Method of relative differences for mixed. Method of relative (percentage) differences of deterministic factor analysis

(to contents)

Example 1. Create a factor system of gross output volume that is functionally dependent on the following indicators:

· number of days worked by one employee per year (D);

· average hourly output per worker (AC);

· average working day (P);

· average daily production per worker (DV);

· average annual output production by one worker (GW);

· average annual number of workers (UA).

Solution:

Factor model of gross output volume:

VP = CR*GV or VP = CR*D*DV or VP = CR*D*P*CHV.

Example 2. Based on the initial data of Table 14 (in italics), determine the absolute and relative change in sales revenue and the magnitude of the influence of volume and price products sold for this indicator using the following methods:

· chain substitutions;

· absolute differences;

· relative differences;

· integral;

· logarithms

based on model:

B =VRP * C,

where B is revenue from sales of products,

VRP – volume of products sold,

P – price of sold products.

Table 14

Indicators	Base	Report	Changes
Indicators	Base	Report	abs.	rel.
1	2	3	4=3-2	5=4/2*100%
1.Volume of products sold, thousand units.	10	12
2.Price of products sold, thousand rubles.	7	10		42,8
3. Revenue (2*3), million rubles.		120		71,4

Solution:

1. Chain substitution method

We calculate the value of revenue by sequentially replacing the basic values of factor indicators with the values of the reporting period:

B 0 =VRP 0 * C 0 = 10 * 7 = 70 million rubles.

In condition1 =VRP 1 * C 0 = 12 * 7 = 84 million rubles.

B 1 =VRP 1 * C 1 = 12 * 10 = 120 million rubles.

Let's evaluate the influence of each factor separately:

∆V V RP = In condition1 - In 0 =84 - 70 = 14 million rubles.

∆V C = V 1 – V condition1 =120 - 84 = 36 million rubles.

Examination:

∆V= V 1 -V 0 =∆V V RP +∆V C =120-70=14+36=50 million rub.

2. Absolute difference method

∆V V RP = ∆ VRP *C 0 = 2*7 = 14 million rubles.

∆V C =VRP 1 * ∆C = 12 * 3 = 36 million rubles.

Examination:

3. Relative difference method

∆V V RP = V 0 *(∆VRP/VRP 0)= 70*(2/10)=14 million rubles.

∆V C =(V 0 +∆V V RP ) *(∆C/C 0)= 84*(3/7) = 36 million rubles.

Examination:

∆B= 120-70=14+36=50 million rubles.

4. Integral method

∆V V RP = 0,5*∆ VRP *(C 0 + C 1) = 0.5*2*(7+10) = 17 million rubles.

∆V C = 0.5*∆C*(VRP 0 +VRP 1) =0.5*3*(10+12) = 33 million rubles.

Examination:

5. Logarithm method

∆V V RP = ∆V*lg( VRP 1 /VRP 0)/lg(B 1 / B 0) = 50*(0.079/0.23) = 17 million rubles.

∆V C =∆V*lg(C 1 /C 0)/lg(B 1 / B 0) = 50*(0.15/0.23) = 33 million rubles.

Examination:

∆B= 120-70=17+33=50 million rubles.

Conclusion: calculations showed that the greatest impact on the increase in sales revenue was caused by an increase in product prices. Three out of five methods gave the same results on the magnitude of the factorial influence on the performance indicator. The use of the integral method and the logarithm method made it possible to take into account the interaction of factor indicators with each other and, as a result, more accurately determine their influence on the effective indicator, in particular, to identify a stronger influence of the volume factor.

Example 3. Based on the initial data (in italics) given in Table 15, determine the absolute and relative change in gross profit from product sales and the magnitude of the influence of factors on gross profit by the method of proportional division and the equity method, using the model:

where Pr - gross profit from product sales,

B – revenue from sales of products,

C – cost of goods sold.

Table 15

Indicators	Basic year	Reporting year	Changes
Indicators	Basic year	Reporting year	abs.	rel.
			4=3-2	5=4/2*100%
1.Revenue, thousand rubles.	56 377	62 849	6472	11,48
2. Cost, thousand rubles.	46 496	57 738	11242	24,18
3.Gross profit (1-2), thousand rubles.	9881	5111	4770	48,27

Solution:

1. Proportional division method

thousand. rub.

