Chain substitution method. The first way: the method of chain substitutions

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The most common method of factor analysis is the method of chain substitutions. The essence of this method lies in the consistent substitution into the original formula for determining the effective indicator of the reporting values ​​of the factors under study.

The assessment of the influence of individual factors on the performance indicator involves the implementation of a number of calculations.

1. The reporting value of the first studied factor is substituted into the initial basic formula for determining the effective indicator and the first intermediate value of the effective indicator is calculated.

2. The result obtained is compared with the base value of the performance indicator. This allows us to estimate the magnitude of the influence of the first factor.

4. The result obtained is compared with the previous one and the influence of the second factor on the performance indicator is established.

5. The procedure is repeated until the actual value of the last of the factors entered into the model is substituted into the original basic formula.

There is a rule for substituting factors: first, the influence of quantitative factors characterizing the influence of extensiveness is evaluated, and then qualitative factors characterizing the influence of intensity. It is on the qualitative factors that the entire indecomposable remainder falls.

Example:

Let us represent the volume of production as the product of labor productivity (qualitative intensive factor) and the number production workers(extensive quantitative factor).

The base value of the volume of production is equal to:

No = Pto * Cho

Where: No - basic value of production volume; Pto - the basic value of labor productivity; Cho is the base value of the number of employees.

Thus, two factors influence the value of the volume of production: intensive - a change in the productivity of production workers and extensive - a change in the number of production workers.

Let's evaluate the influence of each of these factors.

1. Substitute in the formula the actual value of the quantitative factor - the number of employees:

Nch \u003d H1 * Pto

Where: P1 - the actual value of the number of production workers.

The influence of a change in the number of employees, or an extensive factor, on the absolute change in the volume of production is determined by the expression:

DNest \u003d Nh - No

As a percentage of the total change in output:

DN total = N1 – N0

DN Rel. ext = (DNest / DNtotal) * 100%

This indicator characterizes the share of extensive factors in the overall change in the analyzed indicator.

2. We carry out the substitution of a qualitative factor - labor productivity:

Npt \u003d Ch1 * Fri1

The share of the intensive factor in the total change in sales volume will be:

DN Rel. int = (DNint / DNtotal) *100%

Task 1.

Based on the data on the activities of the organization (table No. 1), assess the impact of extensive and intensive factors on the change in the volume of sales. Table:

1) Assessment of the influence of the extensive factor - changes in the number of production workers:

Nch \u003d 202 * 450 \u003d 90900 tr.

DN total \u003d 95000 - 90000 \u003d 5000 tr.

DNest \u003d 90900 - 90000 \u003d 900 tr.

Thus, due to the growth in the number of workers, the volume of products sold increased by 900 thousand rubles.

DNrel.ext = 900/ (95000 - 90000) = 900/5000 * 100= 18%

The share of the extensive factor in the total change in the volume of production was 18%.

2) Evaluation of the influence of the intensive factor:

Npt \u003d 202 * 470.3 \u003d 95000.6 tr.

DN int \u003d 95000.6 - 90900 \u003d 4100.6 tr.

Due to the growth of labor productivity of workers, the volume of production increased by 4100.6 thousand rubles.

DNrel.int = 4100.6/5000 * 100= 82%

The share of influence of the intensive factor on the change in sales amounted to 82%.

When performing calculations by the method of chain substitutions, it is possible to use not only the absolute values ​​of factors, but their increments. In this case, the value of the change in the effective indicator is immediately obtained.

When using this method, the following rules are followed:

  1. When determining the influence of a quantitative factor, the increment of this factor is multiplied by the value of the basic qualitative factor.
  2. When determining the influence of a qualitative factor, its increment is multiplied by the reported value of the quantitative factor.

DNch \u003d (Ch1 -Cho) * Pto \u003d DCh * Pto

DNpt \u003d (Pt1 - Pto) * P1 \u003d DPt * P1

In our task:

1. The change in the volume of production under the influence of a change in the number (extensive factor) is equal to:

DNh \u003d (202 - 200) * 450 \u003d 900 tr.

2. The change in the volume of production under the influence of changes in labor productivity (intensity factor) is equal to:

DNpt \u003d (470.3 - 450) * 202 \u003d 4100.6t.r.

The total influence of factors is equal to:

DN,o = 900 + 4100.6 = 5000.6 tr.

The assessment of the influence of intensive and extensive factors can be carried out on the basis of relative changes in the initial and calculated parameters.

