Экономические науки/8. Математические методы в экономике

Cand.Econ.Sci. Shevchenko N.Yu.

Donbass state machine-building academy, Kramatorsk, Ukraine

Cand.Econ.Sci. Ostankova L.A.

Kramatorsk economical and humanitarian institute, Kramatorsk, Ukraine

THE MODELLING OF AN ENTERPRISE’S BANCRUPTCY RISK

The economic security of the enterprise is such a condition of a given subject of economic activity under which the vital components of the enterprise’s structure and activity are characterized by a high level of protection against undesirable changes. To achieve this, the enterprise is obliged to follow the strategy which ensures a sufficient level and increase of the social-and-economic potential, a steady development of business and preparedness for the likely undesirable changes in the sphere of its operations. [1]

As for the interaction with the external environment subjects which results in an enterprise’s gaining profit, it is, as a rule, defined as a factor of major interest for the enterprise. Then it is logical to assume that what makes an economic security criterion for the enterprise is the profit which is obtained in the result of the interaction with the external environment subject, the profit which is left to the enterprise’s discretion. If there is no profit, or even when there are losses incurred, one cannot speak about observing an enterprise’s interests, nor about its economic security. In this case the enterprise is really facing the threat of bankruptcy. [2-5] The aim of the given research is to evaluate the level of an enterprise’s economic security by means of estimating the risk level of its bankruptcy.

It is believed that the approach to the analysis of the bankruptcy risk can be essentially strengthened by combining an account of quantitative(financial) and qualitative(indicative) indices in the analysis, while the indices have to be examined not only statically but in the dynamics as well on the basis the vague approach. [5]

The vague sets theory has found its wide application in technology and economy. However, these methods are quite rarely employed in the practical work of this country’s industrial enterprises. Let us examine the method of the vague logic in the context of analysis of the bankruptcy risk of an industrial enterprise.

In compliance with [5], at the first stage we enter the base sets and subsets of conditions which are described by natural language:

А) The full set of conditions E of the enterprise is broken into five subsets of a kind:

E₁ – the subset of conditions „Marginal trouble”;

E₂ – the subset of conditions „Trouble”;

E₃ – the subset of conditions „Average quality”;

E₄ – the subset of conditions „Relative prosperity”;

E₅ – the subset of conditions „Marginal prosperity”.

Б) The full set of levels of bankruptcy risk G in keeping with set E is broken into five subsets ():

G₁ – subset „Critical level of bankruptcy risk”;

G₂ – subset „High level of bankruptcy risk ”;

G₃ – subset „Medium level of bankruptcy risk ”;

G₄ – subset „Low level of bankruptcy risk ”;

G₅ – subset „Insignificant bankruptcy risk ”.

В) For a certain financial or administrative index Х_i, the full set of its values В_i is broken into five subsets:

B_i1 – subset „Very low level of index Х_i”,

B_i2- subset „Low level of index Х_i”,

B_i3 – subset „Medium level of index Х_i”,

B_i4 – subset „High level of index Х_i”,

B_i5 – subset „Very high level of index Х_i”.

Let’s make an assumption:

–  increase of index Х_i leads to lowering down of the level of bankruptcy risk. If, for the given index, an opposite tendency is observed, then in the analysis it has to be replaced by the opposite one;

–  additional stipulation of correspondence of the sets B, Е і G is fulfilled: if at the time of the analysis all the indices have, according to the classification, the level of subset B_ij, then the enterprise situation is qualified as E_j, and the extent of bankruptcy risk – as G_j.

At the second stage, we are forming a range of indices X={Х_i} of the total number N, which, we believe, affect in the most significant way the evaluation of an enterprise’s bankruptcy risk, as well as estimate different, by their nature, spheres of business and financial life of the enterprise.

1)  Х₁ – ratio of autonomy (relation of one’s own capital to hard currency of the balance),

2)  Х₂ – ratio of liquidity of circulating assets by internal funds (relation of the net circulating capital to circulating assets),

3)  Х₃ – ratio of intermediate liquidity (relation of the sum total of funds and accounts receivable to short-term liabilities),

4)  Х₄ – ratio of absolute liquidity (relation of the sum total of funds to short-term liabilities),

5)  Х₅ – liquidity of all assets in annual computation (relation of profit from realization to the average cost of assets for the given period),

6)  Х₆ – profitability of overall capital (relation of net profit to the average cost of liabilities for the given period).

For the next step, we relate each index Х_i to the level of its significance for the analysis– r_i: al indices have equal significance, then (=1/6).

Vague descriptions in the method structure of the risk analysis appear due to an expert’s uncertainty in the process of classification. For example, the expert cannot draw a strict distinction between a “high” and a “critical” level of the bankruptcy risk, or when it is necessary to draw a distinction between a medium and low level of a parameter value. Taking this into account, vague descriptions are to be applied with the following in mind [5]:

1)  the expert builds up a linguistic variable with its term set of meanings; in order to structurally describe the linguistic variable the expert chooses its corresponding quantitative equivalent which gains values from zero to one;

2)   for each value of the linguistic variable the expert relates the belonging function of a financial index level to a particular vague subset. In our case it is expedient to employ traspezoid-like vague figures and a corresponding function of belonging. In the given research, we formulate linguistic variables as “Parameter value” for the classification of values of the financial indices, and “Level of bankruptcy risk” for the classification of the bankruptcy risk levels of an industrial enterprise.

Further we formulate the linguistic variable which is characterized by the set [6], where – a name of the linguistic variable; – term-set of the linguistic variable , that is a set of linguistic values of the variable, whereas each of these values is a vague variable with the definition field ; – syntactical rule which generates the naming of the verbal meanings of the linguistic variable ; – semantic rule, which puts each vague variable into correspondence with the vague set – the content of the vague variable .

At the last stage, the bankruptcy risk level g is evaluated:

, (1)

where .

The general dynamics tendency of the risk level is of a minus kind, therefore the level of economic security increases: the enterprise is capable of maintaining stability as well as withstanding external and internal threats.

In conclusion, it can be with full certainty said that the bankruptcy risk by the end of the period examined is insignificant, while the result obtained gives grounds to speak of a high level of the economic security. Moreover, the low risk level is attributed to the qualitative administering of the enterprise. This is practically manifested in the financial equivalent, and the necessity to use the treated methods for the vague qualitative-and-quantitative analysis of the industrial enterprise’s financial position as a threat indicator of its bankruptcy is further confirmed.

Literature

1 Spifanov, А.О. Regional’na economica / А. О. Spifanov, І. V. Salo. – К., 2000. – Gl.5. – S. 184-211.

2 Nikeshin, S.N. Vneshnyaya sreda economicheskih system / S. N. Nikeshin. – SPb. : Dva-tri, 1994. – 466 s.

3 Organizatsiya, planirovaniye, upravleniye deyatel’nostiyu promishlennyh predpriyatiy : ucheb. posob. / s. Е. Kamenipera, F. M. Rusinova. – М. : Vysshaya shkola, 1984. – 335 s.

4 Averkin, А.N. Nechetkye mnozhestva v modelyah upravleniya i iskustvennogo intellekta / А.N.Аverkin, N.Z.Batyrshin, А.F.Blishun. – М. : Nauka, 1986. – 312 s.

5 Nedosekin, А.О. Metodologicheskye osnovy modelirovaniya finansovoy deyatel’nosty s ispol’zovaniyem nechetko-mnozhestvennyh opisaniy. – http: // www.nedosek.ru