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Criteria for evaluating the effectiveness of the risk management system. Building risk management systems Evaluation of the effectiveness of risk management is carried out on the basis of

In the system of consistent risk management functions, the most important role is played by assessment of the effectiveness of the risk management system.

Management efficiency is the ratio of the total result of management activity to the cost of resources expended to achieve it.

The effectiveness of managerial activity is significantly influenced by a number of factors, the totality of which can be conditionally divided into two main groups.

The first group includes factors that have a direct direct impact on the effectiveness of administration, such as:

♦ management potential of the organization, ie the totality of all resources available to the management system;

♦ total costs for the maintenance and operation of the management system - are determined by the nature, method of organization, technology and scope of work to implement management functions;

♦ control effect, i.e. the totality of all economic, social and other benefits that the organization receives in the process of implementing management activities.

All of the above indicators can be defined as the main factors of management efficiency.

The second group is formed by secondary factors that have an indirect impact on the effectiveness of the management system. These factors include:

♦ qualifications of managers and executors;

♦ capital-labor ratio of the management system, i.е. the degree and quality of providing administrative employees with auxiliary means (computers, office equipment, etc.);

♦ socio-psychological conditions in the labor collective;

♦ organizational culture.

As part of the management efficiency criteria, general and particular indicators can be distinguished. General indicators characterize the final results of the organization's activities, and private indicators characterize the efficiency of the use of certain types of resources.

To assess the effectiveness of the management of commercial enterprises, it is most appropriate to use such general indicators as profit and profitability.

The total amount of profit received by an enterprise for a certain period usually consists of profit from the sale of products (works, services), profit from other sales and profit from non-sales operations.

Profit from the sale of products, services or work performed is determined as the difference between the total proceeds from the sale of products (excluding value added tax and excises) and the amount of production and sales costs included in the cost.

Profit from other sales is defined as the difference between the amount received from the sale of property or other material assets of the enterprise, and their residual value.

Profit from non-sales operations is calculated as the difference between income and expenses for operations not related to the sale of the company's products or its property.

The composition of income from non-operating operations includes:

♦ income from financial investments of the enterprise in securities;

♦ income from leased property;

♦ balance of received and paid fines;

♦ positive exchange differences on foreign currency accounts and operations in foreign currency;

♦ receipts of amounts on account of repayment of receivables written off in previous years at a loss;

♦ profit of previous years, revealed and received in the reporting year;

♦ amounts received from buyers on recalculations for products sold last year;

♦ interest received on the company's accounts with credit institutions.

Non-operating expenses of the enterprise are formed as a result of summing up:

♦ shortages and losses from the loss of material assets and funds;

♦ negative exchange rate balance on foreign currency accounts and transactions in foreign currency;

♦ losses of previous years identified in the reporting year;

♦ writing off accounts receivable;

♦ uncompensated losses from natural disasters;

♦ costs for canceled orders;

♦ legal costs;

♦ the cost of maintaining mothballed production facilities.

The balance sheet profit received by the enterprise is distributed between the state and the enterprise. After the introduction of income tax into the relevant budgets, the enterprise has at its disposal cash resources, which form its net profit. The net profit of the enterprise is directed to the accumulation fund, the consumption fund and the reserve fund.

Based on the order of profit formation, its factorial analysis is carried out. The main purpose of factor analysis is to assess the dynamics of balance and net profit indicators, to identify the degree of influence on the financial results of a number of factors, including:

♦ increase or decrease in production costs;

♦ growth or decrease in sales volumes;

♦ improving the quality and expanding the range of products;

♦ identification of reserves to increase profits.

The most important indicator characterizing the effectiveness of the management of a commercial enterprise is its profitability. Profitability is defined as the profit received from each ruble of the spent means.

The system of profitability indicators is formed on the basis of the composition of the property of the enterprise and the business operations carried out by the enterprise. From this point of view, there are:

1) the profitability of the property of the enterprise - is defined as the ratio of net profit to the average value of the assets of the enterprise;

2) profitability of non-current assets - represents the ratio of net profit to the average value of non-current assets;

3) profitability of current assets - is calculated as the ratio of net profit to the average value of current assets;

4) return on investment - the ratio of profit from investment projects to long-term costs for their implementation;

5) return on equity - the ratio of net profit to the amount of equity capital;

6) profitability of borrowed funds - is defined as the ratio of fees for the use of loans to the total amount of long-term and short-term loans;

7) profitability of sold products - the ratio of net profit to proceeds from the sale of products.

