Models for assessing the risk of bankruptcy - Comprehensive...

Bankruptcy risk assessment models

In modern economic science, a large number of methods and models for diagnosing the crisis state of an enterprise are proposed. At the same time, considering the shortcomings of the means and methods of analysis considered, the problem of developing an adequate approach with the minimum number of errors remains relevant.

The risk of bankruptcy is related to the impossibility of the enterprise fulfilling its obligations to creditors and (or) the state on the amount of claims and within the period provided for by the bankruptcy law of enterprises.

The risk of bankruptcy by its nature and by the mechanism of impact is more complex both in the methodology of recognition and in the ways it is managed. This is explained by the multiplicity of the most diverse factors, the correlation of the causes that affect the indicators of financial and economic activity. For example, only the financial status of an organization involves the risks of loss of liquidity, financial independence, loss of equity, a decrease in business activity and financial results (Figure 14.5).

Fig. 145. Classification of risk factors

Identifying risk factors and assessing the degree of risk of bankruptcy is a proactive measure and allows us to specify the directions for further integrated research and crisis management.

The problem of predicting bankruptcy is associated with an increase in the number of insolvent enterprises. So it was right after the end of the Second World War in connection with a sharp reduction in military orders. The obviousness and severity of the problem has reminded of itself during the current financial crisis.

Discriminant models developed with the help of mathematical statistics methods and built on financial coefficients have the greatest diagnostic significance and allow predicting the deterioration of the financial condition for the future.

A study of 183 US firms that experienced financial difficulties for 10 years revealed that the most reliable indicators for the diagnosis of bankruptcy are a reduction in the ratio of net working capital to the amount of all assets, profit on the net equity of the enterprise, the ratio of net worth to debt , coverage ratio of interest payments.

Before the bankruptcy of enterprises, these coefficients were below the normal level and tended to decrease.

The system of five indicators for forecasting bankruptcy, built by financial analyst William Beaver, which is widely known in modern practice, includes the following coefficients:

• Beaver ratio;

• return on assets;

• Financial leverage;

• coverage ratio of assets by net working capital;

• Coefficient of coverage.

Each indicator was defined by the regulatory limits of significance, according to which the firms studied were divided into three categories: prosperous, firms five years before bankruptcy, firms a year before bankruptcy (Table 14.8).

Currently, regression, or discriminant factor models are widely known in the practice of bankruptcy diagnostics. Great interest in their application is caused, firstly, by the possibility of obtaining a concrete assessment of the risk of insolvency, and secondly, by the high effectiveness of forecasting. Regression models based on financial statistics for enterprises reflect real patterns of development. This, in particular, explains a large number of models for forecasting bankruptcy: according to various estimates, the number of statistical models of this kind ranges from 100 to 200.

Multiple regression models, or discriminant factor models, have a general form

where I 0 is a free member; x } - the value of the corresponding factor; a 1 - the coefficient characterizing the importance of the factor; Y - the value of the aggregate integrated metric.

Based on the values ​​of the integral indicator, all the organizations under investigation are divided into bankrupts and successfully operating companies.

The most famous models for forecasting the risk of bankruptcy were developed by E. Altman, a professor of finance at New York University, and were targeted separately for corporations, industrial and non-industrial enterprises.

In foreign financial practice, the most commonly used is the so-called I for calculating the probability of bankruptcy. E. Altman's score (credit rating index), obtained in 1968 with the help of multiplicative apparatus discriminant analysis. This original model is used to diagnose the bankruptcy of large enterprises whose shares are quoted on the US stock market.

The five-factor regression equation is applied to the improved models of bankruptcy forecasting, each coefficient of which is endowed with a certain weight established by the statistical way. In general, the Altman solvency index (2-count) has the form

where K! - Share of net working capital in assets (Net working capital/Total assets); To 2 - the ratio of accumulated profit to assets (retained earnings of previous years should be taken into account together with the retained earnings of the reporting year); To 3 - profitability of assets, calculated on the balance sheet profit; K 4 - the ratio of the market value of all ordinary and preferred shares of the enterprise to borrowed funds; To 5 - asset turnover.

Depending on the value of the 7-account on a certain scale, an estimate of the likelihood of bankruptcy occurrence is established for two years.

Modified variants of forecasting models of bankruptcy Altman built for non-stock companies and non-manufacturing enterprises.

The Altman model for industrial enterprises is as follows:

For non-manufacturing enterprises, a four-factor model with a set of the same indicators is proposed:

where X ] - SOS/A; X 2 - P /A; X 3 - P/A; Х 4 - СК/ZК; X 5 - LH/A; SOS - own working capital; A - total assets; Р - undistributed profit; Р - balance profit before payment of taxes; SC - own capital; ZK - borrowed capital; M - Revenue from sales.

Depending on the calculated value of the integral indicator, Altman established a scale of probability of bankruptcy (Table 14.9).

The pivotal indicator of the Altman's 7-score of the five-factor model can take values ​​in the range from -14 to +22. If an enterprise has a 2-account value of more than 2.99, it falls into the number of financially stable. Enterprises for which a 2-count is less than 1.81 are insolvent, and the interval from 1.81 to 2.99 is an uncertainty zone.

If the received value of the 2-account for the modified Altman model for industrial non-joint-stock enterprises is less than 1.23,

standing (bankruptcy) of the enterprise. If/& gt; 2.9, the company operates stably and bankruptcy is unlikely.

