The chain substitution method is used. Chain substitution method

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 changes in the value of the performance indicator by gradually replacing the base value of each factor indicator in the scope of the performance indicator with the actual value in the reporting period. For this purpose, a number of conditional values of the performance indicator are determined, which take into account changes in one, then two, three, etc. factors, assuming that the rest do not change. Comparing the value of an effective indicator before and after changing the level of one or another factor makes it possible to eliminate the influence of all factors except one, and determine the impact of the latter on the increase in the effective indicator.

The degree of influence of one or another indicator is revealed by sequential 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 = a 0 ⋅b 0 ⋅C 0 ;

Y conv.1 = a 1 ⋅b 0 ⋅C 0 ; U a = Y condition.1 – U 0 ;

Y conv.2 = a 1 ⋅b 1 ⋅C 0 ; Y b = Y condition.2 – Y condition.1;

Y f = a 1 ⋅b 1 ⋅C 1 ; Y c = Y f – Y condition.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 = 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 changing it arbitrarily can lead to incorrect results. In the practice of analysis, the influence of quantitative indicators is first identified, and then the influence of qualitative indicators. Thus, if it is necessary to determine the degree of influence of the number of workers and labor productivity on the size of industrial output, then first establish the influence of the quantitative indicator of the number of workers, and then the qualitative indicator of labor productivity. If the influence of quantity and price factors on the volume of industrial products sold is determined, then the influence of quantity is first calculated, and then the influence of wholesale prices. Before starting calculations, it is necessary, firstly, to identify a clear relationship between the indicators being studied, secondly, to distinguish between quantitative and qualitative indicators, 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 use of the chain substitution method requires knowledge of the relationship of factors, their subordination, and the ability to correctly classify and systematize them.

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

The chain substitution method has a significant drawback, the essence of which boils down to the emergence of an indecomposable remainder, which is added to the numerical value of the influence of the last factor. This explains the difference in calculations when changing the substitution sequence. This drawback is eliminated by using a more complex integral method in analytical calculations.

The essence and purpose of the index method. An algorithm for calculating the influence of factors using this method for different models.

The index method is based on relative indicators of dynamics, spatial comparisons, plan implementation, expressing the ratio of the actual level of the analyzed indicator in the reporting period to its level in the base period (or to the planned or other object).

Using aggregate indices, it is possible to identify the influence of various factors on changes in the level of performance indicators in multiplicative and multiple models. For example, let’s take the index of the cost of marketable products:

It reflects the change in the physical volume of marketable products (q) and prices (R) and is equal to the product of these indices.

The method of chain substitutions 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 changes in the value of the performance indicator by gradually replacing the base value of each factor indicator in the scope of the performance indicator with the actual value in the reporting period. For this purpose, a number of conditional values of the performance indicator are determined, which take into account changes in one, then two, three, etc. factors, assuming that the rest do not change. Comparing the value of an effective indicator before and after changing the level of one or another factor makes it possible to eliminate the influence of all factors except one, and determine the impact of the latter on the increase in the effective indicator.

Y 0 = a0?b0?C0;

Ycondition 1 = a1?b0?C0 ; U a = Ycondition 1 – U 0;

Ycondition.2 = a1?b1?C0; Yb = Ycondition 2 – Ycondition 1;

Yf = a1?b1?C1; Yс = Yф – Ycondition 2 and etc.

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

Ya + Yь + Yс = Yф – Y0.

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.

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

Overall change in result Ау = у - y 0 consists of the sum of changes in the resulting indicator due to changes in each factor with other factors fixed, i.e.,

Let us clearly consider the features of using this method.

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

Original model: N=R x 7", ac x x hour. Model type - multiplicative. When solving a problem by the method of chain substitutions and methods derived from it, the elimination technique is used.

Using the elimination technique, when assessing the influence of each factor on the performance indicator, it is assumed that other factors do not influence the change in the performance indicator, i.e. in the original model, the basic values of factors are successively replaced with the values of the reporting period.