Using the above profitability indicators, it is possible to evaluate not only the overall efficiency of the organization's management system, but also the effectiveness of the use of certain types of resources (assets) of the enterprise.

It is much more difficult to assess the effectiveness of the management of non-profit organizations. From the point of view of assessing the effectiveness of functioning, all non-profit organizations can be divided into two main groups:

1) organizations whose performance can be assessed using economic indicators;

2) organizations whose performance results are expressed in non-economic terms, such as a decrease in the level of morbidity or crime, an increase in the level of education, an improvement in the environmental situation, etc.

To evaluate the effectiveness of organizations included in the first group, you can apply the same methods as for evaluating the effectiveness of commercial organizations.

It is much more difficult to evaluate the effectiveness of the functioning of organizations that are part of the second group. Currently, there are almost no methods for converting non-economic indicators into economic ones.

Even in those industries where such techniques are available, they do not find wide practical application. For example, a methodology has long been developed for calculating the economic damage caused to nature due to pollution of water sources by discharges from industrial enterprises. At the same time, when assessing the effectiveness of projects for the construction of new treatment facilities, the prevented damage is not taken into account. Thus, it turns out that most environmental programs are unprofitable from an economic point of view.

Therefore, the main direction in the development of methods for assessing the economic efficiency of non-profit organizations and programs should be the development of methods for converting non-economic indicators into economic ones. This will more objectively and fully take into account the impact of various factors on the performance of a particular organization or project.

The modern business world is dynamic. After two years of intertime (2014-2015), the features of a new reality are gradually emerging for the prospects for business development in Russia. Under the conditions of a shrinking market and a weak ruble, enterprises are forced to form and develop their export potential in every possible way, which will require additional management restructuring. In this regard, the risk management system, which one way or another will have to be created by enterprises, can become an attractive resource for investors and a success factor in foreign and domestic markets.

The essence of risk management

This article echoes the materials of the article on the topic of organizational aspects. Risk management is proposed to be understood as a set of targeted procedures for identifying, assessing and reducing risk to the values set by the strategic choice, which involves a multi-stage implementation process. The economic goal of management is to reduce or compensate for damage to the organization in the event of adverse consequences of decisions.

Under the conditions of uncertainty in the economic activity of an enterprise, risk management is a set of regulation of strategic, tactical, design and operational-production relations. An integrated approach has a number of advantages (the corresponding diagram is located below), and from the position of management functions, almost the entire arsenal of management tools is involved, including components of financial management, logistics, economics, accounting, sales, etc. The complex of procedures is aimed at:

forecasting risk events and their identification;
rationale for risk aversion;
justification of risk acceptability;
risk minimization using the available range of tools;
elimination of the causes and consequences of risky events;
adaptation of companies that survived the crisis period to new business conditions;
bankruptcy protection.

Diagram showing the benefits of a comprehensive approach to risk management

The uncertainty of activity is weakly correlated with the scale of activity. Indeed, regular management, which can be deployed in large enterprises, gives a significant "head start" in comparison with empirical methods of management in small businesses. But, firstly, the cost of management increases dramatically, and secondly, the very number of risk factors becomes much larger. Therefore, it can be confidently stated that one of the conditions for the success of the activity is the implementation by the management of the business, regardless of its size, of anti-risk measures. Another question is how systematic is risk management?

The objects of management are the actual risk, economic relations accompanying probable adverse events and risky investments. The subjects of management can be considered both in the broad and in the narrow sense of the word. From a common position, they are all members of the organization's team, including managers and employees. In a narrow sense, subjects are specially authorized managers, employees and divisions of the company. The goals and objectives of risk management are related to the stages of business development and its passage through the stages of the life cycle. The scheme for changing the composition of management objectives at the stages of the organization's activities and the tasks corresponding to them are shown in the diagram below.

