Factor analysis. Factor analysis of profit. Factor analysis of sales profit

1. 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 investigated, the more accurate the results of the analysis and the 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) the methodology of both systemic study and measurement of the impact of factors on the value of performance indicators is understood.

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 (predictive).

Deterministic Factor Analysis is a methodology for studying the influence of factors, the relationship of which with an effective indicator is of a functional nature, i.e. the effective indicator can be presented as a product, a quotient or an algebraic sum of factors.

Stochastic factor analysis is a technique for studying the influence of factors, the connection of which with the effective 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 \u200b\u200bof the increase in the function, depending on a 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 at different enterprises. It depends on the optimal combination of other factors affecting this indicator.

When 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 means of logical induction - from particular, individual factors to generalizing ones.

Factor analysis may be single-stage and multi-stage. The first type is used to study factors of only one level (one level) of subordination without their detailing into their component parts. For example, y \u003d a - b. In multistage factor analysis, factors a and b are detailed into their constituent elements in order to study their behavior. The detailing of the factors can be continued further. In this case, the influence of factors of various levels of subordination is studied.

Staticthe analysis is used to study the influence of factors on performance indicators at the relevant date. Dynamicanalysis is a technique for studying causal relationships in dynamics.

Retrospectivefactor analysis studies the reasons for the change in performance indicators over the past periods, and promising -explores the behavior of factors and performance indicators in perspective.

The main tasks of factor analysis are as follows:

· Selection of factors that determine the investigated performance indicators;

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

· Determination 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 a factorial model, i.e. 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 this case, they usually proceed from principle: the more the complex of factors is investigated, the more accurate the analysis results 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 value of effective indicators is achieved through their systematization.

In deterministic analysis to determine the magnitude of the influence of individual factors on the change in effective 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 the analysis of factors of production. 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 relation to 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 departments.

The multiplicative models can be summarized 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 employee.

Multiple models:

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

where ZT is the 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 ruble. commercial products, profitability indicators, etc.

The most versatile of complex deterministic models is the way chain substitution... Its essence consists in a sequential consideration of the influence of individual factors on the overall result. In this case, the basic or planned indicators are sequentially replaced with actual ones and the new result obtained after 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 - the basic values \u200b\u200bof the factors influencing the generalizing indicator y;

a 1, b 1, c 1 - the actual values \u200b\u200bof the factors;

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

The total change ∆у \u003d у 1 –у 0 consists of the sum of changes in the resulting indicator due to the change in each factor with fixed values \u200b\u200bof the remaining 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 method of differences is determined as the product of the deviation of the studied factor by the basic or reported value of another factor, depending on the chosen sequence of substitution:

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 \u003d (a - b) x c. It is used in cases where the source data contains previously determined relative deviations of factor indicators in percent.

For multiplicative models like y \u003d ax 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 boils down to the emergence of an indecomposable residue, 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 where this or that factor is placed in the deterministic model.

To get rid of this drawback, deterministic factor analysis in multiplicative, multiple and mixed models uses integralmethod. The use of the integral method allows obtaining more accurate results of calculating the influence of factors in comparison with methods of chain substitution, absolute and relative differences and avoiding 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, it is decomposed between them in proportion to their isolated impact on the effective 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. Moreover, the cost is out current assets increased by 300 thousand rubles, and turnover - 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 \u003d * 300 \u003d -7.5%;

∆Р about \u003d * (- 100) \u003d + 2.5%.

Indexthe 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 reported value with the base one.

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

∑q 1 p 1 - ∑q 0 p 0 \u003d (∑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 the volume of sales (turnover), taken in the prices of the corresponding years, has the form:

And the index of physical turnover:

Logarithm methodused to measure the influence of factors in multiplicative models. In this case, the calculation results, 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 calculation accuracy is provided. If, during integration, 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 newer areas 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), a visual analysis of this matrix can be performed. With an increase in the number of signs (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, which are functions of the parameters under study, 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 connection between features, makes it possible to identify latent (hidden) generalizing characteristics of the organizational structure and mechanisms of development of the phenomena and processes under study.

Example: suppose that n cars are evaluated according to 2 criteria:

x 1 - the cost of the car,

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

If 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

Characteristic 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.

To carry out factor analysis, the 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 \u003d), and the columns correspond to the features (j \u003d).

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

Average value j sign,

Standard deviation.

This transformation is called standardization.

