Analysis by factors. Factor analysis of profit. Factor analysis of sales profit

1. The concept, types and tasks of factor analysis.

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

Each performance indicator depends on numerous and varied factors. The more detailed the influence of factors on the value of the effective indicator is studied, the more accurate the results of the analysis and assessment of the quality of the work of enterprises. Hence, an important methodological issue in the analysis is the study and measurement of the influence of factors on the value of the studied economic indicators.

Under factor analysis (diagnostics) refers to the methodology and systematic study and measurement of the impact of factors on the magnitude of performance indicators.

There are the following types of factor analysis:

Deterministic (functional) and stochastic (correlation);

Direct (deductive) and reverse (inductive);

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 relationship with the performance indicator is functional in nature, i.e. the effective indicator can be represented as a product, private or algebraic sum of factors.

Stochastic factor analysis is a methodology for studying the influence of factors, the relationship of which with the performance indicator, in contrast to the functional one, 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, 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 not be the same in different enterprises. It depends on the optimal combination of other factors affecting this indicator.

At direct factor analysis, the study is carried out in a deductive way - from the general to the particular. Back factor analysis carries out the study of cause-and-effect relationships by the method of logical induction - from private, individual factors to general ones.

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

Static the analysis is used when studying the influence of factors on the performance indicators for the relevant date. Dynamic analysis is a technique for studying cause-and-effect relationships in dynamics.

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

The main tasks of factor analysis are the following:

selection of factors that determine the studied performance indicators;

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

· definition of the form of dependence between factors and: effective indicator;

Modeling the relationship 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;

· work with factorial model, i.е. its practical use for managing economic processes.

The selection of factors for the analysis of one or another indicator is carried out on the basis of theoretical and practical knowledge acquired in this industry. In doing so, they usually proceed from principle: the more complex factors are studied, the more accurate the results of the analysis will be.

At the same time, it must be borne in mind that if this complex of factors is considered as a mechanical sum, without taking into account their interaction, without highlighting the main determining ones, then the conclusions may be erroneous. In economic analysis, an interconnected study of the influence of factors on the magnitude of performance indicators is achieved through their systematization.

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

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 are an algebraic sum of indicators and have the following form:

Such models, for example, include cost indicators in conjunction with production cost elements 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 divisions.

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 - average headcount workers;

CB is the average output per worker.

Multiple Models:

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

where ST is the average stock of goods;

RR - one-day sales volume.

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

Examples of such models are cost indicators for 1 ruble. marketable 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. At the same time, the basic or planned indicators are successively replaced by actual ones and the new result obtained after the replacement is compared with the previous one.

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

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

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

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

The total change ∆y=y 1 -y 0 is the sum of the 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 by the difference method is defined as the product of the deviation of the studied factor by the base 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 the effective indicator in multiplicative and mixed models of the form y = (a - c) x s. It is used in cases where the initial data contain previously defined relative deviations of factorial indicators in percent.

For multiplicative models of the type y = a x in 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 is the appearance 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 effective indicator varies depending on the place on which this or that factor is placed in the deterministic model.

To get rid of this shortcoming, 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 of calculating the influence of factors compared to the methods of chain substitution, absolute and relative differences and to avoid an ambiguous assessment of the influence of factors because in this case the results do not depend on the location of the factors in the model, but an additional increase in the effective indicator, which is formed from the interaction of factors, decomposed between them in proportion to their isolated impact on the performance indicator.

In some cases, to determine the magnitude of the influence of factors on the growth of the effective indicator, the method can be used proportional division. For example, the return on assets decreased by 5% due to an increase in the company'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. So, due to the first factor, the level of profitability decreased, and due to the second, it increased:

∆Р main = *300 = -7.5%;

∆Р about \u003d * (-100) \u003d + 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 comparing the reporting value with the base value.

The classic problem solved using the index method is the calculation of the influence of quantity and price factors on the volume of sales according to the 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 is the influence of quantity;

∑q 1 p 1 - ∑q 1 p 0 – price influence.

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

And the index of physical trade:

Log method used to measure the influence of factors in multiplicative models. In this case, the results of the calculation, as in the case of integration, do not depend on the location of the factors in the model, and in comparison with the integral method, a higher accuracy of calculations is provided. If, when integrating, the additional gain from the interaction of factors is distributed equally between them, then using the logarithm, the result of the combined action of the factors is distributed in proportion to the share of the isolated influence of each factor on the level of the effective indicator. This is its advantage, and the disadvantage is the limited scope of its application.

Basic provisions

Factor analysis is one of the new branches of multivariate statistical analysis. This method was originally developed to explain the correlation between input parameters. The result of the correlation analysis is a matrix of correlation coefficients. With a small number of features (variables), it is possible to conduct a visual analysis of this matrix. With an increase in the number of features (10 or more), visual analysis will not give positive results. It turns out that the whole variety of correlations can be explained by the action of several generalized factors that are functions of the studied parameters, while the factors themselves may be unknown, but they can be expressed through the studied features. The founder of factor analysis is the American scientist L. Thurstone.

Modern statisticians understand factor analysis as a set of methods that, on the basis of a really existing relationship between features, makes it possible to identify latent (hidden) generalizing characteristics of the organizational structure and mechanisms for the development of the phenomena and processes under study.

Example: suppose n cars are evaluated on 2 features:

x 1 - the cost of the car,

x 2 - the duration of the working life of the motor.

Under the condition that x 1 and x 2 are correlated, a directed and rather dense cluster of points appears in the coordinate system, formally displayed by the new axes and (Fig. 5).

Fig.6

Feature F 1 and F 2 is that they pass through dense clusters of points and, in turn, correlate with x 1 x 2 .Maximum

the number of new axes will be equal to the number of elementary features. Further development of factor analysis showed that this method can be successfully applied in problems of grouping and classifying objects.

Presentation of information in factor analysis.

For factor analysis, information must be presented in the form of an m x n matrix:

The rows of the matrix correspond to the objects of observation (i=), and the columns correspond to the features (j=).

Features that characterize an object have different dimensions. In order to bring them to the same dimension and ensure the comparability of features, the initial data matrix is usually normalized by introducing a single scale. The most common method of normalization is standardization. From variables to variables

Mean j sign,

standard deviation.

This transformation is called standardization.

Basic Factor Analysis Model

The basic model of factor analysis has the form:

z j- j-th sign (random value);

F 1 , F 2 , …, F p- general factors (random values, normally distributed);

u j- characteristic factor;

 j1 ,  j2 , …,  jp – load factors characterizing the significance of the influence of each factor (model parameters to be determined);

General factors are essential for the analysis of all features. Characteristic factors show that it refers only to the given th attribute, this is the specificity of the attribute, which cannot be expressed through factors. Factor loads  j1 ,  j2 , …,  jp characterize the magnitude of the influence of one or another common factor in the variation of a given trait. The main task of factor analysis is to determine factor loadings. dispersion S j 2 of each feature can be divided into 2 components:

the first part determines the action of common factors – commonality h j 2 ;

the second part determines the action of the characteristic factor - characteristic - d j 2 .

