Altman ratio (creditworthiness index). This method was proposed in 1968 by the famous Western economist Edward I. Altman. The creditworthiness index was constructed using the apparatus of multiplicative discriminant analysis (MDA) and allows, as a first approximation, to divide business entities into potential bankrupts and non-bankrupts.
In constructing the index, Altman examined 66 businesses, half of which failed between 1946 and 1965 and half of which were successful, and examined 22 analytical ratios that could be useful in predicting possible bankruptcy. From these indicators, he selected the five most significant and built a multivariate regression equation. Thus, the Altman index is a function of some indicators characterizing economic potential enterprise and the results of its work for the past period. In general, the creditworthiness index (Z-score) has the form:
Z = 1.3 X1 + 1.4 X2 + 3.3 X3 + 0.6 X4 +1.0X5 (1)
Where X1 is working capital/amount of assets;
X2 – retained earnings/amount of assets;
X3 – operating profit/total assets;
X4 – market value of shares/debt;
X5 – revenue/amount of assets.
The results of numerous calculations using the Altman model have shown that the general indicator Z can take values within the range of [-14, +22], while enterprises for which Z>2.99 are among the financially stable, enterprises for which Z<1,81 являются безусловно-несостоятельными, а интервал составляет зону неопределенности.
Table 1
The degree of probability of bankruptcy according to E. Altman
The Z-coefficient has a common serious drawback - essentially it can only be used in relation to large companies that list their shares on stock exchanges. It is for such companies that you can get an objective market valuation own capital.
Practice shows high accuracy of assessments and bankruptcy forecasts using z-scores for large and medium-sized companies.
In 1983, Altman developed a modified version of his formula for unlisted companies:
Z = 0.717X1 + 0.847X2 + 3.107 X3 + 0.42 X4 + 0.995X5 (2)
(here X4 is the book value, not the market value of the shares). The “borderline” value here is 1.23.
The Altman coefficient is one of the most common. However, a careful study of it shows that it is composed incorrectly: member X1 is associated with a management crisis, X4 characterizes the onset of a financial crisis, while the rest - an economic one. From the point of view of a systematic approach, this indicator has no right to exist.
In general, according to this formula, enterprises with profitability above a certain limit become completely “unsinkable”. In Russian conditions, the profitability of an individual enterprise is significantly exposed to the danger of external fluctuations. Apparently, this formula in our conditions should have lower parameters for different profitability indicators.
Other similar criteria are known. So the British scientist Taffler proposed in 1977. four-factor predictive model, which was developed using the following approach:
Using computer technology, at the first stage, 80 ratios are calculated based on data from bankrupt and solvent companies. Then, using a statistical technique known as multivariate discriminant analysis, a solvency model can be constructed by determining the partial ratios that best distinguish the two groups of companies and their ratios. This selective calculation of ratios is typical for determining some of the key dimensions of corporate performance, such as profitability, working capital adequacy, financial risk and liquidity. By combining these indicators and putting them together accordingly, the solvency model produces an accurate picture of the financial health of the corporation. A typical model for analyzing publicly traded companies takes the form:
Z = 0.53X1 + 0.13X2 + 0.18 X3 + 0.16 X4 (3)
x1=profit before tax/current liabilities;
x2=current assets/total liabilities;
x3=current liabilities/total assets;
x4=revenue / amount of assets.
If the Z-score value is greater than 0.3, this indicates that the company has good long-term prospects; if it is less than 0.2, then bankruptcy is more than likely.
In Russia, the system of criteria for determining the structure of the balance sheet of enterprises is unsatisfactory was approved by Decree of the Government of the Russian Federation dated June 20, 1994 N 498 “On some measures to implement legislation on the insolvency (bankruptcy) of enterprises”, adopted in pursuance of the Decree of the President of the Russian Federation dated December 22, 1993. No. 2264 “On measures to implement legislative acts on the insolvency (bankruptcy) of enterprises.” Based on the norms of civil law, the most important features of a legal entity are the presence of separate property and its independent property liability. Every enterprise, being a legal entity, is responsible for the results of economic activities with all its property.
Federal Law "On Insolvency (Bankruptcy)" No. 6-FZ dated January 8, 1998. establishes for all legal entities engaged in entrepreneurial activities uniform grounds for declaring them insolvent (bankrupt), as well as a uniform procedure for the liquidation of such legal entities. Thus, the legislation does not provide for any exceptions with respect to liability for the obligations of enterprises in various industries and areas economic activity, and it is precisely this approach that was implemented in the above-mentioned resolution of the Government of the Russian Federation.