Basic Factor Analysis Model

The basic model of factor analysis is as follows:

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

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

u j - a characteristic factor;

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

Common factors are essential for the analysis of all attributes. The characteristic factors show that it refers only to the given characteristic, this is the specificity of the characteristic, 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 feature. The main task of factor analysis is to determine factor loadings. Variance S j 2 of each feature can be divided into 2 components:

the first part determines the action of common factors - the generality of h j 2;

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

All variables are presented in a standardized form, therefore the variance - state sign S j 2 \u003d 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 share of the variance of the feature attributable to k th factor.

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

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

A - matrix factor loadings... It can be obtained in various ways, currently the method of principal components or principal factors is the most widely used.

Computational procedure of the method of principal factors.

Solving the problem using principal components is reduced to a step-by-step transformation of the initial data matrix X :

X- matrix of initial data;

Z - matrix of standardized feature values,

R - matrix of pairwise correlations:

Diagonal matrix of eigen (characteristic) numbers,

 j are found by solving the characteristic equation

E –Unit matrix,

 j is the dispersion index of each principal component,

subject to standardization of the initial data, then \u003d m

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

This really means a decision m systems of linear equations for each

Those. each eigenvalue corresponds to a system of equations.

Then find V- matrix of normalized eigenvectors.

The factor mapping matrix A is calculated by the formula:

Then we find the values \u200b\u200bof the principal components using one of the equivalent formulas:

The aggregate of four industrial enterprises is assessed according to three characteristic features:

average annual output per employee x 1;

profitability level x 2;

The level of return on assets x 3.

The result is presented in a standardized matrix Z:

By matrix Z the matrix of pairwise correlations is obtained R:

Let us find the determinant of the matrix of pairwise correlations (for example, using the Faddeev method):

Let's construct the characteristic equation:

Solving this equation, we find:

Thus, the original elementary features x 1, x 2, x 3 can be generalized by the values \u200b\u200bof three main components, and:

F 1 explains about the whole variation,

F 2 -, and F 3 -

All three main components account for 100% of the variation.

Solving this system we find:

Systems for  2 and  3 are constructed in a similar way. 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 the normalized matrix V.

Note that the equality \u003d E.

We obtain the matrix of the factor mapping from the matrix relation

Within the meaning of each element of the matrix A represents the partial coefficients of the correlation matrix between the original feature x j and main components F r. Therefore all elements.

The equality implies the condition r- number of components.

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

The factor analysis model will take the form:

Let's find the values \u200b\u200bof the principal components (matrix F) according to the formula

The center of distribution of the values \u200b\u200bof the principal components is at the point (0,0,0).

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

Consider the question of the wording of the names of the main components.

We denote w 1 - a set of insignificant weight coefficients, which includes elements close to zero ,,

w 2 - a set of significant weights,

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

w 2 - w 3 - a subset of the weighting factors involved in the formation of the name.

We calculate the coefficient of information content for each main factor

The set of explicable features is considered satisfactory if the values \u200b\u200bof the informativeness coefficients lie within the range of 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 \u003d 1 w 1 = ,w 2 ={a 11 ,a 21 ,a 31 },

For j \u003d 2 w 1 ={ a 12 , a 22 }, w 2 ={ a 32 },

For j \u003d 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%. with the greatest contribution of the feature x 2, the meaning of which is profitability. correct for the name of the feature F 1 will production efficiency.

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

F 3 is determined by components x 1 ,x 2 - may not be considered in the analysis because she 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 the Internet. Publishing house "Nomidzh", M.-1998, section 2.13. Performing regression.

L.A. Soshnikova, 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 Probability theory and mathematical statistics. –M. - Higher school - 1991.

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

Comparison of two means of normal general 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). For independent samples of volumes n and m, extracted from these populations, the sample means x in and y in were found.

It is required to test the null hypothesis based on the sample means at a given level of significance, which states that the general means (mathematical expectations) of the considered populations are equal to each other, i.e., H 0: M (X) \u003d M (Y).

Taking into account that the sample means are unbiased estimates of the general means, i.e. M (x in) \u003d M (X) and M (y in) \u003d M (Y), the null hypothesis can be written as follows: H 0: M (x in ) \u003d M (y in).

Thus, it is required to check that the mathematical expectations of the sample means are equal to each other. This task 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 correct, that is, the general means are the same, then the difference in the sample means is insignificant and can be explained by random reasons and, in particular, by a random selection of sample objects.

