A general model based on the DuPont system of financial analysis for identification, analysis and solution of a potential crisis in a business

55 ‘ A Gene al Model Based on he DuPon Sys em o Financial Analysis o Iden i ica ion, Analysis and Solu ion o a Po en ial C isis in a Business JOSEF KASIK1 ( co esponding au ho ) and PETR SNAPKA2 1 Assis an P o esso , Depa men o Business Adminis a ion, Facul y o Economics, VŠB-Technical Uni e si y o Os a a, Os a a, Czech Republic, e-mail: jose [email p o ec ed] 2 P o esso , Depa men o Managemen , Facul y o Economics, VŠB-Technical Uni e si y o Os a a, Os a a, Czech Republic, e-mail: pe .snapka@ sb.cz ARTICLE INFO ABSTRACT Recei ed Ma ch 30, 2020 Re ised om Ap il 29, 2020 Accep ed July 12, 2020 A ailable online decembe 15, 2020 The pu pose o his a icle is o c ea e a gene al model using he da a commonly a ailable in he manage ial accoun ing sys em o he signaliza- ion o a possible po en ial c isis. The c i ical le el o he inpu a iables in luencing he e u n o equi y (ROE) and e u n on sales (ROS) was heo- e ically de e mined based on he DuPon sys em o inancial analysis. To de e mine ac ual amoun o he inpu a iables o he es o hei c i ical amoun in a eal company, we conside ed hei a e age amoun based on a simple a i hme ic mean. Fo he eal analysis in a po en ially h ea ened company, we conside ed one mon h as a ime uni o he ime in e al in a ange o 14 mon hs. We de e mined he a e age ac ual amoun s o he inpu a iables using con idence in e als. Because o he ela i ely small sample, we used S uden 's -dis ibu ion o he cons uc ion o con idence in e als o he inpu a iables. An analy ical model-based sys em app oach based on analysis o he complex alue chain was used. By he means o logical de i a ions and es ing his analy ical model-based sys em app oach in a eal company, we p o ed, ha his model enables no only o de e mine he c i ical le el o he inpu a iables leading o a c isis in a business bu also o calcula e hei new adjus ed amoun , which he business needs o each so ha a po en ial c isis can be sol ed. The p esen ed heo e ical model was success ully applied o sol e a eal po en ial c isis in a pa icula Czech company which suppo s he co ec ness and p ac ical applicabili y o his gene al model. The e a e wo main ad an ages o his model: 1) i can use he da a commonly a ailable in he manage ial accoun ing sys em, 2) his model is gene ally alid, i.e., i can be used in any business p oduc- ing goods o se ices. JEL classi ica ion : G01, G32, M21 DOI: 10.14254/1800-5845/2020.16-4.5 Keywo ds : Po en ial c isis, model, DuPon sys em, p o i ma gin, inpu a iables, c i ical le el ELIT Economic Labo a o y T ansi ion Resea ch Podgo ica Mon eneg in Jou nal o Economics Kasik, J., Snapka, P. (2020), “A Gene al Model Based on he DuPon Sys em o Financial Analysis o Iden i ica ion, Analysis and Solu ion o a Po en ial C isis in a Business”, Mon eneg in Jou nal o Economics, Vol. 16, No. 4, pp. 55-66. 56 INTRODUCTION Recen ly, mo e han e e , we ha e ealized he g owing impo ance o he c isis managemen . The numbe o businesses ha will ace c isis immedia ely o in he nea u u e will ce ainly inc ease d ama - ically. The ques ion does no s and i he c isis occu s bu when i occu s. The si ua ion equi es p esen - ing and discussing new app oaches and models o p edic o sol e he c isis. Analy ical ac i i y ocused on he signalling o a po en ial c isis in a business is e y signi ican o he e ec i e decisions o he s akeholde s (Pa en and Deephouse, 2007; Pos e al., 2002). I ’s a ques- ion o e ec i e decision-making ela ed o he u u e business de elopmen wi h an aim o c ea ion an e ec i e alue c ea ion p ocess (Keul, 2009; Wienga en e al., 2015). I ’s also a ques ion o decision- making ela ed o well- imed solu ion o a po en ial c isis based on analy ically ob ained signalling in o - ma ion abou possibili y o i s occu ence. This signalling in o ma ion is e en mo e signi ican i i enables occu ence o adequa e ime space o he o ma ion and ealiza ion