Conduct factor analysis. Multivariate analysis: types, examples, methods of analysis, purpose and results. Absolute difference method

All processes occurring in business are interconnected. There is both a direct and indirect connection between them. Various economic parameters change under the influence of various factors. Factor analysis (FA) allows you to identify these indicators, analyze them, and study the degree of influence.

The concept of factor analysis

Factor analysis is a multidimensional technique that allows you to study the relationships between the parameters of variables. In the process, the structure of covariance or correlation matrices is studied. Factor analysis is used in a variety of sciences: psychometrics, psychology, economics. The basics of this method were developed by psychologist F. Galton.

Objectives of the

To obtain reliable results, a person needs to compare indicators on several scales. In the process, the correlation of the obtained values, their similarities and differences is determined. Let's consider the basic tasks of factor analysis:

Detection of existing values.
Selection of parameters for a complete analysis of values.
Classification of indicators for system work.
Detection of relationships between resultant and factor values.
Determining the degree of influence of each factor.
Analysis of the role of each value.
Application of the factor model.

Every parameter that affects the final value must be examined.

Factor analysis techniques

FA methods can be used both in combination and separately.

Deterministic Analysis

Deterministic analysis is used most often. This is due to the fact that it is quite simple. Allows you to identify the logic of the impact of the company’s main factors and analyze their impact in quantitative terms. As a result of the DA, you can understand what factors should be changed to improve the company's performance. Advantages of the method: versatility, ease of use.

Stochastic Analysis

Stochastic analysis allows you to analyze existing indirect relationships. That is, there is a study of indirect factors. The method is used if it is impossible to find direct connections. Stochastic analysis is considered complementary. It is only used in certain cases.

What is meant by indirect connections? With a direct connection, when the argument changes, the value of the factor will also change. An indirect connection involves a change in the argument followed by a change in several indicators at once. The method is considered auxiliary. This is due to the fact that experts recommend studying direct connections first. They allow you to create a more objective picture.

Stages and features of factor analysis

Analysis for each factor gives objective results. However, it is used extremely rarely. This is due to the fact that complex calculations are performed in the process. To carry them out you will need special software.

Let's consider the stages of FA:

Establishing the purpose of the calculations.
Selection of values that directly or indirectly affect the final result.
Classification of factors for complex research.
Detecting the relationship between the selected parameters and the final indicator.
Modeling of mutual relationships between the result and the factors influencing it.
Determining the degree of impact of the values and assessing the role of each parameter.
Use of the generated factor table in the activities of the enterprise.

FOR YOUR INFORMATION! Factor analysis involves very complex calculations. Therefore, it is better to entrust it to a professional.

IMPORTANT! When carrying out calculations, it is extremely important to correctly select factors that influence the results of the enterprise. The selection of factors depends on the specific area.

Factor analysis of profitability

A profitability analysis is carried out to analyze the rationality of resource allocation. As a result, it is possible to determine which factors most influence the final result. As a result, only those factors that best influence efficiency can be retained. Based on the data obtained, you can change the company's pricing policy. The following factors may influence the cost of production:

fixed costs;
variable costs;
profit.

Reducing costs provokes an increase in profits. In this case, the cost does not change. We can conclude that profitability is affected by existing costs, as well as the volume of products sold. Factor analysis allows us to determine the degree of influence of these parameters. When does it make sense to do it? The main reason for this is to reduce or increase profitability.

Factor analysis is carried out using the following formula:

Rв= ((W-SB -KRB-URB)/W) - (WB-SB-KRB-URB)/WB, Where:

VT – revenue for the current period;

SB – cost price for the current period;

KRB – commercial expenses for the current period;

URB – management expenses for the previous period;

VB – revenue for the previous period;

KRB – commercial expenses for the previous period.

Other formulas

Let's consider the formula for calculating the degree of impact of cost on profitability:

Rс= ((W-SBot -KRB-URB)/W) - (W-SB-KRB-URB)/W,

CBO is the cost of production for the current period.

Formula for calculating the impact of management expenses:

Rur= ((W-SB -KRB-URot)/W) - (W-SB-KRB-URB)/W,

URot is management expenses.

The formula for calculating the impact of business costs is:

Rк= ((W-SB -KRo-URB)/W) - (W-SB-KRB-URB)/W,

CR is commercial expenses for the previous time.

The total impact of all factors is calculated using the following formula:

Rob=Rv+Rс+Rur+Rk.

IMPORTANT! When making calculations, it makes sense to calculate the influence of each factor separately. Overall PA results are of little value.

Example

Let's consider the organization's indicators for two months (for two periods, in rubles). In July, the organization's income amounted to 10 thousand, production costs - 5 thousand, administrative expenses - 2 thousand, commercial expenses - 1 thousand. In August, the company's income amounted to 12 thousand, production costs - 5.5 thousand, administrative expenses - 1.5 thousand, commercial expenses - 1 thousand. The following calculations are carried out:

R=((12 thousand-5.5 thousand-1 thousand-2 thousand)/12 thousand)-((10 thousand-5.5 thousand-1 thousand-2 thousand)/10 thousand)=0.29-0, 15=0.14

From these calculations we can conclude that the organization’s profit increased by 14%.

Factor analysis of profit

P = RR + RF + RVN, where:

P – profit or loss;

РР – profit from sales;

RF – results of financial activities;

RVN is the balance of income and expenses from non-operating activities.

Then you need to determine the result from the sale of goods:

PP = N – S1 – S2, where:

N – revenue from the sale of goods at selling prices;

S1 – cost of products sold;

S2 – commercial and administrative expenses.

The key factor in calculating profit is the company's sales turnover.

FOR YOUR INFORMATION! Factor analysis is extremely difficult to perform manually. You can use special programs for it. The simplest program for calculations and automatic analysis is Microsoft Excel. It has tools for analysis.

One of the main tools of economic research is factor analysis, which is a section of multivariate statistical analysis that combines methods for estimating the dimension of many observed variables by examining the structure of covariance or correlation matrices. Unlike other analysis methods, it allows analysts to decide two main tasks: compactly and comprehensively describe the subject of measurement and identify the factors responsible for the presence of linear statistical correlations between the observed variables.

