An example of factor analysis of sales profit. Factor analysis of sales profit

Interrelation of economic phenomena. Introduction to factor analysis. Types of factor analysis, its main tasks.

All phenomena and processes of economic activity of enterprises are interconnected, interdependent and conditional. Some of them are directly related to each other, others indirectly. For example, the amount of gross output is directly influenced by factors such as the number of workers and the level of their labor productivity. All other factors influence this indicator indirectly.

Each phenomenon can be considered as a cause and as a consequence. For example, labor productivity can be considered, on the one hand, as the reason for changes in production volume and the level of its cost, and on the other hand, as a result of changes in the degree of mechanization and automation of production, improvement in labor organization, etc.

Each performance indicator depends on numerous and varied factors. The more detailed the influence of factors on the value of the performance indicator is studied, the more accurate the results of the analysis and assessment of the quality of work of enterprises. Hence, an important methodological issue in the analysis of economic activity is the study and measurement of the influence of factors on the value of the economic indicators under study. Without a deep and comprehensive study of factors, it is impossible to draw informed conclusions about the results of activities, identify production reserves, and justify plans and management decisions.

Under factor analysis understands the methodology for a comprehensive and systematic study and measurement of the impact of factors on the value of performance indicators.

The following are distinguished: types of factor analysis:

deterministic and stochastic;

direct and reverse;

single-stage and multi-stage;

static and dynamic;

retrospective and prospective (forecast).

Deterministic factor analysis is a methodology for studying the influence of factors whose connection with the performance indicator is functional in nature, i.e. when the effective indicator is presented in the form of a product, quotient or algebraic sum of factors.

Stochastic analysis is a methodology for studying factors whose connection with a performance indicator, unlike a functional one, is incomplete and probabilistic (correlation). If with a functional (complete) dependence with a change in the argument there is always a corresponding change in the function, then with a correlation connection a change in the argument can give several values ​​of the increase in the function depending on the combination of other factors that determine this indicator. For example, labor productivity at the same level of capital assets may not be the same at different enterprises. This depends on the optimal combination of other factors affecting this indicator.

At direct factor analysis The research is conducted in a deductive manner - from the general to the specific. Reverse factor analysis carries out the study of cause-and-effect relationships using the method of logical induction - from particular, individual factors to general ones.

Factor analysis can be single stage And multi-stage. The first type is used to study factors of only one level (one level) of subordination without detailing them into their component parts. For example, at = A X b. In multi-stage factor analysis, factors are detailed A And b into constituent elements in order to study their behavior. The detailing of factors can be continued further. In this case, the influence of factors at different levels of subordination is studied.

It is also necessary to distinguish static And dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Finally, factor analysis can be retrospective, which studies the reasons for the increase in performance indicators over past periods, and promising, which examines the behavior of factors and performance indicators in perspective.

The main tasks of factor analysis are as follows.

1. Selection of factors that determine the performance indicators under study.

2. Classification and systematization of factors in order to provide an integrated and systematic approach to the study of their influence on the results of economic activity.

3. Determination of the form of dependence between factors and the performance indicator.

4. Modeling the relationships between performance and factor indicators.

5. Calculation of the influence of factors and assessment of the role of each of them in changing the value of the effective indicator.

6. Work with the factor model (its practical use for managing economic processes).

Selection of factors for analysis of one or another indicator is carried out on the basis of theoretical and practical knowledge acquired in this industry. In this case, they usually proceed from the principle: the larger the complex of factors studied, the more accurate the results of the analysis will be. At the same time, it is necessary to keep in mind that if this complex of factors is considered as a mechanical sum, without taking into account their interaction, without identifying the main, determining ones, then the conclusions may be erroneous. In ACD, an interconnected study of the influence of factors on the value of performance indicators is achieved through their systematization, which is one of the main methodological issues of this science.

An important methodological issue in factor analysis is determining the form of dependence between factors and performance indicators: functional or stochastic, direct or inverse, linear or curvilinear. It uses theoretical and practical experience, as well as methods for comparing parallel and dynamic series, analytical groupings of source information, graphical, etc.

Modeling of economic indicators (deterministic and stochastic) also represents a complex methodological problem in factor analysis, the solution of which requires special knowledge and practical skills in this industry. In this regard, this issue is given a lot of attention in this course.

The most important methodological aspect in ACD is influence calculation factors on the value of performance indicators, for which the analysis uses a whole arsenal of methods, the essence, purpose, scope of application of which and the calculation procedure are discussed in the following chapters.

And finally, the last stage of factor analysis - practical use of the factor model to calculate reserves for the growth of a productive indicator, to plan and predict its value when the production situation changes.

5.2. Classification of factors in the analysis of economic activity

The meaning of factor classification. Main types of factors. The concept and difference between various types of factors in ACD.

The classification of factors is their distribution into groups depending on common characteristics. It allows you to gain a deeper understanding of the reasons for changes in the phenomena under study, and to more accurately assess the place and role of each factor in the formation of the value of effective indicators.

The factors studied in the analysis can be classified according to different criteria (Fig. 5.1).

By their nature, factors are divided into natural-climatic, socio-economic and production-economic. Natural and climatic factors have a great impact on the results of activities in agriculture, mining, forestry and other industries. Taking into account their influence allows us to more accurately assess the results of the work of business entities.

TO socio-economic factors include the living conditions of workers, the organization of cultural, sports and recreational work at the enterprise, the general level of culture and education of personnel, etc. They contribute to a more complete use of the enterprise’s production resources and increase the efficiency of its work.

Production and economic factors determine the completeness and efficiency of use of the enterprise’s production resources and the final results of its activities.

Based on the degree of impact on the results of economic activity, factors are divided into major and minor. TO main include factors that have a decisive impact on the performance indicator. Secondary those that do not have a decisive impact on the results of economic activity in the current conditions are considered. Here it is necessary to note that the same factor, depending on the circumstances, can be both primary and secondary. The ability to identify the main, determining factors from a variety of factors ensures the correctness of the conclusions based on the results of the analysis.

Of great importance when studying economic phenomena and processes and assessing the results of enterprises’ activities is the classification of factors into internal And external, that is, on factors that depend and do not depend on the activities of a given enterprise. The main attention in the analysis should be paid to the study of internal factors that the enterprise can influence.

