Early Insolvency Prediction as a Key for Sustainable Business Growth

Abstract

This research aimed to determine whether and how financial analysis combined with machine learning can support decision-making for sustainable business growth. This study was conducted using a sample of 100 Serbian companies whose bankruptcies were initiated between 2019 and 2021 to identify key factors that distinguish solvent from insolvent companies. Two neural networks (NNs) were trained and tested to predict these discriminating factors one year (Y-1) and two years (Y-2) before bankruptcy initiation. Initially, a total of 37 predictor variables were included, but prior to modeling, variable reduction was performed through VIF analysis and t-tests. The training dataset comprised 70% of the sample, while the remaining 30% was used for testing. Both NNs utilized a softmax activation function for the output layer and a hyperbolic tangent for the hidden layers. Two hidden layers were included, and training was conducted over 2000 epochs using the gradient descent algorithm for optimization. The research results indicate that poor cash management is the first sign of possible insolvency one year in advance. Additionally, the findings reveal that retained earnings management can serve as a reliable bankruptcy predictor two years in advance. The overall predictive accuracy of the NN models is 80.0% (Y-1) and 73.3% (Y-2) for the testing dataset. These findings demonstrate how selected ratios can support bankruptcy prediction, providing valuable insights for company proprietors, management, and external stakeholders.

1. Introduction

When it comes to having a business, one of the important issues is sustainable business growth. Sustainable growth is a concept focused on the future business and based on the long-term survival of the company and the creation of value [1]. Sustainable business growth is the outcome of a growing understanding of the value-generating potential of sustainable markets, as well as a significant shift in corporate strategies toward greater social and environmental goals [2]. Many businesses are turning to sustainable growth to differentiate themselves, boost their brand image, and expand into new markets [3]. Growth, sustainability, and innovation are three manifestations of an enterprise’s capacity for sustainable growth [4]. Protecting the bankruptcy of the firms plays a vital role in making the organization sustainable [5].

Contemporary business conditions in which today’s companies operate require companies to be able to fulfill their obligations in order to not be eliminated by competitors. Executives make many of the decisions without analyzing the information related to the future perspective of the firm’s performance. In such uncertain conditions, risk increases, and the firm faces a crisis that leads to financial distress and even bankruptcy [6,7]. A company is said to be insolvent or under financial distress if it is unable to pay its debts as they become due, which is aggravated if the value of the firm’s assets is lower than its liabilities [8]. The inability to settle liabilities may be due to a lack of funds or the weaknesses of the management in the use of these funds. The inability to settle the liabilities leads to financial distress for the company [9]. The evaluation of corporate financial distress has attracted significant attention globally as a result of the increasing number of corporate failures worldwide. There is thus an immediate and compelling need for more effective financial distress prediction models [10].

The problem of predicting insolvency has intrigued the scientific community for a long time. During the years, starting from mid-1960s, insolvency prediction models have evolved significantly from discriminant analysis to advanced machine learning methods, such as neural networks. An artificial neural network (ANN) is a mathematical model that is inspired by the information processing capabilities of the human brain [11]. Lukić et al. emphasize that neural network knowledge is a key prerequisite for improving business operations through a higher degree of control efficiency [11]. As the literature states, neural networks contribute to the improvement of managerial decision quality [12]. Anandarajan et al. [13] applied artificial neural networks to solve many problems, emphasizing bankruptcy prediction. In addition to bankruptcy prediction, the use of neural networks in financial economics and business forecasting is broad and includes time series modeling, risk assessment, stock market prediction, foreign exchange rate forecasting, GDP forecasting, and more.

According to the author’s knowledge, similar research on bankruptcy prediction using artificial neural networks methodology has not been carried out in Serbia. The authors noticed this lack of research and recognized it as a gap, and for this purpose, they carried out the research. The motivation for empirical research in insolvency prediction is the early detection of the financial distress of the company and crisis prevention that most often leads to bankruptcy. The main aim of the research is to develop a neural network model that can reliably predict insolvency in companies in the Republic of Serbia. The research examines whether financial indicators can be reliable support for insolvency prediction one and two years in advance because a one-to-two-year time horizon allows timely intervention and proactive measures to be taken.

Bearing in mind previous research and empirical studies, as well as research conducted by Lin [14], Kim and Kang [15], Ravisankar et al. [16], and Bredart [17], the following hypothesis was set:

Hypothesis 1.

Artificial neural networks combined with financial ratios can be a reliable basis for bankruptcy prediction of Serbian companies one and two years in advance.

The research results provide company management, investors, creditors, and other stakeholders with the information necessary to identify potential financial distress and implement strategies to improve the company’s financial health. Research results can be beneficial for business owners on the one hand, but also for external stakeholders on the other hand, since they can indicate what variables are the main future insolvency predictors. Finally, the research results partially eliminate the observed lack of research the existing literature related to the early insolvency prediction in Serbian companies.

This research paper is organized as follows. The first part is related to the literature review. The next chapter refers to the sample, variables, and research methodology explanation. In the third chapter, research has been conducted and analyzed. The final chapter includes the research results discussion and conclusion.

2. Theoretical Background

Based on the distinction between companies with a high probability of failure and healthy companies, this paper aims to indicate the financial variables that predict the distress of Serbian companies. In this direction, we will rely on previous research and key empirical studies on the issue of corporate bankruptcy prediction based on neural networks. According to the author’s knowledge, only Simić et al. [18] dealt with this research topic in the Serbian market. They developed a hybrid MDA-SOM model based on the application of MDA analysis and specific neural networks called the self-organized SOM map. They predicted the financial insolvency of Serbian medium-sized and large companies with an accuracy of 95% during the period 2008–2009.

Reviewing previous research, we start with the research conducted by Altman [19], who used a database of 1000 Italian companies to predict company failure over a period of one year based on the analysis of financial structure, indebtedness, liquidity, profitability, and internal financing. Relying on research results, he concluded that neural networks are an effective means to successfully categorize groups of companies from the aspect of their financial and operational performance. Using neural network methodology, Callejón et al. [20] developed a bankruptcy prediction model on a sample of 1000 industrial companies, that is, they compared 500 companies that are in the process of bankruptcy and 500 active companies in the time period 2007–2009. Relying on the financial information of insolvent companies in two years in relation to the date of insolvency, the obtained bankruptcy prediction model had a high degree of accuracy exceeding 92% in the sample classification. Analyzing fifty-one pairs of healthy and failed public industrial companies in the UK, Charitou et al. [21] also used neural network methodology to predict bankruptcy one, two, and three years before the event itself. The developed model showed an overall correct classification accuracy of 83% one year before the onset of bankruptcy, i.e., for all three years before the onset of insolvency at 78%. They also indicate that neural networks have a wider range of applications in business beyond bankruptcy prediction, including financial prediction, credit analysis, fraud detection, and bond rating.

