Chain substitutions in economic analysis. 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.

Algebraic sum the influence of factors must necessarily be equal to the overall 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 that is added to numerical value 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 most common method of factor analysis is the method of chain substitutions. The essence of this method lies in the sequential substitution of the reported values of the factors under study into the initial formula for determining the effective indicator.

Assessing the influence of individual factors on the performance indicator involves performing a number of calculations.

1. The reporting value of the first factor under study 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 obtained result 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 obtained result is compared with the previous one and the influence of the second factor on the effective indicator is established.

5. The procedure is repeated until the actual value of the last factor 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 assessed, and then - qualitative ones, characterizing the influence of intensity. It is on the qualitative factors that the entire indecomposable remainder falls.

Example:

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

The basic value of production volume is:

No = Pto * Cho

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

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

Let us evaluate the influence of each of these factors.

1. Let's substitute the actual value of the quantitative factor - the number of employees - into the formula:

Nch = Ch1 * Pto

Where: N1 is the actual value of the number of production workers.

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

DNest = Nch - No

As a percentage of the total change in production volume:

DN total = N1 – N0

DN rel. ext = (DNest / DNtot) * 100%

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

2. We carry out the substitution quality factor– labor productivity:

Npt = P1 * Pt1

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

DN rel. int = (DNint / DNtot) *100%

Task 1.

Based on data on the organization’s activities (Table No. 1), assess the influence of extensive and intensive factors on changes in volume products sold.Table:

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

Nch = 202 * 450 = 90900 tr.

DN total = 95000 – 90000 = 5000 tr.

DNest = 90900 - 90000 = 900 tr.

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

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

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

2) Assessment of the influence of the intensive factor:

Npt = 202 * 470.3 = 95000.6 tr.

DN int = 95000.6 - 90900 = 4100.6 tr.

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

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

The share of the influence of the intensive factor on the change in sales volume was 82%.

When performing calculations using the chain substitution method, you can use not only the absolute values of factors, but their increments. In this case, the magnitude of the change in the effective indicator is immediately obtained.

When using this method, the following rules are followed:

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

DNch= (Ch1 -Cho) * Pto = DЧ * Pto

DNpt = (Pt1 - Pto) *Ch1 = DPt * Ch1

In our task:

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

DNch = (202 - 200) * 450 = 900 tr.

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

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

The total influence of factors is equal to:

DN,o = 900 + 4100.6 = 5000.6 tr.

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

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

In our task:

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

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

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

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

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

DNint = 5000 - 900 = 4100 tr.

This method is convenient to use in cases where a quantitative factor is 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.

The studied indicator can be expressed through factors, the influence of each factor on the change in the studied indicator is calculated. The chain substitution method can be used for direct and inverse relationships between the indicators being studied and the factors that form it.

When using the chain substitution method, the studied indicators are expressed through factors or a factor model is built, then the initial one is determined ( basic) factor model ( what is it compared to?) and final ( reporting) factor model ( what is being compared). In the factor model used in the chain substitution method, quantitative factors are necessarily given first, and then qualitative ones.

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 basic value of each factor in the original factor model is replaced by its actual value along the chain).

Interim performance indicators are calculated. The difference in intermediate values is equal to the change in the effective indicator due to the factor being replaced. ( The difference between each subsequent and previous performance indicator characterizes the influence of a specific factor on the change in the indicator being studied.)

Overall change in result ∆ y = y 1 - y 0 consists of the sum of changes in the resulting indicator due to changes in each factor with other factors fixed, i.e.

The combined influence of factors gives the overall change in the indicator being studied.

Number of performance indicator calculations per unit more number measured factors.

Advantages this method:

Versatility of use (used in the analysis of any type of model),

Fairly easy to use.

However, this method has significant flaw- depending on the chosen order of factor replacement, the results of factor decomposition have different meanings.

As a result of applying this method, a certain indecomposable residue is formed, which is added to the magnitude of the influence of the last factor. But in practical calculations, the accuracy of assessing the influence of factors is neglected, highlighting the relative importance of the influence of one or another factor. The problem of an indecomposable remainder is solved using the logarithmic and integral methods, when, due to the properties of the logarithmic and integral functions, there is no indecomposable remainder.

However, there are some rules governing the substitution sequence:

If there are quantitative and qualitative indicators in the factor model, the first step is to substitute quantitative factors;

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

In a formalized form, the algorithm for applying the chain substitution method is described as follows.

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

Original model: N = H × t × V.

Model type - multiplicative.

Solution. When solving a problem by the method of chain substitutions and methods derived from it, the elimination technique is used: to assess the influence of each factor on the effective indicator, it is assumed that other factors do not influence the change in the effective indicator, i.e. in the original model, the basic values of factors are successively replaced with current ones (of the reporting period).

Table - data for the task

N 0 = H 0 × t 0 × B 0 = 15 × 1600 × 0.2 = 4800 thousand rubles. - basic value.

Determining the impact of the change average number workers per volume of output.

