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QUILIBRIUM
Quarterly Journal of Economics and Economic Policy
Volume 13 Issue 3 September 2018
p-ISSN 1689-765X, e-ISSN 2353-3293
www.economic-policy.pl
ORIGINAL PAPER
Citation: Kliestik, T., Vrbka, J., & Rowland, Z. (2018). Bankruptcy prediction in Visegrad
group countries using multiple discriminant analysis. Equilibrium. Quarterly Journal of
Economics and Economic Policy, 13(3), 569–593. doi: 10.24136/eq.2018.028
Contact to corresponding author: tomas.kliestik@fpedas.uniza.sk; Institute of Technology
and Business in Ceske Budejovice, Okruzni 517/10, 37001 Ceske Budejovice, Czech Re-
public
Received: 4 May 2018; Revised: 12 July 2018; Accepted: 27 July 2018
Tomas Kliestik
Institute of Technology and Business in
Ceske Budejovice, Czech Republic
Jaromir Vrbka
Institute of Technology and Business in
Ceske Budejovice, Czech Republic
Zuzana Rowland
Institute of Technology and Business in
Ceske Budejovice, Czech Republic
Bankruptcy prediction in Visegrad group countries using multiple
discriminant analysis
JEL Classification: G17; G33
Keywords: bankruptcy; prediction model; discriminant analysis; Visegrad group; financial
analysis
Abstract
Research background: The problem of bankruptcy prediction models has been a current
issue for decades, especially in the era of strong competition in markets and a constantly
growing number of crises. If a company wants to prosper and compete successfully in
a market environment, it should carry out a regular financial analysis of its activities, evalu-
ate successes and failures, and use the results to make strategic decisions about the future
development of the business.
Purpose of the article: The main aim of the paper is to develop a model to reveal the un-
healthy development of the enterprises in V4 countries, which is done by the multiple dis-
criminant analysis.
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
570
Methods: To conduct the research, we use the Amadeus database providing necessary
financial and statistical data of almost 450,000 enterprises, covering the year 2015 and 2016,
operating in the countries of the Visegrad group. Realizing the multiple discriminant analy-
sis, the most significant predictor and the best discriminants of the corporate prosperity are
identified, as well as the prediction models for both individual V4 countries and complex
Visegrad model.
Findings & Value added: The results of the research reveal that the prediction models use
the combination of same financial ratios to predict the future financial development of
a company. However, the most significant predictors are current assets to current liabilities
ratio, net income to total assets ratio, ratio of non-current liabilities and current liabilities to
total assets, cash and cash equivalents to total assets ratio and return of equity. All devel-
oped models have more than 80% classification ability, which indicates that models are
formed in accordance with the economic and financial situation of the V4 countries. The
research results are important for companies themselves, but also for their business partners,
suppliers and creditors to eliminate financial and other corporate risks related to the un-
healthy or unfavorable financial situation of the company.
Introduction
The development of a corporate financial situation is an issue of a financial
analysis, but it also helps to identify the causes of the corporate develop-
ment by searching the detail relationship between financial indicators and
information. It does not satisfy only with quantifiable information, but also
searches non-quantifiable (non-financial) information. A comprehensive
view requires to consider a company as an integral part of the economic
environment, in which the company is located; for instance, business sec-
tor, market position, raw material base, energy demand, supply position
(Sedlacek, 2011). It is important, however, to monitor and evaluate not only
the current financial situation of the company, but also the future develop-
ment (see Meluzin et al, 2018a, pp. 148–169; Meluzin et al, 2018b, pp. 63–
79; Meluzin et al., 2017, pp. 171–187). The basis of predicting is the
knowledge of the current state of the corporate financial health and the
development of key indicators, which is forwarded to the next period using
predictive models.
Efforts to recognize the causes of instability in the organization at an
early stage and to avoid their acute stage led to the formation of specific
methods of predictive financial analysis, which are called early warning
systems. The role of early warning systems should be to respond to finan-
cial distress, which represents the state of the company that is opposed to
extreme financial health. Financial distress is usually defined as the state of
an enterprise when it has serious payment problems, which must be ad-
dressed either by a radical change in its structure or by a change in business
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
571
activities. An objective criterion of financial stress is often referred to as
bankruptcy (Grunwald & Holeckova, 2007, pp. 6).
Methods of the financial situation prediction distinguish, with a reason-
able reliability, between the companies that are prosperous and those that
do not prosper. However, this activity requires the total financial and eco-
nomic performance of a company be expressed in a current, concise and, if
possible, one-digit expression. To get this discriminator, it is necessary to
assume the choice of well-differentiated indicators and methods enabling
them to be summarized (Zalai, 2000, pp. 12–14). The paper is focused on
the use of the method of multiple discriminant analysis, which in the practi-
cal part of the paper used to form the prediction models in conditions of V4
economies. The main aim of the paper is to develop a model to reveal the
unhealthy development of the enterprises in V4 countries, which is done by
the multiple discriminant analysis.
The originality of the research lies in the formation of the complex
model of Visegrad countries, identifying the crucial predictor and determi-
nants than can best discriminate the groups of prosperous and non-
prosperous companies. The formation of both individual V4 models and the
complex V4 model would be beneficial for all market subject, as it closely
reflects the current political, economic and financial situation in the reached
countries.