Dynamics of goals and composition of risk management tasks by stages of company development

The concept and content of risk management systems

The risk management system (RMS) as a set of interrelated elements, on the one hand, contains two subsystems: managing and managed. In addition, the RMS is a component of a higher-ranking system - corporate management and is guided by the requirements of the organization's strategy. On the other hand, the system includes a technological complex of management and a complex of organizational tools and structures. Pay attention to the scheme "Buildings of the RMS" presented below. It displays the main elements of the risk management system.

Scheme "Building RMS" in the relationship of technological and organizational aspects

The enterprise risk management system is an element of the internal control and risk management mechanism, which is part of the corporate governance, a technological tool and tools that ensure the effectiveness of risk management. This system provides organizational prerequisites, principles and structures for designing, implementing and improving the organization's risk management business processes. Thus, the RMS creates an infrastructure for risk management on a regular basis.

Ensuring the minimization of the level of uncertainty regarding the achievability of the tasks set for management, the development and practical development of risk management processes is the main goal of the RMS. Under the specified tasks, the results to be achieved according to the development strategy are considered in the programs of the tactical and operational levels. The RMS serves the regulated management of assessed risks, as well as maintaining the integral risk of the company at the level of the preferred acceptable risk. The scheme of interrelation of integral risk management with stakeholders is placed below.

Conflict resolution scheme for business leaders through integral risk management

The risk management system, especially in large companies, is called the corporate risk management system (CRMS). In addition to simply expanding the abbreviation, this, as a rule, entails increased requirements for the level of regulation of activities within the system. From the position of solving the main tasks in the CRMS, the following stages are sequentially performed.

RMS diagnostics at the level of business units and the entire company.
Development of the main structures of the CRMS (organizational, informational, financial, etc.).
Creation of regulatory and methodological support for the CRMS.
Structuring databases according to identified risks and risk events that have taken place.
Development of mechanisms for monitoring and reporting on emerging events.
Identification, identification and assessment of risks, drawing up a plan for their minimization and compensation.
Formation of a risk map.
Integration of the map update procedure into the business planning process.
Analysis and assessment of the facts of response to risk events.

Specifics of risk management standardization

Risk management systems at domestic enterprises are built on the basis of Western standards that are rather poorly adapted to our realities. I do not consider here the experience of banks and insurance companies. It seems that in this sector of the economy the point of no return has been passed and the pace of development of risk management and the RMS supporting them can be considered satisfactory. Are you interested in what Russian companies can rely on, primarily in the manufacturing sector, in order to quickly increase their risk management potential? To do this, you need to touch on the history of the development of a systematic approach to risk management in the world and in our country.

Diagram of the world history of the development of standards in the field of risk management

Composition of current national and international standards in the field of risk management

Above is a diagram of the history of standardization and the composition of existing standards in the field of risk management in the world. It is obvious that in order for a Russian enterprise to meet the needs of investors and inspire confidence in the international arena, the approach to building a CRMS should be at least close to world standards. And in order to meet the requirements of exchange trading platforms, international and Russian corporate legislation, the system itself must be transparent and understandable to a competent stakeholder.

The COSO ERM risk management model is not a standard and is a deep methodological development. Therefore, the COSO cube is difficult to ignore and not emphasize its main postulates. Below are two diagrams that give an overview of this concept. In the model:

defines the basic concepts of the internal control system;
the main components of the risk management process are described in detail;
an integrated risk management model is presented in a cubic visual form;
developed the principles of this management system;
the functions and responsibilities of participants in the risk management process are formulated;
the management process itself is described;
recommendations were given to external and internal stakeholders in ensuring the successful functioning of the RMS in companies.

Key Components of the COSO ERM Risk Management Model

The company always remains face to face with its risks and defends itself from threats and the consequences of their implementation at internal borders. Regulators also have their place on the "far approaches to the front of the fighting." And the support of regulators, of course, is necessary for business. Another thing is that domestic standards are "tracing paper" from Western counterparts. At the same time, it should be understood that the actual practice of the general mass of firms in developed countries has gone far ahead due to a longer history and a different level of managerial culture. However, as a basis, the resources provided by the regulators are useful for starting the implementation of the CRMS.

