Problems ad Persecives of Maageme, 24 Absrac ACCOUNTING TURNOVER RATIOS AND CASH CONVERSION CYCLE Pedro Orí-Ágel, Diego Prior Fiacial saemes, ad esecially accouig raios, are usually used o evaluae acual maagerial erformace ad redic he cosequeces of heir decisios (firm value or fiacial disress). For a beer udersadig of he emirical resuls, ad o imrove he correc evaluaio of maagerial decisios, i is ecessary o esablish a li bewee accouig raios ad cocree maagerial decisios. This aer aalyses he relaioshi esablished bewee accouig urover raios ad he eriod of ime se cocludig ad oeraioal rocess. I order o achieve his urose, o oly a se of ossible averages of real coversio eriods are defied, bu also he codiios ha guaraee ha accouig urover raios offer a good aroach o hem are esablished. I geeral, he codiios which eable o aroach accouig urover raios o good erms are difficul o acce i firms oeraig i growig or decliig mares, wih seasoal demad or wih log oeraig cycles. O he oher had, some ossible aleraives which, wihou eedig more iformaio, ca hel o measure real coversio eriods of ime i a more accurae way are also roosed ad illusraed. Iroducio 2 Keywords: Accouig, iformaio, measureme, iveory corol. The rece research lieraure relaed o he aalysis of accouig iformaio ca be classified io wo fields: fiacial disress redicio ad fudameal aalysis. The fiacial disress redicio research uses saisical echiques o classify firms io oe of a umber of muually exclusive grous (Gombola, Hasis, Kez ad Williams, 987; Pla ad Pla, 99, ad, from aoher oi of view, Rezlaff-Robers, 996). O he oher had, fudameal aalysis research ess which accou iformaio is he ey value-driver ha roduces growh i cororae securiies (Ou ad Pema, 989; Dechow, 994 ad Chariou, 997). I accordace wih his belief i he uiliy of emirical research resuls, some auhors have roosed o develo models wih more heoreical coe i order o icrease he udersadig of he resuls of emirical research. For isace, Lev ad Thiagaraa (993) 3, afer he verifyig ha mos of fudameal aalysis is subsaially a saisical search of he accouig iformaio useful i securiy valuaio, roosed o iroduce a search guided by heory or by exers; udgeme as a aural exesio of he saisical search rocedure. Followig his idea, his wor develos a heoreical ierreaio of accouig urover raios. These raios have bee widely used i academic wors 4 ad rofessioal racice 5. The D. Ecoomía De La Emresa, Uiversidad Auóoma De Barceloa 893 Bellaerra (Barceloa), Sai, Fax: 34-3- 58 25 55, E- Mail : Pere.Ori@Uab.Es, Diego.Prior@UAB.ES 2 A relimiary versio of his wor was reseed i he 2h. Aual Cogress of he Euroea Accouig Associaio ad has beefied by he suggesios made by Salvador Carmoa. The auhors have received fiacial suor from DGICYT PB 94-78 ad DGES PB 95-6 resecively. 3 See Lev ad Thiagaraa (993), age 9. 4 See, for examle, Williamso R. W. (984). 5 See Che ad Shimerda (98).
2 Problems ad Persecives of Maageme, 24 uderlyig reaso of heir geeral acceace cosiss i he fac ha hese raios rovide o oly valuable iformaio abou worig caial qualiy maageme, cash-geeraig abiliy of oeraios ad shor-erm liquidiy ris of a firm (Bacer ad Gosma, 98; Sicey, 993; Saccurao, 994) bu also abou he oeraig efficiecy level (Holsrom, 994). O he oher had, i Ozca ad McCue (996) a urover raio is cosidered i order o quaify a global fiacial erformace idex, ad i Gombola, Hasis, Kez ad Williams (987) ad i Drae ad Peavy (995) urover raios have bee ried o see wheher hey coai iformaio useful i he redicio of fuure fiacial roblems. Fially, he aer of Ciro, Robbie ad Wrigh (997) illusraes how he ledig baers use resricive raio coveas (which iclude receivables days ousadig) i loa coracs. This wor sars by focusig o he urover raios ad wih heir iverse ierreed as a aroximaio of he average days se i a oeraioal rocess 6. These ime variables iegrae he global worig caial ime variable cash coversio cycle (e ime-ierval bewee acual cash exediures o urchase of roducive resources ad he ulimae recovery of cash receis from roduc sales): () Receivables coversio eriod () Iveory coversio eriod (-) Payme deferral eriod () Cash coversio cycle The mai obecive here is o clarify he assumios which mus be osed o be able o deduce he amou of days se comleig a oeraioal rocess from urover raios. Iiially, i Secio, differe weighed averages of days ha a grou of uis (commodiies, sales or urchases, all hree magiudes which ca be exressed o oly i hysical bu also i moeary erms) have bee i a cocree rocess uil i has bee comleed are defied. Afer his, i Secio 2, hese averages of days are relaed o he usually emloyed accoua based urover raios. This relaioshi will allow us o evaluae he degree of reliabiliy of he imlici assumios made by he aalys who uses accouig iformaio ad urover raios