The purpose of the paper is the formation of an econometric model of
the corporate financial health, considering national conditions, using the
results of the multiple discriminant analysis. We consider the formation of
the complex V4 model and subsequent identification of mutual significant
predictors and discriminants to be the main contribution of the paper.
The paper is divided into four main parts. Literature review depicts the
most important pieces of research being done in the field of prediction
models, using the multiple analysis, focused on the Visegrad group (V4).
The primary aim and the methodology of the multiple discriminant analysis
are determined in Research methodology. Description of the models de-
veloped in condition of individual V4 countries and the complex V4 model,
as well as their validation by ROC curve are portrayed in chapter Results.
Discussion compares and analyzes the studies and research of other authors
in the field of prediction models used a developed in V4 countries.
Literature review
The first findings in the field of future financial distress, i.e. future corpo-
rate financial development, appeared in the thirties of the 20th century. The
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
572
first to address the issue was Fitz Patrick when he published a study in
1931, comparing the development of indicators in insolvent and solvent
companies. He pointed out that the development of selected corporate indi-
cators differed in both groups of companies long time before the financial
distress itself. Merwin (1942) also dealt with the issue when he published
research in 1942, which aimed to compare the arithmetic means of selected
corporate indicators in successful and unsuccessful companies (Zalai, 2000,
pp. 12–14). A little later H. I. Ansoff (Grunwald & Holeckova, 2004, pp.
32) formulated assumptions that strategic failures are indicated by weak
signals. The more information we have, the lesser the ignorance, the threat
can be identified and the effects localized.
This type of financial analysis, known as an ex-ante analysis, was later
developed by Tamari (1966, pp. 15–21) and Beaver (1966, pp. 111–115)
and in two years by Altman (1968, pp. 609–611). These authors are also
considered the founders of the scientific prediction of the financial health
and enterprise future development. The formation of a prediction is an ef-
fort to predict the financial development in individual enterprises and to
prevent them from financial collapses. The mentioned authors have verified
dozens of indicators that they think can be used to predict the insolvency. It
is characteristic for the indicators that their level in prosperous or non-
prosperous companies is different. Another feature is a divergent develop-
ment of indicators long before the financial distress.
Altman´s model using multiple discriminant analysis is still considered
to be extremely relevant, as evidenced by several of its significant modifi-
cations (Altman 1977, 2000, 2002, 2014). The popularity of the model was
summed up by Mandru et al. (2010, pp. 83–87), based on which the Alt-
man's model is still solid and durable, despite being formed more than 30
years ago. This view was confirmed by other studies (Li & Ragozar, 2012,
pp. 19; Satish & Janakiram, 2011, pp. 206; El Khoury & Al Beaino, 2014,
pp. 18; Al Khatib & Al Bzour, 2011, pp. 215–217). On the other hand, for
instance, Wu et al. (2010, pp. 34–45), Grice & Dugan (2001, pp. 151–166)
or Pitrova (2011, pp. 76) came to the opposite conclusion. The results of
these studies show that the accuracy of the prediction models is significant-
ly reduced when the model is used in another industry, at another time or in
a different trading environment than the data used to derive the model.
Therefore, it is essential to develop a model for each country, accepting its
economic, political and entrepreneurial uniqueness.
Authors and researchers in the field of predictions models have verified
dozens indicators, which they think can help to predict the insolvency. For
these indicators, it is characteristic that their level in prosperous or non-
prosperous enterprises is different as well as the divergent development of
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
573
indicators long time before the crisis itself. Methods of forecasting a finan-
cial situation require the overall financial and economic performance of
a firm to be expressed by a current and unambiguous expression. Thus, it is
necessary to assume the choice of well-differentiated indicators and method
summarizing them (Zalai, 2000, pp. 12–14). Another important thing is to
consider the conditions of the national economy, its legislation, operation
of financial instruments, but also the external factors, prediction models can
indicate the risks, weak and strong points of the financial health of the
company.
As the paper is devoted to the use of the method of multiple discrimi-
nant analysis to form the prediction models in the conditions of V4 econo-
mies, the research interest is aimed at the models formed I the Visegrad
group: Chrastinova (1998), Gurcik (2002), Zalai (2000), Gajdka and Stos
(1996, pp. 59–63), Prusak (2005), Maczynska (2004, pp. 42–45), Hamrol et
al. (2004, pp. 34–38), Holda (2001), Virag and Hajdu (1996, pp. 42–53),
Doucha (1995) and Neumaierova and Neumaier (1995, pp. 7–10; 1999, pp.
32–75; 2001, pp. 23–39; 2005). Specific conditions in Slovak and Czech
environment were searched also by Rybarova et al. (2016, pp. 298–306),
Karas and Reznakova (2014, pp. 214–223) or Reznakova et al. (2013, pp.
203–208) who focus on specific economic areas. The complex review of
research into corporate bankruptcy prediction in Visegrad group countries
is presented in the study of Prusak (2018); Karas and Reznakova (2018);
Kliestikova et al. (2017); Zvarikova et al. (2017) and Boratynska (2016).
