**3. Methodology**

In the conditions of the Slovak Republic, the municipality can conduct business activities as a legal entity in its own name (mainly in the case of smaller municipalities), with the help of a contributory/budgetary organization, or as a business firm established by the municipality. The municipality can also use its property to support the business activities of other entities located in its territory.

The aim of this paper was the economic evaluation of the managemen<sup>t</sup> of municipal firms at the level of rural local self-governments under the conditions of the Slovak Republic on the basis of selected available economic indicators—profitability and volume of sales. At the same time, we analyzed the relationship between these economic indicators and the size of the firm, longevity, or number of employees. For this purpose, we set research hypotheses, through which we tested the relationships between individual factors or differences based on them.

To answer the research question using the second economic indicator (volume of sales), one research hypothesis (H2) is defined, which is verified by means of four partial hypotheses focusing on individual identification factors as follows:

The individual hypotheses are processed in a dataset of 137 municipal firms with the following characteristics (see Table 1).


**Table 1.** Description of the selected variables.

Source: own processing.

Defining individual research hypotheses determines the apparatus of mathematical– statistical methods that are used for their evaluation. The basis was the verification of the normal distribution by means of the Shapiro–Wilk test (see Vavrek et al. 2020):

$$SW = \frac{\left(\sum u\_i \mathbf{x}\_i\right)^2}{\sum u\_i^2 \sum \left(\mathbf{x}\_i - \overline{\mathbf{x}}\right)^2} \tag{1}$$

where: *ui*constant;

 *xi*value of *i*-th statistical unit;

*x*average value of variable.

Due to the nature of the data for the evaluation of partial hypotheses (H1a, H1b, H3a, H3b), the Kruskal–Wallis test was used:

$$Q = \frac{12}{n(n-1)} \sum\_{i=1}^{I} \frac{T\_i^2}{n\_i} - 3(n+1) \tag{2}$$

where: *n*number of observations and sample size, respectively;

*ni*number of observations in *i*-th group;

*T*2*i*total number of orders in the *i*-th group.

Due to the nature of the data for the evaluation of partial hypotheses (H2a, H2b, H4a, H4b), a simple regression linear model calculated using the least squares method was used, while the explanatory value of the regression linear model thus created was verified using the coefficient of determination:

$$R^2 = \frac{\sum\_{i=1}^{n} \left( y\_i - \hat{y}\_i \right)^2}{\sum\_{i=1}^{n} \left( y\_i - \overline{y}\_i \right)^2} \tag{3}$$

where: *yi*measured value of dependent variable;

> *y* ˆ *i*estimated value of dependent variable;

*yi*estimated value of dependent variable.

All analyses and calculations were processed using MS Excel, Statistica 13.4 and Statgraphics XVIII.

The reason for choosing rural municipalities is the fact that according to the OECD, the Slovak Republic is a rural country and the majority of the population lives in the countryside. This is also confirmed by Table 2, which shows that of the total number of municipalities in the Slovak Republic (2890), rural municipalities make up 95.33%, which represents 2755 municipalities out of the total number. There are 2,526,748 inhabitants in rural municipalities, who represent 46.30% of the total inhabitants of the Slovak Republic.

**Table 2.** Number of municipalities and number of inhabitants in municipalities in Slovak Republic on 31 December 2019.


Source: Statistical Office of the Slovak Republic, own processing.

In addition to being a rural country, the Slovak Republic is also characterized by a fragmented settlement structure (see also Vavrek 2015). This is also confirmed by Table 3, which shows that in terms of the number of small municipalities with less than 5000 inhabitants, most of them are located in the Prešov region, while the least rural municipalities are in the Bratislava region. The presence of a large number of small rural municipalities also has an impact on the overall economy of the region. In the Bratislava region, where the least small municipalities are located, the largest regional GDP per capita is generated. The Prešov region, with the largest number of municipalities with less than 5000 inhabitants, generates three times less regional GDP compared to the Bratislava region.


**Table 3.** Demographic and economic characteristics of Slovak regions on 31 December 2019.

> Source: Statistical Office of the Slovak Republic, own processing.