o he ac ions enabling sol ing he po en ial c isis. This is especially ele an o po en ial c ises, which can de elop o he nex phases: wa ning signals, acu e s age and ampli ica ion, which can e en lead o a business bank up cy (Tu ne , 1976; Fink, 1986; Mi o and Pea son, 1993; Roux-Du o , 2007). Some app oaches and models o analysing po en ial c ises in a business a e desc ibed in li e a u e. Howe e , hese models usually assume ha a se o da a is app oxima ely no mally dis ibu ed. By his, some businesses, which by hei excessi e alues wi hin ex ao dina y si ua ions may all down o a c i- sis, a e excluded. In addi ion, hese models use his o ical da a, and hus a e no cong uen wi h he ac- ual possibili ies o he solu ion o capi al de elopmen in a business. The capi al de elopmen in a busi- ness is a e lec ion o e ec i eness o non-e ec i eness o he alue-c ea ing p ocess. Hence, he objec- i e o his pape is o c ea e a new o iginal app oach o he signaliza ion o a possible po en ial c isis in an en e p ise. Based on he DuPon sys em o inancial analysis, a new gene al model o iden i ica ion and sol ing po en ial c isis in a business is c ea ed and desc ibed in de ail. 1. THEORETICAL BACKGROUND The e a e wo main app oaches used o analyses o a po en ial c isis in a business. One o he ana- ly ical model-based sys em app oaches how o ob ain in o ma ion associa ed wi h he occu ence o a po en ial c isis in he en e p ise is an app oach based on analysis o he complex alue chain. Kasik and Snapka (2019) desc ibed he unc ional s uc u e o his chain. This chain s a s wi h he de e mina ion o he p oduc s based on he cus ome s’ needs and con inues o he nex sys em elemen s o he alue chain. The aim is o achie e he ou pu e ec o he las elemen (block) a he end o he alue-c ea ing chain, i.e. manu ac u e and sale o he demanded-by-cus ome s p oduc s, and ob ain he sales o he p oduc s being sold (Elsubbaugh and Rose, 2004; Ad o and Mo iceau, 2013; Robe and Laj ha, 2002). The sales, espec i ely hei pa , a e used as own capi al esou ces o he ep oduc ion o ealiza ion o he complex alue chain. In ou case o analyses, i will be a business, which uses a low p oduc ion me hod. In he case o appea ance o ailu es in luencing beha iou o pa icula elemen s o he alue chain, a possible po en ial c isis occu s in his uni o in he business as a whole. The po en ial c isis is signal- ized a he end o he alue chain. I is an insu icien le el o he olume o he p oduc ion and p ima ily o he sales o he manu ac u ed and sold p oduc s in ela ion o he p ice and demanded quan i y o he p oduc . In he gi en ime, i will exp ess i sel in an insu icien amoun o c ea ion o he inancial e- sou ces o he equi ed ep oduc ion o he alue chain in he business. I a business does no c ea e he a ge -expec ed inancial esou ces om i s manu ac u ing and selling ac i i ies, i is in dange o a po en ial c isis. The e o e, a po en ial c isis in a business mani es s wi h he insu icien p o i abili y. Tha is why he e is a need in managemen o he alue chain in a business o ha e an ea ly wa ning sys em o a po en ial c isis. Tha means o ge signalling in o ma ion o analysing and decision-making based on c i ical alues o he inpu a iables, o ming ou pu s om pa icula elemen s o he a iable chain wi h ela ion o he speci ied es ing c i e ion o he ou pu s om hese elemen s. 57 We ocused ou analyses on he businesses ha ensu e he ep oduc ion o hei alue chain by c e- a ing and using hei own capi al. I means ha hey ha e o be p o i able. They ha e o ul il he condi- ion o p o i abili y measu ed by he p o i ma gin a io. This a io is also known as e u n on sales o ROS (Fai ield and Yohn, 2001; Jansen e al., 2012). The p o i ma gin is also one o he a ios o he DuPon sys em decomposing he e u n on equi y o ROE (B ealey e al., 2012; Higgins, 2012; Palepu, 2007; Soliman, 2008). We use he decomposi ion o ROE in he ollowing o m (1): ROE = x x x x (1) whe e EAT means ea nings a e axes, EBT means ea nings be o e axes, EBIT means ea nings be o e in e es and