Refining the Best-Performing V4 Financial Distress Prediction Models: Coefficient Re-Estimation for Crisis Periods

Abstract

Financial distress prediction models have been extensively utilised to assess the financial health of companies. However, their predictive accuracy can be significantly affected by extraordinary economic disruptions, such as the COVID-19 pandemic. Traditional models, particularly those designed for stable economic conditions, necessitate evaluation and potential adaptation to maintain their effectiveness during unprecedented circumstances. This study seeks to evaluate the performance of financial distress prediction models developed by authors from the Visegrad Four (V4) when applied to Slovak automotive companies before, during, and after the COVID-19 pandemic. Initially, the best-performing models from those selected were identified in the pre-pandemic period (2017–2019). The performances of these models were subsequently analysed during the pandemic and post-pandemic periods (2020–2022). Finally, their coefficients were re-estimated to enhance accuracy while preserving the original variables, ensuring the interpretability of any changes. The objective is to identify the models with the highest performance during the pre-pandemic period, assess their reliability under crisis conditions, and suggest improvements through coefficient re-estimation. While the majority of models experienced significant declines in performance during the pandemic, some retained adequate predictive accuracy. The re-estimated coefficients improved the overall accuracy of the models and also enhanced the sensitivity of some, offering stakeholders the option to utilise either the original or adjusted models based on their specific context. To complement the analysis, we also constructed new models for the pandemic and post-pandemic periods, allowing for a more comprehensive evaluation of financial distress prediction under changing economic conditions. This study provides a framework for adapting financial prediction models to unprecedented economic conditions, contributing valuable insights for researchers and practitioners seeking to enhance predictive tools within dynamic economic environments.

1. Introduction

The ability to predict financial distress in companies is critical in economic forecasting, enabling stakeholders to mitigate risks, allocate resources effectively, and prevent severe financial repercussions. Accurate financial distress prediction is especially vital in sectors such as the automotive industry, which is highly susceptible to global economic fluctuations. Over recent decades, numerous models have been developed and utilised to assess companies’ financial stability, with notable contributions from researchers in Central and Eastern Europe, particularly from the Visegrad countries (the Czech Republic, Hungary, Poland, and Slovakia) [1,2,3]. These models have traditionally relied on financial indicators and statistical methods that reflect the economic conditions in the region, providing a region-specific foundation for evaluating company health [4,5].

However, the COVID-19 pandemic introduced unprecedented disruptions to global economies, significantly affecting businesses’ operational and financial performance across all sectors [6,7]. These new and non-standard factors can significantly impact companies’ financial stability and affect the effectiveness of existing prediction models. Although existing prediction models may be built on robust mathematical and statistical principles, their ability to predict financial distress during a pandemic may be limited [8]. New and unexpected factors such as government stimulus measures, moratoriums on loan repayments, temporary closures of businesses, and fluctuations in markets can affect the performance of these models. In this context, models that were once reliable under stable economic conditions may exhibit reduced accuracy in times of crisis. This raises a critical question about the robustness and adaptability of traditional financial distress prediction models when applied to post-pandemic conditions. Therefore, much attention is paid to analysing and updating existing bankruptcy prediction models to consider new factors and improve their accuracy in a pandemic environment. This may include adjusting weighting factors, adding new predictive variables, or modifying mathematical algorithms based on new data and experience gained during the pandemic.

Although the automotive industry faced particular challenges, including supply chain disruptions and shifts in consumer demand, research exploring the pandemic’s impact on model performance remains limited. To address these gaps, this study evaluates the effectiveness of financial distress prediction models originally developed by authors from Visegrad countries when applied to Slovak automotive companies’ financial data across two periods. The analysis first assesses the models’ performance during the pre-pandemic period (2017–2019), identifying the models with the highest prediction performance. Subsequently, the top-performing models are selected and applied to data from the pandemic period (2020–2022) to examine any changes in predictive performance. Observing a notable decline in performance during the pandemic, we proceeded to re-estimate the coefficients within each model. This re-estimation approach preserves the original variables and statistical methods, adapting the models to reflect the changed economic conditions better.

By examining financial distress prediction models under varying economic conditions, this study offers valuable insights into the limitations of traditional models under unprecedented challenges like the COVID-19 pandemic. The findings underscore the importance of continuous evaluation of predictive models’ performance to ensure their reliability during economic instability. The study provides a framework for enhancing financial risk assessment tools for practitioners and policymakers, especially within sectors like automotive sensitive to global disruptions. For researchers, the study offers a methodology for evaluating and refining existing models.

The following sections of this paper are organised as follows. In the Literature Review section, we highlight the current state of financial distress prediction, focusing on the situation within the Visegrad region. The Section 2 describes the data used in the study, explains the study methodology, and describes the models selected for the study. The Section 3 presents the empirical results, first analysing the predictive accuracy of the selected models during the pre-pandemic period, then contrasting these findings with the models’ performance in the pandemic period, re-estimating the models’ coefficients to address pandemic-induced economic changes, and, finally, presenting a newly created model for the comparison of results from the pandemic and post-pandemic periods. The Section 4 offers a discussion of the key insights and practical implications of our findings while also mentioning the main study limitations and suggesting directions for future research. The Section 5 concludes the study.

Literature Review

Predicting companies’ financial condition is a widespread area of economic research. Since Fitzpatrick published the first study on this topic in 1932, bankruptcy prediction has become a subject of interest for various researchers and industry professionals.

Bankruptcy prediction models are especially prevalent in economically advanced Western countries. Models developed in the latter half of the 20th century are still used today. Beaver [9] introduced univariate analysis, becoming a pioneer in the field of bankruptcy prediction. Building on this research, Altman [10] applied multivariate discriminant analysis to create a model for predicting bankruptcy. Later, in 1980, Ohlson developed a new model based on logistic regression [11]. In 1984, Zmijewski proposed the application of a probit model for predicting company bankruptcy [12]. Altman’s model, as well as Ohlson’s logit model, were developed within the context of the US economy. Since then, numerous other models have been created across various countries worldwide. In addition to modern machine learning techniques, traditional methods such as logistic regression, multivariate discriminant analysis, and classification trees remain commonly used [13,14,15].

Dasgupta et al. [16] compared the performance of logistic regression and discriminant analysis models using neural networks. Their research found that the performance of neural networks was higher than the other two mentioned methods. However, the authors also noted that the performance of neural networks was not significantly higher than that of the other models. Huo et al. [17] conducted a comparative study on bankruptcy prediction for restaurant firms using multivariate discriminant analysis (MDA) and logistic regression models. The study revealed that while both models were effective, logistic regression provided more accurate predictions, especially in volatile industries like hospitality.

Inam et al. [18] applied artificial neural networks (ANN), logistic regression, and multivariate discriminant analysis to predict the bankruptcy of companies in Pakistan. The study compared the predictive power of these techniques, highlighting the performance of ANNs over classical statistical methods. While still effective, logistic regression and discriminant analysis showed limitations in handling non-linear relationships.

The first ex-ante analysis in Slovakia was published by Chrastinova [19]. The so-called CH-index model was designed specifically for Slovak agricultural enterprises based on discriminant analysis. Another well-known Slovak model is the G-index, developed using a discriminant analysis for agricultural enterprises [20]. Since then, several authors have created new models or examined the applicability of existing models within the Slovak context. Gavurova et al. [21] explored the accuracy of various bankruptcy prediction models within the Slovak business environment. The study highlighted that traditional models like Altman’s Z-score required customisation for specific regions, as macroeconomic variables such as inflation and interest rates affected the models’ predictive accuracy. This research underlines the need to adapt prediction models to local economic conditions to enhance their utility [21]. Horvathova and Mokrisova [22] conducted a comparative analysis of neural networks and classical discriminant analysis in predicting bankruptcy. The study demonstrated that neural networks offered greater accuracy than discriminant analysis. However, the researchers acknowledged the continued relevance of classical methods like discriminant analysis for simpler datasets and interpretability.

