Alexander Shemetev (copyright protection),

PhD (Finance), MBA, Master in anti-crisis financial

Management, Master in Linguistics

Saint-Petersburg, 2012 (February)

For further questions, please, contact me at:

Anticrisis2010@mail.ru

Financial analysis of companies" bankruptcy,

recommended to use in the modern Russian conditions

Abstract: This paper has the most modern methods of bankruptcy forecasting recommended to use in the modern Russian conditions. This paper tells about the achievements of the Great scientists in economy. This paper also discloses some methods created by Alexander Shemetev to forecast bankruptcy: Alexander Shemetev"s method for calculating the optimal portfolio with the set returns which improves Harry Markowitz method for the Russian market; The self-model of Alexander Shemetev for firms" bankruptcy forecasting based on synthesis of 42-years experience of Ghent University.

Key words: bankruptcy, analysis, economy, finance, portfolio of shares, Harry Markowitz, William F. Sharpe, John Burr Williams, Stephen Alan Ross, William Henry Beaver, Edward I. Altman, Stuart Altman, John Fulmer, Gordon Springate, Sofie Balcaen, Hubert Ooghe, Eric Verbaere.

Bankruptcy ... There is so much meaning inside this word.... Many companies afraid this word as much as they afraid of fire. And some companies are trying to make themselves bankrupt for various reasons, thus, often afraid this word for real-open-bankruptcy-situation as much as they afraid of fire too. Bankruptcy - is an ancient word. Roots of this word are in a term "bank".

What is a bank today? This is a credit institution, which together can focus a full economic and financial flows not only for a separate market segment, and also for the whole national economy .... How many crises caused "bankruptcies" of the banks in Russia and in the world ....

Formerly, in antiquity, people did not think much what a bank is; and the place and niche that formerly was occupied by "trapezzits" is now busy by the modern credit institutions.

Great-grandfathers of modern banks were then money-changers, which in Greece were called trapezzits. These money-changers sat at tables, which in the Roman Empire were called "Bankus" or, simply, in the vernacular, some people called them "banks." In Greece, Hellas, such a bench was called trapeza.

These two words gave the name to the two traditions of naming the banks (bank - is a Roman tradition, and trapeza - is a Greek tradition).

And if a group of modern banks-in-bankruptcy can sometimes cause these heavy-duty chain reactions of defaults in the economy that may cause even national or global crises; - just imagine what happened then, in ancient times, when some groups of rich money-exchangers ruined at once .... The trading inside a whole region could be frozen due to it for a certain period of time. It was difficult to continue to trade, when there is no place to exchange the money, to take loans, guarantees, sureties and so on....

The moneychangers" bench was broken in the event of insolvency, which in Latin was pronounced as "bankrupt" ("bank-Rotto" - split bench - the lat.). Antiquity has passed .... and the bankruptcy phenomenon still persists... Both: the term bankruptcy and its meaning lived side by side for a few thousand years....

How to calculate the bankruptcy of a company? How to analyze it? How to prevent it? Mankind from the earliest stages of the civilization"s development has been trying to answer these questions....

In the first stages of civilization development people believed that bankruptcy with all its consequences - is the handiwork of the gods themselves.... They understood a term "ruin" under bankruptcy. Therefore, to prevent bankruptcy one should appease the gods....

And who can do it better than the Templars-sorcerers, the "priests" of those ancient temples? Thus, temples often became the center of the ancient settlements, which served as a repository of wealth, and the "priests" were trying to forecast revenues (which depended on the harvests, wars, disasters and other factors) through mystical rituals....

At the same time, they developed an astrological prediction of bankruptcy ... .. In those times, people did not know what is bankruptcy and insolvency. They determined it in total as a "lack of money," "lack of wealth". They believed that money and wealth - these are very close synonyms, originating from the "crop failure", "catastrophic events", "anger of the gods", ... These first mystical theories of definition and prediction of bankruptcy, insolvency, and getting rich, over time, gave the beginning to all the other theories.

The first scientific theories to predict bankruptcy appeared in Europe during the Renaissance, and in Japan - in the late 17th century. Even then, there originated and gradually developed two initially independent schools for prediction of bankruptcy.

European School on the first stage taught that all has its mechanisms (mills, people, nature, cash handling, ....). So there is the concept of the mechanism of circulation of money, that is, laws that can cause wealth of nations or individuals, or their impoverishment that is, bankruptcy. From the Renaissance to the early twentieth century, there originated several theories attempting to explain the main causes of bankruptcy in the broadest sense in economic science in Europe. Then it was understood as the impoverishment of the individual company or an individual.

In Japan, for the period from the late 17th century until the second half of the twentieth century, there was born a diametrically opposite approach to determining the causes of bankruptcy, and the description of an effective mechanism for predicting bankruptcy: Techno-economic analysis with adjustment for component of mass psychology. This approach, which began its rise in the late 17th - first half of the 18th century in Japan - it gave the rise to many areas of trend analysis of the enterprise, including the prediction of bankruptcy...

In the twentieth century, people were more likely to use mathematics in economics and finance. At the same time, there began to emerge an approach, which can be called the Comprehensive financial analysis. In the first half of the twentieth century there were few calculations, and the students were taught to financial analysis only for 1-2 academic semesters, knowing that all the necessary material has been passed so yet. At the beginning of the twentieth century, the financial analysis was limited to the calculation of several coefficients and trends, as well as to several recommendations contained in themselves some like the form of "life experience of some businessman." These recommendations and the coefficients are valuable even today, and they reflect not all the specifics aspects of the company in today's dynamical world of globalization and mass-, relatively much more aggressive, competition, than there was it in the early twentieth century.

The first scientific approach to a quantitative prediction of bankruptcy included the establishment of the first prototypes of linear discriminant models of William H. Beaver with his followers. You may ask me: "And what is the linear discriminant model?". The basis of this model is the concept of discrimination. I think you all know what it is! We have a lot of examples of discrimination: gender, skin color, the material status, age, education, the popularity and fame, and so on .... And we subconsciously and consciously ask ourselves rarely for a clear indication of how one person or one object is in a higher priority than the others. So, no one says that the star, whose sold his albums over a million during the last - is more than twice more important than the artist, who sold his albums just over an half a million.... They just say that one likes some certain star, and the other like the other star....

Discriminant approach to financial analysis means that we accurately and unambiguously define the parameters as financial indicators/ratios as more-or-less-important than the other indicators/ratios in predicting the bankruptcy. The word "linear" in this analysis indicates that the so-called simple mathematical model is to be constructed, whose function graphically (visually) is a straight line. A straight line means that the more of a factor A we bring, the more (or less) is the linear function proportionately. A word discriminant in this approach means that the model is divided into components, set-parameters/factors, some of which are more important and significant in predicting bankruptcy than the others.

I stopped at such a detailed explanation of the value connotations (explaining the meaning of words) not accidentally in discussing the linear discriminant approach. The fact is that today this approach in predicting bankruptcy is the most common.

In one of my previous books: "Anti-crisis financial management for commercial firms directors and business owners", I adapted a significant set of techniques for application of bankruptcy prediction in the modern Russian reality. You can"t just take an American or European model, developed in the past, and to apply it to the Russian reality in relation to the nowadays in it.... That is why the adaptations are necessary, the interpretation of how you can use one or another favorite technique to be applied for the Russian reality and to your company ....

Now, let's consider what an arsenal of methods of forecasting bankruptcy exists today.

Classification of methods of forecasting bankruptcy

The first person to think that bankruptcy can be predicted mathematically, was William Henry Beaver. He was born in 1940 in Illinois, the United States. He was an only child. His father, through his hard work, managed to break out of a simple miner to the level of qualified mining engineer. His mother was from a large family and worked from an early age in order to feed his four brothers and sisters. W.H. Beaver attended the University of Notre Dame (Chicago). After receiving a bachelor's degree, he was able to enroll in graduate school. Almost simultaneously, he began to conduct research, including on predicting bankruptcy. Then he became interested in the work of British mathematician Ronald Aylmer Fisher (1890 - 1962) concerning the linear discriminant mathematical models and their applications in statistics, in the division of parameters into two components with high precision, published by R.A. Fisher in 1936.

W.H. Beaver begins a fundamental study on the relation of financial reporting, and bankruptcy. In a literal sense: using rulers, pencils, posters, coasters and a simple adding machine, he gradually begins to write financial performances down. The study of the bankrupt companies and non-bankrupt-ones directs him to the fundamental conclusion that the financial statements can provide comprehensive information about the probability of insolvency of any company, and companies can be divided among themselves on the solvent and insolvent by the method of discrimination, developed by R.A. Fisher. His master's thesis on the subject of accounting had been implemented on a high scientific level, so that within 30 minutes after defending his master's thesis, he defended it as doctor in the same board at the same ceremony of protection, after a lunch break in 30 minutes in 1965 year. He often joked afterwards that it took a full 30 minutes to become a doctor of science! After that, he published a series of papers on how to find out about the difficulties of company by studying the financial statements.

His book [1] was devoted to these issues, and it brought him a worldwide fame, as well as another his 60 publications, published around the same time. In this case, the manuscripts of them all he made manually!

Winner of many international awards in accounting, one of the three most prominent Chartered Accountants listed in the Accounting Hall of Fame, in the U.S.. At one time he was President of the Association of Public Accountants of the United States, from 1979 to 1981. He is one of the leading theoreticians of GAAP. He is also a honorary Professor of the Hall of Fame after Joan Estelle Horngren at Stanford University, USA. The fame of W.H. Beaver and the relevance of his research have led many financiers to start their own independent research into the prediction of bankruptcy.

William Henry Beaver Model is important because he, knowing full accounting, was able to identify key indicators, which signal about the bankruptcy of the company. W.H. Beaver fully appropriately considered the borrowed capital as the first indicator of bankruptcy due to the fact that company can not to pay its obligations due to sudden changes in market conditions. He considered a commercial risk as the second factor, which is reflected in oversupply of inventory and accounts receivable increase, especially, in the long run. And the third factor - it's a liquidity crisis, when a company may suffer due to the lacks of liquidity.

William Henry Beaver was and is not just a theoretician in predicting the bankruptcy, and also he is a large prominent scientist in the field of complex financial analysis of company.

Today it is a lot of time has passed since 1965, when it was put forward the theory that the bankruptcy of companies can be predicted based on its financial statements. For 45 years the international scientific community has come up with a lot of models to predict bankruptcy:

1) Linear - discriminant analysis;

2) Logistics (probabilistic) analysis;

3) Build a decision tree (sequential division of enterprises);

4) The regulatory approach;

5) The legal approach;

6) The trend method;

7) A qualitative method;

8) The genetic model;

9) The models for tracking the primary factors of the environment on a basis of correlation and regression analysis;

10) Models with non-financial indicators;

11) Models of neural networks (the latest);

12) Scoring method.

Let's look at these methods in more detail:

1) Discriminant analysis

The first bankruptcy prediction models were based on linear discriminant statistical analysis of R.A. Fisher (Ronald Aylmer Fisher), 1936. Linear-discriminant analysis (LDA) was originally designed to accurately split the array of statistical data on the two mathematical clouds of values according to the specified linear discrimination parameter. However, the most commonly used three-cloud model of linear discrimination, where the third cloud is the so-called "zone of uncertainty", which included an array of data, which clearly does not correspond to any discriminatory field.

If the R.A. Fisher discriminatory analysis, for example, to be applied to partition an array of hot and cold objects, all the "warm objects", which clearly can not be attributed neither to hot nor to cold, will remain in this third area of uncertainty.

According to the theory of linear discrimination, the objects of the cloud of uncertainty must be looked at the dynamics. In more simple terms, in our example, this means that warm objects to be observed in the dynamics of what happens to them: they are warming or getting colder and colder over time.

The very idea of using the linear discrimination is to derive an equation that would break all the companies into those that are highly likely to go bankrupt in the future, and those who do not go bankrupt in the future. This idea is itself very promising.

Edward Altman logically completed the W.H. Beaver"s study by creating the first accurate model, which became known at the public as the Z-model. Right now we"ve only touched the basis of the theory of analysis. We shall discover the models themselves a bit further.

There are two types of components in linear discriminant analysis: b and x. X - is an accounting measure or inferred on this basis financial ratio. Recall W.H. Beaver, who said that the company's activities may well be traced by analyzing the reports. Component X even now carries a part of the theory, according to which it is derived directly from the financial statements. Because of this fact, the X component is a direct legacy of W.H. Beaver"s studies.

Along with it, there is a mathematical component b.

This component - is the linear coefficient of discrimination - it is direct legacy of the author of the model of a linear discrimination, this is the legacy of R.A. Fisher. Component b is designed to divide each company for two groups of companies: Bankrupt and Non-bankrupt - it is based on an analysis of statistical data on bankrupt companies.

Classically, the equation of linear discriminant analysis is recorded in the same form in which it was opened by Edward Altman:

(233)

This function is the discriminant function, where:

b1, ... .., bn - the regression (significance) coefficients. The higher the regression coefficient, the more significant X is. These coefficients are to be calculated in prior to the ready model. That is why they are represented as constants in the ready models themselves.

X1, ... ..., Xn - financial performance coefficients.

Z * - cut-off point (this point separates, as if it cuts off, all the enterprises to possible bankrupt and non-bankrupt).

Thus, the main characteristics of the linear-discriminant model with cut-off points are:

1) regression coefficients;

2) financial performance indicators;

3) cut-off point;

4) The classification rules.

Initially it was assumed that the R.A. Fisher linear discrimination method will share all of the companies to "bankrupt" and "not bankrupt" exactly, and, therefore, they thought primary to built models without the "gray clouds", which characterizes the uncertainty.... However, the "unambiguous model" quickly gave way to three ways of models results" interpretation in which the third was the area of a cloud of uncertainty values.

The analysis of any company by the linear discrimination models must always be focused to the dynamics! This is similar to the

For example, if you imagine that hot objects - they are 100% bankrupt, and cold objects - they are 100% not bankrupt, then there has to be very likely next. Imagine the plate with two teapots on it: , one was removed from the fire - and the other is still there.

Using a linear discrimination, viewed in the dynamics, we can find that the hot kettle, which is removed from the heat has gradually been becoming colder and colder; and the one that is on fire - no. Thus, the first kettle gradually passes into the category of cold objects, and the other one - remains hot until all the water in it boils away....

Similarly, things are going with bankruptcy. Linear-discriminant analysis should be used only in the dynamics. Then it will be able to accurately reflect not only the fact whether the company goes bankrupt, as the fact whether the analyzed company looks like the one that had once gone bankrupt, in the way it was taken into account in the model ... If you like, then there is a high probability that it can repeat the fate of the bankrupt company... Other extreme - when a company is similar to the analyzed successful companies... Therefore, such a company, too, with a high probability is successful in the similar way to the other successful companies that were taken into the consideration when creating the certain model...

Thus, the linear discriminant analysis - is an analysis based on projection of the analogy of one company to another; the projection which was considered a success or a bankrupt in the construction of linear discriminant model. This theory was and still is so simple and brilliant, that still methods of Altman and other linear methods of discriminant analysis are used in predicting bankruptcies of major global companies today. For example, in 2008 Altman's 1968 model and model of Gordon Springate were used in predicting the bankruptcy of Ford and General Motors, which showed that these companies are very similar to those at the foundation of Edward Altman and Gordon Springate"s models were regarded as bankrupt [2] ....

Thus, the linear discriminant analysis involves splitting companies into those that are similar to bankrupt companies, and those that are similar to the successful companies that have been investigated to construct and improve models. Often this type of models has a "gray zone". Thus, it appears that there are three classes of companies:

Class 1 - All businesses, Z-index for which is below the gray zone - they are bankrupt, according to the model.

Class 2 - All businesses, the coefficients for which are higher than the gray zone - they have good financial stability.

Class 3 - All businesses, Z values for which fall into the gray zone, and so they are in the zone of uncertainty. That is, we can not definitely say - if they are bankrupt or not.

Most commonly used methods of estimating the probability of bankruptcy are the methods offered by the Western economist Edward Altman, the so-called Z-models. They are based on multivariate regression analysis of 100 companies located in the boundary condition. Edward Altman proposed a regression equation whose general form is:

(234)

There are linear-discriminant and other bankruptcy predictive models. And let us, dear reader, discuss them a bit later in more detail. Now, let us, together with you, my dear reader, look the other existing models for predicting the bankruptcy.

2) The regulatory approach

Governmental attempts to control and predict bankruptcy have relatively recent origins. Slightly more than 100 years ago the situation was so, that the State applied a special legal approach to the bankrupt party. For most countries that meant, that the debtor was a mortgage for lenders himself.

However, the situation has changed rapidly during the nineteenth century. Then the liberal spirit prevailed in European and American societies, and the bankrupt person was more and more often forgiven. There appeared the postponements of debt, partial repayments of the loan, the removal of the debt in the natural kind, and so on.

At that time, there were no regulations in relation to bankruptcy. And gradually to be bankrupt began turn out ... from dangerous thing to the advantageous cases... From now, a company in the liberal countries could gain credits to cover them at the expense of other loans, and then to get some more debt, then it could transfer all the money on someone else's expense and to declare itself a bankrupt, in accordance with the law, while leaving a portion of the debt .... and even most part of the debt ...

In the developed countries in the early twentieth century, the bankruptcy case could last for many years, during which the debtor"s bankrupt estate was gradually sold. It was rumored that many bankruptcies were .... fictitious, while, in most cases, people couldn"t find reasonable evidences for that. Thus, there was a problem of normative financial analysis.

The twentieth century brought changes to financial analysis. The story rapidly unfolded in such a way that the world gradually became more and more bipolar: on the one hand, there were the totalitarian regimes that could tightly control the activity of economic entities; on the other hand, there were market economies that increasingly needed to standardize the process of financial analysis to identify the companies and fictitious bankruptcies ... .. Years had passed, and in 1920 there were developed the first prototypes of predictive failure ... .. The State had to consolidate and standardize the financial analysis to develop a series of standards. And almost always, as happens in such cases, the most difficult was to deduce the parameters of the comparison .... since the critical exponents should be compared with some critical standards ....

Norms began to be developed, and there was "new old problem": joint stock companies participating in each other and having the right to initiate procedures for fraudulent bankruptcy of associates to write off debts of affiliates .... And with a flow of assets "from point A to point B with the subsequent writing off of debts back to a fictitious point A to purchase a cheap point A property at the bankruptcy procedure by the point C, which is "independent" from the point B"...

Joint stock companies often created subsidiaries that were recruited debt, then they declared bankruptcy, the bankrupt's estate was to be sold for the whole property "on the cheap" to "independent companies"; it gave funds to pay some parts of debts for some other creditors, and the rest sums - they were written off due to bankruptcy.... However, the operations such as "A B A", the world did not stop on them .... There were also some more sophisticated operations such as "M M", who shared major shareholders (M / large packages of shares /) and minority (also M / small stakes shareholders /)... One M-people could manage their companies and companies" property flows ... while the other M-people could manage only their money-flows... As a result, the assets were divided: the major shareholders stayed with company"s assets in the end, while the minority shareholders stayed only with company"s debts in the end.

With the development of standards, the effectiveness of their use was often reduced.... This is perhaps the main problem of predicting the bankruptcy by any method, in particular, by the regulations, which was originally designed as a "panacea" to eliminate this problem.

From the beginning of the twentieth century, the State attempted to normalize the prediction of bankruptcy by the legal doctrines: first, tough - then - by more and more soft ones. The basis of valuation was the legal approach, which we consider with you, my dear reader, a little later. Now let"s consider a more general approach, the normative one.

The norm ... .. In planned economies the norm - it's a real planning tool. Standards are always associated with the legislative methods of partition the companies into two groups: those that fit into the norm, and those that do not fit the norm. The standards are of two types: authoritarian and liberal. Authoritarian norms rigidly setting the boundaries of rules that must comply with certain actors in the economy. For instance, the banking sector has especially many authoritarian regulations. So if, for example, the Russian Central Bank is not satisfied the H1 (Cook"s ratio of capital sufficiency) norm of capital adequacy for a certain particular bank, it may lead to revocation of a license by the Central Bank, which in itself is a prelude to the bankruptcy of a credit institution.

Most companies of other branches also have authoritarian regulations. For the most part, they are not directly related to the bankruptcy. For example, there is an authoritarian standard, under which all companies must keep the money in the bank over the limit, except in certain cases stipulated by law (such as some cases of salary for employees).

Authoritarian regulatory approach is directly related to the legal approach, which we shall consider with you, my dear reader, a little later.

A liberal regulatory approach assumes that there are some certain established norms, which, in contrast to the authoritarian rules, - are not mandatory, but desirable. Examples of such rules we are with you, dear reader, have already considered (in my previous papers): own funds ratio must be greater than 0.2, the current liquidity - greater than 1-2. Regulations often differ themselves from country to country. For example, in the U.S. we would have not met the stringent standards on the availability of internal funds; at the same time when the norm of current liquidity of more than 0.2 - 0.3 - is considered as a good indicator.

So we came up with you, dear reader, close to the application of the normative approach in the prediction of bankruptcy in Russia. It is implemented using the following ratios: current liquidity ratio, availability of own funds to restore the solvency and loss of ability to pay.

The structure of the company's balance sheet can be considered unsatisfactory, and the company - as insolvent under the following conditions:

a) Current Liquidity Ratio (CLR) at the end of the reporting period has a value of less than 1.2 [3];

b) The own funds" sufficiency ratio (OFR) - is less than 0.1 [4].

When the poor balance sheet structure is found - it is necessary to verify the real possibility of the company to restore its solvency; it is made by the ratio-to-restore-the-solvency (RRS6) calculation for a period of 6 months:

(235)

Where: CCLR(BEGINNING), CCLR(END) - these are the actual values of the coefficient of current liquidity at the beginning and at the end of the reporting period; 6 - is the period to restore the solvency, expressed in months, T - is the reporting period, expressed in months. 2 - is the upper normative value of the coefficient of current liquidity. RPAR - is the ratio of pay-ability-renewal (the other name for this ratio).

If the value of the coefficient shows less than 1, it is necessary to calculate the rate-of-loss-of-ability-to-pay (LAP3):

(235.1)

Where: T - is the reporting period, expressed in months; CCLR(BEGINNING), CCLR(END) - these are the actual values of the coefficient of current liquidity at the beginning and at the end of the reporting period; RPAL - is the ratio of pay-ability-loss (the other name for this ratio). This formula will be met by us again in the further text.

So, if all the coefficients were lower than what is prescribed by the standards, then it indicates a high share of the probability of bankruptcy. Other means mean that a company, with a high probability, will not go bankrupt in the near future.

Besides the above standard-method, there are a number of other regulations. Thus, the Russian Federation Government Resolution #367 (from 25.06.2003) describes the performance standards for analyzing the financial condition of the company. For example, assuming that the ratio of the average value of liabilities to be paid to the average value of sales revenue (CAVL/AVR) must be less than 1:

(236)

Where: AvLmonth-aver- this is the average value of liabilities to be paid. It can be calculated for a going-concern as the amount of short-term borrowed funds (STL) for the reporting period to a number of months in that period. Revmonth-aver- this is the average value of revenue. It can be calculated similarly to indicator AvLmonth-aver, and instead of STL one should use the proceeds (Rev).

Now, let's go back to where I started the whole conversation: let"s go back to a fraudulent bankruptcy and regulations relating to its prevention. In Russia the fictitious bankruptcy is regulated by FSDN Decree number 33-R (from 08/10/99) "On the issue guidance for the examination of the presence (absence) of signs of a dummy or intentional failure". This ruling clearly pronounces that the fictitious bankruptcy is possible only during the legal procedure of bankruptcy (see legal approach as to when this procedure is initiated).

Alexander Shemetev, on the basis of legal acts of bankruptcy, designed for you, dear reader, a number of the following formulas that reflect the basic legal requirements for examination for signs of fraudulent bankruptcy. The ratio of the presence of signs of fraudulent bankruptcy can be calculated by the algorithm:

(237)

Where: MobAF - is the value of current assets, calculated in accordance with the signs of fraudulent bankruptcy. MobAF = sum of current assets, including long-term receivables, net of value added tax (VAT): line: 290 - line: 220 from number 1 OKUD form (Balance). line: - a designation to line from reporting form. So, line: 290 - is the 290 line from number 1 OKUD form (Balance). STLF - is the sum of short-term obligations calculated in accordance with the signs of fraudulent bankruptcy. STLF = sum of short-term borrowings, net of deferred income, consumption fund and reserves for liabilities and charges, increased by the value of PFS: line: 690 - line: 640 - line: 650 - line: 660 + PFS. PFS - is the sum of all penalties, fines, sanctions. β - is a correction factor of liquidity of MobAF, which characterizes the liquidity of current assets (β is always ≤ 1).Thus, β = 1 means that 100% of MobAF is completely liquid. The β coefficient which is different from the value 1 should be considered whenever possible. If the value of (237) is greater than 1, there are the signs of fraudulent bankruptcy - otherwise these signs are absent.

In addition, the FSDN Order number 33-R (RFSDN number 33-R) refers to some additional measures and methods of identification the signs of fraudulent bankruptcy (as you will recall, this can be done only in respect to companies located in one of the 5 stages of bankruptcy) . Among these features it involves the analysis of changes in parameters describing the degree to which the obligations of the debtor are secured for its creditors. It is also expected an analysis of the conditions of transactions of the debtor to its creditors. At the same time, the domestic insolvency law school has developed an outstanding paradox in calculating the norms of the financial analysis in such situations. To get an acquaintance with it, let's consider the algorithm of calculating the indicators stated by RFSDN number 33-R. It requires an analysis of the fraudulent bankruptcy procedures. The author of this paper transformed the text of these law regulations into simply-to use formulas and algorithms.

1) The first indicator is security of the debtor"s obligations to creditors by debtor"s assets (SDODA):

(238)

Where: TBSF - is the amount of assets, calculated in accordance with the definition of fictitious bankruptcy. This is the amount of assets for the difference in organizational costs, VAT on acquisitions and losses. (AP+OP)F - Is the sum of "accounts payable" as defined for purposes of examination for signs of fraudulent bankruptcy: the sum of all borrowings of the company, including long-term (line: 590 + 690 from number 1 form on OKUD), except for deferred income and reserves for future expenses, other current liabilities (line: 640, line: 650, line: 660 from form number 1 on OKUD).

I can tell you about the following paradox. Since 2008, under paragraph 3 of the Order of the Ministry of Finance of the Russian Federation #53-N (from 27.12.2007) and paragraph 4 of PBU-regulation 14/2007, organizational costs are no longer part of the 04 accounts ("Intangible Assets"), and they are now directly related to the "Retained earnings / accumulated losses" (through number 84 account), thus, the line 111 from number 1 OKUD form is no longer valid.

Analysis of the characteristics of fictitious bankruptcy should be based on the reporting forms of the company.

2) The second indicator is the indicator (237), discussed earlier.

3) The third indicator is the inequality of the secured obligations by net assets, which is not strictly fixed by the legislator:

(239)

Where: AF - is the amount of company"s assets, as it is calculated in accordance with the laws of the fictitious bankruptcy of the Russian Federation. It is calculated as the sum of current and noncurrent assets (line: 190 + line: 290) net of VAT on acquisitions, debt of founders as deposits in authorized capital (line: 244 from number 1 OKUD form), own shares repurchased (it is related to short-term financial investments, line: 250 number 1 OKUD form). OF - is the amount of liabilities of the company, in the form it is adopted for the purpose of fictitious bankruptcy analysis. It is calculated as the sum of short-and long-term debt (line: 590 + 690 number 1 OKUD form) net of deferred income and accrued liabilities (line: 640 and line: 650 number 1 OKUD form). PFS and β indicators were considered previously, which may adjust the amounts of assets and liabilities.

Indicators (237) (238) and (239) should be considered in the dynamics. In the case of signs of fraudulent bankruptcy, RFSDN number 33-R regulation provides an examination of transactions of the debtor. By deliberately unfavorable conditions of the transaction legislator considers the following. Understatement / overstatement of the price of delivered / procured goods, works and services, compared with the current market conditions. It is also next: the obviously disadvantageous to the debtor-company at the payment terms on the realized or acquired property agreements. It is also next: any form of encumbrance or alienation of property of the debtor, including the encumbrance or alienation of property by obligations, unless it is accompanied by an equivalent reduction of debt.

Signs of fraudulent bankruptcy can be deduced only inside a company based in bankruptcy procedures. In addition, the indicators (237) (238) and (239) in the dynamics suggest the presence of signs of fraudulent bankruptcy. Also, if the security claims of the creditors were deteriorated over time, and transactions made by the debtor do not correspond to market conditions, as well as when it goes in confrontation to the norms and customs of business turnover - in this case, the signs of fraudulent bankruptcy can be deduced.

Prior to 2003 - 2005's statistics on cases of fictitious bankruptcies in Russia was such, that there was an extremely small percentage of companies that fall under the definition of "fictitious bankruptcy". Today the situation has slowly been changing [5].

In general, it has been gradually developing: the standard method for predicting bankruptcy and making an adequate response algorithm in the presence signs of certain types of bankruptcy, both in Russia and in the world. There remain a number of complex regulatory incidents in each country, including in Russia.

For example, there is a P. Jani legal casus, who is concerned over the fact that the Russian state actually has not determined what a Legal entity is as a result of a terminological conflict. Legal entity - is the basic term of the Russian legislation in the bankruptcy procedures. The Russian Civil Code says that the Legal entity is an entity registered its activities in the manner prescribed by law. At the same time, the Russian Criminal code provides a Section about the punishment to Legal entity for failing to register its business activity.

According to Section 197 of the Criminal Code, the responsibility for a fictitious bankruptcy is to be applied to the head of the organization, or owner of the organization or individual entrepreneur.

There is a conflict of norms in the fraudulent bankruptcy of Russia found by Sergei Gordennik and O. Kuznetsova. This conflict of norms actually means that the founder and director of the company can not be held liable for fictitious bankruptcy due to a conflict of definitions. It is due to the next fact. According to the Russian legislation, the legal punishment is provided to "the owner of an individual enterprise / organization". And there is the Russian Federation Federal Law "On Business". This Federal Law provides that: "... individual enterprise is an enterprise owned by a citizen by right of ownership or members of his family on the right of common ownership, unless otherwise stipulated in the contract between them." This type of enterprise would have to be converted into business partnerships or eliminated before July 01, 1996, according to the Russian Federal Law regulations. And before this date, these enterprises/organizations referred to the type of businesses for which the bankruptcy procedure couldn"t be used at all (? 1, Section 65 of the Russian Federation Civil Code). Consequently, the owner of an individual company may not be a subject of proceedings in cases of fictitious bankruptcy. Interpretation of the owner as a founder, representative of the board of directors and similar entities is not legitimate from a legal point of view.

There is a collision of term "owner of organization". This collision was first time found by O. Kuznetsova, who drew attention to the following. According to Section 213 of the Civil Code, legal persons are themselves the owners of their property. And according to Section 48 of the Civil Code, organization is a subject and never an object of legal interrelations - and it can"t be owned by anyone.

Legal collisions and collisions of definitions - this is only a part of the problems of the standard method. It is, by the way, the problem of legal approach as a part of standard method.

Another part of the problem is the actual efficiency of bankruptcy prediction by normative method. An increasing proportion of the rules follow the qualitative method today, according to which an expert himself or herself determines the vast majority of financial options in the company and their effect on the probability of bankruptcy.

Thus, the regulatory apparatus of predicting bankruptcy in many ways goes closer to the approach of William Henry Beaver, who also determined the probability of bankruptcy by expert analysis of financial statements with the application of a mathematical apparatus.

3) The legal approach

Regulatory approach with regard to bankruptcy is known to mankind for a long time ....It is applied to those companies for which there is a filed or may be filed for court proceedings in bankruptcy.

The legal approach is known to society since ancient times. Bankruptcy proceedings have been one of the toughest industries in the ancient world and in ancient times, as security for the obligation of the debtor was property of the debtor, the debtor himself and his family.... Cruelty procedures for bankruptcy and the consequences of judicial decisions - it was widespread during the entire period of the Middle Ages and early Renaissance. The Norway-region legislation was particularly cruel towards the debtor prior to the New-times beginning. And at the end of the XVIII century things started to change rapidly... Law started to fix more and more aspects of bankruptcy, and, at the same time, the developing then ideas of humanism turned violent legislation to one of the most peaceful just for less than 100 years period.

