“Business performance assessment of small and medium-sized enterprises: Evidence from the Czech Republic”

Business performance assessment is one of the basic tasks of management. Business performance can be assessed using a number of methods. The basic ones include financial analysis, Balanced Scorecard or Economic Value Added (EVA). The paper is focused on SME business performance assessment based on Economic Value Added, calculated using the INFA build-up model. According to this method, companies were divided into four categories. The first category included companies with a positive EVA value. The second category included companies with negative EVA, but with the eco- nomic result above the risk-free rate. The third category included companies with a positive economic result above the risk-free rate. The fourth category included compa- nies with a negative economic result. The model did not include companies with negative equity. The input represented 15 predictors based on their financial statements. The data were normalized and all extreme values, likely caused by a data rewriting error, were removed. Company performance is visualized by comparing Principal Component Analysis and Kohonen neural networks. Compared to similar research, the methods are compared using the data that analyzes the performance of companies. Both methods made it possible to visualize the given task. With regard to the purpose of facilitating the interpretation of the results, for the given case, the use of PC seems to be more appropriate. be very useful for the interpretation of the results supporting the decision-making process (Marakas, 1999). The objective is to compare the use of the PCA method and Kohonen neural networks (Matlabacademy, 2019) for the visualization purposes in the classification of businesses. A com-parison of these methods (Brosse et al., 2001) has already been ana-lyzed in technical fields (Blayo & Demartines, 1991). Newly, these methods are also used to analyze economic factors predicting the performance of small and medium-sized enterprises in the Czech Republic. Thus, the paper is aimed at assessing SMEs’ business performance based on Economic Value Added, calculated using the INFA build-up model.


INTRODUCTION
When running a business, it is often necessary to make decisions in very complex processes (Synek, 2011). Assessing the influence of individual predictors is often difficult and time-consuming, especially in the case of a dimensional decision problem when individual predictors influence the result (Oo & Thein, 2019). For business managers, mathematical models are often difficult to understand and interpret. Here, the visualization of data can be very useful for the interpretation of the results supporting the decision-making process (Marakas, 1999). The objective is to compare the use of the PCA method and Kohonen neural networks (Matlabacademy, 2019) for the visualization purposes in the classification of businesses. A comparison of these methods (Brosse et al., 2001) has already been analyzed in technical fields (Blayo & Demartines, 1991). Newly, these methods are also used to analyze economic factors predicting the performance of small and medium-sized enterprises in the Czech Republic. Thus, the paper is aimed at assessing SMEs' business performance based on Economic Value Added, calculated using the INFA build-up model.

Business performance assessment
There are several approaches to assessing business performance. The traditional approach deals with horizontal and vertical financial analysis (Vochozka, 2011), where it is possible to assess a wide range of indicators from activity to Return on Equity (ROE), which is the most frequently used one. ROE is calculated as follows: , where EAT is earning after tax, E is equity.
The approach using horizontal and vertical analysis has a number of benefits and shortcomings. The main shortcomings include an independent view of individual indicators that can often be distorted by the character of the business or high degree of risk, which is not considered in the formula.
Another possible approach is Value Based Management (Nývltová & Marinič, 2010). This method compares the overall benefit of the investment with its costs. The calculation is carried out using the following formula: where Rt is the total return to the shareholder; Pt + 1 is the value (price) of investment at the end of the period (given by the share price and number of shares); Pt is the value (price) of investment at the beginning of the period (given by the share price and number of shares); Dt + 1 is dividend yield.
This method is the base of the approaches based on Market value added and Economic value added. Performance can be assessed in terms of economic value added (Neumaierová, 1998), whose results can be used for business management (Neumaierová, 2003). Moreover, EVA results can be used as an input for business valuation (Mařík, 2011), as an assessment of financial health of companies (Vrbka & Rowland, 2019) or as a motivation system for managers (Kislingerová, 2007).
On the other hand, the performance can be assessed by Balanced Scorecard (Kaplan & Norton, 1992). Alternative possibilities of business performance assessment can include neural networks and others (Machová & Vochozka, 2019).
This study also focuses on Economic Value Added, since it is a clearly measurable method that is also suitable for small and medium-sized enterprises.