Table 2.4

Data for the task

Index	Basic	Reporting	Absolute change, +/-	Relative increase, % (by what percentage)
average number
workers, people ( R); time worked by one job -
no one, man-hours (T shs); average hourly output,
thousand roubles. (X is)

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

Previous output value N 0= 4800 thousand rubles. By changing the number, we got the output volume N" = 5120 thousand rubles. We believe that this change in output volume is caused by a change in the number of employees.

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

2. Let us determine the effect of changes in the time worked by an employee on the volume of output. Using the elimination technique, we obtain the second intermediate value of production volume:

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

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

Change in output volume due to changes in average hourly output:

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

which corresponds to an absolute change in the result:

those. the calculations were done correctly.

The resulting data are presented in table. 2.5.

Influence of factors on output volume

Table 2.5

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

? 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, the disadvantage of the chain substitution method is indicated: “The presence of an indecomposable remainder. The need to determine the substitution sequence.” Let's look at this shortcoming.

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

If the model is represented 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 to the calculation using the original model: N=V ac x RxT" ac , The resulting difference is called indecomposable residue. The indecomposable remainder is obtained due to the different values of the factors involved in the definition N' when changing the order of substitutions during the elimination process.

To ensure unambiguous results obtained from calculations, the following rules for applying the method are used:

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

Y 0= a 0*b 0*C 0;

Y conditional 1= a 1*b 0*C 0 ; U a= Y conditional 1 – U 0;

Y conv.2= a 1*b 1*C 0; Y b= Y conditional 2 – Y conditional 1;

Y f= a 1*b 1*C 1; Y c = Y f – Y conditional 2i 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= 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.

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Introduction

chain substitution economic

Deterministic factor analysis has a fairly strict sequence of procedures:

· construction of an economically sound deterministic factor model;

· choosing a method of factor analysis and preparing conditions for its implementation;

· implementation of counting procedures for model analysis;

One of the methods of factor analysis is the method of chain substitution.

The chain substitution method is used to calculate the influence of individual factors on the corresponding performance indicator. It is based on the elimination method. Elimination is a logical technique by which the influence of factors is eliminated and one is singled out as the object of study. It is used to study the quantitative influence of each factor on the general indicator.

This method of analysis is used only when the relationship between the objects being studied is of a functional nature, when it is presented in the form of a direct or inversely proportional relationship. The resultant indicator must be depicted as an algebraic sum, product or quotient.

1.Conceptmethodchainsubstitutions

The essence of the method of chain substitutions is the sequential replacement of the basic value of the partial indicators included in the calculation formula with the actual value of these indicators, as well as measuring the impact of the replacement on the change in the value of the general indicator. That is, an additional conditional value is determined that shows what the general indicator would be if one factor changed while the others remained unchanged. This quantity is usually called substitution. If there are more than two factors, then you have to define several substitutions, or rather, a chain of interconnected substitutions. Hence the name of the method. After each substitution, all the mathematical operations provided for by the calculation formula are performed, and its previous value, which was available before the substitution, is subtracted from the resulting value of the generalizing indicator. The difference obtained in this way will show the magnitude of the influence of the substituted particular indicator on the value of the general indicator. Bakanov M.I., Sheremet A.D. Theory of economic analysis M.: Finance and Statistics, 2004 - P.197.

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

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

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

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

The influence of factor characteristics on the effective indicator is established on the basis of the formula for the analytical relationship between the studied indicators:

* dependence of type A = B + C + D is called dependence of additive type;

* dependence type A = B C D - multiplicative;

* type dependence - multiple;

* dependence type, or, or, or A = (B + C) D - mixed model.

