Use of regression analysis to forecast cash flows

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 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ 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.