At the same time, in many cases, with developed production connections and relationships, the results of each enterprise are significantly influenced by the activities of other enterprises, for example, the uniformity and timeliness of supplies of raw materials, their quality, cost, market conditions, inflationary processes, etc. Often the results of enterprises' work are reflected in changes in the field of specialization and production cooperation. These factors are external. They do not characterize the efforts of a given team, but their study makes it possible to more accurately determine the degree of influence of internal causes and thereby more fully identify the internal reserves of production.

To correctly assess the activities of enterprises, factors must be divided into objective And subjective Objective ones, such as a natural disaster, do not depend on the will and desires of people. Unlike objective reasons, subjective reasons depend on the activities of legal entities and individuals.

According to the degree of prevalence, factors are divided into are common And specific. General factors include factors that operate in all sectors of the economy. Specific are those that operate in a particular sector of the economy or enterprise. This division of factors allows us to more fully take into account the characteristics of individual enterprises and industries and make a more accurate assessment of their activities.

Factors are distinguished according to the period of influence on the results of economic activity: permanent And variables. Constant factors influence the phenomenon under study continuously, throughout the entire period of time. The impact of variable factors manifests itself periodically, for example, the development of new technology, new types of products, new production technology, etc.

Of great importance for assessing the activities of enterprises is the division of factors according to the nature of their action into intensive And extensive. Extensive factors include factors that are associated with a quantitative rather than a qualitative increase in the performance indicator, for example, an increase in the volume of production by expanding the sown area, increasing the number of livestock, the number of workers, etc. Intensive factors characterize the degree of effort and labor intensity in the production process, for example, increasing crop yields, animal productivity, and the level of labor productivity.

If the analysis aims to measure the influence of each factor on the results of economic activity, then they are divided into quantitative And high quality, complex And simple, straight And indirect, measurable And immeasurable.

Quantitative factors are considered that express the quantitative certainty of phenomena (number of workers, equipment, raw materials, etc.). Quality factors determine the internal qualities, characteristics and characteristics of the objects being studied (labor productivity, product quality, soil fertility, etc.).

Most of the factors studied are complex in composition and consist of several elements. However, there are also those that cannot be broken down into their component parts. In this regard, factors are divided into complex (complex) And simple (elemental). An example of a complex factor is labor productivity, and a simple one is the number of working days in the reporting period.

As already indicated, some factors have a direct impact on the performance indicator, while others have an indirect impact. Based on the level of subordination (hierarchy), factors of the first, second, third and subsequent levels of subordination are distinguished. TO first level factors These include those that directly affect the performance indicator. Factors that determine the performance indicator indirectly, using first-level factors, are called second level factors etc. In Fig. 5.2 shows that the factors of the first level are the average annual number of workers and the average annual production output per worker. The number of days worked by one worker and the average daily output are second-level factors relative to gross output. Factors of the third level include the length of the working day and average hourly output.

The impact of individual factors on the performance indicator can be quantified. At the same time, there are a number of factors whose influence on the performance of enterprises cannot be directly measured, for example, the provision of housing for personnel, childcare facilities, the level of personnel training, etc.

5.3. Systematization of factors in the analysis of economic activity

The need and significance of systematization of factors. Basic ways of systematizing factors in deterministic and stochastic analysis.

A systematic approach in ACD necessitates an interconnected study of factors, taking into account their internal and external connections, interaction and subordination, which is achieved through systematization. Systematization in general is the placement of the phenomena or objects being studied in a certain order, identifying their relationship and subordination.

One way to systematize factors is to create deterministic factor systems. Create a factor system - means to present the phenomenon under study in the form of an algebraic sum, a quotient, or a product of several factors that determine its magnitude and are in functional dependence with it.

For example, the volume of gross output of an industrial enterprise can be represented as the product of two first-order factors: the average number of workers and the average annual output per worker per year, which in turn depends directly on the number of days worked by one worker on average per year and the average daily output per worker . The latter can also be decomposed into the length of the working day and average hourly output (Fig. 5.2).

The development of a deterministic factor system is achieved, as a rule, by detailing complex factors. Elementary ones (in our example - the number of workers, the number of days worked, the length of the working day) are not decomposed into factors, since they are homogeneous in their content. With the development of the system, complex factors are gradually detailed into less general ones, which in turn are even less general, gradually approaching elemental (simple) in their analytical content.

However, it should be noted that the development of factor systems to the required depth is associated with some methodological difficulties and, above all, with the difficulty of finding factors of a general nature that could be represented as a product, a particular one, or an algebraic sum of several factors. Therefore, deterministic systems usually cover the most general factors. Meanwhile, the study of more specific factors in ACD is significantly more important than general ones.

It follows that improving the methodology of factor analysis should be aimed at the interrelated study of specific factors, which are, as a rule, in a stochastic relationship with performance indicators.

Of great importance in the study of stochastic relationships is structural and logical analysis of the relationship between the studied indicators. It allows you to establish the presence or absence of cause-and-effect relationships between the studied indicators, study the direction of the connection, the form of dependence, etc., which is very important when determining the degree of their influence on the phenomenon under study and when generalizing the results of the analysis.

Analysis of the structure of the connection between the studied indicators in ACD is carried out using the construction structural and logical block diagram, which allows us to establish the presence and direction of the connection not only between the factors being studied and the performance indicator, but also between the factors themselves. By constructing a block diagram, you can see that among the factors being studied there are those that more or less directly affect the performance indicator, and those that affect not so much the performance indicator as each other.

For example, in Fig. Figure 5.3 shows the relationship between the cost per unit of crop production and factors such as crop yield, labor productivity, amount of fertilizer applied, quality of seeds, degree of mechanization of production.

First of all, it is necessary to establish the presence and direction of the relationship between the cost of production and each factor. Of course, there is a close connection between them. In this example, only crop yield has a direct impact on the cost of production. All other factors influence the cost of production not only directly, but also indirectly, through crop yields and labor productivity. For example, the amount of fertilizer applied to the soil helps to increase crop yields, which, other conditions being the same, leads to a reduction in the cost per unit of production. However, it is also necessary to take into account that an increase in the amount of fertilizer applied leads to an increase in the amount of costs per hectare of crops. And if the amount of costs increases at a higher rate than the yield, then the cost of production will not decrease, but increase. This means that the relationship between these two indicators can be both direct and inverse. It similarly affects the cost of production and the quality of seeds. Purchasing elite, high-quality seeds causes an increase in costs. If they increase to a greater extent than the yield from using higher quality seeds, then the cost of production will increase, and vice versa.

The degree of mechanization of production affects the cost of production both directly and indirectly. An increase in the level of mechanization causes an increase in the cost of maintaining fixed assets of production. However, at the same time, labor productivity increases and productivity increases, which helps reduce production costs.