Justifiably applying the method of principal components, intended to replace correlated factors with uncorrelated ones, and also limiting itself to the study of the most significant informative factors and excluding the rest from the analysis, thereby simplifying the interpretation of the results, factor analysis appears as a technique for a comprehensive and systematic study of the dependence of other factors on the value of the criterion performance indicator .

Main types of factor analysis are: deterministic, functional(resultative criterion indicator, which is a product of partial or algebraic sum of factors); stochastic, correlation(if there is an incomplete or probabilistic connection between the resultant and factor indicators); direct, deductive(From general to specific); reverse, inductive(from particular to general); static and dynamic; retrospective and prospective; single-stage and multi-stage.

Factor analysis begins with checking its mandatory conditions, according to which: all signs are quantitative; the number of features is twice the number of variables; the sample is homogeneous; the distribution of the original variables is symmetrical; the study of factors is carried out using correlating variables. Factor analysis is carried out in several stages: selection of factors; classification and systematization of factors; modeling 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 effective indicator; practical use of the factor model (calculation of reserves for growth of the effective indicator). Based on the nature of the relationship between indicators, methods of deterministic and stochastic factor analysis are distinguished (Table 1.5).

Factor analysis methods

Table 1.5

Methods	a brief description of
Deterministic factor analysis	Deterministic factor analysis- this is a technique for the influence of factors that are functionally related to the criterion performance indicator, which allows us to present the criterion indicator of the factor model as a quotient, product or algebraic sum of variables. Deterministic factor analysis is characterized by the following methods:chain substitutions; absolute differences; relative differences; integral; logarithms
Stochastic	Stochastic analysis- a methodology for studying factors whose connection with the criterion performance indicator is, in contrast to the functional connection, incomplete, probabilistic (correlation) in nature. With a correlation connection, by changing the argument depending on the combination of other variables that influence the value of the performance indicator, you can obtain a number of values for the increase in the function, while with a functional (complete) dependence, a change in the argument always leads to corresponding changes in the function. Stochastic analysis is carried out using the following methods factor analysis: pair correlation; multiple correlation analysis; matrix model; mathematical programming; game theory
Static and dynamic	Static factor analysis is practiced in order to assess the influence of factors on criterion performance indicators on a specific date, and dynamic - to identify the dynamics of cause-and-effect relationships
Retrospective and prospective	Factor analysis can be used as retrospective character (identify the reasons for changes in the value of the performance indicator over the past period), and perspective(to study the influence of factors on the value of the criterion indicator in the future)

For economic analysis, it is important to use deterministic modeling and different types of deterministic factor models designed to model correlations between the criterion effective factor and other variable factor indicators. The essence of this modeling is to present the relationship of the indicator under study with factors as a specific mathematical equation expressing a functional or correlation relationship.

Deterministic factor models make it possible to study the functional relationship between the studied indicators if the following requirements are met when constructing a factor model: the factors included in the model must be real and not abstract; factors must be in a cause-and-effect relationship with the performance indicator being studied; indicators of the factor model must be quantitatively measurable; it must be possible to measure the influence of individual factors; First, quantitative factors are written into the factor model, then qualitative ones; If there are several quantitative or qualitative factors in a factor model, then factors of a higher order are recorded first, and then lower ones.

The most widely used in factor analysis are the following: types of deterministic factor models(Table 1.6).

Types of deterministic factor models

Table 1.6

Factorial

models

a brief description of

Additive

They are used if the criterion performance indicator is presented in the form of an algebraic sum of a number of factor parameters of the indicators:

The developed factor model can be subjected to additional transformations when the ongoing research deepens, using a number of methods and techniques for these purposes. The final results of the economic analysis of the organization’s business depend on how realistically and accurately the developed models reflect the relationship between the indicators being studied. Modeling additive factor systems involves the implementation of a sequential decomposition of the factors of the original factor system into component variables:

at= a + b.

Thus, the first level factors a and b depend, in turn, on a number of other factors:

a= c + d, b= e+ m,

y = c+ d+ e+m.

Factorial models	a brief description of
Multiplicative models	They are used in cases where the criterion performance indicator is expressed as a product of a number of factor indicators: The essence of modeling multiplicative factor systems lies in the detailed sequential decomposition of the complex factors of the original factor system into factor factors: at= I X b. The magnitude of the first level factors a and b, in turn, depend on a number of other factors: a = c X, b = e X T, y=cxdexm*
Multiple models	If a criterion performance indicator can be defined as the ratio of one factor indicator to another, then The following are distinguished: methods for transforming factorial multiple models: 1)elongation(transforms the numerator by replacing one factor or a number of factors with the sum of homogeneous indicators): 2) formal decomposition(extends the denominator by replacing one or a number of factors with the sum or product of homogeneous indicators):
	3) extension(transforms the original factor model by multiplying the numerator and denominator of the ratio by one indicator or several new indicators):

Criteria-based performance indicators can be decomposed into factors in various ways and presented as different types of deterministic factor models. The modeling method is chosen depending on the object of study and the goals set, as well as on the professional knowledge and skills of the analyst.

Most methods for assessing factors in determination models are based on elimination, the most universal method of which is chain substitutions, used to measure the influence of factors in all types of factor determination models: multiplicative, additive, multiple and mixed (combined). Thanks to this method, it is possible to assess how individual factors influence the value of the criterion performance indicator, gradually replacing the basic value of each factor of the indicator as part of the criterion indicator with the actual value in the reporting period. To do this, a number of conditional values of the criterion performance indicator are calculated, taking into account the sequential change of one, two or more factors, with the remaining values remaining unchanged. A comparative assessment of the change in the value of a criterion parameter before and after a change in the level of a particular factor makes it possible to exclude (eliminate) the influence of all factors, except for the one whose impact on the increase in the performance indicator is determined.

The influence of one or another indicator is assessed by sequential subtraction: from the second calculation of the first, from the third - the second, etc. In the first calculation, all values are planned, in the last - actual. For example, the calculation algorithm for a three-factor multiplicative model is as follows:

In algebraic form, the sum of the influence of factors is equivalent to the total increase in the criterion performance indicator:

If this equality is not observed, the analyst should look for errors in his calculations. Based on this, a rule has been developed according to which it follows that the number of calculations per unit is greater than the number of indicators of the given equation.