In these rural municipalities (up to 5000 inhabitants), a total of 318 municipal enterprises were registered in 2021, based on data from the Register of Financial Statements. Most municipal firms were based in the Prešov region, and the least number in the Bratislava region. However, the base file database also included municipal firms with an incomplete range of data, municipal firms in bankruptcy or municipal firms that have already ceased to exist. For this reason, we decided to analyze a sample of municipal firms in the time period 2015–2019. A sample consisting only of municipal firms that fulfilled the following parameters was used: data are available for the entire reference time period 2015–2019; the entity is not in bankruptcy; the subject did not cease to exist on 1 January 2021 and is performing its activity, i.e., is active. The number of municipal firms which fulfilled all of the abovementioned parameters was 137.

#### **4. Results and Discussion**

In the conditions of Slovakia, the municipality as a legal entity has the right to conduct business through any form in accordance with act no. 513/1991 Coll.—Commercial Code as amended. Pursuant to the provisions of the Commercial Code, as of its entry into force on 1 January 1992, commercial firms may also be established by municipalities. The municipality can establish a business firm as the sole shareholder or as the sole companion. In such a case, the competence of the general meeting is performed by the statutory body of the municipality, which is the mayor of the municipality. The advantage of this form of managemen<sup>t</sup> is that the municipality, based on the use of its own property for business purposes, can simultaneously ensure revenues to the municipal budget and also solve the problem of unemployment. The problem with this form of conducting business with municipal property is the big concentration of decision-making power of the mayor, who, on the one hand, acts as the statutory body of the municipality and, on the other hand, acts as the statutory body of the firm. It follows that, in the process of such a two-pronged decision, he may give priority to his private interest over the public interest. This form of business can lead to the targeted privatization of municipal property. In practice, only capital firms are appropriate for municipalities. According to the Commercial Code, a limited liability company can also be established by one person, and the company can have a maximum of 50 partners. The company is responsible for its liabilities with all its assets, and the partner is liable for the company's liabilities up to the amount of its

unpaid deposit entered in the Commercial Register. The value of the share capital must be at least EUR 5000; this share capital consists of cash and non-cash deposits, and the value of the shareholder's contribution must be at least EUR 750. If the company is founded by one founder, the base is a founding agreement; if there are several founders, then a partnership agreemen<sup>t</sup> is written. In the case of the participation of a municipality in such a company, the founding or social contract is signed by the mayor only with the consent of the municipal council. In this context, we consider it necessary to state that in some companies in which the municipality has an ownership interest, a larger number of partners in the position of various natural and legal persons can participate. Several companies are also registered, where only municipalities are the exclusive partners, in various numbers. An example of a large number of partners can be a company registered by the District Court of Nitra, which unites up to 12 municipalities, and whose subjects of business are mainly activities necessary for municipalities, e.g., waste management, construction activity, operation and maintenance of water supply and sewerage network. Other companies are registered by the District Court of Košice I, which concentrates 18 municipalities and whose subject of business is, in addition to waste managemen<sup>t</sup> and production (Hudec 2011). Although these companies operate in a competitive market environment, their important mission is often to provide services to the population. Their purpose is not only financial gain, but also non-financial profit. This means that, in addition to financial gain, their activities can increase the scope and quality of services provided in the framework of public benefit activities. However, if they focused only on providing services to the inhabitants, and managing loss, the result would be the devaluation of municipal property and eventual bankruptcy. The profitability of municipal firms in individual regions of the Slovak Republic in 2019 is shown in Figure 1. We can observe differences mainly at the level of individual entities, not the group as a whole, which captures the occurrence of remote (or extreme) observations in all regions except the Bratislava region (BA).

**Figure 1.** Profitability of municipal firms: by region, 2019 (hypothesis 1a). Source: own processing.

Statistically significant differences using the Kruskal-Wallis test (Table 4) indicate a different situation in the individual analyzed years, while in 2018 and 2019, the differences between the regions were not demonstrated.

Figure 2 shows the profitability of municipal firms according to the number of employees in 2019 (or size groups). The majority of firms are relatively balanced, but graphic differences can be identified in the number of remote (or extreme) values in individual groups, and in the municipal firms with significantly better or worse results compared to the results of others in the given size group.


**Table 4.** Results of verification of research hypothesis 1a.

Source: own processing.

**Figure 2.** Profitability of municipal firms by number of employees in 2019 (hypothesis 1b). Source: own processing.

Differences in the mean value of profitability of individual groups of municipal firms (using the Kruskal-Wallis test) proved to be statistically significant only in the first of the evaluated years—in 2015. In other years, we did not register differences between municipal firms (see Table 5).