All variables are presented in a standardized form, so the variance - state sign S j2 = 1.

If the general and characteristic factors do not correlate with each other, then the variance of the j-th feature can be represented as:

where is the proportion of the feature variance attributable to k-th factor.

The total contribution of any factor to the total variance is:

The contribution of all common factors to the total variance:

It is convenient to present the results of factor analysis in the form of a table.

	Factor loads	communities
	a 11 a 21 … a p1 a 12 a 22 … a p2 … … … … a 1m a 2m … a pm

factors	V 1 V 2 …V p

BUT- matrix factor loads. It can be obtained different ways, at present, the method of principal components or main factors is most widely used.

Computational procedure of the principal factor method.

Solving the problem with the help of principal components is reduced to a step-by-step transformation of the input data matrix X :

X- matrix of initial data;

Z is a matrix of standardized feature values,

R– matrix of pair correlations:

Diagonal matrix of eigen(characteristic) numbers,

 j find the solution of the characteristic equation

E is the identity matrix,

 j is the dispersion index of each principal component ,

under the condition of standardization of the initial data , then = m

U is the matrix of eigenvectors, which are found from the equation:

In reality, this means a decision m systems of linear equations for each

Those. each eigenvalue corresponds to a system of equations.

Then they find V- matrix of normalized eigenvectors.

The factor mapping matrix A is calculated by the formula:

Then we find the values of the principal components using one of the equivalent formulas:

A set of four industrial enterprises was evaluated according to three characteristic features:

average annual output per employee x 1;

profitability level x 2;

The rate of return on assets x 3.

The result is presented in a standardized matrix Z:

By matrix Z obtained the matrix of pair correlations R:

Let's find the determinant of the pair correlation matrix (for example, by the Faddeev method):

Let's construct the characteristic equation:

By solving this equation we find:

Thus, the initial elementary signs x 1, x 2, x 3 can be generalized by the values of the three main components, and:

F 1 explains roughly the entire variation,

F 2 - , a F 3 -

All three principal components explain the variation completely 100%.

Solving this system, we find:

Systems for  2 and  3 are constructed similarly. For  2 system solution:

Eigenvector matrix U takes the form:

We divide each element of the matrix by the sum of the squares of the elements of the j-th

column, we get a normalized matrix V.

Note that the equality = E.

The factor mapping matrix is obtained from the matrix relation

Meaningfully, each element of the matrix BUT represents the partial coefficients of the correlation matrix between the original feature x j and principal components F r . Therefore, all elements

From the equality follows the condition r is the number of components.

The total contribution of each factor to the total feature variance is:

The factor analysis model will take the form:

Find the values of the principal components (matrix F) according to the formula

The distribution center of the values of the principal components is at the point (0,0,0).

Further, analytical conclusions based on the results of calculations follow after making a decision on the number of significant features and main components and determining the names of the main components. The tasks of recognizing the main components, determining names for them are solved subjectively based on weight coefficients from the mapping matrix BUT.

Consider the issue of formulating the names of the main components.

Denote w 1 is a set of insignificant weight coefficients, which includes elements close to zero,,,

w 2 - set of significant weight coefficients,

w 3 - a subset of significant weighting coefficients that are not involved in the formation of the name of the main component.

w 2 - w 3 - a subset of weight coefficients involved in the formation of the name.

We calculate the coefficient of information content for each main factor

We consider the set of explicable signs to be satisfactory if the values of the informativeness coefficients lie within 0.75-0.95.

a 11 =0,776 a 12 =-0,130 a 13 =0,308

a 12 =0,904 a 22 =-0,210 a 23 =-0,420

a 31 =0,616 a 32 =0,902 a 33 =0,236

For j=1 w 1 = ,w 2 ={a 11 ,a 21 ,a 31 },

For j=2 w 1 ={a 12 ,a 22 }, w 2 ={ a 32 },

For j=3 w 1 ={a 33 }, w 2 ={a 13 ,a 33 },

Feature values x 1 , x 2 , x 3, the composition of the main component is determined by 100%. while the largest contribution of the feature x 2, the meaning of which is profitability. correct for the feature name F 1 will production efficiency.

F 2 is determined by the component x 3 (capital productivity), let's call it efficient use of fixed assets.

F 3 is determined by the components x 1 ,x 2 - may not be considered in the analysis because it explains only 10% of the total variation.

Literature.

Popov A.A.

Excel: A Practical Guide, DESS COM.-M.-2000.

Dyakonov V.P., Abramenkova I.V. Mathcad7 in mathematics, physics and on the Internet. Publishing house "Nomidzh", M.-1998, section 2.13. Performing a regression.

L.A. Soshnikov, V.N. Tomashevich et al. Multivariate Statistical Analysis in Economics, ed. V.N. Tomashevich.- M. -Nauka, 1980.

Kolemaev V.A., O.V. Staroverov, V.B. Turundaevsky Theory of Probability and Mathematical Statistics. –M. - Higher School - 1991.

To Iberla. Factor analysis.-M. Statistics.-1980.

Comparison of two means of normal populations whose variances are known

Let the general populations X and Y be normally distributed, and their variances are known (for example, from previous experience or found theoretically). Based on independent samples of volumes n and m extracted from these populations, the sample means x in and y in are found.

It is required by sample means at a given level of significance to test the null hypothesis, which consists in the fact that the general means (mathematical expectations) of the considered populations are equal to each other, i.e. H 0: M(X) = M(Y).

Considering that the sample means are unbiased estimates of the general means, i.e. M(x in) = M(X) and M(y in) = M(Y), the null hypothesis can be written as follows: H 0: M(x in ) = M(y in).

Thus, it is required to check that the mathematical expectations of the sample means are equal to each other. This problem is posed because, as a rule, the sample means are different. The question arises: do the sample means differ significantly or insignificantly?

If it turns out that the null hypothesis is true, i.e., the general means are the same, then the difference in the sample means is insignificant and is due to random reasons and, in particular, random selection of sample objects.

If the null hypothesis is rejected, i.e., the general means are not the same, then the difference in the sample means is significant and cannot be explained by random reasons. And it is explained by the fact that the general averages themselves (mathematical expectations) are different.

As a test of the null hypothesis, we take a random variable.

The Z criterion is a normalized normal random variable. Indeed, Z is normally distributed, since it is a linear combination of normally distributed X and Y; these quantities themselves are normally distributed as sample means found from samples drawn from populations; Z is a normalized value, because M(Z) = 0, if the null hypothesis is true, D(Z) = 1, since the samples are independent.