i order o quaify he cash coversio cycle eriod. To suor he discussio erms, ad wih he aim of offerig he mos correc ossible soluio we ca fid, a emirical alicaio is reseed as a illusraio of he roblems deeced i he heoreical level (Secio 3). This wor cocludes wih reseig a syhesis of he mai coclusios we have obaied.. Differe ossibiliies i defiig he real weighed average of days of iveory i rocess. We will focus o he accouig eriod as he referece ime i order o aalyse he uis (for examle he ius soc of raw maerials) ha have bee rocessed. Raw maerials are classified io hree differe grous: a) Iiial Soc: Uis which eered he revious eriod bu which have o bee cosumed i sarig he rese accouig year,, where is he value of he bach. To simlify he oaio, i will be assumed ha all of hese uis leave he rocess before he coclusio of he 6 This ierreaio could be see i exboos -Foser (986). 68-69, research aricles -Holmsröm (994)- ad,secially, i Richards ad Laughli (98).
Problems ad Persecives of Maageme, 24 3 curre accouig year. Those uis which come i ad go ou of oe rocess a he same ime cosiue a bach, ad is he umber of baches wih a dae of ery revious o he curre accouig year ad a dae of exi i he curre eriod. b) Uis which eer ad leave he rocess i he same eriod: Their value is, where is he umber of baches wih ery ad exi i he curre accouig year. c) Fial Soc: Those uis which have regisered he ery i he curre eriod, bu will be ou durig he ex eriod. Their value is, ad is he umber of hese baches. Iiial soc: l Ery flow: PROCESS Exi flow: l Fial soc: Toal flow: l Flow of uis which have regisered ery ad exi: Fig.. Curre Accouig Year ad Flows Cosidered Wih he above classificaio, ad aig io accou differe ids of flows, aleraive weighed averages of days (i Figure we rese he flows we are cosiderig) ca be defied. I defiig he ime which bach has bee i he rocess as, differe weighed averages of days i oe rocess, i.e., real average eriods, ca be comued:
Problems ad Persecives of Maageme, 24 4 Days Corresodig еo he Ery Flow This average refers o he days, corresodig o curre ad ex eriods, i which he uis which have bee i he rocess have eered i he curre accouig year. These days are weighed by he ecoomic value of he uis. So his average of days aes io accou he uis ha eer he accouig year ad leave his or he ex year. Tha is o say:. e Days Corresodig o he Exi Flow This average comrises he uis which have goe ou of he curre year. These days are weighed by he ecoomic value of he uis. So his average of days aes io accou he iiial soc ad he uis which eer ad exi i he accouig year, algebraically:. ex Days Corresodig o he Toal Flow We refers his average as he days, coaied i he curre eriod or i ohers, i which he uis which have bee i he rocess assed i i oe or more days of he curre accouig year. These days are weighed by he ecoomic value of he uis. So his average of days aes io accou he iiial soc ad all of he uis which have eered i he curre accouig year, algebraically:. o Days Corresodig o he Uis Tha Eer ad Leave he Process i he Same Period These days are defied as a average which comues he uis ha came i ad we ou of he rocess durig he same eriod. These days are weighed by he ecoomic value of he uis. So his average of days aes io accou oly hose uis which eer ad exi from he curre accouig year, algebraically:
Problems ad Persecives of Maageme, 24 5 fl. Average of Days Corresodig o he Prese Period A weighed average ha cosiders oly he days corresodig o he curre accouig year, ', durig which all of he uis have bee i he rocess. I order o esablish differeces bewee he uis ha came i ad we ou durig he accouig year (' ) ad hose which oly came i or we ou (' < ), hese uis are weighed by coefficie (' ), algebraically: ' ' ' ' ' '. The mos imora roblem relaed o he averages which have us bee defied is ha he sadard accouig sysems do o rovide ay iformaio relaed o he days durig which cerai uis have bee i for a deermied coversio eriod. For his reaso, he exers have o aroximae he average eriod of days usig oly fiacial accou magiudes. The roblem is ha his rocedure imlies he acceace of some relaioshis ha are far from bee graed i advace. I he ex secio we shall describe wha he imlicaios ad he real ossibiliies of he accouig iformaio are o hel i quaifyig he average days of he rue cash coversio cycle. 2. Accouig urover raios as a aroximaio of he real weighed average eriod. I racice i is commolace o use he accouig urover raios as a ool o aroximae he average umber of days. The accouig sysem geeraes iformaio abou he value of he iiial soc, ; he fial soc, ; he average daily soc As ' 365 ad he value of he uis which came i he rocess 7 or hose 7 This iformaio is o icluded i he fiacial saemes, bu, usually, ca be easily exraced from he accouig iformaio sysem.