It should be especially noted that declaring an enterprise insolvent and having an unsatisfactory balance sheet structure does not mean declaring the enterprise insolvent (bankrupt), does not change the legal status of the enterprise and does not lead to civil liability. This is only a state of financial instability of the enterprise recorded by a body authorized by the owner of the property, and such actions do not go beyond the authority of the owner of the enterprise to control the effective use of his property. Therefore, the normative values of the system of criteria are established in such a way as to ensure timely control over the financial condition of the enterprise and the implementation of measures to prevent insolvency, stimulating enterprises to independently overcome the crisis.
Altman model gives an assessment of the probability of bankruptcy based on the balance sheet and income statement.
Based on the Z-score value, the company’s state can be characterized as safe, uncertain (gray zone) and dangerous. There are several calculation formulas for different Altman models (Z-scores). For each model, Altman offers its own zone boundaries.
Here are the calculation formulas for the three most commonly used Altman models:
- Five Factor Model for companies whose shares are quoted on the exchange
- Five Factor Model for companies whose shares not listed on the exchange
- Four-factor model for companies on emerging markets.
The formulas are based on Altman’s presentation “Corporate Credit Scoring Models.” Dr. Edward I. Altman, Stern School of Business, New York University
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In addition to Altman's models, there are others.
General view of the Altman Model
Z = N1*X1 + N2*X2 + N3*X3 + N4*X4 + N5*X5
Where
Ni – numerical factor
Xi – factor calculated according to balance sheet and profit and loss data
The models differ in the factors Xi and the boundaries of the zones.
Factors Xi for all models are calculated using the same formulas with one exception. When calculating X4, for companies whose shares are quoted on the stock exchange, the market value is taken, and for companies whose shares are not quoted on the stock exchange, the amount of equity from the balance sheet is taken.
Altman's five-factor model
for companies whose shares are listed on the stock exchange
Z = 1.2*X1 + 1.4*X2 + 3.3*X3 + 0.6*X4 + 0.999*X5
Zone boundaries:
Altman's four-factor model
for companies in emerging markets
Z’’ = 6.56*X1 + 3.26*X2 + 6.72*X3 + 1.05*X4
As Altman himself said in his interview (February 2016) The Altman Z-Score in Edward Altman's Own Words, he developed this model in the mid-90s based on production and non-production data. manufacturing (manufacturers and non-manufacturers) companies from Mexico, Brazil and Argentina.
Zone boundaries:
| Z>2.6 | safe |
| 1.1 | gray |
| Z | dangerous |
Formulas for calculating factors Xi in the Altman model
The calculation formula using these lines of the Russian balance sheet and profit and loss account is highlighted in yellow
X1= [Working Capital] / Assets
Where
[Working capital] = [Working capital] assets] - [Short term obligations]
X1 = (1250 + 1240) / 1600
X2= [Net Profit] / Assets
X2 = 2400 / 1600
X3= [Earnings before interest and taxes] / Assets
X3 = (2300 + 2330) / 1600
X4= [Market value of shares] / [Liabilities], to calculate Z
X4= [Equity] / [Liabilities], to calculate Z’ and Z’’
X4 = [Market value of shares] / (1400+1500), for Z
X4 = 1300 / (1400+1500) , for Z’ and Z’’
X5= Revenue / Assets
X5 = 2110 / 1600
It can be assumed that for Russian enterprises it is more suitable Altman's four-factor model for companies in emerging markets.
How to make a credit assessment based on financial statements companies? William Beaver compared financial ratios 79 bankrupt firms with indicators of 79 surviving companies. The failed firms had more debt, lower profitability, less available cash and more accounts receivable.
As a result, they had a lower current ratio and a significantly lower absolute liquidity ratio. Surprisingly, these firms had less inventory.
This approach was developed in the works of Edward Altman. The statements of many companies were analyzed, some of which went bankrupt. Altman was looking for a certain formula, depending on the reporting indicators of enterprises, by which one can distinguish between bankrupt and non-bankrupt enterprises. Using statistical methods based on information stock market USA was defined in 1968. Z-score, calculated by the formula:
Z= 1.2X 1 + 1.4X 2 + 3.3X 3 + 0.6X 4 + 1X 5,
- X 1 - own working capital/amount of assets;
- X 2 - retained earnings/amount of assets;
- X 3 - operating profit (earnings before interest and taxes)/total assets;
- X 4 - market value of shares/debt;
- X 5 - revenue/total assets.