The study of relationships between factors shows that of all the factors studied, there is no cause-and-effect relationship between the quality of seeds, the amount of fertilizers and the mechanization of production. There is also no direct inverse relationship between these indicators and the level of crop yield. All other factors directly or indirectly influence each other.

Thus, the systematization of factors allows us to more deeply study the relationship of factors in the formation of the value of the indicator under study, which is very important in the next stages of analysis, especially at the stage of modeling the indicators under study.

5.4. Deterministic modeling and transformation of factor systems

The essence and significance of modeling, requirements for it. Basic types of factorial deterministic models. Methods for transforming factor models. Modeling rules.

One of the tasks of factor analysis is to model the relationships between performance indicators and the factors that determine their value.

Modeling - This is one of the most important methods of scientific knowledge, with the help of which a model (conventional image) of the object of study is created. Its essence lies in the fact that the relationship between the indicator being studied and the factor indicators is conveyed in the form of a specific mathematical equation.

In factor analysis there are deterministic models (functional) and stochastic (correlation). Using deterministic factor models, the functional relationship between the performance indicator (function) and factors (arguments) is studied.

When modeling deterministic factor systems, a number of requirements must be met.

1. The factors included in the model, and the models themselves, must have a clearly expressed character, really exist, and not be invented abstract quantities or phenomena.

2. The factors that are included in the system must not only be necessary elements of the formula, but also be in a cause-and-effect relationship with the indicators being studied. In other words, the constructed factor system must have cognitive value. Factor models that reflect cause-and-effect relationships between indicators have significantly greater cognitive value than models created using mathematical abstraction techniques. The latter can be illustrated as follows. Let's take two models:

1)VP=CR X GW:

2) GV=VP/CR, Where VP - gross output of the enterprise; CR - number of employees at the enterprise; GV - average annual production per worker.

In the first system, the factors are in a causal relationship with the effective indicator, and in the second - in a mathematical relationship. This means that the second model, built on mathematical dependencies, has less cognitive significance than the first.

3. All indicators of the factor model must be quantitatively measurable, i.e. must have a unit of measurement and the necessary information security.

4. The factor model must provide the ability to measure the influence of individual factors, which means that it must take into account the proportionality of changes in the effective and factor indicators, and the sum of the influence of individual factors must be equal to the total increase in the effective indicator.

In deterministic analysis, the following types of most common factor models are distinguished.

1. Additive models:

They are used in cases where the effective indicator is an algebraic sum of several factor indicators.

2. Multiplicative models:

This type of model is used when the performance indicator is a product of several factors.

3. Multiple models:

They are used when the effective indicator is obtained by dividing one factor indicator by the value of another.

4. Mixed (combined) models - this is a combination in various combinations of previous models:

Modeling of multiplicative factor systems in ACD it is carried out by sequentially dividing the factors of the original system into factor factors. For example, when studying the process of formation of production volume (see Fig. 5.2), you can use such deterministic models as:

These models reflect the process of detailing the original factor system of a multiplicative form and expanding it by dividing complex factors into factors. The degree of detail and expansion of the model depends on the purpose of the study, as well as on the possibilities of detailing and formalizing indicators within the established rules.

Similarly carried out modeling of additive factor systems due to the division of one or several factor indicators into component elements.

As is known, the volume of product sales is equal to:

VRP =VBP -VAND,

Where VBP - volume of production; VAND - volume of on-farm use of products.

On the farm, the products were used as seeds (C) and feed (TO). Then the given original model can be written as follows: VRP =VBP - (C + K).

To the class multiple models The following methods of their transformation are used: lengthening, formal decomposition, expansion and contraction.

First method involves lengthening the numerator of the original model by replacing one or more factors with the sum of homogeneous indicators. For example, the cost per unit of production can be represented as a function of two factors: changes in the amount of costs (3) and the volume of output (VBP). The initial model of this factor system will have the form

If the total amount of costs (3) is replaced by their individual elements, such as wages (3P), raw materials and materials (SM), depreciation of fixed assets (A), overhead costs (HP) etc., then the deterministic factor model will have the form of an additive model with a new set of factors:

Where X 1 - labor intensity of products; X 2 - material consumption of products; X 3 - capital intensity of products; X 4 - overhead level.

Formal decomposition method factor system involves lengthening the denominator of the original factor model by replacing one or more factors with the sum or product of homogeneous indicators. If IN = L+M+N+P, then

As a result, we obtained a final model of the same type as the original factor system (multiple model). In practice, such decomposition occurs quite often. For example, when analyzing the production profitability indicator (R):

where P is the amount of profit from sales of products; 3 - the amount of costs for production and sales of products. If the sum of costs is replaced by its individual elements, the final model as a result of the transformation will take on the following form:

The cost of one ton-kilometer depends on the amount of costs for maintaining and operating the vehicle (3) and on its average annual output (GW). The initial model of this system will look like: C tkm = 3 / GV. Considering that the average annual output of a car, in turn, depends on the number of days worked by one car per year (D), shift duration (P) and average hourly output (ChV), we can significantly lengthen this model and decompose the increase in cost into more factors:

The expansion method involves expanding the original factor model by multiplying the numerator and denominator of the fraction by one or more new indicators. For example, if the original model

introduce a new indicator, the model will take the form

The result was a final multiplicative model in the form of a product of a new set of factors.

This modeling method is very widely used in analysis. For example, the average annual output per worker (labor productivity indicator) can be written as follows: GV = VP / CR. If you enter an indicator such as the number of days worked by all employees (D), then we get the following model of annual output:

Where DV - average daily output; D - number of days worked by one employee.

After introducing the indicator of the number of hours worked by all employees (G), we obtain a model with a new set of factors: average hourly output (ChV), number of days worked by one employee (D) and duration of the working day (I):

The reduction method involves creating a new factor model by dividing the numerator and denominator of the fraction by the same indicator:

In this case, the final model is of the same type as the original one, but with a different set of factors.

And again a practical example. As is known, the economic profitability of an enterprise is calculated by dividing the amount of profit ( P) on the average annual cost of fixed and working capital of the enterprise (KL):

R=P/KL.