6 Problems ad Persecives of Maageme, 24 ha we ou durig he year, ha is o say, i he case of raw maerials, hose urchased ad cosumed. Wih he aforemeioed iformaio, i is ossible o comue hese raios: a e As *365 EryFlow ', a ex As *365 ExiFlow ', a f a As *365 Toal Flow o ' As *365 Flowof uishahaveregisered eryadexi, '. Some of he former raios are very exeded ad differ amog hemselves oly i he flow which aears i he deomiaor 8. As oe ca see, he accouig raios, ae, aex, ao ad afl do o coicide wih ay of he averages defied i he revious secio, e, ex, o, fl ad.the reaso is ha hese aroximaios are based o he accouig iformaio ha comues oly he average daily soc of he curre accouig year. The average days comued from he accouig urover raios cosider, oly as days of ermaece of he uis i he iiial soc ad i he fial soc, hose days durig he curre eriod, ', wihou cosiderig he days corresodig o he revious or he followig eriods, (-'). Oly i he average of days, we cosider he days corresodig o he curre accouig year, bu i he deomiaor he weigh of he iiial ad fial soc is reduced, a correcio which has o bee carried ou i he former accouig aroximaios is exressed. If he iiial ad fial soc were ull, all of he heoreical average eriods ad accouig aroximaios would ae o he same value: he average eriod corresodig o he uis ha have regisered ery ad exi durig he curre year (fl). To sum u, he exisece of 8 Usually, he aalys quaifies he Receivables Coversio Period ad he Payme Deferral Period by usig ae ad, o he oher had, he Iveory Coversio Period by meas of aex. See, for isace, Richards ad Laughli (98). This lac of homogeeiy i choosig he flow could add degrees of imrecisio o he cash coversio cycle aalysis.
Problems ad Persecives of Maageme, 24 7 iiial ador fial socs maes i imossible o assure suiable srog similariies bewee ay of he accouig urover aroximaios ad he weighed average of he cash coversio cycle (ay exceio mus saisfy i each case he relaioshi show i Aedix ). Desie hese roblems, i is imora o cosider ha raios ao ad afl, o used i everyday racice, are he miimum ad he maximum limi value, resecively, of he average of days i he year,, uder feasible assumios (see Aedix 2) of he average of days corresodig o he oal flow, o ad also of he days corresodig o he uis which eer ad leave he rocess i he same eriod, fl. I coclusio, wih oly he accouig iformaio oe of he average eriods defied i Secio ca be comued, bu i is ossible o comue a maximum value (a fl ) ad a miimum value (a o ) corresodig o he rue value of hree of he heoreical averages of days cosidered. 3. Emirical alicaio. As a way of illusraig he roosal icluded i revious secio, fiacial saemes of Mari Mariea Cororaio will be used. These daa have already bee used i a former sudy which oied ou he crucial role of he differe average eriods whe evaluaig a firm s liquidiy osiio (Richards ad Laughli, 98). Assumig he roosiios of Richards ad Laughli, we are cocered wih he measureme roblems of his average of days hrough he accouig iformaio, more cocreely he usual accouig based urover raio aalysis. I his way, he ossible errors commied are emhasized ad, furhermore, some racical soluios o avoid, i ar, hese roblems are roosed. I Table he releva iformaio eeded o comue he cash coversio cycle of Mari Mariea Cororaio i four years 9,,, 2 ad 3 is reseed. Table Seleced Fiacial Daa for Our Case Sudy YEAR Year Eded December 3 3 2 Ne sales,758,44,23,53 Cos of goods sold,269,3 876 774 Sales, geeral ad admiisraive exese 92 6 42 32 Dereciaio ad amorisaio 72 66 63 6 Toal oeraig exese,533,257,8 966 Ne oeraig icome 225 83 32 87 Cash ad shor erm ivesmes 24 58 7 46 Noes ad accous receivable 283 227 78 47 Iveories 99 29 99 86 Preaymes ad oher curre asses 6 4 Toal curre asses 72 65 495 393 Accous ayable 33 6 86 78 Salaries, beefis ad ayroll axes 72 48 37 33 Icome axes 2 5 88 36 Curre mauriies of log-erm deb 4 6 6 4 Toal curre liabiliies 429 32 227 6 9 The daa was exraced by Richards ad Laughli (98) from he Aual Reor o Sochholders, 978, ad he reors o he SEC i 975 ad 976.