Review of bankruptcy prediction in V4 countries
In the Slovak business environment, there are also some representatives
of prediction models. Chrastinová (1998) and Gurcik (2002) were the first
authors who applied the methodology of financial health predictions to
companies in the agricultural sector, and Binkert (1999) and Zalai (2000) in
commercial enterprises, using multiple discriminant analysis. Kamenikova
(2005) solved the limitations in the use of foreign models predicting the
financial development of enterprises in the conditions of the Slovak Repub-
lic. Gundova (2015) depicted the main reasons for not using foreign meth-
ods of predicting the financial situation in Slovak companies and empha-
sized the importance of the formation of the national prediction model.
A method for logistic regression to assess the future corporate prosperity
was in our national conditions firstly applied by Hurtosova (2009). Later,
Delina and Pacikova (2013, pp. 101–112) developed a new modified model
in the Slovak business environment while using regression analysis to get
higher predictive performance of the model. Mihalovic (2016, pp. 101–
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
574
118) formed two models based on multiple discriminant analysis and logit
analysis, recommending the use of the latest. Kovacova and Kliestik (2017,
pp. 775–791) introduced a bankruptcy prediction model in the Slovak Re-
public, using logistic regression and they proved significant classification
accuracy of this model, Adamko and Svabova (2016, pp. 15–20) tested the
Altman´s model on the data of Slovak entities; the prediction ability of the
model depends on the model used and year of the quantification. Reznako-
va and Karas (2015, pp. 397–403) presented the results of their research
aimed at the classification ability of prediction models in different envi-
ronment of Visegrad group countries using the Altman´s model.
In the Czech Republic, the pioneers in the prediction models formation
are the Neumaiers, who have developed several models. IN95 (Neumaier &
Neumaierova, 1995, pp. 7–10) was the first model achieving more than
70% accuracy in predictions of corporate financial situation. IN99, IN01
and IN05 were further modifications reflecting the national changes. Jaku-
bik and Teply (2011, pp. 157–176) built a logit model to predict the unfa-
vourable financial situation and they formed a new indicator JT index eval-
uating the economy’s financial stability, which is based on a financial scor-
ing model estimated on Czech corporate accounting data. Hampel et al.
(2012, pp. 243–248) proposed a model based on a function of production,
comparing the results with the Altman´s model. Artificial neural networks
are used to form the bankruptcy prediction model by Vochozka et al.
(2015, pp. 109–113; 2016, pp. 5–18). Kubickova and Nulicek (2017, pp.
494–505) applied regression and try to classify the companies into groups
of healthy and after bankruptcy setting the specific national criteria.
Research in the field of bankruptcy prediction in Poland was focused on
the use of Altman´s model. The first notable outcomes were presented in
the research of Maczynska (1994, pp. 42–45) and Gajdka and Stos (1996,
pp. 59–63). The model of Hamrol et al. (2004, pp. 34–38), known as Poz-
nanski model is famous for its very good classification and prediction abil-
ity of almost 93%. Prusak (2005) suggested two discriminant function, one
to predict the bankruptcy one year in advance, the other one forecasts the
corporate non-prosperity two years in advance. The discriminant analysis is
also used in the model of Holda (2001), Maczynska (2004, pp. 4–9), Korol
(2004, pp. 1–14) or Juszczyk and Balina (2014, pp. 67–94). However, not
only the discriminant analyses are used to develop the Polish prediction
models, some authors use logistic regression, e.g. Pisula et al. (2013, pp.
113–133) or Karbownik (2017) or neural networks (Michaluk, 2003).
The Hungarian prediction models do not have a long tradition. The first
authors are Hajdu and Virag (2001, pp. 42–53) who developed the model
based on the discriminant analysis and logistic regression, using the data of
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
575
the Hungarian companies from 1990 and 1991. The latest research on the
bankruptcy prediction in the Hungarian economic condition was conducted
by Andrea and Dorisz (2015, pp. 426–447), Dorgai et al. (2016, pp. 341–
349) and Bauer and Edrész (2016).
Research methodology
Prediction methods are aimed at comparing financial ratios between pros-
perous and non-prosperous companies. They are used to predict the diffi-
culties of business entities. In order to provide the most accurate infor-
mation, they have gone through several modifications. In practice, it was
found that not all of the indicators have the same reporting ability, and the
use of selected simple ratios provided insufficient and distorted views on
the future business development. For this reason, other ratios and indicators
were used to achieve higher prediction ability. This introduced prediction
models based on more complex, multidimensional statistical methods —
multiple discriminant analysis. Therefore, the aim of the contribution is to
form a prediction model using multiple discriminant analysis and to verify
its classification ability in conditions of business environment of V4 coun-
tries.
In multiple discriminant analysis, the objective is to model one quantita-
tive variable as a linear combination of others variables. The purpose of
discriminant analysis is to obtain a model to predict a single qualitative
dependent variable from one or more independent variable(s). In most cas-
es, the dependent variable consists of two groups or classifications, and we
consider the group of defaulting (non-prosperous) companies and non-
defaulting (prosperous, healthy) companies. Discriminant analysis derives
an equation as linear combination of the independent variables that will
discriminate best between the groups in the dependent variable. This linear
combination is the discriminant function (Kral & Kanderova, 2009). The
objective of the discriminant analysis is to test if the classifications of
groups in the dependent variable (Y) depends on at least one of the inde-
pendent variables (X). In terms of hypothesis, it can be written as:
H0: Y does not depend on any of the Xi’s.