When using the chain substitution method, it is assumed ensuring adherence to a strict substitution sequence, because its arbitrary change is fraught with distortion of the results of the analysis. IN process of analytical procedures It is advisable to identify the influence of quantitative indicators first, then qualitative ones. For example, it is required to assess the impact of the number of employees and labor productivity on the volume of industrial production. To do this, the impact of a quantitative indicator (number of employees) is first assessed, and then a qualitative indicator (labor productivity).

The chain substitution method has a significant drawback since when using it, it should be assumed that the values of the factors change independently of each other. Although in reality they change simultaneously and in interrelation, which entails an additional increase in the effective indicator, as a rule, attached to the last of the factors under study. Thus, the magnitude of the influence of factors on the change in the performance indicator depends on the location of a particular factor in the scheme of the analytical model. This explains the difference in calculations when changing the substitution sequence. Thus, the degree of influence of factors on changes in the criterion indicator varies depending on the place of the factor in the determination model. This disadvantage of deterministic factor analysis is eliminated by using a more complex integral method, allowing to evaluate the influence of factors in multiplicative, multiple and mixed models of multiple additive type.

Absolute difference method- this is a modification of the chain substitution method, in which the change in the criterion indicator due to each factor by the method of absolute differences is defined as the product of the deviation of the studied factor by the basic or reporting value of another factor, depending on the selected substitution sequence:

Relative difference method is intended to assess the influence of factors on the growth of a criterion indicator in multiplicative and mixed models of the form:

It involves finding the relative deviation of each factor indicator and determining the direction and size of the influence of factors as a percentage by sequential subtraction (from the first - always 100%).

When using abbreviated substitution method indicators for calculation are intermediate products with sequential accumulation of influencing factors. Substitutions are made, and then, by sequential subtraction, the influence of the factors is found.

Integral method allows you 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 change in the criterion indicator is measured over infinitely small periods of time by summing the increment of the result, defined as partial products multiplied by the increments of factors over infinitely small intervals.

The use of the integral method provides higher accuracy in calculating the influence of factors compared to the methods of chain substitution, absolute and relative differences, making it possible to eliminate ambiguous assessment of the influence, because in this case the results do not depend on the location of the factors in the model, and the additional increase in the effective indicator arising from for the interaction of factors, is distributed evenly between them.

To distribute additional growth, it is not enough to take its part corresponding to the number of factors, since factors can act in different directions. Therefore, the change in the effective indicator is measured over infinitely small periods of time by summing the increment of the result, defined as partial products multiplied by the increments of factors over infinitely small intervals. The operation of calculating a definite integral is reduced to constructing integrands that depend on the type of function or model of the factor system.

Due to the complexity of calculating some definite integrals and additional difficulties associated with the possible action of factors in opposite directions, in practice specially formed working formulas are used:

1. View model

2. View model

3. View model

4. View model

The main methods of elimination, which are based on relative indicators of dynamics, spatial comparisons, plan implementation (assessed by the ratio of the actual level of the indicator under study with the one being compared), include index method.

Index models make it possible to construct a quantitative assessment of the role of individual factors in the trends in the dynamics of changes in general indicators in statistics, planning and economic analysis. The calculation of any index involves comparing the measured value with the base value. If the index is reflected in the form of a ratio of directly comparable quantities, then it is called individual, and if the index represents the ratio of complex phenomena, then it is called group or total. There are several forms of indices (aggregate, arithmetic, harmonic).

The basis of any form of general index is aggregate index, allowing to assess the degree of influence of various factors on changes in the level of criterion indicators in multiplicative and multiple models. The correctness of determining the size of each factor is influenced by: the number of decimal places (at least four); the number of factors themselves (the relationship is inversely proportional).

Principles for constructing aggregate indexes are: a change in one factor while keeping all others constant. Moreover, if a generalizing economic indicator is the product of quantitative (volume) and qualitative indicators of factors, then when determining the influence of a quantitative factor, the qualitative indicator is fixed at the basic level, and when determining the influence of a qualitative factor, the quantitative indicator is fixed at the level of the reporting period.

Let's assume that Y - a * b * c x d,

Factor index showing how the indicator changes b etc.;

The so-called “general index of changes in the resulting indicator” depending on all factors.

Wherein

Using the index method, it is possible to decompose into factors not only relative, but also absolute deviations of the generalizing indicator, while determining the influence of individual factors using the difference between the numerator and denominator of the corresponding indices, i.e. when calculating the influence of one factor, eliminating the influence of another:

Using the index method of factor analysis, it is possible to decompose into factors not only relative, but also absolute deviations in the general indicator. In other words, the influence of an individual factor can be determined using the difference between the numerator and denominator of the corresponding indices, i.e. when calculating the influence of one factor, eliminating the influence of another.

Let's say:

Where A - quantitative factor, and b- qualitative,

indicator due to factor A;

Absolute increase in the resulting

indicator due to factor b

- absolute increase in the resulting

indicator due to the influence of all factors.

It is advisable to apply the considered principle of decomposing the absolute growth of a generalizing indicator into factors if the number of factors is equal to two (one of them is quantitative, the other is qualitative), and the analyzed indicator is presented as their product, since the theory of indices does not provide a general method for decomposing the absolute deviations of a generalizing indicator into factors when the number of factors is more than two. To solve this problem, the method of chain substitutions is used.

Factor analysis methods are successfully applied in order to objectively assess the influence of factors on the criterion indicator of the organization’s performance. As one example of this approach, consider how changes in the volume of product sales affect the financial results of an organization. As a rule, a change in sales revenue occurs due to: 1) a change in sales volume (in physical terms); 2) changes in selling prices. The total change in sales revenue can be presented as the sum of factor deviations:

Where N x - revenue for the reporting year;

N 0 - base year revenue;

A N- change in revenue as a result of changes in sales volume;

A Np- change in revenue as a result of changes in selling prices for products;

A Nc- change in revenue as a result of changes in the structure of product sales.

Let's imagine the revenue (N) as the product of the selling price (R) on sales volume ( Q):

N 0 = P 0 X Q 0 - base year revenue;

jV, = P, x (2, - revenue of the reporting year.