If we divide the numerator and denominator by the volume of product sales (turnover), we obtain a multiple model, but with a new set of factors: return on sales and capital intensity of products:

And one more example. Capital productivity (CR) is determined by the ratio of gross ( VP) or commercial products ( TP) to the average annual cost of fixed production assets (OPF):

Dividing the numerator and denominator by the average annual number of workers (CR), we get a more meaningful multiple model with other factor indicators: average annual production per worker (GV), characterizing the level of labor productivity and capital-labor ratio (Fv):

It should be noted that in practice, several methods can be used sequentially to transform the same model. For example:

Where FO - capital productivity; RP - volume of products sold (revenue); C - cost of goods sold; P- profit; OPF-average annual cost of fixed production assets; OS - average working capital balances.

In this case, to transform the original factor model, which is built on mathematical dependencies, methods of lengthening and expansion are used. The result is a more meaningful model, which has greater educational value, since it takes into account the cause-and-effect relationships between indicators. The resulting final model allows us to study how capital productivity is affected by the profitability of fixed assets, the relationship between fixed and working capital, as well as the working capital turnover ratio.

Thus, performance indicators can be decomposed into their constituent elements (factors) in various ways and presented in the form of various types of deterministic models. The choice of modeling method depends on the object of study, the goal, as well as the professional knowledge and skills of the researcher.

The process of modeling factor systems is a very complex and crucial moment in ACAD. The final results of the analysis depend on how realistically and accurately the created models reflect the relationship between the studied indicators.

All phenomena and processes of economic activity of enterprises are interconnected and interdependent. Some of them are directly related to each other, others indirectly. Hence, an important methodological issue in economic analysis is the study and measurement of the influence of factors on the value of the economic indicators under study.

Under economic factor analysis is understood as a gradual transition from the initial factor system to the final factor system, the disclosure of a full set of direct, quantitatively measurable factors that influence the change in the performance indicator.

Based on the nature of the relationship between indicators, methods of deterministic and stochastic factor analysis are distinguished.

Deterministic factor analysis is a methodology for studying the influence of factors whose connection with the performance indicator is functional in nature.

The main properties of the deterministic approach to analysis:
· construction of a deterministic model through logical analysis;
· the presence of a complete (hard) connection between indicators;
· the impossibility of separating the results of the influence of simultaneously acting factors that cannot be combined in one model;
· study of relationships in the short term.

There are four types of deterministic models:

Additive Models represent an algebraic sum of indicators and have the form

Such models, for example, include cost indicators in relation to elements of production costs and cost items; an indicator of the volume of production in its relationship with the volume of output of individual products or the volume of output in individual departments.

Multiplicative models can be summarized by the formula

.

An example of a multiplicative model is a two-factor model of sales volume

,

Where H- average number of employees;

C.B.- average output per employee.

Multiple models:

An example of a multiple model is the indicator of the turnover period of goods (in days). T OB.T:

,

Where Z T- average stock of goods; O R- one-day sales volume.

Mixed models are a combination of the above models and can be described using special expressions:

Examples of such models are cost indicators per 1 ruble. commercial products, profitability indicators, etc.

To study the relationship between indicators and quantitatively measure the many factors that influenced the effective indicator, we present general model transformation rules in order to include new factor indicators.

To detail the generalizing factor indicator into its components, which are of interest for analytical calculations, the technique of lengthening the factor system is used.

If the initial factor model is , a , then the model will take the form .

To identify a certain number of new factors and construct the factor indicators necessary for calculations, the technique of expanding factor models is used. In this case, the numerator and denominator are multiplied by the same number:

.

To construct new factor indicators, the technique of reducing factor models is used. When using this technique, the numerator and denominator are divided by the same number.

.

The detail of factor analysis is largely determined by the number of factors whose influence can be quantitatively assessed, therefore multifactorial multiplicative models are of great importance in the analysis. Their construction is based on the following principles:
· the place of each factor in the model must correspond to its role in the formation of the effective indicator;
· the model should be built from a two-factor complete model by sequentially dividing factors, usually qualitative, into components;
· when writing a formula for a multifactor model, factors should be arranged from left to right in the order of their replacement.

Building a factor model is the first stage of deterministic analysis. Next, determine the method for assessing the influence of factors.

Chain substitution method consists in determining a number of intermediate values ​​of the generalizing indicator by sequentially replacing the basic values ​​of the factors with the reporting ones. This method is based on elimination. Eliminate- means to eliminate, exclude the influence of all factors on the value of the effective indicator, except one. Moreover, based on the fact that all factors change independently of each other, i.e. First, one factor changes, and all the others remain unchanged. then two change while the others remain unchanged, etc.

In general, the application of the chain production method can be described as follows:

where a 0, b 0, c 0 are the basic values ​​of factors influencing the general indicator y;

a 1 , b 1 , c 1 - actual values ​​of factors;

y a, y b, are intermediate changes in the resulting indicator associated with changes in factors a, b, respectively.

The total change D у = у 1 – у 0 consists of the sum of changes in the resulting indicator due to changes in each factor with fixed values ​​of the remaining factors:

Let's look at an example:

table 2

Initial data for factor analysis

We will analyze the impact of the number of workers and their output on the volume of marketable output using the method described above based on the data in Table 2. The dependence of the volume of commercial products on these factors can be described using a multiplicative model:

Then the effect of a change in the number of employees on the general indicator can be calculated using the formula:

Thus, the change in the volume of marketable products was positively influenced by a change in the number of employees by 5 people, which caused an increase in production volume by 730 thousand rubles. and a negative impact was had by a decrease in output by 10 thousand rubles, which caused a decrease in volume by 250 thousand rubles. The combined influence of two factors led to an increase in production volume by 480 thousand rubles.

The advantages of this method: versatility of application, ease of calculations.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of factor decomposition have different meanings. This is due to the fact that as a result of applying this method, a certain indecomposable residue is formed, which is added to the magnitude of the influence of the last factor. In practice, the accuracy of factor assessment is neglected, highlighting the relative importance of the influence of one or another factor. However, there are certain rules that determine the substitution sequence:
· if there are quantitative and qualitative indicators in the factor model, the change in quantitative factors is considered first;
· if the model is represented by several quantitative and qualitative indicators, the substitution sequence is determined by logical analysis.

Under quantitative factors in analysis they understand those that express the quantitative certainty of phenomena and can be obtained by direct accounting (number of workers, machines, raw materials, etc.).

Qualitative factors determine the internal qualities, signs and characteristics of the phenomena being studied (labor productivity, product quality, average working hours, etc.).

Absolute difference method is a modification of the chain substitution method. The change in the effective indicator due to each factor using the method of differences is defined as the product of the deviation of the factor being studied by the basic or reporting value of another factor, depending on the selected substitution sequence:

Relative difference method used to measure the influence of factors on the growth of a performance indicator in multiplicative and mixed models of the form y = (a – c) . With. It is used in cases where the source data contains previously determined relative deviations of factor indicators in percentages.

