An aggregate measure of financial ratios using a multiplicative DEA model

Transcription

1 It. J. Fiacial Services Maagemet, Vol. X, No. Y, XXXX A aggregate measure of fiacial ratios usig a multiplicative DEA model Ali Emrouzead* Asto Busiess School, Asto Uiversity, Birmigham, UK a.emrouzead@asto.ac.uk *Correspodig author Emily Cabada Global Leadership & Etrepreeurship, Reget Uiversity, Virgiia Beach, VA, USA ecabada@reget.edu Abstract: This paper examies the problems i the defiitio of the Geeral No-Parametric Corporate Performace (GNCP) ad itroduces a multiplicative liear programmig as a alterative model for corporate performace. We verified ad tested a statistically sigificat differece betwee the two models based o the applicatio of 27 UK idustries usig six performace ratios. Our ew model is foud to be a more robust performace model tha the previous stadard Data Evelopmet Aalysis (DEA) model. Keywords: DEA; data evelopmet aalysis; fiacial ratio; GNCP; geeral o-parametric corporate performace; MNCP; multiplicative o-parametric corporate performace. Referece to this paper should be made as follows: Emrouzead, A. ad Cabada, E. (xxxx) A aggregate measure of fiacial ratios usig a multiplicative DEA model, It. J. Fiacial Services Maagemet, Vol. x, No. y, pp.xxx xxx. Biographical otes: Ali Emrouzead is a Seior Lecturer of Operatioal Research Group at Asto Uiversity, UK. His areas of research iterest iclude performace measuremet ad maagemet, efficiecy ad productivity aalysis as well as data miig. He acted as Guest Editor of special issues i a umber of ourals icludig Joural of Operatioal Research Society ad Aals of Operatios Research i data evelopmet aalysis. He is a member of the Operatioal Research Society of UK, Secretary of Midlad Operatioal Research Society, ad co-fouder of Performace Improvemet Maagemet Software (DEA-PIMsoft). Emily Cabada is a Associate Professor of Operatios at the School of Global Leadership & Etrepreeurship, Reget Uiversity, USA. She also served as a Visitig Professor at Yokohama Natioal Uiversity (2006) ad Iteratioal Christia Uiversity (2007) i Japa. She also taught i the Graduate School at the Uiversity of Sato Tomas i the Philippies. She has Copyright 200X Idersciece Eterprises Ltd.

2 A. Emrouzead ad E. Cabada published articles i operatios ad busiess ourals ad book chapters, ad co-authored a book o performace maagemet. Her research iterests are i performace maagemet, operatios research, applicatios of data evelopmet aalysis models, ad privatisatio. Itroductio I maagerial decisio-makig, the traditioal idicators for performace evaluatio are fiacial ratios such as profitability, leverage, liquidity ad efficiecy ratios, amog others. Fiacial ratios have achieved a widespread use i practice because of their relative simplicity i computatio, easy to uderstad ad serve as valuable tools of iterpretig the fiacial statemets. More importatly, fiacial ratios also eable aalysts to coduct a certai degree of compariso across firms of differet sizes ad of firms with the total idustry. We ca cite may specific applicatios of fiacial ratios, but most fiacial maagemet textbooks have grouped them ito four categories: performace evaluatio, descriptio of the idustry or firm-specific coditios, predictios, ad preparatio of bidig cotracts. As early as 966, a model developed by William Beaver (966) used fiacial statemet iformatio to predict corporate bakruptcy, usig a discrimiat aalysis. Subsequetly, it gaied widespread popularity, but attempts to estimate probabilities of failure istead of classificatios-yielded questioable results. Techically speakig, the statistical assumptio of multivariate ormality i udertakig a discrimiat aalysis is ofte violated. May fiacial ratios are ot ormally distributed because they have lower or upper bouds (Ezzamel et al., 987; Watso, 990). I regressio-based techiques, the assumptio of proportioality is violated ad the distributio is skewed. I the uivariate ratio approach, the maor weakess is o its specificatio requiremet of a small set of idicators to examie but does ot help much the aalyst i the recociliatio of coflictig sigals amog competig ratios. This approach also igored iformatio cotaied i the iterdepedecies betwee ratios. Thus, the pricipal obstacle to the use of traditioal statistical techiques is the techical difficulty of developig a acceptable model (Feradez-Castro ad Smith, 994). The use of fiacial parameters to describe states ad dyamics of fiacial market ad to evaluate corporate performace is widespread i the literature (Bares, 987; Walter ad Robert, 988; Whittigto, 980; Salami ad Martikikaie, 994). Most of these parameters deped o proportios of the appropriate variables rather tha o their actual values. A commo feature of all areas of fiacial ratio aalysis seems to be that while sigificat regularities ca be observed, they are ot stable across differet ratios, idustries ad time period (Salami ad Martikikaie, 994). However, oe maor cautio o the use of ratio aalysis is that a sigle ratio does ot geerally provide sufficiet iformatio from which to udge the overall performace of a firm. Oly whe a group of ratios is used ca reasoable udgemets be made (see Gitma, 2000). Geerally, there is o criterio for selectig a ratio that is agreeable by all users. Therefore, a lack of a obective stadard for selectig the ratios would cause istability ad could ot satisfy the eeds of all users.

