Act Unv. Bohem. Merd. 0, 6(), 5-5, ISSN -85 The Possbltes of Dfference Anlss Utlston n Proft te Assessment Mre Vejsdová Drjová Abstrct: The mn m of ths rtcle s the pplcton of selected methods of dfference nlss to the chosen proft ndctor of eturn on Equt (OE). Frst, the mportnce of the OE ndctor s descrbed n the pper nd then, lso, the possble methods of prmdl decomposton n multplctve structures e. the method of grdul chnges, the decomposton method wth resdue, the logrthmc method nd the functonl method. The prmdl decomposton of the OE top ndctor s mplemented usng the functonl method, the onl one tht cn be used n the cse of negtve volume nde ndctor nd, t the sme tme, ths method s not senstve to the order of the fctors. In concluson, the ssessment of the mpct of prtl nltcl ndctors of prmdl decomposton on the top nlsed ndctor of OE s ccomplshed. The degree of vrous nfluences of sub-ndctors on the OE top ndctor, n the nlsed perods, ws dfferent. The OE ndctor ws most ffected b the Sles Proftblt ndctor on the second level of decomposton. In the frst nd lst ssessment perods, the Sles Proftblt ndctor ws determned b the Cost Effcenc ndctor, n the frst, nd n the second perod, b the cost of sles ndctor. The prtl fctor Fnncl Leverge ffected the OE the lest wthn the ssessment perod. The T Ernngs educton ndctor followng the Interest Ernngs educton ndctor presented the stronger nfluence on the OE fter the Fnncl Leverge ndctor. Ke words: eturn on Equt OE Prmdl Decomposton Functonl Method JEL Clssfcton: C0 G0 Q Introducton The bsc crteron for the ssessment of the proft rte s the eturn on Equt OE, lso known s the eturn on Invested Cptl. Generll, the OE ndctor cn be chrctersed s rto of proft nd equt sources, nvested cptl. The proft, n the proftblt ndctors, cn dffer dependng on whether t s: used Ernngs before Interest nd Tes EBIT, Ernngs before Interest EBT, Ernngs fter Tes EAT or Ernngs fter Tes ncresed b Interest Epenses. The most wdel used form of ernngs n the OE ndctor hs become Ernngs fter Tes, whch best descrbes the trnscton outcome nd s not ffected b the sources from whch the ctvtes of frm re fnnced. The OE ndctor reflects the overll proftblt of compn s own sources nd ther evluton n terms of proft. The level of the OE ndctor depends on the Totl eturn on Equt nd the Interest te on Debt. The ndsputble dvntge of ths ndctor s the possble dentfcton of substntl reltons between nltc ndctors nd the blt to epress these reltons usng smple mthemtcl opertons. Then, the whole sstem of the eturn on Equt decomposton cn be creted, s the top ndctor, to the prtl nltc ndctors. Ths tpe of decomposton s known s prmdl decomposton of OE e. Du Pont Prmdl Decomposton (Dluhošová, 00). Ing. Mre Vejsdová Drjová, Ph.D. Unverst of South Bohem n České Budějovce, Fcult of Economcs, Deprtment of Accountng nd Fnnce, Studentská, 70 05 České Budějovce, e-ml: vejsdov@ef.jcu.cz.