The impact of changes in product sales volume (at constant prices) on changes in revenue is assessed as follows:

The impact of a change in sales price (with a constant volume) on a change in revenue is assessed as follows:

In the process of analysis, the influence of factors such as changes in the sales structure is determined, as well as the share of individual assortment items in the total sales volume in the base and analyzed periods, and then the impact of structural changes on the total sales volume is calculated. Lost revenue as a result of changes in the range of products sold is assessed negatively, while excess revenue is assessed positively.

The main types of models used in financial analysis and forecasting.

Before we start talking about one of the types of financial analysis - factor analysis, let us recall what financial analysis is and what its goals are.

The financial analysis is a method for assessing the financial condition and performance of an economic entity based on studying the dependence and dynamics of financial reporting indicators.

Financial analysis has several purposes:

assessment of financial situation;
identifying changes in financial condition in space and time;
identification of the main factors that caused changes in financial condition;
forecast of main trends in financial condition.

As you know, there are the following main types of financial analysis:

horizontal analysis;
vertical analysis;
trend analysis;
method of financial ratios;
comparative analysis;
factor analysis.

Each type of financial analysis is based on the use of a model that makes it possible to evaluate and analyze the dynamics of the main indicators of the enterprise. There are three main types of models: descriptive, predicative and normative.

Descriptive models also known as descriptive models. They are fundamental for assessing the financial condition of an enterprise. These include: construction of a system of reporting balance sheets, presentation of financial statements in various analytical sections, vertical and horizontal analysis of reporting, a system of analytical coefficients, analytical notes for reporting. All these models are based on the use of accounting information.

At the core vertical analysis lies a different presentation of financial statements - in the form of relative values that characterize the structure of the generalizing total indicators. An obligatory element of the analysis is the dynamic series of these quantities, which makes it possible to track and predict structural changes in the composition of economic assets and the sources of their coverage.

Horizontal analysis allows you to identify trends in changes in individual items or their groups included in the financial statements. This analysis is based on the calculation of the basic growth rates of balance sheet and income statement items.

System of analytical coefficients– the main element of financial analysis, used by various groups of users: managers, analysts, shareholders, investors, creditors, etc. There are dozens of such indicators, divided into several groups according to the main areas of financial analysis:

liquidity indicators;
financial stability indicators;
business activity indicators;
profitability indicators.

Predicative models These are predictive models. They are used to forecast a company's income and its future financial condition. The most common of them are: calculating the point of critical sales volume, constructing forecast financial reports, dynamic analysis models (strictly determined factor models and regression models), situation analysis models.

Normative models. Models of this type allow you to compare the actual results of enterprises with the expected ones calculated according to the budget. These models are used primarily in internal financial analysis. Their essence comes down to the establishment of standards for each cost item for technological processes, types of products, responsibility centers, etc. and to the analysis of deviations of actual data from these standards. The analysis is largely based on the use of strictly deterministic factor models.

As we see, modeling and analysis of factor models occupy an important place in the methodology of financial analysis. Let's consider this aspect in more detail.

Basics of modeling.

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.

Classification and systematization of factors in the analysis of economic activity.

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.

By their nature, factors are divided into natural, socio-economic and production-economic.

Natural factors have a great influence on the results of activities in agriculture, forestry and other industries. Taking into account their influence makes it possible to more accurately assess the results of the work of business entities.

Socio-economic factors include the living conditions of workers, the organization of health-improving work in enterprises with hazardous production, the general level of personnel training, 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. The main ones include factors that have a decisive impact on the performance indicator. Those that do not have a decisive impact on the results of economic activity in the current conditions are considered secondary. It should be noted that, depending on the circumstances, the same factor can be both primary and secondary. The ability to identify the main ones from the entire set of factors ensures the correctness of the conclusions based on the results of the analysis.

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

, subject to the influence of 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. In the process of an organization's work, some factors influence the indicator under study continuously throughout the entire time. Such factors are called permanent. Factors whose influence appears periodically are called

variables (this is, for example, the introduction of new technology, new types of products). And Of great importance for assessing the activities of enterprises is the division of factors according to the nature of their action into intensive

extensive . And Extensive factors include factors that are associated with changes in quantitative, rather than qualitative, characteristics of the functioning of an enterprise. An example is an increase in the volume of production due to an increase in the number of workers. Intensive factors characterize the qualitative side of the production process. An example would be an increase in production volume by increasing the level of labor productivity. 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

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 influence the performance indicator indirectly, with the help of first-level factors, are called second level factors

etc.

It is clear that when studying the influence of any group of factors on the work of an enterprise, it is necessary to organize them, that is, to carry out an analysis taking into account their internal and external connections, interaction and subordination. This is achieved through systematization. Systematization is the placement of the studied phenomena or objects in a certain order, identifying their relationship and subordination. Creation factor systems

is one of the ways of such systematization of factors. Let's consider the concept of a factor system.

Factor systems All phenomena and processes of economic activity of enterprises are interdependent. Relationship between economic phenomena

is a joint change in two or more phenomena. Among the many forms of regular relationships, an important role is played by cause-and-effect (deterministic), in which one phenomenon gives rise to another.

In the economic activity of an enterprise, some phenomena 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. Many other factors indirectly affect this indicator.

In addition, 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. Quantitative characterization of interrelated phenomena is carried out using indicators. Indicators characterizing the cause are called factorial (independent); indicators characterizing the consequence are called effective (dependent). The set of factor and resultant characteristics related by cause and effect is called.

factor system any phenomenon is the construction of a mathematical expression of an existing relationship. Modeling is one of the most important methods of scientific knowledge. There are two types of dependencies studied in the process of factor analysis: functional and stochastic.

A relationship is called functional, or strictly deterministic, if each value of a factor characteristic corresponds to a well-defined non-random value of the resultant characteristic.

A relationship is called stochastic (probabilistic) if each value of a factor characteristic corresponds to a set of values of the resulting characteristic, i.e., a certain statistical distribution.

Model factor system is a mathematical formula that expresses real connections between the analyzed phenomena. In general, it can be presented as follows:

where is the resultant sign;

Factor signs.