axes, S means sales, A means asse s and E means equi y o he analysed o ganiza ional uni . We conside he e ec i e sale o he gi en p oduc o cus ome s o be a base o he ep oduc ion o he business capi al. We de e mine he c i ical limi s o he inpu a iables based on he educed e u n on equi y (ROE) indica o unde he condi ion ha ROE equals ze o, i.e. ROE = 0 . Wi hin his condi ion, alua ion o he equi y is a he ze o alue as he c i ical le el. As will be speci ied in he nex pa o he pape , he p o i ma gin o e u n on sales (ROS) will be conside ed as he educed o m o ROE. We can use he analy ic c i e ion compa ison sys em o he es o possibili y o a po en ial c isis based on he p ojec analysis while de ining he a ge alues o he alue-c ea ing chain and e alua ing he cou se o ealiza ion o his chain in ela ion o he de ined- o -i a ge s (Lee e al., 2017). Fo he compa ison o he possible esul du ing he cou se o he alue-c ea ing p ocess, i is possible o use in o ma ional knowledge de i ed om he de ined c i e ion o a po en ial c isis. I will be, as was al eady men ioned, de e mina ion and use o he c i e ion le el o he inpu a iables o ming ou pu s o he conside ed elemen s (blocks) o he analysis o he speci ied alue-c ea ing chain. Consequen ly, o ou conside a ions, i will be a p oduc alue chain ealized by a business uni . Wi hin hese analy ical compa isons, i will be speci ica ion o c i e ion-based signalling in o ma ion, namely de e mina ion o he c i ical le els o he inpu a iables o he las elemen o he analysed p oduc alue-c ea ing chain. As was al eady men ioned, he es ing c i e ion o he de e mina ion o he c i ical le els o he inpu a iables will be he p o i ma gin o ROS a io as he educed o m o he ROE a io. In case ha we a e no able o ensu e a leas c i ical le el o p o i ma gin, ealiza ion o he equi y ep oduc ion as a esul o own alue-c ea ing ac i i y canno be pe o med (Balezen is e al., 2018; Kozel e al., 2017). This compa ison p o ides in o ma ion whe he i is necessa y o no o ca y ou changes wi hin he analysed alue-c ea ing chain. I can be bo h a phase o p ojec ion o al eady ealiza ion o he analysed chain. O he wise he e is a h ea o a po en ial c isis si ua ion in his chain. A he weigh signi icance o he ealiza ion o sales om he analysed p oduc in case o he speci ied c isis, a po en ial c isis may be signalized in he whole business. While applying his sys em app oach o he de e mina ion o a po en- ial c isis, i is possible ex an e du ing he a ge p ojec ion o he alue-c ea ing chain o di ec ly in eal ope a i e ime and s uggle o he ealiza ion o co ec i e ac ions o he solu ion o a po en ial c isis in his chain. This is a e y impo an aspec o his analy ic app oach. The second analy ic model-based sys em app oach is based on analysis and e alua ion o agg ega e s a is ical da a iles ela ed o he low o capi al in he business. The da a iles a e based on he applica- ion o inancial a ios, which may be moni o ed in businesses o ob ained om he p ima y business da a associa ed wi h he low o capi al. The inancial a ios a e used wi hin di e en ypes o he inan- cial analyses, including models o he e alua ion o business capi al de elopmen , o example, bank- up cy p edic ion models. One o he analy ical me hods used o he c ea ion o hese models is, o ex- ample, he disc imina ion analysis (Al man, 1983; Boďa e al., 2016; Ka as e al., 2017). The used i- nancial a ios o he e alua ion o capi al de elopmen in he business a e ma ked as disc imina o s. By s a is ic es ing he agg ega e da a in ela ion o he delimi ed disc imina o s and applying he s a is ical- ly known p ocedu es o he de i ed disc imina ion unc ion, i is possible o ank he analysed business among businesses heading in o insol ency and bank up cy o among success ul businesses, i.e. wi h an e ec i e low o capi al. 58 2. METHODOLOGY As a basic es ing c i e ion o he e alua ion o he possibili y o a po en ial c isis occu ence, we use he e u n on equi y c i e ion in a educed o m, i.e. he p o i ma gin (ROS) a io. As was al eady