The share of influence of the extensive factor is defined as the product of the rate of change of the quantitative factor by the rate of change of the effective indicator. By multiplying the obtained indicator by the total change in the effective indicator, its change is determined under the influence of the extensive factor. The share of influence of the intensive factor is equal to the difference between the total change in the indicator and the value obtained.

In our task:

1. Let's evaluate the influence of the quantitative factor:

DNrel.ext = (1 / 5.5) * 100 = 18.2%

DNext \u003d 0.18 * (95000 - 90000) \u003d 900t.r.

2. The influence of the intensive factor will be determined by:

DN rel.int = 100% - 18.2% = 81.8%

DNint \u003d 5000 - 900 \u003d 4100 tr.

This method is convenient to use in cases where the quantitative factor is in itself a complex indicator obtained as a result of the interaction of a number of other particular characteristics. For example, the wage fund changes under the influence of changes in the number of employees and their average wages.

Types of deterministic models that use the chain substitution method. Essence and rules of its application. Algorithms for calculating the influence of factors by this method in various types models.

One of the most important methodological issues in AHD is to determine the magnitude of the influence of individual factors on the growth of performance indicators. In deterministic factor analysis (DFA), the following methods are used for this: chain substitution, index, absolute differences, relative differences, proportional division, integral, logarithms, etc.

The first four methods are based on the elimination method. To eliminate means to eliminate, reject, exclude the influence of all factors on the value of the effective indicator, except for one. This method proceeds from the fact that all factors change independently of each other: first one changes, and all others remain unchanged, then two change, then three, etc., while the rest remain unchanged. This allows you to determine the influence of each factor on the value of the studied indicator separately.

The most versatile of these is chain substitution method. It is used to calculate the influence of factors in all types of deterministic factor models: additive, multiplicative, multiple and mixed (combined). This method allows you to determine the influence of individual factors on the change in the value of the effective indicator by gradually replacing the base value of each factor indicator in the volume of the effective indicator with the actual value in the reporting period. For this purpose, a number of conditional values ​​​​of the effective indicator are determined, which take into account the change in one, then two, three, etc. factors, assuming that the others do not change. Comparison of the value of the effective indicator before and after changing the level of one or another factor allows you to eliminate the influence of all factors except one, and determine the impact of the latter on the growth of the effective indicator.

The procedure for applying this method will be considered in the following example (Table 6.1).

As we already know, the volume of gross output ( VP) depends on two main factors of the first level: the number of workers (CR) and average annual output (GV). We have a two-factor multiplicative model: VP = Czech Republic X GV.

The algorithm for calculating by the method of chain substitution for this model:

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

The third indicator differs from the second one in that when calculating its value, the output of workers is taken at the actual level instead of the planned one. The number of employees in both cases is actual. Hence, due to the increase in labor productivity, the volume of gross output increased by 48,000 million rubles. (240,000 - 192,000).

Thus, the overfulfillment of the plan in terms of gross output was the result of the influence of the following factors:

a) increase in the number of workers + 32,000 million rubles.

b) increasing the level of labor productivity + 48,000 million rubles.

Total +80,000 million rubles

The algebraic sum of the influence of factors must necessarily be equal to the total increase in the effective indicator:

The absence of such equality indicates errors in the calculations.

For clarity, the results of the analysis are given in table. 6.2.

If it is required to determine the influence of three factors, then in this case not one, but two conditional additional indicators are calculated, i.e. number of conditional indicators per unit less than number factors. Let's illustrate this on a four-factor model of gross output:

The initial data for solving the problem are given in Table 6.1:

The plan for the production of products as a whole was overfulfilled by 80,000 million rubles. (240,000 - 160,000), including by changing:

a) the number of workers

Using the chain substitution method, it is recommended to adhere to a certain sequence of calculations: first of all, you need to take into account the change in quantitative, and then qualitative indicators. If there are several quantitative and several qualitative indicators, then first you should change the value of the factors of the first level of subordination, and then the lower one. In the above example, the volume of production depends on four factors: the number of workers, the number of days worked by one worker, the length of the working day and the average hourly output. According to Figure 5.2, the number of workers in this case- the factor of the first level of subordination, the number of days worked - the second level, the length of the working day and the average hourly output - the factors of the third level. This determined the sequence of placement of factors in the model and, accordingly, the sequence of their study.

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

We considered an example of calculating the influence of factors on the growth of the effective indicator in multiplicative models.