Thus, each performance indicator depends on numerous and varied factors. The basis of economic analysis and its section is factor analysis- identify, evaluate and predict the influence of factors on changes in the performance indicator. The more detailed the dependence of the performance indicator on certain factors is studied, the more accurate the results of the analysis and assessment of the quality of the enterprises’ work. Without a deep and comprehensive study of factors, it is impossible to draw informed conclusions about the results of operations, identify production reserves, and justify plans and management decisions.

Factor analysis, its types and tasks.

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 can be distinguished: main stages of 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).

Selection of factors for analysis of a particular indicator is carried out on the basis of theoretical and practical knowledge in a particular 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 business activity analysis (ABA), 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 also represents a complex problem in factor analysis, the solution of which requires special knowledge and skills.

Calculation of the influence of factors- the main methodological aspect in ACD. To determine the influence of factors on the final indicators, many methods are used, which will be discussed in more detail below.

The last stage of factor analysis is practical use of the factor model to calculate reserves for the growth of the effective indicator, to plan and predict its value when the situation changes.

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

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. We will consider deterministic factor analysis in detail in a separate chapter.

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-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 for 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 determined model;
it is necessary to study the influence of complex factors that cannot be expressed by one quantitative indicator (for example, the level of scientific and technological progress).

In contrast to the strictly deterministic approach, the stochastic approach requires a number of prerequisites for implementation:

the presence of a population;
sufficient volume of observations;
randomness and independence of observations;
uniformity;
the presence of a distribution of characteristics close to normal;
the presence of a special mathematical apparatus.

The construction of a stochastic model is carried out in several stages:

qualitative analysis (setting the purpose of the analysis, defining the population, determining the effective and factor characteristics, choosing the period for which the analysis is carried out, choosing the analysis method);
preliminary analysis of the simulated population (checking the homogeneity of the population, excluding anomalous observations, clarifying the required sample size, establishing distribution laws for the indicators being studied);
construction of a stochastic (regression) model (clarification of the list of factors, calculation of estimates of the parameters of the regression equation, enumeration of competing model options);
assessment of the adequacy of the model (checking the statistical significance of the equation as a whole and its individual parameters, checking the compliance of the formal properties of the estimates with the objectives of the study);
economic interpretation and practical use of the model (determining the spatio-temporal stability of the constructed relationship, assessing the practical properties of the model).

In addition to dividing into deterministic and stochastic, the following types of factor analysis are distinguished:

direct and reverse;
single-stage and multi-stage;
static and dynamic;
retrospective and prospective (forecast).

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. a 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 are detailed b And

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.

Deterministic factor analysis Deterministic factor analysis.

has a fairly strict sequence of procedures:
construction of an economically sound deterministic factor model;
implementation of counting procedures for model analysis;
formulating conclusions and recommendations based on the results of the analysis.

The first stage is especially important, since an incorrectly constructed model can lead to logically unjustified results. The meaning of this stage is as follows: any expansion of a strictly determined factor model should not contradict the logic of the “cause-effect” relationship. As an example, consider a model linking sales volume (P), headcount (H) and labor productivity (LP). Theoretically, three models can be explored:

All three formulas are correct from the point of view of arithmetic, however, from the point of view of factor analysis, only the first one makes sense, since in it the indicators on the right side of the formula are factors, i.e. the cause that generates and determines the value of the indicator on the left side (consequence ).

At the second stage, one of the methods of factor analysis is selected: integral, chain substitutions, logarithmic, etc. Each of these methods has its own advantages and disadvantages. We will consider a brief comparative description of these methods below.

Types of deterministic factor models.

The following deterministic analysis models exist:

additive model, i.e., a model in which factors are included in the form of an algebraic sum; an example is the commodity balance model:

Where R- implementation;

Inventory at the beginning of the period;

P- receipt of goods;

Ending inventory;

IN- other disposal of goods;

multiplicative model, i.e., a model in which factors are included in the form of a product; An example is the simplest two-factor model:

Where R- implementation;

H- number;

PT- labor productivity;

multiple model, i.e., a model representing a relationship of factors, for example:

where is the capital-labor ratio;

H- number;

mixed model, i.e. a model in which factors are included in various combinations, for example:

Where R- implementation;

Profitability;

OS- cost of fixed assets;
About- cost of working capital.

A strictly deterministic model that has more than two factors is called multifactorial.

Typical problems of deterministic factor analysis.

In deterministic factor analysis, four typical problems can be distinguished:

Assessment of the influence of relative changes in factors on the relative change in the performance indicator.
Assessing the influence of an absolute change in the i-th factor on the absolute change in a performance indicator.
Determining the ratio of the change in the effective indicator caused by a change in the i-th factor to the base value of the effective indicator.
Determination of the share of the absolute change in the performance indicator caused by the change in the i-th factor in the total change in the performance indicator.

Let us characterize these problems and consider the solution to each of them using a specific simple example.

Example.

The volume of gross output (GP) depends on two main factors of the first level: the number of employees (NH) and average annual output (AG).

We have a two-factor multiplicative model: .

Let's consider a situation where both production and the number of workers in the reporting period deviated from the planned values.

Data for calculations are given in Table 1.

Table 1. Data for factor analysis of gross output volume.

Task 1.

The problem makes sense for multiplicative and multiple models.

;

Let's consider the simplest two-factor model.

Obviously, when analyzing the dynamics of these indicators, the following relationship between the indices will be fulfilled:

where the index value is the ratio of the indicator value in the reporting period to the base one.

Let's calculate the indices of gross output, number of employees and average annual output for our example:

According to the above rule, the gross output index is equal to the product of the indices of the number of workers and average annual output, i.e.

Obviously, if we calculate the gross output index directly, we will get the same value: We can conclude: as a result of an increase in the number of employees by 1.2 times and an increase in average annual output by 1.25 times, the volume of gross output increased by 1.5 times. Thus, relative changes in factor and performance indicators are related by the same relationship as the indicators in the original model. This problem is solved by answering questions like: “What will happen if the i-th indicator changes by n%, and the j-th indicator changes by k%?”

Task 2. Is main task deterministic factor analysis; its general formulation has the form: Let- a strictly determined model that characterizes the change in the performance indicator

y main task from

where is the general change in the performance indicator, which develops under the simultaneous influence of all factor characteristics;

The change in the performance indicator is influenced only by the factor.