M. Vejsdová Drjová 6 Lterture revew One of the chrcterstcs of the fnncl nltcl tsks s the dfference nlss of snthetc ndctors nd the quntfcton of the effects tht nfluenced the top ndctor. One possblt of how to solve the tsk s to ppl the method of prmd decomposton of snthetc top ndctor to prtl nltc ndctors. The decomposton llows the dentfcton of prtl effects on the top ndctor. The lnks wthn the prmd decomposton re recorded s mthemtcl equtons nd then the whole prmd reflects sstem of equtons. The most mportnt fctor for prmdl sstem utlston s the methodologcll correct soluton of the constructon of sstem of ndctors nd the method of quntfng the prtculr fctors effects. A cusl relton between the top ndctor nd sub-ndctors s descrbed b Foršková & chtrová (00) usng the functon:, () Ths represents the effect of sub-ndctors on chnges observed n the selected top ndctor. The top ndctor dfference s defned s the sum of prtl effects (dfferences) of the nltcl ndctors, e.: Where: Is the nlsed ndctor. Is the mpct ncrese n the nlsed ndctor. Is the prtl eplntor ndctor. Is the sub-ndctor effect of on the nlsed ndctor. In the prmdl decomposton, the functon (l) cn be epressed b n ddtve or multplctve structure (Dluhošová, 00). The m of ths pper s the prmdl decomposton of the OE ndctor tht uses, onl, multplctve structure of sub-ndctors nd then, lter, the methodolog of multplctve structure wll be further reserched. As Zl et l. (000) nd Zmeškl, Dluhošová & Tchý (00) stted, wthn the process of prmdl decomposton there cn be ppled four bsc methods for multplctve structure the method of grdul chnges, the method of decomposton wth resdue, the logrthmc method nd the functonl method.. The method of grdul chnges In ths method the totl dfference s dvded nto prtl effects. Generll, t s possble to quntf the sub-ndctors effects for n progresson s: j 0 j, j j () (), The dvntge of ths method s the clculton smplct nd the resdue decomposton. In contrst, the mn dsdvntge of ths method s tht the sze of the effects of prtculr ndctors depends on the sequence chrcterstcs. The method of grdul chnges s frequentl used n prctce, but t s lws necessr to mntn the methodolog nd the ndctors sequence.. The method of resdue decomposton Unlke the prevous method, the method of resdue decomposton s not ffected b the ndctors sequence - the decomposton s the onl one nd unque. The problem wth ths method, however, s the estence of the resdul component tht cnnot be unmbguousl nterpreted nd ssgned to prtculr effects. Although, there re severl ws to dvde resdul component nfluences, none of
The Possbltes of Dfference Anlss Utlston n Proft te Assessment 7 them cn be descrbed s beng the most sutble. In prctce, the method s used onl n the presence of the smll resdul component. Generll, for n number of sub-ndctors the fctor effect cn be epressed s: where the resdue s: n.. j, 0 j n j. j 0 n, (),. (5). The logrthmc method The logrthmc method, t the sme tme, tkes nto ccount ll ndctors chnge wthn the eplnton of prtculr effects, there s no problem wth the ndctors sequence nd resdue creton. The onl dsdvntge of ths method s tht t s bsed on logrthms of ndces clcultng, e. the logrthms of ndces must present postve vlue. If the compn mkes loss one er nd cheves proft the second er the logrthms of nde cnnot be clculted. Ths method results from contnul revenue s ln I nd ln I mens the contnul revenue of ndctors nd. The effects of prtculr ndctors re epressed s follows: Where: I 0. The functonl method ln I. ln I, (6), I re the ndces of nlsed nd sub-ndctors.,0 The onl soluton, n whch the logrthms of nde show the negtve vlue, s the utlston for prtculr prt of brnch decomposton b the functonl method. The functonl method tkes nto ccount the effect of ll sub-ndctors wthn the eplnton of prtculr effects. The top ndctor dfference s gven b the sum of dfferences (effects) of sub-ndctors; the totl dfference cn be epressed s:, (7) Where: Is the nlsed ndctor Is the ncrese n the mpct n the nlsed ndctor Is the sub-ndctor Is the sub-ndctor effect on the nlsed ndctor The method s bsed on the dscrete revenues nd whch re the dscrete revenue of ndctors nd. Snce the m of ths functonl method s the quntfng of the sub-ndctors effects, there s the queston of how to rellocte common effects nto prtculr fctors e. how to ssgn the pproprte mportnce to prtculr fctors. Zl et l. (000) mentons number of possble ws of settng the mportnce equll ccordng to the number of sub-ndctors or b the epo-