Using elimination, we get the first intermediate value:

N" = H 1 × t 0 × B 0 = 16 × 1600 × 0.2 = 5120 thousand rubles.

Previous value of production volume N 0 = 4800 thousand rubles. By changing the number, we obtained the output volume N" = 5120 thousand rubles. We believe that the change in output volume is caused by a change in the number of employees. The change in output volume due to a change in the number of employees will be:

∆ N(H) = N" – N = 5120 - 4800 = 320 thousand rubles.

Let's determine the impact of the change time worked by the employee to the volume of output. Using elimination, we obtain the second intermediate value of output volume:

∆ N" = H 1 × t 1 × B 0 = 16 × 1682 × 0.2 = 5382.4 thousand rubles.

Reasoning in a similar way, we obtain a change in output due to a change in hours worked:

∆ N(t) = N" - N" = 5382.4 - 5120 = 262.4 thousand rubles.

Let's determine the impact of the change average hourly output on the volume of production. Third intermediate value of output volume:

N" = N 1 = H 1 × t 1 × B 1 = 16 × 1682 × 0.22 = 5920.64 thousand rubles.

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

∆ N(B) = N" - N" = 5920.64 – 5382.4 = 538.24 thousand rubles.

∆N = ∆ N(H) + ∆ N(t) +∆ N(B) = 320 + 262.4+538.24 = 1120.64 thousand rubles.

The algebraic sum of the influence of factors must be equal to the increase in the effective indicator, otherwise there was an error in the calculation. The results are presented in a table. This is especially important for multifactorial models and when studying the influence of downstream factors.

The influence of factors on output volume is shown in the following table.

Specific gravity the influence of each factor is calculated as the ratio of the influence of each factor to the total deviation.

According to the above calculation, we can do conclusion:

Product output in the reporting period increased by 1120,64 thousand rubles, including:

By increasing the average number of personnel by 320 thousand rubles,

By increasing the time worked by one employee by 262,4 thousand rubles,

Due to production growth – by 538,24 thousand rubles

Increase in production volume

on 48,03% ensured by an increase in the quality indicator of labor productivity,

on 23,42% - increasing the time worked by one employee,

and on 28,56% - additional involvement of employees.

Thus, the increase in output is explained mainly by factors of intensive development.

Example . Model of multiplicative-additive type: P = RP*(C - C)

Where P is profit from sales of products;

RP – volume of product sales;

C – selling price;

C is the cost per unit of production.

Pplan = RPplan*(Tsplan - Plan); ∆P = Pfact - Pplan

P1 = RPfact*(Tsplan - Plan); ∆PRP = P1 - Pplan

P2 = RPfact*(Tsfact - Plan); ∆PC = P2 - P1

Pfact = RPfact*(Tsfact - Sfact). ∆PS = Pfact - P2

Example 1– model of multiplicative type VP = PR*D*P*CV, table 2:

Table 2

Solution 1. VPplan=ChRplan*Dplan*Pplan*ChVplan=1000*250*8*80=160000 thousand UAH;

VP1=ChRfact*Dplan*Pplan*ChVplan=1200*250*8*80=192000 thousand UAH;

VP2=ChRfact*Dfact*Pplan*ChVplan=1200*256*8*80=196608 thousand UAH;

VP3=ChRfact*Dfact*Pfact*ChVplan=1200*256*7.6*80=186778 thousand UAH;

VPfact=ChRfact*Dfact*Pfact*ChVfact=1200*256*7.6*102.8=240009 thousand UAH.

The production plan as a whole was exceeded by UAH 80,009 thousand. (240009-160000), including due to changes:

– Number of workers

∆VPChR=VP1-VPplan=192000-160000=32000;

– Number of days worked by one worker per year

∆VPD=VP2-VP1=196608-192000=4608;

– Average working day

∆VPP=VP3-VP2=186778-196608= -9830;

– Average hourly output

∆VPChV=VPfact-VP3=240009-186778=53231

∆VP=∆VPChR+∆VPCh+∆VPP+∆VPChV=32000+4608-9830+53231=80009

When using the chain substitution method, it is recommended to adhere to a certain sequence of calculations.

First of all, it is necessary to take into account changes in quantitative and then qualitative indicators. If there are several quantitative or qualitative indicators, then you should first change the value of the factors of the first level of subordination, and then the lower one.

In the example given, the volume of production depends on 4 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 Fig. 2.1 the number of workers in this case is a factor of the first level of subordination, the number of days worked is of the second level, the length of the working day and average hourly output are factors of the third level. This determined the sequence of placement of factors in the model and the order of their changes.

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.

It is required to determine by the method of chain substitutions the influence on sales volume (V) of labor factors using the following formula:

Where H is the average number of workers;
D – average number of days worked by one worker per day;
t is the average number of hours worked by one worker per day;
β is the average output per person-day worked.
Therefore, sales volume equal to the product four factors.
Initial data are given in Table 1

Table 1 - Initial data for determining the influence of labor factors on sales volume.