The critical region is built depending on the type of competing hypothesis.

First case. Null hypothesis H 0:M(X)=M(Y). Competing hypothesis H 1: M(X) ¹M(Y).

In this case, a two-sided critical region is built based on the requirement that the probability of the criterion falling into this region, assuming the validity of the null hypothesis, is equal to the accepted significance level .

The maximum power of the criterion (the probability of the criterion falling into the critical region if the competing hypothesis is true) is achieved when the "left" and "right" critical points are chosen so that the probability of the criterion falling into each interval of the critical region is equal to:

P(Z< zлев.кр)=a¤2,

P(Z > zright cr)=a¤2. (one)

Since Z is a normalized value and the distribution of such a value is symmetric about zero, the critical points are symmetric about zero.

Thus, if we designate the right boundary of the two-sided critical region as zcr, then the left boundary is -zcr.

So, it is enough to find the right boundary to find the two-sided critical region Z itself< -zкр, Z >zcr and area of accepting the null hypothesis (-zcr, zcr).

Let us show how to find zcr, the right boundary of the two-sided critical region, using the Laplace function Ф(Z). It is known that the Laplace function determines the probability of hitting a normalized normal random variable, for example Z, in the interval (0;z):

P(0< Z

Since the distribution of Z is symmetrical with respect to zero, the probability that Z falls into the interval (0; ¥) is 1/2. Therefore, if this interval is divided by the point zcr into the interval (0, zcr) and (zcr, ¥), then by the addition theorem Р(0< Z < zкр)+Р(Z >zcr)=1/2.

Due to (1) and (2) we get Ф(zcr)+a/2=1/2. Therefore, Ф(zcr) =(1-a)/2.

From here we conclude: in order to find the right boundary of the two-sided critical region (zcr), it is enough to find the value of the argument of the Laplace function, which corresponds to the value of the function equal to (1-a)/2.

Then the two-sided critical region is defined by the inequalities Z< – zкр, Z >zcr, or an equivalent inequality ½Z½ > zcr, and the area of acceptance of the null hypothesis by inequality - zcr< Z < zкр или равносильным неравенством çZ ç< zкр.

Let us denote the value of the criterion calculated from the observational data as zobs and formulate a rule for testing the null hypothesis.

Rule.

1. Calculate the observed value of the criterion

2. According to the table of the Laplace function, find the critical point by the equality Ф(zcr)=(1-a)/2.

3. If ç zobs ç< zкр – нет оснований отвергнуть нулевую гипотезу.

If ç zobs ç> zcr, the null hypothesis is rejected.

Second case. Null hypothesis H0: M(X)=M(Y). Competing hypothesis H1: M(X)>M(Y).

In practice, such a case occurs if professional considerations suggest that the general average of one population is greater than the general average of another. For example, if an improvement is introduced technological process, it is natural to assume that it will lead to an increase in output.

In this case, the right-handed critical region is built based on the requirement that the probability of the criterion falling into this region, assuming the validity of the null hypothesis, be equal to the accepted significance level:

P(Z> zcr)=a. (3)

Let's show how to find the critical point using the Laplace function. Let's use the ratio

P(0 zcr)=1/2.

By virtue of (2) and (3) we have Ф(zcr)+a=1/2. Therefore, Ф(zcr)=(1-2a)/2.

From this we conclude that in order to find the boundary of the right-handed critical region (zcr), it is enough to find the value of the Laplace function equal to (1-2a)/2. Then the right-handed critical region is determined by the inequality Z > zcr, and the acceptance area of the null hypothesis is determined by the inequality Z< zкр.

Rule.

1. Calculate the observed value of the criterion zobs.

2. According to the Laplace function table, find the critical point from the equality Ф(zcr)=(1-2a)/2.

3. If Z obs< z кр – нет оснований отвергнуть нулевую гипотезу. Если Z набл >z cr – we reject the null hypothesis.

Third case. Null hypothesis H0: M(X)=M(Y). Competing hypothesis H1: M(X)

In this case, a left-sided critical region is built based on the requirement, the probability of the criterion falling into this region, in pre-

position of validity of the null hypothesis, was equal to the accepted significance level P(Z< z’кр)=a, т.е. z’кр= – zкр. Таким образом, для того чтобы найти точку z’кр, достаточно сначала найти “вспомогательную точку” zкр а затем взять найденное значение со знаком минус. Тогда левосторонняя критическая область определяется неравенством Z < -zкр, а область принятия нулевой гипотезы – неравенством Z >-zcr.

Rule.

1. Calculate Zobs.

2. According to the table of the Laplace function, find the “auxiliary point” zcr by the equality Ф(zcr)=(1-2a)/2, and then put z’cr = -zcr.

3. If Zobs > -zcr, there are no grounds to reject the null hypothesis.

If Zobs< -zкр, – нулевую гипотезу отвергают.

aim economic activity enterprise is always a certain result, which depends on many and varied factors. It is obvious that the more detailed the influence of factors on the magnitude of the result is studied, the more accurate and reliable the forecast about the possibility of achieving it will be. Without a deep and comprehensive study of the factors, it is impossible to draw reasonable conclusions about the results of activities, identify production reserves, justify a business plan and make a management decision. Factor analysis, by definition, is a methodology that includes unified methods for measuring (constant and systemic) factor indicators, a comprehensive study of their impact on the magnitude of performance indicators, and theoretical principles underlying forecasting.

There are the following types of factor analysis:

- analysis of functional dependencies and correlation analysis (probabilistic dependencies);

- direct and reverse;

– single-stage and multi-stage;

– static and dynamic;

- retrospective and prospective.

Factor analysis of functional dependencies is a technique for studying the influence of factors in the case when the effective indicator can be represented as a product, quotient or algebraic sum of factors.

Correlation analysis is a technique for studying factors whose relationship with the performance indicator is probabilistic (correlation). For example, labor productivity at different enterprises with the same level of capital-labor ratio may also depend on other factors, the impact of which on this indicator is difficult to predict.

In direct factor analysis, the study is conducted from the general to the particular (deductively). Reverse factor analysis carries out research from private, individual factors to general ones (by induction).

Single-stage factor analysis is used to study the factors of only one level (one stage) of subordination without their detailing into component parts. For example, y \u003d A B. In multistage factor analysis, the factors are detailed BUT and AT: dividing them into their constituent elements in order to study interdependencies.

Static factor analysis is used when studying the influence of factors on performance indicators for the corresponding date. Dynamic - is a technique for studying the relationship of factor indicators in dynamics.

Retrospective factor analysis studies the causes of changes in performance indicators for past periods, prospective - predicts the behavior of factors and performance indicators in the future.