If the null hypothesis is rejected, that is, 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 average (mathematical expectations) themselves are different.

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

Criterion Z - normalized normal random variable. Indeed, the quantity Z is normally distributed, since it is a linear combination of the normally distributed quantities X and Y; these values \u200b\u200bthemselves are distributed normally as sample averages found from samples extracted from general populations; Z is a normalized value, because M (Z) \u003d 0, if the null hypothesis is true, D (Z) \u003d 1, since the samples are independent.

The critical area is constructed depending on the type of the competing hypothesis.

First case... Null hypothesis H 0: M (X) \u003d M (Y). Competing hypothesis H 1: M (X) ¹M (Y).

In this case, a two-sided critical region is constructed 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 level of significance.

The greatest power of the criterion (the probability of the criterion falling into the critical region if the competing hypothesis is valid) 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\u003e z right cr) \u003d a¤2. (one)

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

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

So, it is enough to find the right boundary to find the two-sided critical region Z< -zкр, Z > zcr and the area of \u200b\u200bacceptance of 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 symmetric with respect to zero, the probability of getting Z into the interval (0; ¥) is 1/2. Therefore, if we divide this interval by the point zcr into the interval (0, zcr) and (zcr, ¥), then by the addition theorem P (0< Z < zкр)+Р(Z > zcr) \u003d 1/2.

By virtue of (1) and (2), we obtain Ф (zcr) + a / 2 \u003d 1/2. Therefore, Ф (zкр) \u003d (1-a) / 2.

Hence, 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 the equivalent inequality ½Z1\u003e zcr, and the domain of acceptance of the null hypothesis by the inequality - zcr< Z < zкр или равносильным неравенством çZ ç< zкр.

Let us denote the value of the criterion, calculated from the observational data, through zobl and formulate the rule for testing the null hypothesis.

Rule.

1. Calculate the observed value of the criterion

2. From the table of the Laplace function, find the critical point by the equality Ф (zкр) \u003d (1-a) / 2.

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

If ç zobl ç\u003e zcr - the null hypothesis is rejected.

Second case... Null hypothesis Н0: M (X) \u003d M (Y). Competing hypothesis H1: M (X)\u003e M (Y).

In practice, this occurs when 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, then it is natural to assume that it will lead to an increase in output.

In this case, a right-sided critical area is constructed based on the requirement that the probability of the criterion falling into this area, assuming the validity of the null hypothesis, is equal to the accepted level of significance:

P (Z\u003e zcr) \u003d a. (3)

Let's show how to find the critical point using the Laplace function. We will use the relation

P (0 zcr) \u003d 1/2.

By virtue of (2) and (3) we have Ф (zcr) + a \u003d 1/2. Therefore, Ф (zcr) \u003d (1-2a) / 2.

Hence, we conclude that in order to find the boundary of the right-sided critical region (zcr), it is sufficient to find the value of the Laplace function equal to (1-2a) / 2. Then the right-sided critical region is determined by the inequality Z\u003e zcr, and the region of acceptance of the null hypothesis is determined by the inequality Z< zкр.

Rule.

1. Calculate the observed value of the criterion zobl.

2. Using the table of the Laplace function, find the critical point from the equality Ф (zкр) \u003d (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 Н0: M (X) \u003d M (Y). Competing hypothesis H1: M (X)

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

position of the 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 Zobl.

2. From the table of the Laplace function, find the “auxiliary point” zcr by the equality Ф (zcr) \u003d (1-2a) / 2, and then put z'cr \u003d -zcr.

3. If Zobl\u003e -zcr, there is no reason to reject the null hypothesis.

If Zobl< -zкр, – нулевую гипотезу отвергают.

The purpose economic activity enterprise is always a certain result, which depends on numerous and varied factors. Obviously, 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 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 technique that includes unified methods for measuring (constant and systemic) factor indicators, a comprehensive study of their impact on the value of effective indicators, theoretical principles underlying forecasting.

There are the following types of factor analysis:

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

- forward and backward;

- 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 presented as a product, a quotient, or an algebraic sum of factors.

Correlation analysis is a technique for studying factors, the connection of which with the effective indicator is probabilistic (correlation). For example, labor productivity at different enterprises at 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 (deductive method). Inverse factor analysis carries out research from particular, individual factors to generalizing (by induction).