3 A aggregate measure of fiacial ratios The use of fiacial performace idicators represet a partial measuremet of a corporate performace ad focused oly o short-term results. Fiacial measures are based o sigle iput factors to a corporatio s output, ad do ot have partial effect of other iput(s). Corporate performace is recogised as a multi-dimesioal costruct sice it covers diverse ad various variables (aside from fiacial ratios) (Zhu, 2000). There are other o-fiacial performace idicators that importatly cosidered i today s complex global market eviromet such as maufacturig capability, iovatio capability ad supply-chai relatioship, usig Data Evelopmet Aalysis (DEA) ad fuzzy multi-criteria approach (Tseg et al., 2009). The combied fiacial ad ofiacial idicators for corporate performace evaluatio are also evidet i most curret literature, usig the DEA method (Feroz et al., 2003; Halkos ad Salamouries, 2004; Yag, 2007; Guzma ad Arcas, 2008; Sueyoshi ad Goto, 2009). Fiacial ratio aalysis ca also be used for measurig productio efficiecy ad operatig efficiecy (Moyiha et al., 2006) ad also Wag ad Lee (2008) preseted a clusterig method to idetify represetative of fiacial ratios. It is clear i the precedig discussio that there is a eed to cotiuously search for a more robust method of aalysig fiacial ratios. I the existig efficiecy literature there has bee a icreasig iterest i o-parametric techiques to measure a firm s performace. The most widely used o-parametric method is DEA that have bee applied i the performace evaluatio of baks, fiacial istitutios, uiversities, hospitals ad health orgaisatios, maufacturig ad service idustries, etc. (see Emrouzead et al., 2008). DEA has a uique property that does ot require specificatio of the fuctioal forms for the frotier of performace possibilities compared to traditioal statistical regressio techiques. As such, DEA ca be a alterative method of aalysig fiacial ratios which do ot deped o usustaiable assumptios. DEA is a distributio-free method ad also does ot assig pre-specified weights. Aother strikig characteristic of DEA, which is useful i our preset aalysis, is its ability of providig a aggregate measure of efficiecy, usig multiple outputs ad iputs as idicators of performace. The multi-dimesioal ature of corporate performace is better addressed by the multi-factor criteria of DEA that ca provide a geeral measure of a corporate performace compared to the iadequate covetioal growth accoutig model, which yields oly a partial performace measure. Feradez-Castro ad Smith (994) itroduced a semial model of the Geeral No-Parametric Corporate Performace (GNCP) that combies all fiacial ratios to a sigle measure, usig the stadard DEA model. This semial work was a good startig poit for aggregatig the fiacial ratios ito a sigle measure of corporate performace usig the DEA model whe o iput variables are ivolved. However, we foud that there are critical issues (techical i ature) i usig the stadard DEA model to costruct a aggregate measure. This is the apparet motivatio of this paper, ad we will discuss this i succeedig sectios. This paper offers sigificat cotributios to the performace measuremet o the use of geometric meas with o-dimesioal properties (uit ivariace) rather tha weighted average of ratios. The use of a ew multiplicative DEA model ca provide advatages for extedig the rage of potetial uses for DEA, especially i corporate performace field due to its o-dimesioal ature ad therefore ca be used for the case that all variables are i the form of ratios. Our ew model here provides ew isights that a firm s efficiecy scores are derived from a multi-dimesioal data without a priori of fuctioal forms of the efficiet frotier. This is i cotrast to the arbitrary weights iheret i covetioal multivariate statistical techiques.