The legal approach today involves stringent standards that are applied to potential and actual debtors. In Russia, the bankruptcy is regulated by the applicable law [6].

Legal approach has all the disadvantages of a normative approach we have discussed previously. A person in respect of which the bankruptcy procedure is filed for - this legal person is called a Debtor. Accordingly, persons who have the right to claim against the Debtor are called Creditors.

There is a condition of bankruptcy (to file for it in Russian court):

The debt must be less than 100,000 [7] rubles (circa it is more than 3,000 USD).

For individual entrepreneurs (IE) this amount is reduced to 10,000 rubles.

Penalties, sanctions" sums, arrears of wages and penalties are not included in the principal amount of debt.

There must be three months of overdue of debt.

There must be an entered-into-legal-force court decision on recovery of the debt or a decision of the tax authority or the decision of the customs authority.

Only a legal entity (no individuals) may file for bankruptcy.

If all conditions are met, then the person may be commenced proceedings to its bankruptcy. For IE procedures are the shortest - at once the bankruptcy proceedings, which involves the creation of the bankruptcy estate for sale to pay off to creditors. Probably, the city-forming and related to them enterprises bankruptcy case - is the most protracted, although there are some exceptions....

Total bankruptcy procedures are five: Settlement Agreement, Monitoring, Financial Rehabilitation, External Control, the Bankruptcy Proceedings. A big book can be written for each bankruptcy case in the legal theory and practice. Because of this fact, let"s stop and restrict ourselves to a brief review of the legal approach.

In the previous times, bankruptcy cases in Russia were controlled by the Ministry of Justice. Now the legislator clearly separates the concept of "regulatory authority" (Ministry of Economic Development, which develops the regulatory framework and implement policies for bankruptcy) and the concept of "authority control and supervision" (Federal Registration Service, which prepares the exams for court-appointed trustees, holds a different policy, associated with organizations of arbitration managers; and a representative of this body has the right to participate in any bankruptcy case). The Federal Tax Service (and sometimes the Customs Administration) is a "Notified Body".

The right to file on a petition in bankruptcy has: the debtor himself, creditors, the competent authorities (tax and customs authorities). Application is reviewed within 5 days. It may be returned back for revision and then re-taken again to the 5-day-term and so on, until the application is accepted. Within 15 - 30 [8] days after acceptance of an application, there should be held a meeting to validate the claims of creditors with the Debtor [9]. The court may refuse to initiate bankruptcy proceedings for the following reasons. If the amount of duty is less than 100,000 rubles or 10,000 rubles for IE, excluding fines, penalties, interest, sanction sums [10]. The second reason to cancel the process beginning is next: there is no enforceable court decision on debt payment requirements or decision of the tax / customs authority, or if the 3 month delay in payment had not yet passed. If one has any of these cases - the court must refuse to start its proceedings in the bankruptcy case.

In the case of institution of an action of the bankruptcy procedure - it should be started with the Monitoring procedure, which can last up to 7 months. In this procedure, Interim Manager collects data on the activities of the Debtor to prepare for court the management records of the bankruptcy case.

The onset of monitoring procedures has a number of legal consequences. First, at the request of the Lender (s), it may be suspended the enforcement proceedings in cases related to the reimbursement of funds and other property penalties, with the exception of arrears of wages, compensation under copyright contracts, for moral, material and physical damage as well as the requirements for recovery of property from unlawful possession. Other claims for monetary obligations to the debtor may be made to be executed only in the manner of the Federal Law "On Insolvency (Bankruptcy)".

Second, the founders are denied the right to claim their due share of belonging to them part of the property in connection with their release of the founders; they also lose the right to receive dividends on the company issued securities.

Third, all transactions relating to the provision of guarantees and warranties, loans and credits, assignment of claims, property transactions of more than 5% of book value of assets and other similar operations may be conducted only with the consent of the Interim Manager expressed in writing form.

Within 10 days, the head of the Debtor shall apply to the founders of the Debtor to resolve the issues associated with the ongoing bankruptcy proceedings and appealed to the first meeting of creditors. Monitoring ends by the first meeting of creditors, which shall be appointed by Interim Manager at least 10 days prior to the deadline of the monitoring procedures.

Some members of the First Meeting are accorded the right to vote: if their claims were filed in the prescribed manner and time, and if they are entered in the register of creditors' claims, which was conducted by the Interim Manager. Debtor and the Debtor's representative of the employees are not entitled to vote at the first meeting of creditors. The first creditors' meeting is to decide the future of the debtor: what stage of bankruptcy proceedings to start next (in addition to the monitoring procedure). Please note that the settlement agreement can not be concluded without the consent of the Debtor and certain other entities.

Financial Rehabilitation - is one of statutory alternatives to other procedures of bankruptcy. When the financial rehabilitation is assigned, the Administrative Manager is appointed to conduct this procedure, while the Debtor continues its normal activities, which, however, impose significant restrictions in addition to those that were under the monitoring procedure. In comparison with the other bankruptcy procedures, financial rehabilitation - is rarely used.

Overall, the company's major activities during this period pass through the Administrative Manager. The main activities" areas are: market and book value of the company, the structure of assets and liabilities of the company, the expenses structure of the firm, the Debtor's cash flow structure.

If maximum in two years [11], the debtor can not recover its normal activities to repay obligations - the next bankruptcy procedure is commenced against the Debtor.

External control. The Debtor's managerial bodies are rejected from company"s management automatically with the introduction of this procedure. The only exception when the Debtor's managerial bodies are capable to influence the administrative decisions are connected with transactions of more than 5% of the value of assets and transactions to increase share capital from third parties. External Manager replaces the Debtor's managerial bodies.

During the next 18 months (the period may be extended for another 6 months), he or she will restore the normal activity of the company to satisfy the claims of creditors. All third queue creditors' claims resulting after the introduction of external control are subject to the moratorium, as well as the quantity of interest and penalties over the maximum possible quantity which may be maximum equal to the interest rate of refinancing of Central Bank of Russia. Creditors can not ask for securing of their demands since this stage of the bankruptcy process.

External Manager is required to create a management plan of external control within 1 month after the introduction of external control. This plan should reflect the best way of actions to meet as much claims of the creditors as possible.

After this plan is developed, the additional 2 months are given to convene a meeting of creditors; besides, External Manager should give at least 14 days prior to the meeting the creditors could get acquainted with the plan.

The creditors' meeting will be to review the plan and adopt it by a majority vote. If the plan is waived by making the amendments, - it will go again to similar review procedure. However, the vast majority of cases do not end with this procedure - the next stage is started after this one. The most often stage in such cases after the external control - is Bankruptcy proceedings.

Since the introduction of the bankruptcy proceedings by the arbitration court, the bankruptcy trustee is appointed to lead this procedure. The maximum term of bankruptcy proceedings is 6 months (previously it was 1 year), with the possibility of renewal for another 6 months.

In the bankruptcy proceedings, the Debtor's activity ceases itself, Debtor"s property goes to form the so-called bankruptcy estate, which is then sold off. The money goes to repay the obligations of creditors in accordance with the Russian Civil Code (in queues).

Section 855 of Russian Civil Code provides three queues in the order in which the creditor"s claims should be met and covered. Bankruptcy law also adds two queues: before-the-queue and after-the-queue.

Before-the-queue requirements are applied to the debtor's obligations, which came after the commencement of bankruptcy proceedings in court - they are to be satisfied first of all.

Then it comes the first queue, which enters the compensation requirements of citizens for the caused by debtor moral and physical harm, including harm to life.

The second queue consists of employees of the Debtor, also the authors, who should be paid compensation under copyright contracts, other benefits workers working under labor contracts.

Third queue - it is all the other creditors listed in the register of creditors, as well as authorities.

After-the-queue lenders - it's the lenders who did not, or are otherwise unable to have their claims in the register of creditors' claims.

The third queue is perhaps the most interesting, since there is usually most of the Creditors, which provoked the bankruptcy proceedings. Compensation is paid to creditors of the third queue in a hierarchical order.

First, there should be paid the creditors" claims secured by a pledge of the debtor's property.

Then the debt is paid to all other creditors except for penalties, fines, sanctions and similar requirements.

At least, in the third turn, there should be paid the already mentioned fines, penalties, interests, sanctions, compensations and similar payments.

If the money received is not enough to cover all the liabilities, for instance, in the second queue, the rest of the received money will be shared equally within the creditors of the queue the payments were stopped on in the equal shares.

At the end of bankruptcy proceedings, the bankruptcy trustee must give to the arbitral tribunal his or her report on the completion of payments to creditors. The Court accepts the decision of the completion of bankruptcy proceedings based on the report. A copy of the court statement is sent by the court to the tax authority, which within 5 days is required to exclude the debtor from the register of legal entities. On that date, the bankruptcy trustee powers are terminated, as well as the story of the Debtor...

The legal approach is always very tough normalized by laws of the countries in which there persist the operating companies.

The legal approach is applied to the very last bankruptcy procedure - to the legal bankruptcy procedure. Its purpose is to ensure hierarchically the interests of: society, State, creditors and the debtors then. Since 2002 in Russia all the bankruptcy cases can be proceeded only through the courts, which decision admits or does not recognize the company as bankrupt. Until that time, the firm itself could not recognize themselves as bankrupts.

In addition to the legal framework and legal approach there is the concept of jurisdiction. Jurisdiction of the Russian legal system consists of arbitration courts of the first link (sometimes intermediate arbitration court), the arbitration courts of cassation, arbitration appellate courts and the Supreme Arbitration Court of Russia. Sometimes there is to be distinguished the constitutional element of the judicial system as more supreme legal authority, since no court decision can contradict the Constitution and constitutional litigation. However, the number of cases considered for each subsequent hierarchical authority of the court decreases itself in geometric progression with increasing that hierarchy. Cassation authority requires reexamination of the correct application of rules and facts of the case itself. The court of appellation assumes that all the facts of the case have already been stated by the inferior courts, and they consider only the correct application of legal standards. In exceptional cases, when one discloses new significant details of the case, courts of appeal shall refer the case to the other inferior courts for reconsideration of the facts of the case. The Supreme Arbitration Court is considering legal precedents that reach it. Decisions of the Supreme Arbitration Court in such cases may be an important argument in courts for a similar type of cases.

4) The trend method

Trending method.... It is hard to name the sphere it isn"t used in finance... Of course, the trend method could not ignore the problem of predicting bankruptcy. Unlike other methods, this method never builds a rigid boundary that would divide all the companies to insolvent and solvent. Trending method determines the trend .... which can be positive or negative - and nothing more.

Trending method covers many aspects of the company: the overall dynamics of the book value and its components, the overall dynamics of the market (shareholder) value and its components, the prospects of the company development in the industry, the relationship between the important components of the external and internal environment of the company and the most important performance indicators for the firm at the market, for example, by the method of correlation-regression analysis. Also trending method describes a number of other components.

Its mission: to find out which way is the most appropriate for the company development as well as to establish what trends prevail there: positive or negative. It considers only the trends - and nothing more. The task of the analyst is to develop a plan of anti-crisis measures based on the dynamic trends that would help a separate company to avoid bankruptcy.

The trend method shows nothing like: that is "good" for a company, and that is - "bad." Trending method divides the company functioning to a number of components, and it answers the question on the positive, normal or negative development scenario is the most probable at the occupied by company market segment.

Having examined the trend method in this section, you, dear reader, will know that the trend of the company development tends to its average probable value. You will learn that there is deviation, which determines the risk of developing the trend of the company. You will learn about the mathematical collision of concepts of what a trend risk is (standard deviation) and what are its derivatives and components: I, together with you, my dear reader, shall study the three main mathematical schools that have several different answers to these questions.

I, together with you, my dear reader, shall both know that regardless of the choice of mathematical school and the adoption of any conflict of definitions, you can always follow the correct calculation of the correlation, which shows the dependence of some components from the other.

You will also learn, that people use a correlation to define the structure at risk-trending method, which shows which factors run the risk of fluctuations of "essential" indicators for a company, and will know how you can control these factors. You'll also learn that an important risk of a company is a joint-stock risk that, on the one hand, shows the risk of fluctuations of the market value of a company, and, on the other hand, - the portfolio risk as the most risky component of assets of any company, especially for banks. You"ll also learn how to calculate and optimize the risk following the classical approach. Also, there will be considered a number of separate aspects of the trend method.

The trend method is based not on the vertical, but horizontal analysis. Trending method is of two types: trending method on the balance sheet and trending method for company"s market value.

Trending method on balance - is largely a continuation of the research of William Henry Beaver, who paid much attention to this method, as well as to experts" estimations that proceeded from this method.

Probably, the easiest trend method is in following methods: statistical analysis and index analysis.

Let's start with you from the statistical analysis of the prediction of bankruptcy. Let"s suppose a company develops a definite time in the market. It chooses a number of quality indicators for analysis, which are directly linked with the efficiency of its ongoing activities. For example, it may be a market value, book value, revenue, cost, operating or net profit, and so on. Further, on the basis of correlation-regression analysis, company calculates the dependence of the variables of important factors coming from external and internal environment of the company. For example, if the income was derived, it is necessary to calculate the dependence from the cost, the tax base, sales, trends of market and book value of company, the level of macro-economic instability, trends and changes in competition in the industry and so on.

So, we with you, dear reader, have come close to the concept of correlation-regression analysis. Correlation (r) - is expressed mathematically by a linear relationship between two variables [12]. It is calculated by the formula:

(240)

It should be noted that:

(241)

Where X and Y - is a pair of variables, the relationship between them is to be calculated; n - is the number of observations (the more observations - the more accurate calculation is), - this is the average value of observed variables X and Y; Cov (X, Y) - is a ratio of covariance, which shows the relationship between two variables; - these are the standard deviations, which show the total amount that the value will be rejected averagely for any measure.

One should take a variety of variables relevant to the company as X. One should take Y variables of the environment that actually lay its influence or may lay its influence to the development of important for company indicators.

These indicators measure a variety of business settings and activities of the company, according to the author of this paper, they should be used in financial analysis. Let me offer you to consider the following simple example you to better understand the material on these values. Suppose that the earnings of IE "N.I. Stella" in the next month will be with probability 10% (equal to 0.1) 12,000 USD, with probability 20% chance 15,000 USD, with a probability of 15% 17,000 USD, with a probability of 15% 19,000 USD, with a probability of 20% 22,000 USD, with a probability of 9% 24,000 USD, with a probability of 11% this merchant will suffer a loss due to the onset of legal events A (15,000 USD). The sum of the probabilities must be equal to 100%, which is actually of no surprise, because, at least something should happen with our IE "N.I. Stella" in the next month! Then the expected revenue of IE "N.I. Stella" will have the following value:

0.1*12,000+0.2*(15,000+22,000)+0.15*(17,000+19,000)+0.09*24,000+0.11*(-15,000)=14,510 USD

This is how the average probability of return in the market calculation looks like (APRM:

(242)

Where: Bi - is the probability of the i-th income; Mi - is the sum of the i-th income.

You probably ask me how to determine the probability of obtaining or shortfall of income for a certain company? In mathematical terms, this is a subjective consideration. The probability of each event must be determined by each participant in the market independently. Many large firms even make attempts to create neural networks to program and calculate the probability of occurrence of events.... At the same time, the neural networks were unable to calculate the recent crisis! Unfortunately!

An entrepreneur also assesses the risks of obtaining or shortfalls in certain share of the profits from the company for a future period or periods. Since quantitative estimates of probability are not always reliable, the actual value may be different from what you expected. Hence we face with the concept of risk.

This is the most subjective aspect of the project evaluation, because the risk is assessed each person individually, as well as probabilistic assessment are also individual. The probability of deviation of the actual value from the expected one is: the higher, the wider spread of values for a random variable.

Therefore, people use the so-called standard deviation () as a measure of risk inherent in the solution with a probabilistic outcome. standard deviation () - is RMS (root-mean-square) absolute deviation of possible values of a random variable from the expected value.

Analyzing a substantial body of econometric and statistical literature on the subject, the author of this paper came to the conclusion that there are three approaches to the calculation of the variable (): variation (classical and weight), information-atomic (classical and weight) and atomic (classical and weight). To simplify the perception of the following material, the author of this paper gives his own interpretation of what shows each approach in the best degree.

Selecting the calculation way does not affect to the overall correlation coefficient, which is used in the analysis. The main thing that: deviation, average-mean and covariance were to be calculated within the tradition of the same school of mathematics.

A variation approach to the analysis [13]. It is divided into two types of approaches: the classical and weight.

The classical approach to the analysis of variations:

(243)

Where: - the average value of X, calculated by the formula (241); Xi - the value of i-th parameter.

In this example, the risk for the company not to make a profit in each future period is most likely to be:

This 32,402 value shows the average probability deviation of amounts of expected revenue of this IE in the next month. That is, the IE will receive 14,510 USD of income in the next period. However, with a high probability, this quantity will vary from -1,691 to 30,711 USD of income. Such a high probabilities" oscillation of income obtaining is due to probability of obtaining a loss in the following month.

In addition to the absolute standard deviation (σ) it is sometimes used some other types of standard deviation in the analysis. The absolute deviation is intended to show the maximum probability of deviations from the average spread of the expected value of profits. However, if you want to estimate the most probable value of the deviation (rather than the total scale as it is in the calculation of (σ)), then use a standard measure of standard deviation (σS):

(244)

Where: Ai - is the likelihood (probability) of each i-th value of the parameter X.

The above calculation corresponds to the weighted approach to analysis of variance. For example, a standard measure of standard deviation for IE "N.I. Stella" will be the value:

This quantity represents the total probability no longer; this quantity represents the most probable scatter of level of income for the IE "N.I. Stella": + / - 5471 USD from the magnitude of the average expected return.

However, along with the variation approach, there is an information-atomic approach [14], which also consists of the classical and the weighted sub-approaches. This approach is based on the theory of avoiding excessive mathematical information, and it carries the index of n1 observation. The theory is in just getting rid of it, turning it to the (n-1) index, knowing that it doesn"t carry any information load, due to the fact it can be easily calculated from the algorithm itself.

Atomicity of the approach is that it calculates the fair value of the deviation for a single atomic ("indivisible," "independent") element rather than the same value for the total sample.

The classical school of information-atomic approach involves the following calculation of the absolute standard deviation:

(245)

So, for our IE "Stella" the value of standard deviation is:

This value characterizes rather the most probable deviation than the deviation of the total, and the deviation per unit of the parameter. It is clear, that the overall deviation in the USD approximately corresponds to the total deviation probability of 1 type of scenario in the future.

The weighting approach for the information-atomic school includes:

(247)

For IE "N.I. Stella" this quantity is equal to 4467 USD. According to the information-atomic approach, this quantity will reflect the most probable spread of the parameters of revenue in the period ahead.

In addition to information-atomic approach, there is simply an atomic approach [15]. This approach is based on the fact that, despite the hatching of the first variable n in the number of observations, it nevertheless should be considered in the calculation, the calculation to become more objective. The atomic approach also has two sub-approaches: the classical and weight.

The classical approach involves the calculation of the absolute standard deviation from the formula:

(248)

For IE "N.I. Stella" this quantity when using this approach is equal to: 12 199 USD.

Along with the classic, there is the weight sub-atomic approach within this school, which requires the calculation of standard deviation:

(249)

For IE "N.I. Stella" this quantity when using this approach is equal to: 4136 USD.

I want to draw your attention to the coverage of issues concerning the calculation of the basic indicators relative to dynamics and probability analysis among various scientific schools. As it can be seen from the calculation, choice of school significantly changes the result. The author of this paper has used a component of loss probability for illustrative purposes; the palette to show the spread of variations, depending on the type of school and sub-schools in the calculation of these quantities. In our example, the palette of the standard deviation scatter was as follows: from 4136 USD up to 32 402 USD. So let's talk about what a math-school one should choose for business-calculations?

Author of this paper thinks that the variational approach reflects the specific version of the spread of values in the best way possible. However, the choice of mathematical school - it is always a subjective process. Let's analyze what is the effect from the choice of mathematical scientific school.

The choice of method for calculating the standard deviation significantly affects the calculation of the covariance coefficient, which is calculated as follows.

Covariance at a weight variational approach is equal to:

(250)

Or, if you use the classic variational approach, it is:

(251)

In the information-atomic approach, the covariance is calculated as follows:

(252)

And at the atomic approach - the calculation of covariance is reduced to:

(253)

What the specified account affects on? Covariance shows the relationship between two variables. However, in determining the inter-dependence of two variables we have the support of the correlation coefficient (r), that always converges between all schools and all approaches at any mathematical approach. Correlation (r) - is the ratio of covariance to the multiplication of standard deviations of two variables. The similarity of this ratio is defined by the following properties of fractions:

(254)

That is, the expression (254) shows that for any distortion of the numerator and denominator of the fraction in an equal value (α) / only by multiplying or dividing / the value of the fraction remains unchanged. Thus, the third (1/3) - this is the same as 2/6, and the same thing as 3/9 - the same end result is obtained. Similarly happens in the calculation of the correlation coefficient - the result is the same, if the calculation of covariance and standard deviation of each variable was provided under the same method in the same school of mathematics!

Now, let's get back to our talking about the definition of standard deviation in the analysis of the company. The author of this paper suggests using a variational approach with a focus on classical variational approach. First, this approach does not require the calculation of the probability distribution. Second, this calculation is much simpler to calculate and distribute the deviation of the whole set of events, rather than one based on the average event.

Thus, the classical variational approach with IE "Stella" shows the average income of 14,510 USD with a standard deviation of 32 402 USD.

If the value of standard deviation (ơ) is to be divided by the most-likely-probability of the profit margin, we obtain a coefficient of variation:

(255)

In this example, the coefficient is equal to: .

This substantial value of the coefficient of variation shows that the spread of values in the future is so great, that there is a significant risk for the specified IE not to get the expected average amount of income in the next month. If we take other values of standard deviations, we obtain the average risk. This value is the coefficient of variation, which shows the absolute risk.

It can be measured the stiffness of competition at the market and the stability of the company's position on it by using a coefficient of variation. If the coefficient of variation is significant, it probably says, on the one hand, the rigidity of competition, on the other hand, the instability of the company's position in the market.

And, in any case, to approve these terms more reasonable - you need an additional market and marketing strategy analysis. This topic will be touched a little later in my other publications and in the second part of my future book in English.

The calculations often use the variance (D or σ^2) / theoretical value of the scatter of the values /, which is the standard deviation in the square:

(256)

Sometimes, when there are some more complex calculations, for example, the portfolio planning, you want to calculate the amount of variance of two variables, which is equal to:

(257)

Where: a and b - are constants, ie, numbers. X and Y - these are the variables themselves; dependencies and other relations among these X and Y are to be determined.

r - is the correlation coefficient, the calculation of which we have already discussed with you, my dear reader.

Most often, the constants a and b in the sum of the variance of two variables do not exist, that is, they are equal to 1^2 = 1. In this case, the formula (257) one should be set 1 instead of a and b, that is, so they are omitted in the calculation.

Also important is the decomposition formula for the sum of two average-means:

(258)

Where: a and b - are constants, ie numbers. X and Y - these are the variables themselves, which average is to be calculated.

Sometimes the constants a and b in the sum of the average-mean of two variables do not exist, that is, they are equal to 1^2 = 1. In this case, the formula (258) should be set 1 instead of a and b, that is, so they are omitted in the calculation.

Harry Markowitz

You'll probably ask me: How is it used in the analysis and prediction of bankruptcy? It is used as follows. In the west, most companies take the form of ownership. Also, a significant portion of the profits companies invest into the equity market. Specificity of joint operations is such that at one period they can make a substantial income, and at another - they can bring a significant loss, which may even push any company to be a bankrupt. In this case, the optimization of risk is most commonly used. The first who came up to optimize the risk was Harry Markowitz.

Harry Markowitz (Harry Markowitz) was born in Chicago in 1927, and he was the only child in the family. Since his childhood, he played the violin and loved reading. In high school he became interested in physics and astronomy, as well as philosophy. After receiving a bachelor's degree at the University of Chicago, Mr. Markowitz decides to choose economy as his specialization. After graduating, he chooses the topic of his doctoral dissertation the application of mathematics in predicting the development trends of securities.

John Burr Williams

At those times people evaluated securities by using the method of future-costs-reduction to the current cost (by PV - Present Value), the so-called NPV - Net Present Value. This method was developed by John Burr Williams (1900 - 1989) in 1938. This was the topic of his doctoral thesis in economics: "The theory of investment value". In this dissertation John Bur Williams puts forward the NPV theory [16] and the theory of Investments" partitions to cash flows (CF - Cash flow), which he then discounted.

I think you, dear reader, are familiar with the theory of John Burr Williams? Harry Markowitz almost immediately noticed a weak point of this theory: it does not pay enough attention to risk...! In 1952, Mr. Markowitz creates his theory of the portfolio risk analysis by using the methods of probability theory, mathematical statistics and matrix algebra. His paper brought him a worldwide fame. However, the theory was then not quite finalized yet. He faced with a question: how to optimize the portfolio, which consists not of 2 - 3 securities, but of the n number of securities.

In 1952 he began work in a RAND corporation, where he became acquainted with the mathematician George Bernard Dantzig. In 1955, the new modified by G. Markowitz theory becomes the basis of his doctoral dissertation, which he successfully defended then at the University of Chicago. However, his subject was so new for the economy then, that the chairman of Dissertation Council, Milton Friedman (founder of the theory of monetarism with Anna Schwartz, a Nobel laureate in economics) on the Protection noticed that his thesis has quite insignificant relation to the economy! However, only in 1959, his portfolio theory received a modern form in the Harry Markowitz book "Portfolio Selection: Efficient Diversification of Investments"; in this book he described the theory which was applicable not only to securities, and for the investments in general.

Currently, Harry Markowitz teaches at the University of California at San Diego. He is a Nobel Prize Laureate in Economics (1990). His interests have changed a little since then. Today, he has been developing software for optimization of various forms of risk. In particular, his current interest is hedge.

Today there are many variations of the calculation of portfolio risk by H. Markowitz. Harry Markowitz himself used the method of constructing a covariate matrix of observations. Let's see what it is at an example. Let some company called "Prometheus" (A) has a direct competitor called "Sovtek" (B). Both companies place their shares after the IPO.

During the whole year there were made the observations in stock prices" fluctuations; these observations revealed that when the stock price (Spr.) A was 100 USD per share, the stock B was 200 USD per share which was fair for 5% of all cases.

Similarly, those studies let them to compile and perform the covariate matrix of observations:

Covariate matrix of observations of stock prices of A and B

The stock price (Spr.) and its fluctuation, as you remember, reflects the market value of the company. It is clear that the sum of covariate matrix must be equal to 100%. There is a theory of expectation, according to which the expectation of constant tends to zero. Thus, the stock price can not be equal, for example, 100.00000 .... USD per share, never - even in the slightest, it will always differ from the specified value. Thus, in constructing a covariate matrix one should use a range of values (eg, from 90 to 110 USD per share); column average value (Spr.) indicates the average specified value, that is exactly 100, knowing that this corresponds with the range of values.

The average price of the stock A will be equal to: 17%*100+28%*120+26%*80+ +29%*60 = 88.8 USD. The average price of the stock B will be equal to: 18%*(200+210+280)+24%*160+22%*190 = 204.4 USD.

The dispersion of the stock of A from the average is equal to: 17%*125.44+28%*973.44+26%*77.44+29%*829.44=554.56. The dispersion of the stock of B from the average is equal to: 18%*(19.36+31.36+5715.36)+24%*1971.36+22%*207.36=1556.64.

As you remember, the root of the variance is the standard deviation. The standard deviation of stock price A is: 23.549. The standard deviation of the stock B is: 39.45.

The covariance is calculated as follows:

The covariance in this example is: -2.464-9.6096+1.5488+2.5344+1.8816+10.4832-1.9712-8.064+16.9344+47.1744-33.264-195.96-9.9456-124.675+27.35+76.723-8.064-17.9712+7.6032+29.03=-190.72.

For example, the value of -2.464 has been calculated as: 5%*(100-88,8)*(200-204,4)= -2,464. Other parameters of covariance were calculated similarly.

Knowing the value of the data, we can calculate the correlation (r), which is the ratio of covariance to the sum of standard deviations:

-190.72÷(23.549*39.454)= -0.20527

Let us examine now how to read the value of the correlation coefficient. The correlation coefficient can take values from -1 to +1. If the value tends to +1, it indicates a substantial link of variables, which means an increase of one parameter leads to an equivalent increase in another parameter. In this example, it would mean that an increase in the stock of one company leads to a corresponding increase in the share price on the other one. If the value of r tends to -1, it indicates the presence of feedback linear dependence of one variable on another. In our example this would mean that the increase in the rate of one share leads to a significant depreciation in the share price of the other one share. To minimize the risk - it is desirable to make a portfolio of stocks with the inverse correlation. The correlation coefficient value 0 means that the variables are linearly unrelated. There may be the presence of another type of nonlinear relation of these variables (eg, r(Sin2X + Cos2X) = 0, and, at the same time, these functions are related: Sin2X + Cos2X = 1).

Knowing the value of the correlation, we can now add the variance by using the formula (257). The overall risk will be expressed by the value of standard deviation, which is the root of the variance. The sum of the average portfolio"s returns which consists of two stocks, we can calculate from (258). Let"s take a step in the portfolio of 10%. Then the distribution of risk and return will be calculated in accordance with the following matrix system of H. Markowitz:

Matrix yield / risk of portfolio by Harry Markowitz for companies A and B

Portfolio"s yield is always lower than the yield on the most profitable security in the portfolio. However, the portfolio risk can be significantly lower then the risk of securities it consists of, in relation to profitability. From this example, it is clear that if the investor would choose the optimal portfolio from the ratio of yield / risk, then he or she ought to be composed of approximately 30% of the shares of company A and 70% of the company B shares. This can be represented graphically.

Chart: The yield / risk curve of portfolio

The I quadrant shows a graphical function of return-profitability/risk (P / σ). It is seen that the yield of the portfolio can not be higher the yield from the most profitable security inside portfolio, stock B. However, the ratio of portfolio risk / return is much lower than the risk/yield of each individual security included in it. Optimal portfolio, in terms of risk, is achieved by a portfolio consisting of 70% - 75% of stocks B and about 30% - 35% of A.

In this example, the risk is relatively linear (IV quadrant), and the function of yield / risk ( I quadrant) - is concaved, indicating the decrease in yield / risk function at the optimum, in terms of risk, portfolio. Quadrant II is the econometric projection line drawn at an angle of 45 degrees. In Quadrant III, thus, it is projected yield function of the optimal portfolio. It is seen, that the yield and risk curve themselves at 169 point, while in the area of return and in excess of it profitability and risk grow in substantial pace.

Thus, the yield of the optimum in terms of risk portfolio is 169 USD, and its risk is equal to 34.2 USD.

William F. Sharpe

However, in practice, not all investors prefer low risk with optimal yield. Some people prefer to take the risk, and some would prefer not to optimize the return / risk portfolio, and simply to take the least or most profitable security.

Also, not all portfolios consist of only two types of securities .... In this case, the algorithm is slightly different.

There are several classical approaches for determining the price and the ideal portfolio of securities at the market. Let us, my dear reader, consider three of them: a model of CAPM [17], APT model, a regression-matrix analysis.

We'll begin with you to review the CAPM model. CAPM model was developed by William F. Sharpe.

In 1955, William F. Sharpe achieved a Bachelor degree in Economics at the University of California, Los Angeles, USA. Literally within a year there, he protects his master's thesis. Within the next 5 years in this University, he received a doctorate in economics. In 1961 he moved to Washington, where he receives a chair of assistant professor at the University of Washington. At the same time, he gets a contract with the Boeing Corporation to conduct extensive research. In 1963, IBM invites him as a consultant. After that, he was able to work on a set of companies, including assistance in financial models developing for McKinsey Company. In 1963-1964, he published a series of papers describing the model of CAPM. Since then, his model spread around the world: both in science and in practical application. William Sharpe has hundreds of international awards, at the same time, he almost never identifies by himself his model CAPM won the Nobel Prize in Economics (1990/1991). William Sharp - is the author of over than 800 papers on economics and finance. The most popular models which were brought by him are: CAPM and APSIM, which allow everyone to track pricing in financial markets. William Sharpe himself likes to mention the β coefficient, which is the basis of CAPM model as the Sharpe ratio.