Depending on which method of model analysis is chosen, factor decompositions may differ. Therefore, in the context of this task, let us consider the main methods of analyzing factor models.

Basic methods of deterministic factor analysis.

One of the most important methodological factors in ACD is determining the magnitude of the influence of individual factors on the increase in performance indicators. In deterministic factor analysis (DFA), the following methods are used for this: identifying the isolated influence of factors, chain substitution, absolute differences, relative differences, proportional division, integral, logarithm, etc.

The first three methods are based on the elimination method.

Eliminate means to eliminate, reject, exclude the influence of all factors on the value of the effective indicator, except one. This method is based on the fact that all factors change independently of each other: first one changes, and all others remain unchanged, then two change, then three, etc., while the rest remain unchanged. This allows us to determine the influence of each factor on the value of the indicator under study separately.

Let's give a brief description of the most common methods.

Let us recall that when using this method, the order in which the values of the factors change is of great importance, since the quantitative assessment of the influence of each factor depends on this.

First of all, it should be noted that there is not and cannot exist a single method for determining this order - there are models in which it can be determined arbitrarily. Only for a small number of models can formalized approaches be used. In practice, this problem is not of great importance, since in retrospective analysis it is important to trends and the relative importance of this or that factor, and not to precise estimates of their influence.

Nevertheless, to maintain a more or less uniform approach to determining the order of replacement of factors in the model, general principles can be formulated. Let us introduce some definitions.

A sign that is directly related to the phenomenon under study and characterizes its quantitative aspect is called primary or quantitative.

These signs are: a) absolute (volumetric); b) they can be summed up in space and time. Examples include sales volume, headcount, cost of working capital, etc. Features that relate to the phenomenon under study not directly, but through one or more other features and characterize the qualitative side of the phenomenon being studied are called or secondary high quality

These signs are: a) relative; b) they cannot be summed up in space and time. Examples include capital-labor ratio, profitability, etc. The analysis identifies secondary factors of the 1st, 2nd, etc. orders, obtained by sequential detailing.

A strictly determined factor model is called complete if the effective indicator is quantitative, and incomplete if the effective indicator is qualitative. In a complete two-factor model, one factor is always quantitative, the second is qualitative. In this case, it is recommended to start replacing factors with a quantitative indicator. If there are several quantitative and several qualitative indicators, then you should first change the value of the factors of the first level of subordination, and then the lower one.

As you can see, the second indicator of gross output differs from the first in that when calculating it, the actual number of workers was taken instead of the planned one. The average annual output per worker in both cases is planned. This means that due to the increase in the number of workers, production output increased by 32,000 million rubles. (192,000 - 160,000).

The third indicator differs from the second in that when calculating its value, the output of workers is taken at the actual level instead of the planned one.

The number of employees in both cases is actual. Hence, due to increased labor productivity, the volume of gross output increased by 48,000 million rubles.

(240,000 - 192,000).

Thus, exceeding the plan for gross output was the result of the influence of the following factors:

The algebraic sum of factors when using this method must necessarily be equal to the total increase in the effective indicator:

The absence of such equality indicates errors in the calculations.

Other methods of analysis, such as integral and logarithmic, can achieve higher accuracy of calculations, but these methods have a more limited scope and require a large amount of calculations, which is inconvenient for conducting operational analysis.

Task 3.

In a certain sense, it is a consequence of the second standard problem, since it is based on the resulting factor decomposition. The need to solve this problem is due to the fact that the elements of factor decomposition are absolute values that are difficult to use for spatio-temporal comparisons. When solving problem 3, the factor decomposition is supplemented with relative indicators: α Economic interpretation: the coefficient shows by what percentage compared to the base level the performance indicator has changed under the influence of the i-th factor.

;

Let's calculate the coefficients

for our example, using the factor decomposition obtained earlier by the method of chain substitutions:

Thus, the volume of gross output increased by 20% due to an increase in the number of workers and by 30% due to an increase in output. The total increase in gross output was 50%.

Economic interpretation: the coefficient shows the share of the increase in the performance indicator due to the change in the i-th factor. There is no question here if all factor characteristics change unidirectionally (either increase or decrease). If this condition is not met, solving the problem may be complicated. In particular, in the simplest two-factor model, in such a case, the calculation according to the given formula is not performed and it is considered that 100% of the increase in the effective indicator is due to a change in the dominant factor characteristic, i.e., a characteristic that changes in the same direction as the effective indicator.

In a certain sense, it is a consequence of the second standard problem, since it is based on the resulting factor decomposition. The need to solve this problem is due to the fact that the elements of factor decomposition are absolute values that are difficult to use for spatio-temporal comparisons. When solving problem 3, the factor decomposition is supplemented with relative indicators: γ for our example, using the factor decomposition obtained by the chain substitution method:

Thus, the increase in the number of workers accounted for 40% of the total increase in gross output, and the increase in output - 60%.

This means that an increase in production in this situation is the determining factor.

1. Concept, types and tasks of factor analysis.

2. Methods for measuring the influence of factors in deterministic analysis.

Under 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 enterprises’ work. Hence, an important methodological issue in the analysis is the study and measurement of the influence of factors on the value of the economic indicators under study. factor analysis (diagnostics)

The following are distinguished: understands the methodology for systematically studying and measuring the impact of factors on the value of performance indicators.:

types of factor analysis

Deterministic (functional) and stochastic (correlation);

Direct (deductive) and reverse (inductive);

Single-stage and multi-stage;

Static and dynamic;

Deterministic factor analysis Retrospective and prospective (forecast).

is a methodology 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. is a methodology for studying the influence of factors whose connection with an effective indicator, unlike a functional indicator, is incomplete, probabilistic (correlation). If with a functional dependence, with a change in the argument, a corresponding change in the function always occurs, 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.

At direct In factor analysis, 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.

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, y = a - b. In multi-stage factor analysis, factors a and b are detailed into their component elements in order to study their behavior. The factors can be further detailed. In this case, the influence of factors at different levels of subordination is studied.

Static analysis is used to study the influence of factors on performance indicators as of the relevant date. Dynamic analysis is a technique for studying cause-and-effect relationships over time.