The main tasks of factor analysis are the following:

- selection, classification and systematization of factors that affect the studied performance indicators;

– determination of the form of dependence between the factors and the performance indicator;

– development (application) mathematical model relationships between the result and factor indicators;

- calculation of the influence of various factors on the change in the value of the effective indicator and comparison of this influence;

– making a forecast based on a factorial model.

From the point of view of the impact on the results of financial economic activity enterprises, the factors are divided into major and minor, internal and external, objective and subjective, general and specific, fixed and variable, extensive and intensive.

The main ones are the factors that have the most noticeable effect on the result. Others are called secondary. It should be noted that, depending on the circumstances, the same factor can be both primary and secondary.

Internal refers to the factors that the company can influence. They should be given the most attention. However external factors(market conditions, inflationary processes, conditions for the supply of raw materials, materials, their quality, cost, etc.), of course, are reflected in the results of the enterprise. Their study allows us to more accurately determine the degree of impact internal factors and provide a more reliable forecast of production development.

Objective factors do not depend on the will and desires of people (in contracts, these factors are referred to as force majeure; it can be a natural disaster, an unexpected change in the political regime, etc.). Unlike objective causes, subjective causes depend on activity. individual people and organizations.

General factors are characteristic of all sectors of the economy. Specific are those that operate in a particular industry or enterprise. Such a division of factors makes it possible to take into account the characteristics of individual enterprises more fully and to make a more accurate assessment of their activities.

Fixed and variable factors are distinguished by the period of impact on the results of production . Constant factors have an impact on the phenomenon under study continuously throughout the entire period under study (reporting period, production cycle, product life, etc.). The impact of variable factors is one-time, irregular.

Extensive factors include those that are associated with a quantitative, rather than qualitative, increase in the result 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 qualitative changes in the production process, for example, an increase in crop yields as a result of the use of new types of fertilizers.

Factors are also divided into quantitative and qualitative, complex and simple, direct and indirect. Quantitative factors, by definition, can be measured (number of workers, equipment, raw materials, labor productivity, etc.). But, often the process of measuring or searching for information is difficult, and then the influence of individual factors is characterized qualitatively (more - less, better - worse).

Most of the factors studied in the analysis consist of several elements. However, there are also those that are not decomposed into component parts. In this regard, the factors are divided into complex (complex) and simple (single-element). An example of a complex factor is labor productivity, and a simple one is the number of working days in reporting period.

Factors that have a direct impact on the performance indicator are called direct (direct action factors). Indirect ones influence through the mediation of other factors. Depending on the degree of mediation of influence, factors of the first, second, third and subsequent levels of subordination are distinguished. Thus, direct action factors - first level factors. Factors that determine the performance indicator indirectly, with the help of first-level factors, are called second level factors etc.

Any factorial analysis of indicators begins with the modeling of a multifactorial model. The essence of building a model is to create a specific mathematical relationship between factors.

When modeling functional factor systems, a number of requirements must be observed.

1. The factors included in the model must actually exist and have a specific physical meaning.

2. Factors that are included in the system of factor analysis of indicators must have a causal relationship with the indicator under study.

3. The factor model should provide a measure of influence specific factor to the overall result.

In the factor analysis of indicators, the following types of the most common models are used.

1. When the resulting indicator is obtained as an algebraic sum or difference of the resulting factors, apply additive models, for example:

where is the profit from product sales,

- revenues from sales,

- production cost products sold,

- business expenses

- administrative expenses.

Multiplicative models are applied when the resulting indicator is obtained as a product of several resulting factors:

where is the return on assets,

– return on sales,

- return on assets,

- average cost organization's assets for the reporting year.

3. When the performance indicator is obtained by dividing one factor by another, apply multiples models:

Various combinations of the above models give mixed or combined models:

;

etc.

In the practice of economic analysis, there are several ways to model multifactorial models: lengthening, formal decomposition, expansion, reduction and division of one or more factor indicators into constituent elements.

For example, using the extension method, you can build a three-factor model of the return on assets of an organization as follows:

;

where is the turnover of own organization's capital,

- the coefficient of independence or the share of equity in the total assets of the organization,

- the average cost of equity capital of the organization for the reporting period.

Thus, we have obtained a three-factor multiplicative model of the profitability of the organization's assets. This model widely known in the economic literature as the Dupont model. Considering this model, we can say that the profitability of the organization's assets is influenced by the profitability of sales, the turnover of equity capital and the share of equity capital in the total mass of the organization's assets.

Now consider the following return on assets model:

where - the share of revenue attributable to 1 rub. complete production cost,

- the share of current assets in the formation of assets,

- the share of stocks in the formation of current assets,

- inventory turnover.

The first factor of this model speaks about the pricing policy of the organization, it shows the basic margin, which is directly embedded in the price of products sold.

The second and third factors show the structure of assets and current assets, the optimal value of which makes it possible to save working capital.

The fourth factor is determined by the amount of output and sales of products and speaks of the efficiency of using production stocks, physically it expresses the number of turnovers that stocks make in the reporting year.

Equity method is used when it is difficult to establish the dependence of the analyzed indicator on private indicators. The method lies in the fact that the deviation according to the generalizing indicator is proportionally distributed among the individual factors under the influence of which it occurred. For example, you can calculate the impact of a change in balance sheet profit on the level of profitability using the formula:

R i = R·(  i / b) ,

where  R i- change in the level of profitability due to an increase in profits under the influence of the factor i, %;

R- change in the level of profitability due to changes in balance sheet profit, %;

 b - change in balance sheet profit, rub.;

 i- change in balance sheet profit due to the factor i.

Method of chain substitutions allows you to measure the influence of individual factors on the result of their interaction - generalizing ( target) indicator, calculate deviations of actual indicators from standard (planned).

Substitution is the replacement of the basic or normative value of a particular indicator with an actual one. Chain substitutions are successive replacements of the base values of particular indicators included in the calculation formula with the actual values of these indicators. Then these influences (the influence of the replacement on the change in the value of the studied generalizing indicator) are compared with each other. The number of substitutions is equal to the number of partial indicators included in the calculation formula.

The method of chain substitutions consists in determining a number of intermediate values of the generalizing indicator by successively replacing the basic values of the factors with the reporting ones. This method is based on elimination. To eliminate means to eliminate, exclude the influence of all factors on the value of the effective indicator, except for one. At the same time, 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 rest remain unchanged, and so on.

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

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

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

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

The total change  y=y 1 -y 0 is the sum of the changes in the resulting indicator due to changes in each factor with fixed values of the other factors:

The algorithm of the chain substitution method can be demonstrated by the example of calculating the effect of changes in the values of partial indicators on the value of the indicator, presented in the form of the following calculation formula: F = a· b· c· d.