In multiple models the algorithm for calculating factors for the value of the studied indicators is as follows:

where FD- return on assets; VP- gross output; OPF - average annual cost fixed production assets.

Method for calculating the influence of factors in mixed models:

a) Multiplicatively-additive type P = VP R (C - FROM)

where P- the amount of profit from the sale of products; VP P - the volume of sales of products; C - selling price; C - unit cost of production;

In a similar way, the influence of factors is calculated for other deterministic mixed-type models.

Separately, it is necessary to dwell on the methodology for determining the influence structural factor on the increase in the effective indicator using this method. For example, sales revenue (AT) depends not only on the price (C) and quantity of products sold (VPH), but also from its structure (UDi ). If the share of products of the highest quality category, which is sold at higher prices, increases, then revenue will increase due to this, and vice versa. The factorial model of this indicator can be written as follows:

In the process of analysis, it is necessary to eliminate the influence of all factors, except for the structure of the product. To do this, we compare the following revenue indicators:

The difference between these indicators takes into account the change in revenue from the sale of products due to changes in its structure (Table 6.3.).

It can be seen from the table that due to the increase specific gravity second-class products in the total volume of its sales, revenue decreased by 10 million rubles. (655 - 665). This is the unused reserve of the enterprise.

See also:

9. Method of chain substitutions

The chain substitution method is the most universal of the elimination methods. It is used to calculate the influence of factors in all types of deterministic factor models: additive, multiplicative, multiple and mixed (combined). This method allows you to determine the influence of individual factors on the change in the value of the effective indicator by gradually replacing the base value of each factor indicator in the volume of the effective indicator with the actual value in the reporting period. For this purpose, a number of conditional values ​​of the effective indicator are determined, which take into account the change in one, then two, three, etc. factors, assuming that the rest do not change. Comparison of the value of the effective indicator before and after changing the level of one or another factor allows you to eliminate the influence of all factors except one, and determine the impact of the latter on the growth of the effective indicator.

The degree of influence of this or that indicator is revealed by successive subtraction: the first is subtracted from the second calculation, the second is subtracted from the third, etc. In the first calculation, all values ​​are planned, in the last - actual. In the case of a three-factor multiplicative model, the calculation algorithm is as follows:

Y 0 \u003d a 0? b 0? C 0;

Y conditional 1 = a 1 ?b 0 ?C 0 ; At a = Y conv.1 – U 0 ;

Y conditional 2 \u003d a 1? b 1? C 0; Y b \u003d Y conv. 2 - Y conv. 1;

Y f \u003d a 1? b 1? C 1; Y s \u003d Y f - Y conditional 2 and etc.

The algebraic sum of the influence of factors must necessarily be equal to the total increase in the effective indicator:

Y a + Y b + Y c \u003d Y f - Y 0.

The absence of such equality indicates errors in the calculations.

This implies the rule that the number of calculations per unit is greater than the number of indicators of the calculation formula.

When using the chain substitution method, it is very important to ensure a strict substitution sequence, since its arbitrary change can lead to incorrect results. In the practice of analysis, first of all, the influence of quantitative indicators is revealed, and then - qualitative ones. So, if it is required to determine the degree of influence of the number of employees and labor productivity on the size of output industrial products, then first establish the influence of the quantitative indicator of the number of employees, and then the qualitative productivity of labor. If the influence of quantity and price factors on the volume of industrial products sold is clarified, then the influence of quantity is first calculated, and then the influence of wholesale prices. Before proceeding with the calculations, it is necessary, firstly, to identify a clear relationship between the studied indicators, secondly, to distinguish between quantitative and qualitative indicators, and thirdly, to correctly determine the sequence of substitution in cases where there are several quantitative and qualitative indicators (main and derivatives, primary and secondary). Thus, the application of the method of chain substitution requires knowledge of the relationship of factors, their subordination, the ability to correctly classify and systematize them.

An arbitrary change in the substitution sequence changes the quantitative weight of a particular indicator. The more significant the deviation of the actual indicators from the planned ones, the greater the differences in the assessment of the factors calculated with different substitution sequences.

The chain substitution method has a significant 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. This explains the difference in calculations when changing the substitution sequence. The noted drawback is eliminated when a more complex integral method is used in analytical calculations.