8 Problems ad Persecives of Maageme, 24 Source: Richards ad Laughli (98) Wih he iformaio i he able, he cash coversio cycle derived from accouig urover raios ca be comued. Table 2 Cash Coversio Cycle for Our Case Sudy Accouig Aroximaio by Ery Flow, A e YEAR Year Eded December 3 3 2 Accouig Turover Raios: Receivables Turover 6.89 7. 7.46 Iveory Turover 6.7 5. 4.62 Payables Turover (*) 8.4 8.6 8.7 Cash Coversio Cycle: Receivables Coversio Period 53 days 5 days 49 days Iveory Coversio Period 59 days 72 days 79 days Oeraig Cycle 2 days 23 days 28 days Payme Deferral Period - 45 days - 42 days - 42 days Cash Coversio Cycle 67 days 8days 86 days Accouig Aroximaio by Exi Flow, A ex YEAR Year Eded December 3 3 2 Accouig Turover Raios: Receivables Turover 6.67 6.87 7.27 Iveory Turover 6.22 5.5 4.55 Payables Turover (*) 7.86 8.38 8.6 Cash Coversio Cycle: Receivables Coversio Period 55 days 53 days 5 days Iveory Coversio Period 59 days 72 days 8 days Oeraig Cycle 4 days 25 days 3 days - Payme Deferral Period - 46 days - 44 days - 42 days Cash Coversio Cycle 68 days 8 days 88 days (*) Cos of goods sold lus sales, geeral ad admiisraive exeses divided by accous ayable lus salaries, beefis ad ayroll axes. Due o he fac ha iformaio abou he daily average soc of iveories, receivables or ayables is o ossessed, hese mus be aroximaed as he average bewee iiial ad fial socs. The firs doub ha aears is which accouig urover raio should be used, he ery Richards ad Laughli (98) imlicily use fial socs as a roxy of daily average soc.
Problems ad Persecives of Maageme, 24 9 (ae) or he exi (aex) flow versio.the decisio is o rivial sice, wih he exceio ha he iiial exisece is equal o he fial exisece, here could be differeces bewee he days calculaed by oe mehod or aoher. Thus, he accouig aroach ha uses he ery flow will be suerior o ha which uses he exi flow whe he iiial soc is suerior o he fial soc. These differeces icrease whe, i he same way, he differeces bewee iiial ad fial socs icrease, he raio aex is grea, ad he ery flow is mior, aalyically, a e a ex Iiial Soc FialSoc a Ery flow ex Iiial Soc FialSoc a Exiflow e. The decisio crieria i choosig he correc accouig raio would be relaed o he oe which bes aroximaes oe of he heoreical averages defied i Secio. I oher words, which of he assumios defied i Secio coais more degrees of reliabiliy. I our case, sice i is very difficul o guaraee which of he assumios is he mos credible, he Receivables Coversio Period, he Iveory Coversio Period ad he Payme Deferral Period wih he ery (ae) ad exi (aex) flow accouig versios are comued. As ca be see i Table 2, he differeces are less ha wo days i all cases because he differece bewee iiial ad fial soc i relaio o ery or exi flow is egligible. The aalysis carried ou i he revious secio has show ha oe of he reviously calculaed raios could be ierreed as a weighed average of days which a umber of uis have bee i a cocree rocess. The oly iformaio which is ossible o exrac is he ierval of values bewee which hree of he five average eriods defied i Secio could be icluded i. As ca be see i Table 3, he Receivables Coversio Period i Year 3, could vary bewee 47 ad 63 days, i could be 6 days uder or days above ha calculaed hrough he ery flow, which is 53 days, or 8 days uder or above ha which is calculaed hrough he exi flow, which is 55 days. As oe ca areciae, i Year he iervals of he error vary bewee 37 days i he case of he Iveory Coversio Period ad days of he Payme Deferral Period. These iervals grow whe he Cash Coversio Cycle is calculaed; for examle, for he Year 3, i could vary bewee 46 ad 88 days, a ierval of oscillaio of 42 days. Maximum ad Miimum Values of Cash Coversio Cycle Table 3 YEAR MAXIMUM VALUE 3 2 Receivables Coversio Period (a fl ) 63 days 6 days 57 days Iveory Coversio Period (a fl ) 7 days 9 days 2 days Oeraig Cycle 33 days 5 days 59 days - Payme Deferral Period (a ol ) - 45 days - 38 days - 38 days Cash Coversio Cycle 88 days 3 days 2 days YEAR MINIMUM VALUE 3 2 Receivables Coversio Period (a o ) 47 days 46 days 44 days Iveory Coversio Period (a ol ) 5 days 6 days 65 days Oeraig Cycle 98 days 6 days 9 days We ca also cosider he oal (ao) ad he eriod (afl) flow, bu i racice hese raios are o used.