One-stage factor analysis is used to study factors of only one level (one level) of subordination without their detailing into their component parts. For instance, y \u003d A · B. In multi-stage factor analysis, factors are detailed A and IN : separating them into their constituent elements in order to study interdependencies.

Static factor analysis is used to study the influence of factors on performance indicators at the relevant date. Dynamic - is a technique for studying the relationships of factor indicators in dynamics.

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

The main tasks of factor analysis are as follows:

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

- determination of the form of dependence between factors and an effective indicator;

- development (application) of a mathematical model of the relationship 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 factor model.

In terms of impact on financial results economic activity enterprises, factors are divided into major and minor, internal and external, objective and subjective, general and specific, constant and variable, extensive and intense.

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

Internal factors are called factors that an enterprise can influence. They should receive the greatest attention. but external factors (market conditions, inflationary processes, conditions of supply of raw materials, materials, their quality, cost, etc.), of course, affect the results of the enterprise. Their study allows you 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 to denote these factors, the term is used - force majeure; it can be a natural disaster, an unexpected change of the political regime, etc.). Unlike objective, subjective reasons depend on the activity individuals and organizations.

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

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

Extensive factors include factors that are associated with a quantitative rather than qualitative increase in the effective indicator, for example, an increase in the volume of production by expanding the cultivated 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 some that cannot be decomposed into component parts. In this regard, factors are divided into complex (complex) and simple (single-element). An example of a complex factor is labor productivity, and a simple factor is the number of working days per reporting period.

The factors that have a direct impact on the effective 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 factors - factors of the first level... The factors that determine the effective indicator indirectly, using the factors of the first level, are called second-tier factors etc.

Any factor analysis of indicators begins with modeling a multivariate 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 really exist and have a specific physical meaning.

2. The factors that are included in the system of factor analysis of indicators should have a causal relationship with the studied indicator.

3. The factor model should provide a measure of the impact specific factor on the overall result.

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

1. When the effective indicator is obtained as an algebraic sum or the 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 used when the resulting indicator is obtained as the product of several resulting factors:

where is the return on assets,

– profitability of sales,

- capital productivity of assets,

- average cost organization assets for the reporting year.

3. When the effective 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 of modeling multifactorial models: lengthening, formal decomposition, expansion, reduction and dismemberment of one or more factor indicators into their constituent elements.

For example, using the extension method, you can build a three-factor model of the organization's asset profitability as follows:

;

where is the turnover of own capital of the organization,

- coefficient of independence or the share of equity capital in the total mass of the organization's assets,

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

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

Now consider the following ROI model:

where is the share of proceeds per 1 rub. complete cost of production,

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

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

- inventory turnover.

The first factor of this model speaks about the organization's pricing policy; it shows the basic markup, which is incorporated directly into the price of the products sold.

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

The fourth factor is due to the size of the output and sales of products and speaks about the efficiency of using inventories, physically it expresses the number of revolutions that the inventories make during the reporting year.

Equity method used when it is difficult to establish the dependence of the analyzed indicator on particular indicators. The method consists in the fact that the deviation for the generalizing indicator is proportionally distributed among the individual factors, under the influence of which it occurred. For example, you can calculate the effect of changes in the 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 increased profits under the influence of a factor i, %;

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

 b - change in balance sheet profit, rubles;

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

Chain substitution method allows you to measure the influence of individual factors on the result of their interaction - generalizing ( target) indicator, calculate the deviation of the actual indicators from the standard (planned).

Substitution - replacing the base or standard value of a particular indicator with an actual one. Chain substitutions are successive replacements of the base values \u200b\u200bof the particular indicators included in the calculation formula with the actual values \u200b\u200bof these indicators. Then these influences (the effect of the replacement made 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 private indicators included in the calculation formula.

The method of chain substitutions consists in determining a number of intermediate values \u200b\u200bof the generalizing indicator by sequentially replacing the basic values \u200b\u200bof the factors with the reporting ones. This method is based on elimination. To eliminate means to eliminate, to eliminate the influence of all factors on the value of the effective indicator, except for one. At the same time, proceeding from the fact that all factors change independently of each other, i.e. first, one factor changes, and all the others remain unchanged. then two change while the others remain unchanged, etc.

