pe cen age e o s o he same h ee obse a-
ions: 67,90/o, 84,50/o,
and
23,50/o.
These pe cen age e o s a e gene ally highe
han
hose p <
duced by he model.
The
limi ed es ca ied
ou
canno how-
e e p o e he supe io i y
o
he eg ession model. The eg es-
sion model should be implemen ed
and
he esul s ob ained
compa ed wi h he p esen sys em. Only hen can he ac ual
p edic i e abili y
o
he model be es ablished.
Conclusion
The easu e
o
any co po a ion needs
o
o ecas as accu a ely
as possible he u u e cash posi ion
o
his company so as o:
(a) P o ide in ad ance o he cash equi emen s
o
his
ope a ions;
(b) minimize he cos
o
bo owings;
and
(c) a oid loss
o
s anding wi h his banke s.
To
aid he easu e in o ecas ing his sho e m cash lows,
wo eg ession models we e de eloped, one
o
o ecas cash
in lows
and
he o he
o
o ecas cash ou lows.
The
esul s
ob ained om hese models indica e ha he models may yield
supe io o ecas s
o
hose ob ained om he p esen sys em.
Owing
o
lack
o
da a
he es canno be conside ed adequa e
bu ne e heless he model should be implemen ed
o
es ablish
i s ac ual p edic i e pe o mance.
Re e ences
Cha e jee,
S.
& P ice,
B.
1977.
Reg ession Analysis By Example.
New
Yo k: John
Wiley
& Sons,
In.:.
Daniel, C.S. & Wood, F.S.
1971.
Fi ing Equa ions To Da a.
New
Yo k: John Wiley & Sons, Inc.