In addition, several new models have been developed by Slovak researchers. The V4 financial distress prediction model was developed by Kliestik et al. [1] based on the data on enterprises from V4 countries during the periods of 2015 and 2016 using the multiple discriminant analysis by the authors [1,23]. Valaskova et al. [6] developed models for enterprises in V4 countries, achieving over 88% accuracy using multiple discriminant analysis. The study identified total indebtedness ratios as the most significant predictor, providing valuable insights into the post-pandemic economic environment. Kovacova and Kliestik [24] created the logit and probit models in their study. The study’s results indicate that the model based on logit functions slightly outperforms the classification ability of the probit model in predicting bankruptcies in the Slovak Republic. Durica and Adamko [25] created a prediction model for Slovak companies based on multiple discriminant analysis with a classification accuracy of over 82%.

In the Czech Republic, the Neumaier and Neumaierová family of financial distress prediction models—IN95, IN99, IN01, and IN05—are the most well-known Czech predictive models and significantly contribute to financial health assessment in the Czech Republic. These models were designed to adapt to local economic conditions and provide robust predictions of financial distress by evaluating various financial indicators [26,27]. These models are also often used for predicting the financial state of the companies in Slovakia.

Karas and Srbova [28] developed a prediction model for the Czech construction industry, addressing the sector’s unique financial characteristics. Their study critiques traditional models like the Altman Z-score, highlighting their limited applicability to construction firms. Horak et al. [29] compared multivariate discriminant analysis (MDA), artificial neural networks (ANNs), and support vector machines (SVMs) for bankruptcy prediction of Czech industrial companies. Their findings indicated that ANNs and SVMs performed better than MDA. However, the authors emphasised the continued use of classical methods like MDA in certain practical applications due to their simplicity and ease of interpretation. Pech et al. [30] analysed the performance of various bankruptcy prediction models over five years, finding that Zmijevski’s model achieved the highest overall success rate. Their study highlighted significant variations in model accuracy across industries, recommending sector-specific adjustments to improve predictions. Camska and Klecka [31] focused their research on comparing the performance of financial distress prediction models under different economic conditions, including periods of growth and recession. The authors emphasise how changing economic environments influence model accuracy and highlight the importance of incorporating industry specifics in the prediction models.

Recent studies from Polish authors have introduced innovative approaches to financial distress prediction, leveraging both traditional and advanced methodologies. Machine learning models, enhanced with oversampling techniques, achieved up to 99% predictive accuracy, highlighting the utility of ensemble learning for addressing imbalanced datasets in financial forecasting [32,33]. Ensemble classifier models, including boosting and bagging, outperformed traditional single-classifier approaches when tested on data on Polish firms, providing robust early warnings of financial distress over a two-year horizon [34]. Another study focused on logit and discriminant models tailored to the Polish industrial sector, emphasising the need for locally adapted prediction methods over unadjusted global models [35]. Hybrid machine learning techniques, such as those combining XGBoost and artificial neural networks, further improved predictive accuracy by dynamically integrating advanced algorithms and addressing imbalances in Polish financial datasets [33]. Multivariable models also outperformed univariate approaches for Polish manufacturing companies, confirming that combining multiple financial indicators yields better predictions of financial distress [36].

In Hungary, the first Hungarian model was constructed by Virag and Hajdu [37] based on the data on Hungarian enterprises covering the period 1990–1991. The authors created a model using both MDA and logistic regression. However, many studies related to prediction models from Hungarian authors are in their national language, so they are difficult to use for an international reader.

As is visible, financial distress prediction models have historically been widely used to predict the financial distress of firms. In recent years, the development of prediction models has gained further attention due to the global economic shocks triggered by the COVID-19 pandemic. The pandemic significantly impacted global economies, leading to widespread financial distress across numerous sectors. Several studies have analysed the performance and adaptations of existing prediction models during the pandemic. However, several authors found that the pandemic revealed several limitations in using traditional financial distress prediction models and the need for more dynamic models capable of incorporating sudden economic shocks.

For instance, Lubis and Gandakusuma [38] conducted a re-estimation of traditional models, finding that the original Altman Z-score required significant adjustments to remain accurate during the pandemic. Candera [39] conducted a comparative analysis of service companies during the pandemic period and found that traditional models such as the Springate and Altman Z-scores underperformed, as they failed to account for non-financial variables that became critical during the pandemic.

Al Qamashoui and Mishrif [40] conducted a study on predicting bankruptcy risks in distressed insurance companies in Oman during the pandemic period. The authors used the Altman Z-score model to assess financial distress in both pre- and post-pandemic periods (2019–2020). The study revealed that while traditional financial models, such as the Z-score, could predict financial distress to some extent, they were less effective when used in the volatile insurance sector, mainly due to external factors such as market instability and government intervention during the pandemic. The authors recommended incorporating real-time data and non-financial factors to improve model accuracy. Similarly, Dengang and Oktafiani [41] have called for the inclusion of external factors like market conditions, government interventions, and non-financial metrics.

Stoyancheva et al. [42] assessed the bankruptcy risk in Bulgarian agricultural enterprises using several classical models, including the Altman, Springate, and Fulmer models. The study highlighted that while these models provided accurate predictions before the pandemic (2019), they required adjustments during the pandemic period. The research suggests that sector-specific factors must be integrated to improve prediction accuracy. Similarly, Purwanti et al. [43] analysed the banking sector in Indonesia and found that model accuracy during the pandemic was significantly reduced, emphasising the need for real-time data and adaptive algorithms.

2. Materials and Methods

For the purpose of this study, we collected data on 80 enterprises from the automotive industry. The main reason for choosing this sector was that the industry has been a dominant economic sector in the Slovak Republic for a long time. It creates conditions for the development of other economic activities and is also the most important component of GDP creation in the economy of the Slovak Republic [44,45]. Data were collected from publicly available financial statements of Slovak companies on the website www.finanstat.sk. The period under the study covers the pre-pandemic years, 2017–2019, and then three pandemic years, 2020–2022.

The next step was the assessment of the financial state of the companies each year, i.e., classifying the companies into one of the two groups: healthy or in crisis.

As amended, the rule for determining the company’s financial state was based on Act 513/1991 Coll—Commercial Code. The Commercial Code contains special provisions governing a company in crisis, the main aim of which is to strengthen the protection of creditors who are not connected with the company in question regarding property or personal ties. The term “crisis”, as used in this study, represents an unfavourable economic status arising from the fulfilment of accounting and legal assumptions specified by law. A company’s crisis is not decided by a state authority or an authority of the company in question, and it is a state that can arise at any time during the company’s existence.

According to the wording of this Commercial Code, a company is in crisis if it is in financial distress (I. level of crisis) or is threatened with financial distress (II. level of crisis, so-called expected financial distress). As amended, these two legislative terms are further defined in the subsequent legislation—Act No. 7/2005 Coll.—on financial distress and restructuring. A company’s financial distress is manifested either by its insolvency (if it is late in paying at least two monetary obligations to at least two creditors for more than 90 days after their due date) or by its extension (if it has more than one creditor and the value of its obligations exceeds the value of its assets). Subsequently, the status of “threatened financial distress”, based on the company’s accounting, is defined as a state when the level of coverage of liabilities by equity is lower than 0.8 (equity-to-debt ratio). The explanatory memorandum in the relevant legislation states that the criterion is defined in such a way as to detect possible financial difficulties of the company relatively early, avoiding financial distress and possibly subsequent bankruptcy.

As follows from the provisions of the legislation in question, identifying insolvency as an identifier of a company in crisis is not algorithmic, since such information is not commonly available in financial statements. For this reason, in the study we work only with the equity-to-debt ratio indicator, which, according to the interpretation of the relevant legislation, is a sufficient indicator of a possible crisis of a company.