Economic Value Added (EVA)
EVA is calculated using the build-up model as follows (Neumaierová, 1998). There is an alternative approach based on the CAPM method (Vochozka, 2011); however, it is not suitable for small and medium-sized enterprises.
First of all, cost of equity is calculated: where A represents total assets, E is Equity, D is long-term liabilities, r d is cost of borrowed capital, and WACC -average weighted cost of capital.
The average weighted cost of capital is calculated as follows: where r business is business risk, r FinStab is financial stability risk, r f is risk-free rate, and r LA is risk involved in capital structure.
Economic value added is finally calculated as follows: where ROE is return on equity, and r e -alternative cost of equity.

Principal component analysis
Principal component analysis is a method that reduces the number of predictions. Generally, the reduction of decision problem to the key components is very important for the management, since it clarifies the decision process and makes the interpretation easier. The reduction is carried out by means of converting the original predictors, which are partly correlated into a new space with a reduced number of predictors (Shaw, 2003) that are independent of each other. Due to this fact, complex methods with reduced data can be applied, and new predictors can be used to visualize the task more easily. The method appeared at the beginning of the 20th century (Pearson, 1901), and was subsequently developed and named (Hotelling, 1933). Its greater use is associated with the development of information technology, where visualization plays a significant role and is not time-consuming in terms of individual partial measurements.
An important feature of this method is that each of the new components is a linear combination of the original predictors. This prevents the loss of the original data. The linear combination of the individual parts of the predictors into a component enables monitoring the variance of the relevant component. The greater the variance, the more important is the component for the prediction. Sorting the individual components by variance allows dividing the components into significant and less significant and determining the percentage importance of the component. Business management thus has the information on the parameter that influences decision making, as well as on the importance of this parameter. In practice, it is not possible to address absolutely all the facts in the micro and macro environment. For this reasons, various systems are used, such as ABC, where management is first and foremost committed to the most important components with the greatest impact on the result, and subsequently to other components. Figure 1 shows the principle of PCA. On the left side, there is a data set whose location in space is determined by two predictors. On the right side, there is a line that best defined the data in the given space. The slope of the line is determined on the basis of minimizing the distance between the individual dots from the line.  The line in Figure 1 (the right side) is a new component (dimension) of PCA, which shows the greatest variance for the given task. Due to this, it is possible to redraw the task into a one-dimensional space ( Figure 2). This redrawing causes minimal distortion of the data compared to the situation when the data is entered in the x-or y-axis (in the previous case). Thus, it was possible to reduce the number of variables with a minimum loss of information. The PCA method also allows other dimensions to be calculated and data displayed with nearly zero loss of information.

Kohonen networks
Kohonen networks (Kohonen, 1982) are neural networks that learn without a teacher (Vojáček, 2006). The basic idea consists in the random arrangement of neurons in two-dimensional space (Kohonen, 1989). In the following steps, the individual neurons are moved to represent certain data clusters on the basis of the predictors (Buhmann & Kuhnel, 1992). Each predictor is connected with an individual neuron. The strength of the connection determines the position of a given neuron (Vondrák, 2000). The principle is shown in Figure 3. Figure 3 shows Kohonen network with nine neurons (3x3), and two inputs (predictors), which are connected with the individual neurons.

METHODOLOGY AND DATA
After generation from the Bisnode's Albertina database, the data set contained a total of 42,592 data rows. Each row contained the following information: 1. Identification of a company: name, company identification number, municipality, region, municipality size.
2. Information about a company: NACE, number of employees, code of NACE5A, M_NACE, OKEČ5A, year of financial statement.
3. Financial statements for the given year: balance sheet, profit and loss account, statement of cash flows.
Preparation of data (MS EXCEL): 1. Calculation of EBIT (by adding taxes, interests and EAT).