M. Vejsdová Drjová 8,,..., n nentl functon e /...,,, n w e / w e e or ccordng to the modfcton Zl et l. (000), lso sttes tht there s no cler crteron for the mportnce opton, but tht, ccordng to the uthor, the functonl method provdes more stble results whch re nerest to the results obtned b mens of logrthmc method for the postve ndces. Therefore, wthn the functonl method, the best method wll be chosen lloctng equll ccordng to the number of ndctors. The net dvntge of the functonl method, s Zmeškl, Dluhošová & Tchý (00) sttes, s tht ths method s not senstve to the fctors sequence n the clculton, whch s the bsc requrement for the method of grdul chnges pplcton. The functonl method equton s stted b Dluhošová (00). ( j Mterl nd Methodolog j j k k j j k j k k j m mk j k m...) The selected compnes smple conssts of the 9 domestc grculturl ltd. compnes wthn the perod 00-007. The mn crteron for selectng the domestc grculturl ltd. compnes s ts combned producton (crop producton combned wth the lvestock producton), specfed ČSÚ, where the speclston rto s less thn 66% (whch mens tht one sngle tpe of ctvt does not rech more thn 66% of the totl producton). Another comprble crteron of the compnes smple s the number of emploees nd the ctegor of sset turnover, both ccordng to CSÚ. The selected dt smple contns the domestc grculturl compnes wth no more thn 99 emploees nd where the sset turnover does not eceed 99 mllon CZK wthn the perod 00-007. The dt requred for the prmdl decomposton re bsed on the fnncl sttements of the compnes; ther blnce sheets nd proft/loss ccounts over the perod 00-007. The mn focus of ths pper s to quntf the prtl effects of nltcl fctors (ndctors) on the chnge of the snthetc eturn on Equt ndctor OE. The prmdl decomposton method s ppled to quntf the nfluence of the snthetc OE nde. The prmdl decomposton s the grdul decomposton of the top ndctor nto the prtl, nltcl sub-ndctors. The result s the dentfcton of the prtl nfluences on the top ndctor. The functonl method, whch s not et commonl known nd used, ws ppled to quntf the mpct on the OE ndctor. Another reson wh ths method ws selected s the fct tht, there were negtve ndctors pperng durng the prmdl decomposton nd, therefore, the logrthmc method could not be used. Moreover, the functonl method s not senstve to the fctor order, whch s the bsc ssumpton for usng the method of grdul chnges. The functonl method does not contn the resdul component, whch s creted durng the decomposton nd t s mpossble to be ssgned to the prtl nfluences. The decomposton of OE, s presented n Sellng & Stckne (990) ws chosen for the pplcton of the functonl method. Accordng to the uthors, the decomposton of OE nd the trnsfer to the domestc ncome ctegor s s follows: OE = OA * (EBT/EBIT) * (EAT/EBT) * A/VK (8) Where OA (eturn on Assets) ndctes the return of the totl cptl, (EBT/EBIT) ndctes the nterest n cses of ernngs reducton, (EAT/EBT) represents the t ncome reducton, (A/VK) ndctes the fnncl leverge. The OA ndctor s further broken down nto the product of sles proftblt ndctor (EBIT/T) nd the sset turnover ndctor (T/A): OA = (EBIT/T) * (T/A).
The Possbltes of Dfference Anlss Utlston n Proft te Assessment 9 The Sles proftblt nde cn be further broken down to show product of Cost of Sles (N/T) nd eturn on Costs (EBIT/N): EBIT/T = (N/T) * (EBIT/N). The complete prmdl decomposton of the OE cn be chrctersed ths w: OE OA * (EBT/EBIT) * (EAT/EBT) * A/VK (EBIT/T) * (T/A) (N/T) * (EBIT/N) Quntfcton of the sngle fctors, for the product of four prtl ndctors of the method, s possble when the weghts re equll dstrbuted ccordng to the number of ndctors. The scheme then looks lke ths. The quntfcton of the fctors, for the product of two prtl ndctors of the functonl method, s possble under the ssumpton tht the weghts re equll dstrbuted ccordng to the number of ndctors. If the crter re met the scheme looks lke ths:,.