H1: Y depends on at least one of the Xi’s.
Business failure can take various forms, different changes and conse-
quences. In particular, the consequences are the engine of the research and
development of methods and models to anticipate failure with certain ahead
of time. To be able to form a model for V4 countries, it was necessary to
have appropriate data base; we used the financial and statistical indicators
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
576
from the Amadeus database from 2015 (for all independent variables, i.e.
for all financial variables) and 2016 (for the dependent variable, i.e. corpo-
rate prosperity).
To develop a prediction model in Visegrad countries we work with the
following data:
− financial data of following countries: the Slovak Republic, the Czech
Republic, Poland, Hungary, Romania, Bulgaria, Lithuania, Latvia, Esto-
nia, Slovenia, Croatia, Serbia, Russia, Ukraine, Belarus, Montenegro
and Macedonia.
− a statistical Nomenclature of Economic Activities in the European
Community (NACE classification) including the following economic
categories: A — agriculture, forestry and fishing; B — mining and quar-
rying; C — manufacturing; D — electricity, gas, steam and air condi-
tioning supply; F — construction; G — wholesale and retail trade; H —
transporting and storage; I — accommodation and food service activi-
ties; J — information and communication; N — administrative and sup-
port service activities; P — education; Q — human health and social
work activities..
− the conditions set out in the Amadeus database were used to determine
the size criteria; a large enterprise is considered to be an enterprise that
meets at least one of the following conditions: operating revenue ≥ 10
million EUR, total assets ≥ 20 million EUR and employees ≥ 150. A
medium-sized enterprise is an enterprise fulfilling at least one of the
conditions: operating revenues ≥ EUR 1 million, total assets ≥ EUR 2
million and employees ≥ 15. If the enterprise is not included in any of
the previous categories, it is a small enterprise.
− to determine the independent variables used to develop a prediction
model, we focused on indicators determined by outstanding authors as
the key predictors of financial health. We analyzed the studies and re-
search of Sharifabadi et al. (2017, pp. 164–173), Tian et al. (2015, pp.
89–100), Bellovary et al. (2007, pp. 1–43), Ravi Kumar and Ravi (2007,
pp.1–28), Dimitras et al. (1996, pp. 487–513) and Kliestik et al. (2016,
pp. 89–96; 2018, pp. 791–803). Based on the analysis, we selected the
following indicators, Table 1.
The listed parameters for all countries and for the relevant time period
(2015 and 2016) were obtained from the Amadeus database. Given the lack
of required data in individual country variables, some variables had to be
excluded from further investigation — financial indicators X03, X05, X06,
X13, X14, X17, X19, X23, X28, X29, X31, X32, X33, X34. Subsequently,
we deleted the enterprises which did not state the value of the dependent
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
577
variable, i.e. it was not possible to determine whether an enterprise is pros-
perous or non-prosperous.
The multiple discriminant analysis consists of the following methodo-
logical steps:
1. Choosing a sufficiently large sample that accept some of the rules for
determining the appropriate sample size to perform the discriminant
analysis. The general agreement is that there should be at least 5 cases
for each independent variable, bet at least 20 cases. As we work with
more than 2.7 million cases, the condition is met.
2. The tests of equality of group means measure each independent variable'
s potential before the model is created. Each test displays the results of
a one-way ANOVA for the independent variable using the grouping var-
iable as the factor. If the significance value is greater than the given lev-
el of significance (we consider 0.05), the variable probably does not
contribute to the model.
3. We identify the value of Box´s M which tests the assumption of equality
of variance-covariance matrices in the groups. A high value of Box´s M
with a small p-value indicates violation of this assumption.
4. Canonical correlation of discriminant function and test of its statistical
significance, which is used to assess the quality of the model and it
measures the association between the groups in the dependent variable
and the discriminant function. It works with two measures Eigenvalue
and Wilk´s lambda. Eigenvalue is a ratio between the explained and un-
explained variation in a model. The bigger the eigenvalue, the stronger
is the discriminating power of the function. In discriminant analysis, the
Wilk’s Lambda is used to test the significance of the discriminant func-
tions. Mathematically, it is one minus the explained variation and the
value ranges from 0 to 1.s
5. Assessment of the values of the standardized canonical discriminant
function coefficients and of correlation coefficients that help identify the
best discriminants. The standardized canonical discriminant function
coefficients provide information about the discrimination ability of indi-
vidual indicator; the closer the coefficient to zero, the smaller the impact
on the discriminant process. Otherwise, correlation coefficients calcu-
late the strength of the relationship between dependent and independent
variables, thus the higher the value the better the discrimination ability
of the indicator.