Examination :

thousand. rub.

2. Method share participation

thousand. rub.

Examination :

thousand. rub.

Conclusion: gross profit from product sales in the reporting period decreased by 4,770 thousand rubles. or by 48.27% compared to the base period due to the rapid growth of product costs over the growth of sales revenue. The share of the negative impact of cost growth on the decrease in gross profit amounted to 63.46% (3027.23/4770*100%).

Example 4. Based on the data in Table 16, determine the existence of a relationship between sales revenue and advertising costs, calculate the correlation coefficients, determination coefficients and determine the correlation ratio.

Table 16

Solution: Let's calculate the derivatives for analysis in Table 17:

Table 17

			X*Y	X 2	Y2	Y x
			2800	1600	4900
			3024	1764	5184	71,2
			2584	1444	4624	68,8
			2990	2116	4225	73,6
			3520	1936	6400	72,4
			3600	2304	5625	74,8
			3900	2500	6084
Total	308	508	22418	13664	37042	506,8

Based on the table, we build a system of equations

from here

The relationship equation describing the dependence of sales revenue on advertising costs received the following expression:

Y x =46+ 0,6 x

Let's calculate the correlation coefficient:

Let's calculatecoefficientdetermination:

Conclusion: in this case, the relationship between the indicators is insignificant, the value of the coefficient of determination indicates that revenue from product sales depends by 22% on advertising costs, and other factors account for 78% of the change in its level.

Task 2.1. Convert the analytical formula using the expansion method:

where GW is annual output (labor productivity);

CR – average number of personnel,

in such a way that it reflects the dependence of labor productivity on capital productivity and capital-labor ratio.

Problem 2.2. Using the reduction method, transform the analytical formula:

where FO is the capital productivity of fixed assets production assets;

VP – gross output for the year;

OPF – average annual cost fixed production assets,

in such a way that it reflects the relationship between the average annual output of one worker and the capital-labor ratio.

Problem 2.3. Using the extension method, transform the analytical formula:

where ME is the material intensity of products;

MR – costs of material resources;

B – revenue,

in such a way that it reflects the relationship between the material intensity of raw materials and materials, fuel intensity, energy intensity, material intensity of other costs.

Problem 2.4. Systematize the factors that determine the amount of profit from product sales:

- revenue (B);

- sales volume (VRP);

- total costs (Z);

- unit price (P);

- structureproducts ();

- unit cost (C)

and write down the factor model of profit.

Problem 2.5. Transform the analytical formula using the expansion method so that it reflects the dependence of return on assets on the value of return on sales and asset turnover.

Problem 2.6. Create a factor model, where the factor indicators are the volume of gross output and the average annual cost of fixed production assets. Using the method of chain substitution, determine the quantitative influence of factors on the performance indicator if:

· gross output for the reporting period increased compared to the plan from 78,000 to 82,000 rubles;

· the average annual cost of fixed production assets decreased from 72,000 to 70,000 rubles.

Problem 2.7. Based on the data in Table 18, create a factor model of profit from product sales and calculate the influence of factors on the change in its amount in all possible ways.

Table 18

Indicator	Base year	Reporting year
Product sales volume, pcs.	8 000	8 400
Sales price, thousand rubles.
Product cost, thousand rubles.

Problem 2.8. Based on the data in Table 19, create a factor model of the dependence of the volume of production on the average annual cost of fixed assets and capital productivity and, using the integral method and the method of absolute differences, determine the magnitude of the influenceI factor indicators on effective.Volume of production, million rubles.

21409

22287

Average annual cost of fixed assets, million rubles.

23000

23447

Problem 2.9. Using the data in Table 20, create a factor model of a multiple-additive type and, using the equity method, determine the impact of changes in sales profit, the average annual cost of fixed assets and the value working capital to change the production profitability indicator.

Table 20

Indicator

Base year

Reporting year

Profit, thousand rubles

55,25

65,16

Average annual cost, thousand rubles:

fixed assets

working capital

500

350

520

385

Problem 2.10. The duration of capital turnover decreased by 25 days. Calculate the influence of factors on changes in the duration of capital turnover using the method of proportional divisiontaking into account changes in factor indicators given in table 21.