The defined ratio of own capital to liabilities is the threshold for identifying not only an impending bankruptcy but also actual financial distress, since the range of values also includes negative values of this indicator. Therefore, if the company’s value of the equity-to-debt ratio (equity to liabilities) in a particular year was lower than 0.08, the company was considered in crisis, i.e., having financial troubles (denoted by the value Y = 1). On the contrary, if the ratio was higher or equal to 0.08, the company was considered to be in a healthy financial condition (denoted by the value Y = 0). This approach for evaluating the company’s financial state is grounded in practises commonly used in Slovakia. Specifically, the above-mentioned classification criterion based on the equity-to-debt ratio aligns with local financial regulations and common business assessment practises [1,7,46]. In Slovakia, this threshold is widely used as an indicator of financial instability, reflecting a company’s limited equity buffer relative to its debt obligations.

Besides the above-mentioned reason, the rationale for our approach was the following. The companies operating in Slovakia are subject to Slovak laws and economic conditions, and consequently, their financial state is evaluated mainly by stakeholders in Slovakia, including managers, investors, and policymakers, who must make decisions based on the financial realities governed by Slovak jurisdiction. Therefore, even when employing foreign models to predict a company’s future financial state, we considered domestic criteria for evaluating financial health, as they are grounded under the domestic regulatory framework and economic context, and the company’s financial outputs reflect the environment in which it operates. Using Slovak-specific criteria, the analysis remains relevant and applicable for Slovak companies, regardless of the origin of the used prediction model.

The distribution of the companies’ states in individual years is in

Table 1. Distribution of companies into the groups of healthy companies and companies in crisis.

Company State/Num. of Companies	2018	2019	2020	2021	2022
In crisis	13	15	13	13	11
Healthy	67	65	67	67	69

.

The purpose of this study is to find the predictive models from the authors originating from V4 countries with the highest prediction performance in the period before the pandemic. For this reason, we collected the 13 models listed in

Table 2. Selected models.

Model	Citation	Year of Creation	Model Accuracy [%]	Sample Size	Sample Period	Sector	No. of Ratios
Altman	[47]	1968	72	66	1946–1965	manufacturing	5
Taffler–Tisshaw	[48]	1977	99	92	NA	manufacturing	4
IN 01	[21]	2002	76	1915	NA	industry	5
IN 05	[26]	2005	97	1526	2005	manufacturing	5
Ruckova	[49]	2008	NA	NA	NA	NA	4
Karas–Srbova	[28]	2019	77	4420	2011–2015	construction	4
Durica–Adamko	[25]	2016	82.2	109,550	NA	all sectors	5
Kliestik et al. V4	[1]	2018	85.7	449,781	2015–2016	all sectors	11
Kliestik et al. SK	[1]	2018	82.7	105,708	2015–2016	all sectors	9
Zmijevski	[50]	1984	NA	840	NA	NA	3
Poznanski	[51]	2004	93	100	1999–2002	commercial companies	4
Tomczak	[52]	2020	92%	10,700	2002–2012	manufacturing	5
Virag–Hajdu	[53]	1996	90	10,000	1990–1991	NA	4

. Three of them were models from Slovak authors, four from Czech authors, three from Polish and one from Hungarian authors. The reason for using only one Hungarian model was that Hungarian authors usually publish their studies in their native language; thus, they are rarely understandable to international readers. Therefore, we used a study written in English containing such a prediction model that could be easily used to evaluate the companies’ financial state. Moreover, for comparison, we also used Altman’s and Taffler’s models as well-known benchmarks. We used Altman’s model in the modified Z-score version from 1999. We chose this modified model because it was created to assess the financial health of non-US companies, which was an acceptable element for our analysis.

Table 3. Selected models coefficients.

Variable Name	Variable Description	Altman	Taffler–Tisshaw	IN 01	IN 05	Ruckova	Karas–Srbova	Durica–Adamko	Kliestik et al. V4	Kliestik et al. SK	Zmijevski	Poznanski	Tomczak	Virag–Hajdu
X1	Working capital/Total assets	1.20
X2	Retained earnings/Total assets	1.40					3.116
X3	EBIT/Total assets	3.30
X4	Book value of equity/Book value of total liabilities	0.60
X5	Total sales/Total assets	1.00	0.16
X6	EBIT/Current liabilities		0.53			0.53
X7	Current assets/Liabilities		0.13			0.13
X8	Current liabilities/Total assets		0.18			0.18			1.03
X9	FIXED assets/Total assets											4.288
X10	Total assets/Liabilities			0.13	0.13
X11	EBIT/Total assets (=Total liabilities)			0.04	0.04		−12.054	0.51					−1.30
X12	Total revenue/Total assets			3.97	3.92
X13	Current assets/Current liabilities			0.21	0.21
X14	EBIT/Interest			0.09	0.09
X15	Current assets/Current liabilities							0.25	0.024		−0.004	1.588
X16	Current liabilities/Total Sales							−0.207
X17	Working capital/Total assets							0.282
X18	Equity/Total liabilities							0.618					1.95
X19	Net income/Shareholders equity								−0.589
X20	Net income/Total assets								−1.158		−4.513	3.562
X21	Total liabilities/Total assets								1.87		5.679
X22	Current assets/Total assets								−0.452					3.66
X23	Cash and cash equivalents/Total assets								0.613
X24	Cash and cash equivalents/Current liabilities								−0.012
X25	Return on assets								0.731	−0.004			2.19
X26	Return on equity								0.173
X27	Return of sales (EBIT)												2.70
X28	Profit margin								−0.475
X29	(Cash and cash equivalents + Short-term investments)/Current liabilities									0.003				1.36
X30	Debt/Shareholders equity									0.0004
X31	Net working capital/Total assets									0.0003
X32	Profit(loss) on sales/net revenues for sales											6.791
X33	$(\mathrm{Short}-\mathrm{term} \mathrm{liabilities} \bullet$365)/sales												−0.001
X34	CashFlow/total liabilities													1.63
X35	CashFlow/Total assets													0.034
X36	EAT/Total assets						20.8
X37	Current liabilities/Sales						2399
Constant		-	-						−1.47	−0.24	−4.34	−2.37	−1.30	−0.62
Safe zone—financially healthy company		Z > 2.9	T > 0.3	IN01 > 1.77	IN05 > 1.6	Zr > 0	M < −0.6	DA > 0.02	Z < 0	Z < 0	X < 0	PM > 0	ST < 0.51	MVH > 0
Red zone—company in financial distress		Z ≤ 1.81	T < 0.2	IN01 ≤ 0.75	IN05 < 0.9	Zr < 0	M > −0.6	DA < −0.06	Z ≥ 0	Z ≥ 0	X ≥ 0	PM ≤ 0	ST ≥ 0.51	MVH ≤ 0
Grey zone		1.81 < Z ≤ 2.9	0.2 ≤ T ≤ 0.3	0.75 < IN01 ≤ 1.6	0.9 ≤ IN05 ≤ 1.6			−0.06 ≤ DA ≤ 0.02	-

presents the variables and their estimated coefficients of the 13 models selected for the analysis.

All these models were used to predict the financial state of companies in the pre-pandemic period. For this purpose, we used the original variables from these models. The predictions for these models were then compared to the company’s actual state in the following year. As the models were all created to predict the company’s financial state over one year, we were able to assess the performance of the models in the pre-pandemic period by comparing the predictions with the actual state of the company. For example, the predictions that used values of financial ratios from the year 2017 were compared to the companies’ states in 2018, etc.

The performance of the models was evaluated based on the confusion matrix, see

Table 4. Confusion matrix.

		$\mathbf{Predicted} \mathit{Y}$
		0	1
$\mathrm{Actual} Y$	0	True Negative (TN)	False Positive (FP)
	1	False Negative (FN)	True Positive (TP)

. In the confusion matrix, a true negative case (TN) is a company that was correctly predicted as financially healthy (marked by Y = 0, both actual and predicted) and a true positive case (TP) is a company that was correctly predicted to be in financial distress (marked by Y = 1, both actual and predicted). Moreover, a false positive case (FP) is a company that was predicted to be in financial distress (predicted Y = 1), although, in fact, it was in a good financial state (actual Y = 0), and a false negative (FN) case is a company that was predicted to be financial healthy (predicted Y = 0), although, in fact, it was in financial distress (actual Y = 1).