men- ioned, as a c i ical limi associa ed wi h he possibili y o a po en ial c isis, we conside he c i ical limi , a which ROS will equal ze o, i.e. ROS = 0. O cou se, based on he DuPon analysis, he e is also ROE = 0. In his case, he inal ou pu om he analysed alue-c ea ing p ocess causes simple ep oduc ion. Howe e , when changing he le el o inpu a iables in he di ec ion o wo sening he cou se o he alue- c ea ing p ocess, a po en ial c isis in a business can be iden i ied and signalized. No only p o i abili y and alue c ea ion is h ea ened, bu also i he si ua ion is no sol ed p ope ly, he e is a eal isk o he business bank up cy. The alues o he indica o s p esen ed in he o mula (1) a e quan i ied o he de e mined ime. The analysed p oduc is conside ed o be an inpu om he alue-c ea ing chain. I has, howe e , a unda- men al economical meaning o he business e enues (sales) in conside ed p ac ical example. Wi h ega d o he p esen ed ini ial conside a ions, we will be in e es ed in a pa ial a io o he de- composed ROE a io, and ha is he e u n on sales a io in he ollowing o m (2). ROS = (2) I he alue o his a io will be ze o, i.e. ROS = 0, hen i is clea ha he alues o he o he a ios in he DuPon sys em canno a ec he esul ing alue o he o al ROE a io. I s alue will be a he ze o le el, i.e. ROE = 0. Tha is why o he nex conside a ions, we will go analy ically om his a io unde he c i e ion condi ion ha ROS = 0. A e ha ing inse ed he a iables in o he o mula (2), we will ge i in a o m (3). ROS = 1 - (3) whe e p is he a e age p ice, o which he analysed p oduc is being sold in mone a y uni s pe piece, i.e. [m.u./pc] o he e alua ed pe iod o ime, Q is he a e age p oduced and sold quan i y o he ana- lysed p oduc in pieces o he e alua ed pe iod o ime, i.e. [pc/ ], FC is he a e age le el o ixed ( ela- i ely ixed) cos s o he e alua ed pe iod o ime in mone a y uni s pe pe iod o ime, i.e. [m.u./ ], and is he a e age le el o he uni a iable cos s in mone a y uni s pe piece, i.e. [m.u./pc] o he e alua ed pe iod o ime. In ou example, we conside a pe iod o one mon h wi hin he whole pe iod o he de e mina ion o he a e age amoun o alues o he inpu a iables. I is necessa y o dec ease he es ing pe iod wi h ega d o he possible g ow h o equency o ailu es in he alue chain, which can ini ia e a new c isis. The c i ical le el o hese a iables will be de i ed wi hin ul ilmen o he condi ion o a po en ial c i- sis in he analysed o ganiza ional uni , i.e. o ROS = 0. They will be conside ed o be signalling in o - ma ion o a po en ial c isis in he analysed o ganiza ional uni . The i s ask will be de i a ion o he c i ical amoun o he inpu a iables de e mining he le el o ROS unde condi ion ha ROS = 0. In ela ion o he o mula (3) o he de e mina ion o he le el o ROS, i will be hus he delimi a ion o c i ical le el o ou al eady men ioned inpu a iables which we desig- na e as he c i ical le els wi h he ollowing symbolic indexing: (pc); (Qc); (FCc); ( c). I means o he con- di ion ha ROS=0. Consequen ly, we will speci y o mulas o he de e mina ion o he c i ical le el o pa icula a iables, namely: a) c i ical amoun o he inpu a iable (p), i.e. (pc) pc = + A (4) b) c i ical amoun o he inpu a iable (Q), i.e. (Qc) 59 Qc = (5) c) c i ical amoun o he inpu a iable (FC), i.e. (FCc) FCc = (pA – A) . QA (6) d) c i ical amoun o he inpu a iable ( ), i.e. ( c) c = pA - (7). I one o he abo e-men ioned inpu a iables achie es he ac ual amoun de e mined acco ding o he o mulas om (4) o (7), hen his in o ma ion signalizes a po en ial c isis. A e age alues om he da a ile o he achie ed alues o hese a iables in he analysed business uni will be applied o he de e mina ion o a c i ical amoun o he inpu a iables. Tha is why we designa e he alue o hese a iables in he o mulas om (4) o (7) by index (A) as he ac ual alues, i.e. pA, QA, FCA, and A. I also can be a le el de e mined, o example, based on s a egic analysis. F om he abo e-men ioned o mulas (4) o (7) and ela ions o pa icula inpu a iables, i is clea how he alue o he inpu