Bankruptcy Prediction for Sustainability of Businesses: The Application of Graph Theoretical Modeling
Abstract
:1. Introduction
2. Material and Methods
- = working capital/total assets
- = retained earnings/total assets
- = earnings before interest and taxes/total assets
- = book value of equity/book value of total liabilities
- = sales/total assets
- = overall revised index
- Current Ratio = Current assets/Short-term liabilities (CR)
- Return on assets = EBIT/Total assets (ROA)
- Total assets turnover ratio = Total sales/Total assets (TATR)
- Total debt to total assets = Total debt/Total assets (TDTA)
- Credit period ratio = Short-term liabilities/Sales (CPR)
Feature | Authors |
---|---|
CR | Li and Sun [65]; Chen and Du [66]; Kainulainen et al. [67]; Callejón et al. [68]; Lin et al. [69]; Režňáková and Karas [70]; Cultera and Bredart [61]; Liang et al. [71]; Zelenkov et al. [72]; Chou et al. [73]; Volkov et al. [74]; Son et al. [75]; Korol [43]; Farooq and Qamar [76]; Shen et al. [44]; Vuković et al. [77]; Tumpach et al. [78]; Yan et al. [79]; Chen et al. [31]; Rahman et al. [80]; Park et al. [81]; Pavlicko et al. [82]; Papíková and Papík [83]; Pavlicko and Mazanec [84]; Mousavi et al. [85]; Qian et al. [86]; Smith and Alvarez [87] |
ROA | Altman [50]; Li and Sun [65]; Hu [88]; Chen and Du [66]; Premachandra et al. [89]; Kainulainen et al. [67]; Zhou et al. [90]; Cultera and Bredart [61]; Zelenkov et al. [72]; Volkov et al. [74]; Korol [43]; Farooq and Qamar [76]; Shen et al. [44]; Tumpach et al. [78]; Qian et al. [86]; Pavlicko and Mazanec [84] |
TATR | Altman [50]; Platt and Platt [91]; Li and Sun [65]; Chen and Du [66]; Kainulainen et al. [67]; Tomczak et al. [92]; Režňáková and Karas [70]; Lin et al. [69]; Zelenkov et al. [72]; Du Jardin [93]; Chou et al. [73]; Vuković et al. [77]; Park et al. [81]; Chen et al. [31]; Rahman et al. [80]; Papíková and Papík [83]; Pavlicko and Mazanec [84] |
TDTA | Šnircová [62]; Platt and Platt [91]; Premachandra et al. [89]; Chen and Du [66]; Hu [88]; Yeh et al. [94]; Kainulainen et al. [67]; Režňáková and Karas [70]; Lin et al. [69]; Zhou et al. [90]; Chou et al. [73]; Volkov et al. [74]; Zelenkov et al. [72]; Arroyave [95]; Le et al. [96]; Farooq and Qamar [76]; Vuković et al. [77]; Shen et al. [44]; Yan et al. [79]; Chen et al. [31]; Pavlicko et al. [82]; Park et al. [81]; Qian et al. [86]; Papíková and Papík [83]; Pavlicko and Mazanec [84] |
CPR | Šnircová [62]; Mendes et al. [97]; Lin et al. [69]; Du Jardin [93]; Jabeur [98]; Wyrobek [99]; Karas and Srbova [63]; Shen et al. [44]; Park et al. [81]; Qian et al. [86]; Smith and Alvarez [87] |
2.1. Graph Theory Application
2.2. Confusion Matrix
- True Positive () is the total counts of correctly classified positive examples.
- False Positive () is the total counts of negative examples incorrectly classified as positive.
- False Negative () is the total counts of positive examples incorrectly classified as negative.
- True Negative (): is the total counts of correctly classified negative examples.
2.3. Precision-Recall Curves
2.4. Model Building
Algorithm 1: Permanent of company |
Data: Matrix , Vector , Scalar s ; |
2.5. Optimization of Coefficients
3. Results
Metric | Value |
---|---|
Accuracy | 0.9516 |
Precision | 0.7647 |
Recall | 0.7222 |
F1-score | 0.7429 |
0.3928 |
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | |
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CR | … | ||||||
ROA | … | ||||||
TATR | … | ||||||
TDTA | … | ||||||
CPR | … |
2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | ||
---|---|---|---|---|---|---|---|---|
CR | Median | 1.17 | 1.24 | 1.21 | 1.28 | 1.34 | 1.33 | 1.34 |
Mean | 1.92 | 1.84 | 1.90 | 1.73 | 1.92 | 2.11 | 2.34 | |
ROA | Median | 0.07 | 0.06 | 0.06 | 0.07 | 0.05 | 0.04 | 0.03 |
Mean | 0.11 | 0.08 | 0.08 | 0.11 | 0.05 | 0.05 | 0.02 | |
TATR | Median | 1.73 | 1.41 | 1.50 | 1.58 | 1.50 | 1.30 | 1.22 |
Mean | 1.89 | 1.67 | 1.68 | 1.69 | 1.66 | 1.43 | 1.40 | |
TDTA | Median | 0.69 | 0.65 | 0.61 | 0.61 | 0.58 | 0.58 | 0.60 |
Mean | 0.66 | 0.63 | 0.61 | 0.60 | 0.60 | 0.60 | 0.63 | |
CPR | Median | 0.33 | 0.33 | 0.32 | 0.29 | 0.29 | 0.31 | 0.33 |
Mean | 0.46 | 0.53 | 0.55 | 0.38 | 0.40 | 0.54 | 1.41 |
Graph Theoretical Model | Altman Z’-Score | |
---|---|---|
Accuracy | 0.9516 | 0.4409 |
F1-score | 0.7429 | 0.2239 |
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Horváthová, J.; Mokrišová , M.; Bača, M. Bankruptcy Prediction for Sustainability of Businesses: The Application of Graph Theoretical Modeling. Mathematics 2023, 11, 4966. https://doi.org/10.3390/math11244966
Horváthová J, Mokrišová M, Bača M. Bankruptcy Prediction for Sustainability of Businesses: The Application of Graph Theoretical Modeling. Mathematics. 2023; 11(24):4966. https://doi.org/10.3390/math11244966
Chicago/Turabian StyleHorváthová, Jarmila, Martina Mokrišová , and Martin Bača. 2023. "Bankruptcy Prediction for Sustainability of Businesses: The Application of Graph Theoretical Modeling" Mathematics 11, no. 24: 4966. https://doi.org/10.3390/math11244966
APA StyleHorváthová, J., Mokrišová , M., & Bača, M. (2023). Bankruptcy Prediction for Sustainability of Businesses: The Application of Graph Theoretical Modeling. Mathematics, 11(24), 4966. https://doi.org/10.3390/math11244966