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

where a 0, b 0, c 0 - the basic values \u200b\u200bof the factors influencing the generalizing indicator y;

a 1, b 1, c 1 -
actual values \u200b\u200bof factors;

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

The total change  у \u003d у 1 –у 0 consists of the sum of changes in the resulting indicator due to the change in each factor with fixed values \u200b\u200bof the remaining factors:

The algorithm of the method of chain substitutions can be demonstrated by the example of calculating the influence of changes in the values \u200b\u200bof particular indicators on the value of the indicator, presented in the form of the following calculation formula: F = a· b· c· d.

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

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

The total 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 particular 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 calculation is checked 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 the deviations under the influence of changes in particular indicators:

F 1 –F 0 = F 1 +F 2 +F 3 +F 4 .

The advantages of this method: versatility of use, simplicity of calculations.

The disadvantage of the method is that, depending on the chosen order of replacement of factors, the results of factorial decomposition have different meanings... This is due to the fact that as a result of the application of 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 evaluating factors is neglected, highlighting the relative importance of the influence of one factor or another. 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;

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

Quantitative factors in the analysis are understood to be those that express the quantitative certainty of phenomena and can be obtained by direct accounting (the number of workers, machines, 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 in the form of a multiplicative model. The change in the value of each factor is determined in comparison with the base value, for example, planned. Then these differences are multiplied by the rest of the particular indicators - the multipliers of the multiplicative model. But, note, when passing 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 factors remaining before it (on the left) are taken in the values \u200b\u200bof the reporting period.

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

TC m = Q· m· P m.

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

change in production volume  Q= Q 0 – Q 1 ;

change in the rates of consumption of materials per accounting unit  m = m 0 – m 1 ;

change in price per unit of material  P m = P m 1 – P m 0 .

Further, the influence of individual factors on the generalizing indicator is determined, i.e. the amount of material costs. In this case, the particular indicators standing in front of the indicator for which the difference was calculated are left in their actual value, and all those following it - in the basic one.

In this case, the effect of changes in the volume of output  Q for the amount of material costs will be:

 TC mQ = Q· m 0 · P m 0 ;

the impact of changes in material consumption rates  TC mm:

 TC mm = Q 1  m· P m 0 ;

impact of price changes on materials  TC mp:

 TC mp = Q one · m 1  P m.

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

 TC m =  TC mQ +  TC mm +  TC mp.

However, in practice, situations are more common when one can only assume the presence of a functional dependence (for example, the dependence of revenue ( TR) from the amount of produced and sold products ( Q): TR = TR(Q)). To test this assumption, use regression analysis by which a function of a certain type is selected ( F r(Q)). Then, on the set of definition of the function (on the set of values \u200b\u200bof the factor indicator), the set of values \u200b\u200bof the function 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 \u003d (a - c) . from. It is used in cases where the source data contains previously determined relative deviations of factor indicators in percent.

For multiplicative models like y \u003d a . in . c the analysis method is as follows:

find the relative deviation of each factor indicator:

determine the deviation of the effective indicator at due to each factor

The integral method avoids the drawbacks inherent in the chain substitution method and does not require the use of techniques for the distribution of the indecomposable remainder over factors, since it has a logarithmic law of redistribution of factor loads. The integral method allows achieving 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 using a personal computer and is reduced to the construction of integrands that depend on the type of function or model of the factor system.

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

1. View model:

2. View model :

3. View model:

4. Model view:

A comprehensive analysis of the financial condition assumes a wide and full research of all factors that influence or can influence the final financial results activities of the organization, which, ultimately, are the main goal of the organization.

The results of the analysis should be used to make the correct management decisions the administration of the organization and informed investment decisions by the shareholders-owners.

ASSIGNMENT 2

It is known that during the reporting period, the average payroll number of workers increased from 500 to 520 people, the average number of hours worked by one worker per day - from 7.4 to 7.5 hours; the average number of days worked by a worker per year decreased from 290 to 280 days; the average hourly output of a worker has decreased from 26.5 rubles to 23 rubles. The volume of production decreased from 28,434.5 thousand rubles. up to RUB 25,116 Using the method of relative differences, evaluate the influence of factors on the change in output. Make reasoned conclusions.

DECISION

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, people
Average number of hours worked per day per day, h
Average number of days worked by a worker per year, days
Average hourly output, RUB		26,5
Output volume, t.	VP	28434,5	25116	3318,5

We have a model of the form

VP \u003d H * t * N * F,

In this case, the change in the effective 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 increase of the first factor, expressed as a decimal fraction.

To calculate the influence of the second factor, it is necessary to add its 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 of the Proth factor.