**Table 5.** Results of verification of research hypothesis 1b.


Source: own processing.

Based on the above, it is not possible to confirm partial research hypothesis 1a, which means that differences in the profitability of municipal firms from the point of view of the region in which the municipal firm operates are not statistically significant. The same conclusion can also be stated in the case of partial research hypothesis 1b, when the differences in the profitability of municipal firms in terms of the number of employees are also not statistically significant. Based on this evaluation of partial research hypotheses 1a, 1b, we also reject research hypothesis 1.

In partial research hypothesis 2a, we assume the dependence of the profitability of municipal firms on the size of the municipality in which the municipal firm is located, while the degree of this dependence in 2019 is shown in Figure 3. This dependence can be expressed by a linear regression model with Profit = 0.92936 × number inhabitants (R<sup>2</sup> = 0.09%).

**Figure 3.** Dependence of profitability of municipal firms on the size of the municipality in 2019 (hypothesis 2a). Source: own processing.

In the individual analyzed years 2015–2019, we observe similar results, while each time the dependence of profitability on the number of inhabitants is positive, it means as the population of the municipality grows, so does the profitability of municipal firms in this municipality (Table 6). However, the regression models themselves reach a low significance value expressed by the coefficient of determination.


**Table 6.** Results of verification of research hypothesis 2a.

Source: own processing.

Within the second partial research partial hypothesis 2b, we assume an increase in profitability together with an increase in the time of operation of the municipal firm on the market—its longevity. The results in 2019 shown in Figure 4 and the regression function P2019 = 1.84035 × longevity indicate a positive dependence, which is, however, influenced by other factors that are not included in this model (R<sup>2</sup> = 2.74%).

**Figure 4.** Dependence of profitability of municipal firms on its longevity in 2019. (hypothesis 2b). Source: own processing.

As in the previous case, in the individual analyzed years, 2015–2019, we can see similar results, while each time the dependence of profitability on the longevity of municipal firms on the market is positive, this means that the number of days a municipal firm operates on the market increases its own profitability (Table 7). Such an interpretation of the results is also influenced by their low explanatory power, as the variability of the dependent variable is significantly influenced by other factors.


**Table 7.** Results of verification of research hypothesis 2b.

Source: own processing.

Based on the above, especially very low values of the coefficient of determination (R2), it is not possible to confirm the linear dependence of the profitability of municipal firms on the size of the municipality in which the municipal firm is located, and so partial research hypothesis 2a cannot be confirmed. We also observe very low values of the coefficient of determination in the case of the second partial research hypothesis 2b, so similarly, partial research hypothesis 2b cannot be confirmed. Based on this evaluation of partial research hypotheses 2a, 2b, we also reject research hypothesis 2.

The volume of sales of municipal firms in 2019 by individual regions is shown in Figure 5. With the exception of the Bratislava region (BA), we observe municipal firms in each of the regions, whose results deviate from other results in individual regions, which can be described as remote and extreme values, respectively.

**Figure 5.** Volume of sales of municipal firms by region, 2019 (hypothesis 3a). Source: own processing.

The occurrence of such municipal firms with different results persists across the years 2015 to 2019, which we label as homogeneous. The differences between the individual regions did not prove to be statistically significant or stable, which we deduce from the absolute values captured in Table 8.

Based on Figure 6, we can state that with the growth of the number of employees (size group), the volume of sales of municipal firms also increases. The results, with the exception of the first group (up to 10 employees), are relatively balanced, as we do not observe the occurrence of remote (or extreme) results.


**Table 8.** Results of the verification of research hypothesis 3a.

Source: own processing.

**Figure 6.** Volume of sales of municipal firms by number of employees in 2019 (hypothesis 3b). Source: own processing.

Differences in the mean value of the volume of sales of individual size groups (using the Kruskal–Wallis test) proved to be statistically significant in each of the evaluated years, 2015, 2016, 2017, 2018 and 2019. The size of the municipal firm is, therefore, a factor influencing the volume of sales (see Table 9).



Source: own processing.