Altman models according to a study by American analysts allow in 95% of cases to predict bankruptcy of the company for a year ahead and in 83% of cases - two years in advance.

In Table. 14.10 shows an example of calculating the five-factor Altman/-model for manufacturing enterprises.

Table 14.10

Calculation of Altman's 5-factor 2-model for production enterprises

Diagnostics of the five factor Altman model for manufacturing plants shows that last year the company in question was in the zone of ignorance, ie, by the received

the accuracy of the forecast can not be established, and in the reporting year the risk of bankruptcy became maximum, the value of 0.869 is less than the threshold level, which means that the enterprise has a high risk of bankruptcy.

The solvency assessment model that characterizes the probability of payment delays based on the integral indicator obtained was proposed by the French economists J. Conan and M. Golder using the following algorithm:

where X, - the ratio of the amount of cash, short-term financial investments and short-term receivables to the balance currency; X 2 - the ratio of equity and long-term loans and credits to the balance currency; X 3 - the ratio of costs for servicing loans to sales proceeds; X 4 - the ratio of labor costs to the net profit of the organization; X 5 - the ratio of profit before interest and taxes to borrowed capital.

The probability of delayed payments, depending on the value of the integral indicator, ranges from 10 to 100% (Tables 14.11 and 14.12).

Table 14.11

Probabilistic estimates of payment delays on the model of J. Conan and M. Golder

The value of I









Probability of late payments,%









Table 14.12

Calculated data of the solvency assessment model of J. Conan and M. Golder



values ​​



Short-term accounts receivable + Cash and short-term financial investments/

/Result of the asset




End of the table. 14.12



values ​​


Constant capital (own +

+ long-term loans) = (Own + long-term capital)/Total of liabilities




Interest for using credit resources/Net revenue




Wages/Net Income




Profit before taxes and interest payments/Loan capital




Integral measure




Probability of late payments,%



The integral figure, last year equal to 0.296, characterizes the 100% probability of payment delays, and in the reporting period the situation deteriorated significantly - this is indicated by the integral indicator, the actual value of which repeatedly exceeded the 100% insolvency risk barrier.

The mechanical use of Western models in United States practice often leads to biased and inaccurate forecasts. The ego is explained by the discrepancy between domestic conditions of management and the peculiarities of economic development of countries with a traditionally market economy. In this regard, United States scientists have developed models that most accurately reflect the conditions of the transition phase of our economy.

The first models for diagnosing possible bankruptcy, destined for domestic enterprises, were obtained by RS Sayfullin and GG Kadykov. To assess the financial condition of enterprises, it is suggested to use coefficients with accepted normative values. The probability of bankruptcy is determined by the rating number. If all the coefficients of the model are within the limits of the criteria values, the rating number will assume a value of 1, and the organization will be assessed as having a satisfactory state of the economy. The financial condition of enterprises with a rating number of less than 1 is characterized as unsatisfactory:

where K 0 - the coefficient of security for own funds with a normative value greater than 0.1 (CK - LV)// AO; K тп is the ratio of current liquidity, the normative value of which is greater than 2 (A t /P t ); To () 6 - asset turnover ratio, should be greater than 2.5 (L/A); To m - return on sales, the ratio of profit from sales to revenue for each industry is an individual value (R/L); To pr - Return on equity, the ratio should be greater than 0.2.

In Table. 14.13 shows the calculated data of the model of bankruptcy diagnostics RS Sayfullin and GG Kadykov.

Table 14.13

Calculation data of the model of bankruptcy diagnostics RS Sayfullin and GG Kadykov



values ​​

T 0

Current Ratio




Coefficient of own funds (SC - AB)/AO




Asset Turnover Ratio




Profitability of real-life products, coefficient




Return on equity




Integral measure




As you can see from the table, none of the calculated financial ratios corresponds to the minimum regulatory level, therefore, the rating number will not equal 1. In the enterprise under study, the rating value has a negative value, as the ratio of own funds demonstrates their lack of turnover. This indicates an unsatisfactory state of the enterprise's economy with the growth of crisis phenomena.

Scientists of the Irkutsk State Economic Academy have calculated a four-factor model for forecasting the risk of bankruptcy, which has the following appearance:

where K 1 - the ratio of own working capital to assets; K 2 - the ratio of net profit to own capital; To 3 - asset turnover; To 4 - the ratio of net profit to the cost of production.

The threshold values ​​of the integral indicator and the corresponding probability of bankruptcy are given in Table. 14.14, and the calculated data for the diagnosis of bankruptcy for the four-factor H-model - in Table. 14.15.

Table 14.14

The probability of bankruptcy in accordance with the value

Model I

Meaning I

The probability of bankruptcy, %

Less than 0

Maximum (90-100)


High (60-80)


Average (35-50)


Low (15-20)

Greater than 0.42

Minimum (up to 10)

Table 14.16

Estimated data of bankruptcy diagnostics on the four-factor D-model of Irkutsk GEA



values ​​


T 0

^ - the ratio of own working capital with assets




To 2 - the ratio of net profit to own capital




To 3 - the ratio of sales proceeds to assets




To 4 - the ratio of net profit to the cost of production




Meaning I



Probability of bankruptcy





The calculated four-factor model of the Irkutsk GEA characterizes the enterprise as having the maximum risk of bankruptcy, estimated at 90-100%: for both periods considered, the value of the indicator R has a negative value. In the reporting year, the changes were even more negative, which can be assessed as the inevitability of approaching bankruptcy.

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