The sales plan was exceeded by UAH 351.4 thousand. (3155.2-2803.8). In order to determine how the function (V) was affected various factors, let's make the following calculations.
First calculation. All indicators are planned.
900 · 301 · 6.9 · 1.5 = 2803.8 thousand UAH.
Second calculation. The average number of workers is actual, and the remaining indicators are planned:
1000 · 301 · 6.9 · 1.5 = 3115.4 thousand UAH.
Third calculation. The number of workers and the number of days they worked are actual, and the remaining indicators are planned:
1000·290·6.9·1.5 = 3001.5 thousand UAH.
Fourth calculation. The number of workers, the number of days and hours worked are actual, and the planned output:
1000·290·6.8·1.5 = 2958 thousand UAH.
Fifth calculation. All indicators are actual:
1000·290·6.9·1.6 = 3155.2 thousand UAH.
Next, we will analyze the influence of factors on sales volume.
The deviation of the actual sales volume from the planned one was due to the influence of the following factors:
1) The increase in the number of workers is determined by subtracting the first from the second calculation: 3115.4 – 2803.8 = +311.6 thousand UAH.
2) Reducing the number of days worked - the second result is subtracted from the third:
3001.5 – 3115.4 = -113.9 thousand UAH.
3) Reduction average duration working day – the third is subtracted from the fourth: 2958.0 – 3115.4 = -43.5 thousand UAH.
4) Increase in average hourly output: 3155.2 – 2958.0 = +197.2 thousand UAH.
Total deviation: 3155.2 – 2803.8 = +351.4 thousand UAH. or 311.6 – 113.9 – 43.5 + 197.2 = 351.4 thousand UAH.
Consequently, two factors had a positive effect on sales volume and two factors had a negative effect.
The calculation shows that the enterprise had day-long and intra-shift downtime. If the company had not allowed an increase in no-shows and intra-shift downtime, sales volume would have increased by UAH 157.4 thousand. (113.9 + 43.5).

Method of chain substitutions of 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.

Y0 = а0⋅b0⋅С0;

Ycondition 1 = а1⋅b0⋅С0; Ua = Ycondition 1 – U0;

Ycondition.2 = а1⋅b1⋅С0; Yb = Ycondition 2 – Ycondition 1;

Yf = a1⋅b1⋅C1; Yс = Yф – Ycondition 2, 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 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.

Method chain substitutions is the most versatile of methods elimination.

Way absolute differences is a modification way chain substitutions.
Integral method allows you to achieve a complete decomposition of the effective indicator by...

3. Method elimination (exceptions): a) way chain substitutions, b) way absolute differences (deviations)

- way chain substitutions(determination of a number of intermediate values
- integral method(based on the logarithmic law of redistribution of factor loadings).

Method chain substitutions is the most versatile of methods elimination. It is used... more ».

...calculating the influence of factors compared to ways chain substitutions, absolute and
Thus, the use of integral method no need to know the whole process...

Index method allows you to decompose into factors not only relative, but also absolute deviations
To solve this problem it is used method chain substitutions.

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for example, when using method chain substitutions, and can greatly distort the result...

The influence of these factors can be calculated ways chain substitutions, absolute differences, relative differences or integral method.

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Purpose of the service. The online calculator is designed to analyze the influence of individual factors on the performance indicator by chain substitution method(see example).

Instructions. To solve problems by chain substitution method select the number of factors. The resulting solution is saved in a MS Word file.

Chain substitution method can be used in all types of deterministic factor models (additive, multiplicative, multiple, combined) to calculate the magnitude of the influence of a factor on the result.

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 are calculated that take into account the change in one, two, etc. factors, assuming that other factors remain unchanged. Comparing the magnitude of the result before and after changing the level of a particular factor allows one to eliminate the influence of all factors except one.

Algorithm of the chain substitution method for a multifactor multiplicative model

Y = a * b * c * d

1. Calculate the planned indicator: Y0 = a0 * b0 * c0* d0;

3. Calculate the actual indicator: Y1 = a1 * b1 * c1* d1;

4. By sequentially subtracting the obtained indicators, we find the change in the effective indicator due to the factors:
ΔYа = Y condition.1 – Y0;
ΔYb = Y condition.2 – Y condition.1;
ΔYс = Y condition.3 – Y condition.2;
ΔYd = Y1– Y condition.3;
5. We calculate the total deviation of the actual indicator from the planned one, which is equal to the sum of factor deviations:
ΔY = Y1 - Y0 = ΔYа + ΔYb + ΔYс + ΔYd

Recommendations when using this method:
A) first of all, changes in quantitative indicators are taken into account, then qualitative ones;
B) first, factors of the first level of subordination are taken into account, then the second, etc.

Example. The initial data for calculating the influence of factors are basic: (y0 = 1.58; a0 = 12940; b0 = 8210) and actual: (y1 = 1.53; a1 = 13950; b1 = 9124;). Calculate the influence on the deviation of the performance indicator (y) of each of its determining factors (a, b).

Chain substitutions in economic analysis. Chain substitution method

Algorithm of the chain substitution method for a multifactor multiplicative model

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