West Pomeranian University of Technology
Summary
Process of Polish transformations (economic turnabout) which the beginning had place in year 1989 is not an easy in practice. It didn't wait also analyses until in the area of the theory of running a company.
An element of examinations was shown in the presented text, of which getting the fuzzy model of the financial processes in enterprise as the dynamic system about the changing structure. System can be applied in the situation of supporting the de-cision in current managing the enterprise. To get through non-periodic changes in the financial structure it is possible effect of rationalization the dynamic processes in the enterprise.
Keywords: rating, enterprise ratio analysis, specimen model of the enterprise, fuzzy description of enterprise state
1. Introduction
Identification and evaluation of an enterprise state require consideration of many financial and economic ratios and categories. Their huge number and variety are the reason for problems with explicit enterprise description as well as interpretation of the obtained results. Taking into consid-eration the human perception possibilities, it is necessary to reduce the dimensionality of the evaluation space. The same reasons induce simplification of the analysis by distinguishing certain, moderately uniform subsets of values. Abandoning the precise value determination of each de-scriptive feature for the benefit of describing these values with inter-vals allows for a simplified description and, at the same time, makes it more flexible and better adjusted to real conditions.
The aim of the article is to present the possibilities for describing an enterprise state with the use of fuzzy attributes as well as determination of the fuzzy measure of its financial situation. The text proposes a method for fuzzification of the enterprise descriptive features and determination of the set of important attributes. Also, an example description of one possible state is presented.
2. Review of previous solutions with regard to the evaluation of enterprise situation
An enterprise, being the research subject, will be treated as a dynamic system. Obviously, the dynamics of this system is characterised by long time constants. However, without any limitations, it might be assumed that an enterprise is a dynamic system. Interest in the problem of studies on the current analysis and predictions of the enterprise state appeared in the late 20s and early 30s of the 20th century as a result of the economic crisis.
The aim was, then, only to provide a reliable possibility of predicting the enterprise bankrupt-cy. Since then, the search has been continued for methods which would allow not only for reliable prediction of bankruptcy (forecast and dynamic elements), but also for possibly accurate evalua-tion of the current enterprise situaevalua-tion (static task). A huge number of features of varied character which might be used to describe an enterprise as a research subject as well as many (usually non-measurable) interferences in the enterprise environment make it more complicated to study the description of the enterprise state with the use of traditional mathematical methods. For many years, researchers have been trying to estimate the development possibilities or predict bankruptcy based on e.g. financial statements.
First attempts at such analyses with regard to distinguishing the features (attributes), from among the set of descriptive features, which are of the greatest importance for the evaluation of the enterprise financial situation were made by e.g. A. Fitzpatrick in 1932 and T. Merwin in 1942. Another step was attempts at predicting the bankruptcy in one or two-year time horizon. A pioneer of these studies was Professor E. Altman, whose models were adjusted many times to the local conditions in the individual countries (also in Poland, e.g. studies of Hołda, Wierzba, Gajdka and Stos) or developed in order to increase their accuracy. Other methods were used later, such as the logit analysis (e.g. studies of Stpie and Str k of 2005) or the popular neural networks.
Models based on neural networks became very useful as they appeared to provide a relatively high accuracy of state prediction. The use of a network with one hidden layer developed by Wilson and Sharde in 1994 allowed for predicting the enterprise bankruptcy with 97.5% accuracy1. Simi-lar studies were also conducted in Poland, e.g. by K. Michaluk based on 258 reports of Polish companies. Classification accuracy fluctuated from 78.6% to 97.2%, depending on the assumed bankrupt/non-bankrupt proportions in the training and testing sets2 Also, attempts were made at the evaluation of enterprises state with the use of optimal filtration, decision trees or multifunc-tional methods of discrimination analysis. All these methods, however, referred to the attributes in the form of precisely defined financial ratios, i.e. numbers given in a precise numerical form.
A natural step in the evaluation of these methods is an attempt at referring to “generalised” descriptive features. It is all the more important as most financial ratios cannot be explicitly assigned the required values. The required values (benchmarks) are usually the value intervals or even recommendations as to the highest, lowest possible value, etc. Fuzzification of the descriptive features should make the enterprise description more natural.
Two-value descriptions (precise, dichotomic) of bankrupt/non-bankrupt type are relatively easy to realize, but multi-state (multi-level, multi-value) classification provides more possibilities in spite of being more difficult. It not only allows for making decisions for several classes of e.g.