Then the base value F will be equal to F 0 = a 0 · b 0 · c 0 · d 0 ,

and the actual: F 1 = a one · b one · c one · d 1 .

General deviation of the actual indicator from the baseline  F (F=F 1 –F 0) is obviously equal to the sum of deviations obtained under the influence of changes in particular indicators:

F = F 1 +F 2 +F 3 +F 4 .

And changes in private indicators are calculated by successive substitutions in the formula for calculating the indicator F actual parameter values a, b, c, d instead of basic

The verification of the calculation is carried out by comparing the balance of deviations, i.e. the total deviation of the actual indicator from the baseline should be equal to the sum of deviations under the influence of changes in particular indicators:

F 1 –F 0 = F 1 +F 2 +F 3 +F 4 .

Advantages of this method: versatility of application, ease of calculation.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of the factor expansion 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 assessing factors is neglected, highlighting the relative importance of the influence of one or another factor. However, there are certain rules that determine the sequence of substitution:

if there are quantitative and qualitative indicators in the factor model, the change in quantitative factors is considered first of all;

if the model is represented by several quantitative and qualitative indicators, the substitution sequence is determined by logical analysis.

In analysis, quantitative factors are those that express the quantitative certainty of phenomena and can be obtained by direct accounting (the number of workers, machine tools, raw materials, etc.).

Qualitative factors determine personal traits, signs and features of the studied phenomena (labor productivity, product quality, average working day, etc.).

A variation of the method of chain substitutions is the method of calculation using absolute differences. In this case, the objective function, as in the previous example, is presented as a multiplicative model. The change in the value of each factor is determined in comparison with the base value, for example, the planned one. Then these differences are multiplied by other partial indicators - multipliers of the multiplicative model. But, we note, when moving from one factor to another, a different value of the multiplier is taken into account. The multipliers after the factor (on the right), by which the difference is calculated, remain in the value of the base period, and all remaining before it (on the left) are taken in the values of the reporting period.

Let's show this on the example of the influence of individual factors on the amount of material costs TC m, which are formed under the influence of three factors: the volume of output in physical terms Q, consumption rates of materials per accounting unit of production m and material prices Pm.

TC m = Q· m· Pm.

First, the change in each factor in comparison with the plan is calculated:

change in output  Q= Q 0 – Q 1 ;

change in material consumption rates per accounting unit  m = m 0 – m 1 ;

price change per unit of material  Pm = Pm 1 – Pm 0 .

Next, the influence of individual factors on the generalizing indicator is determined, i.e. the cost of materials. At the same time, private indicators that precede the indicator by which the difference is calculated are left in their actual value, and all following it are in the base value.

In this case, the effect of a change in the volume of output  Q the cost of materials will be:

TS mQ = Q· m 0 · Pm 0 ;

the impact of changing material consumption rates  TS mm:

TS mm = Q 1  m· Pm 0 ;

the impact of price changes on materials  ts mp:

ts mp = Q one · m 1  Pm.

The total deviation of the amount of material costs will be equal to the sum of the deviations of the influence of individual factors, i.e.

TC m = TS mQ + TS mm + ts mp.

However, in practice, situations are more common when one can only assume the existence of a functional dependence (for example, the dependence of revenue ( TR) from the number of produced and sold products ( Q): TR = TR(Q)). To test this assumption, use regressive analysis, with the help of which a function of a certain type is chosen ( F r(Q)). Then, on the set of function definitions (on the set of values of the factor indicator), the set of function values is calculated.

The method of relative differences is used to measure the influence of factors on the growth of the effective indicator in multiplicative and mixed models of the form y = (a - c) . With. It is used in cases where the initial data contain previously defined relative deviations of factorial indicators in percent.

For multiplicative models like y = a . in . with the analysis technique is as follows:

find the relative deviation of each factor indicator:

determine the deviation of the effective indicator at for each factor

The integral method avoids the disadvantages inherent in the chain substitution method and does not require the use of methods for distributing the irreducible remainder over factors, since it has a logarithmic law of redistribution of factor loadings. The integral method allows you to achieve a complete decomposition of the effective indicator by factors and is universal in nature, i.e. applicable to multiplicative, multiple, and mixed models. The operation of calculating a definite integral is solved with the help of a PC and is reduced to the construction of integrands that depend on the type of function or model of the factorial system.

You can also use the already formed working formulas given in the special literature:

1. View model:

2. View model :

3. View Model :

4. View Model :

A comprehensive analysis of the financial condition involves a wide and full study all factors that affect or may affect the final financial results activities of the organization, which, ultimately, are the main goal of the organization's activities.

The results of the analysis carried out should be used to make the right decisions. management decisions administration of the organization and reasonable investment decisions by shareholders-owners.

TASK 2

It is known that during the reporting period the average number of workers on the payroll increased from 500 to 520 people, the average number of hours worked per worker per day - from 7.4 to 7.5 hours; the average number of days worked by a worker per year was reduced from 290 to 280 days; the average hourly output of a worker decreased from 26.5 rubles to 23 rubles. The volume of output decreased from 28434.5 tr. up to 25116 tr. Using the method of relative differences, evaluate the influence of factors on the change in the volume of output. Draw reasoned conclusions.

SOLUTION

Relative difference method is used to measure the influence of factors on the growth of the effective indicator only in multiplicative and additive-multiplicative models.

Table 1

Initial data for calculation

Index	Designation	Base year	Reporting year	Deviations (+;-)
Average payroll number of workers, pers.
Average number of hours worked by one worker per day, hours
Average number of days worked by a worker per year, days
Average hourly output, rub.		26,5
Output volume, tr.	VP	28434,5	25116	3318,5

We have a view model

VP \u003d H * t * N * F,

In this case, the change in the performance indicator is determined as follows

According to this rule, to calculate the influence of the first factor, it is necessary to multiply the base (planned) value of the effective indicator by the relative growth of the first factor, expressed as a decimal fraction.

To calculate the influence of the second factor, it is necessary to add the change due to the first factor to the planned (basic) value of the effective indicator and then multiply the resulting amount by the relative increase in the Proth factor.

The influence of the third factor is determined similarly: it is necessary to add its growth due to the first and second factors to the planned value of the effective indicator and multiply the resulting amount by the relative growth of the third factor.

Similarly, the influence of the fourth factor

Let's summarize the factors that contributed to the formation of revenue in the reporting year:

increase in the number of workers 1137.38 t.

increasing the number of hours worked per worker

per day 399.62 t.

changes in the number of working days -1033.5 t.

Changes in average hourly output -3821.95 tr.