Scheme of the composition of regulators that determine the requirements for the RMS

Algorithm for building CRMS in a company

You and I remember the axiom that management and its components are connected with the company's strategy. It defines the principles of management activities and the main focus points. The specifics of risk management is that the local risk management strategy undergoes a major adjustment in the middle of the management process. To build a RMS, the company's experience in the practical application of financial and economic theory, tax and civil law, external regulatory assets and standards is important.

Internal and external pillars of building RMS in the company

Building a risk management system according to the model proposed below is based on the experience of Russian companies with a focus on the COSO methodology. This model implies the following steps of the algorithm.

Analysis of the environment. First of all, they analyze the elements of the external environment (the activities of the Central Bank of the Russian Federation, the State Duma, the Ministry of Finance, the Federal Tax Service, etc.), the business environment, market conditions, and business resources. All this creates external risk factors.
Establishing customer risk management processes. The success of the implementation of the CRMS depends on this. Very often in Russian companies, the customer is the financial service, which is associated with the dominant role of financial risks in the functioning of the company. In a number of cases, the customer is the general director, and it is especially valuable if his undertakings are supported by the position of the main shareholders.
Determination of the organizational structure of the control subsystem. The system can be managed by a dedicated specialist or the head of a separate division, who coordinates various areas: risky investments, insurance operations, venture investments. This organizational structure is called the concentrated model. The second variant of RMS organization can be a distributed risk management model.
Development of regulatory documentation of the system: risk management policies, provisions (concepts) for risk management, risk declarations. The policy serves as the main document of the CRMS and is publicly available on the corporate portal.
Development and adjustment of the corporate risk map. Here, measures are cyclically implemented to identify, identify and assess the risks of the company.
Development of a risk management strategy. In the strategy, in addition to the principles of choosing methods for dealing with risks, mechanisms for their financing, a special place is occupied by indicators of the effectiveness of the RMS and the distribution of areas of responsibility between the management company and business units.
The actual implementation of the risk minimization and compensation program.
Development of an operational risk management process.
Regular audit of the CRMS.
Implementation of procedures for informing about changes in the CRMS.
Creation and development of control and monitoring systems.
Implementation of procedures for saving and archiving information generated in the system.

RMS Implementation Principles

The principles of the functioning of the RMS in the company also determine the processes of its implementation and development. These principles are subject to compliance by managers responsible for the implementation of the system procedures by specialists and all employees of the company.

The principle of goal orientation. The goals are written in the company's strategic documents: development strategies, strategic action plan, corporate maps, business plans.
The principle of balancing risks and profits. The RMS should promote a balance between risk and profitability (profitability) of the business, taking into account the requirements of legislative acts and the provisions of internal regulations.
The principle of accounting for uncertainty. Uncertainty is present in any business activity and is an integral part of the decisions made in the company. RMS serves to systematize information about the sources (factors) of uncertainty and helps to reduce it.
The principle of system. A systematic approach allows you to timely and fully identify, identify and assess risks, reduce their negative consequences or compensate for the impact on performance.
The principle of quality information. RMS requires timely, secure and accurate information to function. When making decisions, however, it is necessary to take into account the limitations and assumptions of the sources of information, the possible subjectivity of the position of experts and the peculiarities of the methods used for assessing and modeling risk situations.
The principle of assigning responsibility for risk management. The concept of "risk owner" is introduced, this status is assigned to one of the company's managers. He is given responsibility for the appropriate management procedures within the given powers and functional composition.
The principle of efficiency. The RMS should provide a reasonable and economically justified combination of management effectiveness and costs for its organization and production.
The principle of continuity. The RMS functions in conditions of regularity (cyclicity) of the main processes and their continuity. The processes of the system originate at the time of the development of the company's strategy and cover all areas of its activity.
The principle of integration. The decision-making system at all levels of management should include the subject area of RMS. Decisions are developed and approved taking into account the circumstances and the likelihood of adverse consequences associated with their adoption.
The principle of expansion. RMS involves the identification, assessment and settlement of all possible threats to activities, not limited to financial and insured risks. According to the last three principles, the schemes of their main elements are presented below.

