Economic analysis

Methods in economic analysis:

1. Traditional

Methods of economic statistics (absolute values, relative values, average values, indices, groupings)

Classical methods of economic analysis (balance method, comparisons, fact plan, comparisons with previous periods, comparisons with the performance indicators of the leading industry indicators, comparison by averages, horizontal analysis, vertical analysis, trend analysis - used to build time series, deterministic methods factor analysis)

2. Mathematical

Stochastic factor analysis (correlation analysis, regression analysis, dispersion)

Methods for optimizing indicators (economic and mathematical methods, optimization programming)

Deterministic Factor Analysis (DFA)

It is a methodology for studying the influence of factors, the relationship of which with the performance indicator is of a functional nature.
methodology for conducting DFA

1. Determine the resulting indicator and factors affecting it

2. Build a relationship model

3. The reception of the analysis is selected

4. The influence of factors is calculated (first quantitative, then qualitative)

5. Conclusions are formulated (if the stimulant is a quantitative indicator, then this is an extensive development, if a qualitative one, it is intensive)

Limiters when conducting factor analysis: all factors act on each other independently; if there are several factors of one group, first promising primary, and then secondary.

1. Additive model

2. Multiplicative

3. Multiple model

4. Combined (mixed)

Characteristics of DFA methods

1. The method of chain substitutions is to determine a number of intermediate values ​​of the effective indicator by successively replacing the basic values ​​of the factors with the reporting ones, the difference between the intermediate values ​​is equal to the change in the effective indicator due to the variable factor (universal for all types).

Algorithm: the value of the deviation between the actual and the base value is determined; the magnitude of the influence of a single factor is revealed, for this, one of the factors is sequentially changed in the chain of factors and the calculated value of the indicators is calculated, provided that the remaining factors remain unchanged; examination.

Task: to determine the change in the volume of output due to changes in such factors as the average number of employees, hours worked per employee and average hourly output.

Conclusion: output in the reporting period increased by 1120 compared to the base period, including due to an increase in the number of workers, the output increased by 320 tr. due to the increase in hours worked by one worker, the output increased by 262 tr. and due to the increase in output by one worker, the output increased by 538 tr.

The absolute difference method is a simplified technique of the chain substitution method, but it is used only in multiplicative and some combined methods.

Algorithm: the influence of individual factors is calculated by multiplying the absolute change of the studied factor by the baseline or actual values ​​of other factors, depending on the selected sequence.

The essence and purpose of the method of relative differences. Scope of its application. Algorithm for calculating the influence of factors in this way.

Relative difference method, like the previous one, it is used to measure the influence of factors on the growth of the effective indicator only in multiplicative and additive-multiplicative models of the type V= (a - b)c. It is much simpler than chain substitutions, which makes it very efficient under certain circumstances. This primarily applies to those cases where the initial data contain previously determined relative increases in factor indicators in percentages or coefficients.

Consider the methodology for calculating the influence of factors in this way for multiplicative models of the type V = BUT X AT X FROM. First, you need to calculate the relative deviations of factor indicators:

Then the change in the effective indicator due to each factor 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 relative growth the first factor, expressed as a percentage, and the result divided by 100.

To calculate the influence of the second factor, you need to add the change due to the first factor to the planned value of the effective indicator and then multiply the resulting amount by the relative increase in the second factor in percent and divide the result by 100.

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

Let's fix the considered technique on the example given in tab. 6.1:

As you can see, the calculation results are the same as when using the previous methods.

The method of relative differences is convenient to use in cases where it is required to calculate the influence of a large complex of factors (8-10 or more). Unlike the previous methods, the number of calculations is significantly reduced.

A variation of this method is acceptance of percentage differences. We will consider the methodology for calculating the influence of factors with its help using the same example (Table 6.1).

In order to establish how much the volume of gross output has changed due to the number of workers, it is necessary to multiply its planned value by the percentage of overfulfillment of the plan by the number of workers CR%:

To calculate the influence of the second factor, it is necessary to multiply the planned volume of gross output by the difference between the percentage of the plan fulfilled by the total number of days worked by all workers D% and the percentage of completion of the plan for average headcount workers CR%:

The absolute increase in gross output due to a change in the average length of the working day (intra-shift downtime) is established by multiplying the planned volume of gross output by the difference between the percentage of the plan fulfilled by the total number of hours worked by all workers t% and the total number of days they worked D%:

To calculate the impact of average hourly output on the change in the volume of gross output, the difference between the percentage of the implementation of the plan for gross output VP% and the percentage of plan fulfillment by the total number of hours worked by all workers t% multiply by the planned volume of gross output VPpl:

The advantage of this method is that when it is applied, it is not necessary to calculate the level of factor indicators. It is sufficient to have data on the percentage of fulfillment of the plan in terms of gross output, the number of workers and the number of days and hours worked by them for the analyzed period.