Based on the analysis of 5500 borrowers from the microfinance companies in Peru in the time period from 2003 to 2008, Blanco et al. [22] developed a credit scoring model based on the use of multi-layer perceptron neural networks as a frequently used neural network type in all studies of business. He mentioned that most of the conducted research showed that there is a higher accuracy of prediction of the artificial neural network model compared to traditional credit scoring models such as linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), and logistic regression (LR). Further, Atiya [23] developed a bankruptcy prediction model of US companies for credit risk based on neural networks and showed that the usage of the proposed indicators in the developed model in relation to traditional financial indicators provides a significantly higher degree of forecasting accuracy, from 81.46% to 85.5% for the prediction of the future three-year period, concluding that neural networks are constructed in such a way as to predict default in the future three-year period, which represents a rather long period of time. Similarly, Eriki and Udegbunam [12] confirmed the greater predictive ability of neural networks in relation to the discriminant analysis technique from the aspect of bankruptcy prediction. By analyzing the operations of 44 Nigerian companies in the period from 1987 to 2006, they pointed out that a neural network is a precious tool for managers in improving the process of making business decisions. Bapat and Nagale [24] and Virag and Kristof [25] also confirmed the greatest prognostic ability of neural network models in comparison with discriminant analysis and logistic regression models in predicting company bankruptcy. Conducting a study on a sample of 144 Indian companies in the time period 1991–2013, Bapat and Nagale [24] indicated the importance of prediction for financial institutions, auditors, investors, and creditors in determining companies that will face bankruptcy three years before the bankruptcy.

Research conducted by Inam et al. [6] also confirmed that artificial neural networks are a better means of predicting the bankruptcy of manufacturing and service Pakistani companies one year before the bankruptcy, with a prediction accuracy of as much as 88.9% compared to the model of multivariate discriminant analysis and binary logit regression. They stated that the methodology of artificial neural networks is a widely used method since it uses the advantages of technology and does not require special conditions in terms of predictor variables. Research conducted by Kouki and Elkhaldi [26] on a sample of 60 companies in Tunisia showed that neural networks are the most effective predictive tool in the short term, that is, MDA and logit regression are the most effective predictive tools in a period of two to three years before company distress. In order to find the best prediction model for financial failure, Chen and Du [27] used the artificial neural networks methodology based on a backpropagation network (BPN) and data mining techniques to research the business of 34 healthy and 34 companies that faced financial failure in Taiwan during the period 1999–2006. The obtained results showed that the probability of predicting business failure is an 82.14% accurate percentage for two seasons before the financial failure occurred and that neural networks are more effective than traditional financial methods in predicting potential financial difficulties. Charalambous et al. [28] conducted a comparative analysis of the artificial neural network models with logistic regression and the backpropagation algorithm. On a sample of 139 matched pairs of healthy and bankrupt American companies, the artificial neural network showed superior prediction results in all three years before the bankruptcy. Finally, Yim and Mitchell [29] highlighted the importance of hybrid neural networks as an effective tool that has primacy over all traditional statistical mathematical techniques in predicting company distress one year before the onset of bankruptcy. The predictive superiority of the artificial neural network model in bankruptcy prediction is also found in the research findings of Anandarajan et al. [11], Lee et al. [30], Brockett et al. [31], Chung et al. [32], Kim [33], Ciampi and Gordini [34], Lee and Choi [35], and Sehgal et al. [36].

Emphasizing that neural networks are used to detect non-linear relationships and have a good result in company failure prediction problems, Alfaro [37] applied artificial neural networks to a sample of European companies, using financial indicators and qualitative determinants such as activity, company size, and legal structure. Starting from the fact that companies face bankruptcy if they do not achieve settled goals in terms of solvency, profitability, and survival, this study researched the impact of financial indicators on the prediction of business failure of 1180 Spanish companies in the time period from 2000 to 2003. Furthermore, Barboza et al. [38] researched corporate failure prediction one year before bankruptcy using neural networks and other machine learning models. By analyzing the performance of American and Canadian companies in the period 1985–2013, relying on characteristics such as liquidity, profitability, leverage, growth, and size, they proved that artificial neural networks have approximately 10% lower predictive ability than other machine learning models.

Further, Chinedu et al. [39] tested the predictive ability of the genetic algorithm and neural network method on a sample of 66 listed manufacturing companies in Nigeria, concluding that the genetic algorithm model outperforms the model of neural networks in predicting company bankruptcy. On the other hand, Zebardast et al. [40] showed a higher accuracy of the neural network model for predicting bankruptcy (91.2%) compared to the genetic algorithm model (86.5%), testing the ability of the mentioned models in predicting bankruptcy on the sample of 126 Tehran companies in the time period 2006–2011. Likewise, Rafiei et al. [41] developed a model based on neural networks for predicting the bankruptcy of manufacturing companies in Tehran, which showed a higher predictive ability of the neural network model of 98.6% and 96.3% compared to the genetic algorithm model of 92.5% and 91.5% in training and holdout samples. Finally, Abdelwahed and Amir [42] developed a new corporate distress prediction model named the evolutionary bankruptcy model with a high degree of adaptability and accuracy by combining a genetic algorithm and an artificial neural network. Research by Back et al. [43] showed that the neural network model achieves the highest accuracy and precision when a genetic algorithm is used for variable selection, noting that genetic algorithms are a useful method for finding the indicators that best correspond to neural networks.