1
Korol T., Prusak B., Enterprise bankruptcy and the use…. 2
financial standing, but also provides the possibility for “rejecting” the samples which cannot be classified to any of the previously defined classes. An example of the multi-value enterprise evaluation is credit-rating evaluation. The concept refers to a complex evaluation of the entity financial reliability taking into consideration e.g. the analysis of its ability to meet any future liabilities and forecast with regard to financial ability in future3.
Due to a range of processes occurring in the entities' environment, credit-rating has become a widely used tool of modern, effective financial management both in entities, being the money recipients and those being the money providers. It is a comfortable tool for deter-mining the investment risk level and, as a result, for demanding the payment of suitable bonus for risk financ-ing on a specific level (bank grantfinanc-ing a loan with a correspondfinanc-ing interest rate)4.
3. Research base characteristics
The studies were conducted on a sample of 305 enterprises, all of which were Polish ones listed on the Warsaw Stock Exchange in the years 2006÷2007. As each year was re-corded sepa-rately in the data base, 610 study samples were used. The descriptive features were financial ratios constructed based on the available financial statements. The choice of ratios was not accidental and their selection was conducted based on the analysis of literature with regard to enterprises financial standing as well as on the example of other researchers’ experience. The study sample included the ratios which were considered to be of extreme importance for most researchers. Apart from that, the set of ratios was supplemented with ratios representing other omitted aspects of financial analysis. For each financial statement included in the base, 19 financial ratios were calculated (independent variables) as well as dependence to one of four rating classes (dependent variable – output). Some of the selected ratios together with their economic interpretation are included in the table below:
Table 1. Selected financial ratios
Ratio Used by: Economic interpretation
individual result equity capital P. Fitzpatrick A. Hołda D. Witkowska S. Sojak, J. Stawicki
Measures the ability of enterprise equity to generate profit
equity capital outside capital
P. Fitzpatrick C.L. Merwin K. Michaluk
Informs about the capital structure and debt level
sales income total assets
E.I. Altman, B. Prusak L.V. Springate J. Gajdka, D. Stos
J. Fulmer, B. Back, T. Laitinen, K. Sere
E. Rahimian, S. Singh
K. Michaluk, K. Lee, I. Han, Y. Kwon
Determines the sales value generated by a single unit of the company property
3 Dziawgo D., Credit – rating. Risk and bonds on the international…. 4 Dziawgo D., Credit – rating imperfections, in Enterprise finance…
Ratio Used by: Economic interpretation K. Beermann Current assets current liabilities C.L. Merwin, H. Beaver A. Hołda, B. Prusak D. Appenzeller, K. Szarzec, E. I. Altman, R. Haldeman, P. Narayan-an, D. Hadasik
S. Sojak, J. Stawicki H. Koh, S. Tan
B. Back, T. Laitinen, K. Sere, D. Witkowska
Determines the enterprise ability to due settlement of short-term liabilities with regard to the use of current assets share capital balance sum E. I. Altman, R. Haldeman, P. Narayanan H. Koh, S. Tan
Ratio of share capital part in total assets
net result balance sum
W. H. Beaver, J. Gajdka, D. Stos, E. I. Altman, R. Haldeman, P. Nara-yanan
D. Appenzeller, K. Szarzec, H. Koh, S. Tan, B. Back, T. Laitinen, K. Sere K. Michaluk, K. Lee, I. Han, Y. Kwon
D. Witkowska
Determines the size of net profit made by a unit of capital engaged in the company assets
total operating income total assets
A. Hołda E. M czyska D. Witkowska
Indicates the income value generated by a single unit of capital engaged in the company property
operating result balance sum
B. Prusak B. Back
Informs about effectiveness of the use of all company resources independent from method of financ-ing
Source: Elaboration prepared by MSc J. Staczuk (Faculty of Economics, West Pomeranian University of Technology) based on Korol T., Prusak B., Enterprise bankruptcy and the use of artificial intelligence, CeDeWu Publishing House, Warsaw, 2005.
The descriptive features were marked in the following way:
•Attribute Wx, e.g. W1, W2, W3, where x is the ratio number from 1 to 19
•Study sample Ax or Bx, where x is company identification number in the base, letter A stands for 2006 and letter B – 2007. The samples were treated identically, independent from the year they came from.