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The result of deterministic factor analysis is the decomposition of the increase in the effective indicator due to the general influence or change in factor characteristics into the sum of partial increases in the effective indicator, which are due to a change in only one factor. To do this, in addition to the index, specially developed methods, which are sometimes called techniques, are used in economic analysis. The main ones are the method of differences and the method of identifying the isolated influence of factors. In turn, the method of differences includes methods of chain substitutions, absolute (arithmetic) differences and relative (percentage) differences.

The method of chain substitutions is considered to be the main method of elimination. It is used in the study of functional dependencies and is intended to measure the impact of a change in factor characteristics on a change in the effective indicator with a constant (fixed) value of others.

To do this, the basic values ​​​​of each factor (planned, last period) are successively replaced by its actual data (reporting). The results of the successive replacement of each factor-indicator are compared. The difference between each subsequent and previous indicators characterize the influence of the factor, subject to the elimination of the influence of all other factors.

Based on the above, the method of chain substitutions is often called the method of sequential, gradual isolation of factors.

When applying the method of chain substitutions, one should adhere to a clear order for replacing factors:

First of all, volumetric (quantitative) indicators are replaced;

In the second - structural;

Third, quality.

In cases where there are several quantitative or qualitative indicators in the analytical model, the order is established among them - first they replace the main, primary (general) indicators, and then the secondary, derivative (partial) ones (Fig. 11.2).

Rice. 11.2. The sequence of replacing indicators when applying the method of chain substitutions

We will consider the general scheme for receiving chain substitutions using the example of a chotirox-factor multiplicative model:

where T - effective indicator;

a, b, c, d - factor indicators, and a - a qualitative indicator; c - structural indicator; c, d - volumetric (quantitative) indicators and indicator d is primary relative to indicator c.

Let's compare the actual values ​​of indicators (index "1") with the planned ones (index "0"). The total deviation of the T indicator from the plan will be:

.

For further calculations, we will rebuild our analytical model in the order necessary for the replacement of indicators. Then:

;.

Let us determine the variation of the effective indicator due to the change in all factors and each separately:

General impact of factors;

Influence of factor d;

Influence of factor c;

Influence of factor b;

Influence of factor a;

In this way:

Example. According to the data given in the table, calculate the influence of factors on the deviation of the cost of output in the reporting year compared to the previous one (Table 11.5).

1. Define the total change in output:

(thousand UAH).

2. Calculate the influence of individual factors as a change in output:

a) the impact of a change in the number of workers on a change in output:

b) the impact of a change in the number of days worked by one worker on a change in output:

c) the impact of changes in the average shift duration on the dynamics of output:

d) the impact of changes in labor productivity on changes in output:

Deviation balance:

Thus, in the reporting year compared to the previous year, the output increased by 429.3 thousand UAH. It was influenced the following factors: change in the number of workers, the number of days worked, the duration of the work shift and the average hourly output (labor productivity).

Thus, due to the increase in the number of workers, output increased by 269.5 thousand UAH. Due to the reduction in the number of days worked, the output decreased by UAH 64.68 thousand. The increase in the duration of the shift led to an increase in output by 34.16 thousand UAH, and an increase in labor productivity - by 190.32 thousand UAH.

The reception of absolute (arithmetic) differences by the reception of relative differences is a modification of the reception of chain substitutions. It can be used to determine the influence of factor indicators on the result in multiplicative and mixed models. It is better to use the method of absolute differences when the original data already contain absolute deviations in terms of factor indicators. However, this method is inappropriate to use for multiple models.

Consider the algorithm for calculating the influence of factors using the method of absolute differences using the example of the chotirox factor multiplicative model, which was used above in the method of chain substitutions:

There are absolute deviations of the actual values ​​of each factor indicator from the base ones:

;

;

;

.

As a result:

According to the above example (Table 11.5), we determine the influence of factors on the change in output using the reception of absolute differences.

1. Total change in output:

(thousand UAH).

2. The impact of changes in individual factors on the dynamics of output, namely:

a) number of employees:

(thousand UAH);

b) the number of days worked by one worker:

(thousand UAH);

c) average shift duration:

(thousand UAH);

d) labor productivity:

(thousand UAH).

Deviation balance:

It can be seen from the example that the method of absolute differences gives the same results of the influence of factors as the method of chain substitutions.