Figure 3. Kohonen network
Source: Own processing according to Vondrák (2000). The modification reduced the data set from 42,592 rows to 29,611 rows (in Table 2). The resulting data set also contains a complete financial statement with several calculated data stated above. The data can thus be considered predictors (more than 100). For these reasons, the resulting set of companies will be reduced to the main components, and in accordance with the Neumaiers' methodology (Ministry of Trade and Industry, 2019), a category of the companies will be determined following the scheme below.
• Companies with positive profit and negative EVA value, but exceeding the risk-free rate rf -re > ROE > rf.
• Companies with positive profit, where ROE does not achieve the risk-free ratere > rf > ROE > 0.
• Companies with negative profit.
The data will be involved in further analyses. The main predictors are as follows: • Total assets -CZK thousands.
• Fixed intangible and tangible assets depreciation -CZK thousands.
• Income tax on ordinary and extraordinary activity -CZK thousands.
Displaying more than 20,000 companies was complicated because their high number caused the creation of continuous color clusters that covered less frequent clusters in groups. For these reasons, the number of companies was reduced to 4,000. The percentage of individual categories remained the same. The data was normalized for the methods, as otherwise, the methods would provide erroneous results (Abdi & Williams, 2010). The normalization was carried out using the "normalize" command. Furthermore, extreme values were removed using the "outliers" command.

RESULTS AND DISCUSSION
In the first phase, the PCA analysis was carried out. With the normalized data set, the following command was executed: By means of pareto (procenta) command, a new graph was generated ( Figure 4). Figure 4 clearly shows that it is possible to obtain about 80% of the information from the first three components, and more than 70% from the first two components. The remaining components are thus of relatively negligible importance.
By means of the "biplot" command, it is possible to see how the individual parts participate in a given component. A positive value represents a positive correlation, while a negative value represents a negative correlation. The result is shown in Figure  5. Using the "gscatter" command, the position of companies in two-dimensional space can be visualized.
In the next stage, Kohonen neural network with the dimensions of 5x5 was created. When creating this network, it is possible to see the mutual dependence of the individual predictors. The result can be seen in Figure 7. The more different color for each node, the less dependent the relevant pre-Source: Own processing.  Particularly the right part of the graph shows that for certain clusters, Kohonen network al-lows creating a representative element (neuron), which will be in the relevant category by company performance.
By means of the "gscatter" command, the position of companies in two-dimensional space can be visualized. Moreover, it is possible to distinguish the individual sets of companies from each other by means of color (see Figure 6). Figure 6 clearly shows 4 groups of companies created in the graph. These groups represent the category of a company according to the INFA methodology. Thus, to Source: Own processing.

Figure 5. Individual parts involved in a component
Source: Own processing.

CONCLUSION
This study calculated business performance based on Economic Value Added, which is the key information for business management. The calculation method was based on the INFA build-up model. On the basis of this value, performance of these enterprises was visualized using selected items of accounts. Despite its spatial complexity, it was possible to carry out the visualization so that it is useful for the management.
Both methods can be used to visualize company performance. Performance visualization can facilitate the decision-making process in a number of cases (e.g. about the cooperation with a given company, equity investment, etc.). Both methods can provide analytic tools to identify which parameters were used to decide on the classification in a concrete group. With regard to the allowed extent of the paper, these analytic methods were presented and described from the perspective of the most important outcomes.
The objective of the analysis was to simplify the decision-making process by means of visualization. In other words, the visualization was supposed to lead to a segmentation that could be easily interpreted. Given the purpose of the analysis, PCA seems to be a more effective visualization method in this particular case due to easier and more unambiguous identification of the classification of individual companies into sets that express company performance. It is also easier to understand and interpret a company's position in a given space.
The limitation of the study is mainly in the input data, which is based on the obligation of companies in the Czech Republic to publish their financial statements. Nevertheless, the statements are subject to tax optimization, which can be quite easy to implement in the case of small enterprises. In other words, a category 3 or 4 company may, in fact, bring a sufficient return on resources for the owner. However, this return is not shown in the financial statement with respect to the tax deduction. Finally, it shall be mentioned that, despite the legal obligations, not all companies complete financial statements. This is especially true for companies in difficulty. This distorts a number of companies in individual categories.