Total -3318.45 thousand rubles

Thus, based on the method of relative differences, it was found that the total influence of all factors amounted to -3318.45 tr, which coincides with the absolute dynamics of the volume of output according to the condition of the problem. A slight discrepancy is determined by the degree of rounding in the calculations. Positive influence had an increase in the average payroll number of workers by 20 people in the amount of 1137.8 thousand rubles, a slight increase in the working day of one worker by 0.1 hours led to an increase in output by 399.62 thousand rubles. A negative impact was exerted by a decrease in the average hourly work of one worker by 3.5 rubles. per hour, which resulted in a decrease in output by -3821.5 tr. The decrease in the average number of days worked by one worker per year by 10 days led to a decrease in output by -1033.5 tr.

TASK 3

Using the economic information of your enterprise, evaluate it financial stability based on the calculation of relative indicators.

SOLUTION

Joint Stock Company "KRAITEHSNAB", registered by the Registration Chamber of the Mayor's Office of Krasnodar No. 10952 dated May 14, 1999, PSRN 1022301987278, hereinafter referred to as the "Company", is a closed joint stock company.

The Company is a legal entity and operates on the basis of the Charter and the legislation of the Russian Federation. The Company has a round seal containing its full corporate name in Russian and an indication of its location, stamps and forms with its name, its own emblem, as well as a trademark registered in the prescribed manner and other means of visual identification.

Full corporate name of the Company in Russian:
Closed joint-stock company"KRAITEHSNAB". Abbreviated corporate name of the Company in Russian: CJSC KRAITEHSNAB.

Location (postal address) of the Company: 350021, Russian Federation, Krasnodar Territory, Krasnodar, Karasunsky administrative District, st. Tram, 25.

Closed Joint Stock Company "KRAITEHSNAB" was established without limitation of the period of activity.

The main subject of the Company's activity is trading and purchasing activities, intermediary, brokerage.

Let's analyze the indicators of financial stability of the organization under study (table 2).

table 2

Analysis of indicators of financial stability of CJSC "Kraitekhsnab" in absolute terms

Indicators	2003	2004	2005	2005 to 2003
Indicators	2003	2004	2005	(+,-)	Growth rate, %
1. Sources own funds	7371212,4	6508475,4	7713483,3	342 270,9	1004,6
2. Non-current assets	1339265,0	1320240,0	1301215,0	38 050,0	97,2
3. Sources of own working capital for the formation of stocks and costs	6031947,4	5188235,4	6412268,4	380 321,0	1006,3
4. Long-term loans and borrowings
5. Sources of own funds, adjusted for the amount of long-term borrowings	6031947,4	5188235,4	6412268,4	380 321,0	106,3
6. Short-term loans and borrowings	1500000,0	2000000,0	1500000,0
7. The total value of sources of funds, taking into account long-term and short-term borrowings	7531947,4	7188235,4	7912268,4	380 321,0	105,0
8. The amount of stocks and costs circulating in the asset balance	9784805,7	10289636,4	11152558,8	1367753,1	114,0

End of table 2

Indicators	2003	2004	2005	2005 to 2003
Indicators	2003	2004	2005	(+,-)	Growth rate, %
9. Excess sources of own working capital	3752858,3	5101401,1	4740290,4	987432,2	126,3
10. Surplus of sources of own funds and long-term borrowed sources	3752858,3	5101401,1	4740290,4	987432,2	126,3
11. Surplus of the total value of all sources for the formation of reserves and costs	2252858,3	3101401,1	3240290,4	987 432,2	143,8
12. Three-complex indicator (S) of the financial situation	(0,0,0)	(0,0,0)	(0,0,0)

When analyzing the type of financial stability of an enterprise in dynamics, a decrease in the financial stability of an enterprise is noticeable.

As can be seen from Table 2, in 2003, and in 2004, and in 2005, the financial stability of CJSC "Kraitekhsnab" in terms of a 3-complex indicator of financial stability can be characterized as "Crisis-unstable state of the enterprise", since the enterprise does not have enough funds for the formation of stocks and costs for the implementation of current activities.

Let's calculate the coefficients of financial stability of CJSC "Kraitekhsnab" (Table 3).

Table 3

Financial stability ratios of CJSC "Kraitekhsnab"

Indicators	2003	2004	2005	(+,-)
Indicators	2003	2004	2005	2004 2003	2005 to 2004
Autonomy coefficient	0,44	0,37	0,30	0,06	0,08
Debt to equity ratio (financial leverage)	1,28	1,67	2,34	0,39	0,67
The ratio of mobile and immobilized means	11,56	13,32	18,79	1,76	5,47
The coefficient of the ratio of own and borrowed funds	0,78	0,60	0,43	0,18	0,17
Agility factor	0,82	0,80	0,83	0,02	0,03
Inventory and cost coverage ratio with own funds	0,62	0,50	0,57	0,11	0,07
Industrial property ratio	0,66	0,61	0,48	0,05	0,13
Short-term debt ratio, %	15,9	18,4			10,1
Accounts payable ratio, %	84,1	81,6	91,7		10,1

The analysis of financial stability in terms of relative indicators, presented in Table 3, indicates that, according to the indicators presented in the table, compared with the base period (2003), the situation at CJSC “Kraitekhsnab” as a whole worsened in 2004 and slightly improved in the reporting 2005 G.

The indicator "Coefficient of autonomy" for the period from 2003 to 2004 decreased by -0.06 and in 2004 amounted to 0.37. It's below normative value(0.5) at which borrowed capital can be compensated by the property of the enterprise. The indicator "Coefficient of autonomy" for the period from 2004 to 2005 decreased by -0.08 and in 2005 amounted to 0.30. It is also below the normative value (0.5) at which borrowed capital can be compensated by the property of the enterprise.

The indicator "Coefficient of the ratio of borrowed and own funds" (financial leverage), for the period from 2003 to 2004 increased by 0.39 and in 2004 amounted to 1.67. The indicator for 2004 to 2005 increased by 0.67 and in 2005 amounted to 2.34. The more this ratio exceeds 1, the greater the company's dependence on borrowed funds. The permissible level is often determined by the operating conditions of each enterprise, primarily by the speed of turnover of working capital. Therefore, it is additionally necessary to determine the rate of turnover of circulating assets and accounts receivable for the analyzed period. If receivables turn around faster than working capital, which means a fairly high intensity of receipts at the enterprise Money, i.e. The end result is an increase in equity. Therefore, with a high turnover of material working capital and an even higher turnover of accounts receivable, the ratio of own and borrowed funds can be much higher than 1.

The indicator "Ratio of mobile and immobilized means" for the period from 2003 to 2004 increased by 1.76 and in 2004 amounted to 13.32. The indicator for 2004 to 2005 increased by 5.47 and in 2005 amounted to 18.79. The normative value is specific to each individual industry, but other things being equal, the increase in the coefficient is a positive trend.