Based on the above, it is not possible to confirm partial research hypothesis 3a—the differences in the volume of sales of municipal firms from the point of view of the region in which the municipal firms operate are not statistically significant. The exact opposite conclusion can be stated in the case of research hypothesis 3b—the differences in the volume of sales of municipal firms in terms of the number of employees are statistically significant. Therefore, based on the evaluation of partial research hypotheses 3a, 3b, it is not possible to unequivocally reject or confirm research hypothesis 3. This conclusion is also confirmed by the research of municipal firms in Sweden. Municipalities in this country employ on average 18% of the country's total workforce. In some municipalities, where municipal firms focus on social services in relation to the elderly or children, this share can be much higher, even at the level of 30%. If municipalities do not create municipal firms, but create conditions for business activities of private firms, this share is much lower. However, in such a case, there is no statistically significant correlation between employment in municipalities and employment in the vicinity of the municipality in terms of population density (Fölster et al. 2016). The situation is similar in all historical regions of Poland, where more than four-fifths of local self-governments have taken measures to increase the number of local jobs, two-fifths of which were municipalities in Greater Poland. This area thus pursued a more dynamic development policy through the development of municipal business activity (Gorzelak 2019). Within partial research hypothesis 4a, we assume the dependence of the volume of sales of municipal firms on the size of the municipality in which the municipal firm is located (as well as in the case of their profitability). The degree of this dependence in 2019 is shown in Figure 7, while it can be expressed by a linear regression model with a function in the form S2019 = 85.1138 × number of inhabitants of the municipality (R<sup>2</sup> = 18.07%).

**Figure 7.** Dependence of profitability of municipal enterprises on the size of the municipality in 2019 (hypothesis 4a). Source: own processing.

In the individual analyzed years, 2015–2019, we observe similar results, while each time the dependence of profitability on the number of inhabitants is positive, it means that with the growth of the population in the municipality, the volume of sales of municipal firms in this municipality is also growing (Table 10). Low values of the coefficient of determination (R2) indicate that the volume of sales of municipal firms is significantly influenced by other factors, not only the number of inhabitants in the municipality.


**Table 10.** Results of verification of research hypothesis 4a.

Source: own processing.

The second partial research hypothesis 4a assumes an increase in the volume of sales together with an increase in the time of operation of the municipal firm on the market—its longevity. The results in 2019 shown in Figure 8 and the regression function S2019 = 42.5075 × longevity illustrate positive dependence, which, however, can be marked as partial (R<sup>2</sup> = 33.02%).

In the case of partial research hypothesis 4b, we can see similar results in the individual analyzed years, 2015–2019, while the dependence of the volume of sales on the time of operation on the market (longevity of municipal firm) is significantly positive. As the number of days a municipal firm operates on the market increases, so does its profitability (Table 11).

**Figure 8.** Dependence of the volume of sales of municipal firm on its longevity in 2019 (hypothesis 4b). Source: own processing.

**Table 11.** Results of verification of research hypothesis 4b.


Source: own processing.

Based on the above, especially the very low values of the coefficient of determination (R2), it is not possible to confirm the linear dependence of the volume of sales of municipal firms on the size of the municipality in which the municipal firm is located. Therefore, partial research hypothesis 4a cannot be confirmed. The same conclusions are drawn in the case of the second partial research hypothesis, when we observe low values of the coefficient of determination, so partial research hypothesis 4b cannot be confirmed. The volume of sales of municipal firms with the population of the municipality as well as the time of operation on the market is growing, but these are not the only factors on which these results depend. Based on such an evaluation of partial research hypotheses 4a, 4b, we also reject research hypothesis 4.

## **5. Conclusions**

In the Slovak Republic, rural areas represent 86% of the territory in which 43% of the population live. It is a heterogeneous area in which natural, human and economic resources are used. The Slovak countryside is characterized by a highly diverse physical environment, a wide range of economic activities, a characteristic network of social relations and centuries-old cultural traditions.

Economic activities in rural municipalities are developed not only by the private sector, but also by the municipalities themselves through their municipal firms. Analyses showed that in 2021, 318 municipal firms had their headquarters in rural municipalities. In the analysis of mutual relations of the most important economic indicators, profit and sales and number of employees, longevity or size, we found that differences in the profitability and sales volume of municipal firms from the perspective of the region in which the municipal firm operates are not statistically significant. It is also not possible to confirm the linear dependence of the profitability of municipal firms on the size of the municipality in which the municipal firm is located. However, it is possible to confirm the positive dependence between the growth of the population of the municipality and the growth of sales of municipal firms based in this municipality. However, low values of the coefficient

of determination (R2) indicate that the volume of sales of municipal firms is significantly affected by other factors, not only the number of inhabitants of the municipality.