4 A. Emrouzead ad E. Cabada The remaiig part of this paper is orgaised as follows. Sectio 2 describes the GNCP model ad problems of usig this model. Sectio 3 itroduces a multiplicative liear programmig as a alterative model for corporate performace. This is followed by results ad discussio i Sectio 4. Sectio 5 presets our coclusio ad future research. 2 Corporate performace model developmet To develop our corporate performace model, we first describe the GNCP model of Feradez-Castro ad Smith (994) ad show why this model becomes problematic. We the develop the alterative multiplicative o-parametric corporate performace model for our empirical aalysis. 2. GNCP model Mostly DEA is udertake with absolute umerical data, which amog other thigs reflect the size of the uits of observatio. There are may cases reported i the DEA literature (Emrouzead et al., 2008) that the authors used ratio variables rather tha absolute umbers as iputs (iput ratios) ad/or outputs (output ratios). For example, a health database presets almost all its idicators i the form of ratios, such as expediture as a percetage of GDP, discharge rates from hospital per,00,000 populatio, ad aual umber of days lost through sickess per employee. Holligsworth ad Smith (2003) explaied that the CCR formulatio of Chares et al. (978) should ot be used; istead, the BCC formulatio of Baker et al. (984) must be used whe iput or output variables iclude a ratio. As oe of the maor developmets towards aggregatio of fiacial ratios, Feradez-Castro ad Smith (994) reformulated DEA to itroduce a model to combie a set of fiacial ratios to a sigle measure ad called it GNCP. This approach has bee used by may authors for compariso of DMUs (firms) ad i the presece of ratio outputs (for example, see Salias-Jimeez ad Smith, 996; Mar-Moliero ad Serrao-Cica, 200; Halkos ad Salamouris, 2004; Blacard et al., 2006). More examples ca be foud i the DEA comprehesive literature (Emrouzead et al., 2008). Let us start with the defiitio give by Feradez-Castro ad Smith (994, p.24). Suppose that there are N firms which are appraised o m fiacial ratios, ad that the observed ratios for firm are {r i ; i =,, m}. The problem of assessig the performace of a firm (say firm 0 ) ca be represeted as a liear programme. It is assumed that the ratios are ordered such that a higher level of ratio is preferred to a lower level. The, the GNCP approach of Feradez-Castro ad Smith (994) is preseted i Model, which we refer to it as GNCP efficiecy score of firm 0 : max h s.t. i = = r λ hr ; i =,, m λ = i0 λ 0 =,, ()