Indicator "Coefficient of maneuverability", for the period 2003 - 2004. decreased by -0.02 and at the end of Dec. 2004 was 0.80. This is higher than the standard value (0.5). The indicator for the period 2004 to 2005 increased by 0.03 and in 2005 amounted to 0.83. This is higher than the standard value (0.5). The coefficient of maneuverability characterizes what share of sources of own funds is in a mobile form. The normative value of the indicator depends on the nature of the enterprise's activity: in capital-intensive industries, its normal level should be lower than in material-intensive ones. At the end of the analyzed period CJSC "Kraitekhsnab" has a light structure of assets. The share of fixed assets in the balance sheet currency is less than 40.0%. Thus, the enterprise cannot be classified as a capital-intensive production.

Indicator "Coefficient of provision of reserves and costs with own funds", for 2003-2004. decreased by -0.11 and in 2004 amounted to 0.50. The indicator for the period 2004-2005 increased by 0.07 and in 2005 amounted to 0.57. This is below the standard value (0.6 - 0.8), as in 2003, 2004 and 2005. The enterprise lacks its own funds for the formation of reserves and costs, which was also shown by the analysis of financial stability indicators in absolute terms.

BIBLIOGRAPHY

The procedure for monitoring the financial condition of organizations and accounting for their solvency. federal Service Russia for insolvency and financial recovery: Order of March 31, 1999 No. 13-r // Economics and Life. 1999. No. 22.
Bakanov M.I., Sheremet A.D. Theory of economic analysis. –M.: Finance and statistics, 2006.
Evaluation of the economic performance of a trading enterprise ON THE EXAMPLE OF THE MAIN PERFORMANCE INDICATORS OF THE ENTERPRISE SHOW THE USE OF 6 PRIVATE METHODS AND RECEPTIONS OF ECONOMIC ANALYSIS Financial condition trade organization and evaluation of economic indicators
2013-11-12

You remember that all the phenomena and processes of the economic activity of an enterprise are interconnected and interdependent. Some of them are directly related, others indirectly.

For example, the amount of profit from the main activity directly depends on the volume and structure of sales, price and unit cost of production. All other factors affect this indicator indirectly.

Each phenomenon can be considered both as a cause and as a consequence.

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

Each performance indicator depends on numerous and varied factors. The more detailed the influence of the factor on the value of the effective indicator is studied, the more accurate the results of the analysis and assessment of the quality of the enterprise's work. Therefore, the study and measurement of the influence of factors on the value of the studied economic indicators is important. methodological issue economic analysis. Without a deep and comprehensive study of the factors, it is impossible to draw reasonable conclusions about the results of activities, identify production reserves, justify plans and management decisions.

There are the following types of factor analysis:

Deterministic and stochastic;

Direct and reverse;

Single-stage and multi-stage;

Retrospective (historical) and prospective (forecast).

deterministic factor analysis is a technique for studying the influence of factors, the relationship of which with the performance indicator is of a functional nature. That is, when the effective indicator is presented as a product, private or algebraic sum of factors.

Stochastic analysis is a technique for studying factors whose relationship with the performance indicator is incomplete, probabilistic (correlation).

What is the difference between functional and correlation dependence?

With a functional dependency, with a change in the argument, there is always a certain change in the function. With a stochastic relationship, a change in the argument can give several changes 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 not be the same in different enterprises.

At direct factorial The analysis of research is carried out in a deductive way from the general to the particular.

inverse factorial analysis carries out the study of cause-and-effect relationships by the method of induction - from particular individual factors to general ones.

single stage factor analysis is used to study the factors of only one level (one stage) of subordination without their detailing into component parts.

For example: profitability = profit / production volume.

At multistage factor analysis is the detailing of factors into constituent elements in order to study their behavior.

For example: profit = sales volume - costs

The detailing of factors can be continued further, that is, the influence of factors of different levels of subordination is being studied.

Static factor analysis is used when studying the influence of factors on performance indicators for a certain date.

Dynamic factor analysis - a technique for studying cause-and-effect relationships in dynamics.

Retrospective factor analysis studies the causes of changes in performance indicators for past periods.

Prospective factor analysis explores the behavior of factors and performance indicators in the future.

To conduct a factor analysis, it is necessary to establish which indicators will be studied, and how they are related to each other.

The selection of factors for analysis is based on the theoretical and practical knowledge of the analyst. 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. but the factors should be considered not as a simple set of figures, but taking into account the interaction, highlighting the main and secondary connections.

The relationship between factors and the resulting feature can be direct or inverse, rectilinear or curvilinear. To select the type of connection, theoretical and practical experience, methods for comparing parallel and dynamic series, analytical grouping of information, graphics, etc. are used.

The defining stage of factor analysis is modeling.

Modeling- this is one of the methods of scientific knowledge, with the help of which a model (conditional image) of the object of study is created. Its essence lies in the fact that the relationship of the studied indicator with the factor is transmitted in the form of a specific mathematical equation.

In deterministic factor analysis, the following are distinguished: types of factor models:

1. Additive models are used in cases where the effective indicator is an algebraic sum of several factorial indicators.

For example, the element cost model : P \u003d MZ + ZP + SS + A + Rproch,

Where P - the total amount of expenses of the enterprise, MZ - material costs, ZP - wage, SS - deductions for social insurance, A - depreciation, Рproch - other expenses.

2. Multiplicative Models, in which the performance indicator is the product of several factors.

For example, determining the wages of an employee with a piece-rate form of remuneration: ZP \u003d St x K.

Where ZP is wages, St is the rate for 1 product, K is the number of products produced.

3. Multiple models, in which the effective feature is obtained by dividing one factor indicator by another.

For example Fri =GDP: NPP,

Where PT is labor productivity, VVP is the volume of output, NPP is the number of industrial and production personnel.

1. Mixed (combined) models- a combination in various combinations of previous models.

To determine the magnitude of the influence of individual factors on the change in performance indicators, the following are used: factor analysis methods:

1. chain substitution;

2. absolute differences;

3. relative differences;

5. proportional division;

6. integral;

7. logarithm

The most commonly used are the first four methods based on the elimination method.

elimination- exclusion of the influence of all factors on the value of the effective one, except for one - the one being studied.

This method is based on the fact that all factors change independently of each other: first one changes, and all others remain unchanged, then the second, third, etc. change. with the rest unchanged, this makes it possible to determine the magnitude of the influence of each factor on the value of the studied indicator separately.

The most versatile is chain substitution method . It allows you to determine the influence of individual factors on the change in the effective indicator by gradually replacing the base value of each factor indicator in the volume of the effective indicator with the actual one.

Calculations are carried out according to the following scheme.