Some of the selected prediction models classify companies not only in the two groups mentioned but also contain a grey zone. However, the resulting confusion matrix in this study contain only companies classified as healthy and in crisis. The companies in the uncertain grey zone were excluded from further analysis, as their financial state cannot be determined with certainty.

For evaluating the performance of the selected models, the following evaluation metrics were utilised. First, the model’s accuracy is given as the ratio of correctly predicted companies among all companies (Equation (1)):

$$Acc={\displaystyle \frac{TP+TN}{TP+FP+TN+FN}}$$

(1)

and then, the model’s sensitivity is given as the ratio of correctly predicted financial troubles among all the companies with financial troubles (Equation (2)):

$$Sen={\displaystyle \frac{TP}{TP+FN}}$$

(2)

Then, five models (one benchmark model and one model from each country) with the highest performance (accuracy and sensitivity) of their predictions in the pre-pandemic period were selected for further analysis. These models were further used to evaluate their performance in the pandemic period covering 2020–2022. Similarly, as before, the company’s financial state prediction for each pandemic year was compared to its actual state in the following year.

Finally, if the performance of the selected models in the pandemic period dropped significantly, the models’ coefficients and their thresholds were re-estimated, preserving the original models’ variables. These adjusted models were created using the same technique as the original models (by discriminant analysis). Finally, the adjusted models were compared to the original ones. The re-estimated coefficients reflect changes in the financial environment while preserving the original set of variables and the statistical methodology employed by the models’ authors. Furthermore, the main goal was to compare the original models with their re-estimations, not only in terms of their predictive performance but also regarding the importance of the variables and the impact of individual variables on categorising companies as non-prosperous.

All selected models in the study were originally created using discriminant analysis. Therefore, the next section briefly characterises this method.

Discriminant Analysis

Discriminant analysis (DA) is a statistical technique employed to classify entities into at least two distinct groups based on predictor variables. It achieves this by constructing a discriminant function that maximises group separation. DA has been widely applied in various disciplines, including finance, where it aids in predicting corporate financial health [54]. In assessing corporate financial health, the models created by DA serve to differentiate between financially robust and distressed companies by analysing financial ratios and other pertinent indicators.

Mathematically, DA aims to determine a linear combination of independent variables $X_1,X_2,\dots ,X_p$, which forms the discriminant score expressed as

$$D={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_p{X}_p$$

(3)

where D is the discriminant score, $p$ is the number of the predictor variables, $X_1,X_2,\dots ,X_p$ are the predictor variables, and ${\mathsf{\beta }}_0,{\mathsf{\beta }}_1,\dots ,{\mathsf{\beta }}_{\mathrm{p}}$ are the coefficients to be estimated; their estimations are often denoted by ${\mathrm{b}}_0,{\mathrm{b}}_1,\dots ,{\mathrm{b}}_{\mathrm{p}}$.

The estimation of the coefficients relies most commonly on maximising the ratio of between-group variance ($S_B$) to within-group variance ($S_W$), defined as the objective function

$${\displaystyle \frac{w^T{S}_{B}w}{w^T{S}_{W}w}}$$

(4)

Here, $w$ represents the vector of discriminant coefficients. The matrices $S_B$ and $S_W$ are computed as:

$$S_B=\sum _{g=1}^G{n}_g\left({\mu }_g-\mu \right){\left({\mu }_g-\mu \right)}^T$$

(5)

$$S_W=\sum _{g=1}^G\sum _{i=1}^{n_g}\left(X_{gi}-{\mu }_g\right){\left(X_{gi}-{\mu }_g\right)}^T$$

(6)

where $G$ is the number of groups,${ n}_g$ is the sample size in group $g$, ${\mu }_g$ is the mean vector of group $g$, $\mu$ is the overall mean vector, and $X_{gi}$ represents the observations in group $g$. The optimal solution for $w$ is obtained by solving the generalised eigenvalue problem

$$S_{B}w=\lambda S_{W}w$$

(7)

where $\lambda$ represents the eigenvalue, indicating the separation achieved by the discriminant function [55,56].

The discriminant function is validated using metrics such as Wilks’ Lambda, which tests the significance of the discriminant power and classification accuracy through cross-validation. Assumptions such as multivariate normality and homogeneity of covariance matrices are essential for the validity of DA. In practice, normality assumption is often violated; for example, financial data often exhibit non-normality. While deviations from these assumptions may impact the results, DA remains robust under moderate violations [54,56] and DA can still proceed with caution.

Despite several limitations of the discriminant analysis and its stringent assumptions and the increasing preference for more advanced classification techniques in financial distress prediction research, we relied on maintaining the original method of model creation for the following reasons:

• Employing a different, although sophisticated, machine learning technique would require constructing entirely new models instead of re-estimating existing ones. Developing such a new model would allow for the comparison of predictive performance between the models but would render it impossible to compare the re-estimated models with their pre-crisis versions regarding the coefficients of the variables.
• Discriminant analysis is frequently selected by researchers due to its interpretability and transparency. It provides a clear insight into the model, enabling the interpretation of each financial ratio’s contribution through its estimated coefficients. This level of interpretability is not achievable with advanced machine learning models, which only provide output predictions without exploring the underlying relationships, even though they offer a high prediction accuracy. Thus, they are very suitable for the predictive goal of model development but cannot be recommended for the descriptive goal.
• Considering the amount of data for this study, simpler methods such as discriminant analysis are recommended. Advanced modelling techniques often require large amounts of data to achieve high prediction performance.
• In terms of usability for stakeholders, the transparency of the discriminant analysis enables them to interpret the economic impact of individual financial indicators on their company’s financial state.

3. Results

Table 5. Application of Altman’s and Taffler–Tisshaw models in the pre-pandemic period.

Altman		2018			2019			Taffler–Tisshaw		2018			2019
		Predicted		Total	Predicted		Total			Predicted		Total	Predicted		Total
		1	0		1	0				1	0		1	0
Actual	1	9	20	29	11	21	32	Actual	1	0	3	3	2	1	3
	0	2	37	39	1	33	34		0	11	59	70	12	61	73
Total		11	57	68	12	54	66	Total		11	62	73	14	62	76
Accuracy		67.60%			66.70%			Accuracy		80.80%			82.90%
Sensitivity		31.00%			34.40%			Sensitivity		0.00%			66.70%

,

Table 6. Application of Slovak models in the pre-pandemic period.

Durica–Adamko		2018			2019			Kliestik et al. V4		2018			2019			Kliestik et al. SK		2018			2019
		Predicted		Total	Predicted		Total			Predicted		Total	Predicted		Total			Predicted		Total	Predicted		Total
		1	0		1	0				1	0		1	0				1	0		1	0
Actual	1	5	2	7	7	1	8	Actual	1	8	55	63	5	54	59	Actual	1	5	8	13	7	5	12
	0	7	63	70	7	64	71		0	5	12	17	10	11	21		0	8	59	67	8	60	68
Total		12	65	77	14	65	79	Total		13	67	80	15	65	80	Total		13	67	80	15	65	80
Accuracy		88.30%			88.90%			Accuracy		25.00%			20.00%			Accuracy		80.00%			83.80%
Sensitivity		71.40%			87.50%			Sensitivity		12.70%			8.50%			Sensitivity		38.50%			58.30%

,

Table 7. Application of Czech models in the pre-pandemic period.

IN 01		2018			2019			IN 05		2018			2019
		Predicted		Total	Predicted		Total			Predicted		Total	Predicted		Total
		1	0		1	0				1	0		1	0
Actual	1	10	19	29	11	17	28	Actual	1	10	23	33	12	20	32
	0	2	28	30	0	26	26		0	2	31	33	0	29	29
Total		12	47	59	11	43	54	Total		12	54	66	12	49	61
Accuracy		64.40%			68.50%			Accuracy		62.10%			67.20%
Sensitivity		34.50%			39.30%			Sensitivity		30.30%			37.50%
Ruckova		2018			2019			Karas–Srbova		2018			2019
		Predicted		Total	Predicted		Total			Predicted		Total	Predicted		Total
		1	0		1	0				1	0		1	0
Actual	1	2	11	13	4	10	14	Actual	1	2	11	13	0	15	15
	0	5	62	67	3	63	66		0	40	27	67	42	23	65
Total		7	73	80	7	73	80	Total		42	38	80	42	38	80
Accuracy		80.00%			83.75%			Accuracy		80.00%			83.75%
Sensitivity		15.38%			28.57%			Sensitivity		15.38%			28.57%

,

Table 8. Application of Polish models in the pre-pandemic period.