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

The influence of the quadruple factor is similar

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

increase in the number of workers 1137.38 t.

increase in the number of hours worked by one work

per day 399.62 tons.

changes in the number of working days -1033.5 t.

Changes in the average hourly output -3821.95 thous.

Total -3318.45 tons.

Thus, on the basis of the method of relative differences, it was found that the total influence of all factors was -3318.45 thousand rubles, which coincides with the absolute dynamics of the volume of output according to the condition of the problem. The 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 the volume of production by 399.62 thousand rubles. A negative impact was exerted by a decrease in the average hourly work per worker by 3.5 rubles. per hour, which gave a decrease in the volume of production by -3821.5 thousand rubles. A decrease in the average number of days worked by one worker per year by 10 days led to a decrease in production volumes by -1033.5 thousand rubles.

ASSIGNMENT 3

Using the economic information of your company, assess its financial stability based on the calculation of relative indicators.

DECISION

Joint Stock Company KRAYTEHSNAB, registered by the Registration Chamber of the Krasnodar City Hall No. 10952 dated May 14, 1999, OGRN 1022301987278, hereinafter referred to as the “Company”, is a closed joint stock company.

The Company is a legal entity and acts on the basis of the Charter and 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 letterheads 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 "KRAYTEHSNAB". Abbreviated corporate name of the Company in Russian: CJSC "KRAYTEHSNAB".

Location (postal address) of the Company: 350021, RF, Krasnodar Territory, Krasnodar, Karasunsky Administrative District, st. Tram, 25.

Closed Joint Stock Company "KRAYTEHSNAB" was created without limitation of the term of activity.

The main subject of the Company's activity is trade and procurement, intermediary, brokerage.

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

table 2

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

Indicators	2003 year	2004 r.	2005 year	2005 to 2003
Indicators	2003 year	2004 r.	2005 year	(+,-)	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 equity, adjusted by the amount of long-term borrowed funds	6031947,4	5188235,4	6412268,4	380 321,0	106,3
6. Short-term credit and borrowed funds	1500000,0	2000000,0	1500000,0
7. The total amount of sources of funds, taking into account long-term and short-term borrowed funds	7531947,4	7188235,4	7912268,4	380 321,0	105,0
8. The amount of inventories and costs circulating in the balance sheet asset	9784805,7	10289636,4	11152558,8	1367753,1	114,0

End of table 2

Indicators	2003 year	2004 r.	2005 year	2005 to 2003
Indicators	2003 year	2004 r.	2005 year	(+,-)	Growth rate, %
9. Surplus sources of own working capital	3752858,3	5101401,1	4740290,4	987432,2	126,3
10. Surplus sources of own funds and long-term borrowed sources	3752858,3	5101401,1	4740290,4	987432,2	126,3
11. The surplus of the total value of all sources for the formation of stocks 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)

Analyzing the type of financial stability of the enterprise in dynamics, a decrease in the financial stability of the enterprise is noticeable.

As can be seen from Table 2, both in 2003, and in 2004, and in 2005, the financial stability of CJSC "Kraitekhsnab" according to the 3 complex indicator of financial stability can be characterized as "Crisisly unstable state of the enterprise", since the enterprise does not have enough funds to form inventories 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 year	2004 r.	2005 year	(+,-)
Indicators	2003 year	2004 r.	2005 year	2004 2003	2005 to 2004
Autonomy ratio	0,44	0,37	0,30	0,06	0,08
Debt to equity ratio (leverage)	1,28	1,67	2,34	0,39	0,67
Ratio of mobile and immobilized funds	11,56	13,32	18,79	1,76	5,47
Equity to debt ratio	0,78	0,60	0,43	0,18	0,17
Maneuverability coefficient	0,82	0,80	0,83	0,02	0,03
Coverage ratio of stocks and costs 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 suggests that, according to the indicators presented in the table, in comparison with the base period (2003), the situation at CJSC "Kraitekhsnab" as a whole worsened in 2004 and somewhat improved in the reporting 2005 g.

The "Autonomy Ratio" indicator for the period from 2003 to 2004 decreased by -0.06 and in 2004 amounted to 0.37. This is below the standard value (0.5) at which the 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 standard value (0.5) at which the borrowed capital can be compensated by the property of the enterprise.