Retrospective factor analysis studies the reasons for changes in performance indicators over past periods, and promising - examines the behavior of factors and performance indicators in the future.

The main objectives of factor analysis are the following:

· selection of factors that determine the performance indicators under study;

· classification and systematization of factors in order to ensure the possibility of a systematic approach;

· determination of the form of dependence between factors and: performance indicator;

· modeling of 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;

· work with a factor model, i.e. its practical use for managing economic processes.

The selection of factors for the analysis of a particular indicator is carried out on the basis of theoretical and practical knowledge acquired in this industry. In this case, they usually proceed from principle: the more complex of factors is studied, the more accurate the analysis results 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 economic analysis, an interrelated study of the influence of factors on the value of performance indicators is achieved through their systematization.

In deterministic analysis To determine the magnitude of the influence of individual factors on changes in performance indicators, the following methods are used: chain substitution, index, absolute differences, relative differences, proportional division, integral and logarithm.

The simplest deterministic mathematical models widely used in factor analysis. In the practice of analysis, various types and types of models are used.

Additive models represent an algebraic sum of indicators and have the following 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 in a generalized form can be represented by the following formula.

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

where H is the average number of employees;

CB – 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 ЗТ – average stock of goods;

OR – 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.

The most versatile of complex deterministic models is the way chain substitution. Its essence lies in the consistent consideration of the influence of individual factors on the overall result. In this case, the basic or planned indicators are successively replaced with actual ones and the new result obtained after the replacement is compared with the previous one.

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

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

a 1 , b 1 , c 1 – actual values of factors;

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

The total change ∆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 other factors:

The 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:

The method of relative differences is used to measure the influence of factors on the growth of an effective indicator in multiplicative and mixed models of the form y = (a – b) x c. It is used in cases where the source data contains previously determined relative deviations of factor indicators in percentages.

For multiplicative models of the type y = a x b x c, the analysis technique is as follows:

Find the relative deviation of each factor indicator:

Determine the deviation of the effective indicator y due to each factor

The method of chain substitutions and the method of absolute differences have a common drawback, the essence of which boils down to the emergence of an indecomposable remainder, which is added to the numerical value of the influence of the last factor. 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 a deterministic model.

To get rid of this drawback, deterministic factor analysis in multiplicative, multiple and mixed models uses integral method. The use of the integral method makes it possible to obtain more accurate results for calculating the influence of factors compared to methods of chain substitution, absolute and relative differences, and to avoid ambiguous assessment of the influence of factors because in this case the results do not depend on the location of factors in the model, but an additional increase in the effective indicator, which is formed from the interaction of factors and is distributed between them in proportion to their isolated impact on the performance indicator.

In a number of cases, to determine the magnitude of the influence of factors on the growth of a performance indicator, the method can be used proportional division. For example, return on assets decreased by 5% due to an increase in the enterprise’s assets by 200 thousand rubles. At the same time, the value of non-current assets increased by 300 thousand rubles, and current assets decreased by 100 thousand rubles. This means that, due to the first factor, the level of profitability decreased, and due to the second, it increased:

∆Р main = *300 = -7.5%;

∆Р rev = *(-100) = +2.5%.

Index the method is based on relative indicators expressing the ratio of the level of a given phenomenon to its level in the past or to the level of a similar phenomenon taken as a base. Any index is calculated by measuring the reporting value with the base value.

The classic problem solved using the index method is to calculate the impact of quantity and price factors on sales volume according to the following scheme:

∑q 1 p 1 - ∑q 0 p 0 = (∑q 1 p 0 - ∑q 0 p 0) + (∑q 1 p 1 - ∑q 1 p 0),

where ∑q 1 p 0 - ∑q 0 p 0 – influence of quantity;

∑q 1 p 1 - ∑q 1 p 0 – influence of prices.

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

And the physical trade turnover index:

Logarithm method used to measure the influence of factors in multiplicative models. In this case, the calculation results, as with integration, do not depend on the location of the factors in the model and, compared to the integral method, higher calculation accuracy is ensured. If, during integration, the additional increase from the interaction of factors is distributed equally between them, then using logarithm, the result of the joint action of factors is distributed in proportion to the share of the isolated influence of each factor on the level of the performance indicator. This is its advantage, but the disadvantage is the limited scope of its application.

Careful planning is essential to the success of any business. Its basis is factor analysis of various indicators, which allows us to justify plans and assess the quality of accounting and control systems. Based on the results, tactics and strategy of the enterprise are developed. Most often, factor analysis is carried out in relation to profit in order to determine how this indicator is affected by the quality and volume of products and labor productivity. For trading enterprises, sales analysis is most important.

The task of studying financial results is to monitor the implementation of plans and determine what objective and subjective factors influence the level of income. The calculation process uses accounting data and information from the business plan. Based on the results, reserves are determined to increase net income.

Calculations are carried out according to:

gross, taxable,
basic goods (services, works)
income from other sales
non-operating income

Research objectives:

determine deviations for each characteristic
explore the change and structure of each indicator
evaluate the performance of an enterprise for a certain period

The structure and composition of income, dynamics in comparison with previous time periods, the impact of the chosen accounting policy on each type of profit and the amount of deductions for dividends and taxes are analyzed.

It is important to take into account all the factors affecting the result of business activity:

income from transactions with currencies, deposits, bonds, shares
losses from hopeless losses, penalties, fines, penalties
rental income, received penalties, fines, penalties
losses from negative profits of previous periods and natural disasters
costs of paying taxes and contributions to extra-budgetary funds

The main indicator of successful work is high profitability. A study of the dependence of this indicator for the entire enterprise and for each area of activity is required. The profitability of sales, return on invested capital, investments and costs are assessed. Calculations are carried out for each type of profit (gross, sales, net).

Factor analysis consists of several stages:

selection of factors
their systematization and classification
modeling relationships between a factor and a result
determination of each factor and calculation of its influence on the result of economic activity
developing recommendations that allow the results to be used in practice

Key elements: changes in profitability, income and expenses.