The research conducted by Fedorova et al. [44] showed that the use of neural networks for bankruptcy prediction on a sample of Russian manufacturing companies provides an accuracy of prediction of 89%, which is in line with the modern bankruptcy prediction approaches based on ANNs, which strive to provide an accuracy greater than 90%. Starting from two types of neural networks, backpropagation multi-layer perceptron (MLP) and the radial basis function network (RBFN), the conducted research showed a greater prognostic power of the first type, i.e., backpropagation multi-layer perceptron (MLP). On the other hand, Cheng et al. [45] found that the performance of the RBFN model shows superior predictive results compared to the backpropagation neural network and traditional logit analysis in analyzing distress prediction of companies listed on the Taiwan Stock Exchange. In order to develop and evaluate dynamic models for predicting the bankruptcy of European companies, Korol [46] also used, among others, a multi-layer artificial neural network model that indicated a prediction accuracy of 87.4% three years before the onset of bankruptcy, i.e., 93.4% the year before the onset of bankruptcy. He also pointed to the improvement of the efficiency of the bankruptcy prediction model, both in the short and the longer period of time, i.e., longer than five years before the onset of bankruptcy. According to the obtained results, the effectiveness of prediction via a multi-layer artificial neural network shows good results in the horizon of forecasting up to 6 years before the onset of bankruptcy: a value of 80.8%. It is important to note that the definition of bankruptcy risk is of particular importance for investors and other decision-makers. In that way, research by Mselmi et al. [47] showed that the use of a multi-layer perception artificial neural network provided an accuracy of predicting the bankruptcy of small- and medium-sized French companies of 87.14% one year before the onset of bankruptcy and 88.57% two years before the onset of bankruptcy, indicating that this method provides an early warning signal to managers about impaired performance, takes corrective actions, and reduces the risk of financial difficulties.

3. Variables, Research Sample, and Methods

This research is based on financial analysis and the artificial neural network (NN) machine learning method. Financial analysis includes ratio indicators. A summary of all variables initially considered as independent (explanatory) variables for modeling is presented in

Table 1. Independent variables summary.

Symbol	Variable Calculation	Literature Source
ROA	Net Income/Total Assets	Back et al. [43], Atiya [23], Charitou et al. [21], Yim and Mitchell [29], Neophytou and Molinero [49], Virag and Kristof [25], Ryu and Yue [50], Chung et al. [32], Chen and Du [27], Simić et al. [18], Lin [14], Kim and Kang [15], Ravisankar et al. [16], Rafiei et al. [4], Blanco et al. [22], Callejón et al. [20], Zebardast et al. [40], Korol [46], Sehgal et al. [36], Chinedu et al. [39].
CR	Current Assets/Current Liabilities	Back et al. [43], Charitou et al. [21], Neophytou and Molinero [49], Virag and Kristof [25], Ryu and Yue [50], Abdelwahed and Amir [42], Yim and Mitchell [29], Chung et al. [32], Alfaro [37], Chen and Du [27], Lin [14], Ravisankar et al. [16], Kim and Kang [15], Kim [33], Rafiei et al. [41], Callejón et al. [20], Zebardast et al. [40], Bredart [17], Bapat and Nagale [24], Inam et al. [6], Korol [46], Sehgal et al. [36], Chinedu et al. [39].
WC/TA	Working Capital/Total Assets	Back et al. [43], Neophytou and Molinero [49], Charitou et al. [21], Abdelwahed and Amir [42], Ryu and Yue [50], Alfaro [37], Simić et al. [18], Chung et al. [32], Ravisankar et al. [16], Rafiei et al. [41], Eriki and Udegbunam [12], Bapat and Nagale [24], Barboza et al. [38], Inam et al. [6], Sehgal et al. [36].
RER	Retained Earnings/Total Assets	Back et al. [43], Charitou et al. [21], Neophytou and Molinero [49], Ryu and Yue [50], Chung et al. [32], Lin [14], Simić et al. [18], Kim and Kang [15], Ravisankar et al. [16], Eriki and Udegbunam [12], Bapat and Nagale [24], Barboza et al. [38], Inam et al. [6], Sehgal et al. [36], Chinedu et al. [39].
EBIT/TA	EBIT/Total Assets	Atiya [23], Charitou et al. [21], Neophytou and Molinero [49], Ryu and Yue [50], Alfaro [37], Chung et al. [32], Simić et al. [18], Callejón et al. [20], Eriki and Udegbunam [12], Bredart [17], Bapat and Nagale [24], Barboza et al. [38], Inam et al. [6], Korol [46], Chinedu et al. [39].
S/TA	Sales/Total Assets	Neophytou and Molinero [49], Charitou et al. [21], Ryu and Yue [50], Alfaro [37], Chung et al. [32], Ravisankar et al. [16], Rafiei et al. [41], Blanco et al. [22], Bapat and Nagale [24], Eriki and Udegbunam [12], Inam et al. [6], Chinedu et al. [39].
QR	(Current Asset Inventories)/ Current Liabilities	Yim and Mitchell [29], Virag and Kristof [25], Chung et al. [32], Rafiei et al. [41], Lee and Choi [35], Zebardast et al. [40], Mselmi et el. [47], Inam et al. [6], Korol [46], Chinedu et al. [39].
TD/TA	Total Debt/Total Assets	Back et al. [43], Ryu and Yue [50], Chen and Du [27], Lin [14], Kim and Kang [15], Ravisankar et al. [16], Callejón et al. [20], Zebardast et al. [40].
CA/TA	Current Assets/Total Assets	Back et al. [43], Charitou et al. [21], Neophytou and Molinero [49], Ryu and Yue [50], Virag and Kristof [25], Alfaro [37], Chung et al. [32], Chen and Du [27], Ravisankar et al. [16], Kim and Kang [15], Fedorova et al. [44], Bapat and Nagale [24], Douglas [51], Inam et al. [6], Sehgal et al. [36], Chinedu et al. [39].
DR	Total Liabilities/Total Assets	Virag and Kristof [25], Neophytou and Molinero [49], Charitou et al. [21], Chung et al. [32], Tinoco and Wilson [52], Blanco et al. [22], Bapat and Nagale [24], Chinedu et al. [39].
C/TA	Cash/ Total Assets	Back et al. [43], Abdelwahed and Amir [42], Virag and Kristof [25], Ryu and Yue [50], Alfaro [37], Chung et al. [32], Kim and Kang [15], Ravisankar et al. [16], Kouki and Elkhaldi [26], Blanco et al. [22], Korol [46], Sehgal et al. [36].
OCF/TA	Operations Cash Flow/Total Assets	Back et al. [43], Atiya [23], Neophytou and Molinero [49]. Abdelwahed and Amir [42], Ryu and Yue [50], Charitou et al. [21], Callejón et al. [20], Douglas [51], Bapat and Nagale [24], Sehgal et al. [36], Chinedu et al. [39].
OCF/TL	Operations Cash Flow/ Total Liabilities	Neophytou and Molinero [49], Charitou et al. [21], Tinoco and Wilson [52], Bapat and Nagale [24].
LIQ	Current Liabilities/Total Assets	Charalambous et al. [28], Charitou et al. [21], Neophytou and Molinero [49], Bapat and Nagale [24], Inam et al. [6], Korol [46], Chinedu et al. [39].
OCF/TD	Operations Cash Flow/Total Debt	Back et al. [43], Ryu and Yue [50], Alfaro [37].
QA/TA	Quick Assets/ Total Assets	Back et al. [43], Charitou et al. [21], Ryu and Yue [50], Bapat and Nagale [24], Neophytou and Molinero [49], Ravisankar et al. [16], Kim and Kang [15], Kim [33], Inam et al. [6].
CA/S	Current Assets/Sales	Neophytou and Molinero [49], Ryu and Yue [50], Charitou et al. [21], Chung et al. [32], Simić et al. [18], Bapat and Nagale [24], Chinedu et al. [39].
EBIT/Int	EBIT/Interest	Back et al. [43], Kim and Kang [15], Chung et al. [32], Kouki and Elkhaldi [26], Korol [46].
Inv/S	Inventory/Sales	Back et al. [43], Neophytou and Molinero [49], Charitou et al. [21], Ryu and Yue [50], Chung et al. [32], Chen and Du [27], Simić et al. [18], Kim and Kang [15], Ravisankar et al. [16], Kim [33], Bapat and Nagale [24], Chinedu et al. [39].
OI/TA	Operating Income/Total Assets	Back et al. [43], Atiya [23], Ravisankar et al. [16], Rafiei et al. [41].
OCF/S	Operations Cash Flow/Sales	Neophytou and Molinero [49], Charitou et al. [21], Bapat and Nagale [24], Chinedu et al. [39].
NI/S	Net Income/Sales	Charitou et al. [21], Chung et al. [32], Kim and Kang [15], Rafiei et al. [41], Bapat and Nagale [24].
LTD/TA	Long-Term Debt/Total Assets	Ravisankar et al. [16], Mselmi et al. [47], Sehgal et al. [36], Chinedu et al. [39].
NW/TA	Net Worth/Total Assets	Takahashi et al. [53], Mohamad [54], Ahn and Kim [55], Blanco-Oliver et al. [56].
Cash/Current Liabilities	Cash/Current Liabilities	Back et al. [43], Ryu and Yue [50], Alfaro [37], Chung et al. [32], Fedorova et al. [44], Zebardast et al. [40], Inam et al. [6].
OCF/CL	Operations Cash Flow/ Current Liabilities	Back et al. [43], Neophytou and Molinero [49], Charitou et al. [21], Lin [14], Bapat and Nagale [24], Chinedu et al. [39].
WC/S	Working Capital/Sales	Neophytou and Molinero [49], Alfaro [37], Simić et al. [18]
Cap/A	Capital/Assets	Yim and Mitchell [29], Virag and Kristof [25], Neophytou and Molinero [49], Kim and Kang [15], Rafiei et al. [41], Lee and Choi [35], Douglas [51], Bapat and Nagale [24], Inam et al. [6].
NS/TA	Net Sales/Total Assets	Back et al. [43], Virag and Kristof [25], Lin [14], Bapat and Nagale [24], Barboza et al. [38].
NW/TL	Net Worth/Total Liabilities	Mohamad [54], Mahato [57], Wagan et al. [58].
NCI	No Credit Interval	Tinoco and Wilson [52], Fedorova et al. [44], Liang et al. [59].
LOG_TA	Total Assets (log)	Alfaro [37], Callejón et al. [20], Douglas [51], Mselmi et al. [47].
CFNI/D	Cash Flow (Net Income)/Debt	Brockett et al. [31], Kouki and Elkhaldi [26], Virag and Kristof [25], Chen and Du [27], Ravisankar et al. [16], Inam et al. [6].
OCF	Operations Cash Flow	Mossman et al. [60], Anandarajan et al. [11].
OE/OI	Operating Expenses/ Operating Income	Douglas [51], Africa [61], Asyikin [62].
QA/S	Quick Assets/Sales	Back et al. [43], Charitou et al. [21], Neophytou and Molinero [49], Ryu and Yue [50], Simić et al. [18], Kouki and Elkhaldi [26], Bapat and Nagale [24].
S/Inv.	Sales/Inventory	Jo et al. [63], Virag and Kristof [25], Rafiei et al. [41], Liang et al. [59].