For multiplicative models like y = a . V . The analysis technique is as follows:

· find the relative deviation of each factor indicator:

· determine the deviation of the performance indicator at due to each factor

Example. Using the data in table. 2, we will analyze using the method of relative differences. The relative deviations of the factors under consideration will be:

Let's calculate the impact of each factor on the volume of commercial output:

The calculation results are the same as when using the previous method.

Integral method allows you to avoid the disadvantages inherent in the chain substitution method, and does not require the use of techniques for distributing the indecomposable remainder among factors, because it has a logarithmic law of redistribution of factor loads. The integral method makes it possible to achieve a complete decomposition of the effective indicator into factors and is universal in nature, i.e. applicable to multiplicative, multiple and mixed models. The operation of calculating a definite integral is solved using a PC and is reduced to constructing integrand expressions that depend on the type of function or model of the factor system.
1. What management problems are solved through economic analysis?
2. Describe the subject of economic analysis.
3. What distinctive features characterize the method of economic analysis?
4. What principles underlie the classification of techniques and methods of analysis?
5. What role does the method of comparison play in economic analysis?
6. Explain how to construct deterministic factor models.
7. Describe the algorithm for using the simplest methods of deterministic factor analysis: the method of chain substitutions, the method of differences.
8. Characterize the advantages and describe the algorithm for using the integral method.
9. Give examples of problems and factor models to which each of the methods of deterministic factor analysis is applied.

This may be of interest (selected paragraphs):

Factor analysis is understood as a method of complex and systematic study and measurement of factors for the value of effective indicators.

The following types of factor analysis are distinguished: deterministic (functional)

stochastic (probabilistic)

Deterministic factor analysis – this is a technique for assessing the influence of factors whose connection with the performance indicator is functional in nature, i.e. the effective indicator can be presented as a product, quotient or algebraic sum of factors.

Methods of deterministic factor analysis:

chain substitution method

index

integral

absolute differences

relative differences, etc.

Stochastic analysis – a methodology for studying factors whose connection with an effective indicator, unlike a functional indicator, is incomplete, probabilistic.

Methods of stochastic factor analysis:

correlation analysis

regression analysis

dispersive

component

modern multivariate factor analysis

discriminant

Basic methods of deterministic factor analysis

THE CHAIN ​​SUBSTITUTION METHOD is the most universal; it is used to calculate the influence of factors in all types of factor models: addition, multiplication, division and mixed.

This method allows you to determine the influence of individual factors on changes in the value of the performance indicator by replacing the base value of each factor indicator with the actual value in the reporting period. For this purpose, a number of conditional values ​​of the performance indicator are determined, which take into account the change in one, then two, three, etc. factors, assuming that the rest do not change.

Comparing the value of an effective indicator before and after changing the level of one or another factor allows us to exclude the influence of all factors except one and determine its impact on the increase in the effective indicator.

The algebraic sum of the influence of factors must necessarily be equal to the total increase in the effective indicator. The absence of such equality indicates mistakes have been made.

INDEX METHOD is based on relative indicators of dynamics, spatial comparisons, plan implementation (indices), which are defined as the ratio of the level of the analyzed indicator in the reporting period to its level in the base period (or to the planned or other object).

Using indices, you can identify the influence of various factors on changes in performance indicators in multiplication and division models.

The INTEGRAL METHOD is a further logical development of the considered methods, which have a significant drawback: when using them, they assume that the factors change independently of each other. In fact, they change together, are interconnected, and from this interaction an additional increase in the effective indicator is obtained, which is added to one of the factors, usually the last one. In this regard, the magnitude of the influence of factors on the change in the performance indicator changes depending on the place in which one or another factor is placed in the model under study.

When using the INTEGRAL method, the error in calculating the influence of factors is distributed equally between them, and the order of substitution does not matter. The error distribution is carried out using special models.

Types of finite factor systems, the most frequently encountered in the analysis of economic activity:

additive models

multiplicative models

;

multiple models

;
;
;,

Where y– effective indicator (initial factor system);

x i– factors (factor indicators).

In relation to the class of deterministic factor systems, the following are distinguished: basic modeling techniques.

,

those. multiplicative model of the form
.

3. Factor system reduction method. Initial factor system
. If we divide both the numerator and denominator of the fraction by the same number, we get a new factor system (in this case, of course, the rules for selecting factors must be followed):

.

In this case we have a finite factor system of the form
.

Thus, the complex process of forming the level of the studied indicator of economic activity can be decomposed using various techniques into its components (factors) and presented in the form of a model of a deterministic factor system.

Modeling the return on capital indicator of an enterprise ensures the creation of a five-factor profitability model, which includes all indicators of intensification of the use of production resources.

We will conduct a profitability analysis using the data in the table.

CALCULATION OF KEY INDICATORS FOR THE ENTERPRISE FOR TWO YEARS

Based on the basic indicators, we will calculate the indicators of intensification of production resources (rub.)

Five-factor model of return on assets (advanced capital)

.

We will illustrate the methodology for analyzing the five-factor model of return on assets using the method of chain substitutions.

First, let's find the profitability value for the base and reporting years.

For base year:

For the reporting year:

The difference in the profitability ratios of the reporting and base years was 0.005821, and as a percentage - 0.58%.

Let's look at how the five factors mentioned above contributed to this increase in profitability.

In conclusion, we will compile a summary of the influence of factors on the deviation of profitability of the 2nd year compared to the 1st (base) year.

Total deviation, % 0.58

Including due to the influence of:

labor intensity +0.31

material consumption +0.28

depreciation capacity 0

Total cost: +0.59

capital intensity −0.07

working capital turnover +0.06

Total advance payment −0.01

The functioning of any socio-economic system (which includes an operating enterprise) occurs in conditions of complex interaction of a complex of internal and external factors. Factor- this is the cause, the driving force of a process or phenomenon, determining its character or one of its main features.

Under factor analysis understands the methodology for a comprehensive and systematic study and measurement of the impact of factors on the value of performance indicators.

In general, the following main ones can be distinguished: stages (tasks) factor analysis:

Setting the purpose of the analysis.

Selection of factors that determine the performance indicators under study.

Classification and systematization of factors in order to provide an integrated and systematic approach to the study of their influence on the results of economic activity.

Determination of the form of dependence between factors and the performance indicator.