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The method of chain substitutions consists in determining a number of intermediate values ​​of the effective (generalizing) indicator by successively replacing the basic values ​​of the factors with the reporting ones. The difference between intermediate values ​​is equal to the change in the effective indicator due to the replaced factor.

Overall change in result ay = y - at 0 is the sum of the changes in the resulting indicator due to the change in each factor with the remaining factors fixed, i.e.,

Let us visually consider the features of using this method.

Example 1 Determine the change in the volume of output due to changes in such factors as the average number of employees, the time worked by one employee and the average hourly output. The data are given in table. 2.4.

original model: N=R x 7" ,as x x h. The type of the model is multiplicative. When solving the problem by the method of chain substitutions and methods derived from it, the elimination method is used.

With the help of the elimination technique, when assessing the influence of each factor on the performance indicator, it is assumed that the remaining factors do not affect the change in the performance indicator, i.e. in the original model, the basic values ​​of the factors are sequentially replaced by the values ​​of the reporting period.

Table 2.4

Task Data

Index

Basic

Reporting

Absolute change, +/-

Relative growth, % (by how many percent)

average headcount

workers, people ( R); time worked by one job

nick, man-hours (T shs); average hourly output,

thousand roubles. (X is)

1. Let's determine the impact of changes in the average number of employees on the volume of output. Using the elimination technique, we get the first intermediate value:

Previous output value N0= 4800 thousand rubles. By changing the number, we got the volume of output N"= 5120 thousand rubles We believe that this change in output is caused by a change in the number of employees.

The change in the volume of output due to the change in the number of employees will be

2. Let's determine the impact of a change in the time worked by an employee on the volume of output. Using the elimination technique, we obtain the second intermediate value of the output volume:

Arguing similarly to the above, we get a change in output due to a change in hours worked, which will be

3. Let's determine the impact of changes in the average hourly output on the volume of output. The third intermediate value of the volume of output:

Change in output due to change in average hourly output:

4. We will check the performed calculations using the balance method. The total influence of factors on the change in the volume of output will be

which corresponds to the absolute change in the result:

those. calculations are correct.

The resulting data are presented in table. 2.5.

Influence of factors on the volume of output

Table 2.5

Conclusion. Output in the reporting period increased by 1,120 thousand rubles compared to the base period, including due to an increase in:

  • ? the average headcount by 320 thousand rubles, which ensured an increase in output by 29%;
  • ? hours worked by 262 thousand rubles, which ensured an increase in output by 23%;
  • ? output by 538 thousand rubles, which ensured an increase in output by 48%.

In table. 2.3, as a disadvantage of the method of chain substitutions, it is indicated: “The presence of an indecomposable remainder. The need to determine the sequence of substitution. Let's take a look at this shortcoming.

Example 2. Changing the sequence of substitutions gives different results of calculating the influence of individual factors.

If the model is presented as

AN(X 4dC) = 5280 - 4800 = 480 thousand rubles, i.e. we get a difference of 58 thousand rubles. (538 thousand rubles - 480 thousand rubles) compared with the calculation for the original model: N=Vac x RxT"ac, The resulting difference is called indecomposable remainder. The indecomposable remainder is obtained due to the different values ​​of the factors involved in the definition N' when changing the order of substitutions in the process of elimination.

For the uniqueness of the results obtained in the calculations, the following rules for applying the method are used:

  • ? the effective and factor indicators are determined;
  • ? a model of the factor system is compiled, its type is determined;
  • ? factor indicators are divided into quantitative and qualitative (see paragraph 2.3), main and secondary;
  • ? when compiling a factor model, quantitative factors are put first, and then qualitative ones; if there are several quantitative and qualitative factors, then the main ones are put first, and then the secondary ones, depending on them.

Analysis- a way of knowing objects and phenomena environment, based on the division of the whole into its constituent parts and the study of them in all the variety of connections and dependencies. Thus, analysis consists in determining the essence of a process or phenomenon on the basis of studying all its constituent parts and identifying the patterns of its development.

Economic analysis originated within the framework of political economy, whose history goes back to the ancient and Middle Ages (Xenophon, Plato, Aristotle, and others; W. Petty, D. Ricardo, S. Sismondi, and others).

AHD

AHD studies economic activity of the enterprise, economic phenomena and processes occurring at the enterprise.

Subject AHD are cause-and-effect relationships of economic phenomena and processes at the enterprise (ie, up to the balance bar); economic processes of enterprises, socio-economic efficiency and final financial results of their activities, formed under the influence of objective and subjective factors.