Composition of procedures of the RMS continuity principle

Scheme of the main elements of the RMS expansion principle

Assessment of the company for risk management

What should a company do if it is only thinking about implementing RMS or if elements of the system are already present, but it is not clear how and in what direction to move on? Experts recommend in this case to analyze the risk management system at the enterprise in order to determine its strengths and weaknesses and ways for further development.

It would be very useful for current and potential stakeholders in the company's activities and in investing in it to learn about the real state of affairs from the position of regular risk management. In 2015, the KPMG consulting group conducted a study “Risk Management Practices in Russia”, in which 48 respondents were asked about RMS diagnostics. The results of the answers are presented in the diagram below.

Results of a survey of 48 Russian companies on the diagnosis of SUR.

Risks can be mitigated in various ways. As an example illustrating the diversity of approaches to the same problem, consider the risk management situation of a large industrial installation. The purpose and principle of its operation in this case do not play a special role.

The main hazardous event is a plant accident, which may be accompanied by fire, explosion, damage to components and assemblies, human casualties, etc. Of course, first of all, preventive measures to reduce the risk, as well as measures to reduce the scale of possible damage, should be carried out. Reliability-critical components and mechanisms, fire and explosive materials are identified, and measures are taken to improve the safety of the installation. Various systems are also installed; monitoring the development of hazardous processes, smoke sensors, temperature sensors, etc. An action plan is being developed for the evacuation of personnel in the event of an accident, and employees are trained in the rules of conduct in such situations.

The situation with risk management at the first stage is simplified due to the fact that there are technical standards for the safety of various machines and devices, the observance of which is mandatory for industrial enterprises. Therefore, it is relatively easy to determine the list of risk reduction measures that need to be implemented in the first place.

However, then the question inevitably arises of how to further reduce the level of risk. And in this case, the implementation of additional preventive measures no longer seems obvious, since all of them are associated with certain costs. Risk reduction requires the introduction of safe technologies and materials, the renewal of the technical park, the improvement of control and warning systems, insurance - the payment of an insurance premium, self-insurance - deductions to the reserve fund. At the same time, the final effect of these measures can be assessed by the degree of compensation or elimination of possible losses in the future. If we correlate the costs of risk management and the degree of reduction of future losses, then we can obtain an assessment of the effectiveness of risk management measures from an economic point of view.

You can also evaluate the effectiveness of risk management in terms of ensuring the overall sustainability of the enterprise. As an example, consider a situation where an organization decides to invest in improving the reliability and continuity of a manufacturing plant or industrial plant. Financial measures, such as insurance, are more suitable for these purposes. It is known that, starting from a certain level, the costs of direct risk reduction with the help of organizational and technical measures grow at a faster rate than the risk itself decreases. In other words, if increasing the reliability of a device from 97 to 98% requires a certain amount S , then increasing the reliability from 98 to 99% requires several times more costs, for example, 2 S . One hundred percent reliability, as is known, is never achieved, i.e., in this case, the costs are equal to infinity.

In this situation, risk insurance seems to be a more preferable procedure, since the costs of it are usually proportional to the volume of risks (provided that they are homogeneous).

The above example illustrates that, starting from a certain level of risk reduction, the enterprise faces the problem of comparative evaluation of various methods of influencing risk and choosing the best one. Methods can be compared on the basis of various criteria, including economic ones.

General approaches to evaluating the effectiveness of risk management methods

Evaluation of the effectiveness of applying one or another risk management method depends on the criterion that underlies the comparison. There are two most common approaches to developing criteria:

selection of a critical parameter that should not go beyond acceptable limits;

economic benefit.

The first approach is closely related to compliance with safety standards and ensuring the sustainability of the enterprise. For example, there are safety standards for workers in hazardous industries or environmental pollution for the population. Within the framework of this approach, various risk management activities are evaluated on the assumption that they all reduce the level of a critical parameter to the required value.

Purely financial mechanisms, such as insurance and self-insurance, are aimed primarily at compensating for the consequences of adverse events. Their comparison with other methods of risk management is possible if a certain financial parameter is chosen as a criterion, for example, the maximum amount of losses leading to the ruin of an enterprise.