5 A aggregate measure of fiacial ratios Notice that, i cotrast to the origial Chares et al. (978) DEA model, o iputs are specified. The decisio variables i this liear programme are h, the proportio by which all the firm s ratios ca be icreased, ad {λ ; =,, }, which idicate the weight placed o each of the firms i formig the efficiecy frotier for firm 0. The efficiecy of firm 0 is the give by h. Feradez-Castro ad Smith (994) used this model to evaluate the performace of 27 idustries usig six fiacial ratios icludig cash positio, liquidity, workig capital positio, leverage, profitability ad turover. Emrouzead ad Ami (2009) have recetly show that the stadard DEA model may produce icorrect results i the presece of a ratio variable. The mai two problems of usig ratio as a iput ad/or a output i DEA are covexity ad proportioality properties of Productio Possibility Set (PPS). 2.2 The covexity issue DEA is defied based o observed uits ad by fidig the distace of each uit to the border of the PPS. The covexity is oe of the uderlyig properties of the PPS. It is obvious that the weighted sum of ratios does ot equal the ratio of weighted sum of omiators ad the weighted sum of deomiators, hece the covexity of ratio variable may cause problem i defiig PPS for DEA (for details, see Emrouzead ad Ami, 2009). 2.3 The proportioality issue The proportioality axiom i DEA models is aother uderlyig property of PPS, ad it defies as if output icreases by that same proportioal chage the there are costat returs to scale (CRTS), sometimes referred to simply as returs to scale. It is obvious that this property also does ot satisfy whe data are i the form of ratios, sice if the omiators ad deomiators icreased (decreased) by the same proportioal chage the ratio will ot be chaged (for details, see Emrouzead ad Ami, 2009). 3 MNCP model A ivestigatio of Model shows that the metioed problems arise because the covexity ad the proportioality properties of PPS both are correct whe arithmetic operatios are cosidered. I the case of GNCP the output variables are i the form of ratios, ad therefore ay arithmetic combiatio of ratios is meaigless. Alteratively, a multiplicative model should be cosidered. The aggregate measure results i that the multiplicative GNCP is of piecewise log-liear form rather tha piecewise liear form. A importat property of this model is that it uses the cocept of the geometric mea with o-dimesioal (uits ivariace) properties, ad hece, it is more suitable for all fiacial ratios data (see Emrouzead ad Ami, 2009). I this model, the validity proportioality assumptio for ratios is stregtheed.

6 A. Emrouzead ad E. Cabada For this purpose, we propose a Multiplicative No-parametric Corporate Performace (MNCP) model as follows. max h s.t. λ i = λ = r hr ; i =,, m = i0 λ 0 =,, This model is a specific case of multiplicative DEA model iitially proposed by Baker ad Maidiratta (994) (see also Seiford ad Thrall, 990). However, the differece is that ulike the stadard multiplicative DEA, similar to GNCP there is o iput ratio i this model. We use the followig trasformatio to covert the above multiplicative model to a liear programmig (Baker et al., 2004). Si h r = e r λ ; i =,..., m i 0 Now, replace the obective i Model 2 by i = hexp ε m ( s ) i= i (2) where S i 0 represets slacks ad ε is the o-archimedea ifiitesimal. Assume g = log(h) ad ρi = log( ri), employig the above trasformatio ad takig logarithm from equatio (2) we could coclude the followig model. max g + ε st.. m Si i= λ ρ si = g+ ρi o ; i =,, m i = (3) = λ, s 0 ; i =,, m & =,, λ = i Note that Model 3 is a output maximisatio ad efficiecy is iverse to the optimum value of obective fuctio i equatio (2). After solvig equatio (3) the efficiecy of firm 0 ca be obtaied from: h = g. e

7 A aggregate measure of fiacial ratios I most cases the fiacial ratios are values betwee 0 ad. I these cases the MNCP Model 3 caot be used directly sice the log-trasform of value less tha is egative, however MNCP requires positive values. Hece, we suggest usig the MNCP model after scalig the data as follows: Step. Assume all variables are positive, fid the miimum of each variable across all fiacial sector ad assume R = mi{ ri; i =,... m & =,... } ε, where ε is a positive value less tha mi{ ri; i =,..., m & =,..., }. The use of this ε guaratees a positive value for the log-trasform. Step 2. Amed the MNCP Model 2 to the followig model max h s.t. = λ = λ ri ri 0 h ; i =,, m R R = λ 0 =,, Obviously, we have sice λ λ λ λ r r r r i i i i = = = = = = λ = R R R R = = (4) Hece = λ R = ( R) λ = R, sice. λ = = λ ri ri 0 h implies that = R R =. r R i = λ ri 0 h, i.e. R r i = λ hr i 0.