Objects analysis are the economic results of economic activity, such as production and sales of products, cost, use of various factors of production, financial condition and results, profit, etc.

The AHD method is a systematic comprehensive study, measurement and generalization of the influence of factors on the performance of an enterprise by processing in specialized ways, a system of plan indicators, accounting, reporting, and other sources of information.

The tasks of AHD follow from its functions. Main functions economic analysis:

Studying the nature of the operation of economic laws, establishing patterns and trends in economic phenomena and processes in the specific conditions of the enterprise;

Scientific substantiation of current and long-term plans;

Control over the implementation of plans and management decisions;

Evaluation of the effectiveness of the use of economic resources;

Search for reserves to improve production efficiency based on the study of best practices and achievements of science and practice;

Evaluation of the results of the enterprise's activities in terms of the implementation of plans, the level of economic development achieved and the use of existing opportunities;

Development of measures for the use of reserves identified during the analysis, etc.

    Essence economic analysis and diagnosis of HD.

Economic analysis how the science is the result of the development of productive forces and production relations. In the context of expanding the scale of production and the creation of complex production systems, the role of economic analysis in the process of making managerial decisions is constantly increasing.

AHD- a comprehensive study of the work of the enterprise, its structural divisions in order to objectively assess the results of activities and identify reserves for further improving the efficiency of activities.

Distinguish:

1. general theoretical economic analyh(macroeconomic), which studies economic phenomena and processes at the level of the global and national economy;

2. economic analysis on the level managing subject(microeconomic) to study the economics of individual enterprises.

Economic analysis- a system of special knowledge aimed at the analysis and diagnosis, prediction of PCD. Has an applied character.

AHD principles:

    Compliance of the results and methods of analysis of the state. – economic, political, social, international politics and legislation.

    Scientific nature of research

    Complexity of analysis

    A systematic approach to the study of objects of analysis

    Objectivity, specificity and accuracy of the analysis

    Analysis efficiency

    Efficiency and planning

    A wide range of workers should participate in the analysis and use its results

Diagnostics– recognition of the state of the object under study by indirect signs.

Economic diagnostics- assessment of the state of eq objects in order to identify problems and ways of their further development.

Diagnostics of the enterprise activity consists in establishing and studying signs, measuring the main characteristics that reflect the state of the economic entity in order to predict deviations from stable average and standard values ​​and prevent violations of the normal course of work.

The use of diagnostics involves:

1) Definition of indicators characterizing the object of study

2) Establishment of a group of factors

3) Establishing the form of the relationship of these factors

4) Evaluation of the scorecard

5) Choice of methods

Essence of diagnostics- to study and establish signs that reflect the state of the object in order to predict possible deviations from the norms.

    Types of analysis, classification.

The classification of AHD is important for a correct understanding of its content and tasks and is carried out on row signs:

1) on branch sign:

- branch- the methodology takes into account the specifics of individual sectors of the economy, such as industry, agriculture, construction, trade, etc.;

- intersectoral- represents the methodological and methodological basis of economic analysis.

2) on sign time:

- preliminary(promising) - necessary to justify management decisions, plan targets, forecast expected results;

- subsequent(retrospective) - necessary to control the implementation of the plan, identify unused reserves, an objective assessment of the performance of the enterprise;

retrospective analysis is divided on the:

Operational (current), which is performed immediately after the completion of business transactions or changes in short periods of time (shift, day, etc.);

Final (final) for the reporting period (month, quarter, year).

3) on spatial sign:

- on-farm- studying the activities of only the enterprise under study;

- inter-farm- to compare the performance of two or more enterprises.

4) on objects management:

- technical- economic analysis studying the interaction of technical and economic processes and their impact on performance;

- financially- economic, which focuses on financial aspects and results;

- audit (accounting) analysis– expert assessment and diagnostics financial condition and sustainability;

- socially- economic analysis, which studies the relationship of social economic processes, their impact on the performance of the enterprise;

- economic- statistical analysis- to study mass social phenomena at various levels;

- economic- ecological analysis;

- marketing analysis. (analysis of markets and external environment)

5) on methodology study:

Comparative;

Diagnostic (express analysis);

Factorial (study of the influence of factors on the resulting indicator);

Marginal (based on a causal relationship between sales volume, cost and profit, as well as dividing costs into fixed and variable);

Economic and mathematical analysis (optimization methods);

Stochastic (dispersion, correlation, component);

Functional cost analysis (method of identifying reserves), etc.