Classification was done as examination of membership in one of 4 classes specified in accord-ance with credit risk groups. The applied scale (group set) is analogical to commonly known and used 6-grade credit-rating scale (the scale depends on individual rating agencies) Membership in a certain class is tantamount to evaluation of the financial situation, and weak financial status results in increased financial risk (and, thus, credit risk), while membership in a group of enter-prises with good financial situation reduces the risk. Characteristics of the individual classes is included in the table below, which also presents enterprises description in currently used 6-state scale for comparison. It might be assumed that the choice of a 4-state scale is in a way analogical to the linguistic description of cooperation risk used by world rating agencies.
Table 2. Characteristics of the states determining the enterprises activity risk in the proposed 4-state scale in comparison to current 6-state scale
State in 4-state scale
State characteristics in 4-state scale State in 6-state scale
State characteristics in 6-state scale
Risk class A
Counterpart of classes 1 and 2 in 6-grade scale Company in a good or perfect financial situation. High profit-ability, liquidity, low debt. Fully reliable contractor (borrower). Loan can be granted on general conditions or even preferential conditions.
Risk class 1
Contactor (borrower) is in a very good financial situation and is fully reliable. Possible economic relationship on preferable conditions.
Risk class 2
Contactor (borrower) is in a good financial situation and is reliable. Possible economic relationship on generally acceptable conditions.
Risk class B
Counterpart of class 3 in 6-grade scale. Company in a good financial situation, but there are certain short-term finan-cial problems. Good contractor (borrower). Loan available provided there is additional security of its repayment. Repayment monitoring is advisable here.
Risk class 3
Contractor (borrower) in a good financial situation, but there are short-term financial problems. Possible economic relationship provided there are additional securities of liabilities.
Risk class C
Counterpart of class 4 in 6-grade scale. Company endangered with deteriorat-ing financial situation. Restructurdeteriorat-ing actions are definitely advisable. Con-tractor (borrower) has minimum credit standing. Loan available only if strong and certain repayment securities are presented.
Risk class 4
Contractor (borrower) in a worse financial situation, endangered with deteriorating financial situation. Economic relationship possible only if strong and certain securities of liabilities are presented.
Risk class D
Counterpart of classes 5 and 6 in 6-grade scale The enterprise financial situation is very bad; company’s functioning in the future is very uncer-tain. There is a real bankruptcy risk or the company has already declared bankruptcy. Unreliable contractor (borrower).
Risk class 5
Contractor (borrower) is in a bad financial situation and is unreliable; the company’s future financial situation is uncertain. Economic relationship practically impossible.
Risk class 6
Contractor (borrower) in a very bad financial situation, completely unreliable. Further company’s func-tioning is endangered.
Source: Private study.
Letter symbols were used on purpose to mark the states as they are characteristic for scales used by international rating agencies. Numerousness of the individual classes in the study sample is presented in figure 1.
Figure 1. Proportions of cases from each class Source: Private study.
Numerousness of the individual classes is similar with a slightly decreased share of state D. this is the result of the polish economic life specifics where there are relatively few companies going bankrupt and access to financial documentation of the companies in crisis is difficult (or falsified).
4. Fuzzy evaluation of enterprises situation
The study included 19 financial ratios, which were calculated for each enterprise. The next step was the choice of a sub-set of ratios which best described the company’s financial situation. Ka packet was used for selection of attributes (input attributes). Selection of at-tributes in We-Ka pack requires definition of attributes evaluation method and data set search method. CfsSub-setEval was chosen as an evaluator for the purpose of the study and genetic search of the ratios space was used. The evaluator estimates the best sub-set of attributes-ratios with regard to their predictive abilities taking into consideration the degree of redundancy between them. A sub-set is chosen, which strongly correlates with the explained variable and is possibly weakly correlated in itself5 The use of this method allowed for determination of 4 attributes which best describe the dependent variable. As table 3 shows, the following 4 ratios were chosen for further analysis: W3, W11, W13 and W18.