Source: Authors’ illustration.

. All the ratios are chosen primarily based on the research paper by Bellovary et al. [48], other mentioned previous research, and empirical studies. The ratios were calculated for 2 years before the status of insolvency, considering the fact that the main aim of the research is to examine whether financial indicators can be reliable support for insolvency prediction one (Y-1) and two (Y-2) years in advance. A one-to-two-year time horizon allows timely intervention and proactive measures to be taken. It provides stakeholders, such as company management, investors, and creditors, with a sufficient window to identify potential financial distress and implement strategies to improve the company’s financial health. The business environment is constantly changing, and longer-term forecasts may be subject to higher uncertainty and volatility. On the one hand, predictive models developed for shorter timeframes can leverage more recent and relevant financial data, making them more accurate in assessing the current financial health and bankruptcy risk of a company. On the other hand, a one-to-two-year time horizon aligns with the typical planning and budgeting cycles of companies. It allows the bankruptcy prediction model to be more operationally relevant and practical for management to incorporate the predictions into their strategic decision-making processes.

A total of 37 independent variables were considered at the beginning of the research. Dependent variables are related to the status of solvency or insolvency. Dependent variables are dichotomous, meaning they can only have two values. Dependent variables have the following coding: 0 = insolvent company and 1 = solvent company.

The research sample consists of 100 firms from the Republic of Serbia of various sizes and economic activities. The sample is balanced, which further means that the number of solvent companies is equal to the number of insolvent companies (50:50); which is aligned with the methodology of most traditional and modern insolvency/bankruptcy prediction models (Altman [64]; Deakin [65]; Obradović, et al. [66]). The sample is balanced by business activity, operating years, and company size. A company is considered insolvent if it initiated bankruptcy proceedings, and operating companies that did not initiate bankruptcy proceedings are considered solvent. Solvent companies were selected on a random basis but aligned with the above-mentioned balancing criteria. All insolvent companies were selected from the Bankruptcy Supervision Agency [67]. In accordance with the publicly available data at the time of starting the research, bankruptcies initiated in the time period 2019–2021 were taken into account. Financial statements for one year and two years prior to the initiation of bankruptcy were used, i.e., 2017–2020, from the webpage of the Business Registers Agency [68] (see Figure 1).