7. Group centroids are the means of the discriminant function scores for
each participant group. They show the typical location of an enterprise
from a participant group on a discriminant function. The centroids are in
a unidimensional space, one centre for each group. SPSS for centroid
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
578
calculation uses the model constant to make an intentional correction so
that the weighted average of the centroid (weighted by the number of
enterprises in the individual groups) is 0. The result is that it is enough
to compare the Z-score value to zero — the positive value then means
a non-prosperous enterprise, while the negative value determines
a prosperous enterprise.
8. The discriminant function is written using the calculated unstandardized
canonical discriminant analysis coefficients.
9. The classification and discrimination ability of the model and its valida-
tion are verified.
10. The construction of ROC curves to test the classification ability of the
model using the area under curve.
We used the IBM SPSS Statistics software, v. 24, to develop the mod-
els.
Results
To develop the prediction models, we firstly focus on the models for par-
ticular Visegrad countries, then on the formation of the general V4 predic-
tion model.
The data was obtained from the Amadeus database, which provides fi-
nancial and statistical information about:
− 105,708 Slovak enterprises. Considering the dependent variable, there
are two possible future development strategies, prosperity (marked by 0)
and non-prosperity (marked by 1). The database of Slovak enterprises is
determined by 81,292 prosperous enterprises and 24,416 non-
prosperous ones.
− 62,794 Czech companies divided into the group of prosperous compa-
nies 50,058 and 12,736 non-prosperous companies;
− 28,908 Polish companies with the majority of prosperous companies
26,210 and 2,698 non-prosperous companies;
− 252,371 Hungarian companies providing the information about 205,448
prosperous companies and 46,923 non-prosperous companies.
The first step to develop the model is to assess the results of the tests of
equality of group means, Table 2.
P-values in the Sig. column are compared with the given significance
level (α = 0.05), if the p-value is below the significance level, there are
statistically significant differences between prosperous and non-prosperous
enterprises in the mean values of the considered statistical indicators. It
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
579
means that all variables can be used as the appropriate discriminator, except
for:
− X16, X18, X20, X24 and X37 in Slovakia,
− X16, X18, X20 and X24 in the Czech Republic,
− X1, X11, X16, X18, X24, X30 and X37in Poland,
− X11, X12, X16, X18, X20, X24, X30, X36 and X37 in Hungary.
The results indicate, that the conditions in these countries are really sim-
ilar, as they consider the same discriminators of the prosperity.
The results of the Box test (Table 3) show that the covariance matrices
cannot be considered as identical, so we use the assumption of different
covariance matrices in SPSS calculation. The log determinants of the vari-
ance-covariance matrices of each group are distant.
The following part of the outputs contains a canonical correlation of the
discriminant function and a test of its statistical significance (Table 4).
They assess the overall quality of the model, whether the canonical dis-
criminatory functions sufficiently differentiate individual groups.
The canonical correlation between the discriminant function and ex-
planatory variables is statistically significant (Sig. < α), however, the value
of the canonical correlation is relatively low in all four cases.
The results of the absolute values of standardized coefficients of canon-
ical discriminatory function (Table 5) give the information about the dis-
crimination ability of individual indicators to distinguish prosperous and
non-prosperous companies. The value of coefficients, which are close to
zero, have only very small impact on the discriminant process. Negative
values of coefficient contribute to an alternative membership in the group.
The results show that the best discriminants are slightly different in indi-
vidual V4 countries, but the same indicators are repeating. We can summa-
rize that indices X10, X27, X2 and X4 are the ones with the best discrimi-
nation ability . The reason is that net income, profit or the level of liabilities
in an enterprise are used to calculate these ratios, which, if negative (profit)
or exceeding the value of assets (liabilities), indicate an unfavourable situa-
tion of the enterprise, which may lead to its future non-prosperity or bank-
ruptcy.
Considering the correlation coefficients between the discriminatory
function and the individual explanatory variables, the best discrimination
ability seems to have X7, X27 and X10 in Slovakia and Bohemia; X10,
X28 in Hungary and Poland. High correlation coefficient value has also
X15, which was not used in the final function, as the result of the step
method shows, that its contribution after the inclusion of other variables is
not sufficient.
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
580
For each enterprise, it is possible to calculate the Z-score using non-
standardized canonical discriminant coefficients and, comparing its value
with the group centroid to decide if the enterprise belongs to a group of
prosperous or non-prosperous enterprises. SPSS uses the constant of the
model to make a targeted correction when calculating centroids, so that the
weighted average of centroids (weighted by the number of enterprises in
the individual groups) is zero. Consequently, it is enough to compare the Z-
score value to zero, the positive value then determines a non-prosperous
enterprise, the negative indicates the prosperous enterprise.
Using the non-standardized coefficients of the canonical discriminant
function, the discriminant equations of the predictive model for V4 coun-
tries can be written.