5
Table 3. Ratios statistics and choice of attributes subsets for further study
Sym
bol Ratio name Average Minimum Maximum
Standard deviation
Selected ratio W1 ROE 0.0737 -32.576 16.003 1.5578
W2 Liabilities structure ratio 3.1510 -0.863 142.179 7.5864 W3 Working capital ratio 0.1948 -6.548 1.001 0.4673
9
W4 Assets structure ratio 0.0723 -0.998 5.446 0.2705 W5 Assets use effectiveness 0.1259 -1.779 6.774 0.3829 W6 Property turnover ratio 1.1679 0.000 11.338 1.0965 W7 Current liquidity 5.4900 0.004 1017.824 43.3032 W8 Total debt 0.4621 0.007 7.305 0.5251 W9 Overall property profitability 1.2450 0.002 11.354 1.1155 W10 Liabilities coverage with
property 4.1526 0.137 144.810 7.6359 W11 Operating profitability of
property 0.1033 -1.780 2.425 0.2590
9
W12 Sales profitability 0.8786 -307.000 357.790 24.1740 W13 Share capital property share 0.2321 0.000 5.686 0.4639
9
W14 Reserves turnover 0.1491 0.000 9.375 0.4548 W15 Quick liquidity 5.0419 0.004 1017.824 43.3284 W16 Cash debt coverage ratio 0,3853 -2,396 23,107 1,5479 W17 ROA 0.0742 -1.785 5.446 0.2784 W18 Gross ROA 0.1099 -1.785 2.426 0.2693
9
W19 Liabilities coverage ratio 0.4709 -2.056 31.862 1.6613
Source: Private study.
The next stage of the study was projection (conversion) of numerical values into linguistic variable values. The task was quite difficult as:
1)few ratios are given optimal values which they should assume (it must be considered that even the values provided in literature are not coherent);
2)the provided optimal values most frequently indicate two or maximum three sub-classes (optimal/non-optimal value or too low/optimal/too high value); such division significantly limits the construction of a sufficiently rich linguistic scale;
3)For some ratios it is necessary to use a benchmark method taking into consideration the market situation at a given moment and competition (e.g. reserves turnover ratio is significantly different for various branches);
Therefore, statistic methods supported with expert's knowledge were used while converting the numerical values into fuzzy sets. The space of ratios numerical values was divided into the rating membership classes and the range of assumed values was specified in each rating class. Values for individual classes overlapped to a greater or lesser extent, which was a significant problem while determining the membership function to the attribute fuzzy value. A serious prob-lem appeared to be the way in which to specify the range of numerical values so that the membership functions could be reliable and not reduce the excessive range of values which can be assumed in a given rating class.
The range of the ratios values for a given rating class can only be determined in an empirical way taking into consideration the limitations resulting from e.g. the available data set (which affects the assumed ratios values).
Influence of the data set on the assumed values depends on such properties of the available set as:
a)The number of companies from each branch included in a data set b)The economic situation during the data collecting period
c)The number of companies which belong to a given rating class (the smaller the set, the more difficult the statistical reasoning and the higher probability of error)
d)Mistaken data resulting from purposeful (or accidental) activity of company managers The basic assumption for the proposed fuzzy evaluation is its universality. Thus, the data set was considered as a whole without distinguishing the range of ratios in the individual branches. In order to determine the range of sharp values projected onto a specific class of linguistic descrip-tion, statistical methods and expert’s knowledge were used while observing the two rules mentioned above, i.e. precise evaluation and moderate limitation of the values set. As the type and shape of the membership function affects the accuracy of the model6 and selection of the simplest membership functions makes it possible to reduce the number of errors connected with improper model7, trapezoidal models, i.e. simple membership functions were used in practice. Percentiles were used to define the range of sharp values for each fuzzy rating class. It was assumed that the values located between 40th and 60th percentile are the first to have membership in a function of value equal 1.
Box plots showing the distribution of the averages and standard deflections for 4 selected rati-os are presented below:
6
Tavakkoli M., Jamali A., Ebrahimi A. New method to…, 2010. 7
Ratio W3 Ratio W11 ĝrednia ĝrednia±Błąd std ĝrednia±Odch.std 1 2 3 4 Rating -1,2 -1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 W 3 ĝrednia ĝrednia±Bł ĝrednia±Odch.std 1 2 3 4 Rating -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 W 1 1 lk Ratio W13 Ratio W18 ĝrednia ĝrednia±Błą ĝrednia±Odch.std 1 2 3 4 Rating -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 W 1 3 ĝrednia ĝrednia±Błąd std ĝrednia±Odch.std 1 2 3 4 Rating -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 W 1 8
Figure 2. Descriptive characteristics of statistical features for four selected ratios presented in table 3 Source: Private study.
The plots present the distribution of ratios values for each class.