Problems ad Persecives of Maageme, 24 - Payme Deferral Period (a f l ) - 52 days - 49 days - 48 days Cash Coversio Cycle 46 days 57 days 6 days YEAR INTERVAL OF POSSIBLE VALUES 3 2 Receivables Coversio Period 6 days 5 days 3 days Iveory Coversio Period 9 days 3 days 37 days Oeraig Cycle 35 days 45 days 5 days - Payme Deferral Period 7 days days days Cash Coversio Cycle 42 days 56 days 6 days The reseed resuls show some lis bewee he ierval of variaio of he ossible values of he heoreical eriods of say, (, o, fl), ad he accouig aroaches hrough he flow of eries or exis, (ae, aex). Tha is o say, he more value for he accouig aroaches he more value for he ierval of variaio 2, a o a f 2 365 ( iiial soc fialsoc) 2 ( oal flow)( exercise flow) 365 4 a e 2 aex 2 365. This siuaio is give because he weigh of he iiial ad fial soc iside he oal flow of uis decreases. I accordace wih his idea, i is ossible o icrease he recisio degree i he calculaio of he heoreical eriods by reducig he iervals of variaio gaherig he iformaio of diverse years. The, grouig several years ogeher meas ha he weigh of he iiial ad fial soc iside he flow of oal uis is mior ad i herefore dimiishes he ossibiliies of error i he calculaio of he average of days. Cash Coversio Cycle wih Reduced Error Term Table 4 YEAR MAXIMUM VALUE (32) (2) Receivables Coversio Period (a fl ) 58 days 56 days Iveory Coversio Period (a fl ) 69 days 84 days Oeraig Cycle 27 days 4 days - Payme Deferral Period (a f ol ) - 43 days - 42 days Cash Coversio Cycle 84 days 98 days YEAR MINIMUM VALUE (32) (2) Receivables Coversio Period (a o ) 5 days 49 days Iveory Coversio Period (a ol ) 58 days 68 days Oeraig Cycle 8 days 7 days 2 We have cosidered ha he average soc is equal o he average value of he iiial ad fial soc.
Problems ad Persecives of Maageme, 24 -Payme Deferral Period (a fll ) -49 days -47 days Cash Coversio Cycle 59 days 7 days The resuls obaied i aggregaig years are reseed i Table 4. To do his he flows corresodig o subseque years are defied. Figure 2 reses he addiio of receivables flows corresodig o Years ad 2 ad Figure 3 he flows corresodig o Years 2 ad 3. Iiial soc: 47 Ery flow:,23,44 PROCESS Average soc: 87 Exi flow: 2,573 Fial soc: 227 Toal flow: 2,8 Flow of uis which have regisered ery ad exi: 2,426 Fig. 2. Flows Cosidered i Receivables Addig Years ad 2
2 Problems ad Persecives of Maageme, 24 Iiial soc: 78 Ery flow:,44,758 PROCESS Average soc: 23.5 Exi flow: 3,93 Fial soc: 283 Toal flow: 3,376 Flow of uis which have regisered ery ad exi: 2,95 Fig. 3. Flows Cosidered i Receivables Addig Years 2 ad 3 Table 4 shows ha he ierval of ossible values corresodig o he Cash Coversio Cycle whe we combie wo years reduces he ierval of ossible values o half of he value reseed i Table 3. I syhesis, aig eriods of ime wih leghs of years reduce he ierval defied by he urover accouig raios imes, aroximaely, so i is ossible o gai i recisio. A he ime of comarig differe comaies, or whe we wa o mae redicios of he fuure, we could be ieresed i his icreme i he recisio of he ierval. However, i also reses icoveieces, erhas very imora whe he evoluio of a cocree firm is evaluaed, sice he comarisos really are made bewee iervals of a miimum of years. I he examle show i Table 4, oe could oly comare he evoluio bewee Year ad Year 3, sice Year 2 aears i all of he calculaios. Coclusio This wor has aalysed he roblems of evaluaig