The sample was divided (70:30) into two sub-samples: the training (70%) and testing (30%) sample. The training sample is used for NN model development, while the testing sample is used to verify the model on unseen data. Multi-layer perception (feedforward) neural networks will be trained and tested as machine learning techniques in order to develop two models for insolvency prediction. A neural network will be generated using the SPSS v.26 program. An artificial neural network (ANN) is a mathematical model that is inspired by the information processing capabilities of the human brain [69]. Neural networks are models that consist of three layers: inputs, hidden layer(s), and output layers. It is possible to have one or more hidden layers. The input layer receives information from the outside world, the hidden layer performs the information processing, and the output layer produces the class label or predicts continuous values. The values from the input layer entering a hidden node are multiplied by weights and a set of predetermined numbers, and the products are then added to produce a single number. The net sum of the weighted inputs entering a node j and the output activation function that converts a neuron’s weighted input to its output activation (the most commonly used is the sigmoid function) are given by the following equation [70]:

$$S_j={\sum }_{i=1}^n{x}_i{w}_{ij} \mathrm{and} O_j=\frac{1}{1+e^{S_j}} \mathrm{respectively}.$$

The function of the simplest multi-layer perceptron (MLP) neural network can be described as follows [71]:

$$o\left(x\right)=f(w_0+\sum _{i=1}^n{w}_i{x}_i)=f(w_0+w^{T}x)$$

where w₀ refers to a constant and w = (w₁, …, w_n) is a vector that contains all synaptic weights without a constant. The vector of all input variables is presented as x = (x₁, …, x_n).

Modeling with neural networks requires several decisions: data format, number of hidden layers, activation function for output layer and hidden layer(s), variable reduction to avoid model complexity and overfitting, model evaluation method, etc. When it comes to hyperparameters of the ANN, we decided to include two hidden layers in neural network models due to the fact that a lot of authors suggest exactly two or have an upper limit of two hidden layers (Gupta and Raza [72]; Panchal et al. [73]; Karsoliya [74]). It is important to emphasize that there is no unique rule for choosing an activation function. In accordance with other work related to neural networks in insolvency prediction (Jencova et al. [75]; Bhatia and Rangoonwala [76]; Fialova and Folvarcna [71], Paule-Vianez et al. [77]), the softmax function was selected for the output layer and hyperbolic tangent for the hidden layers. According to Sharma et al. [78], the softmax function is a combination of multiple sigmoid functions, and for classification problems, a combination of sigmoid functions gives better results. We used the gradient descent optimization algorithm as one of the most used optimization algorithms that updates the model parameters iteratively. The learning rate was set to 0.1 (Min and Lee [79]; Neves and Vieira [80]; Hájek and Olej [81], 2013; Sreedharan et al. [82]) and the momentum was set to 0.2, referring to other insolvency prediction research papers (Hung et al. [83]; Andone and Sireteanu [84]; Hung and Chen [85]; Vieira, et al. [86]; Hájek and Olej [81], Rodan et al. [87]). Batch training was selected as the most suitable type of training for small samples because it minimizes total error [77]. The training was conducted in 2000 epochs (Hájek and Olej [81]; Tumpach [88]).

Final variable selection is performed using a t-test and VIF analysis, which is the case in most bankruptcy/insolvency prediction models, regardless of the modeling method chosen (Cho et al. [89], Yoon and Kwon [90], Gordini [91]). All the financial ratios that passed a t-test (significant difference in mean values between solvent and insolvent companies) and Variance Inflation Factor (VIF) test are qualified for neural network modeling. It is considered that multicollinearity exists when the VIF value is greater than 10, according to O’Brien [92]. Therefore, ratios with higher VIF than the above-mentioned limit are excluded from further analysis. All the variables (financial ratios) were normalized to fall in a range from 0 to 1:

((x-min))/((max-min))

Model evaluation is performed using a confusion matrix (i.e., classification table) and the following indicators:

Accuracy is related to the total number of correct predictions (insolvent + solvent) by a model.

Accuracy = (True _positive + True _negative)/(True _positive + True _negative + False _positive + False _negative)

Precision shows how reliable the model is in classifying observations as bankrupted.

Precision = (True _positive)/(True _positive + False _positive)

Recall (sensitivity) is an indicator that measures the ability of a model to identify insolvent companies. When the model classifies an insolvent firm as a solvent, it is commonly called a Type I error in the bankruptcy prediction literature.

Recall = (True _positive)/(True _positive + False _negative)

The specificity of the model measures the number of correctly classified solvent firms. When the model classifies a solvent firm as insolvent, it is commonly called a Type II error in the bankruptcy prediction literature.

Specificity = (True _negative)/(True _negative + False _positive)

Also, the indicator of model classification power is the ROC curve (area under the curve). The area under a receiver operating characteristic (ROC) curve, abbreviated as the AUC, is a single scalar value that measures the overall performance of a binary classifier [93]. The AUC is an effective way to summarize the overall diagnostic accuracy of the test. It takes values from 0 to 1, where a value of 0 indicates a perfectly inaccurate test and a value of 1 reflects a perfectly accurate test. In general, an AUC of 0.5 suggests no discrimination (i.e., ability to diagnose patients with and without the disease or condition based on the test), 0.7 to 0.8 is considered acceptable, 0.8 to 0.9 is considered excellent, and more than 0.9 is considered outstanding [94].

4. Research Results

4.1. Predicting Insolvency One Year before Occurrence (Y-1)

Results of the t-test for the Y-1 period are presented in

Table 2. T-test for equality of means (Y-1).

Variable	t	df	Sig. (2-Tailed)
ROA (Y-1)	−4.8269	98.0000	0.0000
CR (Y-1)	−4.4554	98.0000	0.0000
WC/TA (Y-1)	−2.2434	98.0000	0.0271
RER (Y-1)	−3.8764	98.0000	0.0002
EBIT/TA (Y-1)	−4.9624	98.0000	0.0000
S/TA (Y-1)	−2.1970	98.0000	0.0304
QR (Y-1)	−4.3151	98.0000	0.0000
TD/TA (Y-1)	2.2012	98.0000	0.0301
DR (Y-1)	2.2012	98.0000	0.0301
C/TA (Y-1)	−3.4742	98.0000	0.0008
OCF/TA (Y-1)	−2.1629	98.0000	0.0330
OCF/TL (Y-1)	−2.1629	98.0000	0.0330
OCF/TD (Y-1)	−2.1253	98.0000	0.0361
CA/S (Y-1)	2.1871	98.0000	0.0311
OI/TA (Y-1)	−2.1970	98.0000	0.0304
NI/S (Y-1)	−2.5003	98.0000	0.0141
NW/TA (Y-1)	−5.6787	98.0000	0.0000
C/CL (Y-1)	−3.9581	98.0000	0.0001
OCF/CL (Y-1)	−2.3283	98.0000	0.0220
Cap/A (Y-1)	−5.6787	98.0000	0.0000
NS/TA (Y-1)	−4.2742	98.0000	0.0000
NW/TL (Y-1)	−5.6787	98.0000	0.0000
CFNI/D (Y-1)	−3.6697	98.0000	0.0004
OE/OI (Y-1)	2.8081	98.0000	0.0060
QA/S (Y-1)	2.0028	98.0000	0.0480

Source: SPSS.