Modeling the relationships between performance and factor indicators.

Calculation of the influence of factors and assessment of the role of each of them in changing the value of the performance indicator.

Working with the factor model (its practical use for managing economic processes).

In other words, method task- transition from a real large number of signs or causes determining the observed variability to a small number of the most important variables (factors) with minimal loss of information (methods that are similar in essence, but not in mathematical terms - component analysis, canonical analysis, etc.).

The method arose and was initially developed in problems of psychology and anthropology (at the turn of the 19th and 20th centuries), but now the scope of its application is much wider.

Purpose of factor analysis

Factor analysis- determining the influence of factors on the result - is one of the strongest methodological solutions in the analysis of the economic activities of companies for decision making. For managers - an additional argument, an additional “angle of view”.

The feasibility of using factor analysis

As you know, you can analyze everything ad infinitum. It is advisable at the first stage to implement an analysis of deviations, and where necessary and justified, to apply the factor analysis method. In many cases, a simple analysis of deviations is enough to understand that the deviation is “critical”, and when it is not at all necessary to know the degree of its influence.

Factors are divided into internal and external, depending on whether the activities of a given enterprise affect them or not. The analysis focuses on internal factors that the enterprise can influence.

Factors are divided into objective, independent of the will and desires of people, and subjective, influenced by the activities of legal entities and individuals.

According to the degree of prevalence, factors are divided into general and specific. Common factors operate in all sectors of the economy. Specific factors operate within a particular industry or a specific enterprise.

Types of factor analysis

The following types of factor analysis exist:

1) Deterministic (functional) - the effective indicator is presented in the form of a product, quotient or algebraic sum of factors.

2) Stochastic (correlation) - the relationship between the effective and factor indicators is incomplete or probabilistic.

3) Direct (deductive) – from the general to the specific.

4) Reverse (inductive) – from the particular to the general.

5) Single-stage and multi-stage.

6) Static and dynamic.

7) Retrospective and prospective.

Depending on the type of factor model, there are two main types of factor analysis - deterministic and stochastic.

Deterministic factor analysis is a technique for studying the influence of factors whose connection with the effective indicator is functional in nature, that is, when the effective indicator of the factor model is presented in the form of a product, quotient or algebraic sum of factors.

This type of factor analysis is the most common, since, being quite simple to use (compared to stochastic analysis), it allows you to understand the logic of the action of the main factors of enterprise development, quantify their influence, understand which factors and in what proportion it is possible and advisable to change to increase production efficiency.

Deterministic factor analysis has a fairly strict sequence of procedures:

1.building an economically sound deterministic factor model;

2. choosing a method of factor analysis and preparing conditions for its implementation;

3.implementation of counting procedures for model analysis;

Basic methods of deterministic factor analysis

Chain substitution method; Absolute difference method; Relative difference method; Integral method; Logarithm method.

Stochastic analysis is a methodology for studying factors whose connection with a performance indicator, unlike a functional one, is incomplete and probabilistic (correlation). The essence of the stochastic method is to measure the influence of stochastic dependencies with uncertain and approximate factors. Stochastic method It is advisable to use for economic research with incomplete (probabilistic) correlation: for example, for marketing problems. If with a functional (complete) dependence with a change in the argument there is always a corresponding change in the function, then with a correlation connection a change in the argument can give several values ​​of the increase in the function depending on the combination of other factors that determine this indicator. For example, labor productivity at the same level of capital-labor ratio may be different at different enterprises. This depends on the optimal combination of other factors affecting this indicator.

Stochastic modeling is, to a certain extent, a complement and deepening of deterministic factor analysis. In factor analysis, these models are used according to three main reasons:

It is necessary to study the influence of factors for which it is impossible to build a strictly determined factor model (for example, the level of financial leverage);

It is necessary to study the influence of complex factors that cannot be combined in the same strictly deterministic model;

It is necessary to study the influence of complex factors that cannot be expressed in one quantitative indicator (for example, the level of scientific and technological progress).

It is also necessary to distinguish static And dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Finally, factor analysis can be retrospective, which studies the reasons for the increase in performance indicators over past periods, and promising, which examines the behavior of factors and performance indicators in perspective.

Factor analysis can be single-stage or multi-stage. The first type is used to study factors of only one level (one level) of subordination without detailing them into their component parts. For example, . In multi-stage factor analysis, factors a and b are detailed into their component elements in order to study their behavior. The detailing of factors can be continued further. In this case, the influence of factors at different levels of subordination is studied.

It is also necessary to distinguish between static and dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

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Identification of the relationship between performance indicators and factor indicators, the form of dependence between them. Features of the application of the elimination method, integral and index methods. Mathematical methods of factor analysis.

Factors are the conditions of economic processes and the reasons influencing them.

Factor analysis is a technique for a comprehensive systemic study and measurement of the impact of factors on the value of a performance indicator.

All phenomena and processes of economic activity of enterprises are in relationships, interdependence and interdependence. One of them directly are interconnected, others - indirectly . For example, the amount of profit from the core activities of an enterprise is directly influenced by such factors as the volume and structure of sales, selling prices and production costs. All other factors influence this indicator indirectly. Each phenomenon can be considered both as a cause and as a result. For example, labor productivity can be considered, on the one hand, as the reason for changes in the volume of production, the level of its cost, and on the other hand, as a result of changes in the degree of mechanization and automation of production, improvement in labor organization, etc. If this or that indicator is considered as a consequence, as a result of the action of one or more causes and acts as an object of study, then when studying relationships it is called an effective indicator. Indicators that determine the behavior of an effective characteristic are called factor indicators.

Each performance indicator depends on numerous and varied factors. The more detailed the influence of factors on the value of the performance indicator is studied, the more accurate the results of the analysis and assessment of the quality of work of enterprises. Hence, an important methodological issue in the analysis of economic activity is the study and measurement of the influence of factors on the value of the economic indicators under study. Without a deep and comprehensive study of factors, it is impossible to draw reasonable conclusions about the results of activities, identify production reserves, justify plans and management decisions, predict performance results, and assess their sensitivity to changes in internal and external factors.

Under factor analysis understand the methodology for comprehensive and systematic study and measurement of the impact of factors on the value of performance indicators.

The following are distinguished: types of factor analysis:

Deterministic (functional) and stochastic (probabilistic);

Direct (deductive) and reverse (inductive);

Single-stage and multi-stage;

Static and dynamic;

Retrospective and prospective (forecast).

Based on the nature of the relationship between indicators, methods of deterministic and stochastic factor analysis are distinguished.