The prediction model of Slovakia
2 4 7 10 11
12 15 27 28
1.565 0.025 0.408 7.663 2.268 0.419
0,35 0.926 6.082 0.107
SK
y X X X X X
X X X X
= − + − − + − +
+ + +
(1)
The prediction model of the Czech Republic
2 4 7 8 10
12 21 27 28 35
1.016 0.007 0.884 2.168 0.343 2.526
0,416 0.592 2.561 0.352 1.075
CZ
y X X X X X
X X X X X
= − + − + − + +
− − + −
(2)
The prediction model of Poland
2 4 7 10 11
12 15 26 28 35
1.563 0.075 1.388 0.658 3.001 0.676
1.067 1.043 0.048 0.458 1.213
PL
y X X X X X
X X X X X
= − + − + + − +
+ − + −
(3)
The prediction model of Hungary
2 9 10 11
12 21 22 28
1.516 0.057 1.380 3.967 0.681
1.561 1.607 0.051 0.647
H
y X X X X
X X X X
= − + − + − +
− − −
(4)
To conclude, the models of individual V4 countries are build using the
same variables, financial ratios, but different coefficients. However, some
ratios are used in all models (X2, X10, X12 and X28), which indicates the
similarities of economic and financial environment of the countries. We
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
581
find it important to form the unique model used for all Visegrad countries,
which has the following discriminant function:
4 2 4 7 10 11
12 15 22 27 28 35
1.470 0.024 0.589 1.158 1.870 0.452
0.613 1.030 0.012 0.731 0.173 0.475
0.244 0.522
V
y X X X X X
X X X X X X
CZ SK
= − + − − + − +
+ − + + − +
+
(5)
Variables CZ and SK are dummy variables, which acquire two numeri-
cal values to define a certain change or a qualitative variable category. Zero
is used when the given variation or category does not occur and one de-
notes the opposite situation, i.e. the occurrence of a given variation or cat-
egory (or the presence of a particular observed attribute) (Hebak, 2005). In
the case of V4 prediction model, one is used when calculating the Z score
of Slovak and Czech enterprises, otherwise zero.
However, for the practical use of the model it is necessary to have suffi-
cient discrimination ability. Based on the classification table (Table 6), it is
obvious that the developed models have relatively high total discrimination
ability, more than 80%. The best is the discrimination ability of the Polish
model, however, the complex V4 model is also highly ranked.
Discussion
Prediction models have become an important and inseparable part of corpo-
rate financial analysis. It is important to detect early signs of unpleasant
financial situation and to use effective methods to assess the financial state
of the companies. The practice in the long-term horizon shows that the use
of the models in different time, economic, political and financial environ-
ment is disputatious. Thus, the Visegrad countries have tried to develop the
models, which could be used in their specific conditions.
As the models were developed to be able to predict the future financial
development and prosperity and thus the classification ability to reveal non-
prosperous entities is crucial, it is necessary to achieve high level of classi-
fication ability in this sphere. The best ability to classify the non-
prosperous companies characterizes the Hungarian model (93%), the Slo-
vak model (87.7%), the Czech model (87.3%), V4 model (85.9%) and fi-
nally the Polish model (79.1%).
In order to assess the overall performance of the models, the validation
of the models was assessed by the ROC curve that evaluates the classifica-
tion accuracy of the models by the area under curve (AUC). The ROC
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
582
curves of the prediction models are portrayed in Figure 1. As evident in the
figure, the area under the curve is large enough, the AUC value is 0.90 for
Slovakia, 0.916 for the Czech Republic, 0.93 for Hungary, 0.894 for Poland
and 0.908 for V4 model, indicating a good classification ability off all
models, confirming the results in the classification table.
Analysing the results, the classification ability of the model is higher
when considering individual national environment. It was proved by Rez-
nakova and Karas (2015, pp. 617–633) performing the test of the discrimi-
nation ability of the Altman bankruptcy model using a group of 5,977 com-
panies operating in one of the V4 countries. They found that the discrimina-
tion accuracy of a model falls significantly when it is used in a different
environment. Considering the national environment and the specificity of
individual economy is also highlighted by Szetela et. al. (2016, pp. 839–
856) as well as Antonowicz (2014, pp. 35–45). On the other hand, the low-
er discrimination ability can be a results of the method used to derive the
model (Karas & Reznakova, 2014). The proof is the research of Mihalovic
(2016, pp. 101–118), which reveals that the accuracy of logit and probit
models overdo prediction ability of multiple discriminant analysis and lo-
gistic regression.
The results indicate that the models should be formed in accordance
with the economic and financial conditions and environment of the coun-
tries to have the significant classification ability, considering appropriate
combination of statistical methods and model variables.
Conclusions
Financial analysis has become an integral part of comprehensive financial
management and planning in each business entity. Timely quantification of
determinants causing negative financial development is realized by ex-ante
financial analysis. The common characteristic is the calculation of selected
indicators, which can indicate potential negative development. These indi-
cators are signs of early warning of the future unfavourable financial devel-
opment of the company. A prerequisite of forecasting is the knowledge of
the level and state of relevant indicators that determine the current financial
state of the company. Based on this background information and by the
application of appropriate prediction models, financial developments and
future prosperity can be predicted. A prediction that helps determine the
future prosperity or non-prosperity of the company should therefore be
accurate, timely and interpret correctly the observed financial facts.
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
583
In order to be a successful company in the present dynamic changing
economic environment, it is necessary not only to maintain a good corpo-
rate financial condition, but also to take care of its financial development in
the future. However, the use of retrospective financial methods seems to be
ineffective and insufficient. The development of the prediction models
accepting the specificities of individual countries is thus of vital im-
portance.