The indicator "Ratio of debt and equity" (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 dependence of the company on borrowed funds. The permissible level is often determined by the operating conditions of each enterprise, primarily by the rate of turnover of working capital. Therefore, it is additionally necessary to determine the rate of turnover of material circulating assets and accounts receivable for the analyzed period. If receivables turn over faster than working capital, which means a rather high intensity of receipts to the enterprise money, i.e. as a result - an increase in own funds. Therefore, with a high turnover of material working capital and an even higher turnover of accounts receivable, the ratio of the ratio of own and borrowed funds can much exceed 1.

The indicator "Ratio of mobile and immobilized funds" 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 for each individual industry, but other things being equal, an 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 December. 2004 was 0.80. This is above the standard value (0.5). The indicator for the period from 2004 to 2005 increased by 0.03 and in 2005 amounted to 0.83. This is above the standard value (0.5). The coefficient of maneuverability characterizes what share of sources of own funds is in mobile form. The normative value of the indicator depends on the nature of the enterprise's activities: 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 an easy asset structure. The share of fixed assets in the balance sheet total is less than 40.0%. Thus, the enterprise cannot be classified as a capital-intensive production.

Indicator "Coefficient of supply of stocks 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 lower than 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 on insolvency and financial recovery: Order of March 31, 1999 No. 13-r // Economy and Life. 1999. No. 22.
Bakanov M.I., Sheremet A.D. The theory of economic analysis. –M .: Finance and Statistics, 2006.
Evaluation of the economic indicators of a trading enterprise ON THE EXAMPLE OF THE MAIN INDICATORS OF THE COMPANY'S PERFORMANCE SHOW THE USE OF 6 PRIVATE METHODS AND METHODS OF ECONOMIC ANALYSIS Financial condition trade organization and assessment of economic indicators
2013-11-12

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

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

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

For example, labor productivity can be viewed, on the one hand, as a cause of changes in the volume of production, production costs, and on the other hand, as a result of changes in the degree of mechanization and automation of production, improvement of labor organization, 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 investigated, the more accurate the results of the analysis and the assessment of the quality of the enterprise. Therefore, the study and measurement of the influence of factors on the value of the studied economic indicators is an important methodological issue of 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).

Deterministicfactor analysis is a technique for studying the influence of factors, the connection of which with the effective indicator is of a functional nature. That is, when the effective indicator is presented as a product, quotient or an algebraic sum of factors.

Stochastic analysis is a technique for studying factors, the relationship of which with the effective indicator is incomplete, probabilistic (correlation).

What is the difference between functional and correlation dependence?

In a functional dependence with a change in the argument, there is always a certain change in the function. With a stochastic connection, a change in the argument can give several changes in the function, depending on a 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 at different enterprises.

When direct factorial analysis studies are 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 means of induction - from particular individual factors to generalizing ones.

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

For example: profitability \u003d profit / production.

When multistagefactor analysis provides details of factors into their constituent elements in order to study their behavior.

For example: profit \u003d sales volume - costs

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

Staticfactor analysis is used to study the influence of factors on performance indicators at a certain date.

Dynamicfactor analysis is a method for studying causal relationships in dynamics.

Retrospective factor analysis examines the reasons for changes in performance indicators over the past periods.

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

To carry out 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 carried out on the basis of the analyst's theoretical and practical knowledge. In this case, they usually proceed from the principle: the larger the complex of factors is investigated, the more accurate the results of the analysis will be. but the factors should be considered not as a simple set of numbers, but taking into account the interaction, highlighting the main and secondary connections.

The relationship between factors and an effective trait can be direct or inverse, straight or curved. To select the type of connection, theoretical and practical experience is used, methods of comparing parallel and time series, analytical grouping of information, graphics, etc.

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 research object is created. Its essence lies in the fact that the relationship of the studied indicator with the factor indicator is transmitted in the form of a specific mathematical equation.

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

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

For example, a cost model by item : R \u003d MZ + ZP + SS + A + Rproch,

Where P is the total cost of the enterprise, MH - material costs, Salary - wages, SS - social insurance contributions, A - depreciation, Pproch - other expenses.

2. Multiplicative modelsin which the effective indicator is the product of several factors.

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

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

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

for instance PT \u003dVVP: Chppp,

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

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

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

1. chain substitution;

2. absolute differences;

3. relative differences;

5. proportional division;

6. integral;

7.Logarithm

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

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

This method is based on the fact that all factors change independently of each other: first one changes, and all the 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 the method of chain substitution

	product of factors	factor influence
	product of factors	factor influence
Null substitution
First substitution. First factor
Second substitution. Second factor
Third substitution. Third factor.
Fourth substitution. The 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
commercial products, thousand UAH (TP)
average number of workers, people (CR)
average number of days worked per employee (D)
average duration of 1 working day, hour. (H)
average hourly output of one worker, thousand UAH / hour, (V)

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

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

Therefore, the factorial model will look like:

TP \u003d CHR x D x H x V.