It was found that when Z 3) the enterprise is most likely in a prosperous zone and is far from bankruptcy.
Before 1965, 97% of non-bankrupt firms had an indicator value above the threshold level. Altman's model predicted bankruptcy of companies quite well for 2 years and with 70% accuracy for 5 years. We emphasize the probabilistic (statistical) nature of the conclusions based on the Z-coefficient; for an individual enterprise this conclusion may be incorrect.
Z = 0.717X 1 + 0.847X 2 + 3.107X 3 + 0.42X 4 + 0.995X 5,
- X 4 - book value of shares/debt.
The “threshold” value of the Z-ratio for “bankrupt” companies is 1.23, for “prosperous” companies - 3.
Was also received formula for non-manufacturing companies:
Z = 6.56X 1 + 3.26X 2 + 6.72X 3 + 1.05X 4,
- X 4 - book value of shares / debt.
The “threshold” value of the Z-ratio for “bankrupt” companies in the non-production sector is 1.1, for “prosperous” companies - 2.6. Please note that there is no indicator X 5 - revenue / total assets.
In 1972, Roman Lis received UK formula:
Z = 0.063X 1 , + 0.057X 2 + 0.092X 3 + 0.001X 4,
- X 4 - equity / debt capital.
The “threshold” value of the Z-score for “bankrupt” companies is 0.037.
The formula valid for Russia is difficult to determine. Most likely, it is currently impossible, since bankruptcy procedures are often determined by non-economic factors. But the practice of using Altman Z-coefficients on some Russian enterprises confirms the possibility of determining the trend of changes in financial condition, i.e., when the financial condition worsened, the Z-ratio worsened, and vice versa.
This model, also known as the Z-score or creditworthiness index, is the most common in global analytical practice. The Altman group of indicators includes several models. The best known of these is the 1968 five-factor model.
Table - Altman two-factor model
The probability of bankruptcy in a two-factor model is determined at the level:
50% if Z=0;
Less than 50% if Z< 0 и уменьшается вместе с уменьшением Z;
More than 50% if Z > 0 and increases as Z increases.
Table - Altman's Five Factor Model
Interpretation of the five-factor model:
Z > 2.99 financially stable enterprises;
Z< 1,81 безусловно - несостоятельные предприятия;
The interval constitutes a zone of uncertainty, that is, in this interval it is impossible to say anything definite about the possibility of bankruptcy.
When calculating component X4, the problem of market valuation of the company's equity arises. In such cases, the share price cannot serve as a sufficiently adequate assessment of share capital, since the transaction mainly records the transfer of control over the company, and not the normal investment process.
To evaluate companies whose shares are not listed on the stock exchange, Altman proposed a modified version of the five-factor model:
Z = 0.717 X1 + 0.847 X2, + 3.107 X3 + 0.42 X4 + 0.995 X5
Model J. Conan And M. Golder
French economists J. Conan and M. Golder, using the method developed by E. Altman, built a model that looks like this:
Z = -0.16Х1 – 0.22Х2 + 0.87Х3 + 0.10Х4 – 0.24Х5, Where
X1 - attitude Money and accounts receivable to the balance sheet currency;
X2 - the ratio of equity and long-term liabilities to the balance sheet currency;
X3 - the ratio of loan servicing costs (or the price of borrowed capital) to sales revenue (after tax);
X4 - the ratio of labor costs to the organization’s net profit;
X5 is the ratio of earnings before interest and taxes (balance sheet profit) to borrowed capital.
The probability of delayed payments by firms with different values of the Z indicator can be represented as a scale:
In the equation, the authors draw attention to the dominant role of factor X3 - the ratio of financial costs to sales revenue in comparison with the other four coefficients. In fact, the influence of this factor exceeds the combined influence of all others.
Fulmer model
The model was created based on the processing of data from sixty enterprises - 30 that failed and 30 that were operating normally - with an average annual balance of 455 thousand US dollars. The initial version of the model contained 40 coefficients, the final version uses only nine.