M. Vejsdová Drjová 50 esults nd Dscusson The followng tble dspls the nput dt for the functonl method. The vlues re the nnul verge of the smple, whch re computed s smple rthmetc men. Tble Input Dt (Thous. CZK) 00 9 005 9 006 9 007 9 Ernngs before Tes (EBT) 5560 69 5080 85 Ernngs before Interest nd Tes 698 598 656 Ernngs fter Tes 998 00 0870 Assets 8708 966 9809 05 Equt 7705 68 680 6955 Sles 76 556 87 8 Costs 06989 059 99 97 Source: Author s own reserch The three followng schemes dspl the prmdl decomposton of return on equt nd quntf the effects of prtl, nltcl ndctors on the nlsed ndctor, usng the ppled functonl method durng the reportng perods 005/00, 006/005, 007/006. Pcture Prmdl Decomposton OE 005/00 Indctor l OE perod 0 Perod 0.09 0.009 dfference Yeld dscrete -0.00875-0.60 Absolute nfluence -0.00875 OA 9 EBT/EBIT 0 EAT/EBT A/VK 0.070 0.007 0.805 0.7958 0.89897 0.85.66.75-0.00658-0.7756 * -0.00995-0.00 * -0.0586-0.050 * 0.006 0.0076-0.00677-0.000-0.008 0.0005 EBIT/T T/A 0.0589 0.05 0.688 0.5987-0.00770-0.06 * -0.09-0.0598-0.0085-0.009 N/T 5 EBIT/N 6 0.90969 0.9 0.0676 0.056 0.005 0.0060-0.00855-0.0 0.00006-0.0090 Notes: 7 Absolute Influence; 8 eturn on Equt; 9 eturn on Assets; 0 Interest on Ernngs educton; T Ernngs educton; Fnncl Leverge; Sles Proftblt; Asset Turnover; 5 Cost of Sles; 6 eturn on Costs. Source: Author s own reserch
The Possbltes of Dfference Anlss Utlston n Proft te Assessment 5 Pcture Prmdl Decomposton of OE 006/005 ndctor OE 8 perod 0 perod 0.009 0.08 Dfference Yeld ds- 0.00 0.070 Absolute nfluence 0.00 OA 9 EBT/EBIT 0 EAT/EBT A/VK 0.007 0.00 0.7958 0.7760 0.85 0.855.75.50 0.005 0.085 * -0.065-0.0087 * 0.000 0.007 * -0.0-0.0506 0.008-0.00065 0.00007-0.0007 EBIT/T T/A 0.05 0.055 0.5987 0.5987 0.009 0.0765 * 0.0086 0.0068 0.008 0.0000 N/T 5 EBIT/N 6 0.9.076 0.056 0.05 0.69 0.88-0.0007-0.0570 0.000-0.007 Notes: 8 eturn on Equt; 9 eturn on Assets; 0 Interest on Ernngs educton; T Ernngs educton; Fnncl Leverge; Sles Proftblt; Asset Turnover; 5 Cost of Sles; 6 eturn on Costs. Source: Proper reserch Tble no. summrses the results of the sub-ndctors nfluence durng the selected perod. The sub-ndctors re ssgned n order bsed on ther degree of nfluence on the eturn on Equt nde. Tble The Influence of Anltcl Prmeters Indctor 005/00 006/005 007/006 Influence order Influence Order Influence order Interest Ernngs educton -0.000. -0.00065. 0.0067. T Ernngs educton -0.008. 0.00007 6. 0.007. Fnncl Leverge 0.0005 5. -0.0007. -0.0007 6. Asset Turnover -0.009. 0.0000 5. 0.0067. Cost of Sles 0.00006 6. 0.000. -0.000 5. eturn on Costs -0.0090. -0.007. 0.090. Totl -0.00876 --- 0.00 --- 0.00 --- Source: Proper reserch
M. Vejsdová Drjová 5 Pcture Prmdl Decomposton of OE 007/006 Indctor OE Perod 0 Perod 0.08 0.0797 Yeld 0.0.8 Dfference dscrete Absolute nfluence 0.0 OA EBT/EBIT EAT/EBT A/VK 5 0.00 0.068 0.7760 0.8800 0.855 0.99.50.9 0.008 0.99 * 0.07 0. * 0.0609 0.0795 * -0.005-0.0 0.055 0.0067 0.007-0.0007 EBIT/T 6 T/A 7 0.055 0.0 0.5987 0.60 0.060 0.8 * 0.0 0.050 0.0988 0.0067 N/T 8 EBIT/N 9.076 0.997 0.05 0.09-0.00-0.0875 0.086 0.908-0.000 0.090 Notes : eturn on Equt; eturn on Assets; Interest on Ernngs educton; T on Ernngs educton; 5 Fnncl Leverge; 6 Sles Proftblt; 7 Asset Turnover; 8 Cost of Sles; 9 eturn on Costs. Source: Proper reserch Pcture Influence of sub-ndctors 0.05 0.00 Influence of Sub-ndctor 0.05 0.0 0.05 0.0 0.005 0 005/006 006/007 007/008-0.00 Interest on T on Ernngs Fnncl Incomes Cost of Sles eturn on Ernngs educton Leverge Proftblt Costs educton Anltcl Indctor Source: Author s own reserch Pcture clerl shows tht the degree of nfluence concernng the sub-ndctors chnged n gven perod of tme. In 005/00, there ws decrese of.6% n the OE (e. decrese b 0.00875) n the frst wve of the equton decomposton. Ths ws, mnl, due to the decrese n the eturn on Assets, b 77 % (0.0067), b % decrese n T Ernngs educton (0.008),