he Cash Coversio Cycle hrough accouig iformaio. To do so, differe averages of days ha a ui has bee i a rocess have bee defied. Aferwards, hese defiiios have bee comared wih he accouig aroaches habiually used by aalyss. Oe of he mai coribuios of his ar of he wor lies i showig he assumios which are beig carried ou whe he accouig aroaches are ierreed as heoreical average eriods which some uis have bee i i he oeraig rocess. The resuls show ha i all of he cases assumios mus be carried ou wih a lac of owledge abou heir
Problems ad Persecives of Maageme, 24 3 degree of fulfilme. The ye of assumios made seems o be more difficul o be fulfilled i he followig siuaios: a) I o seady sae firms (firms which are growig or decliig). b) Firms devoed o aciviies which require maiaiig log oeraig cycles. c) Firms which, due o iflueial exeral facors, have o-sable worig caial requiremes. I is ieresig o highligh ha he accouig iformaio allows us o esablish some limis bewee which some of he averages of defied days will vary, ad ha hese limis will allow us o formulae a clearer ierreaio of he accouig raios. Subsequely, a racical alicaio of he roosed raios has bee carried ou, wih secial emhasis o he roblems of quaificaio. More secifically, he widh of he iervals bewee which some of he heoreical average eriods could vary is show. The ossibiliy of grouig he years cosidered i he average i order o gai recisio i he calculaio of he average eriods aalysed has also bee roosed. This roosal has drawbacs, maily, whe he evoluio of he Cash Coversio Cycle i a cocree comay for a log eriod of ime is aalysed, sice he comarisos are o carried ou from year o year. I oher words, a very recise quaificaio of he heoreical cash coversio cycle ca be obaied, bu he rice o be aid is ha he average eriod which mus be cosidered coais eriods of ime which corresods o wo years or more. For his reaso, his rocedure is o very useful if we are ieresed i aalysig he chages i he Cash Coversio Cycle wih secial focus o he very ear shor erm eriods of ime. Neverheless, we believe ha our roosal reses some ieresig feaures which ca be used by he aalys if icreasig he reliabiliy of he aalysis is cosidered as a fudameal goal. So, he, if o a yearly basis he worig caial maageme of wo firms is beig bechmared, he differeces bewee he eriods derived from he accouig urover raios have o be ae oe of wih more ieres if he ierval of ossible values (afl - ao) reses lile differeces raher ha if hese differeces are big. I oher words, as a ool i shor erm fiacial aalysis, he ierval could exercise as a idicaor of degree of accuracy whe we are quaifyig he Cash Coversio Cycle usig oly exeral accouig iformaio. Whe he aalys has fiacial saemes corresodig o several eriods, his roblem ca be cosiderably reduced because he ca reduce he ierval of maximum ad miimum values ad, comaraively, he ca also verify he imac of imroveme or deerioraio i he maageme of worig caial magiudes. To coclude, our wor has bee direced owards rovidig addiioal ools for fiacial saemes aalysis i order o obai a more accurae diagosis or worig caial maageme. Neverheless, here are sill some usolved quesios which eed more aeio i he fuure. Amog hem, a ossible fuure exesio could be how o mae sure ha coversio days measured by he same rules are beig added: he receivables coversio eriod aes sales rices while he iveory coversio eriod is measured usig oeraig coss rules.