The chain substitution method consists of sequentially replacing the planned value (actual data for the previous period) with its actual value, while all other indicators are considered unchanged. In recalculations, first of all, planned values are replaced with actual values of the reporting period for quantitative and structural indicators, and then for qualitative indicators. The size of the influence of a factor is determined by subtracting the results of the previous one from the results of the subsequent substitution (from the second - the first, from the third - the second, etc.). Sheremet A.D., Sayfulin R.S. Methodology of financial analysis - M.: INFRA-M, 2004 - P.104

When determining the influence of two factors, three calculations are made, three factors - four calculations, four factors - five calculations, etc.

Let us represent the dependence of the effective indicator on the factors influencing it with the following formula:

where A is the effective analyzed indicator;

B - quantitative factor;

C - quantitative factor;

D - quality factor.

When determining the influence of three factors on the performance indicator, the following operations are performed.

Calculation of the performance indicator for the base period:

Apl = Vpl*Spl*Dpl

The calculation of the first substitution is carried out by replacing the basic value of the first quantitative factor with its current value:

A1 = Vf*Sppl*Dpl

The calculation of the second substitution involves replacing the base value of the second quantitative factor with the current value:

A2 = Vf*Sf*Dpl

Calculation of the performance indicator for the current period:

Af = Vf*Sf*Df

Influence on the performance indicator of the 1st quantitative factor:

DAV = A1 - Apl

Influence of the 2nd quantitative factor:

DAS = A2 - A1

Determining the impact of a qualitative factor on the performance indicator:

DAD = Af - A2

The sum of the found value of factor deviations must correspond to the total total change in the considered performance indicator:

YES = Af - Apl

YES = DAV + DAS + YAD

Before you begin the calculations, you must:

* identify a clear relationship between the studied indicators;

* distinguish between quantitative and qualitative indicators;

* correctly determine the substitution sequence in cases where there are quantitative and qualitative indicators Kovalev V.V. Financial analysis M.: Finance and statistics, 2004 - P.145.

It should be recognized that calculations using the method of chain substitutions have a certain degree of convention; in particular, the determination of the order of factors in the chain of factors, and therefore their replacement, is conditional. From a formal point of view, these options are equal, but when calculating the size of the influence of factors they give different results. Therefore, it is necessary to justify the preference of one of the options. In economic analysis, this issue is resolved by analogy with the principles of constructing indexes in statistics. According to them, primary quantitative factors are weighted by the basic values of secondary qualitative factors, and secondary factors are weighted by the reported values of quantitative ones. From this point of view, the first substitution should be considered correct.

If there are many factors, then first of all they replace quantitative indicators, secondly - structural indicators, and lastly - qualitative indicators Kanke A. A., Koshevaya I. P. Analysis of the financial and economic activities of an enterprise. M.: Forum, 2005 - P.189.

The disadvantage of this method is that the calculation results depend on sequential replacement, starting with the quantitative factor. Making mistakes during the first substitution leads to unreliable results for all other factors. In addition, it is very labor-intensive, especially in cases where the summary indicator is decomposed into a large number of factors. Therefore, simplified versions of the chain substitution method are more often used - the method of absolute and relative deviations.

The essence of calculations using the method of absolute deviations is as follows: the size of the influence of each factor is determined by multiplying the absolute deviation from the basic value for a given factor by the values of other factor factors. In this case, other factor factors are taken in basic or reporting values, depending on the place of the analyzed factor in the chain of factors.

The essence of the method of percentage differences is that the size of the influence of individual factor factors on the general indicator is determined on the basis of differences in the percentage of plan completion for interrelated indicators (and not for the factors under study) Kreinina M.N. Financial condition of the enterprise. Methods of assessment M.: ICC "Dis", 2003 - P.129.

The percentage difference method is also a variation of the chain substitution method, so all three calculation methods should give the same results when analyzing the influence of the same factors.

2.Exampleusemethodchainsubstitutions

Initial data are given in table 1:

Table 1

The average daily wage (DA) will be:

· in the base period 6182500/(920 x 220.8)=30.44 rubles. in a day

· in the reporting period 6849800/(930 x 236.3)=31.17 rubles. in a day.