Table - Fulmer Model
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5.528x 1 +0.212x 2 +0.073x 3 +1.27x 4 -0.12x 5 +2.335x 6 +0.575x 7 +1.083x 8 -3.075 |
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P non-discord |
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ChP+Am |
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Log 10 (VB-NMA-DFV-NDS-DZ) |
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|
__OA__ |
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Log 10 (PDN/% payable+1) |
In this case, X7 is correctly determined in terms of the elements of the asset in thousands of US dollars as of the date of preparation of the analyzed report. If H< 0, крах неизбежен. Точность прогнозов, сделанных с помощью данной модели на год вперёд - 98 %, на два года - 81 %.
Most often, Z-models are used to assess the probability of bankruptcy of an enterprise. , proposed by the famous Western economist Edward Altman , which involves calculating a creditworthiness index.
The simplest of these models is the two-factor model. For it, two main indicators are selected, on which, according to E. Altman, the probability of bankruptcy depends:
* coverage ratio (characterizes liquidity);
* coefficient of financial dependence (characterizes financial stability).
Based on an analysis of Western practice, the weighting coefficients of each of these factors were identified.
Z = -0.3877 - 1.0736 K p + 0.579 K fz,
where K p -- coverage ratio (ratio of current assets to current liabilities);
To the federal law, the coefficient of financial dependence, defined as the ratio of borrowed funds to the total amount of liabilities.
For enterprises with Z = 0, the probability of bankruptcy is 50%. If Z< 0, то вероятность банкротства меньше 50% и далее снижается по мере уменьшения Z. Если Z >0, then the probability of bankruptcy is more than 50% and increases with Z.
The advantage of the model is that it can be used in conditions of a limited amount of information about the enterprise, but this model does not provide high accuracy in predicting bankruptcy, since it does not take into account the impact on financial condition enterprises and other important indicators (profitability, return on assets, business activity).
In Western practice, multifactorial models by E. Altman are more often used.
In 1968, he proposed a five-factor model for predicting bankruptcy. The creditworthiness index was constructed using the apparatus of multiplicative discriminant analysis (MDA) and allows, as a first approximation, to divide business entities into potential bankrupts and non-bankrupts.
In constructing the index, Altman examined 66 businesses, half of which failed between 1946 and 1965 and half of which were successful, and examined 22 analytical ratios that could be useful in predicting possible bankruptcy. From these indicators, he selected the five most significant ones for the forecast. He included these indicators in a linear discriminant function:
X 1 - ratio of own current assets to the amount of assets;
X 2 - return on assets (redistributed profit to the amount of assets);
X 3 - level of return on assets (ratio of profit to total assets);
X 4 - the ratio of equity and borrowed capital or the ratio of the market value of shares to borrowed capital;
X 5 - asset turnover (or the ratio of proceeds from sales to the amount of assets).
Based on these coefficients, E. Altman developed a five-factor Z-model, which is one of the main methods for assessing the probability of bankruptcy of enterprises and is widely used in the USA:
Z 5 = 1.2* X 1 + 1.4* X 2 + 3.3* X 3 + 0.6* X 4 +1.0* X 5, (3)
where X1, X2, X3, X4, X5 are coefficients in the form of fractions of units.
The level of threat of enterprise bankruptcy for joint stock companies open type is assessed according to table 1.1.
Table 1 - Level of threat of bankruptcy according to the Altman model
Z - coefficient has a common serious drawback - essentially it can only be used in relation to large companies that list their shares on stock exchanges. It is for such companies that it is possible to obtain an objective market assessment of equity capital. (9, pp. 74-76)
For closed joint stock companies and enterprises whose shares are not quoted on the market, the following Altman model is recommended:
Z = 0.7 * X 1 + 0.8 * X 2 + 3.1 * X 3 + 0.4 * X 4 + 1.0 * X 5, (4)
where X 4 is the coverage ratio at book value, i.e. the ratio of the book value of share capital (total book value of the company’s shares) to short-term liabilities;
Comparison constant -- 1.23
If Z< 1,23, то это признак высокой вероятности банкротства.
If Z> 1.23, then this indicates its low probability.
The forecast accuracy in this model over a one-year horizon is 95%, over two years - up to 83%, which indicates the merits of this model. However, there are opinions according to which, in conditions transition economy It is not advisable to use the Altman model. The arguments of the supporters of these opinions are:
* incomparability of factors generating the threat of bankruptcy;
* differences in the accounting of individual indicators;
* the influence of inflation on their formation;
* discrepancy between the book value and market value of individual assets and other objective reasons.