. Only the variables with significant differences between the means of the two samples (bankrupt and solvent companies) are presented (p < 0.05). This further means that the following 25 variables qualified for further neural network modeling.

The next step in the process is detecting collinearity via the VIF indicator. After the analysis, 12 variables that are presented in

Table 3. Variance Inflation Factor (Y-1).

Variable	Tolerance	VIF
ROA (Y-1)	0.477	2.095
WC/TA (Y-1)	0.412	2.429
RER (Y-1)	0.452	2.21
QR (Y-1)	0.347	2.884
OCF/TL (Y-1)	0.518	1.929
CA/S (Y-1)	0.558	1.792
OI/TA (Y-1)	0.646	1.547
C/CL (Y-1)	0.565	1.771
OCF/CL (Y-1)	0.524	1.91
NW/TL (Y-1)	0.389	2.57
CFNI/D (Y-1)	0.4	2.498
OE/OI (Y-1)	0.657	1.522

Source: SPSS.

were selected for further modeling in accordance with acceptable limits for VIF values.

The visual representation of the artificial neural network is shown in Figure 2. The connection between neurons is demonstrated by different lines colors and thicknesses. Links with a blue line indicate that the weight between the given variables is a value less than 0, and conversions with a grey line indicate that the weight at this point has a value greater than 0. If the line is thicker, the weight values are numbers from 0 and conversely, thinner lines indicate values closer to 0 [75]. When it comes to NN architecture, the developed NN has 12 input layers, which are all the variables that passed the VIF test. It has four nodes in the first hidden layer and three nodes in the second hidden layer. The output layer has two nodes, one for insolvency outcome (code 0) and the other for solvency outcome (code 1). Parameter estimates are presented in Appendix A.

Next, we focus on the confusion matrix (

Table 4. Confusion matrix (Y-1).

			Classification
Sample	Ground-truth	0	Predicted 1	Percent Correct
Training	0	31	4	88.6%
	1	8	27	77.1%
	Overall Percent	55.7%	44.3%	82.9%
Testing	0	13	2	86.7%
	1	4	11	73.3%
	Overall Percent	56.7%	43.3%	80.0%

Source: SPSS.

). The accuracy of the NN model is 82.9% for the training dataset and 80.0% for the testing sample. The precision of the NN model is 79.5% and 76.5% for the training and testing datasets, respectively, while recall is 88.6% and 86.7% for the training and testing datasets, respectively. The specificity of the NN model is 77.1% for the training sample and 73.3% for the testing sample. Close incorrect prediction values in the case of the training and testing datasets indicate that the neural network is not overfitted during the training phase. It can be concluded that the neural network performs better in detecting insolvent companies compared to solvent ones (88.6% and 86.7% of correct insolvent classifications for the training and testing datasets, respectively), meaning that “Type I” errors are lower than “Type II” errors. The “Type I” error value is 4/35 companies for the training dataset and 2/15 companies for the test dataset. The “Type II” error value is 8/35 and 4/15 companies for the training and testing datasets, respectively.

Table 5. ROC curve area (Y-1).

Area Under	Curve
Status 0/1	0 1	0.899 0.899

Source: SPSS.

shows the area under the ROC curve. This value demonstrates that if a company from the insolvent category and a company from the solvent category are randomly selected, there is a 0.899 probability that the pseudo-probability predicted by the developed model for the insolvent company in the insolvency category is higher than the pseudo-probability predicted by the model for the solvent company in the insolvency category one year before insolvency occurs. This value of the ROC curve area is considered excellent.

The importance of each variable is presented in Figure 3. It can be concluded that variable CCL (Cash/Current Liabilities) has the greatest effect on the classification power of the neural network in the Y-1 period. It is followed by OITA (Operating Income/Total Assets), NWTL (Net Worth/Total Liabilities), and CFNID (Cashflow Net Income/Debt) ratio indicators, which have normalized importance higher than 80%. Results indicate that companies with insufficient cash amounts to cover current liabilities are the ones becoming insolvent in the year to come, meaning that lack of liquidity is the first sign of possible insolvency in the short term—one year in advance.

4.2. Predicting Insolvency Two Years before Occurrence

T-test results for the Y-2 period are presented in

Table 6. T-test for equality of means (Y-2).

Variable	t	df	Sig. (2-Tailed)
ROA (Y-2)	−2.2773	98	0.0249
CR (Y-2)	−2.5725	98	0.0116
RER (Y-2)	−4.3665	98	0
EBIT/TA (Y-2)	−2.2965	98	0.0238
QR (Y-2)	−3.0413	98	0.003
NW/TA (Y-2)	−4.0167	98	0.0001
C/CL (Y-2)	−2.7334	98	0.0074
Cap/A (Y-2)	−4.0167	98	0.0001
NS/TA (Y-2)	−3.1314	98	0.0023
NW/TL (Y-2)	−4.0167	98	0.0001
LOG_TA (Y-2)	2.6562	98	0.0092
CFNI/D (Y-2)	−3.3986	98	0.001

Source: SPSS.

. The following 12 variables met the criteria to be part of further modeling.

Variance Inflation Factor results for the Y-2 period are presented in

Table 7. Variance Inflation Factor (Y-2).

Variable	Tolerance	VIF
ROA (Y-2)	0.267	3.745
CR (Y-2)	0.427	2.344
RER (Y-2)	0.348	2.874
QR (Y-2)	0.276	3.629
C/CL (Y-2)	0.714	1.4
NS/TA (Y-2)	0.388	2.576
NW/TL (Y-2)	0.463	2.16
CFNI/D (Y-2)	0.302	3.313
LOG_TA (Y-2)	0.933	1.072

Source: SPSS.