As it was mentioned above, the linguistic values for each attribute were defined with the use of trapezoidal membership functions.8
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5. The rules basis and fuzzy state description
A set of simple rules was defined with the use of specified linguistic attribute values and ex-ample base. Due to a limited character of this publication, only 4 selected decision rules describing each state will be presented. The rules were established based on financial statements of 4 enter-prises randomly chosen from the base. While establishing the rules, the same weights were assumed for each attribute. The rules were obtained in the following form:
R1: IF W3 = very high AND W11 = very high AND W13 = low AND W18 = very high THEN Rating = A
R2: IF W3 = high AND W11 = high AND W13 = average AND W18 = high THEN Rating = B R3: IF W3 = average AND W11 = average AND W13 = low AND W18 = high THEN Rating = B
R4: IF W3 = low AND W11 = low AND W13 = very high AND W18 = low THEN Rating = A
A serious problem which occurs while constructing the base of fuzzy rules describing each of the states is the weight of each attribute. One of the most popular methods of assigning weights is the method of pair wise linguistic comparisons matrix proposed by T. Saaty9.
6. Conclusions
The studies conducted based on financial data of Polish companies listed on the stock ex-change made it possible to obtain characteristics for four financial states of an enterprise. This fuzzification complies with real distribution of features in the examined companies’ population. It is significant because, as a result of different economic conditions and accountancy standards, the average values and ratios distributions might vary in each country. Thus, it is not possible to project in an easy way any characteristics developed on the basis of specific data onto foreign financial data.
The presented description is a fragment of a real one which might consist of hundreds of ex-amples. However, already in this stage it is visible that the presented method for characterizing the situation is easily perceptible and understandable.
9
%LEOLRJUDSK\
[1] Dziawgo D., Credit – rating. Risk and bonds on the international financial market, Scientific Publishing House PWN, Warsaw, 1998.
[2] Dziawgo D., Credit – rating imperfections, in Enterprise finance, scientific editor Ostaszewski J., Warsaw School of Economics, Collegium of Management and Finance, Monographs and scientific elaborations, Warsaw, 2005.
[3] Hall M. A. Correlation-based Feature Subset Selection for Machine Learning, Hamilton, New Zealand, 1999.
[4] Korol T., Prusak B., Enterprise bankruptcy and the use of artificial intelligence, Warsaw, Cedewu, Warsaw, 2005.
[5] Michaluk K., Effectiveness of models predicting enterprises bankruptcy, Enterprise finances in the face of globalization, Joint work edited by Pawłowicz L., Wierzba R., Szczecin, Cedewu 2000.
[6] Piegat A., Fuzzy modelling and controlling, Exit, 1998.
[7] Saaty T. A Scaling Method for Priorities in Hierarchical Structures, J. of Mathe-matical Psychology. 1977. vol. 15. No 3. p. 234–281.
[8] Tavakkoli M., Jamali A., Ebrahimi A. New method to evaluate financial performance of companies by fuzzy logic: case study, drug industry of Iran, Asia Pacific Journal of Finance and Banking Research Vol. 4. No. 4. 2010.
[9] Wen-Ying Cheng, Ender Su and Sheng-Jung Li, A financial distress pre-warning study by fuzzy regression model of TSE-listed companies, Asian Academy of Management Journal of Accounting and Finance, Vol. 2, No. 2, 2006, p. 75–93.
ZASTOSOWANIE LOGIKI ROZMYTEJ
DO OCENY KONDYCJI PRZEDSIĉBIORSTW POLSKICH
Streszczenie
Proces polskich przemian (ekonomiczny zwrot), którego początek miał miejsce w roku 1989 nie był i nie jest procesem łatwym. Nie doczekał siĊ teĪ analiz w obsza-rze teorii zarządzania pobsza-rzedsiĊbiorstwem.
W prezentowanym tekĞcie pokazano element badaĔ, których celem jest uzyska-nie rozmytego modelu finansowego przedsiĊbiorstwa, jako systemu dynamicznego o zmieniającej siĊ strukturze. System taki moĪe okazaü siĊ pomocnym w sytuacji wspomagania decyzji w bieĪącym zarządzaniu przedsiĊbiorstwem. Poprzez okreso-we zmiany struktury finansookreso-wej uzyskaü moĪna efekt racjonalizacji procesów dynamicznych zachodzących w przedsiĊbiorstwie.
Słowa kluczowe: rating, analiza wska nikowa przedsibiorstwa, wzorcowy model przedsibior-stwa, rozmyty opis stanu przedsibiorstwa
Leonard Rozenberg Kinga Tomaszewska Patrycja Trojczak-Golonka Katedra Inynierii Zarz dzania Wydział Informatyki
Zachodniopomorski Uniwersytet Technologiczny w Szczecinie ul. ołnierska 49, 71-210 Szczecin
e-mail: lrozenberg@wi.zut.edu.pl ktomaszewska@wi.zut.edu.pl ptrojczak@wi.zut.edu.pl