In the present paper, we used the method of multiple discriminant analy-
sis to evaluate the future development enterprises in V4 countries. Using
the sample of 449,781 enterprises we formed prediction model for each V4
country and a complex V4 model based on eight to ten predictors (financial
indicators). The models are formed using the same combinations of pre-
dictor, but different coefficient. However, few of them are included in each
model: X2 (current assets to current liabilities ratio), X7 (net income to
total assets ratio), X10 (ratio of non-current liabilities and current liabilities
to total assets), X12 (cash and cash equivalents to total assets ratio) and
X28 (return of equity). The same predictors were determined as the best
financial ratios in providing the information about the discrimination ability
of individual indicators to distinguish prosperous and non-prosperous com-
panies considering the absolute values of standardized coefficients of ca-
nonical discriminatory function. All developed models have more than 80
% classification ability; their validation was proved by ROC curve achiev-
ing the level of more than 90% in almost all cases, indicating perfect classi-
fication ability of all models. However, the research has some limitation, as
the results of the multiple discriminant analysis may not be perceived suffi-
cient, as not compared to other methods (e.g. logistic regression, classifica-
tion and regression trees), which is the issue for further research, to reveal
which method is the most appropriate to predict the financial health of the
company.
The main purpose of the paper was the formation of the complex model
of Visegrad countries, complex and individual, identifying the crucial pre-
dictor and determinants than can best discriminate the groups of prosperous
and non-prosperous companies. The formation of both individual V4 mod-
els and the complex V4 model would be beneficial for all market subject,
as it closely reflects the current political, economic and financial situation
in the searched countries.
Equilibrium. Quarterly Journal of Economics and Economic Policy, 13(3), 569–593
584
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Annex
Table 1. Selected financial ratios
Financial Ratios
X1 Sales/Total assets X20 Net income/Sales
X2 Current assets/Current liabilities X21 Non-current liabilities/Total Assets
X3 Gross profit/Total assets X22 Cash and cash equivalents/Current
liabilities
X4 Net income/Shareholders equity X23 Cash flow/Current liabilities
X5 EBITDA/sales X24 Working capital/Sales
X6 (Non-current + current
liabilities)/EBITDA X25 Current ratio
X7 Net income/ Total assets X26 Liquidity ratio
X8 Working capital/Total assets X27 Return on assets
X9 Operating profit/Total assets X28 Return on equity
X10 (Non-current + current liabilities)/total
assets X29 Shareholder liquidity ratio
X11 Current assets/Total assets X30 Solvency ratio (liability-based)
X12 Cash & cash equivalents/Total assets X31 Cash flow/Operating revenue
X13 Cash flow/Total assets X32 Net assets turnover
X14 Cash flow/(Non-current + current
liabilities) X33 Interest paid
X15 Current liabilities/Total assets X34 Gross margin
X16 Current assets/Sales X35 Profit margin
X17 Operating profit/interest paid X36 Net current assets
X18 Stock/Sales X37 Working capital
X19 Cash flow/Sales
Table 4. Summary of Canonical Discriminant functions
Eigenvalues
Function
Eigenvalue % of
Variance Cumulative % Canonical
Correlation
SK 1 0.074 100.0 100.0 0.263
CZ 1 0.045 100.0 100.0 0.208
PL 1 0.066 100.0 100.0 0.249
H 1 0.051 100.0 100.0 0.220
Wilks' Lambda
Test of
Function(s) Wilks' Lambda Chi-square df Sig.
SK 1 0.931 5,030.925 9 0.000
CZ 1 0.957 1,844.708 11 0.000
PL 1 0.938 1,346.199 10 0.000
H 1 0.952 531.344 8 0.000
Table 2. Test of equality of group means for V4 countries
Slovakia Czech republic Poland Hungary
Ratio Wilks'
Lambda
Sig. Wilks'
Lambda
Sig. Wilks'
Lambda
Sig. Wilks'
Lambda Sig.