Deterministic factor analysis is a technique for studying the influence of factors whose connection with the performance indicator is functional in nature, i.e. the effective indicator can be presented as a product, quotient or algebraic sum of factors.

Stochastic factor analysis explores the influence of factors whose connection with the performance indicator, unlike the functional one, is incomplete, probabilistic (correlation). If with a functional (complete) dependence with a change in the argument there is always a corresponding change in the function, then with a stochastic connection a change in the argument can give several values ​​of the increase in the function depending on the combination of other factors that determine this indicator. For example, labor productivity at the same level of capital-labor ratio may be different at different enterprises. This depends on the optimal combination of all the factors that form this indicator.

With direct factor analysis The research is conducted in a deductive manner - from the general to the specific. Back factor analysis carries out the study of cause-and-effect relationships using the method of logical induction - from particular, individual factors to general ones. It allows you to assess the degree of sensitivity of performance results to changes in the factor under study.

Factor analysis can be single-stage or multi-stage. Single stage used to study factors of only one level (one level) of subordination without detailing them into their component parts. For example, y = a b. With multi-stage factor analysis Factors a and b are detailed into their constituent elements in order to study their essence. The factors can be further detailed. In this case, the influence of factors at different levels of subordination is studied.

It is also necessary to distinguish between static and dynamic factor analysis . The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Finally, factor analysis can be retrospective , which studies the reasons for changes in the results of economic activities over past periods, and prospective , which examines the behavior of factors and performance indicators in perspective.

Main tasks of factor analysis

1. Selection of factors for the analysis of the studied indicators.

2. Classification and systematization of them in order to provide a systematic approach.

3. Modeling the relationships between performance and factor indicators.

4. Calculation of the influence of factors and assessment of the role of each of them in changing the value of the effective indicator.

5. Working with the factor model (its practical use for managing economic processes).

To study the influence of factors on business results and calculate reserves, the analysis uses methods of deterministic and stochastic factor analysis, methods for optimizing solutions to economic problems(see picture).

Determining the magnitude of the influence of individual factors on the increase in performance indicators is one of the most important methodological tasks in ACD. In deterministic analysis, the following methods are used for this: chain substitution, absolute differences, relative differences, index, integral, proportional division, logarithm, balance, etc.

The main properties of the deterministic approach to analysis:

Construction of a deterministic model through logical analysis;

The presence of a complete (hard) connection between indicators;

The impossibility of separating the results of the influence of simultaneously acting factors that cannot be combined in one model;

Studying relationships in the short term.

Let's consider the possibility of using the main methods of deterministic analysis, summarizing the above in the form of a matrix

Matrix of application of deterministic factor analysis methods

Legend: + used;

- not used

There are four types of deterministic models:

Additive models represent an algebraic sum of indicators and have the form:

Such models, for example, include cost indicators in relation to elements of production costs and cost items; an indicator of the volume of production of goods in its relationship with the volume of output of individual products or the volume of output in individual departments.

Multiplicative is the sequential division of the factors of the original system into factor factors. Models in a generalized form can be represented by the formula:

An example of a multiplicative model is a two-factor model of gross output: VP = CR * SV

where CR is the average number of employees;

CB - average annual output per employee.

Multiple models: y = x1 / x2.

An example of a multiple model is the indicator of the turnover period of goods (TOB.T) (in days): TOB.T = 3T / OR, (1.9)

where ST is the average stock of goods;

OP - one-day sales volume.

Mixed models are a combination of the above models and can be described using special expressions:

Examples of such models are cost indicators per 1 ruble. manufactured products, profitability indicators, etc.

1. The most universal of the methods of deterministic analysis is the method of chain substitution.

It is used to calculate the influence of factors in all types of deterministic factor models: additive, multiplicative, multiple and mixed (combined). This method is based on elimination.

Elimination is the process of gradually eliminating the impact of all factors on the value of the performance indicator, except one. Moreover, based on the fact that all factors change independently of each other, i.e. First, one factor changes, and all the others remain unchanged. Then two change while the others remain unchanged, etc.

This method allows you to determine the influence of individual factors on changes in the value of the effective indicator. The essence of this technique is to identify from all the existing factors the main ones that have a decisive influence on the change in the indicator. For this purpose, a number of conditional values ​​of the performance indicator are determined, which take into account changes in one, then two, three and subsequent factors, assuming that the rest do not change. This means that in the calculations, private planned indicators are successively replaced with reporting ones, and the results obtained are compared with the available previous data. Comparing the values ​​of a performance indicator before and after changing the level of one or another factor makes it possible to eliminate the influence of all factors except one and determine the impact of the latter on the growth of the performance indicator.

When using the chain substitution method, the sequence of substitutions is of great importance: First of all, it is necessary to take into account changes in quantitative and then qualitative indicators. Using the reverse sequence of calculations does not provide a correct characterization of the influence of factors.

Thus, the use of the chain substitution method requires knowledge of the relationship of factors, their subordination, and the ability to correctly classify and systematize them.

In general, the application of the chain production method can be described as follows:

y0 = a0 ∙ b0 ∙ c0 ;

ya = a1 ∙ b0 ∙ c0 ;

yb = a1 ∙ b1 ∙ c0 ;

y1 = a1 ∙ b1 ∙ c1 ;

where a0, b0, c0 - basic values ​​of factors influencing the general indicator y;

a1, b1, c1 - actual values ​​of factors;

ya, yb, - intermediate values ​​of the resulting indicator associated with changes in factors A And b, respectively.

The total change Δу = у1 – у0 consists of the sum of changes in the resulting indicator due to changes in each factor with fixed values ​​of the remaining factors. Those. the sum of the influence of individual factors should equal the overall increase in the performance indicator.

∆y = ∆ya + ∆yb + ∆yc = y1– y0

∆ya = ya – y0 ;

∆yb = yb – ya ;

∆yc = y1 – yb.

The advantages of this method: versatility of application, ease of calculations.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of factor decomposition have different meanings.

2. The method of absolute differences is a modification of the method of chain substitution.

The method of absolute differences is used to calculate the influence of factors on the growth of a performance indicator in deterministic analysis, but only in multiplicative models (Y = x1 ∙ x2 ∙ x3 ∙∙∙∙∙ xn) and models of multiplicative-additive type: Y = (a - b) ∙c and Y = a∙(b - c). And although its use is limited, due to its simplicity it is widely used in ACD.