The multiplicative model is based on the product of indicators. In our case, it is written by the formula:

MOUTH=W x D x R

Chain substitution method: sequentially substitute the indicators:

2. First intermediate value (we use the RR of the reporting period):

ROT1.1=31.17 x 220.8 x 920 = 6331.7 thousand rubles.

3.Second intermediate value (we use the RR and D of the reporting period):

ROT1.2 = 31.17 x 236.3 x 920 = 6776.2 thousand rubles.

4.The meaning of the reporting period:

ROT2=31.17 x 236.3 x 920 = 6849.8 thousand rubles.

Differences showing the impact of each indicator:

· average daily wage: 6331.7-6182.5= 149.2 thousand rubles.

· number of man-days worked: 6776.2-6331.7= 444.5 thousand rubles.

· number of employees: 6849.8-6776.2= 73.6 thousand rubles.

· total: 149.2+444.5+73.6= 518.1 thousand rubles.

Let’s start with the absolute difference method by defining deviations:

· according to daily earnings 31.17-30.44 = 0.73 rub.

· according to man-days worked 236.3-220.8 = 15.5 man-days

· by number of employees 930-920=10 people.

Let us now determine the influence of these deviations:

1.All indicators for the base period:

ROT1=30.44 x 220.8 x 920 = 6182.5 thousand rubles.

2. Impact of changes in daily earnings:

0.73x 220.8 x 920 = 149.2 thousand rubles.

3. Impact of changing man-hours worked:

31.17 x 15.5 x 920 = 444.5 thousand rubles.

4. Impact of changes in the number of employees:

31.17x 236.3x 10 = 73.6 thousand rubles.

5.Total: 149.2+444.5+73.6= 518.1 thousand rubles.

The index method is based on the definition of indices; in our case:

average daily earnings: 31.17/30.44=1.024 (+2.4%)

man-days worked: 236.3/220.8=1.07 (+ 7%)

headcount: 930/920 = 1.011 (+ 1.1.%)

The product of these indices gives 1.108, i.e. ROT increases by 10.8% (6849.8 thousand rubles against the initial indicator of 6182.5 thousand rubles).

Conclusion: the main factor is the increase in the number of man-hours worked.

Conclusion

The chain substitution method is used to calculate the influence of individual factors on the corresponding aggregate indicator. Chain substitution is widely used in analyzing the performance of individual enterprises and associations. This method is used only when the relationship between the phenomena being studied is strictly functional in nature, when it is presented in the form of a direct or inversely proportional relationship.

In these cases, the analyzed aggregate indicator as a function of several variables should be depicted as an algebraic sum, product or quotient of one indicator divided by another. The chain substitution method consists of sequentially replacing the planned value of one of the factors with its actual value; all other indicators are considered unchanged. Consequently, each substitution is associated with a separate calculation: the more indicators in the calculation formula, the more calculations there are. The degree of influence of a particular indicator is revealed by sequential subtraction: the first is subtracted from the second calculation, the second is subtracted from the third, etc.

Listusedliterature

1. Bakanov M.I., Sheremet A.D. Theory of economic analysis M.: Finance and Statistics, 2004 - 288 p.

2. Kanke A. A., Koshevaya I. P. Analysis of the financial and economic activities of the enterprise. M.: Forum, 2005 - 288 p.

3. Kovalev V.V. Financial analysis M.: Finance and statistics, 2004 - 432 p.

4. Kreinina M.N. Financial condition of the enterprise. Methods of assessment M.: ICC "Dis", 2003 - 224 p.

5. Krylova T. Financial management M.: 1997 - 328 p.

6. Sheremet A.D., Sayfulin R.S. Methods of financial analysis - M.: INFRA-M, 2004 - 176 p.

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The chain substitution method is used. Chain substitution method

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