The CAPM theory suggests, that there are two types and kinds of risk at the stock market: systematic (as determined by macroeconomic factors - it is a general market risk for all shares outstanding); haphazard/unsystematic (specific for this particular company). The theory suggests that there is the Beta coefficient (β), which reflects the amplitude of oscillation of specific stock returns compared to the total market return on this equity market as a whole.

Methods of assessment of capital assets suggest that the expected return of an asset depends only on systematic risk of an asset, and not of the total risk (which is equal to the sum of systematic and unsystematic). The model assumes that unsystematic risk is not related to the expected return of an asset, so it can only be cured by diversifying the portfolio of assets. Also, the model assumes that the market is perfect, transaction costs are zero. All investors evaluate the market rate of return alike.

Then, under these model conditions, the next formula is working:

(259)

Where: Roc(eq) - is the Expected Return on equity; RF - is the risk-free rate of return on investment; (RM-RF) - is the risk premium; RM - is the average market yield; β - is measuring the systematic risk. This coefficient is linking the yield of the target firm with average market returns. Let"s look at how we can calculate the β coefficient.

The β coefficient is calculated on the basis of statistical data. In this case, we consider a stock market for a relatively long period. Then, the β coefficient is calculated as follows:

(260)

Where: Y - is the change of profitability of the company"s shares; X - is the change in the average market yield (usually they take some index: RTS bet, S & P 500 index, Dow Jones index and so on), T - is the period, the number of observations for which the data comes .

Usually, β takes values between 0.3 and 2, although it may be equal to -2.

If β = 1, then R = RM, - this means that the expected profitability of the company is directly proportional to the average market return.

Investments in companies, in which β > 1, are defined as aggressive investments: the risk of investments in which is more than the average at the market. This means the following. Let β for some companies is 1.5. Then this means that, for example, if the Dow Jones or RTS (in assessing the Russian companies), rose by 1%, the stock price of the company rose by 1.5%, and conversely, if the index fell by 1%, the stock price fell by 1.5%.

Investments in companies in which β < 1 are defined as investments protected from the risk: the risk of investing in them is less than the market average, and the yield is usually lower too. If the profitability of such companies is higher than the average for the market, these companies and their shares are called "blue chips" - high-yield low-risk companies.

For companies it holds the following. If the coefficient β is equal to, for example, 0.5, - this means that if the Dow Jones or RTS market index increase itself by 1%, the company's shares will increase themselves in price by 0.5%, and if the index falls by 1%, the company's stock would fall by only 0.5%.

Agriculture with traditional chain industries (production of milk, bread, meat, flour, grain, ... ..) refers to this type of companies, so they are significantly more stable in times of crisis. β, on average, for successful companies in the world for agricultural sector is 0.2, that is, for example, the decline of the index of industrial goods by 50% will fall the agricultural sector of not more than 10%! And again, if there is a theft inside a specific company, poor production, the old production funds - such companies are strongly vulnerable for crises too.

Some innovative industries may have a low β rate. Real estate (not all) also has this indicator low, - no more than 0.3. At Coca-Cola, for example, the index is much higher - it is an average of 0.7, which also refers it to the conservative companies.

The vast majority of the remaining companies are of the type β>1, which means that in a normal economy they generate substantial revenues, and in times of crisis .... they may lose everything! Therefore, these companies will probably have reason to diversify and keep some assets in more conservative areas of the economy.

Thus, the CAPM theory offers to evaluate each valuable paper separately. The theory offers to gain a portfolio from the securities that risks and returns mostly satisfy a particular investor.

You can also perform financial analysis and stability analysis of a company in the market at the expense of the specified model. If the coefficient β > 1, it refers to an aggressive company. If it is approximately equal to 1 (from 1.3 to 0.85), this company belongs to the moderate, in terms of profitability and risk. If the coefficient β < 1, then a company belongs to the conservative ones - it is more resistant to the crisis, and in normal times, it doesn"t develop itself as rapidly as the rest of the market.

Let us now consider the model of APT [18].

It should tell you a few words about the appearance of this theory. William Sharpe's model, developed in September 1963, gave the ground for extensive research on market pricing of shares. 13 years later, there appeared a theory, which was a logical extension of the theory of CAPM.

Initially, Stephen Alan Ross had not planned to be a financier - he was more interested in the exact sciences. In 1965 he received a Bachelor degree (with Honors) in Physics. However, at the same time, he immediately changed his interests and began intensively studying economics. Just over 5 years he managed to transform himself from a BS in Physics to PhD in economics at Harvard University by defending his doctoral dissertation. Dozens of his papers on various subjects appeared at this time. Soon, however, two of his theories appeared in light, which brought him international fame: Arbitrage Pricing Theory (APT) and agency theory (Theory of Agency). And also, he is a famous theorist in the field of binominary pricing of financial derivatives. Together with this, he managed to make a significant contribution to the analysis of pricing problems in the neutral risk conditions.

Stephen Alan Ross

When the career of Stephen Ross had just begun, he hardly thought that he would become known as theorist in the field of securities. APT theory was developed by Stephen Ross in 1976. At that time he was a very famous financier, a theorist of discipline, I and You would have called corporate finance or finance of enterprises (organizations). In 1975 he almost finalized his APT theory as a theory for constructing an optimal ratio of assets of the company. Then he had no idea that his theory would be significantly longer to be applied at the stock market.... In 1976 - 1980-ies, he suggests that non-standard CAPM modeling, as part of the APT, allow the company to build an optimal portfolio and the optimal structure of its assets. However, the leading financial companies in the U.S. were more interested in his models to explain the pricing at the stock markets. Dozens of his models are in use today by the largest financial corporations in the world. A special place among these models has his APT theory (Arbitrage Pricing Theory).

APT theory is quite complicated to understand. Because of this fact, we restrict ourselves with you, dear reader, by a very brief consideration of its foundations. This theory suggests that the financial market seeks to achieve a perfect balance. Thus, β for each stock market tends to 1. Consequently, the speculative motive is lost, as well as the arbitrage transactions at the stock market.

However, this theory suggests that pricing in the stock market depends on macroeconomic indicators: GDP, GNP, CPI, inflation, bond yields and other factors. Thus, market volatility of portfolio returns are not the sole determinant of prices motive, as it is assumed in the CAPM model.

Then the expected yield of the portfolio is:

(261)

Where: - is the expected return on individual stocks; a0 - is a risk-free rate of return on investments; ai - is a risk premium for the i-th factor; ui - is the volatility of the expected return from the i-th risk factor.

Because of the fact that the market balances the price of each share over time, leveling it, there can be sharp fluctuations in the price per share, causing speculative or arbitrage yield of securities, it imposes certain conditions on the acquisition of a profitable portfolio.

According to the theory, the optimal portfolio should include arbitrage-priced securities, ie securities that have not yet managed to balance by the market.

Every occurrence of arbitrage series of securities depends on j factors, which may develop themselves, as a minimum, of 3 different scenarios: pessimistic, optimistic and normal. All j factors that affect the fluctuation of stock prices are broken into separate components. Each component determines the optimal portfolio. And then the optimal portfolio is smoothed by mathematical transformations so that it described all the j embedded-in factors as fully as possible.

Portfolio, dependent on one single factor, with the appearance of the arbitrage securities" party can be optimal if:

(262)

This value - is the income from an operation with securities for the transformation of the portfolio. MPR - is the market price of the replaced stock portfolio, or of a stock, or of some other asset which is traded for the planned optimal portfolio. Pi - is the price of the i-th asset for replacement in exchange for securities portfolio. Xi - this is the optimal structure of the i-th asset, which is to be converted. Xi is calculated from the equations:

(263)

Variables g and y denote the optimal position of income and the amount of the i-th asset of portfolio in scenario number 1. The variables k and z denote the optimal position of income and the amount of the i-th asset of portfolio in scenario number 2. Variables h and f denote the optimal position of income and the amount of the i-th asset of portfolio in scenario number 3. And so on.

Let us, for clarity, analyze the following example.

Suppose the expected return of shares of Asian companies depends on the factor of expected economic growth in Asia in the next month. There are three scenarios: a positive (Asia will have a significant increase), normal (Asia will be all about the same), pessimistic (Asian indexes fall sharply).

Let the company called JSC "Cobalt" has portfolios of Asian companies ? 1, ? 2, ? 3, ? 4. Conditional data on companies" portfolios and their costs are listed in the table below:

Table: Forecast value of the companies" portfolios by the APT model

So, if we optimize the portfolio by selling the asset number 1, then the company has the opportunity to earn the following amount arbitrageurs [19]:

Thus, the optimal portfolio 1 (OP) with the choice of asset portfolio as a privileged one should be constructed as follows:

(264)

Optimal portfolio is determined by the formula (262): hence, such a portfolio is more optimal than the existing one. Converting an existing portfolio to the best one by the sale of 52% of the portfolio number 2 share, 47.945% of the portfolio number 4 share and the acquisition of an additional 195.2% of the portfolio number 3 share and selling number 1 portfolio will bring to company 0.171205 thousand $ of income. And it should be done immediately, because the theory arbitrageur assumes that the market will soon equalize the fair price for portfolios by aligning them.

The effect of arbitrageurs is calculated as follows:

(265)

ΣArb - is the amount earned by using arbitrageurs. ΣA - is the sum of sold asset for the portfolio optimization.

In our example, the effect of arbitrageurs" use is 0.1%. It is normal for an additional income of the company, which also minimizes the risk of a more optimal portfolio. The lower risk and higher return - the best it is for a company - it is always so! Sometimes a company can earn a substantial profit by portfolio optimization or to avoid significant losses....

However, one should also calculate an alternative. And if the company "Cobalt" sold other portfolio instead of a portfolio number 1, would it receive more revenue from arbitrage portfolio optimization?

We can verify this in the next calculation. Let JSC "Cobalt" to sell portfolio number 2. Then the arbitrage income is:

This is the second version of the optimal portfolio; its arbitrageur is equal to:

Since the market price is equal to 210, then the effect of arbitrageurs will be negative (-16,44 ÷ 210 = - 7.83%). The portfolio optimization can"t be applied in this case, so as not to incur losses. There are no arbitrage-in-the-transaction-occurrence.

Let us evaluate whether it is beneficial to sale the third portfolio:

Arbitrageur of the third option of portfolio optimization is:

Optimal portfolio is determined by the formula (262):

That is, if portfolio optimization will occur through the sale of the portfolio number 3, JSC "Cobalt" earns 4.385964 thousand $. The effect of such income will be equal to 2.58% earned in the shortest possible time. Since such an effect in terms of monetary and in terms of % is higher than the effect of portfolio optimizing number 1, it should remain a priority for a while.

It is left only one global variant to compare this option with: portfolio optimization through the sale of the portfolio number 4.

Arbitrageur of third option of portfolio optimization is:

It is clear that the effect of this optimization of the portfolio will be negative:

(-17.85 / 50 = - 35.71%).

So we have to stay on option number 3. Let's now look at how to read data from arbitrageurs and what they mean. In the version number 3, we sell a portfolio number 3. Instead it we acquire 51.22% of the additional shares of portfolio number 1, 26.66% of the additional shares of portfolio number 2 and 24.56% of the additional shares of portfolio number 4.

If the arbitrageur is obtained by more than +/-1, for example, we have a number 1 portfolio value in -2.19, it would mean that company should take the extra 119% of the securities for portfolio number 1 in order to sell them (or to find an equal liquid funds amount in order to buy the new portfolio in a sum equal to the shares of this number 1 portfolio cost).

The theory of arbitrageurs operates mainly on large transactions in the securities market. Major big transactions can significantly affect the supply / demand in the market of shares / securities. Because of this fact, arbitrageur would also expect the shift, which should help the company cause to increase the likelihood of arbitrageurs" income and maximize the amount of income, and also to minimize portfolio risk!

It should also be noted that in the case of small operations/transactions, small companies, according to the theory of APT, should be doing the same thing as the largest companies. This speeds up the circulation in the securities" market, helping to align the price of arbitrageurs the company could ultimately receive more income on its optimal portfolio.

Portfolio is a wide term here. It can include in it a single sort of share, a single portfolio of different shares and other portfolio of different securities (for example, the arbitrageur is good in calculating weather derivatives).

Theory of APT ("Apt") is not in vain consonant in English with a "special ability" in its name. Portfolio Optimization, according to APT, - is a special ability to use the optimization of the portfolio in the short run and make arbitrageurs money, since theory suggests that the long-term portfolio optimization with a useful monetary or risk benefit is impossible, this is due to the fact that the stock market quickly equalizes its prices, removing so the opportunities for arbitrageurs.

You should also pay attention to how the development of events is determined by the dynamics of stock price. There is a method of constructing a covariate matrix. We have already built it, when we created portfolios. That is, for example, in the case of JSC "Cobalt", the firm should determine how there developed negative, normal and positive scenarios in the past. It should analyze the prices" changes for similar stocks. And on this basis - a firm can build a matrix of covariate changes in the price of the securities / portfolio A, depending on the dynamics of the critical exponent (in this case - the dynamics of the Asian indices and the overall level of economic development).

However, the arbitrageur - it's much more complicated subject. Building a system of linear equations - is only the "surface of the iceberg" of the arbitrage operations calculation. To deepen the material, let's imagine that a company JSC "Cobalt" follows the scenario number 3, that is, by selling a portfolio number 3, and for the money to acquire an additional 51.2% of the portfolio number 1, 26.6% of the portfolio number 2, 24.56% of the portfolio number 4. Then the structure of the portfolio is as follows:

Table: Forecast value of the company's portfolio by the APT model

The amount of the portfolio at the present value is equal to 615.614, which is 4.385964 less than it was in the original portfolio. The above mentioned amount will be an arbitrageur of JSC "Cobalt". Let the scenarios are equally probable. Then we assume, for the abstraction, that the average earnings per share for any scenario is equal to the following values.

Table: Average price of the company JSC "Cobalt" portfolio by the APT model

Further there was analyzed the relationship between the portfolio and exchange rate (EXR) and the consumer price index (CPI); it was analyzed the dependence of these both macroeconomic indicators to the rate of return on each portfolio by the application of the CAPM model algorithm.

Perhaps this is one of the features of the arbitrageur-pricing model. It uses an algorithm of CAPM, and it is not for calculating the fluctuations of the stock market average rate, it is used for calculating the oscillation between the average market rate shares / securities / portfolio and an important macroeconomic indicators. The result is the same β coefficients, in relation to the macroeconomic indicators.

It was found that the dependence between the yield of each portfolio, the CPI and the EXR adopt the following β coefficients:

Table: The relationship between the indicatorial β and portfolio course by the APT model

I

So, we know the average portfolio yield. According to the model of APT, the expected return () is given by (261):

If there are some newly found portfolio inter-dependences from macroeconomic indicators, we will be able to analyze whether there is an opportunity for arbitrageurs. Multiplier a0 corresponds to the risk-free rate of return on the CAPM model (on which there were calculated the inter-dependences from macroeconomic indicators). Since the CAPM model is used, this multiplier appears in the system of equations, which takes the form:

(266)

The SEC index shows to which security portfolio corresponds each equation. Let us now compose and solve the system of equations for the JSC "Cobalt".

The high sensitivity of the portfolio to fluctuations in the EXR imposes substantial risk on the portfolio. Conversely, a low sensitivity to the second risk factor balances this portfolio.

The author of this paper gave some examples of illustration of various combinations of a0, a1, a2. The above equation is the equation of the identity of the securities in the market. It shows how shares" risks are allocated under the given circumstances. Thus, in the second case, the risk of the market = 0 (this, in fact, is highly unlikely). That is, with the second method of calculation, we deliberately omit the market risk it to be included in the calculation then, after calculating the probability of arbitrageurs.

How to calculate a0 in arbitrageurs" equation by APT? The founder of the model, Stephen Ross, took the return on U.S. government bonds for the risk-free rate of return of investments. Our portfolio is worth 619 thousand USD in terms of expected future income with 615.61 USD. Suppose, for example, it is known that the risk-free rate of return of investment is equal to 616 USD. Let me remind you that all calculations in the example above are carried out per month - the annual rate will vary from one month (which is not surprisingly). Then the risk-free % rate will be 0.06% per month, which roughly corresponds with the taken by us a0.

Let us now examine it with you: how to read the above arbitrageur equation. Prior to its formulation, we estimated that an arbitrageur under given condition is impossible - as we have already held it by selling the number 3 portfolio. However, this equation describes the ability of the remaining securities" portfolios" arbitrageurs in the event of the new securities appearance at the market. For example, suppose a portfolio will have an alternative - a security of company # 6: βEXR = 0.75; βCPI = 0.65. The current price is equal to 28 USD per share (quantity: 10,000 shares). Expected return on it will be 290 thousand USD.

Sensitivity to changes in the EXR for the old portfolio will be:

(267)

For our portfolio: 1/3*1.2+1/3*1.3+1/3*0.8=1.1. S = 1/3 - this is a condition that our portfolio consists equally on 1/3 part of each security.

Expression (267) shows the portfolio sensitivity (SEN) to any U factor, the dependence of which is set by the CAPM. In our case, U - is the EXR changing.

Sensitivity to the CPI for the old portfolio would be 0.566 according to the formula (267).

Thus, there is a new arbitrage opportunity. Namely, the immediate change in the portfolio #1, #2, #4 for the securities #6, which are significantly superior, in terms of returns, and lower, in terms of sensitivity to changes in factors EXR, and a slightly higher sensitivity to the factor of change in the CPI. However, the arbitration shall be made as soon as possible, because the market will quickly adjust the conditions of the securities for company number 6 under the market conditions of return, under the market conditions of the impact of risk and other relevant factors.

So, we"ve looked with you, my dear reader, at the CAPM and APT systems. The ART system is a multivariate method of designing the optimal portfolio by arbitrage transactions, without assuming the availability of risk-free rate at the market (see the solution of equation (266)!). APT also doesn"t involve the calculation of statistical components in predicting the value of the securities: highest probability yield and average deviation from it. These parameters can be set in the model of APT, and they are not systemically-forming-factor. The APT model simulates well the pricing of newly appeared at the market shares. CAPM explains the equilibrium price system on the market and the behavior of security depending on its changes. Thus, the theory of APT, and the theory of CAPM complement each other well.

Along with these methods there is a regression matrix analysis to calculate the optimal structure of the securities portfolio. This analysis was developed by Harry Markowitz. Suppose that there exists on the market a set of n securities. It is better that n was greater than 2. It has been described previously - on how to calculate a total portfolio with a set of two securities.

In this part I, together with you, my dear reader, will create a large portfolio. We need the stock price for the analysis of historical observations; it is desirable to have an each-period cut, as well as it is desirable these cuts-periods to be equal or nearly equal in terms of time periods of data slices.

It is desirable that the number of observations of market fluctuations on the prices of all stocks was greater than 25, even better - 100. Then the error in the historical simulation will be minimal. The formula for calculation of the portfolio with minimal risk (PMIR) is as follows (268):

The bottom line of the resulting inverse matrix, except the last data set, gives the coefficients equal to the optimal fractions of shares of a, b, c, d, e, ..., n, which will form a portfolio with minimum risk. The holders of this portfolio are most likely to receive the expected revenue.

"2" in front of each sign of the row and column at the matrix describes the Joseph-Louis Lagrange"s constant = 2. Cov - is a ratio of covariance, which shows the relationship between each two pairs of shares for the period of observations n. Covariance matrix for this should be calculated in accordance with the formula (253):

The " -1" index above the matrix means no - 1 degree, and that the matrix is not taken forward - it is taken inverse! Once the covariance coefficients will be counted - matrix will need to be inversed to get the best performance in terms of portfolio risk. The formula for calculating the inverse matrix (А^-1) is as follows:

(269)

Where: Det (A) - this is the determinant of the original matrix. We have calculated the determinants of the third-order-matrix at the beginning of this paper. А1,1; А2,2; ....; Аn,n - is the matrix, the derivatives of the first by means of decomposition. Decomposition is:

(270)

Where: i, j - these are the numbers of columns and rows of the matrix (for example, А1,2 i=1; j=2). - This is the determinant of a matrix derived from the original matrix, so that in each matrix it is deleted every i and each j row (for example, for A1,2, there would be deleted 1 row and 2 column).

It should be noted that the method does not involve the calculation of the matrix that consists of 2 or 1 securities, otherwise the formula for calculating the determinant would be different. Formula (269) is valid for computing the determinant of a quadratic matrix of order greater than 2 and less than or equal to 4. Otherwise, the relevance of the calculation has no meaning!

To calculate the extra-large matrices, the author of this paper recommends you reading the literature on the Gauss-Jordan method.

The author of this paper does not recommend to you, my dear reader, to spend time on very large scale matrix calculation by hand (more than 5 - 7 order, as well as for the order less than the specified order). To calculate the inverse of the matrix you need a computer with any mathematical program. To get started, try the most common - Excel. Enter and calculate the covariate matrix (268) in the table in Excel. Do not forget to fill in 0 and 1 at the edges of the matrix, as shown in Equation (268)! Build the next empty table, the size of which is fully comparable with the resulting covariate matrix, and in any case it shouldn"t be completed! Scroll to an empty table with the mouse so the entire table has become blue (ie, selected). In the upper right-hand line of the selected table still selected, enter the following formula.

Excel in English it would be "=MINVERSE()" ["=МОБР()"for Russian], where in parentheses (), select the original matrix from which to calculate the inverse, or enter the cell address of the upper left-hand column and separated by a colon (:) address of the location of the lower right-hand column. Press the key combination: Ctrl + Shift + Enter - and you will get the filled by the computer inverse matrix, which can then be used by you for the analysis! And you can also use any other program on your, Dear Reader, discretion.

Let's now look at an example of calculation of the portfolio with minimum risk. Suppose, the following trends were established as a result of observation of the securities market"s trends:

Table: Monitoring of the market shares of companies A - F from the beginning of 2010 to the beginning of 2011, USD

So, let's get together with you, dear reader, construct the portfolio with minimum risk. We need to extract all the coefficients of covariance to calculate the minimum risk. Calculation of covariance for a given market by the formula (253) is shown in the table below:

Covariance matrix system for companies A - F from the from the beginning of 2010 to the beginning of 2011

Underlined italics is appeared for mirrored ratios (eg, Cov (a, b) and Cov (b, a), which are equal to each other). This covariance matrix is multiplied by 2. The Y cell has 1, which converge to 0, so that eventually they were able to get stock options, where 1 would mean 100% and so on. Now, however, it must be specified to calculate the matrix A as A-1, that is, to compute the inverse of this. I offer you, my dear reader, to use the calculation using the computer (you can calculate it, for instance, in Excel, using the algorithm given by the author of this paper above):

Covariance matrix system portfolio with minimal risk

Row and column %%% show the optimal proportion of each stock so that they form a portfolio with minimum risk. Thus, we see that the optimal portfolio consists of 9.96% of shares A, 45.21% of the shares B, 6.74% of the shares C, 47.14% of the shares D, 10.96% of the shares E, - 20.01% of the shares F. Thus, one should get rid of the shares E, in spite of their continued growth.

Let"s verify the correctness of calculations: the sum of lines%%% (except for the line, where%%% overlap themselves, that is, except at the bottom right of the lines where the opposite %%% is not worth to any shares) should get an equal to +1. Let"s verify it: 9.96%+45.21%+6.74%+47.14%+10.96%-20.01%=1 - it"s true, then a portfolio is defined correctly.

Now, let's see, what does it mean: -20% of shares F. This means that the portfolio in any case should not include share F in itself. And the rest of the portfolio should be excluded 20.01% of other stocks, for which it has a preference for the least! Such a portfolio with a high probability will have a minimal risk.

Profitability of such portfolio is given by:

(271)

PROF - is a yield of the portfolio that consists of securities A, B, C, ...., n. λ - is the proportion of each stock in the portfolio, for example, λA - is the proportion of stocks A in the portfolio, λi - is the share of the i-th stock in the portfolio. - It is a profitability or yield of a certain X-th security in the portfolio.

Let"s suppose we want to diversify risk, and leave all the securities in the portfolio, and to subtract the indicated 20.01% in equal shares from the stock portfolio shares B and D which share is a maximum one. Then the average probable yield of the portfolio with minimum risk is:

The average expected return of a security is equal to the arithmetic mean of the prices for the period analyzed. Arithmetic mean of the stock price fluctuates all the time. The stronger is the vibration - the higher is the risk. The value of risk for one share is determined by the standard deviation. A portfolio risk is defined as:

(272)

The standard deviation is calculated by the formula (245):

Then the portfolio risk for our example is:

The risk of 3.33 USD, or 1.55%, is, most likely, the minimal risk of this portfolio of shares A - F.

When choosing a portfolio with minimal risk, it is very likely to get the same income, which portfolio (from the set of securities) value rose during the study period. It is important to choose super-large observation periods with short each-period data-cuts.

However, not all investors prefer to minimize their risks in the stock market. Some people prefer to have a set by them yield with a high risk - it it all depends on the psychological characteristics of an investor.

Let's imagine that an investor simply took to his note the information about the portfolio with minimum risk. An investor wants to know what the yield of the portfolio with minimum risk is. So, how to calculate a yield? Portfolio yield/profitability (PROF(%)) with minimal risk is (273):

PBEG - it is returns of each type of security at the beginning of the period. For shares A - F the portfolio with minimal risk yield will be 1.37%.

Suppose an investor does not want to yield 1.37%, and it wants to have a portfolio with a given probability which will yield 5%. It should be noted that instead of 5% it can be any return here, and for this example, we"ll consider it as a portfolio return.

The simple linear estimate of profitability is not an appropriate method for the purposes of assessing the portfolio with a given income. Well, yes, it is good to be applied for the situation we saw before. At the same, there is an appropriate method to be used for the purposes of assessing the portfolio with a given income: this is a special kind of qualitative assessment of return of each security - geometric middling return (GMR). GMR - is an indicator that identifies what was the yield of a given security in historical perspective for the analyzed period.

The general formula for calculating the geometric middling return is:

(274)

Where: П - is a sign of the multiplication of all the many components that are included in a set. A - is the price of the i-th financial instrument (security) in the period after when the security was worth the amount of B. n - is the number of prices" data slices, the total number of observations of fluctuations in the price (and not the total number of yields" slices T = n-1 .)

Let's look at a simple example of defining a geometric middling return. Let X security in period 1 was worth $ 100; at the second period its price was $ 101; at the third period its price was $ 104.5. Then the geometric middling of the yield of such security is:

That is, in our example, T = n-1 = 3-1 = 2.

Portfolio with a given income (PGI) is calculated from the matrix multiplication (275):

PGIa, PGIb, ..., PGIn - is an index of portfolio with a specified yield for securities a, b, c, d, e, ...., n, that are included in the portfolio.

Figures 1 and 0 are in parentheses () - it indicates that the rightmost column and bottom row, showing the structure of the portfolio with optimal risk, - they shouldn"t be taken into an account at calculations in the subsequent multiplication of matrices. However, these 1s and 0s are needed in order to obtain adequate inverse matrix, so it was then multiplied by the column matrix.

GMRa, GMRb, ..., GMRn - is a measure of geometric middling of income (GMR) for shares a, b, ..., n, from which the optimal portfolio is to be constructed.

The left part of the calculation is already calculated when determining the structure of the portfolio with minimum risk. Now, let's do the matrix multiplication in accordance with the formula (275):

The resulting column matrix {-0.11211, ...., -0.043688} - shows the covariate distribution of risky securities portfolio, the rate of PGI. PGI will help in determining the structure of the portfolio with the given parameters, because not every investor will prefer a portfolio with minimum risk!

The basic rule of matrix multiplication - is that the string/row is always multiplied by the column. To learn more about the theories of the matrix multiplication, as well as the theories of matrix calculus, you can see, for example, in the works of N.Sh. Kremer, A. Solodovnikov, V.Z. Parton, M.N. Friedman, A.V. Tanana and others.

The matrices can also be multiplied by using a computer. In this case, we consider the calculation in one of the most popular program - MS Excel. Construct the first two matrices whose product we are trying to find (a PGI figure) - this will never be a case of big difficulties for you, my dear reader. First, covariate matrix will be ready already. From this you shouldn"t take into calculation the bottom line and the rightmost column, because they do not belong to the portfolio of securities directly, and they were introduced as auxiliary variables.

The second matrix - this is the results of the calculation of geometric middling return (GMR). Build a matrix that is comparable to the volume of the original sample, except for one line: compliance condition (n-1). Stand with your cursor in the first cell and type the price of the observation period 2 to be divided by the price of number 1 period for the same securities and then press Enter. Extend the marker data to form the resulting table. Below the table, type: "= PRODUCT (column) ^ (1 / (n-1) - 1". Where instead of the word "column" you must select the column of the resulting matrix, and instead of n-1, enter the number of rows of the resulting new matrix. This resulting new matrix, as you, my dear reader, remember, is shorter to 1 line than the number of observations! And as you, my dear reader, remember, he root of the n-th power of A - this is the same as the number A to be raised to the power (1/n). Exponentiation in Most math programs, including Excel, is made with the sign "^".

And finally, calculate the geometric middling of income by multiply the new line of the resulting geometric middling value of return on the price of shares / securities in the very first time. Typically, the geometric middling rate of return is determined by the average for 1 year or 1 months of observation. For example, if you analyze a period of 12 years (the so-called "Decade" in its old-fashion meaning), you will have to calculate the geometric mean rate of return 12 times! You can then determine the average rate of return by any adequate mathematical operations, such as, in the simplest calculation, simply by calculating the arithmetic mean.

So, you've built, and calculated two matrices, - let"s now consider how to multiply them now. Every square matrix is multiplied by the column matrix of similar dimension, then turn out to be the column matrix of the same dimension.

Scroll to the scratch area of the worksheet that is comparable with the matrix-column of the GMR. Type "= MMULT (matr. 1 matr. 2)", where the matr. 1 - is the input of the first matrix (the address of the upper-left line, a colon (:),the address of the bottom right line), matr. 2 - Matrix number 2, on which the product is introduced similar to the matrix number 1. Then you need to press the key combination Ctrl + Shift + Enter. On the screen you will see the result. If you accidentally hover your mouse on the resulting matrix, it will be necessary once again to press the specified key combination, or the program will not allow you to keep working, thinking that you are in an array make your adjustments!

Thus, the data array can be calculated manually or by computer. This array will allow us to find answers to the equation more easily that will allow us to calculate the constants in your optimal portfolio.

The above equation is:

(276)

Where: ASH, BSH, ...., NSH - is the share of securities A, B, ..., N, which is included in the portfolio with minimal risk as it was calculated in the covariate matrix (268).

PGIa, PGIb, PGIc, ..., PGIn - is obtained by multiplying the matrices as it is shown in the formula (275) for the PGI elements for the securities a, b, c, ..., n. It should be noted that a - is a common symbol for the derived measures of the securities A from portfolio, b - of securities B, ...., n - securities N from portfolio. These indicators were introduced in the calculations to facilitate perception. D (A), D (B), D (C), ...., D (N) - it measures the optimum percentage of securities A, B, C, ...., N, in the portfolio of an investor, according to the predefined and named by an investor parameters.

The formula has an Y0 indicator; it is total for the entire system of equations. This indicator converts the utility function given by the investor to a constant, being a common outcome of calculating the Y0 function. The computation of this index is described later.

The geometric average return on the portfolio with minimal risk (Pr(GMR)) will be 2.37494%.This value is calculated from the formula:

(277)

Where: Ai - is a fraction of the i-th security in the portfolio with minimal risk; Pi - this is the actual market price of the i-th security on the end (END) of the observation period and the beginning (BEG) of the of the observation period. GMRi - is a geometric middling return on the i-th security in the portfolio.