6) on coverage studied object:

Solid;

Selective.

7) on content programs:

Complex;

Thematic.

There are also other types of classification of AHD according to various criteria.

    The concept of the method of analysis, classification of methods.

AHD method- this is a systematic comprehensive study, measurement and generalization of the influence of factors on the results of an enterprise's activities by processing in specialized ways, a system of plan indicators, accounting, reporting, and other sources of information.

Method of economic analysis- approach to the study of economic processes in their development.

Peculiarity - A complex approach to the study, the use of a system of interrelated indicators, identifying the causes of changes in indicators, identifying the relationship between m / y indicators, summarizing the results.

1. Comparison- a scientific method of cognition, when an unknown (studied) phenomenon, an indicator is compared with already known (studied earlier) to identify common features or differences between them.

Distinguish the following kinds comparative analysis:

Horizontal - to determine deviations from the baseline;

Vertical - to study the structure of economic phenomena or processes;

trend - to study the relative growth rates and increase in indicators over a number of years to the level of the base year;

One-dimensional - to compare one or more indicators of one object or several objects according to one indicator;

Multidimensional - to compare the performance of several enterprises for a wide range of indicators.

2. Method relative and medium quantities:

ATides relative quantities:

Plan target - the ratio of the planned level of the indicator of the current year to its level last year or to the average for 3-5 previous years;

Implementation of the plan - the ratio between the actual and planned level of the indicator;

Dynamics - dividing the values ​​​​of the indicator of the current period by its level in the previous period (growth or growth rates), which are basic and chain;

Structures - the relative share (specific gravity) of the part in general;

Coordination - the ratio of parts of the whole to each other;

Intensities - characterize the degree of prevalence, development of a phenomenon in the corresponding environment;

Efficiency - the ratio of effect to resources or costs.

Medium quantities calculated on the basis of mass data on qualitatively homogeneous phenomena. They help to determine the general patterns and trends in the development of economic processes.

Medium quantities there are: arithmetic mean (simple and weighted), harmonic mean, geometric mean, chronological mean.

3. Balance method

Balance method serves

Used in the analysis of the security of the enterprise various types resources and the extent to which they are used. Each component of the balance can be expressed through algebraic sum others, while the analysis should take into account the economic meaning of the indicators.

4. Graphic method

Graphs present yourself large-scale representation of indicators, numbers using geometric signs (lines, rectangles, circles) or conditionally artistic figures).

The main types of charts are diagrams.

By his form they there are: columnar, strip, circular, square, linear, curly.

By content distinguish diagrams: comparisons, structural, dynamic, communication graphs (line graph), control.

5. Method groupings- division of the mass of the studied set of objects into qualitatively homogeneous groups according to the corresponding characteristics.

Groupings are used for

AT analysis are used the following kinds:

1) typological;

6. Ways casts indicators in comparable view

A prerequisite for comparative analysis is comparability comparable indicators, suggesting:

    unity of volumetric, cost, qualitative, structural indicators;

    the unity of the time periods for which the comparison is made;

    comparability of production conditions;

    comparability of the methodology for calculating indicators.

The ways to bring indicators into a comparable form are: neutralizing the impact of cost, volume, quality and structural factors by bringing them to a single basis, as well as using average and relative values, correction factors, recalculation methods, etc.

5. Method of chain substitutions, area of ​​use.

Method chain substitutions is in determining a number of intermediate values ​​of the effective indicator by successively replacing the basic values ​​of the factors with the reporting ones. This method is based on elimination. Eliminate- means to eliminate, exclude the influence of all factors on the value of the effective indicator, except for one.

It is assumed that all factors change independently of each other, i.e. first, one factor changes, while all the others remain unchanged, then two change while the rest remain unchanged, and so on.

AT general view The application of the chain setting method can be described as follows:

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

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

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

The total change Δу=у1–у0 is the sum of the changes in the resulting indicator due to the change in each factor with fixed values ​​of the other factors:

It is used in all types of deterministic factorial models.

Using the method of chain substitution, it is necessary to adhere to the following sequence of calculations: you need to take into account the change in quantity, then normative, and then quality indicators.

If there are several quantitative or qualitative indicators, then first you should change the value of factors of the 1st order, and then a lower one.

    Index method, area of ​​use.

Index method- based on relative indicators, allows you to determine the changes in the level of this phenomenon compared to the previous period, with the plan, and also affects changes in private indicators to change the effective feature.