a iable a ec s his c i ical amoun . To sol e a po en ial c isis in he analysed uni , he e is impo an in o ma ion abou a “sa e y gap” ( ese e) in he amoun (Sg). This in o ma ion is gi en by he di e ence o he ac ual amoun o he pa icula inpu a iable and i s c i ical le el. I means ha o sepa a e inpu a iables he sa e y gap ( ese e) is alid unde he ollowing condi- ions: − o he a iable (p), he gap (Sgp) is eal, when i is ue ha pA – pc ˃ 0, i means ha , o example, he ac ual p ice o he p oduc can decline in he ma ke in ime up o he c i ical alue o he p ice; he amoun o he ese e is hen Sgp = pA – pc; − o he a iable (Q), he gap (SgQ) is eal, when i is ue ha QA – Qc ˃ 0, i means ha , o example, he ac ual p oduc ion and sale o he espec i e p oduc can decline in he ma ke du ing a ime up o he c i ical amoun o p oduc ion; he amoun o he ese e is hen SgQ = QA – Qc; − o he a iable (FC), he gap (SgFC) is eal, when i is ue ha FCA – FCc ˂ 0, i means ha he c i ical amoun o he ixed cos s ( ela i ely ixed cos s) is highe han ac ual one. I means ha in he delim- i ed pe iod o ime ixed cos s can inc ease as a esul o si ua ion in he ma ke , o example due o he pu chase o se ices o ope a ion. The ac ual amoun o ese e is hen gi en by a di e ence in absolu e alue be ween he ac ual amoun o he ixed cos s and hei c i ical amoun , i.e |FCA – FCc| = SgFC; − o he a iable ( ), he gap (Sg ) is eal, when i is ue ha A – c ˂ 0, i means ha he c i ical amoun o he a iable cos s pe uni is highe han he ac ual amoun o he a iable cos s pe uni . Wi hin he delimi ed ime, he a iable cos s pe uni can g ow due o he si ua ion in he ma ke . The amoun o ese e is hen gi en by a di e ence in absolu e alue be ween he a iable cos s pe uni in hei ac ual le el and hei c i ical amoun , i.e. | A – c| = Sg . To de e mine ac ual amoun o he inpu a iables o he es o hei c i ical amoun , we conside ed hei a e age amoun based on a simple a i hme ic mean. Fo he analysis, we conside ed one mon h as a ime uni o he ime in e al in a ange o 14 mon hs. We de e mined he a e age ac ual amoun s o he inpu a iables using con idence in e als. Because o he ela i ely small sample, we used S uden 's -dis ibu ion o he cons uc ion o con idence in e als o he inpu a iables (Rémilla d, 2013; F eund and Wilson, 2003). The s anda d e o o he mean (δ) can be de e mined using he o mula (8). δ = . p = µ - m (8) 60 whe e s is he sample s anda d de ia ion, n is numbe o inpu da a, p is a S uden - andom a iable wi h (k) deg ees o eedom (whe eas k = n -1) a he speci ied con idence le el, m is he sample mean, µ is he es ima ed sample mean in ela ion o he s anda d e o o he mean (δ). The sample mean (m) can be de e mined wi h he help o he ollowing o mula (9): m = , (9) whe e (xi) a e alues o inpu da a o he sample and he sample s anda d de ia ion can be de e mined using he o mula (10). (10) Based on o mula (8), i is possible o de e mine a con idence in e al, namely om he o mula (11). µ = m ± . p (11) The o mula (11) can be ans o med o he ange o m (12): µ є <m - . p; m + . p˃ (12) whe e µmin = m - . p and µmax = m + . p. In ou case, hese o mulas will be used o he de e mina ion o ac ual a e age alues o he inpu a iables o he calcula ion o he c i ical le els o he a iables o he signaliza ion o a po en ial c isis. I means ha hese will be inpu da a on he basis o an a i hme ic mean (µ) in in e al (µmin) and (µmax). Fo example, an a e age p ice will be de e mined in an in e al (µ), namely in he amoun o (pAmin) and (pAmax). Fu he we will calcula e he in e als o ac ual a iables, namely o he quan i y o p oduc ion (QAmin) and (QAmax), o he ac ual le el o he ixed cos s (FCAmin) and (FCAmax) and o he ac ual le el o he uni a iable cos s ( Amin) and ( Amax). By using his analysis, we ge wo possible s a is ically-de i ed limi s o he de e mina ion o he c i - ical amoun s o inpu a iables, namely (pcmin) and (pcmax), (Qcmin) and (Qcmax), (FCcmin) and (FCcmax), and ( cmin) and ( cmax). We can use he a e age alues o he inpu a iables as ac ual alues o a speci