4 Problems ad Persecives of Maageme, 24 Refereces. Abarbaell JS ad Bushee BJ (997). Fudameal Aalysis, Fuure Earigs ad Soc Prices. Joural of Accouig Research. 35,, -24. 2. Bacer M ad Gosma ML (98) The use of fiacial raios i credi dowgrade decisios. Fiacial Maageme. Srig, 53-56. 3. Chariou A (997) The role of cash flows accruals i exlaiig securiy reurs: evidece for he UK. The Euroea Accouig Review. 6, 4, 629-652. 4. Che KH ad Shimerda T.A. (98) A Emirical Aalysis of Useful Fiacial Raios. Fiacial Maageme. Srig, 5-6. 5. Ciro D, Robbie K. ad Wrigh M (997) Loa Coveas ad Relaioshi Baig i MBOs. Accouig ad Busiess Research. 27, 4, 277-294. 6. Dechow PM (994) Accouig earigs ad cash flows as measures of firm erformace. The role of accouig accruals. Joural of Accouig ad Ecoomics. 8, 3-42. 7. Drae PD ad Peavy III JW (995) Fudameal Aalysis, Soc Prices, ad he Demise of MiiScribe Cororaio. The Joural of Porfolio Maageme.2, 3, 68-73. 8. Foser G (986) Fiacial Saeme Aalysis. Preice Hall ed., Eglewood Cliffs, Secod Ediio. 9. Galliger GW (997) The curre ad quic raios: do hey sad u o scruiy?. Busiess Credi. 99, 3, 22-25.. Gombola MJ, Hasis ME, Kez JE ad Williams DD (987) Cash Flow i Barucy Predicio. Fiacial Maageme. Wier, 55-65.. Holmsrom J (994) The relaioshi bewee seed ad roduciviy i idusry ewors: A sudy of idusrial saisics. Ieraioal Joural of Producio Ecoomics. 34, 9-97. 2. Krisy JE (994) Coquerig Fiacial Raios: he Good, he Bad ad he Who Cares?. Busiess Credi. 96, 2, 4-9. 3. Lev B ad Thiagaraa R (993) Fudameal Iformaio Aalysis. Joural of Accouig Research. 3, 2, 9-25. 4. Maess TS (994) The Cash-Flow Timelie ad he Credi Maager. Busiess Credi. JulyAugus, -2. 5. Orí P ad Prior D (992) El eriodo de ermaecia de las magiudes de circulae: recisioes y requisios ara su correca deermiació. Revisa Esañola de Fiaciació y Coabilidad. XXI, 7, 65-9. 6. Orí P ad Prior D (993) Por qué os equivocamos al calcular el eriodo medio de maduració? Alguas cosideracioes rácicas. Acualidad Fiaciera. 29, 357-38. 7. Ou JA ad Pema SH (989) Fiacial saeme aalysis ad he redicio of soc reurs. Joural of Accouig ad Ecoomics., 4, 295-329. 8. Ozca YA ad Mcue M (996) Develome of a Fiacial Performace Idex for Hosials: DEA Aroach. Joural of he Oeraioal Research Sociey. 47,,8-26. 9. Pla HD ad Pla MB (99) A oe o he use of idusry-relaive raios i barucy redicio. Joural of Baig ad Fiace. 5, 6, 83-94. 2. Rezlaff-Robers DL (996) A raio model for discrimia aalysis usig liear rogrammig. Euroea Joural of Oeraioal Research. 94,, 2-2. 2. Richards VD ad Laughli EJ (98) A Cash Coversio Cycle Aroach o Liquidiy Aalysis. Fiacial Maageme. 9,, 32-38. 22. Saccurao F (994) The sudy of worig caial. Busiess Credi. 96,, 36-37. 23. Sicey CP (993) Fiacial Saeme Aalysis. A Sraegic Persecive. 2 d. Ediio. The Dryde Press. 24. Tie M (99) A Iduced Theory of Fiacial Raios. Accouig ad Busiess Research. 2, 8, 77-85.
Problems ad Persecives of Maageme, 24 5 25. Welsch GA, Hilo RW ad Gordo PN (988) Budgeig. Profi Plaig ad Corol. Preice Hall Ieraioal, 5 h ediio. 26. Williamso RW (984) Evidece o he Selecive Reorig of Fiacial Raios. The Accouig Review. LIX, 2, 296-299. 27. Wiigo G (98) Some Basic Proeries of Accouig Raios. Joural of Busiess Fiace & Accouig. 7, 2, 29-222.