Scheme of factor analysis by chain substitution method

	product of factors	the magnitude of the influence of the factor
	product of factors	the magnitude of the influence of the factor
Zero substitution
First substitution. First factor
Second substitution. Second factor
Third substitution. Third factor.
Fourth substitution. Fourth factor

B is the basic value of the indicator, F is the actual value of the indicator, R is the result.

There is the following data on the work of the enterprise for the month.

Table 6

Data on the work of the enterprise in January 2007.

index			deviation from plan
marketable products, thousand UAH (TP)
average number of workers, pers. (CR)
average number of working days per worker (D)
average duration of 1 working day, hour. (H)
average hourly output of one worker, thousand UAH / hour, (B)

Let's carry out a factorial analysis of the implementation of the plan for the release of marketable products by the method of absolute differences.

In this case, the effective feature is the volume of marketable products. It is influenced by factors: the number of workers, the number of days worked by one worker, the length of one working day, the average hourly output.

Therefore, the factorial model will look like:

TP \u003d CR x D x H x V.

Please note that in the factorial model used in the chain substitution method, quantitative factors are indicated first and qualitative factors second.

We will calculate the influence of factors in the table.

Table 7

Factor analysis of changes in the volume of output of marketable products

substitution number and factor name	factors affecting the indicator	product of factors	the magnitude of the influence of the factor
substitution number and factor name		product of factors	the magnitude of the influence of the factor

1. Number of workers
2. number of days
3. day length
4. production

Absolute difference method is a simplified version of the method of chain substitutions, when in each substitution the absolute value of the factor, the influence of which is calculated, is replaced by the deviation of its actual value from the planned one. This method is used only in multiplicative models.

Continuation of example 5.

Let's carry out the factorial analysis of changes in marketable products by the method of absolute differences.

1. measure the impact of the number of workers:

(200- 250)x8x12.5=-100,000(UAH)

2. impact of changes in the average number of days worked by one worker: 200 x (22-20) x8 x 12.5 = 40,000 (UAH)

3. the impact of changing the length of the working day:

200x22x(7-8)x12.5 = - 55000 (UAH)

4. the impact of changing the average hourly output:

200 x22x7x (15.5 -12.5) = 92400 (UAH).

Relative difference method used to analyze multiplicative and additive-multiplicative models like

The change in the performance indicator is determined as follows:

According to this rule, to calculate the influence of the first factor, it is necessary to multiply the base value of the effective indicator by the relative growth 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: we add its increase due to the first and second factors to the planned value of the effective indicator and multiply the resulting amount by the relative increase of the third factor, etc.

Let us calculate the influence of factors on the change in the volume of marketable output by the method of relative differences.

1) by changing the number of workers:

500,000 x (-50:250)= - 100,000 (UAH)

2) by changing the number of days

(500,000 - 100,000)х(2:20)= 40,000(UAH)

3) by changing the length of the working day:

(500,000 – 100,000 + 40,000)х(-1:8)= - 55,000 (UAH)

4) by changing the production:

(500,000 - 100,000 + 40,000 - 55,000)x(3:12.5) =92,400 (UAH).

Index method is based on the analysis of relative indicators of dynamics, expressing the ratio of the actual level of the indicator in the reporting period to its level in the base period.

With the help of aggregate indices, it is possible to evaluate the influence of only two factors on the change in the level of the effective indicator in multiplicative and multiple models.

If the denominator is subtracted from the numerator of the formula that forms the index, then absolute increments of the effective attribute will be obtained due to the influence of each factor.

If the last three factors in our example are combined into one complex factor - the average monthly output of one worker, then we can solve this problem using the index method:

The average monthly output of one worker is planned = 20X8X12.5 = 2000 UAH.

The average monthly output of one worker is actual = 22X7X15.5 = 2387 UAH.

The commodity output index looks like:

477,4: 500 = 0,955

Δpq = 477.4 - 500 = - 22.6 (thousand UAH)

The actual output of marketable products decreased by 0.5% compared to the planned output, which amounted to UAH 22.6 thousand.

The influence of changes in the average monthly output is determined using the index of physical volume according to the formula:

Δpq (q) = 596750 – 500000 = 96750 UAH

The impact of changes in the number of workers is determined based on the headcount index:

Δpq (p) = 477400 - 596750 = - 119350 UAH

Thus, due to changes in output, the output of commercial products of the enterprise increased by UAH 96,750, and due to a change in the number of workers, it decreased by UAH 119,350.

Economics, in addition to its specific methods, also uses some general scientific methods- synthesis, analysis, comparisons, abstractions and much more. One of the types of economic analysis is factor analysis, which is a powerful tool that allows not only to decompose this or that into components, but also to determine which component has this or that effect on the process as a whole. In more detail this species analysis will be discussed in this article.

By definition, factor analysis is a kind of mathematical analysis of several variables that allows you to determine what effect a particular variable has on a function. Why is it so important in the economy? This is because none is dependent on only one factor. So, the price depends on supply and demand, wages - on the employee's ability to work and hours worked, the profit of the enterprise - on the totality of all indicators of the company's activities taken together. But how to determine which of the factors has key influence for one indicator or another? This is where factor analysis comes in handy.

Let's start with a simple example. Let's try to make a factorial analysis of the cost. The cost of production is influenced by such factors as the cost of raw materials, wages of workers, depreciation of equipment per unit of production. It turns out that the cost is a function of all these factors, and, in fact, is the sum of the costs of all costs. Thus, an increase in each of these types of costs will lead to an increase in the unit cost of production. It is logical to assume that the cost of raw materials in most cases takes the largest share in the cost of production. We can conclude that it is she who has the greatest impact on the cost, and therefore, it is on the search for cheaper raw materials that it is necessary to concentrate on the search for reserves to reduce costs.

Let's try to produce a factorial Here, everything is somewhat more complicated, because there are factors that contribute to both growth and decrease in productivity. Among the factors contributing to the growth are the quality and reliability of the equipment, the qualifications of the staff, the convenience of the staff, the ratio of working hours and breaks in work. Among the factors that reduce productivity are the number of cases of equipment failure, the presence of "bottlenecks" - production sites with insufficient production capacity, distractions - noise, vibration and other external stimuli. Of course, all of the above factors will have different coefficients in the function, and it is with their help that the degree of influence of one or another factor on labor productivity will be expressed, however general principle is clear: the effect of factors that increase productivity must be strengthened, and factors that reduce labor efficiency must be minimized.

After conducting a factor analysis of a particular phenomenon in the economy, you can draw up a plan of action, according to which it will be possible to minimal cost time and resources to maximize or minimize certain performance indicators of the firm. This will help in as soon as possible to make the company work as efficiently and profitably as possible. Factor analysis is also widely used in macroeconomics - it analyzes the volume of GDP, the ratio of exports and imports, calculates required amount in circulation and many other indicators of the efficiency of the country's economy.

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