The reception of relative (percentage) differences is a kind of chain substitutions reception, which is used in multiplicative models, when the initial data are presented in relative terms. Determining the influence of factors using the reception of relative differences involves the following sequential actions:

To determine the influence of the first factor, the base value of the effective indicator should be multiplied by the relative deviation (growth rate) of the first indicator, taken as a percentage, and divided by 100;

To calculate the influence of the second and subsequent factors, it is necessary to multiply the sum of the base value of the effective indicator and the magnitude of the influence of the previous factors by the relative deviation of the indicator factor in question, expressed as a percentage, and divide by 100.

For example,. Then:

Deviation balance:

According to the above example, we determine the influence of factors on the change in output using the reception of relative differences, first calculating the percentage deviation (growth rate) of the indicators of the reporting year from the previous year (column 5 of Table 11.5):

1. General change in output.

(thousand UAH).

2. Change in output due to changes in the number of employees:

(thousand UAH).

3. Change in output due to a change in the number of days worked:

(thousand UAH).

4. Change in output under the influence of the dynamics of shift duration:

5. Influence of average hourly output on output:

Deviation balance:

As you can see, we got the same results using the methods of chain substitutions and relative differences.

It should be noted that it is advisable to use the reception of relative differences when the initial data for analysis are presented in the form of relative values ​​(for example, the percentage of the plan completed).

Thus, the difference method can be used in the study of deviations of actual values economic indicators from planned ones, as well as when studying the dynamics of indicators. Its advantage is simplicity and versatility of application.

However, this method also has certain disadvantages. Thus, the result of the decomposition of the influence of factors on the effective indicator depends on the observance of the order (sequence) of their replacement. In addition, this method is non-additive in time, that is, the results of the work done, for example, for the year of analysis do not coincide with the corresponding data obtained by months or quarters.

Absolute difference method

It is used in multiplicative and multiplicative-additive models and consists in calculating the magnitude of the influence of factors by multiplying the absolute increase in the factor under study by the base value of the factor located to the right of it and the actual value of the factors located to the left. For example, for a multiplicative factorial model of the type Y \u003d a-b-c-th the change in the magnitude of the influence of each factor on the performance indicator is determined from the expressions:

where /> th, sat, ¿4- values ​​of indicators in the base period; jaf,bf, cf - the same in the reporting period (i.e. actual); Aa \u003d df - Ob, AL \u003d bf - b6, Ac \u003d sf - sb; Asi = b?f - a.

Relative difference method

The method of relative differences, as well as the method of absolute differences, is used only in multiplicative and multiplicative-additive models to measure the influence of factors on the growth of the effective indicator. It consists in calculating the relative deviations of the values ​​of factor indicators with the subsequent calculation of the change in the effective indicator Uf due to each factor relative to the base Yf. For example, for a multiplicative factorial model of the type

Y = abs the change in the magnitude of the influence of each factor on the performance indicator is determined as follows:

The relative difference method, having a high level of clarity, provides the same results as the absolute difference method with a smaller amount of calculations, which is quite convenient when there are a large number of factors in the models.

Proportional division (equity) method

Applies to additive Y = a + b + c and multiple models of type Y= a/(b + c + d), including multilevel ones. This method consists in the proportional distribution of the increase in the effective indicator At by changing each of the factors between them. For example, for an additive model of type Y = a + b + c influence is calculated as

We will assume that Y is the cost of production; a, b, c - material, labor and depreciation costs, respectively. Let the level of the overall profitability of the enterprise decreased by 10% due to an increase in the cost of production by 200 thousand rubles. At the same time, the cost of materials decreased by 60 thousand rubles, labor costs increased by 250 thousand rubles, and depreciation costs - by 10 thousand rubles. Then due to the first factor (a) the level of profitability has increased:

Due to the second (b) and third (c) factors, the level of profitability decreased:

Method of differential calculus

It assumes that the total increment of the function differs into terms, where the value of each of them is determined as the product of the corresponding partial derivative and the increment of the variable on which this derivative is calculated.

Consider a function of two variables: r=/(x, y). If this function is differentiable, then its increment can be represented as

where Ag = (2(-2o)- function change; Oh = ("Г] - ,г0) - change of the first factor; Ay = (y^ - r/()) - change of the second factor.

Sum (dg / dx) Ah + (dg / du) Ay - the main part of the increment of the differentiable function (which is taken into account in the method of differential calculus); 0ud~r ^+d7/ - indecomposable remainder, which is an infinitesimal value for sufficiently small changes in the factors x and y. This component is not taken into account in the considered method of differential calculus. However, when significant changes factors (Oh and ay) there may be significant errors in assessing the influence of factors.