Zmijevski		2018			2019			Poznanski		2018			2019			Tomczak		2018			2019
		Predicted		Total	Predicted		Total			Predicted		Total	Predicted		Total			Predicted		Total	Predicted		Total
		1	0		1	0				1	0		1	0				1	0		1	0
Actual	1	9	4	13	9	3	12	Actual	1	3	10	13	2	10	12	Actual	1	6	7	13	10	2	12
	0	36	31	67	40	28	68		0	63	4	67	11	57	68		0	29	38	67	32	36	68
Total		45	35	80	49	31	80	Total		66	14	80	13	67	80	Total		35	45	80	42	38	80
Accuracy		50.00%			46.25%			Accuracy		8.75%			73.75%			Accuracy		55.00%			57.50%
Sensitivity		69.23%			75.00%			Sensitivity		23.08%			16.67%			Sensitivity		46.15%			83.33%

and

Table 9. Application of Hungarian model in the pre-pandemic period.

Virag–Hajdu		2018			2019
		Predicted		Total	Predicted		Total
		1	0		1	0
Actual	1	6	7	13	8	4	12
	0	36	31	67	36	32	68
Total		42	38	80	44	36	80
Accuracy		46.25%			50.00%
Sensitivity		46.15%			66.67%

present the confusion matrices and evaluation measures for predictions of the financial state of the companies in the pre-pandemic period in 2018 and 2019. The tables are separated for the benchmark models (Altman’s and Taffler–Tisshaw) and models from individual V4 countries. The actual state of the companies is displayed in rows marked by the values 0 for financially healthy companies and 1 for companies in financial distress. The predicted values are in columns with the same notation of the company’s financial state.

These tables assisted the selection of the models with the highest prediction performance in the pre-pandemic period.

3.1. Summary of Models’ Performance in the Pre-Pandemic Period

A summary of the models based on sensitivity and overall accuracy shows their effectiveness in classifying companies as either healthy or in crisis. The combination of these two metrics offers a comprehensive view of the success and reliability of prediction models in identifying future financial troubles of companies one year in advance.

Sensitivity is an important indicator that considers the model’s ability to identify true positive cases from the total number of positive cases, i.e., correctly predict the crisis one year in advance. On the other hand, the model’s accuracy provides an overview of the overall classification success regardless of whether the cases are positive or negative, i.e., correct predictions of both healthy and in-crisis companies one year in advance. Considering both these evaluation measures, we can identify the models from the selected ones with the highest performance of prediction of financial troubles of Slovak automotive companies in the period before the pandemic, i.e., under normal economic circumstances.

Table 10. Summary of evaluation metrics for all models and their average values in pre-pandemic period.

Metrics	Year	Altman	Taffler–Tisshaw	Durica–Adamko	Kliestik et al. V4	Kliestik et al. SK	IN01	IN05	Ruckova	Karas–Srbova	Zmijevski	Poznanski	Tomczak	Virag–Hajdu
Accuracy in %	2018	67.6	80.8	88.3	25.0	80.0	64.4	62.1	80.0	36.3	50.0	8.8	55.0	46.3
	2019	66.7	82.9	88.9	20.0	83.8	68.5	67.2	83.8	28.8	46.3	73.8	57.5	50.0
	avg	67.2	81.9	88.6	22.5	81.9	66.5	64.7	81.9	32.5	48.1	41.3	56.3	48.1
Sensitivity in %	2018	31.0	0.0	71.4	12.7	38.5	34.5	30.3	15.4	15.4	69.2	23.1	46.2	46.2
	2019	34.4	66.7	87.5	8.5	58.3	39.3	37.5	28.6	0.0	75.0	16.7	83.3	66.7
	avg	32.7	33.4	79.5	10.6	48.4	36.9	33.9	22.0	7.7	72.1	19.9	64.7	56.4

provides an overview of the selected evaluation metrics for all models in the pre-pandemic period.

Since our main goal is to identify positive cases (e.g., companies’ financial crises), we consider sensitivity more important than other evaluation metrics because it focuses on the model’s ability to identify all truly positive cases. Of course, we also take into account the overall accuracy values.

3.2. Re-Estimation of Models for Pandemic and Post-Pandemic Period

Based on this, we selected the following five models as the most suitable for verifying the functionality of their predictions during the pandemic period. Among the two benchmark models, we chose the Taffler–Tisshaw model, and among the SK models, we chose the Durica–Adamko model. Among the CZ models, we chose the IN 01. From the PL models, we selected the Tomczak model and the Virag–Hajdu model was also selected as the only HU model.

The further evaluation of the financial state of the companies during the pandemic years 2020–2021 and 2022 after the pandemic continues with the selected five models with the highest performance in the pre-pandemic period.

Table 11. Prediction performance of selected five models in pandemic and post-pandemic period.

Taffler–Tisshaw		2020			2021			2022
		Predicted		Total	Predicted		Total	Predicted		Total
		1	0		1	0		1	0
Actual	1	0	1	1	1	12	13	1	9	10
	0	12	61	73	4	56	60	4	62	66
Total		12	62	74	5	68	73	5	71	76
Accuracy		82.43%			78.10%			82.89%
Sensitivity		0.00%			20.00%			10.00%
Durica–Adamko (SK)		2020			2021			2022
		Predicted		Total	Predicted		Total	Predicted		Total
		1	0		1	0		1	0
Actual	1	7	3	10	6	3	9	6	5	11
	0	5	64	69	5	62	67	3	66	69
Total		12	67	79	11	65	76	9	71	80
Accuracy		89.87%			89.47%			90.00%
Sensitivity		70.00%			66.67%			54.55%
IN 01 (CZ)		2020			2021			2022
		Predicted		Total	Predicted		Total	Predicted		Total
		1	0		1	0		1	0
Actual	1	7	2	9	9	1	10	19	2	21
	0	22	22	44	21	24	45	19	26	45
Total		29	24	53	30	25	55	38	28	66
Accuracy		54.72%			60.00%			68.18%
Sensitivity		77.78%			90.00%			90.48%
Tomczak (PL)		2020			2021			2022
		Predicted		Total	Predicted		Total	Predicted		Total
		1	0		1	0		1	0
Actual	1	33	8	42	0	13	13	0	11	12
	0	6	33	39	41	26	67	46	24	68
Total		39	41	80	41	39	80	42	38	80
Accuracy		82.50%			32.50%			30.00%
Sensitivity		80.49%			0.00%			0.00%
Virag–Hajdu (HU)		2020			2021			2022
		Predicted		Total	Predicted		Total	Predicted		Total
		1	0		1	0		1	0
Actual	1	9	4	13	5	8	13	8	3	11
	0	40	27	67	36	31	67	38	31	69
Total		49	31	80	41	39	80	46	34	80
Accuracy		45.00%			45.00%			48.75%
Sensitivity		69.23%			38.46%			72.73%

presents the confusion matrices of the selected five models in the pandemic and post-pandemic period. The total number of companies varies because some models contain not only financial prosperity and non-prosperity but also grey zones, which we did not include in the tables. Therefore, only the companies where the predictions were unambiguous are included in the table.

Table 12. Summary of evaluation metrics for selected five models and their average values in pandemic and post-pandemic period.

Metrics	Year	Taffler–Tisshaw	Durica–Adamko	IN01	Tomczak	Virag–Hajdu
Accuracy in %	2020	82.4	89.9	54.7	82.5	45.0
	2021	78.1	89.5	60.0	32.5	45.0
	2022	82.9	90.0	68.2	30.0	48.8
	avg	81.1	89.8	61.0	48.3	46.3
Sensitivity in %	2020	0.0	70.0	77.8	80.5	69.2
	2021	20.0	66.7	90.0	0.0	38.5
	2022	10.0	54.6	90.5	0.0	72.7
	avg	10.0	63.7	86.1	26.8	60.1

summarises the total accuracy and sensitivity of the selected models together with the averages of these evaluation measures.