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

We will calculate the influence of factors in the table.

Table 7.

Factor analysis of changes in the volume of commercial output

substitution number and factor name	factors influencing the indicator	product of factors	factor influence
substitution number and factor name		product of factors	factor influence

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 a factor 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 \u003d -100,000 (UAH)

2.the impact of changes in the average number of days worked by one worker: 200 x (22-20) x8x12.5 \u003d 40,000 (UAH)

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

200х22х (7-8) х12.5 \u003d - 55000 (UAH)

4.the effect of changes in average hourly output:

200 х22х7х (15.5 -12.5) \u003d 92400 (UAH).

Relative difference method used to analyze multiplicative and additive-multiplicative models of the type

The change in the effective 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 increase of the first factor, expressed as a decimal fraction.

To calculate the influence of the second factor, it is necessary to add its 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 the same way: we 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, etc.

Let's calculate the influence of factors on the change in the volume of marketable products by the method of relative differences.

1) by changing the number of workers:

500,000 x (-50: 250) \u003d - 100,000 (UAH)

2) by changing the number of days

(500,000 - 100,000) x (2:20) \u003d 40,000 (UAH)

3) by changing the length of the working day:

(500,000 - 100,000 + 40,000) x (-1: 8) \u003d - 55,000 (UAH)

4) by changing the output:

(500,000 - 100,000 + 40,000 - 55,000) x (3: 12.5) \u003d 92,400 (UAH).

Index method 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 assess 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 the absolute gains 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:

Average monthly output of one worker is planned \u003d 20X8X12.5 \u003d UAH 2000.

Average monthly output per worker, actual \u003d 22X7X15.5 \u003d 2387 UAH.

The index of marketable products is as follows:

477,4: 500 = 0,955

Δpq \u003d 477.4 - 500 \u003d - 22.6 (thousand UAH)

The actual output of commercial products in comparison with the planned decreased by 0.5%, which amounted to 22.6 thousand hryvnia.

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

Δpq (q) \u003d 596,750 - 500,000 \u003d 96750 UAH.

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

Δpq (p) \u003d 477400 - 596750 \u003d - 119350 UAH.

Thus, due to the change in output, the output of marketable products of the enterprise increased by 96750 UAH, and due to the change in the number of workers it decreased by 119 350 UAH.

Economic science, 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 you not only to decompose this or that into its components, but also to determine which component has a particular effect on the process as a whole. In more detail given view analysis will be considered in this article.

By definition, factor analysis is a type of mathematical 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 firm's performance taken together. But how to determine which of the factors has a key influence on a particular indicator? This is where factor analysis comes in handy.

Let's start with a simple example. Let's try to make a factor analysis of the cost. The cost of production is influenced by factors such as the cost of raw materials, wages of workers, depreciation of equipment per unit of output. It turns out that the cost is a function of all these factors, and, in fact, is the sum of the values \u200b\u200bof all costs. Thus, an increase in each of these types of costs will lead to an increase in the cost per unit 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 it that has the greatest impact on the prime 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 the cost.

Let's try to produce a factor factor. Everything is a little more complicated here, because there are factors that contribute to both growth and decrease in productivity. Among the factors contributing to growth are the quality and reliability of equipment, the qualifications of personnel, the convenience of the personnel, the ratio of working hours to work interruptions. Factors that reduce productivity include the number of equipment breakdowns, bottlenecks - production areas with insufficient production capacity, distractions - noise, vibration and other external stimuli. Of course, all the above factors will have different coefficients in the function, and it is with their help that the degree of influence of one factor or another on labor productivity will be expressed, however general principle understandable: the effect of factors that increase productivity must be strengthened, and factors that reduce labor efficiency must be minimized.

Having carried out a factor analysis of one or another phenomenon in the economy, one can draw up a certain action plan, according to which it will be possible with minimal cost time and resources to maximize or minimize some indicators of the firm's performance. 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 - the volume of GDP, the ratio of exports and imports are analyzed, required amount in circulation and many other indicators of the efficiency of the country's economy.

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