The essence of the method is that the magnitude of the influence of factors is calculated by multiplying the absolute increase in the value of the factor under study by the base (planned) value of the factors that are to the right of it, and by the actual value of the factors located in the model to the left of it.

y0 = a0 ∙ b0 ∙ c0

∆ya = ∆a ∙ b0 ∙ c0

∆yb = a1 ∙ ∆b ∙ c0

∆yс = a1 ∙ b1 ∙ ∆с

y1 = a1 ∙ b1 ∙ c1

The algebraic sum of the increase in the effective indicator due to individual factors should be equal to its total change Δу = у1 – у0.

∆y = ∆ya + ∆yb + ∆yc = y1 – y0

Let's consider an algorithm for calculating factors using this method in multiplicative-additive models. For example, let’s take the factor model of profit from product sales:

P = VRP ∙ (C - C),

where P is profit from sales of products;

VRP – volume of product sales;

P is the price of a unit of production;

C is the cost per unit of production.

Increase in profit due to changes:

volume of product sales ∆ПВРП = ∆VРП ∙ (Ц0 − С0);

sales yen ∆ПЦ = VРП1 ∙ ∆Ц;

production cost ∆PS = VРП1 ∙ (−∆С);

3. Method of relative differences It is used in cases where the source data contains previously determined relative deviations of factor indicators in percentages. It is used to measure the influence of factors on the growth of a performance indicator only in multiplicative models. Here, relative increases in factor indicators are used, expressed as coefficients or percentages. Let us consider the methodology for calculating the influence of factors in this way for multiplicative models of the type Y = abc.

The change in the performance indicator is determined as follows:

According to this algorithm, to calculate the influence of the first factor, it is necessary to multiply the base value of the effective indicator by the relative increase of the first factor, expressed as a decimal fraction.

To calculate the influence of the second factor, you need to add the change due to the first factor to the base value of the effective indicator and then multiply the resulting amount by the relative increase in the second factor.

The influence of the third factor is determined in a similar way: to the base value of the effective indicator it is necessary to add its increase due to the first and second factors and multiply the resulting amount by the relative increase of the third factor, etc.

The calculation results are the same as when using the previous methods.

The method of relative differences is convenient to use in cases where it is necessary to calculate the influence of a large set of factors (8-10 or more). Unlike previous methods, the number of computational procedures is significantly reduced here, which determines its advantage.

4. The integral method for assessing factor influences avoids the disadvantages inherent in the chain substitution method and does not require the use of techniques for distributing the indecomposable remainder among factors, because it has a logarithmic law of redistribution of factor loads. The integral method makes it possible to achieve a complete decomposition of the effective indicator into factors and is universal in nature, i.e. applicable to multiplicative, multiple and mixed models. The operation of calculating a definite integral is carried out using the computing capabilities of personal computers and comes down to constructing integrand expressions that depend on the type of function or model of the factor system.

Its use makes it possible to obtain more accurate results for calculating the influence of factors compared to the methods of chain substitution, absolute and relative differences, since the additional increase in the effective indicator from the interaction of factors is not added to the last factor, but is divided equally between them.

Let's consider algorithms for calculating the influence of factors for different models:

1) Model view: y = a ∙ b

2) Model view: y = a ∙ b ∙ c

3) View model:

3) View model:

If the denominator has more than two factors, the procedure continues.

Thus, the use of the integral method does not require knowledge of the entire integration process. It is enough to substitute the necessary numerical data into these ready-made working formulas and make not very complex calculations using a calculator or other computer equipment.

The results of calculations using the integral method differ significantly from those obtained by the method of chain substitutions or modifications of the latter. The greater the magnitude of changes in factors, the more significant the difference.

5. The index method allows us to identify the influence of various factors on the studied aggregate indicator. By calculating indices and constructing a time series characterizing, for example, production output in value terms, one can make a qualified judgment about the dynamics of production volume.

It is based on relative indicators of dynamics, expressing the ratio of the level of the analyzed indicator in the reporting period to its level in the base period. Using the index method you can

Any index is calculated by comparing the measured (reported) value with the base one. For example, production volume index: Ivп = VВП1 / VВП0

Indices expressing the ratio of directly comparable quantities are called individual , and the characterizing relationships of complex phenomena are group , or total . Statistics name several forms indices that are used in analytical work - aggregate, arithmetic, harmonic, etc.

By using the aggregate form of the index and following the established computational procedure, it is possible to solve a classic analytical problem: determining the influence of the quantity factor and the price factor on the volume of produced or sold products. The calculation scheme will be as follows:

It should be recalled here that the aggregate index is the basic form of any general index; it can be converted to both the arithmetic mean and the harmonic mean indices.

The dynamics of turnover in the sale of industrial products should be characterized, as is known, by time series constructed over a number of past years, taking into account price changes (this applies, of course, to procurement, wholesale and retail turnover).

The index of sales volume (turnover), taken in prices of the corresponding years, has the form:

General price index:

General indexes- relative indicators obtained as a result of comparison of phenomena covering heterogeneous product groups.

General index of trade turnover (cost of marketable products);

where p1q1 is the turnover of the reporting period

p0q0 − turnover of the base period

p – prices, q – quantity

General price index: Ip =

Average indexes- these are relative indicators used to analyze structural changes. They are used only for homogeneous goods.

Price index of variable composition (average prices):

Constant price index:

6. The method of proportional division can be used in a number of cases to determine the magnitude of the influence of factors on the increase in the performance indicator . This applies to those cases when we are dealing with additive models Y=∑хi and models of multiple additive type:

In the first case, when we have a single-level model of type Y= a + b + c, the calculation is carried out as follows:

In multiple-additive type models, it is first necessary to determine, using a chain substitution method, how much the effective indicator has changed due to the numerator and denominator, and then calculate the influence of second-order factors using the method of proportional division using the above algorithms.

For example, the level of profitability increased by 8% due to an increase in the amount of profit by 1000 thousand rubles. At the same time, profit increased due to an increase in sales volume by 500 thousand rubles, due to an increase in prices - by 1,700 thousand rubles, and due to an increase in production costs, it decreased by 1,200 thousand rubles. Let's determine how the level of profitability has changed due to each factor:

7. To solve this type of problem, you can also use the equity method . To do this, first determine the share of each factor in the total amount of their increases (share ratio), which is then multiplied by the total increase in the performance indicator (Table 4.2):

Calculation of the influence of factors on the performance indicator using the equity method

8. The method of sequential isolation of factors is based on lies a method of scientific abstraction that allows one to study a large number of combinations with simultaneous changes in all or part of the factors.