Development of Altman Five-Factor Model of Assessing the Creditworthiness of an Enterprise

Affiliation(s)

Department of Computational Mathematics and Informatics, Kuban State University, Krasnodar, Russia.

Department of Computational Mathematics and Informatics, Kuban State University, Krasnodar, Russia.

ABSTRACT

In this paper, we propose a method that uses the apparatus of the theory of fuzzy sets, together with the five-factor model of Altman to assess the creditworthiness of an enterprise. Altman’s model is enhanced in two ways: applies integral approximation of the root mean square for the exact calculation of quantitative credit assessment (probability of bankruptcy), and applies the device of fuzzy sets for ordered sets according to the degree of confidence in the resulting probability. Some real examples of the methodology of applications are shown. The article is theoretical in nature, the findings made in the mathematical model have not been tested on a sufficiently large number of enterprises.

In this paper, we propose a method that uses the apparatus of the theory of fuzzy sets, together with the five-factor model of Altman to assess the creditworthiness of an enterprise. Altman’s model is enhanced in two ways: applies integral approximation of the root mean square for the exact calculation of quantitative credit assessment (probability of bankruptcy), and applies the device of fuzzy sets for ordered sets according to the degree of confidence in the resulting probability. Some real examples of the methodology of applications are shown. The article is theoretical in nature, the findings made in the mathematical model have not been tested on a sufficiently large number of enterprises.

KEYWORDS

Estimation of Credit Status of a Company, Altman Model, Fuzzy Sets, Integral Mean-Square Approximation, Newton Method

Estimation of Credit Status of a Company, Altman Model, Fuzzy Sets, Integral Mean-Square Approximation, Newton Method

Cite this paper

Bamadio, B. and Lebedev, K. (2015) Development of Altman Five-Factor Model of Assessing the Creditworthiness of an Enterprise.*Modern Economy*, **6**, 797-807. doi: 10.4236/me.2015.67075.

Bamadio, B. and Lebedev, K. (2015) Development of Altman Five-Factor Model of Assessing the Creditworthiness of an Enterprise.

References

[1] Kovalenko, A.V. (2009) Mathematical Models and Tools for Integrated Assessment the Financial and Economic Condition of the Enterprise. Ph.D. Dissertation, Kuban State Agrarian University, Krasnodar.

[2] Zhdanov, V.Y. (2012) Diagnosis of Risk of Bankruptcy of Industrial Enterprises: The Case of Aviation-Industrial Complex. Ph.D. Dissertation, Moscow Aviation Institute (National Research University), Moscow.

[3] Hiyama, T. and Sameshima, T. (1991) Fuzzy Logic Control Scheme for an-Line Stabilization of Multi-Machine Power System. Fuzzy Sets and Systems, 39, 181-194. http://dx.doi.org/10.1016/0165-0114(91)90211-8

[4] Kofman, A. and Aluja, H. (1992) Hilo. Introduction the Theory of Fuzzy Sets in in Enterprise Management. Minsk, High School.

[5] Hill Lafuente, A.M. (1998) Financial Analysis under Conditions of Uncertainty. Minsk, Technology.

[6] Altman, E.I. (1968) Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. Journal of Finance, 23, 589-609. http://dx.doi.org/10.1111/j.1540-6261.1968.tb00843.x

[7] Bamadio, B., Kuzyakina, M.V. and Lebedev, K.A. (2014) Estimation of a Company Credit Status Based on the Five-Factor “Altman” Model Using Fuzzy Sets and Simulation. Polythematic Network Electronic Scientific Journal of the Kuban State Agrarian University (Journal Kubgau) [Electronic Resource], Kuban State Agrarian University, Krasnodar, No. 10. http://ej.kubagro.ru/2014/10/pdf/39.pdf

[8] Lebedev, K.A. (1996) A Method of Finding the Initial Approximation for Newton’s Method. Computational Mathematics and Mathematical Physics, 36, 6-14.

[9] Babischevich, P.N. (2010) Numerical Methods: Computational Practicum. Librokom, Moscow.

[10] Nesterov, Y.E. (2010) Methods of Convex Optimization. Mccme, Moscow. http://mipt.ru/dcam/upload/abb/nesterovfinal-arpgzk47dcy.pdf

[11] Vasilyev, F.P. (1988) Numerical Methods for Solving Extremal Problems. Nauka, Moscow.

[12] Bazara, M. and Shetty, K. (1982) Nonlinear Programming. Theory and Algorithms, Mir, Moscow.