8 A. Emrouzead ad E. Cabada As results, the obective values of Model 4 ad Model 2 are equal. However, Model 4 ca easily be trasferred to a log-liear form without ay problem as all values are ow ri positive (ote that ; i R sice R r i ; i ). Thus, this model ca be applied to all other ratios simultaeously. 4 Results ad discussio To demostrate that how we could combie the fiacial ratios to a sigle measure, we cosider the same data used by Feradez-Castro ad Smith (994). I order to illustrate the differeces betwee the two GNCP model ad MNCP model, we evaluate the performace of 27 idustries usig six fiacial ratios icludig: cash positio (cash/total assets), liquidity (curret assets/curret liabilities), workig capital positio (workig capital/total assets), leverage (log-term liabilities/total assets), profitability (et icome/total assets), ad turover (sales/total assets). The average ratio for each idustry is reported i Appedix A ad the results for both GNCP ad MNCP models are reported i Table. A score of 00% implies a efficiet idustry, ad below 00% is iefficiet. Table Idustry Combied measure, compariso of GNCP ad MNCP models Combied measure; GNCP (%) Rak-order GNCP Combied measure; MNCP (%) Rak-order MNCP Electrical Chemicals Idustrial plat Overseas trade Furishig stores Costructio Office equipmet Furishig stores I Multiple stores Egieerig Durable goods Costructio Costructio Motor distributors Food retailig Egieerig Metal formig Miscellaeous Istrumet makers

9 A aggregate measure of fiacial ratios Table Combied measure, compariso of GNCP ad MNCP models (cotiued) Idustry Combied measure; GNCP (%) Rak-order GNCP Combied measure; MNCP (%) Rak-order MNCP Trasport Metallurgy Idustrial holdigs Property Fiacial holdigs Mech. egieerig Pharmaceuticals Oil Mea It is oted that there are some egative ratios i the data; however, the MNCP Model 3, like stadard DEA Model 2, requires positive data. For this purpose ay egative ratio, as well as zero ratios, substitutes with a very small positive value (see Ali ad Seiford, 990; Lovell ad Pastor, 995). As described earlier, first we scaled the six variables as follows. As show before the rescalig, it will ot affect the optimum value of Model 3 but allow us to use Model 4, all variables of which are positive. We assume R = ; the models GNCP ad MNCP were applied ad results are reported i Table. The secod ad third colums show the combied measure ad rakig based o the GNCP model of Feradez-Castro ad Smith (994), the last two colums show the combied measure ad rakig based o the MNCP model as developed i this paper. Based o the two models, there are idustries, represetig 4% of the sample, that have produced similar ratigs ad rakigs. These are chemicals, idustrial plat, overseas trade, furishig stores, office equipmet, durable goods, costructio, food retailig, property, fiacial holdigs ad oil (refer to Table ). Sixtee idustries, 59% of the sample, have obtaied differet rakigs ad ratigs. For example, i the multiple stores, GNCP s efficiecy score (68.62%) is much lower tha MNCP s (97.2%) amog others. Overall, the mea efficiecy score (98.3%) i MNCP is higher tha that (85.85%) obtaied i GNCP. To verify the robustess of our ew model, we tested if there is a sigificat differece betwee the two models. We used the o-parametric Wilcoxo rak test sice this is a distributio-free test like the DEA. We foud that there is a sigificat differece (z statistic = 3.56) at 5% probability level i the ratig of idustries betwee GNCP ad MNCP models. Usig the correct measure of MNCP, more idustries are foud to be efficiet at the productio possibility frotier i the aggregate six fiacial ratios (see Figure ). Uder the stadard GNCP, more idustries are foud to be below the efficiecy frotier.