. The following nine variables met the criteria to be included as final components in neural network modeling.

A visual representation of a developed neural network for the prediction of insolvency two years in advance is shown in Figure 4. The developed NN has nine input layers, which are all the variables that passed the VIF test. It has five nodes in the first hidden layer and four nodes in the second hidden layer. The output layer has two nodes, one for insolvency outcome (code 0) and the other for solvency outcome (code 1). Parameter estimates are presented in Appendix B.

Table 8. Confusion matrix (Y-2).

			Classification
Sample	Ground-truth	0	Predicted 1	Percent Correct
Training	0	27	8	77.1%
	1	9	26	74.3%
	Overall Percent	51.4%	48.6%	75.7%
Testing	0	11	4	73.3%
	1	4	11	73.3%
	Overall Percent	50.0%	50.0%	73.3%

Source: SPSS.

presents that the accuracy of the Y-2 prediction NN model is 75.7% for the training dataset and 73.3% for the testing sample. The precision of the model is 75.0% and 73.3% for the training and testing datasets, respectively, while recall is 77.1% and 73.3% for the training and testing datasets, respectively. The specificity of the NN model is 74.3% for the training sample and 73.3% for the testing sample. Close incorrect prediction values in the case of the training and testing datasets indicate that the neural network is not overfitted during the training phase. It can be concluded that neural networks perform better in detecting insolvent companies compared to solvent ones in the training phase (77.1% of correct insolvent classifications), which is not the case in the testing dataset. This indicates that “Type I” errors are lower than “Type II” errors in the training phase, while they are the same in the testing phase. The “Type I” error value is 8/35 companies for the training dataset and 4/15 companies for the test dataset. The “Type II” error value is 9/35 and 4/15 companies for the training and testing datasets, respectively.

Table 9. ROC curve area (Y-2).

Status 0/1

0 1

0.816 0.816

Source: SPSS.

shows the area under the ROC curve. This value demonstrates that if a company from the insolvent category and a company from the solvent category are randomly selected, there is a 0.816 probability that the pseudo-probability predicted by the developed model for the insolvent company in the insolvency category is higher than the pseudo-probability predicted by the model for the solvent company in the insolvency category two years before insolvency occurs. This value of the ROC curve area is considered excellent.

The importance of each variable is presented in Figure 5. It can be concluded that variable RER (Retained Earnings/Total Assets) has the greatest effect on insolvency prediction two years in advance. It is followed by the LogTA (Logarithm of Total Assets) ratio that has normalized importance higher than 90%. Results indicate that retained earnings management and company size (measured as the logarithm of total assets) are significant in predicting insolvency two years in advance.

5. Discussion

Based on the research results, it can be concluded that artificial neural networks combined with financial ratios can be a reliable basis for bankruptcy prediction of Serbian companies one and two years in advance. The research hypothesis is accepted. The results of neural networks provide additional evidence that publicly available information from financial statements can predict failure. Based on the prediction power of developed models, companies can take preventive actions in order to avoid bankruptcy. Furthermore, the users of financial statements can use these models to assess the creditworthiness of the company.

Comparing the results of two models for predicting insolvency, it can be concluded that the model based on predicting insolvency one year before occurrence is more reliable. For example, the accuracy of the Y-1 prediction NN model is 82.9% for the training dataset and 80.0% for the testing sample. On the other hand, the accuracy of the Y-2 prediction NN model is 75.7% for the training dataset and 73.3% for the testing sample. Close incorrect prediction values in the case of training and testing datasets indicate that the neural network is not overfitted during the training phase in both models. The neural network performs better in detecting insolvency companies compared to solvent ones. Correct classifications for the training and testing data in the Y-1 prediction NN model are 88.6 and 86.7. The Y-2 prediction model has the correct insolvent classifications for insolvent companies of 77.1% for the training dataset and 73.3% for the testing data. In both models, “Type I” errors are lower than “Type II” errors. This research indicates that the neural network is more powerful in the short run. Those findings, which indicate that the model based on predicting insolvency in a short-term period is more reliable, are in accordance with the previous research [21,23,46].

Both results of the area under the curve are considered excellent. Furthermore, the results of the area under the ROC curve of two models for predicting insolvency indicate that the Y-1 prediction model has better performance and is better at correctly classifying observations into categories. The Y-1 prediction model has a higher area under the curve (0.899 compared to 0.816 for the Y-2 prediction model). The results of the Y-1 prediction model indicate that there is a 0.899 probability that the pseudo-probability predicted for the insolvent company in the category of an insolvent company is higher than the pseudo-probability predicted for the solvent company in the insolvency category one year before insolvency occurs.

The importance of independent variables in the prediction of insolvency in the Y-1 model indicates that variable CCL (Cash/Current Liabilities) has the greatest effect on the classification power of the neural network in the Y-1 period. The liquidity ratio, measured as the CCL variable, indicates the ability of companies to pay current liabilities in cash. Results indicate that companies with insufficient cash amounts to cover current liabilities are the ones that become insolvent in the year to come, meaning that a lack of liquidity is the first sign of possible insolvency in the short term—one year in advance. Cash represents the most liquid asset, and the optimal cash fund is the key source for companies’ survival. This finding is according to the previous research results, which also indicate that less liquidity measured by a quick ratio provides company failure (Chung et al. [32]; Fedorova et al. [44]), bearing in mind that the concept of optimal liquidity is a main concept for survival and sustainable company growth (Vuković et al. [95]). In addition to this variable, the following variables have normalized importance higher than 80%: OITA (Operating Income/Total Assets), NWTL (Net Worth/Total Liabilities), and CFNID (Cash flow or Net Income/Debt). These research results of independent variables in the prediction of insolvency are similar to the previous research such as Ravisankar et al. [16], Rafiei et al. [41], Blanco-Oliver et al. [56], Ahn and Kim [55], Chen and Du [27], Kouki and Elkhaldi [26], and Douglas et al. [51].