Only the Y0 index remained unknown to us from the optimal portfolio, which is calculated by the formula:

(278)

Where: YIELDdesired - this is the desired level of income for a certain investor for portfolio. YIELDmin.risk - is the level of profitability, which was presented in the portfolio with minimum risk. The most acceptable is the geometric average in calculating the desired rate of return and the portfolio with minimum risk return. Indicators of PGI and GMR for i-th asset are determined from (275) and (274). In our example, the Y0 index is equal to:

Now we can calculate the optimal portfolio with a return of 5% from the system of equations (276):

The sum of these elements is equal to 1 or 100%. Let"s to the biggest in the relative density amount of B securities add the amount of securities A, D, E, F. We obtain that one of the portfolio"s options, which would arrange an investor, with a 5% return will consist of 74.6% of stake B, 25.4 % of stake C. This portfolio is of the most probability closer to the desired by an investor 5% yield in the future. Of course, it may be contrary to policy of diversification of the portfolio.

Often the equation (276) will provide accurate, up to a percent, portfolio structure without negative numbers; and always the result of an expression and a portfolio depends on the specific circumstances which are formed on the securities market.

Alexander Shemetev"s method for calculating the optimal portfolio with the set returns which improves Harry Markowitz method for the Russian market

The author of this paper argues that the expression (276) should be simplified to facilitate strategic decision making. Such high values of the portfolio"s index is due to the fact that the geometric middling price is calculated from the actual prices available on the market, which, in this case, are presented in hundreds of USD, which, as a consequence, multiplies the result of multiplying the expression (276). Although this multiplication does not affect the final mathematical result, it affects significantly to the management of the result, because it gives too great spread of values, which converge at a point 1 (100% of the portfolio). Management decisions on such a portfolio may not be so easy. Because of this fact, the author of this paper developed a method to simplify the result in Harry Markowitz formula to create an optimal portfolio. The method is as follows.

Alexander Shemetev offers to consider not the overall geometric average income equal to the actual values of changes in stock prices. Alexander Shemetev offers to calculate the nominal geometric return (NGR). To calculate this index, you must first calculate the total geometric earnings per share as follows:

(279)

Then the available for the period of observation actual fluctuations in the price of securities must be brought into the conditional price (CP) as follows:

(280)

Where: П - is a sign of the multiplication of all the members of the set components. A - is the price of the i-th financial instrument (security) in the period after when the security was worth the amount of B; n - is the number of data cuts slices in prices, the total number of observations of price fluctuations. ΣPi - is the sum of prices of the i-th security on the market for the entire period of observation. ΣPA - is the sum of prices of all securities in the market, from which it is supposed to build an optimal portfolio for the entire period of observation.

Alexander Shemetev's method of calculating the optimal portfolio,

taking into account market risk

Under these conditions, the author of this paper believes rational to expect the conditional geometric middling return (CGMR), which is calculated using the method developed by Alexander Shemetev on the basis of the following formula (281):

What does it give - the calculation based on this formula? Calculation by this formula will automatically calculate the very structure of the optimal securities" portfolio from the potential one with a given rate of return or risk.

For our example, this conversion rate will give the next most optimal for the investor portfolio:

Such a PGI matrix, in my opinion, more profoundly meets the requirements of the investor and the market conditions prevailing in a certain situation. Indicator Y0 in this case will also change its form to:

This Y0, in my opinion, more profoundly meets the current market conditions. Then the optimal portfolio of shares A - F has the next form:

As it can be seen, the method developed by Alexander Shemetev makes the Harry Markowitz method more precise so it is able to construct the optimal portfolio of n securities traded in the market, with the specified criteria of risk and return. There is no need to recalculate extra large parameters to create an optimal portfolio in this formula. Thus, the most likely form of the optimal portfolio with a return of 5% must be structurally created of: 21.18% of the securities A, 28.64% of the securities B, 0% of the securities C, 44.39% of the securities D, 5.02% of the securities E, 0.77% of the securities F.

The Author of this paper for clarity gave such an example that the H. Markowitz matrix went "out of its scale". It is an often case at the market. The Alexander Shemetev"s method allows one to construct convenient portfolios from the n kinds of securities, regardless of the actual conditions and the specifics of the market.

Alexander Shemetev"s method to refine the H. Markowitz matrix in some extent takes into account the linear and nonlinear market risk by William Sharpe, that could not be resolved in normal circumstances by the theory of Mr. Markowitz.

Not always an investor prefers to build a portfolio of securities with a specified yield. Sometimes it may be of interest an optimal portfolio, which is not of the minimal risk.

There is a method of Harry Markowitz to create such a portfolio, and a technique of VaR.

According to the Harry Markowitz method, for example, if the subject wishes to have a risk higher than the minimum (and hence profitability of the portfolio is increased), the optimal portfolio in terms of risk an investor can create by creating a new system of equations by means of indicator Y0 (risk):

(282)

The denominator of the formula is identical to the denominator of the formula (278), in which there is calculated the rate of Y0. The numerator corresponds to the desired rate of σ-desired of investor"s risk and portfolio minimal risk σ-minimal consistent with minimal risk, which is composed of just turning the optimized covariance matrix (268).

The resulting indicator Y0 (risk) must be substituted to equations" system (276) in place of Y0.This can be done by the method of H. Markowitz, either by the Alexander Shemetev's method with an approximate account of market risk. The resulting system of equations shows the calculation of investor"s portfolio with a given level of risk. Since the calculation is essentially of the same type with the calculation of the portfolio with a given measure of profitability, the example of it we will not consider.

It should be said a few words on the analysis of VaR - Value at Risk . VaR - is a vast series of techniques that are used in many sectors of the economy in the world today. For the securities market, I offer you, my dear reader, to consider the simplest type of VaR only - an analysis of the portfolio in falling market with a probability of accuracy of the analysis of 99%.

The system of VaR equations is quite complicated, because of this fact the author of this paper describes the use of the simplified version by the algorithm by Peter Hart. In particular, this algorithm is incorporated into the simplest mathematical program called Excel.

The VaR algorithm in a falling market needs a bit of calculation. First, you have to calculate the geometric middling returns for each security included in the portfolio estimated by the formula (279), that is, the ratio of returns of each security in each new period in the root equal to the number of observations in - 1 power (power 1 / (n-1)). Second, there is the need for the standard deviation of each security, calculated by the formula (248) or (245), depending on to what mathematical school you can be regarded.

The Geometric middling amount of income place in the table-line editor Excel, and place an empty column near it to be comparable one, where the computer calculates the optimal share of portfolio; highlight it in green. Target cell must become Portfolio"s Yield (PY), which is equal to the sum of products of geometric middling of returns per share for the period (NGRi) and the share of each security in the portfolio (Di):

(283)

Similarly, the values of the standard deviations of each stock in the portfolio, leave a blank line, where you should enter the formula of the share of stocks in the portfolio (the blank cell), multiplied by the standard deviation of a portfolio of 100% of this stock. Enter a single cell, where you should input the sum of standard deviations of the value of the shares in the portfolio that you just wrote.

If you did everything correctly, then you will calculate the geometric average return and standard deviation of each stock in the portfolio. In the other cells you just have to introduce the formula, and the total value must be zero, because the proportion of shares in the optimal portfolio is the thing we still do not know.

Ask an adequate rate of return for a given portfolio (such as 0.02, ie, 2% for the period). Connect Add-In Solver option in Excel. In finding a solution set the portfolio yield cell as the target cell; set it equal to "by value" and enter the desired by you adequate return on the portfolio.

In the graph "by changing the cells" indicate empty cells, which should appear the optimal portfolio"s share of stocks. In the graph "add constraints" add: the sum of lines shares of stock /it can be defined by a colon and the address of the first cell and the last one, and it can be isolated in a separate line on a sheet of Excel, which has the formula entered: the sum of / must be less than or equal to / <= / 1; then add to the sum of these rows that they must be greater than or equal to /> = / 0.

Add restrictions on a cell in Excel, which is registered by the amount of securities" shares in a portfolio of securities /it should be equal to 1/.

Impose a restriction to the count of risk, or standard deviation "is 0" / better to ask a range of values close to 0, depending on the objectives of the investor to assume that the program should have something to be calculated!/. Enter and run by a computer the Peter Hart"s algorithm to find the optimal portfolio with minimum risk. This portfolio will match to VaR 99,9%, because it accurately calculates VaR in the analysis of the algorithm that is programmed by Peter Hart!

For example, in our case with VaR risk parameters from 0% to 5% and maximum return at the given risk - it corresponds to a portfolio that consists of 85.67% of stake in B and 14.327% of stake F.

It should be made the following remark on how to connect the algorithm by Peter Hart: "the search for solutions" for Excel 2007 and 2010. To do this, click on the general settings (the button with the logo of MS office, where the save, open, ....). Bottom right look for an open list: "Excel options", click on this button. Go to the option "Add" and add-ons in inactive, select "search for a solution". At the bottom, under 'control' select 'add-in Excel and press "go". In the dialog box "superstructure" make a tick in front of "the search for solutions". Button and the function "find solutions" will now be available in the new Excel tab "Data"; it is usually at the right.

This will correspond to the VaR optimal portfolio at the market crisis conditions. Portfolio, calculated on the Alexander Shemetev's modification of Harry Markowitz"s techniques will match the optimal portfolio at the risky market. Portfolio designed by Harry Markowitz algorithm will most correctly calculate portfolio in emerging or rising stock market without regard to market risk by William Sharpe (CAPM analysis, therefore, is desirable). Arbitrage portfolio works on all types of market to make revenue from arbitrage operations, assuming that the arbitrageur - is only possible in the economy return on the stock market, because the market quickly balances the securities available and rotating at the market.

The review of methods for the analysis of the optimal portfolio in the securities market - it is only "a drop in the ocean", the total number of methods of forecasting the price of securities. Due to the limited volume of this paper, the other techniques will be omitted in it.

The trend method is not limited by the method of forecasting the development of a single company in the market or prediction of the value of securities issued by some company under investigation or other business-systems that functioning at the market. Trending method involves a study of the factors of uneven value of money over time.

Analysis of the uneven value of money over time can be carried out by two methods: NPV and NFV. Both of these methods are the scope of complex financial analysis indirectly, because of this fact, they will not be involved into a consideration in this paper.

Thus, we"ve considered with you, my dear reader, an important part of the financial analysis of company. The author of this paper believes that in today's world it is impossible to review comprehensively the company's activity in isolation from market fluctuations in the value of its shares, as well as in an isolation from the analysis of the company's securities" portfolio. Even William Henry Beaver believed that fluctuations in market prices of company"s securities are able to derive a business-system from the market forever! Edward Altman picked up the idea of W.H. Beaver and created his famous model of the Altman"s coefficient D, which is relied on the market value of the shares.

In today's world the analysis of the securities" portfolio should be held in conjunction with the rapid analysis and with the more complex one. And the techniques discussed in this part of the paper will be useful for you, my dear reader.

Let's go back to where we began to consider that method of trend - a trend analysis of the overall development of a company: is it positive or negative one, and what are the parameters it is positive or negative one. Then you and I touched on an important component of the trend method: the probability of profitability in the next month. In mathematics, a similar calculation is called the mathematical expectation:

(284)

Where: Pi - is the i-th value of the index; λi - this is the probability of this indicator. Σλi = 1 - it's a prerequisite to the mathematical expectation.

Let us consider such a "terrible" term, as the mathematical expectation, at a simple example. Let some Corporation called Ltd. "Daisy" has the opportunity to earn 100 USD in the next day with a probability of 10%, 120 USD with a probability of 20%, 130 USD with the 30% chance, 85 USD with the probability of 40%. Mathematical expectation of income in the next day will be:

Mathematical expectation is the average rate, which applies itself to the entire set of many tests or observations. Trending method"s important branch is based on the distribution functions, the consideration of which is beyond the scope of this study.

Every entrepreneur himself or herself subjectively assesses the risks for each scenario. That is, the trend method - is a kind of scenario for financial analysis, a kind of wait-if analysis that was already considered yet.

The scenario analysis has some types: classical, wait-if, stress testing, portfolio planning, risk focusing and neural prediction.

As is evident from the wide ranging of types of scenario analysis, people have always wondered: "What will happen with their money if ... .?!". This issue was so important that this expression literally formed the basis of the whole direction of scenario analysis, the Wait-if analysis (literally, "What would happen if ... .?"). It is quite difficult to specify the exact name, who first coined the scenario approach.

There can be built any scenarios: falling revenues, rising cost of purchase of inventory needed for production, the decline in demand for goods and so on. The consequences of each scenario are calculated for each scenario at the expense of a comprehensive financial analysis. The probability is determined by an expert opinion based on a comprehensive mathematical study of the question. I think that we, my dear reader, shall not consider all these numbers of scenarios. Instead, I offer to briefly review the main advantages and disadvantages of the method.

Advantages of the method:

This method allows to calculate the current financial needs accurately, as well as the timing of their occurrence.

Disadvantages of the method:

In this method, there is a significant disadvantage. The forecast is always based on prior periods for which the trend will always be gotten positive. Otherwise, that is, if the trend was negative, then there would arise a question - why is there such a company which from period to period brings only losses. This would be contrary to the first axiom of financial management, under which all economic agents always behave themselves as Homo Economicus, ie, extremely rational. Differences in rationality are possible only in cases of subjective evaluation of values of probabilities of certain events, as well as in cases of the propensity to take risks, and not to create a non-profit enterprise.

The method shows the bankruptcy risk at crisis enterprises only.

In other words, this method inherently assumes that the trend analysis will be generally positive, and it does not include any strategic factors for an enterprise, or force major factors.

5) The qualitative method

Qualitative method - it is always a method of expert evaluation. According to mine opinion, it is the most effective method of analysis, of course, it is fair only in a case when you have found a good expert! There are many peer reviews in the world today.

For example, as you will recall, William H. Beaver expertly suggested a method based on an algorithm for tracking key indicators of crisis activities: borrowed funds, fluctuations in stock prices, commercial risk, overstocking and increased receivables and so on. Each expert has its own set of favorite methods for conducting a comprehensive financial analysis. We will not cover them all - and instead I offer to focus on the method developed by the British Council department, the Audit Committee (hereinafter in text: the British Board of Audit). The method assumes to separate all the existing factors to predict bankruptcy for a company into two major groups of factors.

As the first group of factors, there can be regarded criteria and indicators the unfavorable current values of which as well as the unfavorable dynamics of their changes testify about possible significant financial difficulties in the foreseeable future, including bankruptcy.

As the second group of factors, there can be regarded "alarming beacons", the factors which in themselves are not critical; at the same time, these factors may carry a trend of potential threat for the enterprise"s functioning.

Every time in every region the British Board of Audit recommends the professional approach to define the indicators elating to both groups of indicators.

Along with the British Board of Audit"s method, there is also a method of qualitative analysis of solvency developed by Peter Drucker. This method is based on EVA (Economic Value Added). This method is designed primarily for public companies. P. Drucker believes that the borrowed capital must be paid-off together with its interests; at the same time when the equity capital will be regarded as free, if the value of EVA is positive and is continuing to grow. EVA is calculated as:

(284.1)

Where: EBIT - is an operating profit plus interest payments on debt capital; TBS - is the total carrying value of the company equal to the sum of assets; WACC - is the weighted average cost of capital.

Under the concept of P. Drucker, while EVA is increasing with positive growth, - the investment/owned capital for the company will be more stable and safer than the debt capital. At the same time, in the case of a fall of EVA - investors may start to panic and sell their shares, which will lead to a drop in the value of the business-system, and it can lead to its rapid bankruptcy.

The qualitative method has its advantages and disadvantages. Among the disadvantages, there can be noted a strong dependence on the quality of the expert and subjectivism. Although, in the opinion of the author of this paper, this is a general lack of all the methods, without exception; this is a general lack of all the approaches to financial analysis and prediction of bankruptcy. Any mathematical model always depends on the subject who actually applies it. Moreover, each of the mathematical model itself is subjective, because each of them uses abstractions and removals from the real world, which distort the result. Because of this fact, it is almost impossible to create a unique feature for the description of all financial processes, from accounting to finance, and logistics: because they have to be split up into very many small components.

The advantage of this method is a high level of intelligence, which, of course, depends on an expert. That kind of analysis - is a key piece of analysis following by each model. For example, even the most dysfunctional financial model can be a good financial tool in the hands of some analyst, and vice versa, even the best neural networks can not replace an analyst in any field, except for technical aspect: the calculations themselves.

The very purpose of this paper is to make of you, my dear reader, a more adequate financial analyst, capable on the basis of the quantitative (mathematical, statistical, logical, and so on) models adequately apply a qualitative method of complex financial analysis, the main component of which will always be a sense of tandem of the analytical and mathematical tools.

6) The genetic model

Genetic model, explaining it in a simple language, involves training. The neural network during its operation itself builds new parameters and models, which create more adequate models in the process of their development. The famous theorist of genetic modeling in finance is a professor at Cambridge University and National Taiwan University, Yuh Dauh Lyuu.

As you may have guessed, my dear reader, genetic modeling involves the use of computers. And since all the genetic models are commercial and even military secrets, then you can hardly find them in the press in any case; at least, you will hardly find a really working model. Because of this fact, most likely, it will be you, my dear reader, who will have to create a working genetic model using the materials of this paper and my books for your company!

The genetic model assumes the passage of the following stages in the development of methods to predict bankruptcy.

The result of a genetic model always provides a single comprehensive and valid method of predicting bankruptcy in the industry.

The genetic model assumes the passage of the next fifteen steps:

1) Collect all possible financial data for the industry.

2) Collection of financial data on bankrupt companies.

3) Data collection and primary analysis of all the available mathematical arsenal (linear - discriminant, of score, neural - network and other) to be applied for methods of bankruptcy predicting.

4) Pass all the data available from completing the steps (1) and (2) through all the available methods.

5) Analysis and comparison of results.

6) Find the coefficients of the smoothing and approximation parameters.

7) The selection of the remaining functional methods to predict the bankruptcy.

8) Creating a united model to forecast the companies" bankruptcy based on the effective methods.

9) Newly pass of all the gathered data through the resulting new model.

10) In case when the data gave the same bankruptcy probabilities as it was with the successful models" combination after the (4)-th step completing, - in this case we can testify, that there was created an affective model to predict bankruptcies.

11) Now, all the models used are to be transferred to a really genetic model by means of additional data gathering for operations described in steps (1), (2), (3).

12) The new pass of all the existing data obtained through the steps (1) - (7) to collect really good working methods.

13) Check the old model for adequacy according to new data from steps (1) and (2).

14) Correction of the genetic model in accordance with the new data for practices and successful models of primary data methods (3).

15) The conclusion of a new genetic model that is more adequate to new environment"s conditions.

Etc.

The advantages of the model:

The ability to combine all the advantages available in the arsenal of different models to predict bankruptcy.

Ability to update the model by introducing a new data on the newly bankrupt companies, and by the newly established techniques, as well as changes in reporting by enterprises for subsequent periods.

Ability of this methodology to the "eternal" existence through the gradual evolution of the methodology and analysis by new incoming data.

An ability to create an output equation/model from the genetic model that could provide an opportunity to use the genetic algorithm "manually".

Disadvantages of the model:

The extreme complexity of the calculations.

The need for powerful computers for model building.

The high cost of creating the model.

The complexity of information systems" service.

7) Models of neural networks

Neural networks appeared in the late 1960s when a team of UCLA researchers led by Professor Peter Hart built the first neural network. In parallel with this development team, there were several other teams of scientists working on neural networks creation. It led to a soon creation of full prototypes of neural networks.

The original targets of neural networks in the financial sector was forecasting and monitoring of macroeconomic indicators, including the Federal Reserve System"s indicators. In the 1970s, neural networks had another financial function: modeling of stochastic processes, scenario analysis.

In the 1980s, neural networks have become gradually available not only to public companies, the governmental bodies and some of the mega-corporations; they became available for other companies of large and medium size.

In the 1990s, neural networks are self-learners. In principle, this is the point that turned the development of civilization and technology became more and more oriented to get away from the basic neural networks in favor of genetic modeling in finance, that is, to remove from the hands of financial analysts the task of building the model parameters and building the models themselves.

It should be noted that such a turn in the development of neural programming ultimately will greatly facilitate the work of financial analysts who will remain to use only a qualitative method, that is, carry out expert opinions and analysis.

General scheme of neural networks is as follows:

Scheme: The general principle of neural networks

in procedures of bankruptcy predicting

Neural networks are now some semblance of artificial intelligence that is under investigation and improving now. Their potential can be phenomenal. Therefore, one of area of their application - this is the prediction of the probability of bankruptcy.

Neural networks operate in accordance with the principles outlined in this circuit: the input data is introduced into the computer with the program of neural networks to predict the probability of bankruptcy. Then, the "black box" places the mathematics and logical calculations inside itself. The general principle of computation is not known to anyone - even for the programmers who created the system, it is because of the complexity of the calculations used. The system then gives a result, that is the probability of bankruptcy in the chosen future.

Scheme: A general algorithm of the method of neural networks

Initially, the data on enterprises is collected. This data is then entered into a computer. Then, there is a data conversion made by programmer or some high-level compiler that is able to transform input data into an electron-numeric code. Then it follows the analysis of important (for a given stable scheme and under specified conditions) financial ratios. After this, it creates its own model to estimate the probability of bankruptcy on the basis of neural networks; the analysis is based itself on a data for each company provided.

After the results are collected, and the system automatically checks the results for errors. In the event of material error (materiality criteria is laid down in the computer), the operation is repeated for a certain enterprise. In case of no error detection - computer gives a result which is converted then back by the programmer or compiler of high level so that the data are to be readable. The result of neural networks is the availability to read the data about the probability of bankruptcy for a period of n, represented in machine code.

Advantages of the method:

It is easy to use.

This method is considered as one of the most modern and reliable to date.

Disadvantages of the method:

The need for a sophisticated computer.

The high cost of programming and keeping up of developers.

An ability of an erroneous calculation by the "black box" algorithm, therefore, the end output values may be distorted by the primary "black box" algorithm.

You can not affect the calculation process.

Failures to correct the data.

8) A probabilistic analysis

Probabilistic analysis often goes along with the previously discussed trend method. The most applicable sub-method of this method is a general probabilistic analysis.

This analysis is based on the general principles of probability theory. It is based on the introduction of probabilistic estimates of indicators. For example, the probability of obtaining a business profit of n units in the next year and calculating the risks of non-profit (standard deviation). Then, based on calculations of profit, there can be calculated trends of other indicators too, on the basis of probability theory. After this, it is determined the probability of complete firms" insolvency, ie, bankruptcy.

Then one should construct a system of indicators on a hierarchical structure. After that, these enterprises are subjects for studies on the principle of: a truth - a lie. The provided steps and inner loops under study by probabilistic analysis are called probabilistic algorithm. The end result is that a probabilistic algorithm is always binary (T - truth = the company - is bankrupt; L - lie - the company is not insolvent within a period n).

Subspecies of probabilistic analysis is a method of constructing a decision tree. In this case, the trees are constructed for the sequence of events at different scenarios of each process. Then the probability of each scenario is analyzed through a probabilistic method. One or more branches of this tree will be the probability occurrence of an event of bankruptcy. If such a probability is above a certain limit, it puts a value - true, the company will go bankrupt. Otherwise, it puts 0.

Another kind of this method is developed by Ronald A. Fisher (1890 - 1962) and Chester Bliss (1899 - 1979, Springfield, Ohio). This kind of method is called Probit. Probit - is a binomial model that requires the construction of: the company is bankrupt in mathematical circumstances A, otherwise - it is not bankrupt.

Chester Bliss, the author of the method, in 1934 proposed a method for calculating the number of dead pests, depending on the amount of pesticides in agriculture, which was based on a regression model of the normal distribution function, which he called "probability unit", or Probit. Probit - this is both: a time probabilistic analysis (binominal value of 0 or 1), and regression analysis.

Advantages of the method:

It applies mathematical model of calculation of probability parameters.

Comparative ability to use it manually.

Disadvantages of the method:

Subjective assessment of probabilities. This can lead to distortion of the actual probability of the occurrence of bankruptcy.

The complexity of the calculations.

The probability of a false probabilistic algorithm.

9) Model-based tracking of the primary factors of external environment of the enterprise on the basis of correlation-regression analysis

The method is a kind of trend method. And in Russia, this method has a significant part, because many professionals engage it in their researches, looking for the dependent variables of the environment on the basis of this correlation-regression analysis.

This method can be direct, indirect and complex.

The direct method defines indicators, which are primary for a specific industry and enterprise. For example, for agricultural production, these are the primary variables: yields, prices for basic crop and/or livestock production for an enterprise.

The indirect method investigates indirect indicators of business activity. For example, for agriculture, these will be indirect indicators of energy consumption, as well as the price of the auxiliary and by-products of plants and/or livestock for a particular company. Indirect indicators are always directly or inverse simultaneously correlated with the increase / decrease of the productivity of an enterprise.

When the complex method is used, people apply both of the above methods.

This method involves the passage of calculation through the following steps:

1) Analysis of an industry.

2) Calculation of critical exponents for an enterprise.

3) Analysis of system factors in the industry.

4) Carrying out the calculations of the correlation between industry factors and enterprise data.

5) Analysis of the reserve of financial strength based on correlation and regression analysis.

After receiving the data, you can make predictions and conclusions about the probability of bankruptcy. The probability of bankruptcy will be identically equal to the probability of falling of incidence system factors to their critical values (calculated on the basis of expert estimates).

Advantages of the method:

It applies mathematical model of calculation of probability parameters.

The model considers not only internal enterprise accounting"s financial factors, and primarily it considers the enterprise environmental factors, macro and micro.

Disadvantages of the method:

Subjective choice of system factors. This can lead to distortion of the actual probability of the occurrence of bankruptcy.

The complexity of the calculations.

Implementation of the prognosis of systemic factors is made only on the basis of trend data and probability values of the factors.

10) Evaluation of scoring methods to predict the probability of bankruptcy

When predicting the probability of bankruptcy, it sometimes is appropriate-and-goal-oriented to use a scoring evaluation method.

When scoring method:

(285)

Where: Scorei - is the score from 1 to n of corresponding figure determined in accordance with the applicable formulas (scoring);

Weighti - is the score on a scale of relative importance from 1 to n of a corresponding figure.

RBA - is the resulting bankruptcy assessment - it is the result of complex assessment of rates of the probability of bankruptcy. The most such methods transfer the scoring result to maximum of 4 different scenarios types. The endless many of different end figures resulting in the formula (285) is transformed to the end different scenarios" types on the basis of mathematical rounding. There are two main ways for the rounding of the RBA for different sectors of the economy:

A - 0.35 (1/3). The resulting meanings that are equal to or greater than circa 1/3 or 0.35 (for different methods) are rounded to the other scenario type (to the bigger score); otherwise the scenario type remains unchanged (it is rounded to a smaller side).

B - 0.5. The resulting meanings that are equal to or greater than 0.5 are rounded to the other scenario type (to the bigger score); otherwise the scenario type remains unchanged (it is rounded to a smaller side).

Coefficient of 0.5 is usually used for non-financial sectors.

Sometimes, it is accustomed to use some complex algorithm for calculating the rate of RBA:

RBA =Ω*( RCA + RAA + RRA + RLA + RMA) (286)

Where:

RCA - is the general result of the capital assessment"s performance group"s end results;

RAA - is the general result of the assets assessment"s performance group"s end results;

RRA - is the general result of the return assessment"s performance group"s end results;

RLA - is the general result of the liquidity assessment"s performance group"s end results;

RMA - is the general result of the management assessment"s performance group"s end results;

These figures are calculated on the same algorithm and formulas:

Calculation of capital quality and capital adequacy is conducted as follows:

(287)

The calculation of the quality and sufficiency of the assets is held by the following formula:

(288)

The calculation of the quality of the aggregation of property of company and the adequacy of its liquidity is held by the following formula:

(288.1)

The calculation of the quality and adequacy of return is carried out by the formula:

(289)

The calculation of the quality and adequacy of management is carried out by the formula:

(290)

Ω - is an interrelation ratio of all the indicators included in the scoring system to each other. The default is 1 / 5, if the other discriminant is not installed, such that, for instance, a yield is more important than assets by 10%.

Where: Scorei - is the score from 1 to n of corresponding figure determined in accordance with the applicable formulas (scoring);

Weighti - is the score on a scale of relative importance from 1 to n of a corresponding figure.

Generalizing the result of the situation for the company is as follows: equal to 1 - "good"; equal to 2 - "satisfactory"; equal to 3 - "doubtful"; equal to 4 - "unsatisfactory". These 4 groups correspond themselves with the 4 main scoring scenarios" groups.

Unfortunately, it has not yet selected individual indicators included in the companies" group for the RBA assessment for the most industries at present in the Russian Federation. So, while the scoring bankruptcy forecasting method is rarely used extensively in the Russian Federation to assess the probability of bankruptcy of an average company.

This forces the domestic suppliers of capital and the state bodies to use other models for assessing the solvency of Russian producers, in particular, to use the models of linear-discriminant analysis, which will be discussed in the next part of this paper.

The practical application of basic models for predicting the bankruptcy

When you go to a hospital and hand over analyses, - the purpose of these procedures - is not to "predict the outcome of the disease", the main purpose is to pick the best treatment for your body! Analysis of bankruptcy can be compared to medical criteria. Predicting bankruptcy models can be of different types: models oriented at the value and structure of assets; methods that assess the company's obligations; algorithms, comparing a company with the ideal ones and "unsustainable" ones among the scope of firms at the market; the procedure to estimate the volume of revenue and profit in relation to the critical parameters, and so more .... Just as in medicine, where there are blood tests, pregnancy tests, X-ray and ultrasound, tomography, and so on. The purpose of medical tests - it is not to treat a patient, its purpose is diagnostics and forecasting the chain of treatment operations that are needed to cure each certain patient.... Such diagnostics may reveal acute respiratory disease (ARD) among some patients, bronchitis among the other ones, and somebody has a fracture, and so on. All this is treated in different ways.

There is the same thing when making a prognosis of bankruptcy. The purpose of all tests - is to evaluate the quality of assets and liabilities of a company to determine what they should do next. As well as objective of medical tests for some patients - is to determine this - how much is left to "live" for a certain patient, and how much time is available on its treatment; - it is similar to the analysis and prediction of bankruptcy, where the purpose is to determine how much is left to "live" to a specific company and how much time is available on its "treatment".

In this part of the paper, I together with you, my dear reader, will take a look at the classical tests of bankruptcies, which are similar to the classic medical tests (blood tests, x-rays and so on), and neo-classical models to predict bankruptcies, which is similar to cutting-edge medical tests at the hospital: a DNA test, the test of hair, retina and so on. As well as there are no "modern" and "obsolete" tests at a hospital - there is the same thing at predicting the bankruptcy. As you recall, the author of this paper gave an example that even the most modern research of university of Oxford about the financial state of the world's largest auto manufacturers in 2008 - 2009, respectively, was carried out only on the basis of models of Edward Altman and Gordon Springate in retrospect, with some additional performance trending. Even the most classic models of a financial analysis of bankruptcy are widely used today, showing good performance results.

So let's start predicting bankruptcy of an enterprise. Here again an analogy with the surgeon: mastery of a single method of predicting bankruptcy looks as if our surgeon was able to work only with electric saw in perfection!

Such a surgeon could scare all the clinic's patients only by tales about his or her fairy tale skillfulness! And also you, my dear reader, as a financial analyst, should not be restricted within a single bankruptcy forecasting model; - All models must be used in combination, to know what causes the negative trends of the models and how we can improve the company's activities!

If some company is moving in a questionable direction, - one should consider the Market adequacy of its goods; the level of accounts receivable and unpaid thereon; the level of short-term borrowings in the business system; the situation with long-term debt; hidden interest on loan capital; the situation with the cost of production (what is included in it; and what can be reduced without reducing the quality of the product and other marketing aspects); one should compare the situation with legal actions, if any, that are hanging over the company; the macro-environment should be investigated: what will happen to business in the future, competitor activity, ... - this is the algorithm how to behave in the organization in case of negative trends in the models and indicators of bankruptcies. The crisis models of bankruptcy should be broken down into their components to determine which indicators cause the values that a model shows a negative trend!

You have to know all the crisis-forecasting techniques available in the arsenal. Each of them is good in its own way. Do not take each of them "on faith" in a static - it is necessary to watch them all in dynamics! Has some company been approaching to the critical point or area since some certain moment of time, or has it been moving away from this point!