[13] Karmanov, V.T. (1986) Mathematical Programming. Nauka, Moscow.

[14] Belgorod Technological University, BSTU, Shukhov, V.G. (2013) Membership Functions and Methods of Construction. http://nrsu.bstu.ru/chap22.html

[15] Konysheva, L.K. and Nazarov, D.M. (2011) Fundamentals of the Theory of Fuzzy Sets.

[16] Chalco-Cano, Y., Silva, G.N. and Rufián-Lizana, A. (2015) On the Newton Method for Solving Fuzzy Optimization Problems. Fuzzy Sets and Systems, 272, 60-69. http://dx.doi.org/10.1016/j.fss.2015.02.001

[17] Chang, B., Kuo, C., Wu, C.N. and Tzeng, G.H. (2015) Using Fuzzy Analytic Network Process to Assess the Risks in Enterprise Resource Planning System Implementation. Applied Soft Computing, 28, 196-207. http://dx.doi.org/10.1016/j.asoc.2014.11.025

[1] Kovalenko, A.V. (2009) Mathematical Models and Tools for Integrated Assessment the Financial and Economic Condition of the Enterprise. Ph.D. Dissertation, Kuban State Agrarian University, Krasnodar.

[2] Zhdanov, V.Y. (2012) Diagnosis of Risk of Bankruptcy of Industrial Enterprises: The Case of Aviation-Industrial Complex. Ph.D. Dissertation, Moscow Aviation Institute (National Research University), Moscow.

[3] Hiyama, T. and Sameshima, T. (1991) Fuzzy Logic Control Scheme for an-Line Stabilization of Multi-Machine Power System. Fuzzy Sets and Systems, 39, 181-194. http://dx.doi.org/10.1016/0165-0114(91)90211-8

[4] Kofman, A. and Aluja, H. (1992) Hilo. Introduction the Theory of Fuzzy Sets in in Enterprise Management. Minsk, High School.

[5] Hill Lafuente, A.M. (1998) Financial Analysis under Conditions of Uncertainty. Minsk, Technology.

[6] Altman, E.I. (1968) Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. Journal of Finance, 23, 589-609. http://dx.doi.org/10.1111/j.1540-6261.1968.tb00843.x

[7] Bamadio, B., Kuzyakina, M.V. and Lebedev, K.A. (2014) Estimation of a Company Credit Status Based on the Five-Factor “Altman” Model Using Fuzzy Sets and Simulation. Polythematic Network Electronic Scientific Journal of the Kuban State Agrarian University (Journal Kubgau) [Electronic Resource], Kuban State Agrarian University, Krasnodar, No. 10. http://ej.kubagro.ru/2014/10/pdf/39.pdf

[8] Lebedev, K.A. (1996) A Method of Finding the Initial Approximation for Newton’s Method. Computational Mathematics and Mathematical Physics, 36, 6-14.

[9] Babischevich, P.N. (2010) Numerical Methods: Computational Practicum. Librokom, Moscow.

[10] Nesterov, Y.E. (2010) Methods of Convex Optimization. Mccme, Moscow. http://mipt.ru/dcam/upload/abb/nesterovfinal-arpgzk47dcy.pdf

[11] Vasilyev, F.P. (1988) Numerical Methods for Solving Extremal Problems. Nauka, Moscow.

[12] Bazara, M. and Shetty, K. (1982) Nonlinear Programming. Theory and Algorithms, Mir, Moscow.

[13] Karmanov, V.T. (1986) Mathematical Programming. Nauka, Moscow.

[14] Belgorod Technological University, BSTU, Shukhov, V.G. (2013) Membership Functions and Methods of Construction. http://nrsu.bstu.ru/chap22.html

[15] Konysheva, L.K. and Nazarov, D.M. (2011) Fundamentals of the Theory of Fuzzy Sets.

[16] Chalco-Cano, Y., Silva, G.N. and Rufián-Lizana, A. (2015) On the Newton Method for Solving Fuzzy Optimization Problems. Fuzzy Sets and Systems, 272, 60-69. http://dx.doi.org/10.1016/j.fss.2015.02.001

[17] Chang, B., Kuo, C., Wu, C.N. and Tzeng, G.H. (2015) Using Fuzzy Analytic Network Process to Assess the Risks in Enterprise Resource Planning System Implementation. Applied Soft Computing, 28, 196-207. http://dx.doi.org/10.1016/j.asoc.2014.11.025