Compared to the period before the pandemic, we can say that the prediction accuracy of some of the selected high-performance models dropped significantly (the Polish model of Tomczak) or stayed at the same average level (the other models). Regarding the sensitivity, the models’ performance dropped significantly (Taffler–Tisshaw benchmark model, Durica–Adamko Slovak model, and Tomczak Polish model) or even rose significantly during the pandemic and post-pandemic period (IN01 Czech model and Virag–Hajdu Hungarian model). Comparing the pandemic years 2020 and 2021 with the post-pandemic year 2022, we can say that with some exceptions, the models showed lowered accuracy and sensitivity levels during the pandemic.

Table 13. Adjusted coefficients of five selected models for pandemic and post-pandemic period.

Variable Name	Taffler–Tisshaw			IN 01			Durica–Adamko			Tomczak			Virag–Hajdu
	Original	2021	2022	Original	2021	2022	Original	2021	2022	Original	2021	2022	Original	2021	2022
X5	0.16	0.345	0.449
X6	0.53	0.171	0.072
X7	0.13	0.058	0.151
X8	0.18	−3.861	−3.466
X10				0.13	0.508	0.640
X11				0.04	4.0 × 10−7	−0.001	0.51	4.851	6.89	−1.3	2.43	1.06
X12				3.92	4.369	8.443
X13				0.21	0.258	0.065
X14				0.09	0.073	−0.072
X15							0.25	0.122	−0.757
X16							−0.207	−2.835	2.336
X17							0.282	−3.89	0.321
X18							0.618	0.015	0.562	1.95	−5.00	−4.04
X22													3.66	−3.514	−0.194
X25										2.19	−3.77	−2.90
X27										2.70	0.06	−1.74
X29													1.36	0.224	0.335
X33										−0.001	−0.001	−0.002
X34													1.63	0.19	−1.387
X35													0.034	7.356	12.868
Constant	-	1.233	0.493	-	−1.54	−1.273		2.99	0.963		1.64	1.50	−2.616	2.03	0.025
Safe zone	T > 0.3	T > 0	T > 0	IN01 > 1.77	IN01 > 0	IN01 > 0	DA > 0.02	DA > 0	DA > 0	X < 0	X < 0	X < 0	MVH > 0	MVH > 0	MVH > 0
Red zone	T < 0.2	T < 0	T < 0	IN01 ≤ 0.75	IN01 < 0	IN01 < 0	DA < −0.06	DA < 0	DA < 0	X ≥ 0	X ≥ 0	X ≥ 0	MVH ≤ 0	MVH ≤ 0	MVH ≤ 0
Grey zone	0.2 ≤ T ≤ 0.3	-	-	-			−0.06 ≤ DA ≤ 0.02	-	-	-	-	-	-	-	-

presents the newly estimated coefficients of the selected five models valid during the pandemic and post-pandemic period. The table contains only the variables included in at least one model; the other variables were omitted. The coefficients had to change during and after the pandemic because financial indicators and risk factors took on new meaning in the context of unprecedented economic conditions. These changes reflect the models’ efforts to better capture current realities and predict financial distress risk in a highly uncertain environment.

We also listed the original coefficients for comparison with their changes during the pandemic year 2021 and the post-pandemic year 2022.

During and after the COVID-19 pandemic, the coefficients of prediction models may have changed for several reasons. There are two primary factors of these changes. (i) Changes in the economic environment: the pandemic caused a global economic crisis, a sharp decrease in demand in some sectors and increased uncertainty, which led to a higher risk of financial distress for many companies and thus affected the weight of individual factors in the prediction models. (ii) Increased corporate indebtedness: many companies had to take out loans to survive the period of lower income.

Table 14. Impact of changed coefficient.

Model	Variable with Changed Sign	Change Direction	Condition for Financial Distress	Impact of Changed Coefficient	Possible Economic Interpretation
Tafler–Tisshaw	X7 = Current assets/Liabilities	from positive to negative	T < 0	Before the pandemic, an increase in X7 or X8 meant higher score, thus more likely inclusion of the company in the safe zone; during the pandemic, a higher value of X7 or X8 means a lower score, and the company will be more likely to be placed in the red zone	During the pandemic, higher current assets might indicate inefficiency in asset utilisation or inability to convert them into revenue, possibly due to decreased demand or disrupted supply chains. Companies with high X7 values might be placed in the “red zone” during the pandemic due to poor operational performance despite the apparent liquidity.
	X8 = Current liabilities/Total assets	from positive to negative			Higher current liabilities could signify strategic debt accumulation to maintain liquidity, which may not immediately signal distress due to low interest rates or government support programmes. A higher X8 becomes even more concerning because the company might face significant pressure to meet its short-term obligations amidst potential operational disruptions or reduced revenue.
IN 01	X14 = EBIT/Interest	from positive to negative	IN 01 < 0	Before the pandemic, an increase in X14 meant higher score, thus more likely inclusion of the company in the safe zone; during the pandemic, a higher value of X14 means a lower score, and the company will be more likely to be placed in the red zone	A higher EBIT-to-interest ratio generally suggests good financial health. However, during the pandemic, this might reflect lower interest expenses due to debt restructuring or government subsidies, rather than strong earnings. Alternatively, firms with higher debt-servicing capacity might have faced revenue declines, making high EBIT less indicative of financial stability. A high X14 in this context could thus indicate potential financial fragility, especially if the company is heavily dependent on external factors rather than sustainable earnings.
Durica–Adamko	X15 = Current assets/Current liabilities	from positive to negative	DA < 0	Before the pandemic, an increase in X15 or X17 meant higher score, thus more likely inclusion of the company in the safe zone; during the pandemic, a higher value of X15 or X17 means a lower score, and the company will be more likely to be placed in the red zone	An increase in liquidity ratios might indicate inefficiency or overstocking due to supply chain disruptions. A high X15 ratio in times of crisis signals that the company has current assets, receivables, and inventories that are difficult to convert into cash flow.
	X17 = Working capital/Total assets	from positive to negative			Higher working capital could reflect difficulties in converting assets into sales or cash flow, signalling potential liquidity traps. During an economic crisis, a higher X17 may signal secondary cash flow problems due to past due receivables.
	X16 = Current liabilities/Total Sales	from negative to positive		Before the pandemic, an increase in X16 meant lower score, thus more likely inclusion of the company in the red zone; during the pandemic, a higher value of X16 means a higher score, and the company will be more likely to be placed in the safe zone	Increased current liabilities relative to sales might indicate the use of short-term financing to cover operational costs during reduced sales periods, suggesting strategic liquidity management rather than immediate distress.
Tomczak	X11 = EBIT/Total assets	from negative to positive	X ≤ 0	Before the pandemic, an increase in X11 meant lower score, thus more likely inclusion of the company in the red zone; during the pandemic, a higher value of X16 means a higher score, and the company will be more likely to be placed in the safe zone	During the pandemic, a higher EBIT relative to total assets might indicate effective cost management or asset utilisation, signalling financial stability rather than distress.
	X18 = Equity/Total liabilities	from positive to negative		Before the pandemic, an increase in X18, X25 or X27 meant higher score, thus more likely inclusion of the company in the safe zone; during the pandemic, a higher value of X18, X25 or X27 means a lower score, and the company will be more likely to be placed in the red zone	Higher equity relative to liabilities during the pandemic could suggest inefficient capital utilisation or conservative financing, potentially leading to liquidity challenges. Companies with high self-financing might have had a lot of capital tied up (e.g., in assets) but not enough liquidity to cover short-term expenses.
	X25 = Return on assets	from positive to negative			A higher ROA during the pandemic might reflect temporary profitability spikes or declining asset bases, masking underlying financial issues. During the pandemic, companies ran into financial difficulties and their priority became survival and maintaining liquidity, not maximising return on assets. Companies with low ROA but high cash were in a better position than companies with high ROA but facing cash flow problems.
	X27 = Return of sales	from positive to negative			High profitability per unit of sales during the pandemic could indicate reduced sales volumes or cost-cutting measures that were unsustainable, leading to financial instability.
Virag–Hajdu	X22 = Current assets/Total assets	from positive to negative	MVH ≤ 0	Before the pandemic, an increase in X22 or X34 meant a higher score, thus more likely inclusion of the company in the safe zone; during the pandemic, a higher value of X22 or X34 means a lower score, and the company will be more likely to be placed in the red zone	A higher proportion of current assets to total assets could reflect decreased inventory turnover or accounts receivable collection issues.
	X34 = CashFlow/total liabilities	from positive to negative			Cash flow relative to liabilities might have become less reliable as an indicator due to altered payment cycles or temporary liquidity boosts from government aid