The general model takes all of the following methods and assigns scores. So, the whole comprehensive financial analysis of a company will pull a 0.8 score of 1, then there is a 80% of prediction of bankruptcy. The remaining methods enable us to know the terms: When? All these techniques use an interval from 1 to 3 years. So, what outcomes are possible, and what conclusions we should draw from a deep analysis? After analyzing a company following the set of the methods and models given below - we, most likely, shall come to one of the following results:

If a company is already in the area of bankruptcy and is moving into it further and deeper - it can be argued that it would go bankrupt within a year, with high probability.

If a company is in a critical area of bankruptcy procedures listed below, and the rates vary slowly for the better, then there is a high probability of its bankruptcy in the next two years!

If a company is in the normal zone, and is steadily moving in the crisis zone or the zone of the bankrupt, it can be argued that a high probability of its bankruptcy is possible in the next two - three years!

If a company is in crisis ("gray") zone or in the normal zone. And the trend is sharply positive. That is, it distances itself from the zone of the bankrupt. It can be argued that a company is not threatened by Bankruptcy with high probability in the absence of jumps in a change in its capital.

If Belarusian model went "out of its scale", then there is some probability that within the company there is a discrepancy between the accounting and financial accounting, because the model "off-scale" is primarily due to the predominance of multiple revenue over profits (organization all its funds above the limit is required to keep in bank accounts, and it has to reflect them in any case). This can lead to off-scaling.

If some model shows that the company - is a bankrupt, and another models shows this company - is not a bankrupt: we need to break these models into their components and find out what are the factors and ratios that cause the overstating of some model or models. And if this ratio shows a positive trend for the enterprise, it may show this company most probably is safe from bankruptcy. And, when laying out a model for the enterprise revealed some factor or factors gave poor results and showed negative trends, it may lead to company"s bankruptcy!

In general, you should consider all the models at their dynamics only! Then we can talk about the positive and negative trends in an enterprise.

In general, talking about bankruptcy, I should say that the bankruptcy has three stages:

Stage of latent bankruptcy: It can be traced to the fact that certain financial ratios are not in order. In absolute terms, one can observe the growth of accounts receivable, accounts payable, inventory and finished goods in warehouses. This stage is of the investment cycle crisis, when a company needs a new investment project: the modernization of production lines, the opening of new businesses, developing of new activities ....

Stage of financial instability: A company started to have problems with its liquidity: there was not enough money to cover the current financial needs, and overstocking by raw materials and finished products in storage increases itself (problems with sales and, perhaps, with the production), receivables and payables are also growing. This is the stage of operational cycle crisis, when the domestic problems began to be obvious and to press the company by interfere with its normal operation and output. At the stage of instability operating cycle needs a program for managing capital: equity, long-term and short-term borrowings, the basic production funds and current assets. The purpose of anti-crisis strategy at this stage - is to prevent the onset of an acute crisis of insolvency.

Explicit stage of bankruptcy: A firm has serious problems with sales, and at the same time, funds are sorely lacking themselves. There get started the non-payment of receivables and payables. Enterprise debt is growing. Company may involve additional credits to meet current financial needs, and they are not a measure of taking the company out of the crisis - they simply "patch holes in the budget". There may begin a trial on insolvency (bankruptcy) with all its consequences. The main objective of anti-crisis management at this stage - is to manage the bankruptcy of the enterprise - to do so that an enterprise has left no huge debts uncovered by its owners!

In this section, this paper offers a wide arsenal of crisis-forecasting techniques, from which you can pick up one set of tools that which is right for your company.

The matrix system of forecasting bankruptcy

on the model of William Henry Beaver, 1963

Today, in 2010, Stanford University students often speak highly of their teacher, Professor Emeritus of the University, William Henry Beaver in the following manner. On the one hand, it is a man who when he begins to read an article - then all at once fall asleep right in the classroom .... But if he will postpone reading the article, he is able to explain even the most complicated things by very simple terms! He always treats the ideas of students and, thus, a "weak idea" he always tries to make a strong and fundamental one, motivating them to research in this area. 2 hour classes for its students pass for 10 minutes, with virtually all of the students noted that his study - are the most informative! During his career, W.H. Beaver said his biggest achievement is of bringing up a new generation of accountants and financiers with modern economic thinking. Average, the attendance of lectures of Professor W.H. Beaver - is one of the highest in Stanford. W.H. Beaver is one of the three most influential scientists, accountants and financiers of the twentieth century in the United States (he is one of three U.S. Life Hall of accountants" Fame laureates).

In the middle of last century, William H. Beaver wanted to project an effective five-factor model of bankruptcy forecasting. This is the first quantitative model for forecasting bankruptcy in history.

The matrix system of forecasting bankruptcy on the model of William Henry Beaver, 1963

B - these are the coefficients of Beaver (B - W. H. Beaver), which are expressed as a percentage (for example, 0.62 - must be translated into 62%).

B1 - it is the ratio of net income and the amount of depreciation to the amount of borrowed capital.

B2 - it is the ratio of net income to book value of assets.

B3 - it is the ratio of debt capital to book value of assets.

B4 - it is the ratio of own working capital (shareholders' equity, net of fixed assets sum) to book value of assets.

B5 - it is the ratio of current (mobile) assets to current (short-term) liabilities.

This is the model that get started the search for the best model for predicting bankruptcy. As it can be seen, my dear reader, you may see the W.H. Beaver model is similar to its material and construction to a linear discriminant model, the regression model, and at the same time it looks like a qualitative method (expert defines the differences by himself or herself) and the scoring method (W.H. Beaver, and D. Durand are considered as its founders), and at the beginning of rating system, ....

The next stage of development of predicting bankruptcy science was the publication of the linear discriminant model by Edward Altman.

Analyze the bankruptcy at a rate of Altman

Edward I. Altman and his brother Stuart Altman are respected and renowned economists in the U.S. and in the world. Stuart Altman was born in 1937 and is known as a prominent theorist in the field of health economics. Since the 1970s to early 2000s, he headed various health authorities in the United States. Today, he teaches at the Brandeis University. His younger brother, Edward Altman, was born in 1941. In recent years (from 2002 to 2008), there came in the light the new E. Altman"s works, devoted to the risk of bankruptcy and credit risk in their relationship and interdependence. Since 1963, E. Altman begun to develop a linear-discriminant model to accurately predict bankruptcy. The study ended in 1968 when he was able to develop and test the so-called Z-model. Z-model has proved itself so effective that it is used extensively in the present. The author of this paper has already given an example that, for example, studies of the University of Oxford on the future of Ford, Toyota, General Motors, Chrysler were conducted without the use of financial analysis, and with only two models, E. Altman and G. Springate, with some research of general trends in the stock market and logit analysis of the type (this type of analysis we will discuss later).

Edward Altman suggested a regression equation whose general form is (it is the general form of the equation of Altman):

Z = b 1 x 1 + ......+ b 5 x 5 (293)

It is no accident that I mentioned an expression: "form of the equation of Altman"

in the book came the expression "form of the equation of Altman", because he has developed dozens of models to predict bankruptcy from 1963 to 2012 (the latest model is under its creation for the last decade, and it still has not yet completed). In the present study we shall discuss three main methods of Altman:

1) Analysis of 1968 method.

This is one of the first scientific equations, reflecting the probability of bankruptcy for a certain company. It uses the linear discriminant model. Clipping indicator Z is calculated by the formula (293):

Z = 1.2A+1.4B+3.3C+0.6D+0.999E (294)

Where: A = (working capital) / (total assets)

B = (Retained Earnings) / (total assets)

C = (Operating Income) / (total assets)

D = (Market value of equity shares) / (total liabilities)

E = (Total sales) / (total assets)

To evaluate the results - look at the following table of Altman"s method.

2) Analysis of method of 1972.

This method considers Altman"s coefficient slightly different:

The difference with the above-mentioned model is in the parameter D:

D = (Market value of equity shares) / (total assets)

Z = 1.2A+1.2B+3.3C+0.6D+E (295)

The other parameters are similar to the above calculations:

A = (working capital) / (total assets)

B = (Retained Earnings) / (total assets)

C = (Operating Income) / (total assets)

E = (Total sales) / (total assets)

In the present study I will make an important observation regarding the applicability of the indicator D in this model.

Note: How to adapt the method of Altman for JSC /Joint-Stock Company/ to be applicable for other types of companies: Co. Ltd., Closed corporations, Unitary companies, additional liability societies and JSC that don"t have shares quoted at the market.

Altman technique originally was designed to work only with companies of JSC-form. Even for JSC companies there markets where it is important to estimate the market price of shares, for example, the Russian stock market. The Russian stock market is mostly a path for mergers and acquisitions, rather than a path of market relations. Besides, there are the non-JSC companies. That is why the author of this paper offers to use the sum of the Authorized capital and the additional capital. This technique is motivated as follows: increase in the value of assets leads either to an increase in the authorized capital of an enterprise (this corresponds to an increase of nominal value or additional issue of shares) or to an increase in additional capital (this corresponds to an increase in market value due to increased reliability).

Analyses of the bankruptcy proceedings can be conducted by using the spreadsheets in many programs like MS Excel. The coefficients should be viewed in the dynamics (at least at the beginning of the year and at year-end):

Z (beginning of the year) = 1.2A+1.4B+3.3C+0.6D+0.999E = n

Z (year end) = 1.2A+1.4B+3.3C+0.6D+0.999E = u

If u-n - is a positive number, and the company is not in the area of bankruptcy - it shows a good trend for an enterprise.

Estimates of Z are given in the table below:

Table: The dependence of Z on the probability of bankruptcy

3) Altman's technique of 1983 is estimated differently:

Indicators, according to this method, are similar to the previous models of Altman:

Z = 1.2 * Х1 + 1.4 * Х2 + 3.3 * Х3 + 0.6 * Х4 + Х5 (296)

X1 - working capital / total assets

X2 - retained earnings / total assets

X3 - operating profit / total assets

X4 - the market value of equity shares / total liabilities

X5 - revenue / total assets

For each company there should be considered indicators of the model in the dynamics:

Z (beginning of the year) = 1.2 * Х1 + 1.4 * Х2 + 3.3 * Х3 + 0.6 * Х4 + Х5 = n

Z (year end) = 1.2 * Х1 + 1.4 * Х2 + 3.3 * Х3 + 0.6 * Х4 + Х5 = u

If u-n - is a positive number, and the company is not in the area of bankruptcy - it shows a good trend for an enterprise.

Summary measure of Z can take values in the range [-14, 22]; the companies for which Z> 2.99 fall in the number of financially stable, enterprise, for which Z <1.81 are clearly untenable, and interval [1.81-2.99] is a "gray zone", ie, the zone of uncertainty.

Analysis of methods of forecasting bankruptcy on two-factor model of Altman

This is the simplest method. If you do not have time to apply the bulky models - this technique is the "compact" calculated by the formula (297):

Critical value for a two-factor model of Altman is the value to 0 or higher. If the index is greater than 0 and is moving in the direction of increasing - the probability of bankruptcy in the next 500 days is significant.

Analysis of the model of Gordon Springate

Gordon Springate

Gordon Springate from the beginning wanted to develop a bankruptcy prediction model, which has the same probability of forecasting, as the models of Altman, and having fewer coefficients, and therefore, easier in the calculations. Today, Gordon Springate is a head / in a position of President / of one of the largest business consulting centers in Canada, which was formed with the support of the state. Initially, Mr. Springate developed his model for predicting bankruptcy of industrial companies, and .... The situation is such that it was actively used in agricultural sector. The method is quite effective. As you recall, the model was applied in 2009 at Oxford University in the analysis of the major auto manufacturers. It was applied by Bozeras in 1979, exploring the assets of companies with an average size of $ 2.5 million, showing its effect in 88.0%; it was applied at the same time for large companies by Sands /the assets" saize is in average 63.4 million USD/, showing its efficacy in 83.3%.

Study of the University of Waterloo and the University of Windsor [20], carried out in 2007, showed that among the basic linear discriminant models, the Gordon Springate model has the lowest among the 30 selected by them models class 1 error. Classes of errors in the bankruptcy prediction models are disclosed later.

In 1999/2000, the J. Fulmer and G. Springate models were tested on agricultural enterprises in Hungary [21], and the results showed over 80% accuracy in predicting bankruptcy. It should be noted that both of these models are used extensively in the field of agribusiness.

G. Springate originally created a model that would work well for companies of all sectors of the economy, so if you use all of the above recommendations - that is, if you look the model at the dynamics and analyze the components of the model represented by its coefficients, the model will be a good tool for analyzing the probability of bankruptcy. According to the G. Springate model, Z indicator is:

Z = 1.03*A+3.07*B+0.66*C+0.4*D (298)

Where [22]:

A = (working capital) / (total assets);

B = (Profit before tax and interest (operating profit)) / (total assets);

C = (Profit before tax (= net income + tax value)) / (Current Liabilities);

D = (Revenue) / (total assets).

The rate Z must exceed a critical value of 0.862 a company not to be suspected as a potential bankrupt.

Analysis of the model of John Fulmer, 1984

John Fulmer

John Fulmer - is a Deputy Dean of the Division of Financial Management in business education at the University of Tennessee, USA. In 1966 he received a bachelor's degree at Wofford College. After 4 years, bypassing the master's education, he defended his doctoral dissertation at the University of Alabama on the theme: "Research on the effectiveness of the membership of the Federal Reserve System at private commercial banks", 1970, direction: finance. In his spare time he enjoys golf and moonlights as an economist at the United Methodist Church (a branch of the Anglican Church). John Fulmer is a recognized expert in the field of corporate finance, investment, accounting, financial management, financial statistics (in particular), and banking. Many times he became the best teacher of the year on finance in the U.S. in various categories.

John Fulmer"s model divides the company to potential bankrupts and non-bankrupts. Coefficient V of J. Fulmer models is (299):

Where:

V1 = (Retained Earnings) / (total assets)

V2 = (Revenue) / (total assets)

V3 = (Profit before tax) / (Equity)

V4 = (change in cash balance / total cash flow /) / (Gross Debt)

V5 = (Gross Debt) / (total assets)

V6 = (Current Liabilities) / (total assets)

V7 = log (Tangible non-current assets)

V8 = (Net working capital) / (Gross Debt)

V9 = log ((Earnings before interest and taxes) / (Interest))

Note: log - is a log that basis is 10. Tangible non-current assets are calculated as the sum of non-current assets minus intangible assets.

The critical value for the Fulmer model - it is 0 or below. For up to 1 year prior to bankruptcy, prognostic effect of Fulmer"s model is 98%, and 2 years before bankruptcy - 81% (according to the data of John Fulmer himself).

Research and analysis of Richard Taffler"s bankruptcy prediction models

Richard Taffler teaches finance at the business education department

Richard Taffler

of the University of Manchester, UK. He previously taught for many years at the University of Edinburgh. R. Taffler famously known as an expert in pricing and forecasting trends and changes in the securities market. Currently, Richard Taffler and David Tucket have actively been developing a new concept of market pricing of securities based on the mathematical and the psychological concept of pricing. In 2010, they managed to release the first book, showing the first part of this study. However, we will focus only on the study of the predictive models of bankruptcy within the next 1 - 1.5 years.

Richard Taffler originally wanted to develop a universal algorithm to predict bankruptcy in a way, that with a little research one could adjust the value of the discriminants. Nevertheless, he presented the optimal values of the discriminants for the average company to predict the likelihood of bankruptcy.

It should be noted that for the calculation of this model to analyze the data you need some more companies in the industry in the region to be analyzed. Clipping indicator is calculated as follows:

Т = c0+c1х1 + с2х2 + с3х3 + с4х4,... (300)

Where for a selected company:

x1 = profit before tax / short-term borrowings

x2 = current assets / total liabilities

x3 = short-term borrowings / total assets

x4 = no credit interval Current liquidity Ratio L1 (CR) =

L1 (CR) = (301)

Xn = Other important indicators for the industry

c0, c4 ... - are the coefficients, percentages in parentheses indicate the proportions of the model, x1 measures the profitability, x2 - the state of working capital, x3 - financial risk, and x4 - liquidity.

Richard Taffler presented the average values of the discriminants for general use:

Т = 0 +0.53Х1+0.13Х2+0.18Х3+0.16Х4 (302)

In 1973, Richard Taffler changed X4 rate on:

X4 = revenue / total assets

Т (year beginning) = 0 +0.53Х1+0.13Х2+0.18Х3+0.16Х4

Т (year end) = 0 +0.53Х1+0.13Х2+0.18Х3+0.16Х4

To estimate the probability of bankruptcy one should use the PAS" index.

If PAS"> 50% (model 1970), hence the company's activities is satisfactory, and if less than 50% - it is unsatisfactory.

In 1973, Richard Taffler described in more detail index PAS' (in the model, he changed only factor X4). If PAS' is obtained more than 30%, the company is stable. If PAS' is obtained less than 20%, the company is considered at a potential bankruptcy risk for the next eighteen months.

Research and analysis of bankruptcy prediction models

of Baikal State University of Economics and Law (BSUEL)

Baikal State University of Economics and Law for 80 years is leading the development of economic and legal aspects of management (1930 - 2010). It is located in Russia, the city of Irkutsk. The most cited and, therefore, famous achievement of the University was the R model for predicting the probability of bankruptcy, which was developed in the years when the BSUEL wad just an academy, and its rector was an outstanding scholar Victor P. Ivanitsky (study 1976 - 1987), under whose leadership the R model was released. The ratio R of the model is calculated as follows:

R = 8.38*К1 + К2 + 0.054*К3 + 0.63*К4 (303)

Where:

K1 - working capital / total assets

K2 - the net profit / equity

R3 - revenues from sales / total assets

K4 - net profit / cost integrated

This model should be calculated dynamically, as all previous ones, at least for 1 year:

R (beginning of the year) = 8.38*К1 + К2 + 0.054*К3 + 0.63*К4

R (end of the year) = 8.38*К1 + К2 + 0.054*К3 + 0.63*К4

Note: Too high coefficients of R are often determined by ultra-low rates of included in the coefficients K1-K4 indicators at an enterprise, multiplied then on the whole and fractional numbers. Off-scale model with a high probability testifies the application of the optimization transformation of financial statements - Alexander Shemetev considers; it may cause an abnormal imbalance of "balance".

Analysis of the probability of bankruptcy within 1 - 3 years goes according to the value of the index R of model which is shown in the table below:

Table: The probability of bankruptcy, depending on the rate R

The study of the Belarusian model of analysis of bankruptcy

Belarusian model has been developed by a teacher of Minsk university G.V. Savitskaya in 2003. She studied the activity of 200 agricultural companies of the Republic of Belarus for the period from 1995 to 1998. She found that the activities of agricultural firms lay the most important role to only 5 coefficients.

Model B is calculated as follows:

В = 0.111*X1+13.239*X2+1.676*X3+0.515*X4+3.8*X5 (304)

Each company must consider this factor at the beginning and end of the year:

X1 - working capital / current assets: WC / MobA

X2 - current assets / non-current assets: MobA / ImmA

X3 -revenue from product sales / total assets: Rev/ TBS

X4 - net profit / total assets: NP / TAS

X5 - of equity / total assets: OC(Eq) / TAS

Model is to be looked at the dynamics (at least annually to be reviewed):

В (beginning of year) = 0.111X1+13.239X2+1.676X3+0.515X4+3.8X5

В (end of year) = 0.111X1+13.239X2+1.676X3+0.515X4+3.8X5

* Too high coefficients B can be determined by ultra-low rates included in the coefficients of X1 - X5 by an enterprise, multiplied then on the whole and fractional numbers. Because of this fact, the model is sensitive to the optimization transformations of financial statements that can cause imbalance of the balance sheet - Alexander Shemetev considers.

Table: The probability of bankruptcy by the Belarusian model

Research and analysis of the synthesis technique based on the rate of bankruptcy prediction (RBP) and the model prediction of bankruptcy, based on calculations of the financial needs of an enterprise

The method involves the calculation of the coefficient of bankruptcy prediction (RBP) by the formula:

(305)

The higher is the value of this ratio - the better it is. The threat of bankruptcy for the company comes when it is close to zero or becomes negative.

It is also necessary to calculate separately NWC:

NWC= CURRENT ASSETS - CURRENT LIABILITIES (306)

Where:

NWC - is the Net working capital of an enterprise.

Current liabilities - is, first of all, the 5th section of the balance - Short-term liabilities (loans, accounts payable, payments of dividends, ....).

TBS - is the total balance sheet sum or Grand Total Balance which is equal to the sum of: Total capital and reserves /Equity/; Total long term liabilities; Total current liabilities.

This ratio describes the proportion of net working capital (NWC - net working capital) in the amount of the assets in balance. The higher the value of this factor - the better! The lower is the overall business risk.

You should also calculate the coverage ratio of current financial needs.

Thus, the coverage ratio of current financial needs (CFN) is calculated by the formulas:

Operational CFN = Inv + AR - AP (307)

(308)

Just do not forget, please, to recalculate the operational CFN in the same units as the average daily turnover in revenue. This means that the coverage ratio of CFN you"ll get expressed in days. Take the number of days and calculate the percentage by the proportion method that ranges from 365 days, ie, from 1 year.

Where: AR - accounts receivable; AP - accounts payable; Inv - Inventories.

There are some options:

a) COFCFNCOVERAGE = 25%

One quarter company operates on its creditors (the banks and private lenders);

3 quarters the company is profitable to its owners.

b) COFCFNCOVERAGE = 50%

180 days company works for its creditors (the banks and private lenders);

180 days the company is profitable to its owners.

c) COFCFNCOVERAGE = 100%

Company operates primarily "for the others" without generating income to its owners. The company operates as a sponsor for its creditors.

d) COFCFNCOVERAGE = 150%

The company operates in a large loss; it maintains its creditors!

One should be very careful when analyzing the bankruptcy in this case, because each company has its individual specific features as well as the specifics of its functioning is unique. In overall, the next options in the analysis of bankruptcy are available at this technique:

Table: Forecasting of bankruptcy by this method

So, any financial analysis should be followed by studying a company from the inside! It is necessary to collect additional information about each company under an analysis!

Model of Robert Liss

Robert Liss"s model is used for private and public companies with illiquid shares. Cut-off Z point is calculated as follows:

Z= 0.063 *Х1 + 0.092*Х2 + 0.057*Х3 + 0.001*Х4 (309)

X1 = Working Capital / Assets

X2 = (Operating income + Depreciation) / Assets

X3 = Retained Earnings / Assets

X4 = Owned capital (Equity) / Debt capital

Z (cut-off point) = 0.037 or less.

Model of Silvia Horvathova, Pavol Olejnik and others, Czech Republic, Lithuania and Slovakia, 2008/2009

Silvia Horvathova and Pavol Olejnik (National University of Lithuania and the University of Prague) in 2008 developed their own model of a rapid assessment of the probability of bankruptcy based on a comprehensive analysis of linear discriminant models in their practical application.

Analysis of Olejnik-Horvathova is carried out in accordance with the following matrix:

Matrix of Olejnik-Horvathova for bankruptcy predicting

Where: O-H1 - is a figure equal to the ratio of net book value (NBV) to book value of assets (TBS):

(310)

NBV is equal to the book value of assets net of borrowings and debts.

O-H2 - is a measure of payback of debt, expressed in years:

(311)

Where: BC - is a borrowed capital at the date of the data cut; PBT(YEAR) - is the sum of operating profit for the year.

O-H3 - is the ratio of net cash flow for the period (NCFP) to the carrying amount of production issued during the period (PDP).

(312)

O-H4 - is the ratio of operating profit to book value of assets (ROA, return on assets):

(313)

Professor Eva Kislingerova

On the basis of factors data received by P. Olejnik and S. Horvathova, the team of authors" researches: D. Baran, A. Palfy, Z. Chvancharova, P. Olejnik, S. Horvathova, K. Zalai, J. Shnircova, L. Kalafutova, P. Ruchkova, E. Kislingerova and other, - they developed a linear discriminant model and its explanation for forecasting bankruptcy on the basis of the index of financial stability IFS (314):

Where: X1 - is the ratio of cash flow to debt capital;

X2 - is the ratio of book value of assets to debt capital;

X3 - is the ratio of operating profit (PBT) to book value of assets;

X4 - is the ratio of operating profit (PBT) to book value of production issued for the period (PDP);

X5 - is the ratio of inventories to the book value of assets;

X6 - is the ratio of PDP to the book value of assets.

If the indicator has turned out more than 3, it indicates the maximum level of financial stability and a low probability of bankruptcy.

If the indicator has turned out between 2 and 3, it indicates a high level of financial stability and minimal probability of bankruptcy.

If the indicator has turned from 1 to 2, then it shows good financial stability and a low probability of bankruptcy.

If the indicator has turned from 0 to 1, then it indicates a satisfactory financial strength and the presence of a number of problems that can cause failure in the long run.

If the indicator has turned from -1 to 0, this indicates the latent stage of the company's bankruptcy.

If the indicator has turned from -1 to -2, it indicates a high probability of bankruptcy in the next 2 years.

If the indicator has turned from -2 to -3, it indicates a high probability of bankruptcy within a year.

Research and analysis of Ooghe-Verbaere model for industrial companies

This model is designed for industrial enterprises.

This is a predictive model. For example, if the period - is 2011, the calculation-prediction is provided for 2012, 2013 and 2014. It is used mostly for industrial enterprises.

The authors of this model suggested that the fundamental concept that if the company has problems with financial assets and cash - it is very likely to leave the market within a year; if the enterprise has serious problems with the production and marketing of products - it is a high probability of leaving the market in within the next 2 years; if the enterprise has trouble with finding new investment projects, it is very likely to leave the market within three years or more! So we have three models of bankruptcy:

1) Model of 1 year prior to bankruptcy - is a financial model of bankruptcy. They take financial indicators for the analysis of bankruptcy.

2) Model for the 2 years prior to bankruptcy - is operating (production) model.

3) Model of 3 years prior to bankruptcy - it's investment model.

For each year, there is a point of clipping and its own financial ratios.

This model helps to consider: where the company is currently and what the future awaits it if the current trends in development have been preserved.

A feature of this model is that it takes into account problems with finances (for 1 year before bankruptcy), problems with production (up to 2 years prior to bankruptcy), problems with the investment (for 3 years before the bankruptcy). There are selected individual factors and created the individual models to calculate the probability of insolvency (bankruptcy) for each such issue. The higher is the value of Z in this model, the lower is the risk of insolvency for an enterprise.

Models to predict the probability of bankruptcy by the model of Ooghe-Verbaere are as follows:

1 year prior to bankruptcy model:

Z1 = 2.6803 - 51.3394X1 + 10.087X2 + 4.4145X3 + 2.0318X4 + 2.6314X5 (315)

Where: Z - is the cut-off point, which shows the probability of bankruptcy within the next 1 year;

X1 - is the ratio of short-term debt repayable in the first place, to the total short-term debt;

X2 - is the ratio of total profits to total debt;

X3 - is the ratio of earnings before taxes and interest to total assets;

X4 - is the ratio of equity to total debt;

X5 - is the ratio of cash to current assets.

Cut-off point value = 3.1492 (and less).

2 years prior to bankruptcy model:

Z2 = 0.1837 + 4.6524X1 - 16.5456X2 + 3.2732X3 - 1.7381X4 + 0.0738X5 (316)

Where: Z - is the cut-off point, which shows the probability of bankruptcy within the next 2 years;

X1 - is the ratio of total profits and retained earnings to total debt;

X2 - is the ratio of short-term debt repayable in the first place, to the total short-term debt;

X3 - is the ratio of cash to current assets;

X4 - is the ratio of stocks of finished products to the operating assets;

X5 - is the ratio of cash flow to revenue from sales.

Cut-off point value = 0.1663 (and less).

3 years prior to bankruptcy model:

Z3 = 0.2153 - 18.3474X1 + 3.3847X2 + 2.3601X3 - 1.9230X4 + 0.0617X5 (317)

Where: Z - is the cut-off point, which shows the probability of bankruptcy within the next 3 years;

X1 - is the ratio of short-term debt repayable in the first place, to the total short-term debt;

X2 - is the ratio of total profits and retained earnings to total debt;

X3 - is the ratio of cash to current assets;

X4 - is the ratio of stocks of finished products to the operating assets;

X5 - is the ratio of net profit to total equity capital and long-term debt.

Cut-off point value = 0.3355 (and less).

Dear entrepreneur, please, take this method into your arsenal. It is very reliable and sensitive to the risks. Try to calculate each your investment project.

And as often as possible use the count on this method, so your could always keep a "finger on the pulse" of your company.

There is a trend in practice of financial management of a company. If a company found serious problems with finances - it is a factor that indicates a high risk of bankruptcy within one year! If an enterprise has serious problems with the production - it indicates a high risk of bankruptcy within the next two years. If there are difficulties in the company with investments in exploration and development of new investment projects, there is a high risk of bankruptcy of the enterprise over the next three years.

And if the company was formed the whole complex of problems at the same time, it significantly increases the risk of a state of complete insolvency (bankruptcy) of such enterprise in the near future.

The author of this paper has created for you, my dear reader, a matrix system that reflects the Ooghe-Verbaere concept; fill this matrix with your data, that is, with the data of company that interested you for the analysis, and you will clearly see what are the key components of potential and real risk for your company.

All the three models of bankruptcy are represented in this matrix system. Each of these models has the coefficients that values should be included into the matrix system. The end values of models should be fixed in their dynamics in the matrix system.

When you carefully examine the matrix system, also pay attention to the chart - the scheme created by the author of this paper, to the best imagery and perception and memorization of all the model of bankruptcy prediction of Ooghe-Verbaere.

The matrix system of forecasting of bankruptcy by the method of Ooghe-Verbaere

Diagram: Models for the prediction of bankruptcy by the Ooghe-Verbaere model:

Conan-Holder model (C&H)

This model describes the probability of failure for different values of the C&H index. The C&H index values are presented in table:

Table: Value of the C&H index

The C&H index is calculated as follows:

KG=-0.16X1-0.22X2+0.87X3+0.10X4-0.24X5 (318)

Where:

X1 - Is the share of liquid assets quick for realization in the total assets" sum;

The quick for realization liquid assets are cash, short-term financial investments, short-term accounts payable (less than 1 year of maturity).

X2 - Is the share of sustainable sources of financing in the balance liabilities (total debt);

The sustainable sources of financing in the balance are equity capital plus the sum of long-term borrowings and credits (the long-term deferred liabilities and similar passives are not included into the sustainable sources of financing).

X3 - is the ratio of financing costs to net revenue from sales;

The financing costs are: income tax sum plus the sum of paid interests for a certain period of time.

X4 - is the proportion of staff costs to gross income

The staff costs is the sum of all salaries paid to staff for a certain period of time.

X5 - is the ratio of retained earnings to total debt.

Next to it, I offer you to consider the Alexander Shemetev"s model that collects the 42-years experience of study of the problems of forecasting bankruptcy.

Working-out the self-model of Alexander Shemetev for firms" bankruptcy forecasting based on synthesis of 42-years experience of Ghent University

Sofie (Sofia) Balcaen

Hubert Ooghe

Hubert Ooghe and the Sofie Balcaen - are of the most famous professors of Belgium. They teach and conduct research at the University of Ghent in Belgium. Their range of interests - bankruptcy of commercial companies.

Hubert Ooghe and Sofie Balcaen at the Ghent University in Belgium carried out a series of studies towards the applicability and inapplicability of the basic methods of bankruptcy forecasting. They managed to comprehensively analyze the applicability and inapplicability of the basic techniques of forecasting bankruptcy. As a result, they smashed all the errors contained in the models, in which they identified two types of error: the so-called errors of type 1 and type 2 errors.

They studied the existing methods of bankruptcy forecasting models like: W.H. Beaver 1967, E. Altman 1968, the methodology of Co (Japan, 1982), the method of Fisher (Germany, 1981), the R. Taffler and G. Tishaw methodology (Britain, 1977), technique of E. Altman (1974, France), a technique of Fernandez (Spain, 1988), Swanson and others methodology (Argentina, 1988), E. Altman and P. Narayanan technique (1997), H. Ooghe and E. Verbaere technique (Hungary, 1982), H. Ooghe, P. Joos and De Vos D. technique (Belgium, 1991). In addition, they examined a number of scoring and rating techniques to predict bankruptcy: E. Altman (1993), Bella (1990), P. Joos, H. Ooghe and others (1998), the Kankaanpää-Latirena methodology (1999) and other methodologies. They also examined a number of models to predict bankruptcy, which have no classification features of basic types of bankruptcy prediction models, such as a model of Mossman (1998).