10 A. Emrouzead ad E. Cabada Figure Compariso of GNCP ad MNCP (see olie versio for colours) Uder the ew MNCP model, the validity proportioality assumptio for ratios is sustaied, ad we cofirmed the theoretical assumptios forwarded by Emrouzead ad Ami (2009). Therefore, our ew model is foud to be a more robust performace model tha the previous stadard DEA model. I this paper, the beefits ad maagerial implicatios of MNCP are the followig: It does ot require weights to be determied i combiig ratios for rakig of idustries i cotrast to a multivariate aalysis. Firm s efficiecy scores are derived without a priori of fuctioal forms of the efficiet frotier ad free from statistical distributios. Iefficiet firms ca bechmark the best-practice firms o the frotier ad provides iformatio o feasible targets for improvemets i the ratios. These ew isights may help maagers i their decisio-makig i which ratio dimesios of performace eed improvemets. We have show here the correct ad techically appropriate way of usig a DEA model for fiacial ratio aalysis without discoutig the geeral beefits of the stadard DEA model. This ew multiplicative DEA model ca ope ew areas for extedig the potetial advatages ad applicatios of DEA for performace evaluatio. 5 Coclusios ad future research This research has examied the critical issues i the defiitio of GNCP ad has itroduced a multiplicative liear programmig as a alterative model for corporate performace. The MNCP model is verified, ad prove to be a valid model based o the earlier work of Emrouzead ad Ami (2009) ad the previous beefits as discussed earlier. We verified ad tested a statistically sigificat differece betwee the two models based o the applicatio of 27 UK idustries usig six performace ratios.

11 A aggregate measure of fiacial ratios This research is ust a startig poit ad opes may areas for further ivestigatio o the DEA performace field. Future theoretical research is eeded to draw properties of MNCP such as duality, weights ad returs to scale assumptios. I additio, future empirical research will focus o the maagerial implicatios of MNCP o the performace of ay firms, sub-uits or regios usig all fiacial ratios ad to be combied with other o-fiacial idicators. Aside from the DEA model, other statistical techiques should be used to complemet ad verify the MNCP results. These issues are also the limitatios of this paper. Fially, this research forms as part of a cotiuig research o potetial uses ad applicatios of the o-parametric DEA model as a corporate performace measuremet. Refereces Ali, A. ad Seiford, L.M. (990) Traslatio ivariace i data evelopmet aalysis, Operatios Research Letters, Vol. 9, pp Baker, R.D., Chares, A. ad Cooper, W.W. (984) Models for estimatio of techical ad scale iefficiecies i data evelopmet aalysis, Maagemet Sciece, Vol. 30, pp Baker, R.D., Cooper, W.W., Seiford, L.M., Thrall, R.M. ad Zhu, J. (2004) Returs to scale i differet DEA models, Europea Joural of Operatioal Research, Vol. 54, pp Baker, R.D. ad Maidiratta, A. (986) Piecewise log-liear estimatio of efficiet productio surfaces, Maagemet Sciece, Vol. 32, pp Bares, P. (987) The aalysis ad use of fiacial ratios: a review article, Joural of Busiess, Fiace ad Accoutig, Vol. 4, pp Beaver, W.H. (966) Fiacial ratios as predictors of failure, Joural of Accoutig Research, Vol. 4, pp.7. Blacard, S., Boussemar, J.P. ad Debruye, M. (2006) Assessig maagerial performace usig o-parametric distace fuctios compared to techical ad accoutig ratio aalysis: a applicatio to Frech farms i Nord-Pas-de-Calais specialized i field crops, Lille Ecoomie ad Maagemet, Vol Chares, A., Cooper, W.W. ad Rhodes, E. (978) Measurig the efficiecy of decisio-makig uits, Europea Joural of Operatioal Research, Vol. 2, No. 6, pp Emrouzead, A. ad Ami, G.R. (2009) DEA with ratio data: covexity cosideratio, Applied Mathematical Modellig, Vol. 33, pp Emrouzead, A., Parker, B. ad Tavares, G. (2008) A bibliography of data evelopmet aalysis, Socio-Ecoomics Plaig Sciece, Vol. 42, No. 3, pp Ezzamel, M., Mar-Moliero, C. ad Beecher, A. (987) O the distributioal properties of fiacial ratios, Joural of Busiess Fiace ad Accoutig, Vol. 4, pp Feradez-Castro, A. ad Smith, P. (994) Towards a geeral o-parametric model of corporate performace, Omega, Vol. 22, No. 3, pp Feroz, E., Kim, S. ad R. Raab (2003) Fiacial statemet aalysis: a data evelopmet aalysis approach, Joural of the Operatioal Research Society, Vol. 54, pp Gitma, L. (2000) Priciples of Maagerial Fiace, 9th ed., Addiso-Wesley, USA, pp Guzma, I. ad Arcas, N. (2008) The usefuless of accoutig iformatio i the measuremet of techical efficiecy i agricultural cooperatives, Aals of Public ad Cooperative Ecoomics, Vol. 79, pp Halkos, G.E. ad Salamouris, D.S. (2004) Efficiecy measuremet of the Greek commercial baks with the use of fiacial ratios: a data evelopmet aalysis approach, Maagemet Accoutig Research, Vol. 5, pp