X01_2015 1.000 0.000 1.000 0.022 1.000 0.598 0.999 0.005
X02_2015 0.993 0.000 0.998 0.000 0.999 0.000 0.999 0.009
X04_2015 0.982 0.000 0.991 0.000 0.984 0.000 0.990 0.000
X07_2015 0.978 0.000 0.990 0.000 0.987 0.000 0.989 0.000
X08_2015 0.999 0.000 1.000 0.000 0.997 0.000 0.999 0.007
X09_2015 0.983 0.000 0.995 0.000 0.989 0.000 0.988 0.000
X10_2015 0.953 0.000 0.971 0.000 0.964 0.000 0.977 0.000
X11_2015 0.997 0.000 1.000 0.003 1.000 0.978 1.000 0.247
X12_2015 0.995 0.000 0.999 0.000 0.999 0.000 1.000 0.320
X15_2015 0.959 0.000 0.978 0.000 0.975 0.000 0.982 0.000
X16_2015 1.000 0.769 1.000 0.759 1.000 0.819 1.000 0.846
X18_2015 1.000 0.805 1.000 0.939 1.000 0.637 1.000 0.913
X20_2015 1.000 0.867 1.000 0.837 1.000 0.005 1.000 0.956
X21_2015 0.998 0.000 0.997 0.000 0.995 0.000 0.998 0.000
X22_2015 0.995 0.000 0.999 0.000 0.999 0.000 0.999 0.012
X24_2015 1.000 0.765 1.000 0.905 1.000 0.822 1.000 0.913
X25_2015 0.993 0.000 0.998 0.000 0.999 0.000 0.999 0.009
X26_2015 0.993 0.000 0.998 0.000 0.998 0.000 0.999 0.013
X27_2015 0.981 0.000 0.989 0.000 0.987 0.000 0.987 0.000
X28_2015 0.991 0.000 0.992 0.000 0.986 0.000 0.988 0.000
X30_2015 0.999 0.000 0.999 0.000 1.000 0.072 1.000 0.394
X35_2015 0.988 0.000 0.991 0.000 0.988 0.000 0.991 0.000
X36_2015 1.000 0.042 1.000 0.011 1.000 0.005 1.000 0.091
X37_2015 1.000 0.175 1.000 0.006 1.000 0.130 1.000 0.648
Table 3. Box´s test of equality of covariance matrices
Test Results
SK Box's M 73,577.642
F Approx. 1,633.675
df1 45
df2 135,265,736.122
Sig. 0.000
CZ Box's M 31,570.421
F Approx. 477.001
df1 66
df2 17,657,936.188
Sig. 0.000
PL Box's M 9,814.819
F Approx. 176.938
df1 55
df2 1,617,679.625
Sig. 0.000
H Box´s M 1,679.811
Approx. 46.014
df1 36
df2 4,076,602.240
Sig. 0.000
Table 3. Continued
Log Determinants
Y_2016 Rank
Log
Determinant
SK 0 9
-21.349
1 9
-14.572
Pooled
within-groups 9
-19.941
CZ 0 11
-7.162
1 11
-5.309
Pooled
within-groups 11
-6.347
PL 0 10
-22.728
1 10
-17.901
Pooled
within-groups 10
-22.165
H 0 8
-11.763
1 8
-10.733
Pooled
within-groups 8
-11.587
The ranks and natural logarithms of determinants
printed are those of the group covariance matrices.
Table 5. Standardized canonical discriminant function coefficients and correlation
coefficients
St. can.
coef. Corr. coef St. can.
coef. Corr. coef
SK X02_2015 0.191
-0.302
H X02_2015
0.423
-0.112
X04_2015 -0.425
-0.491
X09_2015
-0.213
-0.483
X07_2015 -1.359
-0.545
X10_2015
1.045
0,682
X10_2015 0.691
0.810
X11_2015
-0.187
0.050
X11_2015 -0.117
-0.199
X12_2015
0.335
-0.043
X12_2015 0.116
-0.267
X21_2015
-0.238
0.175
X15_2015 0.274
0.760
X22_2015
-0.248
-0.108
X27_2015 1.208
-0.512
X28_2015
-0.563
-0.481
X28_2015 0.096
-0.349
CZ X02_2015
0.068
-0.206
PL X02_2015 0.498
-0.139
X04_2015
-0.661
-0.451
X04_2015 -0.891
-0,502
X07_2015
0.363
-0.467
X07_2015 0.096
-0.450
X08_2015
-0.078
-0.083
X10_2015 0.760
0.752
X10_2015
0.902
0.814
X11_2015 -0.188
0.001
X12_2015
0.117
-0.154
X12_2015 0.200
-0.114
X22_2015
-0.141
-0.162
X15_2015 0.249
0.616
X27_2015
-0.453
-0.504
X26_2015 -0.264
-0.156
X28_2015
0.261
-0.435
X28_2015 0.311
-0.455
X35_2015
-0.174
-0.457
X35_2015 -0.144
-0.433
X37_2015
-0.053
-0.063
Table 6. Classification ability of V4 prediction models
Classification Results
Y_2016 Predicted Group Membership Total
0 1
SK Original Count 0 65,988
15,304
81,292
1 2,291
21,425
24,416
% 0 81.2
18.8
100.0
1 12.3
87.7
100.0
CZ Original Count 0 42,131
7,927
50,058
1 1,617
11,119
12,736
% 0 84.2
15.8
100.0
1 12.7
87.3
100.0
PL Original Count 0 23,422
2,788
26,210
1 565
2,133
2,698
% 0 89.4
10.6
100.0
1 20.9
79.1
100.0
H Original Count 0 162,305
43,143
205,448
1 3,290
43,633
46,923
% 0 79.0
21.0
100.0
1 7.0
93.0
100.0
V4 Original Count 0 310,999
52,009
363,008
1 12,197
74,576
86,773
% 0 85.7
14.3
100.0
1 14.1
85.9
100.0
For SK, 82.7 % of original grouped cases correctly classified.
For CZ, 84.8 % of original grouped cases correctly classified.
For PL, 88.4 % of original grouped cases correctly classified.
For H, 81.6% of original grouped cases correctly classified.
For V4, 85.7 % of original grouped cases correctly classified.
Figure 1. ROC curves of the prediction models