Hubert Ooghe, Sofie Balcaen, as well as some other scientists within over 20 years have been investigating the applicability and inapplicability of the various models and methods of forecasting the companies' bankruptcy in different countries. As a result, there were selected a number of models to predict on maximum the probability of bankruptcy. Then they managed to fix several Class 1 and Class 2 bugs for these models, so that the probability of bankruptcy prediction of each model was from 91% to 96%. The authors propose to conduct a study of bankruptcy based on their models which were adapted by them among the best models to predict bankruptcy.

Hubert Ooghe and Sofie Balcaen believe that the company is bankrupt, depending on the failure of three main cycles of activity. First failure cycle makes the investment cycle breakdown - this model predicts failure of up to 3 years before bankruptcy. Then, the second failure cycle makes an operating cycle breakdown - the model predicts failure of up to 2 years before bankruptcy. After this, failure goes to financial cycle by making its breakdown - this model predicts the failure of up to 1 year prior to bankruptcy.

The author of this paper made a research to complete this Ghent university study so it could forecast bankruptcy on the basis of all the Ghent University"s research experience without concentrating on some unique model. The author of this paper also reviewed the components of the Ghent"s university research so it to be applicable for the cases when it is unknown whether the primary financial data is clear or is transformed for making some optimization of company"s activity performance. On the one hand, such interpretation makes the model applicable in the normal occasions, on the other hand, it makes the abnormal occasions comparable with the normal ones.

The most promising models, in the opinion of H. Ooghe and S. Balcaen, are next: a model of E. Altman (1968, USA), Bilderbeek Model (Amsterdam, 1979), Ooghe-Verbaere Model; Christine Zavgren"s Model (1985, USA); Gloubos-Grammaticos logistic-discriminant analysis (Greece, 1988); K. Keasey - P. McGuinness Model (1990, England); P. Joos, H. Ooghe, De Vos D. Model (1991, Belgium).

Each model is re-formatted by H. Ooghe and S. Balcaen and other scientists so that they can now predict the bankruptcy of all three cycles: the investment (3 years prior to bankruptcy), operational / production / (2 years prior to bankruptcy), financial (1 year prior to bankruptcy).

Among the countries that fell under the action of models: there were several Russian companies, companies in the U.S., in Britain, in Germany, in Belgium and in other countries. Total models were tested on tens of thousands companies around the world.

Authors of Ooghe-Balcaen technique had also examined the types of errors in the bankruptcy prediction models, and they concluded that all the errors in the bankruptcy prediction models can be divided into two types: type 1 and type 2.

Type 1 errors related to incorrect assessment of "credit risk", when a firm is classified as a bankrupt, - when company is not bankrupt.

Type 2 errors are related to "commercial risk", when a not-bankrupt-firm goes to be classified as a bankrupt.

I will write an analysis for each model under the old and the updated variant. So let's start to consider them.

I) E. Altman's Z-component in the Ooghe-Balcaen model

1) The "old new" method of E. Altman in 1968, the United States.

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy:

(319)

Dear reader, if you are not against it, let use my Russian book numeration in the formulas. So, the beginning of the numeration will be from 319 equation (it is in the beginning of my book in Russian).

For all models: X1 - is the ratio of NWC: Net working capital (current assets minus current liabilities) to total assets (TAS)

(320)

X2 - the ratio (amount of profit / loss during the reporting period (P/L) and retained earnings of previous years (REPY)) to total assets (TAS):

(321)

X3 - a measure of profitability. The numerator is earnings before taxes and interest / EBIT /, at least equal to the sum of operating profit (PBT - Profit Before Taxes), plus the interest paid (070 line (070) in the profit and loss account plus oversized interests (%%), interest that cannot be attributed to the 070 line / for example, the rate of more than 12.75 - from late 2010 to early 2011/). The denominator is the book value of assets (TAS):

(322)

X4 - a ratio of the cost of equity capital (OC(Eq)) to total liabilities (TL):

(323)

X5 - is the ratio of revenue (Rev) to total assets (TAS):

(324)

The critical point of the model - is +0.0229 or less.

b) Model of operating cycle crisis: two years prior to bankruptcy (325):

The coefficients X1 - X5 - are defined in the previous model of bankruptcy.

The critical point of the model: +0.0221 or less.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (326):

The coefficients X1 - X5 - are defined earlier.

The critical point of the model: less than +0.0190.

2) A new method of E. Altman 1968, the U.S.

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (327):

The coefficients X1 - X5 - are defined earlier.

The critical point of the model: less than +0.0574.

b) Model of operating cycle crisis: two years prior to bankruptcy (328):

The coefficients X1 - X5 - are defined earlier.

The critical point of the model is: - 0.1203, where "-" - is a minus sign.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (329):

The coefficients X1 - X5 - are defined earlier.

The critical point of the model was: - 0.1757, where "-" - is a minus sign.

The results of testing this model (old and new).

When testing revealed 6% error of class 1 and 3% error class 2 (an additional 5% error) in predicting bankruptcy in '01 before the failure.

When testing detected 28% of the errors of class 1 and 6% of the errors of class 2, and 17% additional error in predicting bankruptcy through the operating cycle crisis.

When testing detected 52% of the errors of class 1. Other classes of errors were also found.

The purpose of the model: the prediction of economic bankruptcy under the court decision.

Forecasting Object and Conditions: large industrial enterprises, predicting the probability of bankruptcy through the court procedure. The method predicts bankruptcy, depending on the industry and asset structure.

Type of analysis: linear discriminant analysis.

The number of species of the technique: 5.

Primary sample period for the analysis of the original model: the company for 1946 - 1965 years (19 years).

The Altman"s models calculation is just the very beginning of the Ghent university (Ooghe-Balcaen model) complex models study. The second element of the model is the adjusted J. Bilderbeek model (Amsterdam, The Netherlands, 1979).

II) J. Bilderbeek Z(B) component (Amsterdam, The Netherlands, 1979) in a model of Ooghe-Balcaen

1) The "old new" J. Bilderbeek model, 1979

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (330):

For all models: X6 - a net gain or net profit / NP / (after tax) in relation to equity capital (OC(Eq)):

(331)

X7 - the ratio of accounts payable (AP) to revenue (Rev):

(332)

X5 - was discussed earlier, in the models of Altman (Rev / TAS).

X8 - the ratio of gross value added (GVA) in total assets (TAS). Please note that GVA - a value added created during the reporting period, which represents the difference between the revenue (Rev) and the cost of raw materials and services from third parties. It is believed that GVA is allocated to salaries, dividends, interest, and so on. GVA - a term of management accounting. GVA shows the value of the product on a book or other fair value less than cost of raw materials, as well as direct works and services cost required for the production. As applied to Russian account, this figure can be regarded as Revenue - Cost. Revenue should be adjusted by the amount of revenues and expenses not related to production activities of the company directly: transaction, interest, non-operating and so on, which under the accounting policies are projected through the revenue. Thus, we expect revenues from primary production activities, to then deduct the cost of production. Thus, the index is equal to X8:

(333)

X2 - the calculation of this indicator is shown in a model of Altman:

(334)

The critical point of the model is: less than - 0.4955, where "-" - is a minus sign.

b) Model of operating cycle crisis: two years prior to bankruptcy (335):

The coefficients X2, X5, X8, X7, X6 - are explained earlier.

The critical point of the model is: less than - 0.8523, where "-" - is a minus sign.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (336):

The coefficients X2, X5, X8, X7, X6 - are explained earlier.

The critical point of the model is: less than - 1.5495, where "-" - is a minus sign.

2) A new J. Bilderbeek technique, 1979

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (337):

The coefficients X2, X5, X8, X7, X6 - are explained earlier.

The critical point of the model is: less than - 0.0737, where "-" - is a minus sign.

b) Model of operating cycle crisis: two years prior to bankruptcy (338):

The coefficients X2, X5, X8, X7, X6 - are explained earlier.

The critical point of the model: more than + 0.4924. When this figure is taken more, it mostly matches to reveal facts of primary data discrepancies to make the firm within the selection comparable.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (339):

The coefficients X2, X5, X8, X7, X6 - are explained earlier.

The critical point of the model is: less than - 0.2145, where "-" - is a minus sign.

The results of testing this model (old and new).

In the Bilderbeek model 1 year before the bankruptcy the type 1 and 2 errors were found, and there is not a typical forecasting error of 32% for certain types of companies.

In the 2-years-prior-to-failure-model, the same error of class 1 and 2 were found, and there is not a typical forecasting error of 27% for certain types of companies.

In model 3- years-prior-to-failure-model, the same error of class 1 and 2, and there is not a typical forecasting error of 29% for certain types of companies.

The purpose of the model: prediction of economic bankruptcy by court decision.

Forecasting Object and Conditions: Dutch companies, mainly in Amsterdam. Scope: Industry and Trade.

The number of species of the technique: a method for the parent plus 5 sub-methods, based on two subsidiary methods.

Type of analysis: linear discriminant analysis.

Primary sample period for the analysis of the original model: the company for 1950 - 1975 years (25 years).

III) The Ooghe-Verbaere (OV) component in the Ooghe-Balcaen model

Eric Verbaere

Eric Verbaere - is a well-known financial consultant and professor at the Ghent University, Belgium. For many years he worked with Hubert Ooghe, investigating the causes of failures in the companies. In particular, E. Verbaere is a specialist in industrial companies. The results of his research for many years are being used worldwide in predicting the bankruptcies.

1) The "old new" Ooghe-Verbaere model in the Ooghe-Balcaen model

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (340):

In Ooghe-Verbaere models: X9 - is the amount of late /overdue/ payment of taxes (LPT) and the outstanding payments to social contributions (OPSC) with respect to short-term liabilities (STL). Outstanding amount is taken as a whole for the period, regardless of their maturity"s following facts:

X16 - a ratio of profit / loss after tax (NP) and retained earnings (RetY) of the past to the sum of equity capital (OC(Eq)) and liabilities (TL):

(342)

X13 - is the ratio of cash (MF) and direct cash equivalents / short-term investments (STI) / (MF + STI) to the sum of current / mobile / assets (MobA). STI express the amount of ready money, of "almost money" that can be quickly used to pay the arising liabilities.

(343)

Note: Please note that in Russian accounting practice you will have to deduct the sum of the long-term accounts receivable from the mobile assets.

X14 - the ratio of the cost of: production in progress (PPC), finished goods and goods for resale (FG&GR) and goods shipped and dispatched (SDG) to the sum of net working capital (NWC = MobA - STL):

(344)

X17 - a measure of the total return on permanent capital. The numerator is earnings before taxes and interest / EBIT /, at least, it is equal to the sum of operating profit (PBT), plus the interest paid (070 line in the profit and loss account plus (070), plus oversized percent to pay (%%): an interest that cannot be attributed to the 070 line / for example, the rate of 12.75 and more - from late 2010 to early 2011 in the Russian accountings/). The denominator is the sum of equity capital (OC(Eq)) and long-term liabilities (LTL).

(345)

The critical point of the model is: les than - 0.2047, where "-" - is a minus sign.

b) Model of operating cycle crisis: two years prior to bankruptcy (346A):

Where coefficients: X9, X13, X14 - are described in the previous model.

X10 - The ratio of total profit or loss (NP) to the sum of equity capital (OC(Eq)) and liabilities (TL):

(346)

X15 - the ratio of cash flow (CF) to revenue (Rev). CF - is the difference between the amount of income and the amount of payments for a company for a certain period. The net balance of cash flow at the beginning and end of the period is equal to the sum of money (MF): in the event when company is successful, it must comply with minimum balance of net cash flow.

(347)

The critical point of the model is: less than - 0.2497, where "-" - is a minus sign.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (348):

Where: X11 - Gross yield (GY) before taxes in relation to total assets (TAS). GY - is an expressed in units of currency income from all assets before taxes and certain special payments (usually it relates to the payment of various court-appointed trustees, arbitrage anti-crisis managers and the other such-like special-purposes-equipped-staff). The concept of GY is close to the concept of PBT, as in the GY model the indicator is considered after the payment of interest and before taxes.

(348A)

X12 - the ratio of equity capital (OC(Eq)) to the sum of equity capital (OC(Eq)) and total liabilities (TL).

(349)

The odds X9, X13, X10 have been described previously.

The critical point of the model: less than +2.0996.

According to Hubert Ooghe, E. Verbaere and Sofie Balcaen opinion, the model of Ooghe-Verbaere to be altered in accordance with more modern trends of economic development. For present purposes, they conducted a large study resulted in the updated model of Ooghe-Verbaere.

2) A new Ooghe-Verbaere technique, 2002.

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (350):

Where: The coefficients X9, X16, X13, X14, X17 - have been explained earlier.

The critical point of the model is: less than - 0.4459, where "-" - is a minus sign.

b) Model of operating cycle crisis: two years prior to bankruptcy (351):

Where: The coefficients X10, X9, x13, X14, X15 - are explained earlier.

The critical point of the model is: less than - 0.3420, where "-" - is a minus sign.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (352):

Where: The coefficients X9, X10, X11, X12, X13 - are explained earlier.

The critical point of the model is: less than - 0.4515, where "-" - is a minus sign.

Results of Ooghe-Verbaere model probation (both old and new models).

Ooghe-Verbaere model was developed in Belgium for the evaluation of companies of Belgium, that is, according to the decoded full accountability data. Current research has shown that the old method gives good results in predicting bankruptcy.

Sample period for the old model was relatively small - from 1977 to 1980 (3 years). However, the size of the companies sample was essential. Ooghe-Verbaere model including sampling of all companies of all industries, not specializing in any particular sector of the economy. Ooghe-Verbaere studies led to the creation of another 5 models with different coefficients and discriminants, including 1 model for industrial companies. The new Ooghe-Verbaere model is also intended for use in all sectors.

The method is designed to predict not only the bankruptcy through the court decision, and also the bankruptcy, which had actually the place to be in court, and the company had managed to come to a peace settlement, or the company was able to pay off the debt during the procedures.

Model type: linear discriminant analysis.

IV) The Christina Zavgren model component (1985, USA) in a model of Ooghe-Balcaen

Analysis of C. Zavgren - this is not idle linear discriminant analysis, and the regression analysis method such as logit subspecies of logistic regression.

Doctor of Economics, Christina B. Zavgren was born in 1948 in the United States. She lives in New York. It starts from that point, the models to predict bankruptcy in less than 3 - 5 years term - have nothing positive to bring for a company. In her view, the current perspective is too short, and the company has no way to restore the activity to normal levels, if it is only left to the bankruptcy 1 or 3 years! C. Zavgren compares herself linear discriminant methods, and regression studies to predict the likelihood of bankruptcy with the "crystal ball". Banks, third-party companies, the authorities concerned and the company itself from the inside when conducting such an analysis, it seems to test the balls for whether they are made of crystal or not! If so - then the company with a high probability can "break" due to abrupt changes in the environment of company existence. In this case, the company should know that it is made of "crystal" in advance, so it would have time enough to rebuild the "substance" of internal existence on something more solid! According to C.B. Zavgren, the first cause of failure of all the companies is too high concentration of debt. The second - is the decline in equity markets. The third reason for failure is excessive investment to inventories, which are logically instead of investment in the renewal of fixed assets, which would extend the company 'life' and make it more successful over the time at the competitive market.

All the indicators Z of all models of C. Zavgren to be given further - this is not the individual linear discriminant model, and the degree of the function Z-Logit. All models have the next index (U):

(353)

Where: e - is the exponent - a figure equal to 2.718281828. The exponent e in the Logit type analysis is always raised to the power z, equal to the total linear discriminant function Z:

(354)

Where: a0 - a free term of regression, a1, a2, a3, ...., an - is a linearly discriminants of discriminant analysis such as Logit. x1, x2, x3, ..., xn - this are the financial ratios that are included in the model.

Author will no longer describe the Christina Zavgren model"s U component, and I will describe only the Z component of the linear-discriminant-function, knowing that the outcome of the function Z - is the degree to which one should raise the formula to receive the U indicator.

1) The "old new" Christine Zavgren model in the Ooghe-Balcaen model

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (355):

Where for all the Christine Zavgren"s models: X18 - is the ratio of inventories (Inv) to the sum of the company's revenues (Rev):

(356)

X19 - is the ratio of accounts receivable (AR) to inventories (Inv):

(357)

X20 - is the sum of money (MF) and short-term investments (STI) to company"s book value (TAS):

(358)

X21 coefficient is a measure of instant liquidity of the company. The numerator of full instant liquidity is: MF plus STI plus instantaneous to claim amount of AR (ITCAAR). In the denominator there are the short-term and instant liabilities: if we shall call them the P1 and P2 where P - is passives, 1 - the most instant liabilities, 2 - short-term liabilities, than the denominator can be expressed as next. P1 - it would be the accounts payable (AP), indebtedness to the owners (shareholders), debts that were not covered in time. In Russian accountings, for instance, these would be line codes 620, 630 and 670 OKUD in the Balance sheet form. P2 - it would be the short-term liabilities: credits and loans with term less than 12 month; in Russian accounting accountings these would be line code 610 OKUD in the Balance sheet form.

(359)

X6 - a net gain (after tax) / NP / in relation to equity capital (OC(Eq)):

(360)

X5 - is the ratio of earnings (Rev) to total assets (TAS):

(361)

X22 - a measure, the numerator of which is the amount of deferred income (DefIn), and accrued obligations (AcrO). DefIn - complies with the Russian accounting standards, that is, it is income received in this period and relating to the next. AcrO - is the amount of accrued liabilities and expenses to be paid before the end of the reporting period, and the fact of payment does not take place to be at a certain moment. In the Russian account of these concepts corresponds to the sum of short-term borrowings (STL). The denominator is the sum of equity capital (OC(Eq)):

(362)

The critical point: less than +0.1829.

b) Model of operating cycle crisis: two years prior to bankruptcy (363):

The coefficients X18, X19, X20, X21, X6, X22, X5 - are described earlier.

The critical point: less than +0.0672.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (364):

The coefficients X18, X19, X20, X21, X6, X22, X5 - are described earlier.

The critical point: less than +0.4340.

2) A new method of Christine Zavgren, 2001.

Ooghe-Balcaen overestimated values of the coefficients for the specified method.

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (365):

The coefficients X18, X19, X20, X21, X6, X22, X5 - are described earlier.

The critical point: less than +0.7233.

b) Model of crisis operating cycle: two years prior to bankruptcy (366):

The coefficients X18, X19, X20, X21, X6, X22, X5 - are described earlier.

The critical point: less than +0.7371.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (367):

The coefficients X18, X19, X20, X21, X6, X22, X5 - are described earlier.

The critical point: less than +0.9150.

Data on testing of the model is next. Christine Zavgren"s model was developed in the United States. C. Zavgren comparing two simultaneous flow of financial information: data from the stock market and received from the financial statements" data. All the data she collected on magnetic tape and processed by computer. C. Zavgren made a large sample of companies in the period from 1972 to 1978. The concept of bankruptcy is next. C. Zavgren interpreted Articles 10 and 11 of the Law on Insolvency (Bankruptcy) in the United States, that is, that the bankruptcy term is applicable for companies that had undergone external control and bankruptcy proceedings.

Instead of linear discriminant analysis, C. Zavgren used a close method of logistic regression constructing.

The model was very popular in the U.S. and has 05 subsidiaries models.

Next it will be considered other bankruptcy prediction models included in the Ooghe-Balcaen model.

V) Gloubos-Grammaticos model (1988, Greece)

The main author of the model is Theohari Grammaticos (03.01.1954-present). Born in Greece, studied in New York, in the New York University, where he earned a bachelor's degree with honors (1976), Master of Finance (1980) and Ph.D. /finance/ (1982). In New York, he had the publication of his most significant research in the forecasting of trends in the securities market and prediction of bankruptcy, including the famous bankruptcy prediction model, known by many of today's leading economic and financial experts of the world as one of the 3 - 5 best models to predict bankruptcy. Today, he moved to Luxembourg, and he has served as co-director of the European Investment Bank where he worked from 1990 to the present, and he teaches corporate finance at the University of Luxembourg since 2009.

Globos-Grammaticos model consists of two parallel types of analysis: linear discriminant analysis and logistic regression.

1) The "old new" Gloubos-Grammaticos model (GG)

1.1) The method of linear discriminant analysis

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (368):

The coefficients X1 and X14 were discussed earlier.

X23 - this is the current liquidity ratio. In simple term, it is the sum of current assets (MobA) in relation to short-term liabilities (STL):

(369)

X24 - is the ratio of long-term liabilities (LTL) to total assets (TAS).

(370)

X25 - a relationship of EBITDA to total current liabilities. EBITDA - Earnings Before Taxes Depreciation and Amortization - the sum of earnings before interest, taxes, depreciation and maintenance for fixed assets. It corresponds approximately to the Russian practice of accounting operating profit (PBT) plus interest expense (code line 070 in the profit and loss account, the form number 2 on OKUD (070)) plus non-legislative interest (interest in excess of, dependent on the refinancing rate, which can be attributed at 070 line in Form number 2 in OKUD (%%)) plus depreciation (Am) (code line 140 from form number 5 on OKUD / Annex to the Balance Sheet / Line: depreciation of fixed assets, total).

(371)

The critical point: less than +2.5515.

b) Model of operating cycle crisis: two years prior to bankruptcy (372):

Odds X23, X1, X24, X11, X25 - are explained earlier.

The critical point of the model: less than +2.2070.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (373):

Odds X23, X1, X24, X11, X25 - are explained earlier.

The critical point of the model: less than +2.2441.

1.2) The method of logistic regression logit / LOGIT / GG

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (374):

Where e - is the exponent equal to 2.71828183 always. Exponent is raised to the power function. Let's look at a specified power in details:

(375)

This function is a mathematical function such as logistic regression called logit.

The coefficients X1, X11 and X24 have been explained earlier.

The critical point of the model: less than +0.9573.

b) Model of operating cycle crisis: two years prior to bankruptcy (376):

The model constants are not changing - the critical point is changing.

The coefficients X1, X11 and X24 have been explained earlier.

The critical point of the model is: +0.9848 / if at the same time more than +0.9573 - it speaks of a crisis in operating cycle /.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (377):

The model constants are not changing - the critical point is changing.

The coefficients X1, X11 and X24 have been explained earlier.

The critical point of the model: less than +0.9444.

2) A new Gloubos-Grammaticos model (GG)

2.1) Linear discriminant analysis in GG model

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (378):

Odds X23, X1, X24, X11, X25 - are explained earlier.

The critical point of the model was: - 0.0043, where "-" - is a minus sign.

b) Model of operating cycle crisis: two years prior to bankruptcy (379):

Odds X23, X1, X24, X11, X25 - are explained earlier.

The critical point of the model is: - 0.0006, where "-" - is a minus sign.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (380):

Odds X23, X1, X24, X11, X25 - are explained earlier.

The critical point of the model is: - 0.0033, where "-" - is a minus sign.

2.2) The method of logistic regression logit / LOGIT / GG

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (390):

Let's look at a specified power in detail:

(391)

The critical point of the model: less than +0.8142.

b) Model of operating cycle crisis: two years prior to bankruptcy (392):

The critical point of the model: less than +0.8142 (the same as the previous one).

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (393):

The critical point of the model: less than +0.8138.

VI) Model of K. Keasey and P. McGuinness (1990, 2009, UK)

The model uses the Keasey-McGuinness KM index:

(394)

In the future, the Z indicator calculation will be analyzed, understanding the KM index is taken into an account yet.

1) The "old new" Keasey-McGuinness model

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (395):

Where: Bull figure X21 is already discussed - it is a measure of instant liquidity.

X26 - a relationship of raw materials and similar values (RM) to the amount payable (AP):

(396)

X27 - the ratio of operating profit (PBT) to the amount of revenue (Rev):

(397)

Critical rate: less than +0.1387.

b) Model of operating cycle crisis: two years prior to bankruptcy (398):

X1, X6 - have been described previously.

X18 - is the ratio of inventories (Inv) to the sum of the company's revenues (Rev):

(399)

X28 - the ratio of net profit (NP) to the sum of operating assets (OPA). OPA - this is the company's assets that are directly involved in the main production activity: inventory, rearers and fatteners, work in progress, finished goods, equipment, buildings, accounts receivable, in particular, from buyers and customers. Sometimes there are to be included some other similar assets of that key.

(400)

The critical point: less than +0.0131.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (401):

Odds X4, X26, X27 - are described earlier.

The critical point: less than +0.7939.

2) A new Keasey-McGuinness model

a) Model of the crisis of the investment cycle: 3 years prior to bankruptcy (402):

All the coefficients are explained above.

The critical point: less than +0.1387.

b) Model of operating cycle crisis: two years prior to bankruptcy (403):

Indicators X18, X1, X28, X6 are described previously.

The critical point: less than +0.7853.

c) Model of the crisis of the financial cycle: 1 year prior to bankruptcy (404):

All figures are interpreted earlier.

The critical point: less than +0.8980.

VII) A model of P. Joos, De Vos D. and Ooghe-Balcaen under development

The authors of the model: Hubert Ooghe, Sofie Balcaen, Jan Kamerlink and others. Unfortunately, this model is still being finalized. The authors of the methodology on the one hand, correct discriminants, on the other hand, analyze the results of the model. The authors are firmly fixed within their rights to publish even the first prototype of this model, that is why this part of model is out of estimation in this paper.

Despite the variety of models included in the model of Ooghe-Balcaen, the authors of the model have not yet thought through the issues analyzed by a combination of techniques and refined them by various authors. Because of this, the author of this paper investigated this issue, and I have developed my own model which estimates the probability of bankruptcy by the complex method of Ooghe-Balcaen. This method integrates and finalizes the 42-years-lasting study of the Ghent institute.

Author's method of calculating the probability of failure and term

prior to the bankruptcy following the algorithm of S. Balcaen H. Ooghe

The author of this paper developed a formula based on a combination of regression analysis and logit sample (binary quotient derivative distribution with given parameters), calculating the discriminants also suitable for this model. The formula of the author of this paper clarifies the model of Ooghe-Balcaen regarding the processing of the final result and the prediction of the probability of bankruptcy with high accuracy (at this time for the anti-crisis strategy realization):

(405)

Where: The TTB (Time Till Bankruptcy) figure shows the minimum failure probability of the company timing in years. e - is the exponent, which is equal to 2.71828182845905. Ω - is a figure calculated by the following formula (406):

Where: Ω - is the extent shown above formulas to calculate the probable date of bankruptcy in years. If Ω is greater than 0, it indicates that the number of years over which is most likely the company will go bankrupt.

If Ω = 0,00000 exactly - it says that the company is perfectly resistant to the bankruptcy, regardless of the value of the exponent TTB / 0 indicator feature is caused by the calculation methodology /.

λ - is a measure of whether the method is New (N) or it is an Old one (O). The new method (N) - the method modified by Sofie Balcaen and Hubert Ooghe at the 1990s-2000s (they are represented in the model). The old method (O) - is a method: either the original or the modified by Hubert Ooghe and Sofia Balcaen in the 1970s - 1980s and in prior. The models are given in the description of the model as the old or new ones.

If the model is old, the rate λ is set to 0.3 (30%). If the model is new, the rate λ is set to 0.7 (70%). These proportions of the adequacy of the old and new models are designed by the author of this paper, from the comprehensive empirical material examination and effect calculation towards the old and new companies. The primary material to make the new models from the old ones was gathered by E. Verbaere, S. Balcaen and H. Ooghe mostly in 1970s - 2000s years and is provided by the Ghent University, Belgium.

Δ - is a measure that evaluates method"s trend for the last reporting period (it is better to take a year as a reporting period). If the trend is negative, i.e., the rate for the period is plunged more into a zone of high probability of bankruptcy, the coefficient Δ is equal to 1.015. If the trend is positive, and the company, according to the model, is in the area of high probability of bankruptcy, the coefficient Δ is 0.75. In all other cases the Δ meaning is not much important in the methodology developed by the author of this paper.

Indicator (I /Investment cycle/), after lettering the name in the model, indicates that the model used to forecast the crisis in the investment cycle (3 years prior to bankruptcy).

Indicator (O /Operational cycle/), after lettering the name of the model, indicates that the model is used to forecast the crisis in the operating cycle (2 years prior to bankruptcy).

Indicator (F /Financial cycle/), after lettering the name of the model, indicates that the model is used to forecast the crisis in the financial cycle (1 year prior to bankruptcy).

All other metrics show the values of different models for the prediction of bankruptcy, and they can take two values: 0 (the bankruptcy probability in a certain model is not observed) or 1 (a certain index indicates a high probability of bankruptcy); if some company according to some model is exactly on the border between the sustainable and unsustainable companies - we shall consider this company as a sustainable one.

EAO /Edward Altman Old model/ - a generic term for older (the "old" ones) models, designed by Edward Altman, which are available in the model of Ooghe-Balcaen. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the total value of the discriminant model is in the area of sustainable companies.

EAN /Edward Altman New model/ - is a common name for the new models, primary issued by Edward Altman, which than were modified and are available in a model of Ooghe-Balcaen. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

BAO /J. Bilderbeek (Amsterdam) Old model/ - is a generic term for old models designed by J. Bilderbeek / Amsterdam /, which are available in the model of Ooghe-Balcaen. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

BAN /J. Bilderbeek (Amsterdam) New model/ - is a common name for the new models developed by J. Bilderbeek / Amsterdam /, which are available in the Ooghe-Balcaen model. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

OVO /Ooghe-Verbaere Old model/ - is a generic term for old Ooghe-Verbaere models available in Ooghe-Balcaen model. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

OVN /Ooghe-Verbaere New model/ - is a generic term for new models of Ooghe-Verbaere available in Ooghe-Balcaen model. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

CZO /Christine Zavgren Old model/ - is a generic term for old Christine Zavgren"s models available in Ooghe-Balcaen model. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

CZN /Christine Zavgren New model/ - is a common name for the new models of Christine Zavgren available in Ooghe-Balcaen model. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

GGO /Gloubos-Grammaticos Old models/ - is a generic term for old Gloubos-Grammaticos models available in the Ooghe-Balcaen model. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

GGN /Gloubos-Grammaticos New models/ - is a common name for the new Gloubos-Grammaticos models available in the Ooghe-Balcaen model. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

KMGO /K. Keasey and P. McGuinness Old models/ - is a generic term for old models of K. Keasey and P. McGuinness, available in a model of Ooghe-Balcaen. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

KMGN /K. Keasey and P. McGuinness New models/ - is a common name for the new models of K. Keasey and P. McGuinness, available in a model of Ooghe-Balcaen. The index can take on two values: 1 - if the company is in the area of probability of bankruptcy, or 0 if the value of the discriminant model is in the area of sustainable companies.

If the rate of bankruptcy TTB is above 3 years (the maximum limit for forecasting the bankruptcy in the Ooghe-Balcaen model), it can be stated, that the company has some problems to be solved, and, in general, such companies" failure, according to the Ooghe-Balcaen model, are not at risk. It should just be paid an attention to the indicators which show the crisis trends inside the bankruptcy prognosis models, instead of analyzing the total value of the models themselves.

If the indicator TTB has turned roughly equal 3 (+ / - 0.25 from the value in 3) or less than 3 years, it testifies about a crisis within the company and the need for urgent anti-crisis policy. Areas of anti-crisis policy should be planned, taking into account the values of the indicators inside the crisis-prognosis-methods, for instance, inside the models that show the probability of an event of bankruptcy.

The author of this paper developed an index TTB for clarity. The developed by the author of this paper TTB index lets us to cumulate and to preserve the 42-years-lasting research of the Ghent University in Belgium and the brilliant scientific works of many scientists from the Ghent University and from the worldwide - them to be used combined together in a synergy effect.

TTB presupposes the firms can make their financial report either fair or non-fair - of no difference on whether it is fair or unfair - the final result distortion will not be too much big. That is why some calculation methods and interpretation of some ratios used was a bit changed - to make the cumulative experience of the united researches more applicable to the crisis-reality of the nowadays.