12 A. Emrouzead ad E. Cabada Holligsworth, B. ad Smith, P. (2003) The use of ratios i data evelopmet aalysis, Applied Ecoomics Letters, Vol. 0, pp Lovell, C.A.K. ad Pastor, J.T. (995) Uits ivariat ad traslatio ivariat DEA models, Operatios Research Letters, Vol. 8, pp Mar-Moliero, C. ad Serrao-Cica, C. (200) Bak failure: a multidimesioal scalig approach, Europea Joural of Fiace, Vol. 7, No. 2, pp Moyiha, G.P., Jai, V., McLeod, R.W. ad Foseca, D.J. (2006) A expert system for fiacial ratio aalysis, Iteratioal Joural of Fiacial Services Maagemet, Vol., Nos. 2 3, pp Salami, T. ad Martikikaie, T. (994) A review of the theoretical ad empirical basis of fiacial ratio aalysis, The Fiish Joural of Busiess Ecoomics, Vol. 4, pp Salias-Jimeez, J. ad Smith, P. (996) Data evelopmet aalysis applied to quality i primary health care, Aals of Operatios Research, Vol. 67, No., pp.4 6. Seiford, L.M. ad Thrall, R.M. (990) Recet developmets i DEA: the mathematical programmig approach to frotier aalysis, Joural of Ecoometrics, Vol. 46, pp Sueyoshi, T. ad Goto, M. (2009) Ca R&D expediture avoid corporate bakruptcy? Compariso betwee Japaese machiery ad electric equipmet idustries usig DEAdiscrimiat aalysis, Europea Joural of Operatioal Research, Vol. 96, pp Tseg, F-M., Chiu, Y-J. ad Ja-She, C. (2009) Measurig busiess performace i the high-tech maufacturig idustry: a case study of Taiwa s large-sized TFT-LCD pael compaies, Omega, Vol. 37, pp Walter, B.M. ad Robert, F.M. (988) Accoutig: The Basis for Busiess Decisios, McGraw-Hill, New York. Wag, Y-J. ad Lee, H-S. (2008) A clusterig method to idetify represetative fiacial ratios, Iformatio Scieces, Vol. 78, No. 4, pp Watso, C. (990) Multivariate distributioal properties, outliers ad trasformatio of fiacial ratios, Accoutig Review, Vol. 65, pp Whittigto, R.G. (980) Some basic properties of accoutig ratios, Joural of Busiess, Fiace ad Accoutig, Vol. 7, pp Yag, H-L. (2007) The effect of fiacial idepedece o the performaces of life compaies: a empirical study, Iteratioal Joural of Maagemet, Vol. 24, No. 3, pp Zhu, J. (2000) Multi-factor performace measure model with a applicatio to Fortue 500 compaies, Europea Joural of Operatioal Research, Vol. 23, pp

13 A aggregate measure of fiacial ratios Appedix A Idustry average of fiacial ratio* Idustry Cash positio Liquidity Workig capital positio Leverage Profitability Turover r r 2 r 3 r 4 r 5 r 6 Electrical Chemicals Idustrial plat Overseas trade Furishig stores Costructio Office equipmet Furishig stores I Multiple stores Egieerig Durable goods Costructio Costructio Motor distributors Food retailig Egieerig Metal formig Miscellaeous Istrumet makers Trasport Metallurgy Idustrial holdigs Property Fiacial holdigs Mech. egieerig Pharmaceuticals Oil *Source: Adapted from Feradez-Castro ad Smith (994, p.245)