Example 16.1. Function G has the form z = x-y, for which the initial and final values ​​of the influencing factors and the resulting indicator are known (x&y0, r0, x, y, 2). Then the influence of influencing factors on the value of the resulting indicator is determined by the expressions

Let us calculate the value of the remainder term as the difference between the value of the total change in the function Dr = X ■ y - x0 o g / o and the sum of the influences of the influencing factors r,. + Dz(/ = y0-Ax + xn■ &y:

Thus, in the method of differential calculus, the indecomposable remainder is simply discarded (the logical

differentiation method error). This approximateness of the considered method serves as a disadvantage for economic calculations, where an exact balance of the change in the resulting indicator and the sum of the influence of influencing factors is required.

Factor analysis

Integrated and system studies and measuring the impact of factors on the magnitude of performance indicators.

Functional (deterministic)

Stochastic (correlation)

・Forward and reverse

Statistical

· Dynamic

retrospective and prospective

Main task: selection of factors, classification and systematization, determination of the form of communication, calculation of the influence of the factor and the role of its influence on complex indicators.

Types of factor models:

1 Additive models: y=x1+x2+x3+…+xn=

2 Multiplicative models: y=x1*x2*x3*…*xn=P

3 Multiple models: y=

4 Mixed models: y=

Chain substitution method

A universal method that is used for any factorial models.

Allows you to determine the influence of individual factors on the change in the value of the effective indicator, way. Gradual replacement of the base value of each factor by its actual value.

Replacement begins with the main quantitative factor and ends with a qualitative indicator.

The influence of each factor is determined by successive steps. For 1 step, you can make one replacement. The algebraic sum of the influence of factors should be equal to the total increase in the effective indicator.

Tactics of application:

y=a*b*c where y0,a0,b0,c0 are base values

y1=a1*b1*c1 – actual values

Influence on the growth of the effective indicator of the change in factor a:

∆ y’ a = y’-y0

y''=a1*b1*c0

∆ y'' b = y''-y'0

y'''=a1*b1*c1

∆ y’’’ c = y’’’-y’’0

∆y=∆y a +∆y b +∆y c

Example: TP \u003d K * C

TPpl \u003d Kpl * Cpl - base value

TPF \u003d Kf * Tsf - actual value

TPus \u003d Kf * Tspl

∆TP=TPf-TPpl

∆TPc=TPsl-Tpl

∆TPc=TPav-Tpusl

∆TP=∆TPc+∆TPc

1) TPpl \u003d 135 * 1200 \u003d 16200

2) TPF=143*1370=195910

3) ∆TP=TPf-TPpl=195910-162000=33910

4) TPusl=135*1370=184950

5) ∆TPc=184950-162000=22950

∆TPc=195910-184950=10960

∆TP=22950+10960=33910

Absolute difference method

This is a modification of the chain substitution method. Used only in multiplicative models.

The magnitude of the influence of factors is calculated by multiplying the absolute increase of the used factor by the fictitious value of the factors that are used in the model to the left of it and by the base value of the factors that are to the right.

yb=a0*b0*c0 – basic

y1=a1*b1*c1 – actual

∆у a =∆ a*b0*c0, where ∆а=а1-а0

∆ y b = a1*∆b*c0

∆ y c = a1*b1*∆c

∆TPk = (1370-1200)*135=22950

∆TPc = 1370*(143-145)=10960

∆TP = 195910-162000=33910

Relative difference method

It is desirable to use only in what models? type when you need to calculate the influence of more than 8 factors.

Step 1. We calculate the relative deviations of factor indicators:

y0=a0*b0*c0 ∆а=а1-а0 – absolute deviation

y1=a1*b1*c1 relative deviation:

Step 2. Deviation of the effective indicator due to a change in each factor:

Index Method

The method is widely used for quantification the role of individual factors. All factors change independently of each other.

Based on relative performance indicators, and distribution comparisons, what? Plan.

Defined as a level ratio relative indicator to its level in the base period.

Index methods are used in multiplicative and real models. Allocate individual and group indices. Indices expressing ratios of directly commensurate values ​​are called individual, and are calculated according to indicators for which factor models are not compiled.

Group indices characterize the ratio of what? Phenomena (total indices). Calculated by multifactorial models, index cost marketable products.

Index of the cost of marketable products:

Index of what? What? Shows how much revenue decreased with a decrease in sales.

The price index reflects the amount of change in revenue due to price changes.

Main indicators: gross output (cost of all manufactured products, including unfinished production), marketable products (not including unfinished products), sold products (sold, 91-1 account).

The minimum allowable sales volume is the break-even point.

Max allowable sales volume - at max capacity utilization.

Optimal allowable scope of implementation - methods of research operations.