The analysis of the importance of each variable for the Y-2 model indicates that only two variables have normalized importance higher than 80%. Those variables are RER (Retained Earnings/Total Assets), which has the greatest effect on insolvency prediction two years in advance (more than 90%), and LogTA (Logarithm of Total Assets). Results indicate that the total retained earnings or accumulated profit that the company generates to the total assets and company size are significant in predicting insolvency two years in advance. The main goal of companies is long-term operation and achieving profit. Therefore, high profitability provides stable operating cash flow and reduces the risk of insolvency in the long term. On the other side, unprofitable companies are more likely to go bankrupt. These findings are in accordance with previous research (Alfaro et al. [37]; Ravisankar et al. [16], Mselmi et al. [47]; Callejón et al. [20]). Retained earnings can be reinvested into the business or distributed to shareholders. In the context of bankruptcy prediction, the way a company manages its retained earnings can offer insights into its financial health. Strategic management of retained earnings can serve as early warning signals in bankruptcy prediction. This contributes to a deeper understanding of financial indicators that may anticipate financial distress 2 years in advance. The retained earning ratio’s ascendancy to 100% normalized importance redefines financial strategies. It prompts companies to strategically allocate earnings for long-term growth and risk mitigation, aligning their actions with the most influential predictor of sustained financial health.

Unlike traditional statistical methods, NNs can work successfully with data that contain noisy inputs. NNs have the possibility to predict both numerical and categorical outcomes. Also, the efficiency of NNs is worth mentioning. The advantages of ANNs (NNs) are the following:

• Ability to analyze data patterns in a short time and with enviable precision [96];
• No restrictive statistical assumptions are present in ANN modeling, which is not the case in traditional statistical methods [20,96,97];
• ANNs easily overcome autocorrelation problems [97];
• Incomplete, “noisy”, and inconsistent data are not problematic for pattern recognition in ANNs [96].

ANNs provide a better success rate than other statistical methods [20,25]. Although the research results are important both for business owners and external stakeholders, the main weakness of ANNs is the fact they cannot explain the relationship between the variables. The disadvantages of the ANN modeling method are the following [98]:

• Lack of ability to explain behavior;
• ANN algorithms are not guaranteed to converge an optimal solution;
• ANNs can easily be overtrained to the point of working well on the training data but poorly on the test data.

The selection of the gradient descent algorithm plays a crucial role in the robustness of our neural network model and serves as a deliberate strategy to mitigate overfitting. Gradient descent is a widely accepted optimization technique known for its ability to guide the training process toward convergence while preventing the model from fitting noise or outliers excessively [99]. In practice, some of these disadvantages can be realized by dividing the dataset into three parts or using regularization. Regularization (penalization) is concerned with reducing testing errors so that the model performs well on new data as well as on training data. Regularized or penalized loss functions are those that instead of minimizing the conventional loss function, minimize an augmented loss function that consists of the sum of the conventional loss function and a penalty (or regularization) term that is a function of the weights [100].

6. Conclusions

The research conducted in this paper confirms that insolvency in the short term is predictable by applying a combination of neural networks and financial ratio analysis to the publicly available information from financial statements. Furthermore, it is confirmed that the model based on predicting insolvency one year before occurrence (Y-1) is more reliable than the model based on predicting insolvency two years before occurrence (Y-2).

The accuracy of the NN model is 82.9% for the training dataset and 80.0% for the testing sample. The precision of the NN model is 79.5% and 76.5% for training and testing datasets, respectively, while the recall is 88.6% and 86.7% for the training and testing datasets, respectively. The specificity of the NN model is 77.1% for the training sample and 73.3% for the testing sample. Close incorrect prediction values in the case of the training and testing datasets indicate that the neural network is not overfitted during the training phase. It can be concluded that the neural network performs better in detecting insolvent companies compared to solvent ones (88.6% and 86.7% of the correct insolvent classifications for the training and testing datasets, respectively). The accuracy of the Y-2 prediction NN model is 75.7% for the training dataset and 73.3% for the testing sample. The precision of the model is 75.0% and 73.3% for the training and testing datasets, respectively, while the recall is 77.1% and 73.3% for the training and testing datasets, respectively. The specificity of the NN model is 74.3% for the training sample and 73.3% for the testing sample. Close incorrect prediction values in the case of the training and testing datasets indicate that the neural network is not overfitted during the training phase. It can be concluded that neural networks perform better in detecting insolvent companies compared to solvent ones in the training phase (77.1% of the correct insolvent classifications), which is not the case in the testing dataset.

The research results were conducted on the sample consisting of a total of 100 (50 solvent and 50 insolvent) companies in the Republic of Serbia of various sizes., The sample included balanced sizes, business activities, and operation years. The financial ratio analysis started with 37 independent variables to narrow down the selection to the final 12 variables that qualified for neural network Y-1 modeling, and the final 12 variables that met the criteria were part of Y-2 modeling. Variables found to have normalized importance higher than 80% are Cash/Current Liabilities, Operating Income/Total Assets, Net Worth/Total Liabilities, Cash Flow or Net Income/Debt (for the Y-1 model), Retained Earnings/Total Assets, and the Logarithm of Total Assets (for the Y-2 model).

Serbian companies can use the results of this research if they want to make the company sustainable because it is proven that insolvency protection of the company is fundamentally important in making its business sustainable. Therefore, the top management of Serbian companies should know the reasons that may initiate financial distress and that a lack of liquidity is the first sign of possible insolvency. The research results can help top management prevent financial crises that most often lead to bankruptcy. Results presented in this paper are also instructive for the state government because the government must act to ensure prolonged, stable, and sustainable economic growth, coupled with political stability and institutional efficiencies, which allow Serbian companies to increase their solvency and thrive on sustainable growth.

The practical findings of our research results are as follows:

• Identification of early warning signs: the model presented in this paper provides a unique capability to identify the early warning signs of bankruptcy, allowing companies and stakeholders to take proactive measures. This is particularly crucial in an economic environment like Serbia, where businesses may face various challenges.
• Supporting financial institutions: such a model can benefit financial institutions, investors, and creditors operating in Serbia. Accurate bankruptcy predictions can help these entities manage their risks more effectively and make prudent lending or investment decisions.
• Driving business toward a secure future: a company can take proactive steps to improve its financial health. By addressing issues flagged by the model’s predictions, such as liquidity problems, the company ensures its long-term viability, secures investor trust, and contributes to the overall stability of the business environment.
• Regulatory enhancements: for example, the model showed that poor cash management leads to bankruptcy a year in advance. This information could be shared with regulatory authorities, leading to policy changes or initiatives (for example, favorable loans or some subventions for companies) aimed at improving business conditions and reducing bankruptcy rates.

Recommendations for future research are to include more companies in the sample or to conduct research in a specific industry. The research can also be extended to other countries. To conclude, generating a specific model for one economic activity (e.g., manufacturing, trade, etc.) or specific company size (e.g., SMEs) can be a better option in order to train neural networks with higher generalization power.