ied pe iod o ime in case o a ela i e ma ke s abili y. I we ind ou ha he e a e signi ican changes o ailu es in he ma ke , i is necessa y o use he ac ual alues o he inpu a iables o he consequen ial analysis wi h he e alua ion o he possibili y o a po en ial c isis. 3. MODEL-BASED DETERMINATION OF THE POSSIBILITY OF SOLUTION OF THE RE- AL POTENTIAL CRISIS In his chap e we will speci y he analy ical p ocedu e o model-based de e mina ion o he possibil- i y o solu ion o he eal po en ial c isis. I means ha a leas one o he inpu a iables a ec ing he le el o ROS achie es such an ac ual le el ha i will cause a dec ease o ROS below he c i ical le el o ROS = 0. This will change he heo e ical po en ial c isis o he eal po en ial c isis wi h a possibili y o ans e up o a eal c isis in case ha he occu ed si ua ion is no sol ed. I means ha he ac ually achie ed le el o ROS will be lowe han 0, i.e. ROS < 0. 61 Occu ence o his si ua ion, as was al eady men ioned, can be caused by a change o he o iginal ac ual alue o he inpu a iables de e mining he le el o ROS o a le el, which can be desc ibed as a new ac ual le el . These inpu a iables om he poin o iew o hei le el will be hen symbolically in- dexed as pNA, QNA, FCNA, and NA. The eal po en ial c isis will occu wi h ela ion o he conside ed e alua ing c i e ion, i.e. ROS < 0. Fo example, i means o a p ice inpu a iable ha he le el o new ac ual le el pNA will decline in ela- ion o he p io ac ual le el pA ha his decline ini ia es a si ua ion when ROS < 0. The e is a new si ua- ion in a business ha he amoun o di e ence |pNA – pA| = Δcs, i.e. c isis-signi ican di e ence which leads o a si ua ion ha ROS < 0. Then we can desc ibe he le el o he inpu a iable pNA < pc as c i ical and we can symbolically index i as (pc ). In case ha he di e ence is lowe han Δcs, he e is a ese e in ela ion o he c i ical le el o his a iable (pc ). In he same way, i is possible o conside he o he inpu a iables in luencing he achie ed le el o ROS wi hin he analysed alue-c ea ing chain. 3.1 Model-based solu ion o he eal po en ial c isis Now we will speci y he p oposed possible solu ion o a eal po en ial c isis in a pa icula business uni . I means a si ua ion in he business, when new ac ual le el o any inpu a iable o a iables a ec - ing he le el o he achie ed le el o ROS leads o a si ua ion ha ROS < 0. We will p opose ia modelling a co ec i e analy ical solu ion o he eal po en ial c isis in he business o achie e ul ilmen o he c i i- cal condi ion o he po en ial c isis, i.e. ROS = 0. The achie emen o he s a us o ul ilmen o his condi ion will be de i ed by means o p ojec ion wi h a necessa y co ec ion in he le el o some o he a iables, which in luence he le el o ROS. The designed amoun o he co ec ed (adjus ed) le els o he inpu a iables could be symbolically indexed as pAD, QAD, FCAD and AD. Any changes o he le el which a e highe han he le el which is necessa y o mee he condi ion ROS = 0, i.e. he le el which is newly de ined ia co ec ion o he pa icula inpu a iable, leads o such a si ua ion ha he le el o ROS is highe han 0 (ROS ˃ 0). The co ec i e chang- es o he le el o he inpu a iables o he solu ion o a eal c isis si ua ion ( o example, a he le el o he p oduc p ice) may be conside ed in he ollowing s uc u e: a) we will ca y ou analysis o a possibili y wi h a eal p oposal o co ec i e ac ions wi hin one o he emaining inpu a iables a ec ing he le el o ROS; b) we will ca y ou analysis o a possibili y wi h a eal p oposal o co ec i e ac ions in a pa ial amoun o he emaining inpu a iables enabling a solu ion o he si ua ion, a which ROS < 0. A decision o by which me hod i is possible o sol e he eal c isis si ua ion can be made no ea lie ha a e analy ical e alua ion o a ian s wi h ega d o he possibili ies o ealiza ion o he change o inpu a iables. Now, we a e going o speci y a model-based p esen a ion o ela ions o he de e mina- ion o he co ec i e (adjus ing) amoun o he inpu a iables o he analy ical app oach men ioned abo e unde le e a). We will de i e