The index method can reveal the influence of quantitative and qualitative factors on the studied aggregate indicator. It is used in animation. and multiple, and multiple-additive models.

Types of indexes: individual (without taking into account its connection with other features), aggregate (consisting of two components, the indexed feature itself and the weight feature), average or summary (if taken in connection with other features).

1.har-t relationship between indices of variable and constant weight

2.har-t interrelation of indices of variable composition and indices of structural shifts.

1.Yrd=
,

Ypg=Yp*Yg-product cost index

Yp=
,%-in. prices of constant weight

P=-in.physical.volume

Yg \u003d,% - total change in the cost of production

=-

An. allows you to move from relates. in value

2. Yp=Yp*Yp*Yline of average price shifts-index

Using the index method in the analysis, the following tasks are solved: assessment of changes in the level of the phenomenon; identification of the role of individual factors in the change of the regulatory indicator; assessment of the influence of the structure of co-ty on the dynamics of the average level of the analyzed indicator.

The value of the index shows how many percent the value of the cut indicator has changed due to the change in the indicator under study.

The difference between the numerator and denominator allows us to estimate how many rubles the sharp indicator has changed. due to a change in the studied indicator.

    Balance method, grouping method.

Balance method

Balance method serves to reflect the ratios, proportions of two groups of interrelated and balanced economic indicators, the results of which should be identical.

This method consists in comparing, commensurate two sets of indicators tending to a certain balance. It allows you to identify as a result a new analytical (balancing) indicator.

It is used in the analysis of the security of the enterprise with various types of resources and the completeness of their use.

As an auxiliary, the balance method is used to verify the results of calculations of the influence of factors on the effective aggregate indicator. If the sum of the influence of factors on the effective indicator is equal to its deviation from the base value, then, therefore, the calculations were carried out correctly .

Method groupings- division of the mass of the studied set of objects into qualitatively homogeneous groups according to the relevant indications.

Groupings are used for dependence studies in complex phenomena, the characteristics of which are reflected by homogeneous indicators and different values(characteristics of the equipment fleet by commissioning time, by place of operation, by shift ratio, etc.)

AT analysis are used the following kinds:

1) typological;

2) structural - to study the internal structure of indicators, the ratio of individual parts in it;

3) analytical (causal) - to determine the presence, direction and form of relationship between the studied indicators.

The graphic method has no independent value in the analysis, but is used to illustrate measurements.

In the case where the actions of all factors are unidirectional, it is possible to use circular diagram. The influence of each of the factors is depicted as a circle sector. The sum of all sectors (circle area) is the combined effect of all factors on the change in the performance indicator. The share of the area of ​​the sector in the area of ​​the circle characterizes the specific weight of the influence of the change in the factor on the change in the indicator.

In case of multidirectional influence of factors on the dynamics of the performance indicator, it is recommended vector diagram. The amount of change in the performance indicator under the influence of a change in a particular factor is indicated as a vector. The length of the vector is equal to the amount of change in the effective indicator.

    Method of absolute and relative differences.

Method absolute differences is a modification of the chain substitution method. The change in the effective indicator due to each factor is defined as the product of the absolute increase in the studied factor by the base value of the factors that are to the right of it and the reported value of the factors located to the left of it in the model. It is used in models of multiplicative or multiplicative type.

Method relative differences is also one of the modifications of the chain substitution method. It is used to measure the influence of factors on the growth of the effective indicator in multiplicative models. It is used in cases where the initial data contain previously defined relative deviations of factorial indicators in percent.

For multiplicative models type at = a * in * With technique analysis next:

1. find the relative deviation of each factor indicator:

2. determine the deviation of the effective indicator at for each factor.

To calculate the influence of the first factor, it is necessary to multiply the base value of the cut indicator by the relative increase in the first factor, expressed as decimal fraction. To calculate the change in the influence of the second factor, it is necessary to add the change due to the first factor to its planned value, and multiply the resulting amount by the relative increase in the second factor, etc. used for large models of 8 and more factors, allows you to reduce the calculations.

    Specific gravity method.

Specific Gravity Method- consists in determining the series of factors in the total amount of their growth and determining the influence of each factor on changes in the effective indicator. This method is used in complex models, which is carried out in several stages. At the 1st stage, multiplicative models are built, which are en-Xia by the method of absolute differences, at the 2nd stage En-Xia indicators of entry into the model of the 1st level and represent the usual amount of input. factors.