The TTB index so may be used as the Key-Performing-Indicator (KPI) that provides an additional data about certain firms in a certain market segment analysis. This TTB KPI may reveal the hidden problem that may crush some certain enterprises at the same time when the other models and methods can not to reveal this fact. By analyzing the models that are included in the TTB and the ratios that are included in the models themselves an analyst may reveal a certain hidden crisis inside an enterprise. The less the value of TTB is - the more profound analysis is needed: from the up (TTB) to the down up till the ratios included in certain models that reveal the crisis in a certain enterprise.

By comparing the TTB of one enterprise with the other enterprises in the market, an analyst may receive an additional picture on how his or her firm positions itself in the market through the new prism: how much time is left to some certain scope of firms at certain market segment....

In common say, when calculating the TTB indicator, you, dear reader, may estimate how much Time Till Bankruptcy for a certain company is left if not to realize the urgent anti-crisis-financial-management-strategy. The TTB is calculated in estimated years till bankruptcy which can be recalculated in exact days till the expected bankruptcy which is equal to the time left on urgent anti-crisis policy measures realization.

This is the end of this discussion about the wonderful experience and successes achieved in bankruptcy forecasting sphere for the last 42 years in the Ghent University, Belgium, and also about the accumulation of this experience in one TTB index formula to achieve a synergy effect.

List of sources used in brief description: the publications of the above-mentioned authors which experience was combined in the Ghent University study: Edward I. Altman (1968, 1982, 1997 (together with P. Narayanan); H. Ooghe, S. Balcaen, E. Verbaere, De Vos D., P. Joos, J. Camerlynck, Van Wymeersch, C. De Bourdeaudhuy, (42 years of study); K. Keasey, P. McGuinness, H. Short (1990 - 1992); R.J. Taffler (1982, 1995) and H.J. Tishaw (1977); C. Zavgren (1985); J. Bilderbeek (1979); T. Bell, G. Ribar, J. Verchio (1990); Gloubos-Grammaticos model and the other authors mentioned in the text; also the working papers of the Ghent University, Belgium.

The model of Gibson-Stickney-Schroeder-Clark for predicting the bankruptcy, USA

This model was created and developed by Brian N. Gibson with taking into an account the researches of Stickney, Schroeder and Clark. This bankruptcy prediction model uses the BSM-analysis. BSM - is the name that was coined by professors at Harvard University in 1999 by the first letters of the names of the founders of the algorithm for calculating the derivatives - the Black-Scholes-Merton method.

I think those of you who are faced with their works, now realize that the component of BSM is associated with derivatives / options, and Swaps / assets and liabilities of the company. The fact is that this analysis is specified for the financial analysis of company. Gibson-Stickney-Schroeder-Clark conducted independent tests and analysis of bankruptcies of companies with the most modern computer and identified the main factor that gives an error in calculating the probability of bankruptcy by the classical techniques of financial analysis, developed before 1999 - 2011 period.

This factor - is the lack of analysis of the BSM-type or its equivalent in today's large companies to forecast their bankruptcy probability. This problem was firstly discussed by the professors at Harvard University, USA, in August 1998.

In parallel with the Harvard study, Gibson-Stickney-Schroeder-Clark nearly proved theoretically that the magnitude of the increasing the threat of bankruptcy is due to not considering the factor of BSM may rise to 78% or more of 100% on the regression scale, confirming the problem of accurate analysis methods in practice.

For example, if the model shows the probability of bankruptcy in 10% of 100%, and the BSM-analysis has not been applied, and the company is subject to the specified analysis and operations of this type, the actual probability of bankruptcy of a company may be equal to, for example, 10% + 78% = 88%!

It should be noted that the BSM-analysis can be performed in addition to all the classical and non-classical models of financial analysis and prediction of bankruptcy. It should be noted that some small and some medium-sized companies may not have the operations described by BSM-analysis and its analogues. And these are the medium, large and global companies that create the economic system of different countries in the world today.

BSM - is the common name of "mother" analysis generated by the algorithm BSM developed in 1975 - 1995 period, which began to be used in financial analysis of companies to predict bankruptcy since 1999.

Before you start considering the simplest analogue of the BSM-analysis by Gibson-Stickney-Schroeder-Clark, let us discuss it in prior: you, my dear reader, you can use other, seemingly more appropriate systems and analogues of BSM-analysis for companies that provide the operations that are subjects for this type of analysis.

The first part of the model of Gibson-Stickney-Schroeder-Clark was developed for all types of companies.

Let us finally consider a few more new models. In 2009, the U.S. got an improved model for forecasting bankruptcy of Brain Gibson, Stickney, Schroeder and Clark. The model involves the calculation of the logit analysis of the likelihood of bankruptcy. In this model, the logit function has no cut-off point - its value is the probability of bankruptcy. In the second stage the Logit probability of bankruptcy is adjusted for existing companies" derivative financial instruments, primarily stock options. If such a company is not using this type of derivatives - then the probability of bankruptcy can be considered as already calculated by this model. If options are available, it is necessary to conduct the second stage of analysis.

1) The first stage of analysis: a model of the company's bankruptcy, excluding stock options

The probability of bankruptcy by the model is calculated from the table:

Table: Calculation of the first stage of the model

The notation in the table is given below:

AR(1Y) - it shows the amount of accounts receivable for less than 1 year.

Intercept - is a measure of b0 in the regression model: it does not correspond to any factor - it increases the total model.

AvInv - is the average for the period amount of inventories.

Rev - it is proceeds (revenue).

AvAR - is the average amount of accounts receivable for the reporting period.

MF - it's money (company"s monetary funds).

STFI - these are the short-term financial investments.

TBS - is the balance sheet amount of assets in the total of the balance sheet.

MLA - these are the most liquid assets.

STL - these are the short-term borrowings.

LTL - is a long-term debt.

ImmA - these are the non-current assets.

NWC - is the net working capital equal to current assets minus the sum of short-term obligations.

ICO - Income of Continuing Operations - is an income from continuing operations. Continued operation - is an activity unit of the company at the market segment in the reporting period, which will continue in the next reporting period. In order to understand the concept of ICO, let's look at how moving the profit and loss account. Revenue minus cost is the gross profit. The gross profit adjusted to gross margin of operating income and expenses, you"ll get an operating profit (some theorists consider operating profit as profit before taxes; the operating profit concept reveals the total efficiency of company itself without looking to the payments to other parties from the total companies" profit). If in operating profit to deduct interest payments, amortization and depreciation, as well as income tax, you get the value of ICO. If the ICO to be adjusted for extraordinary income and expenses, we obtain a net profit (Net income). If the net profit to deduct dividends on preferred shares and corporate bonds and certain other spending priorities, you"ll get to the profit sharing (net income applicable to common shares). When applied to the Russian accounting, ICO corresponds to net income before adjustments for extraordinary income and expenses. Besides, the non-recurring income and expenses shouldn"t be included to the calculation of ICO. And finally, there is an income from non-continuing operations (INCO). This quantity - is the opposite to ICO. INCO - is income adjusted for expenses from companies that are no longer part of the holding of this reporting period and, therefore, the cash flow from them will not continue anymore. Often, companies publish NICO reference for investors for a long time, knowing that these companies are no longer a part of them. There are also some other indicators included to NIKO which are beyond the scope of this paper.

So, I think you already understand: how to calculate the first stage of the model. Coefficients are calculated, then they are substituted into the linear discriminant model by using the following formula:

(414)

Further, the value of Y is substituted into the following minus-logit model:

(415)

Where: Bp - is a measure of the probability of bankruptcy by the model. e - is the exponent which is equal to 2.718281828. Y - is the value of the given above function. The resulting fractional number will reflect the probability of bankruptcy for the company over the next 700 days. For example, the Bp index is equal to 0.87 would mean that the probability of bankruptcy is 87%. The higher the obtained value of the Bp - the worse it is for the company!

This type of analysis is minus-Logit (exponent e is raised into the y-th power except for to be raised to the minus y-th power as it is accustomed in a classical logit). Accordingly, the logit analysis shows the probability that the company is not bankrupt (NBp):

(416)

The amount of data of logit and minus-logit analysis should be equal to 1:

(417)

The whole model specified below we agree to call Logit, realizing that the features of the Logit and minus-Logit analysis are already taken into an account.

Let's consider an example. Suppose that there exists a conditional CJSC "Stratum".

The next data on this company is listed below: balance sheet data in thousands of USD; the data for the model calculation is also given in the table below:

Table: Calculation of the probability of bankruptcy for the company "Stratum", thousand USD

In our example, the probability of bankruptcy of the company is 52.15% over the next 700 days. In general, there are signs the company the probability of bankruptcy, on average, about 50%.

2) The company's bankruptcy model taking into account the options and SWAPS

Option - it's kind of security; it's a financial instrument; it's a kind of derivatives, consideration of which is beyond the scope of the paper about the complex financial analysis. In this paper there will be analyzed the options without their substance considering. If you have any questions about the nature of options, you can see my Russian book, in particular, the chapter on IFRS and GAAP, which has a brief consideration of options.

The model involves consideration of options by the Black-Scholes method. To apply the Black-Scholes method - it requires that for each type of contract option there had already been calculated: market / price at the market rate / exercise price (strike price), the term of the option (in the quarters and years), the magnitude of volatility [23], the average / average-periodical rate of dividends (as assessed by quarterly compound interest), discount rate (the equivalent coupon income [24]).

It should be noted that a complex mathematical apparatus is used to calculate volatility. For example, the volatility of the simplest security, part of an option, bond, is calculated by the formula:

(418)

Where: n - number of periods prior to the strike or maturity of the bond; y - is the rate for a certain period; F - is the nominal value of the bond; C = Fc - this is the coupon payment of period. For bonds without embedded options, the value of the left side of the equation is always greater than 0 for obvious reasons. For bonds with embedded options left-hand side can to be as well as not to be greater than 0.

Prominent theorist on the volatility of the financial analysis of options and other securities is a professor at Cambridge and National Taiwan University, an expert in the field of neural networks for financial transactions, Yuh Dauh Lyuu. You can refine the definition of volatility issues and other issues of financial mathematics in the field of securities in his works.

The differential equation of the Black-Scholes option involves optimization of the portfolio to minimize risk:

(419)

Where: C - this is the option value with price S. r - is the instantaneous rate of return of the instrument. t - is a measure of time. σ - is the standard deviation.

Let"s now make a returning to the Black-Scholes method as it is applied to the model of prediction of bankruptcy. The method can be used in accordance with sub-method of Schroeder and Clark (Schroeder & Clark, 1998). There is a need for some additional calculations to apply this formula. First, one must calculate (PVSPX-D) the present value (PV - Present Value) of Stock-Price in X-dividend condition (that is, Ex-dividends, that is, excluding the cost of dividends):

(420)

Since the option, to use the Black-Scholes method, is calculated on a quarterly rate, the multiplier would be 4. T - is a mathematical element that expresses the time, usually it is equal to 1, with an annual interest rate equalization of the option. ARQD - it's average/average-periodical rate of dividends (as it is assessed by quarterly compounding). SP - is the market price of the option /at the market rate/.

The second necessary component for the intermediate calculation is PVEP: present value of the exercise price (strike price):

(421)

Where: EP - it's exercise price (strike price). BEY - is a bond equivalent yield - this is equivalent to the coupon yield, which we considered earlier.

The third essential element is the cumulative rate volatility (QV):

(422)

Where: V - is a measure of volatility.

With these calculations, we can calculate the value of the option-call. It is calculated by the proportions in line with the Black-Scholes equation. It"s necessary to determine the present value of the proportion of the market price of the option (% PVSP), a proportion of the given option exercise price (%PVEP) and from these data to calculate the value of the option-call (COV). In this paper I will not discuss how to calculate it manually - instead, you and I discuss the method of calculation by computer. I think all of you have a table editor Excel. In this editor, perform the following operations. To calculate the % PVSP [25]:

(423)

To calculate the% PVEP:

(424)

Of course, the values (%PVSP) and (%PVEP) show the calculation equations by the Black-Scholes method, through the prism of Schroeder-Clark and Merton"s axioms 1974.

In accordance with the axiom of Merton, if we were making the calculation by methods of classical analysis, (%PVSP) would be equal to:

(425)

A (%PVEP) would be equal to:

(426)

Where: VA - this is the current market value of the option contract, X - is the estimated value of the debt to be paid after the time T; rf - is a risk-free rate estimated by gross method of compounding; div - this is the rate on dividend income, expressed in accordance with the terms of the current market value of the option Contract VA; σA - this is the standard deviation.

Because the fact that the approach for the evaluation of options was developed by Black-Scholes and Merton, the author once again stress that the current models to estimate the probability of bankruptcy, into account in calculating the options, are known as models of BSM (Black-Sholes-Merton) - by the names of the founders of the standard calculation of the cost of this types of derivatives.

You, my dear reader, may also use any classical variant of the BSM models for the options estimating instead of taking the Schroeder-Clark method, if you like. However, when using the BSM You also need to calculate the value of μ (t), which describes the expected market return from the options:

(427)

Where: t - this is the period under review on derivatives. Many leading specialists today prefer to use the Schroeder-Clark method for the BSM, for example, Stephen A. Hillegeist, Elizabeth K. Keating, Donald P. Cram, Kyle G. Lundstedt and others(indicated by the leading scientists in these aspects of the school Northwestern Universities, Harvard, California).

Let's go back to the algorithm of Schroeder-Clark, realizing that the main features of the model BSM are already described.

The value of COV will be:

(428)

This value, if negative, should serve as short-term liabilities of the company in step number 1 in the model, increasing them, or if the value is positive, then go to the relevant date for the company's assets. Thus, this changes the structure of the balance sheet, which has at its hands the option contracts.

The specified calculation is an estimate of options on the model of Black-Sholes by Clark-Schroeder. This approximate calculation is used for predicting the probability of bankruptcy.

Let's consider an example. Let us imagine the considered CJSC "Stratum" has a market option contract that begins January 1, 2011 and ending January 1, 2012. An option contract consists of 200*30 stock options at $ 280 price for execution (strike price). It is known that the market price of the option is 237 $ for an option contract for 01.01.2011y.. Execution time T is thus equal to 1. It is calculated that the magnitude of volatility for a given contract is 72%. The average annual / average-periodical rate of dividends (as assessed by quarterly compounding) is 3%.The level of discount is 7%. It is required to compare: whether a conclusion/output of the option contract will increase the risk of bankruptcy for the company "Stratum".

Table: Calculation of option-call value

According to the model, each such option contract (out of 200*30) increases the value of liabilities, primarily short-term, by the value of the option price. Let the options" lot is equal to 30 USD. Then the company's commitment is estimated to increase by 54.437 * 200 * 30 = 326 620.83 thousand USD. Substituting this value into the regression equation, we find that the probability of bankruptcy of the company is increased to 63.1% in relation to options contracts concluded!

However, the method of Clarke and Schroeder may not be applicable when it comes to contracts-swaps (SWAP [26]). The investigated model we analyzed for bankruptcy estimation offers contracts such as swaps by method of Professor Robert Jensen [27] and standard ED 162-B, developed by the FASB (committee to develop standards for accounting of transactions). Let swaps are tied to any rate, such as LIBOR. SWAP is, on the one hand, the process of options" insurance, on the other hand, the process of "dispute" on the dynamics of interest between the parties. There are two swap rates: the rate of acquisition (receivable rate) and rate of payment. If from the rate of the receivable (SRR - Swap receivable rate) to subtract the rate of payment (SPR - Swap payable rate), we get a clean swap, which is denoted as E, or SNR (Swap net rate):

(429)

Where i - denotes the i-th term of the swap contract.

Let the nominal value of the swap is equal to F / commonly referred to as NA (Notional Amount) /.

Professor R. Jensen"s method is based on the index of the nominal value of NCRP (Notional cash receivable / payable), which he recommends to be denoted as G:

(430)

Then two theoretical values are calculated: the calculated values to obtain (LSR - legal settlement receivable) and calculated values for the payment (LSP - legal settlement payable).

Next, we slightly deviate from the method of R. Jensen towards the Word Association by SWAP standard ED 162-B, developed by the FASB. GAAP also requires a new calculation of G and it is generally similar to the method of R. Jensen. Standard ED 162-B involves the calculation of net present value of the swap.

I think, there is need for manual calculations - instead of it, let us look how we can use the help of computer for this. In the simplest program Excel (which, incidentally, is mentioned in the standard ED 162-B as a suitable program for calculating the present value of the swap) there is a PV [28] (present value) function.

When calculating the PV, enter the SWAP rate to receive in PV to receive, enter the net percent on SWAP into the percent of this PV function (this is the E value, which is considered earlier); the PV sum - is the net sum receivable (the G indicator, which is also considered earlier); the PV period is the indicator (N - t).

N - is the total number of periods during which the swap acts. t - is the current period number for the swap operation (0, 1, 2, 3, ...., N). Thus, the degree of the last swap is always 0. Thus, we can relatively quickly and without departing from the rules of international standards to assess calculation of swap operations for each reporting period.

In order to assess what the company pays for the swap and the counterparty pays that - count rate L, which is equal to -PV:

(431)

Positive or negative for the company amount payable to the recovery of the swap transactions will be calculated based on the index M:

(432)

The index is calculated for each M i-th period of the swap. The indicator shows the actual dynamics of the M growth and profitability increase of operations on swaps.

Thus, the L indicator will show the true value of operations based on swap, and the index M will show which way we expect an increase in profitability.

Proper display of swap transactions in the model to predict bankruptcy discloses the actual financial position of the business-systems in a more objective way.

Typically swaps - this is a long-enough-term-deal, because of this fact, the alleged or actual value of these deals should be attributed to the amount of long-term debt relatively, knowing that any obligation on them will appear later. SWAP in the face of uncertainty is calculated under three scenarios: optimistic, pessimistic and normal. Since the swap is usually tied to a percentage, often to the index of LIBOR, then under the three scenarios should predict the change of the index of an indicator, which determines the value of future royalties or sums paid under the swap transaction.

Let us consider a simple hypothetical example. Let CJSC "Stalker" concludes the swap contract with a bank JSC "East" at par value 150 000 * 30 USD. The term of the contract is 4 years. The contract is tied to the rate of LIBOR. Each year the company receives a 1.51% rate of LIBOR, and pays 9.15%. Let the current LIBOR rate is 7%.

JSC "Stalker" expects LIBOR growth to continue due to the crisis trends in the economy, and the bank hopes to the normalization of situation in the economy and its revival, as a consequence, it expects the fall of rate of LIBOR.

Let they estimate a prognosis projected scenario of change rates of LIBOR, which is shown below. How will the probability of bankruptcy situation change itself for the company CJSC "Stalker" in this scenario, assuming the option contract in the previous example has also been concluded. For solutions" making to be applied the method discussed earlier.

Table: Calculation of the SWAP by standard ED 162-B for a given scenario

It is seen that the amount of company"s debt will be increased in the given scenario. If a company received the previous option contract, the probability of bankruptcy would increase to the amount of 63.15%.

Thus, options and swaps, which is reflected in a company's balance sheet in a special way by inappropriate fair value, - they can significantly increase the risk of bankruptcy; that is why they need a complex comprehensive analysis in prior.

If a company you analyze has no option contracts and swaps, then the financial analysis of the probability of bankruptcy for a company will be much more simple...

If a company that uses derivative instruments (options, swaps) for various purposes, the analysis of the probability of bankruptcy needs a little more time from you my, dear reader! The specified in this part methods will allow you to master the simplest set of tools for financial analysis of a particular type of obligations: options in their interrelationship and interdependence of the probability of bankruptcy in the business-system. The use of modern computers allows you to reduce the effort in handling the material to a minimum.

Comprehensive analysis of the derivatives is beyond the scope of financial analysis of business-systems, therefore, it is beyond the scope of this paper. This paper provides a financial analysis of derivatives only in the part that is most directly linked to conduct a comprehensive financial analysis of the business.

Next, I offer you to consider one more modern model for forecasting bankruptcy, developed in Quebec, Canada.

Model of Quebec, Canada, 2009/2010

Along with the linear discriminant analysis and logit

Hatem Ben-Ameur and Pierre Rostan

analysis there is a different type of analysis: Probit. The Probit analysis was established by Chester Ittner Bliss (1935 / USA, Springfield, Ohio (1899 - 1979)) and Ronald A. Fisher (1890 - 1962), whom we know as the founder of the linear discriminant analysis. You and I will not now be introduced in the mathematical formalism of these models further. Instead, let us consider another model based on a complex logistic regression. The author of this paper gives you the main conclusions of this model.

The model was able to identify a company bankrupt from each branch of the 700 similar companies (total in each sector there was about 10,000 firms for the analysis). The effectiveness of the model is 63.82% - 84.62% depending on the features of a particular type of company. The model is developed by a team of authors: Hatem Ben-Ameur, Bouafi Hind, Pierre Rostan, Raymond Theoret, Samir Trabelsi in 2005/2006, 2009, to analyze and forecast the bankruptcy of American firms. Despite the goal, U.S. firms, the model has been developed in Canada, in Quebec City.

(433)

Q - is the total score of the model.

λ - is a discriminant model parameter, which defaults to 1. After the analysis of whether a company is bankrupt, λ may change itself. If a company as a result of the analysis is evidence of a bankrupt, then λ = 1, otherwise λ = 0. The index P is calculated by the formula (434):

Where: X1 - this is a quotient: the most liquid assets (MLA) to the sum of short-term borrowings (STL):

(435)

X2 - is the ratio: net working capital (NWC) to total assets (TAS):

(436)

X3 - is the ratio: net income/profit (NP) to total assets (TAS):

(437)

X4 - is the ratio of EBIT to capital (OC(Eq)). EBIT - as you remember - is the sum of operating income, interest expense and excessive interests in the Russian accounting.

(438)

X5 - is the ratio of COGS to revenues (Rev). COGS - Cost of Goods Sold. COGS - is the sum of all realized during the period goods at cost, as it were, the cost of goods produced and sold to companies for the period. This figure corresponds to the amount of funds received from buyers and customers for goods, labor, services sold from company"s core activities. COGS does not include operating, non-operating, emergency and other similar income/costs - it only includes directly related to the main activities of the company costs.

(439)

X6 - is a discriminant size of the company. The concept of discriminant size of the company was introduced to the science by Sofia Balkaen, being one of the points of her doctoral thesis defense in 2009. Discriminant company size (DCS) - is the natural logarithm of total assets of the company:

(440)

Where: ln - is the natural logarithm (logarithm of the "e") of the amount of assets denominated in comparable to other companies monetary value. For Russia it is a thousand rubles. For comparison with international companies - thousands of USD It should be noted that very often Sofia Balkaen expressed DCS in million USD. All this will have little value if the company to be compared to the same value, for example, all in rubles ..

When λ = 1, you get a percentage of the quantitative expression of the probability of bankruptcy for up to 3 years. If the probability was obtained less than 50%, instead of λ = 1, we can substitute λ = 0.

The overall probability of bankruptcy prediction at λ = 1 indicates the approximate probability of bankruptcy within the next 2 years.

This completes the analysis of the probability of bankruptcy. Thus, we together with you, my dear reader, considered the absolute approach to financial analysis. Let's look at another fundamental concept of financial analysis: marginal approach.

Analysis of the probability of bankruptcy - is a complex and multifaceted process. However, in this area there is a paradox: exploring effective models for predicting bankruptcy, mankind has invented a set of models, some of them with 98.5% - 100.0% probability that can predict the opposite phenomenon - that a company will not become bankrupt in the next few years ... .. As long as the leader in prediction of "not bankrupt" is the model of Olson, which in some countries has passed with just a splash, with its 100% select of all companies that just do not go bankrupt in the near future.

The new Olson"s model versions: Harvard University version 2009/2010

Olson model was first developed in 1980 and still runs successfully tested. Instead of the classical model of Olson, we consider a more modern model of Olson, modified by the University of Harvard and released in 2009/2010. The model has the form:

(441)

In this model, e - is the familiar constant - the exponent (2.71828 ...). O - is the degree of the erection of the exponent. Indicator O is calculated by the formula (442):

Where:

! - Shows that these ratios regardless of the model value should be paid by particular attention (my dear reader, please, note, that "!" sign here - it is not a factorial sign!).

ln (ΣA) - is the natural logarithm of the assets of company (just count the balance in USD million ($)!).

O1 - this is the ratio of total debt to total assets.

O2 - is the ratio of net working capital to total assets.

O3 - this is the ratio of short-term debt to current assets.

O4 - is the ratio of net profit to total assets.

O5 - this is the sum of: operating income, depreciation deductions by depreciation rules, to total liabilities (total debt).

O6 - is an indicator that can take two values: 1 (if the sum of net income over the past two years is less than zero) or 0 (otherwise).

O7 - is an indicator that can take two values: 0 (net worth of the company / shareholders' equity minus liabilities / is positive) and 1 (if the company's net worth is negative).

O8 is the figure calculated by the formula:

(443)

Where: t - this is the reporting period, respectively, (t - 1) - this is the last reporting period (which is previous to the reporting one); NP - is the net profit, | | - is the mark of the module, meaning that the number inside is always positive.

The result of the calculation model is the parameter H, which must show the likelihood of bankruptcy of a company in a percentage of probability in the next 2 years.

One can interpret the resulting H figure as follows. If the indicator has turned more than 1% - the probability of bankruptcy is essential. Since the upper limit of the probable bankruptcy prediction is 5% of the model, which corresponds to 100% probability of bankruptcy, the figures above 1% are evaluated differently. 1% corresponds to 30% probability of bankruptcy, and 2% corresponds to a 50% chance of bankruptcy, and 3% correspond to the 75% probability of bankruptcy, and 4% corresponds to 90% probability of bankruptcy, and 5% - 100% probability.

All companies whose model"s value was higher than 1% - are at high risk of bankruptcy, according to this methodology.

I think you have already guessed that we will gradually come to the end of the classical financial analysis. Financial analysis of bankruptcy - this is an additional tool for financial analysis of the business. It checks whether a firm stable or not. Its goal - it's not a prediction of disaster; its goal - is the management of probable catastrophe and the anti-crisis development of such company so that at any circumstances it not to become a bankrupt.

Next, I offer you, my dear reader, to consider an alternative approach to financial analysis, which first appeared in Management Accounting: marginal approach.

Marginal approach to financial analysis

The author of this paper immediately emphasize that marginal approach will be discussed in this paper only in so far as it relates to complex financial analysis. I will not consider the particular application of marginal analysis in managerial accounting, operations management and so on - just in financial analysis.

Originally marginal approach originated in economic theory in the construction of effective demand and supply functions. For the first time in the practice of management of the company it came under the banner of the method of incipient management accounting in the 1940s - 1960s. Nobody really thought then that by the end of the twentieth century the scientific world would break out discussion as to whether it is an approach has a right to persist in managerial accounting or it can be replaced by financial analysis and accounting.

Opponents of marginal analysis in managerial accounting are many leading scientists and financial experts. The most ardent critics were some prominent professors of Harvard University. About all this we will talk a little bit later .... In the meantime, let us define the very essence of marginal approach.

In Russia, this approach is a lot written about, and little attention is given to how to adapt this approach to Russian or any other accounting: nobody has a marginal classification of revenues and expenditures which is required in this approach...

Marginal theory suggests that the success of a company depends on its manufactured cost. The higher the costs - the worse it is. Thus it is possible in a few words to describe this approach. If not describe in a nutshell, the name of the approach is in the concept of margin, and not a simple one, it is in the limit one (margin, "Marginal", "Deadline").

Margin in the classical expression is presented as revenue minus cost for a particular transaction or transactions. However, there is a question of limiting the margin. In order to understand it, it is necessary to know the marginal theory of distribution of costs to financial result of company"s activity.

This theory states that all costs in a company can be divided into fixed and variable. Let us together with you, my dear reader, make a reservation in advance with the symbols, which are commonly used in this approach. TR - Total Revenue - is the total amount of revenue. ATR - it is the income per unit of production (on average). FC - Fixed Costs - it is a fixed cost. AFC - Average Fixed Costs - a fixed cost per unit of output. VC - Variable Costs - these are variable costs. AVC - Average Variable Costs - is a variable cost per unit of output. TC - Total Costs - these are gross expenditures. ATC - Average Total Costs - this is the total cost per unit of output. TP - Total Profit - total profit is the difference between revenues and expenditures of all, sometimes it is calculated per unit of production as ATP (Average Total Profit). MR - Margin Revenue - is the ultimate, the marginal revenue. MC - Margin Costs - it is marginal, ultimate cost.

Here we must make some clarifications. Fixed costs - is the theoretical value of costs that amount does not change itself depending on the volume of output. If a company has something or not, rent, property tax, ... .. and other fixed costs the company pays at all times. Variable costs - costs that the theoretical value, the amount of which varies depending on the volume of output.

If, for example, some company produces dumplings, the dumplings" cost per ton will go, probably, about two times less costs than for the production of two tons: it needs less sugar, yeast, flour, dough, fillings, ... ..However, this value is theoretical, because the accounting cost of such a classification does not exist. Let's make a slight digression, and determine how to divide all the company's costs into fixed and variable according to any national accounting reporting!

Alexander Shemetev created his scheme for classification of all the costs into variable ones and fixed once at any main national accounting reporting standard. This scheme, developed by the author of this paper, is given below:

Scheme: Fixed and variable costs of any national reporting standard

080 - is the conditional name code for income/expenditures from operations with shares, securities and received from subsidiary and affiliated companies. (010) - is a conditional name code for revenue - this is the total revenue from the balance sheet form #2 - statement on income and losses. Actually, all the data for this classification should be taken from this #2 form.

It can be clearly seen from the scheme that the production activities are only the very cost, commercial and administrative expenses. Other expenses (interest from investments in other companies, interest incomes/expenditures, non-selling incomes) have no relationship to the production. They reflect the non-productive activities of the company, its specificity, which has no relation to the main activities.

Along with the Alexander Shemetev's method of taking the marginal indicators from accounting data (a method of financial accounting), there is a method of allocating the fixed and variable costs from management-accounting techniques. However, since 1985, the world's largest companies have become increasingly move away from the management accounting and its use in management [29]. Since 1982, the world begins the era of criticism of management accounting by the most eminent professors. The author of this paper will not give the entire material on both critics and protection of managerial accounting (management accounting).

Well-known critics of the management accounting and its methods are the supporters of financial accounting rather than the management accounting. They suggest the marginal analysis may be performed by the financial data. The opponents of management accounting existence are: Robert Kaplan and Thomas Johnson. These authors belong to the Harvard School of Economics and Finance. As practitioners in the financial analysis, they reasonably confirmed that the majority of firms that lose in the competition by just using the methods of management accounting in damage to financial.

They note that the management accounting techniques were developed in the 1950s - 1960s, and only a little fine-tuned further. Such outdated methods, according to these authors, are inferior to more sophisticated methods of financial analysis and accounting. Because of this fact, financial accounting can save huge amount of time, resources and energy at relatively low cost of accuracy. Costs of accuracy - it is a mathematical term, developed for the first time by Ronald A. Fisher. Costs of accuracy - represent the magnitude of error of financial, mathematical or statistical model from a theoretical model that would reflect the all the 100% of facts with full 100% adequacy.

The main controversy in favor for and against the management accounting was developed in the world in the late 1980s - 1990s - 2000s. Currently, managerial accounting is experiencing its "second birth", adopting and assimilating models of financial analysis and accounting. Criticism of management accounting has been so significant that even the major proponents of the theory of management accounting agreed that obsolescence of management accounting models makes it significantly less attractive in the realities of the business than the use of methods and models for financial analysis and accounting. In particular, this position is held Colin Drury, Johnson, Cooper and others.

Because of this, the author of this paper used the method of dividing the cost to constant (FC) and variable (VC) in accordance with the terms of financial management rather than management accounting.

Dear reader, please note that if the amount of revenue already includes in itself all the income from additional activities: Interest income and other non-operating-incomes - such an income must be deducted from the proceeds before the analysis to avoid double counting, since these revenues have no relation to company"s operating activities. Therefore, they should not participate in the establishment of fixed and variable costs from operating activities in order to avoid errors.

The different from marginal method should be applied for calculating the interest, non-operating, emergency and other similar incomes and expenditures!