focuses on the changes in the newly estimated coefficient signs from positive to negative or vice versa compared to those in the original models. The last two columns of the table offer a mathematical and possible economic interpretation of the altered coefficient signs regarding its impact on the value of the discriminant score, thus on the classification of the company in the group of healthy and in-crisis. However, all these interpretations hold true only if the other variables in the model remain constant. It should be noted that these are rather theoretical situations, as financial ratios often contain similar items from the financial statements; thus, the assumption of keeping them constant when one variable changes is purely theoretical. Nevertheless, the results underscore the impact of the pandemic period on the significance and influence of individual financial ratios on the value of the company’s discriminant score.

Table 15. Confusion matrices for adjusted models.

Taffler–Tisshaw		2021			2022
		Predicted		Total	Predicted		Total
		1	0		1	0
Actual	1	10	3	13	7	4	11
	0	10	57	67	9	60	69
Total		20	60	80	16	64	80
Durica–Adamko (SK)		2021			2022
		Predicted		Total	Predicted		Total
		1	0		1	0
Actual	1	8	4	12	7	3	10
	0	8	60	68	10	60	70
Total		16	64	80	17	63	80
IN 01 (CZ)		2021			2022
		Predicted		Total	Predicted		Total
		1	0		1	0
Actual	1	11	2	13	6	4	10
	0	18	44	62	7	54	61
Total		29	46	75	13	58	71
Tomczak (PL)		2021			2022
		Predicted		Total	Predicted		Total
		1	0		1	0
Actual	1	2	5	7	4	4	8
	0	11	62	73	9	63	72
Total		13	67	80	13	67	80
Virag-Hajdu (HU)		2021			2022
		Predicted		Total	Predicted		Total
		1	0		1	0
Actual	1	7	6	13	6	5	11
	0	6	61	67	6	63	69
Total		13	67	80	12	68	80

presents the confusion matrices representing the prediction performance of the selected models with the adjusted coefficients.

3.3. Comparison of Original and Re-Estimated Models

Table 16. Prediction performance measures of original and adjusted models.

Metrics	Year	Taffler–Tisshaw	Durica–Adamko	IN01	Tomczak	Virag–Hajdu
Accuracy in %	original 2021	78.1	89.5	60.0	32.5	45.0
	adjusted 2021	83.75	85.00	73.33	91.4	85.00
	original 2022	82.9	90.0	68.2	30.0	48.8
	adjusted 2022	83.8	83.8	84.5	90.1	86.3
	avg original	80.5	89.7	64.1	31.3	46.9
	avg adjusted	83.8	84.4	78.9	90.8	85.6
Sensitivity in %	original 2021	0.0	70.0	77.8	0.0	69.2
	adjusted 2021	76.9	66.7	84.6	92.3	53.8
	original 2022	20.0	66.7	90.0	0.0	38.5
	adjusted 2022	63.6	70.0	60.0	81.8	54.5
	avg original	10.0	68.3	83.9	0.0	53.8
	avg adjusted	70.3	68.3	72.3	87.1	54.2

presents the performance measures of the adjusted models compared to the original models’ performance during the pandemic and post-pandemic periods.

Regarding accuracy, it is visible that it is significantly higher for the models with adjusted coefficients than for the original models, except for the Durica–Adamko model, where it was pretty high already for the original model. Sensitivity also significantly arose for the Taffler–Tisshaw and Tomczak models in both years and for IN01 in 2021, Durica–Adamko in 2022 and the Virag–Hajdu model in 2022. In averages, the performance of the models either arose slightly or significantly or stayed approximately at the same level. From this point of view, the adjustment of the model’s coefficients during an extraordinary period, such as COVID-19, is highly recommendable, especially when the prediction performance of the original model significantly dropped compared to normal circumstances.

However, regarding the changes in the coefficient values and their signs in the discriminant formulas from negative to positive or vice versa, it must be noted that the empirical findings of this study indicate that some financial ratios exhibit unexpected behaviour during the crisis period, raising concerns about the economic interpretability of the evaluated models. Despite maintaining high predictive accuracy, certain models fail to consistently reflect fundamental financial principles, such as the advantages of higher liquidity, profitability, and lower indebtedness. Therefore, the results suggest that the applicability of these models to contemporary Slovak automotive companies is questionable, highlighting the need for further refinements to ensure both predictive reliability and economic coherence. For this reason, we have developed new models specifically for the pandemic and post-pandemic periods to compare their results with the reviewed and re-estimated models, providing a more comprehensive perspective on financial distress prediction in times of economic instability.

3.4. New Model for Slovak Automotive Companies for Pandemic and Post-Pandemic Period

In crisis situations where pre-crisis models demonstrate diminished performance or illogical financial relationships, it is crucial to develop and regularly review new models to adapt to the evolving economic environment. For this reason, we have created a new model for Slovak automotive companies that is applicable during the COVID-19 pandemic and the post-pandemic period.

Table 17. New models for pandemic and post-pandemic period.

Period	2021	2022
Formula for discriminant score	$D{S}_{2021}=6.320X5-0.652X18 -1.304$	$D{S}_{2022}=5.260X5-0.493X18 -1.096$
Safe zone	$D{S}_{2021}>0$	$D{S}_{2022}>0$
Red zone	$D{S}_{2021}<0$	$D{S}_{2022}<0$
Model’s accuracy	91.4%	91.4%
Model’s sensitivity	92.3%	81.8%

below outlines the main characteristics of the two newly developed models. As potential predictors, all the variables listed in Table 13 were utilised, and the model was constructed through the stepwise selection of the variables. Only two of all the variables were identified as statistically significant, consistent across both periods.

Both created models exhibited a high prediction performance, not only the accuracy of predicting both categories of healthy and in-crisis companies but also the sensitivity for accurate predicting of financial distress. These accuracy and sensitivity values overperformed all models reviewed and re-estimated in previous sections.

As the only significant variables, the following were selected: X5 = Total Sales/Total Assets and X18 = Equity/Total liabilities. Variable X5, also called assets turnover, measures how effectively a company uses its assets to achieve profit, or rather, measures the effectiveness of the business. Companies with low asset turnover may have problems with efficiency and profitability, which is a warning sign of financial distress of the company; on the contrary, companies with extremely high turnover may indicate a business with a low margin. Regarding variable X18, equity ratio, its quantification in times of crisis shows that companies with a higher ratio of equity to total liabilities have a greater ability to survive a decline in sales. During a pandemic, a combination of the ability to generate revenue and maintain financial stability should be maintained in order to avoid financial distress.

4. Discussion

This study highlights the necessity of updating financial distress prediction models to address pandemic-induced economic disruptions. It also contributes to the broader understanding of how traditional models can be adapted for unprecedented circumstances. The findings highlight the necessity of re-estimating the models, maintaining their original variables chosen by their authors, to enhance their applicability in diverse economic conditions.

The findings of this study align with previous research that highlights the limitations of traditional financial distress prediction models during the COVID-19 pandemic and underscores the necessity of adapting these models to incorporate pandemic-specific economic factors. Several studies cited in the Literature Review reached similar conclusions, recommending adjustments to model coefficients or the inclusion of external variables to enhance predictive performance.