he necessa y co ec i e amoun o he inpu a iable upon achie emen o he ac ual le el o one o he inpu a iables, namely he amoun unde hei c i ical le el. I means ha , o example, in case o a p ice as an inpu a iable unde si ua ion ha pA < pc, j. pA = pc , o i is ue pNA < pc, his means ha pNA = pc . Simila ly, i will be also in case o o he inpu a iables. We a e going o desc ibe analy ical app oach o solu ion o he si ua ion in he ollowing example. The e is a si ua ion in a business ha an amoun o inpu a iable is se in he ma ke , namely he p ice a he le el o pA < pc, i.e. a he le el o pc . We will de i e and es a possible co ec i e solu ion o he occu ed si ua ion, i.e. o he eal exis ence o he c isis condi ions in he business. The de e mina ion o he amoun o he necessa y change in he ac ual amoun o he inpu a iable o he solu ion o he c isis si ua ion ini ia ed by he dec ease o he ac ual amoun o he p ice will be de i ed o an inpu a iable which is he quan i y o he p oduc s being manu ac u ed and sold (Q) wi hin he speci ied ime. I means ha o he co ec i e change o he ac ual amoun wi hin he inpu a iable (Q), i.e. o he le el (QA), i is necessa y o de i e an amoun o hei change, namely he le el (QAD) so ha he minimum c i- 62 e ion-based condi ion was me o he le el o ROS, i.e. ROS = 0. I is he le el o QAD as a newly adjus ed amoun o he quan i y. In ela ion o he o mula (3) o he de e mina ion o ROS, we can de e mine a o mula o he de- e mina ion o he le el o he a iable QAD o he c i e ion ROS = 0 as ollows (see o mula 13) QAD = (13) The newly de e mined le el o p oduc ion and sale o he pa icula p oduc has o be u he es ed o check ha i is achie able om he poin o iew o he p oduc ion and sale. I is a ques ion o applica- ion o he es ing c i e ion Qmax ≥ QAD (14) I means, o example, ha i is possible - ia he maximum possible daily p oduc ion and sale o he p oduc Qmax - o ensu e he speci ied mon hly p oduc ion QAD in he business. I means o ensu e ul il- men o he condi ion (14). In case ha he business is no able o ensu e solu ion o he abo e-men ioned eal c isis, namely in ela ion o he p ice si ua ion, i.e. pA = pc , i is necessa y o ca y ou a es o changing he le el o he nex inpu a iable. Fi s ly, we a e going o de e mine he amoun o FCAD o he change in he le el o he ixed cos s again by he applica ion o he ela ion o he de e mina ion o he amoun o ROS unde he condi ion ROS = 0 a he le el o p ice pc . By using he o mula (3) wi h applica ion o he condi ion ha ROS = 0, he le el o he ixed cos s FCAD can be de e mined acco ding o he o mula (15) in he ollowing o m: FCAD = QA (pc – A) (15) We ha e o es he possibili y o educe he le el o he ixed cos s om he exis ing ac ual le el, i.e. FCA o FCNA o he le el o FCAD wi hin he possible a ian s o he educ ion o hese cos s ia pa icula s uc u al i ems o he cos s. In case ha he business is no able o change he le el o ixed cos s (achie ing he le el FCAD o lowe ), i is possible o conside a solu ion o he si ua ion h ough he uni a iable cos . I means o change he le el o A o he le el o AD. De e mina ion o he le el o he inpu a iable AD can be again ca ied ou by using he o mula (3) wi h he applica ion o he condi ion ha ROS = 0. The o mula o he de e mina ion o he amoun o AD will be as ollows (16): AD = pc - (16) In case o he de e mina ion o an in e al o he a e age alues o he inpu a iables, i.e. by he p esen ed s a is ical de e mina ion o he con idence in e al o he sample mean o he inpu a iables, i is possible o p oceed o solu ion o he abo e-men ioned ask a leas on he basis o he limi alues o he inpu a iables. As o a sequence o es ing he possibili y o sol e a eal c isis on he basis o sui abili y o he change o he ac ual le el o he inpu a iable o he newly adjus ed le el, i is possible o analyse he e ec i eness, ealiza ion possibili y, and isks associa ed wi h he implemen a ion o he p oposed change o he inpu a iable. I means ha easie accessibili y in ealiza ion o he change o he le el o he inpu a iable will be ensu ed o such a iables, which a e mo