6 Problems ad Persecives of Maageme, 24 Aedix Assumios uder Which he Accouig Aroximaios Will be Equal o he Differe Average Days of Say A o A e A ex A fl P o - A B C P e D E F G P ex H I J K P fl L M N - P - O P - There is a leer oly i hose cases i which he codiio of equaliy is more geeral ha he case of iiial ad fial socs equal o zero. A: '. Whe he raio bewee he ery flow ad he oal flow of uis which were more ha oe day of he accouig year i he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which have bee rese more ha oe day of he year i he rocess mulilied by he days, of his or oher years, rese. B: ' 2. Whe he raio bewee he exi flow ad he oal flow of uis which were more ha oe day of he accouig year i he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which have bee rese more ha oe day of he year i he rocess mulilied by he days, of his or oher years, rese. C: ' 3. Whe he raio bewee he uis which came i ad we ou of he rocess durig he year ad he oal flow of uis which were more ha oe day of he accouig year i he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which have bee rese more ha oe day of he year i he rocess mulilied by he days, of his or oher years, rese. D: ' 4. Whe he raio bewee he oal flow of uis which were more ha oe day of he accouig year i he rocess ad he ery flow i he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which came i durig he rocess his year mulilied by he days, of his or oher years, rese. E: ' ( ' ) 5. Whe he sum of he iiial soc mulilied by he days rese i his year, is equal o he sum of fial socs mulilied by he days rese i he ex year. F: ' 6. Whe he raio bewee he uis which came i ad we ou of he rocess durig he year ad he ery flow i he rocess is equal o he raio of he sum of daily soc balace ad he
Problems ad Persecives of Maageme, 24 7 sum of he value of he uis which came i he rocess his year mulilied by he days, of his or oher years, rese. G: ' 7. Whe he raio bewee he exi flow i he rocess ad he ery flow of he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which came i he rocess his year mulilied by he days, of his or oher years, rese. H: ' 8. Whe he raio bewee he oal flow of uis which were more ha oe day of he accouig year i he rocess ad he exi flow i he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which we ou of he rocess his year mulilied by he days, of his or oher years, rese. I: ' 9. Whe he raio bewee he ery flow of uis i he rocess his year ad he exi flow i he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which we ou of he rocess his year mulilied by he days, of his or oher years, rese. J: ' ( ' ). Whe he sum of he fial soc mulilied by he days rese i his year, is equal o he sum of iiial socs mulilied by he days rese i he year before. K: '. Whe he raio bewee he uis which came i ad we ou of he rocess durig he year ad he exi flow i he rocess is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which we ou of he rocess his year mulilied by he days, of his or oher years, rese. L: ' 2. Whe he raio bewee he oal flow of uis which were more ha oe day of he accouig year i he rocess ad he uis which came i ad we ou of he rocess durig he year is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which came i ad we ou of he rocess durig his year mulilied by he days rese. M: ' 3. Whe he raio bewee he ery flow i he rocess durig he year ad he uis which came i ad we ou of he rocess durig he year is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which came i ad we ou of he rocess durig his year mulilied by he days rese. N: ' 4. Whe he raio bewee he exi flow of he rocess durig he year ad he uis which came i ad we ou of he rocess durig he year is equal o he raio of he sum of daily soc balace ad he sum of he value of he uis which came i ad we ou of he rocess durig his year mulilied by he days rese. O: ( ' ) ( ' )
8 Problems ad Persecives of Maageme, 24 5. The sum of he iiial ad fial socs balaced by he raio bewee he days of his year rese, ',ad he oal days rese, is equal o he fial soc. P: ( ' ) ( ' ) 6. The sum of he iiial ad fial socs balaced by he raio bewee he days of his year rese, ',ad he oal days rese, is equal o he iiial soc.
Problems ad Persecives of Maageme, 24 9 Aedix 2 Assumios uder Which Accouig Raios a o ad a fl are he Iferior ad Suerior Limis of he Average Periods of Presece o, fl, ad. ) Raio ao will be always less ha or equal o he value of he average days of say of he yearly oal flow o. 2) Raio af will be greaer ha or equal o he value of he average days of resece of he yearly oal flow o, whe: ' ( ) ( ' ) a) The balaced average days of resece oly i he revious year of he iiial socs is o greaer ha he average days of resece of he yearly oal flow. b) The balaced average days of resece oly i he ex year of he fial socs is o greaer ha he average days of resece of he yearly oal flow. Proosiio 2 is also rue if oe of he codiios, a) or b), is o fulfilled, bu heir absolue value is less ha he absolue value of he oher codiio. 3) Raio ao will be less ha or equal o he value of he average days of resece of he uis which came i ad we ou durig he year fo, whe: ' ' ( ) ( f f ) a) The balaced average days of resece oly i his year of he iiial socs is o greaer ha he average days of resece of he uis which came i ad we ou durig he year. b) The balaced average days of resece oly i his year of he fial socs is o greaer ha he average days of resece of he uis which came i ad we ou durig he year. Proosiio 3 is also rue if oe of he codiios, a) or b), is o fulfilled, bu heir absolue value is less ha he absolue value of he oher codiio. 4) Raio afl always will be greaer ha or equal o he value of he average days of resece of he uis which came i ad we ou durig he year fl. 5) Raio ao always will less ha or equal o he value of he average days of resece i he year. 6) The raio afl always will be greaer ha or equal o he value of he average days of resece i he year. All of hese relaios could be obaied wih some algebra. The auhors will mae all of he iformaio requesed available.