Now, when you and I discussed the classification of income and expenditure by marginal model, let's make our first financial analysis using this model. And now the question for those of you, who read my book well and understood the previous material. Imagine that you came to abrupt data about the activities of a company that knows that it works successfully in the market. And in 2009, its cost has exceeded its revenues by 12.3%, and in 2010 - by 13.9%! Also, the cost exceeded revenue in 2008, 2007, 2006 and 2005 .... At the same time, the company ended the year with virtually considerable profit (2.3% of book value), and finished all the previous years with net profit! If other data is unknown, how can that be? What are the sources of financing and the sources of profit for such a business-system? What is the structure of its income? What do you think, my dear reader: what is wrong with this company? Try to try to answer this question by yourself, or you may consult with your accountant. And please try to answer this question by yourself, until you read the proposed solution literally in the next paragraph.

I hope you, my dear reader, were able to answer this question of the author of this paper! In any case, you can compare your answer with the steps below. Probably, the profits are not reflected in earnings because it was related to non-operating income and characteristics of its recording. As the situation from year to year is repeated, it is quite likely, the company receives dividends from associates, which are reflected in the profit and loss account when calculating revenue. If this were only found in one single year, it could mean that the company has discovered unaccounted for (for example, due to an error) income of previous years, or it sold a little of its real estate, or doing something similar. Author of this paper for clarity brought to you, my dear reader, this example you to understand that every company is individual. Now, let's take a closer look to this individual company. The question here arises is: what is rational for a company: to stop the main production activity and to live on dividends and other income, or to continue the production process, when data for this company are as follows:

Table: Reported LLC "Dividend", millions USD

Apparently, the company has three production lines: ? 1, ? 2 and ? 3, which produce relatively homogeneous products. In the future, production lines and related indicators will be denoted simply by their numbers. In order to determine which line of company is more profitable to keep and which - it is more profitable to close - it is necessary to perform the following form of analysis:

Table: Key marginal indicators of LLC "dividend", millions USD

Where: n - is the numerical designation of the production lines or other atomic distribution center costs, for which there are marked the constant and variable costs and total revenue;

KE - these are selling and distribution expenses (commercial expenditutres);

AE - these are management costs.

The remaining denotations have already been given earlier. The author of this paper proposes to divide the total amount of variable costs on atomic distribution centers based on the cost structure or the structure of revenue, or from the structure of production - depending on what data is actually available for analysis.

How to analyze these indicators? Since the sum of net income (loss) from activities of each production line is less than the sum of the fixed costs allocated to the specified line in accordance with the structure of costs, each production line to continue the operation should cover part of the fixed costs, otherwise the company will have an even greater loss of each single or for all the production lines.

Now let's look at another example on the use of fixed and variable costs in the planning of production activities.

To get started let me remind you that we have a conditional company. It is necessary to calculate if it is profitable to invest in a certain project for the production of some conventional products.

In this part of my paper I will analyze the overall strategic plan for the company for the next 8 years. It is the calculation of scenario when among all the investment opportunities a company decides to invest in its own production. So, the terms are next.

Co. Ltd. "Luck" - is a conditional firm with its headquarters deciding on how it is best to invest in Russia.

Co Ltd. "Luck" puts the following conditions for the investment project:

Table: Conditions on the investment project for LLC "Luck"

The main objective for research of investing in its own production:

1 - To investigate whether the project payback of investments is possible, taking into account norms of profit for investors (the time value of money), and what conditions should be created to stimulate the best payback opportunity.

2 - If payback for investments is possible, to investigate the maximization of profit as the main goal of the company in the long run.

3 - To review by complex analysis: the way the Ltd. "Luck" will be able to invest its temporary surplus funds in its own production in the most appropriate way.

Investors, from their part, expect the feasibility of their investments.

The method of FV - Future Value - is a method of estimating the actual cost of the project on its future value, taking into account standards of income for investors. I recommend you, my dear reader, to use this method instead of the NPV calculation, because it is much more simple mathematically, it gives less errors, it gives the same result as the calculated correctly NPV, it demands almost no mathematical skills. The probability of error when using the NPV method is caused by its way to estimate the negative cash flow values over the time. While the method I offer has no such problem at all, and it gives the same result as the correctly calculated NPV. So, let us start from the beginning.

There are two methods to estimate the actual value of the investment project:

1) FV - Future Value - A method of estimating the actual cost of the project on its future value, taking into account norms of income for investors over the time.

2) PV (NPV) - (Net) Present Value - A method of estimating the reduced (discounted) cost of the project, which calculates the discounted at the current date (and for any date in the future) cash flows from the investment project.

FV method is very simple and easy to use. And it is designed for people who are not very friendly with the math. And it does not give errors in the calculations.

A method for PV (NPV) may give some errors; it has errors that are not described in the scientific literature. The method of PV (NPV) has the effect of deceptive value of the investment project. Especially, it is so when the negative cash flows are planned for some business projects in future periods. The PV (NPV) method simply "cuts" these cash flows. Because of this, often unprofitable projects seem to be more profitable, and profitable projects often seem to be unprofitable. This is the "effect of deceptive value" of the investment project, as I call it. I described it more details in my Russian books.

Let"s calculate the first rate of return on the project by the method of FV.

Our time period is greater than 1 year, investor, the parent company Co. Ltd. "Luck" considered advantageous profit interest calculations from the formula of compound interest:

(444)

Where: FV - is the future value of money, taking into account the norm of profit.

PV - is the real cost of the investment project (750 000 USD)

i - Interest earnings on the draft standard.

n - the life of the project in years (8 years).

We will now analyze the established norms of profit:

Table: Calculation of the investment attractiveness of the project

* It"s an average price, because standards are equally and so profit can be calculated simply as the arithmetic mean simple (without the use of the weighted arithmetic mean).

A new branch of LLC "Luck" will produce and then sell conventional products. The estimated project life - is 8 years. After that, the equipment and other must be sold at the liquidation value of 300,000 USD

The investor (parent company LLC "Luck") intends to make a lump sum investment of $ 750 000 USD.

The investor plans to bid the project estimated by one of the following rates: 12%, 15% and 13%, depending on external conditions.

Ltd. "Luck" had extensive analytical studies of the market in which it was found the exact value per unit of output to % of demand for these products at a specified price. The results were as follows:

Table: Value for price and demand based on market research for company "Luck"

And now, my dear reader, I would expect you to answer a question: why it is so that when the price is $12 per unit - there are 80% of customers who wish to buy this product at this market segment, while when we decrease price to $8 per unit - there are only 46% of thou who wishes to buy it?! The price decreased itself by more than 30%, while demand fell by nearly an half?! According to the theory of economy, the lower the price is - the higher is the demand, and vice versa. Why do you, my dear reader, think this supply/demand law was broken here?

This is an effect of "fear of lower prices". The fact is that the price of goods is associated with the quality of the goods for all people, and, at the same time, with its prestige. In fact, it may not be true - in reality, some cheap goods may have much higher quality than some luxurious or just expensive goods, and vice versa. Thus, a juice for 1 dollar and 40 cents per liter may be even more "juicy" and more of-high-quality than the juice for 4 dollars per liter; and the juice for 1 dollar and 40 cents may have an association of low-quality and non-prestigious product.

Quality - this is what the average middle class chooses; prestige - that is what selects the highest class of society. This effect is often associated with the so-called effect of Thorstein Veblen, who in the early 20th century published his book "The Theory of the Leisure Class"; he wrote that "Rich people are afraid of low prices". Therefore, the economic law of demand: the lower the price - the higher the demand - it only works up to a certain limit in the lower price range (and with a definite boundary in the upper one (and that's another theory that has no relation to the majority of situations)). The upper boundary - is a boundary of Exclusive Commodities for Collectors, which by their values are no longer seen as a commodities. People see in them a way to invest their money. For these products the higher the price - so, more often, the higher is the demand (eg, paintings of Van Gogh, ....).

To learn how to conduct such studies, it has been and will be discussed in the continue of my future book written in English; it is yet discussed in my books written in Russian as well as my papers in English which are available for free on-line reading. It's not a secret that marketing analysis - is the most significant "white spot" in the work of enterprises. That is, for example, an important reason of the current world economy and financial crisis: companies couldn"t up-to-time predict the market conjuncture abrupt changes, and so they were unprepared for the anti-crisis strategies application.

At the same time, the improper anti-crisis financial management - is the main reason of the current economy and financial crisis.

In order to analyze the profitability of cash investments, you need to build a cash budget for each time period. For clarity and ease of understanding, let us consider the construction of cash flow in the matrix (table) system at an example of Ltd. "Luck". This is - a large matrix (on the next page). In order to build this matrix analysis, it is necessary to calculate the basic characteristics of cost. How to do it - is shown in a small table (it is before the matrix system on the next page).

Cash flow analysis of any company can be done by following to these analogues.

If you've watched these two tables, then you realize that you can easily cope with the calculation of cash flows for any business (including, your own).

Thus, a breakdown of costs into fixed and variable helps the company to plan its production and sales activities, as well as to analyze its subsidiaries.

The basic principle in the financial analysis of subsidiaries and affiliates is as follows. We both consider the standard Basel-II/Basel-III on the issue, which (the III version) is currently under development. If the ownership share of the parent company is less than 20%, the investments in the company are just investments. Investments are calculated either as securities, or by any other method. The optimal can be called already discussed by us methods arbitrage pricing theory (APT), the theory of optimal portfolio if the market sector, where the company is, is growing, and the method of VaR, if the industry, where the company is, falls.

If the share ownership of the company in a society of more than 20% and there are signs of a significant impact on the development of management decisions in a third party, and, at the same time, the share of ownership does not exceed 50% with the right to control the company, the author of this paper recommends the method of marginal approach to evaluate such companies with the additional use of NFV, NPV, or discounted cash flows at the level of production and sales.

It should be understood that the risky component should be incorporated in the calculation of the prediction of marketing loop, as well as operational and financial cycles in the analysis stage of the company. If the company's share in a society is more than 50% and there are indications of control over the company, then such a company should be analyzed in the first place by means of a comprehensive financial analysis.

Next, let us consider the basic principle of marginal approach for financial analysis of a company. Let's look at two new concepts - marginal revenue (MR - Marginal Revenue (Marginal Yield)) and the marginal cost (MC - Marginal Costs).

MR - this is the revenue per unit of output that we get from the sale of another, an additional one unit of goods, works or services;

MC - these are the additional total costs per unit of output that are associated with the production of another, an additional one unit of goods, works or services.

Below is a schematic chart developed by Alexander Shemetev of the life cycle model of the enterprise by the model of marginal performance.

Schematic chart: The life cycle of the enterprise on the marginal model

RESERVE OF FINANCIAL STRENGTH (STEADINESS)

As it can be seen from the graph, all costs consist of the permanent (FC) and variable (VC). The amount of fixed and variable costs in the chart gives the line TC (Total Costs - total (gross) costs).

Fixed costs are constant only in a single production macro-period, that is, until, as happens a qualitative shift in the production of goods, works and services at the company. This qualitative shift may be result of restructuring the company to complete commissioning of production capacities, establishment of additional production capacity, reserve capacity, large capital investments, growth of administrative and business costs and so on.

As it can be seen, it is a three-dimensional graph. Along the axis of S (total Sum), there is the total value of revenue as well as costs. Along the Q-axis, it is given the number of manufactured goods, works and services. The greater the number of produced goods, the lower cost is obtained as per unit of production, and overall, and ... it is fair relative to a certain period.

On the t-axis it is delayed the time axis. The author of this paper has projected three-dimensional graph into the two-dimensional for greater ease of perception. Dynamics of gross profit varies itself.

With the start of production, there begins to grow also the share of revenue in the company. Gradually, as production increases itself, the amount of revenue begins to cover the fixed costs. Sometimes companies only work for that - to cover their fixed costs and part of variable costs, because downtime costs may be sufficiently more for some certain companies. Clearly, this situation can not last forever, and the company should start to look for profitable investment project to cover its costs, and further it may gradually close the unprofitable production.

And if revenues do not cover the fixed costs of the enterprise, why would it work? Sometimes companies should continue to work for a while, when the activities" stopping now is more expensive than to continue unprofitable activities or a company has a core mean for the society or even for a state as a whole. Such situation, however, may not last for a long time, because the company's goal should be making a profit in the long run, rather than minimizing costs in the event of direct losses. Sometimes, state dotation money replaces a part of income for some certain enterprises so that they may have even some profit for development.

To continue its business a firm needs a strong potential for growth, or it should open the way for a business project, which, in turn, has the potential to grow and bringing income to its owners.

Let"s return to the schedule. Gradually sales start to grow, and the company begins to cover the entire amount and the gross costs. When this happens in the first time, we say that the business system is in a BREAK-EVEN POINT - that is, in a position where it may be repaid its activity by covering the entire amount of production costs. This point is also called a zero threshold for cost-effectiveness and zero return.

The farther we move away from the production break-even point, producing and implementing all the large volumes of goods, the greater it becomes the reserve of financial unsinkable, or a reserve of financial steadiness.

The beginning of this phase for a company means a period of growth in the life cycle of a business-system, consisting of periods of "flowering", maturity and early fall (I used the classification of life cycles of the Adizes, 1998). During this period, the company usually expands its market to the limit by taking a certain segment.

Profit is equal to revenue minus total costs (see line profits, revenues and gross expenses in the chart); profit gradually begins to grow with a zero threshold of profitability. The company is developing ... to a certain point.

As it can be seen from the graph - it is noted by large arrows pointing up and down; - a range of factors influence to the life cycle of company and allow it to grow. Let"s call these factors as raising factors - they potentially stimulate company"s development. And there is a range of factors that oppose to company"s development. Let"s call them decrease (regression) factors.

Gradually, the company's growth is constrained in the market segment... .. This comes at a time when the market potential is fully exhausted. At this point, potential regression comes into action. Just like as it goes at the stock market - the bulls and bears; - just for a company in a market segment they are somewhat different, though, if it is a JSC after an IPO, then the stock market begins to affect a company strongly too. As a whole, both the stock market and in company"s model bulls - are raising factors, and bears - are reducing factors. Their strength corresponds to the total strength of these factors.

If you collect the whole set of factors in several groups, we obtain the following. To the enhance factors there is a group of factors of production facilities and expansion of productive capacity. As you remember, there are two groups of factors: external - the development of the market segment occupied by all means and methods of marketing-management, and internal - they can be divided into a group of extensive and intensive factors. Extensive - it"s a development through additional resources, and intensive - by changing the quality of production and production process. That is, all the positive work "inside" and "outside" of the company, that is, in the external and internal environment (which we already discussed earlier) - is a step-up factor for the company.

At the same time, the decreasing factors have just two main groups:

1) Compression of the value and volume of market segment. Rather, the exhaustion of opportunities for this market segment. A part of the market segment usually belongs to your company, and some - to the competitors.

When you run out of your share of the segment - it may be nowhere to expand to. Of course, you can extend the value of the segment itself, to improve the segment, and so on - that is, to do so, as shown in the consideration of raising factors. And, nevertheless, there is the strength of the exhaustion of the segment"s value at the market. Moreover, it is not just a force of exhaustion, it is the compression force value of the segment; it is due to the fact that more and more competitors enter the market segment. Those competitors both develop their segments and develop their presence at the segments. As a consequence, segments occupied by your company are under threat of capture by competitors due to many factors ... For example, the competitors are just more successful.

2) Life Cycle of the Investment Project. Much depends on what stage of life cycle is a company; much depends on how a company develops its business activities: by following the theory of catastrophism development, or by following the theory of evolutional-wave-development. In fact, the main factor that determines the degree to which the dynamics of activity will develop for a business system - is the factor of the crisis of innovations. This applies particularly to the industrial sector. A lot of Russia"s leading experts point at this problem at this field in Russia, in particular, B.A. Voronin, V.V. Akberdina, G.M. Korkina, L.N. Popova, S.A. Roslyakova and others. Thus, the lack of innovation is a powerful step-down factor for companies in today's society.

As it can be seen, there is a break point at the graph - when the boost factor is exhausted, and the decreasing factor starts to act much more strongly than the increasing factor. The dynamics of earnings declines very rapidly, and this is not an isolated case, and the constant tendency.

What is to do for companies when raising factor is exhausted? The most definitive answer - is that a firm should simultaneously seek means to reduce the impact of reducing factors (eg, to capture market segments of competitors, to attract new audiences, to promote its products into new markets for the business, to develop existing markets, to expand the value of the segment, and so on), and, at the same time, such company should move to another inertial frame of the report - for example, to produce an innovative product that meets existing or new customer needs better than competitors' counterparts, to develop other business projects, in other words, you can diversify your company"s activities in order to reduce the load on the risky capital for your business-system, and so you may encourage the creation of a new life cycle.

As you remember from the evolutionary-wave theory of development, any system tends to crash as long as it can not move smoothly to the next evolutionary level. It is fair for this theory and to the evolution of the enterprise. Each cycle of evolutionary-wave theory can be considered as a such-like graph of theory of catastrophism.

Gradually, after the fall of the dynamics of earnings, company begins to reach the Limit Points of the market by itself, that is, to the point at which the company is once again able to break even. This is the time corresponding to the end of the life cycle of the enterprise, while, at the same time, this is the point of market saturation by products of this company.

Thus, if the market has new products of higher quality or differentially different from products of some excising enterprise, a buyer will most likely seek to buy exactly the differentiated products in this market segment. The largest segment in this case narrows sharply - the market needs fewer products from this enterprise - so, there is a decline in the number of goods sold, which eventually comes to a limit of the enterprise"s market.

What to do in this case? In this case, there is the need for qualitative leap in the development of the company so its development theory continues to be an evolutionary theory instead of catastrophic theory development. Very many scenarios can be used in this case: new innovative project, just a new business project, company development into new markets, market size segments" force expanding, pricing and so on.

And you can still use the old industrial base and to produce products based on it, and you can use additional manufacturing capacity, for instance, to give it to rent. As you can see, there is a lot of options. All this should enable such company to make a profit again.

Well, after that, if things keep going on the theory of catastrophism at such an enterprise, it passes through the point of exhaustion Limit of the market and starts to incur losses. The company begins to involve leverage actively to cover its losses, which further increases the crisis inside the company ... .. And we have talked in detail about this scenario in the first section of this paper (this paper is the second section of it).

Now we discuss a little bit different: Analysis of profit maximization. The point of maximum profit at the chart corresponds to the maximum distance between the curve of the gross costs and gross profits" Curve. Gross profit minus the total cost - that is profit; and the greater the distance on the graph between the lines - the more maximum the profit of a company is. Of course, it is so just when the Revenue line exceeds the line of costs.

If the Revenue line is below the Gross costs, while it is above the line of fixed costs, the stop of such an enterprise at a given time is more expensive than its loss-making operations, even if such activities are not encouraged by enterprise"s bright prospects for its development in the future.

In this case, you can gently go out of such a situation by finding a new investment project, or by selling such a business, or by expanding the size of the market segment, or by finding a new market, or by something else... It all depends on the specific situation.

The graph shows the point of maximum profit by big black line, which is projected into a graph"s left field. The height of this line - this is the maximum amount of profit on this project, which is only possible throughout its life cycle.

The distance from the break-even point to this point of maximum profit is called THE MAXIMUM RESERVE OF FINANCIAL STEADINESS.

The distance from the break-even point to your current level of production in your company - it is your own reserve of financial steadiness. The analysis of the reserve of financial steadiness can be provided by the CVP-analysis (CVP - Costs-Volume-Profit-Analysis).

That is, firstly you are expected to estimate the break-even point for your company, that is, the volume of sales at which your company will not receive any profits or bear losses. And the distance from this point on the graph to your actual position in the market - it is your own reserve of financial steadiness.

The formula to calculate the breakeven point by method of selecting the parameters (at large enterprises with a wide range of products it is very comfortable to use this method) is as follows:

T0=TR-FC-VC=Q*P-Q*AVC-FC=0 (445)

Where: T0 - is the Break-even point, which is equal to 0;

TR - Company" revenue from sales, calculated as the price (P) multiplied by the number of realized goods (Q).

VC - Total variable costs, which are calculated as the value of the variable costs per unit of output (AVC) multiplied by the number of realized goods (Q);

FC - This is the total amount of fixed costs at an enterprise.

It should be said that the gross cost per unit of output (ATC) is equal to the total value of revenue per unit (ATR) at this point.

Generally, quite a lot is written about the CVP-analysis in a lot of scientific literature. So, I think there is no need to stop on it more profoundly in the frames of this paper.

Now let's look at maximizing the profit by this method. Of course, you can use the gross indicators (that is, gross profit, revenue, and so on) to determine it.

And here we will try to answer the question: where is the volume of sales at which profit is maximum? This question can be answered with the use of marginal analysis, that is, by comparing the marginal cost and marginal revenue.

Marginal costs - those costs that are associated with the production of one additional unit of output: goods, works or services. The costs are calculated by the formula:

(446)

Where: MC - Marginal Cost; AVC - Gross costs per unit of output; Q - quantity of goods.

Marginal revenue - this is the additional revenue that we receive from the sale of one additional unit of goods, works or services. Marginal revenue is calculated as follows:

(447)

Where: MR - Marginal revenue; ATR - Gross proceeds from the sale of a unit of production; Q - quantity of goods sold.

The maximum profit will be achieved in the production of output, at which MR = MC, ie, the marginal cost equals to marginal revenue as it is shown in the formula below:

(448)

EBITDA - Earnings before taxes, interest, depreciation and maintenance.

My dear reader, please, note that I offer to use the method of ATC and ATR using to compare the MR and MC and to find the point the profit is maximum. The same thing can be done by using the traditional concept, where in (446) the difference in TC is used instead of the difference in ATC, and in (447) the difference in TR is used instead of the difference in ATR. Using the Average TC and TR may only compare MR and MC to find the maximum profit point, while the usage of simple TR and TC in their total volume will give the actual values of MR and MC. Using both of these methods one may compare the MR with the MC.

As long as the value of marginal revenue exceeds marginal cost in the production of each additional unit of goods - it increases profit. The optimal amount of production is considered to be one in which the value of the marginal cost per unit of output is equal to the marginal revenue. Later, when the marginal cost exceeds marginal revenue, profit margin and profit per unit of output will decline. Therefore, the volume of production when MR = MC Maximizes profit of organization.

Analysis of other forms of financial statements of the company

Other forms of financial statements are the statement of cash flows and statement of changes in equity. Let's examine them in more detail.

Cash Flow Statement (Form number 3 on OKUD) splits the company's activities into a set of cash flows. The first section of this paper series shows on a very simple scheme on how to split any company"s activity into a set of cash-flows. This scheme is in the model of rapid diagnosis of the financial condition of a company making. The name of the scheme is: the matrix of changes in financial results in cash flows. So, I offer not to return to this discussed yet topic.

There is a direct and an indirect method of converting the company"s activity to cash flows. The scheme I just mentioned represents an indirect method. So, considering the indirect method is already discussed, I offer you to consider the direct method further.

Statement of Cash Flows divides the company's activities into three main sections of the structure of its activities: operational (production), investment and financial. Statement of Cash Flows adds to the cash balance at beginning of period the net balances from the cash flows from all the three areas of business-activity.

The positive cash flow from operating activities includes in itself: funds received from customers and clients, including funds to repay debts; received budgetary subsidies and insurance reimbursement, other income.

The negative cash flows from operating activities include: acquisition of goods, works, services and related working capital assets, wages, payment of dividends and interest, payments of taxes and levies, travel expenses, expenses on personnel training, other expenses.

The amount of income minus the expenses from operating activities gives the net cash flow yield from operating activities.

The positive cash flows from investing activities includes in itself: proceeds from the sale of noncurrent assets, including fixed assets, revenue from sales of securities and other financial investments, dividends received, interest earned, repayments of loans which are given to other organizations; others.

The negative cash flows from investing activities includes in itself: the acquisition of subsidiaries, the acquisition of fixed assets, profitable investments in tangible assets and intangible assets, acquisition of securities and other financial investments, loans to other organizations; others.

The amount of income minus expenses of the investment cycle gives the net cash flow from investing activities.

The positive cash flow from financing activities includes in itself: proceeds from issue of shares and other equity securities, income from loans and credits to other organizations, other.

The negative cash flows from financing activities includes in itself: repayment of borrowings (without interest), repayment of capital lease obligations, other.

The amount of income minus expenses from financing activities gives the net cash flow from financing activities.

We considered the splitting of business-activities into a set of cash flows more profoundly in the scheme I"ve mentioned earlier.

Net cash flow (NCF) consists of the following elements:

(449)

Where:

CBPB - is the sum of the cash balance at the beginning of the period;

BOA - is surplus (revenues minus expenses) on cash flow from operating activities;

BIA - this is balance (revenue minus expenses) to cash flows from investing activities;

BFA - this is balance (revenue minus expenses) on cash flow from financing activities.

C - is the net value of the losses or gains from fluctuations in foreign currency to domestic.

The purpose of the analysis of the statement of cash flows is to establish the reasons for lack of money in the company, analyzing the inflows and outflows of cash.

Along with the our direct and indirect method, some theorists, for example, N.Y. Gordo, secrete a liquid cash flow method, which involves the calculation by the formula:

(450)

Where:

LCF - this is the result of liquid cash flow in the company;

LTD - is a designation for the long-term debt (loans);

STB - is a symbol of short-term borrowings (loans);

MF - is a designation of the amount of money;

0 - means the end of the reference period for cutoff of parameters;

1 - marks the end of the reporting period for cutoff of parameters.

You can make forecasts about the excess / shortage of liquid cash flow for the period and to focus efforts on improving / placement of excess funds; you can do it on the basis of often calculation of liquid cash flows, for instance, once time per month.

Along with the report of cash flows, there is the statement of changes in equity (form number 4 on OKUD).

Statement of changes in equity (Form ? 4 to OKUD) is as follows:

Scheme: Statement of changes in equity (Form ? 4 to OKUD)

Notes to the table:

RP -1 - indicates the data at the end of the period, which was before the basic period (RP 0);

Δ - means change;

Reconversion of currencies - is the sum of losses from transactions of foreign currency into the national;

N - means the number;

P - denotes a nominal price (of shares);

"+" - Indicates that capital should be increased by these lines;

"-" - Indicates that capital should be decreased by these lines;

M - represents a low probability of occurrence of the parameter changes in equity in this row;

AC - means Authorized capital;

ADC - means additional capital;

RC - means reserve capital;

RetE - means retained earnings.

The arrows indicate the priority direction of movement of certain key funds that form the capital.

This is the general form of the statement of changes in equity. This report shows: by what means the changes in equity had taken place to be for a certain period. The annex to the form number 4 on OKUD should contain a data on reserves. The structure of reserves is split on end balance, entry, use, and the final residue.

Reserves are divided into three groups: formed in accordance with the law; formed in accordance with the constituent documents; other reserves. Reserves are filled in it for the basic and reporting periods.

Capital in the financial analysis is evaluated in its structure changes (as it is shown in the scheme). Also, capital adequacy is assessed.

A capital is divided into two categories for the analysis of capital adequacy

The analysis of capital adequacy, capital is divided into two categories: Tier I and Tier II capital. Tier II capital is formed by the revaluation of fixed assets and increase the par value of shares. Tier I capital, which is considered as the most stable, includes funds generated from sources, which can not be attributed to capital of the second level.

Now, after reading the paper series on financial analysis, you probably have learned the material. If there is something you do not remember, or remember not so well, you can read the section, which has caused difficulties for you. If the financial analysis itself makes you, my dear reader, considerable difficulties, and you have to do it, in this case for you and for anyone interested in issues of financial analysis I prepared a small summary in two pages with tips and formulas relating to the fact how to conduct a comprehensive financial analysis, with little time, a notepad, a calculator and a pencil - that's enough for it.

There are common tools of analysis. This is similar to the way in building a house there are cocks, hands, cement mixers, shovels and hammers, drills, bricks and so on. And there's a stuff - building materials and factors of production .... (This is like a company that you need to analyze what it is and what it will in the future). Similarly, things are so in the financial analysis: there are many tools of financial analysis, which are designed to make life easier for an analysts, such as how a tap simplifies and accelerates the task of building a high-rise building.

The more effective tools of financial analysis are available for an analytics - the better. This can be compared with the fact that the more a variety of useful devices in construction is (cranes, elevators, computer-aided design, ....) - the simpler, better and faster is the home construction for workers.

The author of this paper has given to you, my dear reader, all the basic material for the financial analysis in this chapter - the rest will depend on how well you use it, from your knowledge and skills. If you do not use all the material from the financial analysis and to apply it successfully, you can be sure that it obligatory will be done by your competitors; actually, they have already been doing so... and they constantly improve their skills.

In addition to the general financial analysis, there are many subtleties that are discussed in my future book in English that I"m about to translate, as it is yet written in my similar book in Russian. We shall look many of such subtleties, with the exception of a comprehensive assessment of business, as the author of this paper has already discussed it in my previous book in Russian (Alexander Shemetev: "Anticrisis financial management self-taught book for commercial firm directors and business owners", Chapter 10: "Business Valuation"). Or you can use any other author on this thematic you like the most.

Next, I offer you to consider a summary of how to make a comprehensive financial analysis for 5 minutes (this is a bit later), and then move on to some details of financial analysis for various types of business systems (this is my future book I"m about to translate into English (it already exists in Russian)).

Summary of rapid diagnosis of the financial condition of the company and development of anti-crisis strategy

It is better to start express-diagnostics of a company under option number 2 (Do you remember what is the version number 1 - it was a model of Dupont).

We begin with the express-diagnostics (here it is represented by the Option number 2):

Express-diagnostic of entity's financial position:

1) Assessment of the balance (the ratio of A (Active) and P (Passive))

Asset for the industry: ImmA: 70%, MobA: 30%; to trade - ImmA: 30%, MobA: 70%. Passives for the industry: OC(Eq): 50 (60)%; TL: 50 (40%). For the trade: OC(Eq): 40 (50)%; TL: 60 (50%).

! Assessment of the dynamics of the balance by year: Seeing the positive and negative trends!

2) Evaluation of balance sheet liquidity:

- CR (Current ratio) = Current A / Current P = MobA/ImmA (min = 1, max = (2-3).

If> (2-3), a company uses its liquid funds in a non-efficient manner.

- C of owned funds sufficiency = (OC(Eq)-ImmA) / MobA (norm> = 0.1 (0.2))

3) Evaluation of financial ratios:

TD/TE = (sum of short- (STL) and long-term debt (LTL)) divided by Equity (own capital) (normal ≤ 0.7 (max 1)), ie, Debt Capital (TL) should be at least less than 70% of equity (OC(Eq)).

C of financial independence = (Equity Capital (OC(Eq)) divided by Total Balance (TBS)) * 100% (rate should be more than 40-60%)

C of financial maneuvering = NWC / OC(Eq) (NWC = Current A - Current P), ie

NWC - net working capital should be divided into equity (OC(Eq)). The higher the obtained value of the coefficient, the better!

C of owned funds sufficiency for inventories financing = NWC/Inventories (Inv), that is:

NWC - Net working capital is necessary to divide by the cost of inventories (Inv). For industrial enterprises - rate 0.6 - 0.8, and for the trade firms this value may be small, up to 0.01).

4) Evaluation of liquidity:

Compilation of aggregate ("weighted", broken by periods Liquidity of assets and liabilities to maturity) ranged balance:

A (Assets) - to be ranged by the degree of liquidity;

P (Passives) - to be ranged by the degree of maturity terms liabilities.

A1 (Cash; Almost cash)> P1 (Accounts payable (AP))

A2 (accounts receivable (AR) less than 12 months. And other current assets, other than inventories) > P2 (short-term loans (STL))

A3 (inventories and costs + AR more than 12 months.) > P3 (Long-term credits and loans)

A4 (ImmA (Noncurrent Assets)) < P4 (OC(Eq)) (it"s a min level of Fin. Sustainability. Indicator A4 - is to ensure the company's own funds sufficiency).

Key liquidity ratios:

CAR = (A1) / P2 (normal 0.2-0.25);

CQR = (A1+A2) / P2 (rate - 0.7-0.8);

CR = (A1+A2+A3) / P2 (normal 1-2.5);

5) Assessment of the dynamics of profit in the Balance: Seeing the positive and negative trends in indicators of revenue, cost and profit!

6) Analysis of current assets (business activity - part) (these are means the company invested in the current operation during each cycle of production: Inventories, accounts receivable, cash, VAT, almost cash.