For factorial research, you can use other indicators, for example profitability:

investments (ratio of the amount in the “bottom line” to the amount of own funds)
equity
assets (the ratio of the amount in the “bottom line” to the total volume of the first section of the balance sheet)
(ratio of the amount in the “bottom line” to the volume of working capital)
sales (ratio of the amount in the “bottom line” to revenue)

The difference between the amounts for the base and current year is calculated, and the factors that influenced the changes are identified.

Research of factors influencing sales profitability

Sales profitability depends on:

volume of goods sold
structure of goods sold
production costs
average price level
business expenses

During the research process, each factor and its impact are assessed.

General indicator of changes in income from sales of goods:

ΔР = Р1 – Р0, where

P1 – profit of the current period
Р0 – profit of the previous period

When calculating the impact of the volume of goods sold on profitability, the increase in volume (in percentage) is first calculated:

ΔQ = Q1 / Q0 * 100 – 100, where

Q1 – revenue of the current period in base prices
Q0 – revenue of the previous period

ΔР1 = Р0 * ΔQ / 100, where

ΔР1 – change in the volume of goods sold

Comparison of data from the base and reporting time periods can create problems, especially if the products are heterogeneous. The problem is solved by using the prices of the previous period as a basis.

The impact on cost is calculated using the formula:

ΔР2 = С0 – С1, where

C0 – cost of goods sold in the reporting period in prices of the previous period
C1 – cost of goods sold in the reporting period at current prices

This formula is also used to calculate the impact of selling and administrative expenses.

Changes in sales value are calculated using the formula:

ΔР3 = Q1 – Q2, where

Q1 – revenue of the current period in current prices
Q2 – revenue of the current period at base prices

To calculate the impact of product structure on profit, the formula is used:

ΔР4 = ΔР – ΔР1 – ΔР2 – ΔР3

To determine the impact of all factors, the formula is used:

ΔР = Р1 – Р0 = ΔР1 + ΔР2 + ΔР3 + ΔР4

Based on the results, reserves are determined that allow. This may be an increase in the volume of products sold, a reduction in the total cost or its individual components, an improvement in the structure (quality, range) of manufactured (sold) products.

Calculation example

To make calculations, you need to take data from the balance sheet for the current and base year.

An example of calculating indicators of factor analysis of sales profit if:

revenue 60,000 and 55,000 (at current prices) or 45,833 (at base year prices)
production cost 40,000 and 35,000
commercial expenses 3,000 and 2,000
administrative expenses 5,000 and 4,000
total cost 48,000 and 41,000
selling price change index 1.2
profit 12,000 and 14,000

(the first indicator refers to the base period, the second to the reporting period).

Profit change:

ΔР = Р1 – Р0 = 12,000 – 14,000 = -2,000

Revenue of the current period in prices of the past: 55,000 / 1.2 = 45,833.

Increase/decrease in sales volume:

ΔQ = Q1 / Q0 * 100 = 45,833 / 60,000 * 100 – 100 = -24%

Impact of volume reduction:

ΔР1 = Р0 * ΔQ / 100 = 12,000 * (-24) / 100 = -1,480

Impact of incomplete (production) cost:

ΔР2 = С0 – С1 = 40,000 – 35,000 * 1.2 = -2,000

Impact of business expenses:

ΔР2 = С0 – С1 = 3,000 – 2,000 * 1.2 = 600

Impact of management expenses:

ΔР2 = С0 – С1 = 5,000 – 4,000 * 1.2 = 200

Impact of changes in selling price:

ΔР3 = Q1 – Q2 = 55,000 – 45,833 = 9,167

Structure influence:

ΔР4 = ΔР – ΔР1 – ΔР2 – ΔР3 = -2,000 – 1,480 – 2,000 + 600 + 200 + 9,167 = 4,467

Influence of all factors:

ΔР = ΔР1 + ΔР2 + ΔР3 + ΔР4 = -1,480 – 2,000 + 600 + 200 + 9,167 + 3,467 = 9,114

The results show that profit in the reporting period decreased due to a decrease in sales volumes and an increase in production costs. The change in the structure and cost of products during sales had a positive impact.

Research on Factors Affecting Gross Profit

When calculating gross profit, the following costs are not taken into account:

commercial
managerial
non-operating
operating rooms
tax
emergency
other

In the example discussed in the previous section, 3 will change:

the cost will be 2,000
influence of structure 3 667
influence of all factors 8 314

The amounts will be less, since commercial and administrative costs that change the total cost are not taken into account.

Research of factors influencing the amount of net profit

All factors influencing this indicator are divided into internal and external. The first group includes accounting methods, methods for forming a cost structure, the second group includes the influence of climate, changes in tariffs and prices for raw materials, changes in contracts, force majeure circumstances. Net profit is calculated by subtracting production costs, administrative and commercial costs, other expenses, and taxes from revenue.

The formula used for calculations is:

∆Rch = ∆P + ∆C + ∆K + ∆U + ∆P + ∆NP, where

∆Р – change in revenue
∆С – change in cost
∆К – change in commercial costs
∆У – change in management costs
∆П – change in other income/expenses
∆NP – change in size after adjustment

When calculating changes in individual factors, the formula is used:

ΔИ2 = И0 – И1, where

И0 – costs of the current period in prices of the past
I1 – costs of the reporting period in current prices

A similar study is carried out on income from additional activities, for example, participation in other enterprises, deposits, deposits in bonds. This allows you to determine the factors influencing profitability and the advisability of investing. For example, if income from interest on deposits has decreased, you should not use this type of investment in the future.

When working with the “bottom line”, a study is also carried out on the quality and use of net profit. This indicator can be improved by reducing the gap between the balance sheet figure and the actual amount of funds. To achieve this, the method and methods of writing off costs and forming reserves are changing.

To study the use of earned funds, a formula is used to calculate the profitability of one share:

Pa = (Pch – Dpr) / Qо, where

Pa – profitability of one share
Pch – net profit
Dpr – amount of dividends per preferred share
Qо – number of outstanding ordinary shares

Net profit is used for:

dividend payments
formation of savings and reserves
contributions to social and charitable funds

Factor analysis can also be performed on these indicators to compare volumes and variances across two or more periods.

Factor analysis makes it possible to more deeply and in detail assess the state of an enterprise’s finances by identifying factors that have the greatest impact on business profitability. Based on the results, you can determine exactly what measures are required.

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