The Possbltes of Dfference Anlss Utlston n Proft te Assessment 5 5% decrese n Interest Ernngs educton (0.000) nd b % ncrese n the Fnncl Leverge ndctor (0.0005). In 006/005, the,7% ncrese n the OE (0.00 ncrese) n the frst wve of the equton decomposton, ws cused, mnl, b 7% ncrese n the eturn on Assets nde (0.008), 5% decrese n the Interest Ernngs educton nde (0.00065), % decrese n Fnncl Leverge (0.0007) nd 5% ncrese n the T Ernngs educton (0.00007). In the lst perod, 007/006.% ncrese n the OE (0.0 ncrese) n the frst wve of the equton decomposton, ws cused, mnl, b 77% ncrese (0.055) n the eturn on Assets, 5% ncrese n the Interest Ernngs educton nde (0.0067), 9% ncrese n the T Ernngs educton (0.007) nd % decrese n the Fnncl Leverge nde (0.0007). In the second level of the Prmdl decomposton of the eturn on Equt, the nfluence ws vsbl more cler. It cn be stted tht the eturn on Assets ws formed, b t lest three qurters, b the Sles Proftblt ndctor. In the thrd level of the prmdl decomposton, the Sles Proftblt, n the frst nd the thrd perod, ws nfluenced, mnl, b the eturn on Costs nde. The Cost of Sles nde nfluenced the Sles proftblt onl b % n the frst perod nd b 5% n the lst perod. The opposte stuton occurred n the second perod. The mjor sub-ndctor nfluences cn be chrctersed n ths w: n 005/00 nd 007/006 the chnge n eturn on Equt ws nfluenced, mnl, b the chnge n the eturn on Costs nde. In the 006/005 perod, the OE nde ws nfluenced, mnl, b the bsolute nfluence of the Cost of Sles ndctors. 5. Concluson From the decomposton of the top ndctor of eturn on Equt the followng concluson cn be drwn. eturn on Equt s nfluenced b eturn on Assets, tton nd b the debt, where the debt nfluence on OE s epressed s the Fnncl Leverge nde nd Interest Ernngs educton. The ncrese n the ndebtedness s utomtcll reflected s n ncrese n the Fnncl Leverge nde. However, t the sme tme, n ncrese n the shre of foregn cptl brngs n ncrese n the Cost of Interest nd cuses the decrese of the Interest Ernngs educton prtl nde. Thus, t depends on whch fctor s the domnnt one, n decdng f the reducton n the proft decreses the dvntge of the Fnncl Leverge or not. The nfluence of the nltcl ndctors on the nlsed top ndctor of OE, n the three perods, looked lke ths. Frstl, t s good to menton tht the nfluence rte of the sub-ndctors on the top ndctor chnged durng the perods. Nevertheless, t s stll possble to summrse the overll order of nfluence of the sub-ndctors wthn three perods. Undoubtedl, t s obvous tht the OE ws mnl nfluenced b the Sles Proftblt ndctor n the second level of the decomposton. Furthermore, the Sles Proftblt ndctor ws, n the frst nd thrd perods, set b the eturn on Costs ndctor, n the frst, nd n the second perod t ws set b the Cost of Sles ndctor. The Sub-ndctor, Fnncl Leverge, nfluenced the OE the lest of ll the ndctors. The T Ernngs educton nde hd slghtl greter mpct on the OE thn the Fnncl Leverge, followed b the Interest Ernng educton nde.
M. Vejsdová Drjová 5 eferences Foršková, D., & chtrová, D. (00). Vužtí nlýz odchlek př hodnocení zskovost fnnčních nsttucí. Sborník příspěvků z 5. meznárodní konference Řízení modelování fnnčních rzk. VŠB-TU Ostrv. 06. ISSN 978-80-8-06-5. Dluhošová, D. (00). Přístup k nlýze fnnční výkonnost frem odvětví n báz metod EVA Economc Vlue Added. Fnnce úvěr. 5(-), 5-559. ISSN 005-90. Dluhošová, D. (00). Fnnční řízení rozhodování v podnku. Prh: Ekopress. s. 5. ISBN 978-80-8699-68-. Sellng, T. I., & Stckne, C. P. (990). Dsggregtng the te of eturn on Common Shreholders Equt: A New Approch. Accountng Horzont. (), 9-7. ISSN 0999-799. Zl, K. kol. (000). Fnnčno-ekonomcká nlýz podnku. Brtslv: Sprnt. s. 85. ISBN 8089085996. Zmeškl, Z., Dluhošová, D., & Tchý T. (00). Fnnční model. Prh: Ekopress. s. 6. ISBN 80-869-87-.