The results of the analysis confirm the fact that general enterprises are specific in comparison with traditional business entities, and it is not possible to analyze them with the general common ratio indicators of financial analysis, such as profitability indicators: ROE and ROA; indicators of activity; indicators of indebtedness; market value or liquidity. These indicators are of large importance from the point of view of comparing business entities, but from the point of view of municipal firms, they are not sufficiently informative, as the reasons for establishing municipal enterprises are different from those of commercial firms. While the business sector creates firms that it knows will make a profit as they provide services and goods that are in demand, it is different for municipal firms. Municipal firms often also provide services that the private sector does not want to provide precisely due to low profitability (e.g., small community services). Municipal firms are established primarily for the purpose of providing services to the population and creating jobs, and only then are they created for profit. The profit and revenue indicators that we analyzed in the case of municipal firms are important from the point of view of their sustainability, but also from the point of view of the financial managemen<sup>t</sup> of municipalities. Through revenues, municipal firms cover their costs and thus reduce their dependence on the municipal budget, as in the event of a decrease in revenue, the municipality usually subsidizes such enterprises through subsidies from its budget. There are similar differences in the case of profit. Part of the profit is invested by municipal firms and part of it flows into the municipal budget. In this way, municipal firms play a significant role in the socio-economic development of the municipality.

Although the business activity of rural municipalities implemented through municipal firms enables revenues to the local budget, the area of business with municipal property is generally not given much attention under the conditions of the Slovak Republic. The reason for this is that there is no system for classifying firms owned by local self-governments. Likewise, legislation at the national but also at the local level does not recognize the concept of a municipal firm and its operation. The results of the analysis confirm that municipal firms are an important part of the local economy and, therefore, it would be appropriate to legislate the existence and functioning of municipal firms as a special form of business with local self-government property. As inspiration for legislation, we recommend EU legislation, which defines the concept of a public firm in Articles 106 and 345, Treaty on the Functioning of the EU, as a firm over which public authorities have a direct or indirect dominant influence.

The results of the analysis also showed that municipal firms, in addition to revenues to the local budget, also create employment in the municipality with a direct impact on local economic development. Nevertheless, insufficient information is available to assess social and other effects of municipal firms. Research in the field of municipal firms under the conditions of the Slovak Republic is still in its infancy. It can be assumed that in the future, other aspects of municipal business could be included in the model and examined, e.g., the Statistical Classification of Economic Activities is fully compatible with the European classification NACE Revision 2 (SK NACE), property information, demographic data and macroeconomic data of individual regions or districts.

By analyzing selected indicators, we aimed to highlight the specificity of business of municipal firms under the conditions of the Slovak Republic. The database for municipal firms is very limited, despite the fact that these firms are an important factor in the development of the territory. Therefore, in order to make the functioning of municipal firms more efficient, their activities and economic stability should be regularly monitored and evaluated, especially from the point of view of local development. Also, to clearly define the legislation adopted at the local level (resolution of the municipal council and principles on the disposal of municipal property), because the municipality's property creates not only economic but also social conditions in the municipalities.

**Author Contributions:** Conceptualization, P.Á. and V.P.; methodology, R.V. and V.P.; software, R.V.; validation, P.Á., R.V., M.D. and V.P.; formal analysis, P.Á., R.V., M.D. and V.P.; investigation, P.Á., R.V., M.D. and V.P.; resources, P.Á., R.V., M.D. and V.P.; data curation, R.V.; writing—original draft preparation, P.Á., R.V., V.P. and M.D.; writing—review and editing, P.Á., R.V., M.D. and V.P.; visualization, P.Á., R.V., M.D. and V.P.; supervision, V.P. and M.D.; project administration, P.Á. and V.P.; funding acquisition, R.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Student Grant Competition in VŠB - Technical University of Ostrava, gran<sup>t</sup> number SP2021/18.

**Acknowledgments:** We would like to thank the anonymous referees for their useful comments and constructive suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.
