55
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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)
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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