For instance, Lubis and Gandakusuma [31] evaluated the Altman Z-score model and found that significant adjustments were required to maintain its predictive accuracy during the pandemic. Their findings emphasised that financial variables alone were insufficient for reliable predictions in the volatile economic environment caused by COVID-19 and highlighted the importance of including external factors such as government policies and market shocks. Similarly, Candera [32] found that traditional models like the Springate and Altman Z-scores underperformed when applied to service companies, as these models failed to account for critical non-financial variables that emerged during the pandemic. Our study corroborates these conclusions, demonstrating that the original coefficients of the selected models developed by V4 authors were inadequate in the pandemic context and re-estimating the coefficients significantly improved model performance. However, the authors recommended model adjustments by incorporating macroeconomic indicators to enhance the prediction performance in predicting bankruptcies during this period. Dengang and Oktafiani [34] also advocated integrating external factors, such as government interventions and market conditions, into prediction models. This approach aligns with the recommendations of Al Qamashoui and Mishrif [33], who found that incorporating real-time data and adjusting existing models improved predictions for distressed insurance companies in Oman during the pandemic period. Similarly, the research by Purwanti et al. [43] analysed Indonesian construction companies and highlighted the necessity of model adjustments to account for government policies and market fluctuations during the pandemic. Stoyancheva et al. [42] conducted a similar assessment of traditional models like Altman, Springate, and Fulmer in Bulgarian agricultural enterprises. They observed that these models required sector-specific adjustments to improve their predictive accuracy during the pandemic. These findings resonate with our study, where the models tailored for pre-pandemic conditions failed to deliver reliable predictions until their coefficients were recalibrated. The coefficient re-estimation was pivotal in restoring the accuracy of the selected models. However, our study did not explicitly include external factors; the re-estimation of coefficients implicitly accounted for the shifts in financial ratios caused by such external influences.

Our results also highlight significant variations in the performance of adjusted models compared to their original versions. For example, while the sensitivity of certain models, such as the Zmijevski model, dropped significantly during the pandemic, recalibration substantially enhanced their predictive capabilities. This observation is consistent with the findings of Purwanti et al. [43], who noted similar performance improvements following model adjustments in the Indonesian banking sector.

Despite its contributions, this study has several limitations. First, its focus on the automotive sector within Slovakia makes it country- and sector-specific, which may limit the generalizability of its findings to other industries or regions with different economic structures. Nevertheless, this study holds significant value also for an international audience as it offers a detailed methodology for adapting financial prediction models to extraordinary economic disruptions, such as the COVID-19 pandemic. By demonstrating the process of coefficient re-estimation and its impact on model performance, the study provides a replicable framework that can be applied to diverse contexts, making it a valuable reference for researchers and practitioners.

Second, the country-specific condition for distinguishing the companies in good financial conditions and in crisis was used in the study. Indeed, the findings most directly apply to Slovakia or countries with similar legislative frameworks and economic structures. Nonetheless, the methodological approach and analytical procedures employed in the study remain robust and could be adapted to other contexts with appropriate adjustments to the distress criteria. We must admit the potential heterogeneity introduced by using models based on different definitions of financial distress. However, some studies used a similar approach. For instance, Kwak and Shi [57] applied models developed in the US to Japanese, Korean, and Chinese companies, adapting the models to local financial environments while recognising differences in bankruptcy definitions. Alaminos et al. [58] conducted research on global bankruptcy prediction models and verified their applicability across different regions, acknowledging the challenges of differing legal and economic contexts. Despite the mentioned potential heterogeneity of the results caused by applying country-specific conditions for companies in crisis, the study results have the potential for future comparative research. By examining financial distress within a specific legislative context, our study contributes to the broader understanding of how local economic and legal conditions influence the prediction of the financial health of the companies. This can inspire future research to explore cross-country comparisons or adaptations of the model to other jurisdictions, thus contributing to the global body of knowledge on financial distress prediction.

Then, the study relies exclusively on financial data, omitting potentially significant non-financial variables such as management decisions or macroeconomic policies, which could further refine the models. However, our approach assumes that any changed macroeconomic conditions would be reflected in a change in the companies’ financial indicators. The primary objective was to maintain the same variables in the models established by previous authors, re-estimating only their parameters. This approach was crucial for comparing the newly estimated coefficients with the original ones and deriving the economic interpretation of any identified changes. Introducing new variables would lead to entirely different models, making it impossible to compare them with the original models regarding the economic implications of the coefficient changes.

Then, some of the models used in the study were created by their authors as sector-specific, thus effectively predicting the financial state of the companies in a particular sector of economic activity. Some of these models (Karas–Srbova, IN 05, Altman) did not demonstrate high prediction accuracy even in the pre-crisis period and, therefore, were not selected for further analysis. Their low prediction accuracy should be indeed caused simply by their inappropriateness for Slovak companies in the automotive industry. On the other hand, some models (Tomczak, Taffler–Tisshaw) were selected as suitable for predicting Slovak automotive companies, even though they were created for different industries. This highlights the importance of verification of the prediction performance of the already existing models.

Next, one of the limitations of this study is the relatively small sample size, particularly concerning the number of companies classified as financially unhealthy. However, it is important to note that the primary objective of this study was not to develop new prediction models but to evaluate and re-estimate the coefficients of existing ones. Therefore, the validity of the models and their predictive power were not influenced by the sample size in this study. Our focus was on observing how the models’ performance changed during the pandemic period rather than drawing definitive conclusions about the financial health of the Slovak automotive industry. Future research could benefit from expanding the sample size or including multiple industry sectors to enhance the robustness and generalizability of the results.

Last, we highlighted the necessity of models’ adjustments under the changed economic conditions. However, it must be noted that these adjustments should be performed only ex post, after collecting enough data on the crisis period, which decreases the usage of re-estimated models in practice. Nevertheless, by understanding how model performance is affected during unprecedented events, practitioners and policymakers can be better prepared to interpret predictions with caution and consider adaptive strategies for future crises. This highlights the importance of similar studies.

Future research could explore several directions. First, expanding the scope of analysis to include additional industries and countries would provide a broader understanding of how economic disruptions impact financial distress prediction models. Second, adding more post-pandemic years to the analysis could offer deeper insights into the long-term effects of economic shocks on financial prediction models, helping to determine whether the observed coefficient changes persist or diminish over time. This extended timeline would enhance the robustness of the findings and provide further validation of the adjusted models’ utility in post-pandemic environments. However, this would be possible only in case of the availability of the necessary data. Next, it should be beneficial to reevaluate the variables or potentially even the modelling approach for such unprecedented periods as the COVID-19 crisis. In this sense, including the exploration of non-linear models or interaction terms in the models that might better capture the complex financial behaviours observed during the pandemic. However, this approach would lead to constructing a completely new model instead of re-estimating the existing ones.

5. Conclusions

This study evaluates the performance of financial distress prediction models from Visegrad authors in the Slovak automotive sector during the COVID-19 pandemic and post-pandemic periods. The research followed a systematic methodology: first, the best-performing models were identified during the pre-pandemic period. Then, their performance was evaluated during the pandemic and post-pandemic years. Finally, the coefficients of these models were re-estimated to reflect the economic disruptions caused by the pandemic while maintaining their original variables and the methodology used by their authors. In addition to re-estimating existing models, we developed new models tailored to the pandemic and post-pandemic periods to provide a comparative perspective on financial distress prediction.

The findings revealed that some models experienced significant declines in predictive accuracy during the pandemic, necessitating adjustments to their coefficients to restore performance. However, certain models continued to perform sufficiently well even during the pandemic, providing researchers and stakeholders with the flexibility to choose between the original models or their adjusted versions, depending on their specific needs and context.

While the research is country- and sector-specific, its implications extend beyond Slovakia and the automotive industry. The methodological framework of coefficient re-estimation provides a scalable approach for adapting financial prediction models to various regions and sectors facing economic disruptions. The study highlights the importance of the continuous evaluation and refinement of predictive models to ensure their reliability in dynamic environments.