Algorithm:

1.determining the deviation of the result. display. 1st level models from baseline: FZP= FZP1- FZP0;

2.m.abs.differences def. the impact of changing private screening, input. in the model of the 1st level, on the lead of the effective feature.

FZP R= R*Z0;

FZP Z = W*R1

3. the model of the 2nd level is built and the absolute deviation is determined:

Z=Ztar+Pprim+Zdop;

Z \u003d Z 1 -Z 0; Ztar=Ztar1-Ztar0;

ZPr=ZPr1-ZPr0;

ZDop=Zdop1-Zdop0

4.determined specific weight and share of private impression growth with the growth of effective impression. level 2 models.

Beats in Ztar = Ztar/ W*100;

Beats in Pr = Etc/ W*100;

Beats in Zdop = Zdop/ W*100

5.determining the effect of changing the display of models of the 2nd level on the lead-well res. 1st level model show.

FZP Z ∙Beep Ztar/100= FZP Ztar,

FZP Pr = FZP W * ud, in Pr /100,

FZP ZDop == FZP B * Beat.in Zdop /100.

    Factor analysis, goal.

Under economic factorial analysis understood gradual transition from the initial factor system to the final factor system, disclosure of the full set of direct, quantitatively measurable factors that affect the change in the effective indicator.

factorial analysis- a methodology for a comprehensive and systematic study and measurement of the impact of factors on the value of the effective indicator.

Exist the following types factorial analysis:

1. deterministic(functional) - the effective indicator is presented as a product, private or algebraic sum of factors.

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

3. Straight(deductive) - from the general to the particular.

4. Back(inductive) - from the particular to the general.

5. Single stage and multi stage.

6. Static and dynamic.

7. Retrospective and prospective.

Stages factorial analysis:

Stage 1. Selection of factors.

Stage 2. Classification and systematization of factors.

Stage 3. Modeling the relationship between performance and factor indicators.

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

Stage 5 Practical use of the factor model (calculation of reserves for the growth of the effective indicator).

    Classification of factors.

Classification of factors according to signs:

1. on his nature:

Basic;

Minor;

2. on degrees impact on the results:

Main

Minor;

3. on relation to object research:

Internal;

external;

4. on dependencies from team:

Objective;

subjective;

5. on degrees prevalence:

specific;

6. on time actions:

Permanent;

variables;

7. on character actions:

Extensive;

Intensive;

8. on properties reflected phenomena:

quantitative;

quality;

9. on his composition:

Complex;

simple;

10. on level subordination:

First order;

second order;

11. on capabilities measurements influence:

measurable;

Immeasurable.

A systematic approach in AHD necessitates an interconnected study of factors, taking into account their internal and external relationships, interaction and subordination, which is achieved through their systematization (creation of a factor system).

    Factor models of analysis and diagnostics.

By character interconnections between indicators distinguish methods deterministic and stochastic factor analysis.

deterministic factorial analysis is a methodology for studying the influence of factors, the relationship of which with the performance indicator is of a functional nature.

Main properties deterministic approach to analysis:

Building a deterministic model by logical analysis;

The presence of a complete (rigid) relationship between indicators;

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

The study of relationships in the short term.

Modeling- the process of presenting the indicator under study with factors, which is transmitted in the form of a specific mathematical equation.

Distinguish four type deterministic models.

1. Additive models represent an algebraic sum of indicators and have the form (cost indicators): Y=∑х i

2. Multiplicative models in a generalized form can be represented by the formula (two-factor model of production volume): Y \u003d X 1 X 2 ... X i

3. Multiple Models ( Turnover time indicator (in days) )): Y \u003d X 1 / X 2

4. mixed models represent a combination of the models listed above and can be described using special expressions (cost indicators for 1 ruble of products, profitability indicators, etc.).

Detailing in factor analysis is largely determined by the number of factors whose influence can be quantified, therefore great importance in the analysis have multifactorial multiplicative models. AT basis them building lie the following principles:

The place of each factor in the model should correspond to its role in the formation of the effective indicator;

The model should be built from a two-factor complete model by sequentially dividing the factors, usually qualitative ones, into components;

When writing a formula for a multifactorial model, the factors should be arranged from left to right in the order in which they are replaced.

Building factorial models the first stage of deterministic analysis. Next, a method for assessing the influence of factors is determined.

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