An enterprise can benefit economically by improving its own safety. In this case, various options for organizing risk management measures are evaluated according to the same principle as investment projects: first, the costs are determined, and then the absolute profit or the rate of return per unit of costs. The level of security achieved in this case does not play a special role, it is determined by the most economically advantageous option chosen.

Economic criteria for evaluating the effectiveness of risk management

The use of any of the risk management methods leads to a redistribution of current and expected financial flows within an enterprise or a financial project. For example, when insuring, part of one's own funds is diverted to pay insurance premiums, as a result of which the project is underinvested and profits are lost. On the other hand, there is an expected future inflow of funds in the form of compensation for losses in the event of an insured event.

The redistribution of financial flows leads to a change in the value of the net assets of the enterprise or project, calculated taking into account the expected cash receipts. Thus, as a criterion for the economic efficiency of applying risk management methods, one can use an assessment of their impact on the change in the value of the enterprise, calculated at the beginning and end of the financial period. For an investment project, the criterion is the impact of risk management methods on the change in the net present value of the project.

Let's give two examples from the field of financial risks.

Example 1. Investment project

Investment project risks are taken into account as part of the discount rate for equity, which is used to calculate the net present value of the project (NPV - net present value). Insurance reduces risk, thereby lowering the discount rate and increasing NPV. On the other hand, insurance implies additional costs for the payment of insurance premiums during the life of the project, which ultimately lead to a decrease in the profit of the project.

The resulting influence of these two opposing factors leads either to an increase or decrease in NPV, thus making it possible to judge the effectiveness of insurance application.

However, investors may demand that the risks of the project be reduced to the necessary limits. In this case, the starting point for evaluating the effectiveness of risk management methods will be to compare the costs of their implementation while ensuring the same required level of risk.

Example 2. Investing in securities

When investing in exchange-traded assets, an investor, based on past years' data on exchange rate fluctuations, can assess with what probability he will receive the required level of income. After that, he can determine his future economic benefit in the form of a mathematical expectation, i.e. as the product of probability and expected profit.

After that, the investor can use hedging methods to reduce risk or insure future profits in the usual way. In the first case, the investor will fix a smaller profit, but with a higher probability, and will also incur the costs of the hedging operation. In the second case, he will fix the desired profit, but will incur significant costs for paying the insurance premium.

In practical terms, for a comparative assessment of the effectiveness of various risk management methods, you can use the method of pairwise comparison and then build a hierarchy of results based on the application of the selected criteria.

Analysis of the economic efficiency of insurance and self-insurance

Analysis Method

Let us consider a method for comparative evaluation of the effectiveness of the two most common financial risk management mechanisms - insurance and self-insurance, which has received the name of the Houston method in Western literature. Its essence lies in assessing the impact of various methods of risk management on the "value of the organization" (value of organization).

The value of the enterprise can be determined through the value of its free assets. Free (or net) assets of an enterprise is the difference between the value of all its assets and liabilities. Decisions to insure or self-insure risk change the value of an enterprise because the costs of these activities reduce the cash or assets that the organization could invest in and make a profit. The model under consideration also takes into account the occurrence of losses in the future from the considered risks.

It is also assumed that both financial mechanisms equally cover the considered risk, i.e. provide the same level of compensation for future losses.

When insuring, the company pays an insurance premium at the beginning of the financial period and guarantees itself compensation for losses in the future. The value of the enterprise at the end of the financial period in the implementation of insurance is expressed by the following formula:

S I = S – P + r (S – P), (33.1)

where S I is the value of the enterprise at the end of the financial period under insurance;

S is the value of the enterprise at the beginning of the financial period;

P is the amount of the insurance premium;

r is the average return on operating assets.

The amount of losses does not affect the value of the enterprise, since they are assumed to be fully compensated by the paid insurance claims.

With self-insurance, the enterprise retains its own risk in full and forms a special reserve fund - the risk fund. The impact on the amount of free assets of fully preserved risk can be estimated by the following formula:

S R = S – L + r(S – L – F) + iF, (33.2)

where S R is the value of the enterprise at the end of the financial period with fully preserved risk;

L - expected losses from the considered risks;

F is the value of the risk reserve fund;

i is the average return on the assets of the risk fund.