e e ec i ely con ollable by business. In gene al, businesses can mo e easily in luence hose inpu a iables ela ed o he cos s o p oduc ion. The le el o possibili y o he change o quan i y o p ice depends on he posi ion o he business in he ma ke . I he business has, o example, a monopoly posi ion, a possibili y o ealiza ion o hese chang- es will be easie and mo e ealis ic han in case o i s lowe compe i i eness. To selec one om he analy ically de i ed a ian s o he solu ion o he eal c isis in he business, we can use decision-making analysis based on he de e mina ion o u ili y o he a ian s, including ex- pe de e mina ion o isks o ealiza ion o a pa icula a ian . I means ha we should assess he e- 63 sul ing e ec o applica ion o he pa icula a ian . Wi hin es ing and e alua ing he u ili y and isk o he pa icula a ian , i is necessa y o p oceed sys ema ically wi hin he elemen s o he alue-c ea ing chain. Fo hese analy ical pu poses, i is possible o use a numbe o me hods, which a e also applied wi hin s a egic managemen , o example, he SWOT analysis, inancial analysis, ma ke ing s a egy me hods, op imiza ion me hods, and s a is ics me hods. 4. APPLICATION OF THE SYSTEMIC PROCEDURE OF THE ANALYSIS OF THE POTENTIAL AND REAL POTENTIAL CRISIS In his chap e , we a e going o in oduce a p ac ical applica ion o he p esen ed heo e ical consid- e a ions. B ie ly, we will p esen how o sol e a eal po en ial c isis in a pa icula business. I will be p e- sen ed on he basis o analysis and e alua ion o he p oduc chain. The pa icula solu ion will be ca ied ou wi hin a p oduc o one o he Czech companies p oducing di e en ypes o p oduc s. One o he p oduc s is also a low-p essu e boile o hea ing he single- amily houses and o wa ming wa e . Applica ion o he heo e ical p ocedu es and conside a ions will be p e- sen ed wi hin his p oduc . Inpu alues based on ac ual alues o he de e mina ion o hei a e age amoun o he inpu a iables we e ob ained om he business in o ma ion sys em. To de e mine he c i ical le els o he inpu a iables o he analysed p oduc wi h he aim o ob ain in o ma ion abou he possibili y o a po en ial c isis, we will use he ela ions om (4) o (7) speci ied in he heo e ical pa . The amoun s o he inpu a iables bo h in he ac ual amoun and in c i ical amoun a e p esen ed in he ollowing able (Table 1). We also calcula ed he pe cen age change o he inpu a iables o ge he c i ical le el om he ac ual le el. The pe cen age change is indexed as (p.c.). Table 1 . The amoun o he inpu a iables (ac ual, c i ical) and hei pe cen age change Inpu a iable Ac ual amoun (A) C i ical amoun (c ) Pe cen age change om he ac ual amoun (p.c.) p 14,717 CZK/pc. 13,148 CZK/pc. -11 % Q 2,101 pcs. 1,636 pcs. -22 % FC 11,593,847 CZK 14,899,787 CZK +28.4 % 7,630 CZK/pc. 9,199 CZK/pc. +20.6 % Sou ce: own elabo a ion Da a in he o m o a a io can be in o ma i ely used o he analy ical speci ica ion o he im- po ance o a pa icula e alua ed inpu a iable om he poin o iew o p io i y o possibili y o a po en- ial c isis o he analysed business alue-c ea ing p oduc p ocess. I is ob ious ha he lowe he pe - cen age change (p.c.), he highe he p obabili y o a po en ial c isis wi hin his inpu a iable. The e is he ollowing impo ance o he inpu a iables wi hin he analysed si ua ion: 1) he p ice o p oduc ion (p), 2) he uni a iable cos ( ), 3) he p oduc quan i y (Q), and 4) he ixed cos s (FC). The in e al-based de e mina ion o a possible le el o he a e age ac ual amoun s o he inpu a iables ia applica ion o he o mulas (9) o (12) is possible o he de e mina ion o he c i ical amoun s and consequen ial ana- ly ical solu ion. The p esen a ion o he in e al amoun o he inpu a iables is in Table 2. Table 2 . In e al amoun o he inpu a iables Inpu a iables in he ac ual amoun Minimum in e al amoun (min) Maximum in e al amoun (max) Rela ion o he max and min amoun pA 14,412 CZK/pc. 15,022 CZK/pc. 104.2 QA 1,084 pcs. 3,118 pcs. 287.6 FCA 5,260,812 CZK 17,926,882 CZK 340.7 A 7,498 CZK/pc. 7,762 CZK/pc. 103.5 Sou ce: own elabo a ion