With self-insurance, the company suffers two types of losses - direct and indirect. Direct losses are expressed as expected annual losses L . In addition to the expected losses L, certain funds must be directed to the reserve fund F in order to compensate for the expected losses, and with some margin. Assets are assumed to be held in a reserve fund in a more liquid form than assets invested in production, so they generate less income. Comparison of the values of S I and S R makes it possible to judge the comparative economic efficiency of insurance and self-insurance.

It should be noted that for greater accuracy of calculations, it is necessary to take into account the discounting of cash flows due to the distribution of losses over time, delays in the payment of insurance compensation associated with the preparation and presentation of claims, and the presence of inflation.

Performance Analysis Results

Let us set ourselves the goal of determining from the Houston model the condition for the effectiveness of using insurance in an enterprise to protect against risks. Mathematically, this condition can be written in the following form:

S I > S R . (33.3)

This suggests that the value of the enterprise at the end of the financial period with insurance should be higher.

Substituting expressions (33.1) and (33.2) into inequality (33.3) and making some transformations, we obtain the following expression:

where P is the insurance premium;

L cp - reduced average expected losses;

F is the size of the risk fund in case of self-insurance;

r is the average return on operating assets;

i is the average return on the assets of the risk fund.

From inequality (33.4) it is already possible to determine the maximum allowable size of the insurance premium, if certain assumptions are made about the values included in it.

The two key parameters on which the compliance or non-compliance with this inequality depends are the average expected losses Lcp and the size of the risk reserve fund F . Let us consider the main patterns characteristic of these quantities.

In order to calculate correctly, in formula (33.4) it is necessary to use the value of expected losses Lcp given at the beginning of the financial period. Real losses are distributed over the observation period, and those that occurred earlier in time have a stronger effect on the change in the value of the enterprise. In this case, to adjust the value of Lcp, you can use the standard procedures for discounting financial flows.

The required size of the risk fund F, which must be formed by the enterprise during self-insurance, can be estimated based on the following considerations. The funds of the risk fund, as already mentioned, are also used by the enterprise to make a profit, since they are “temporarily free” until they are needed to compensate for losses. If the efficiency of using the risk fund were equal to the efficiency of using productive assets (i.e. r = i), then the insurance efficiency condition given by inequality (33.4) would never be met, since the insurance premium P is always greater than the average expected losses: L cp : P > Lcp .

This circumstance follows from the structure of the insurance rate, since in addition to the average losses, it includes the costs of doing business and the profit of the insurance company (as well as other components). Insurance would always be less cost effective than self-insurance. However, as a rule, r > i , since the assets in the risk fund should be kept in a more liquid, and therefore less profitable form. Therefore, there is a range of values of those variables in which insurance will be a more cost-effective mechanism, which will result in an increase in the value of the enterprise.

The size of the risk fund is determined in accordance with the subjective perception of the risk by the insured. To assess this factor, the model uses the previously mentioned concept of the maximum acceptable level of loss L max . It would be logical to set the size of the risk fund equal to the maximum acceptable loss: F = L max

It is important to note that the inequality determines the maximum acceptable insurance premium for the insured based on the internal properties of the insured risks, which are described in the model by the parameters L max and L cp . These parameters can be determined based on statistical data. In their absence, as approximate values of L max and L cp, you can use the available data on other enterprises of a similar profile, or take the values of the maximum and average annual loss from the risks under consideration for a sufficiently long period of time (in amounts reduced to the level of the reference year), adjusted by the coefficient determined by experts.

Based on the analysis of inequality, the following conclusions can be drawn about the impact of various conditions on the effectiveness of the use of insurance in the enterprise.

1. The larger the size of the risk fund formed by the enterprise, the less effective is self-insurance.

2. The effectiveness of self-insurance falls with an increase in the profitability of the enterprise and grows with an increase in the profitability of liquid highly reliable investments. This provision has an obvious economic meaning: with an increase in the profitability of its activities, it is more profitable for an enterprise to invest in production than to divert them to create a risk fund.