Table 21

	Change in average balances, thousand rubles.
Stocks of raw materials and supplies	+2700
WIP balances	+1300
Finished products	- 800
Accounts receivable	+2000
Cash	- 200

Problem 2.11. The relationship between the costs of production and its volume is described by a linear relationship . Based on the data in Table 22, determine the relationship equation coefficients, correlation and determination coefficients, and explain their economic meaning.

No.

Production costs, thousand rubles.

Production volume, thousand rubles.

120

200

130

270

150

280

140

250

180

200

180

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. For this purpose, in addition to index analysis, economic analysis uses specially developed methods, which are sometimes called techniques. 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 the techniques of chain substitutions, absolute (arithmetic) differences and relative (percentage) differences.

The method of chain substitutions is rightfully considered the main method of elimination. It is used in the study of functional dependencies and is intended to measure the impact of changes in factor characteristics on changes in the effective indicator while keeping the other values constant (fixed).

To do this, the basic values of each factor (planned, last period) are successively replaced with its actual data (reported). The obtained results of sequential replacement of each factor-indicator are compared. The difference between each subsequent and previous indicator characterizes the influence of the factor, provided that the influence of all other factors is eliminated.

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

When using the technique of chain substitutions, you should adhere to a clear order of replacing factors:

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

Secondly - structural;

Thirdly, quality.

In cases where the analytical model contains several quantitative or quality indicators, a priority is established among them - first the main, primary (general) indicators are replaced, and then the secondary, derivative (partial) indicators are replaced (Fig. 11.2).

Rice. 11.2. The order of replacing indicators when using the technique of chain substitutions

Let's consider the general scheme for using chain substitutions using the example of a multiplicative multiplicative model:

where T is the effective indicator;

a, b, c, d - factor indicators, with a being 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 the indicators (index "1") with the planned ones (index "0"). The total deviation of the T indicator from the plan will be:

To carry out further calculations, we will rebuild our analytical model in the order necessary to replace the indicators. Then:

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

General impact of factors;

Influence of factor d;

Influence of factor c;

Influence of factor b;

The influence of factor a;

Thus:

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

1. Let us determine the general change in output:

(thousand UAH).

2. Let us calculate the influence of individual factors as a change in output:

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

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

c) the impact of changes in the average shift duration on the dynamics of product 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, product output increased by UAH 429.3 thousand. This was influenced by the following factors: changes in the number of workers, the number of days worked, the length of the work shift and average hourly output (labor productivity).

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

The reception of absolute (arithmetic) differences and 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 results in multiplicative and mixed models. It is better to use the method of absolute differences when the source data already contains absolute deviations in factor indicators. However, this method is not practical for multiple models.

Let us consider the algorithm for calculating the influence of factors using the method of absolute differences using the example of the multiplicative 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 basic ones:

;

As a result:

Based on the data in the above example (Table 11.5), we determine the influence of factors on changes in product output using absolute differences.

1. General change in output:

(thousand UAH).

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

a) number of employees:

(thousand UAH);

b) number of days worked by one worker:

(thousand UAH);

c) average shift duration:

(thousand UAH);

d) labor productivity:

(thousand UAH).

Deviation balance:

The example shows that the method of absolute differences gives the same results of the influence of factors as the method of chain substitutions.

The method of relative (percentage) differences is a variation of the method of chain substitutions, which is used in multiplicative models when the source data is presented in relative values Oh. Determining the influence of factors using relative differences involves performing the following sequential actions:

To determine the influence of the first factor, the basic 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 basic value of the effective indicator and the magnitude of the influence of previous factors by the relative deviation of the factor-indicator in question, expressed as a percentage, and divide by 100.

For example,. Then:

Deviation balance:

Based on the above example, we will determine the influence of factors on changes in product output using relative differences, first calculating the percentage deviation (growth rate) of the reporting year’s indicators from the previous year (column 5 of Table 11.5):

1. General change in output.

(thousand UAH).

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

(thousand UAH).

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

(thousand UAH).

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

5. The influence of average hourly output on product output:

Deviation balance:

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

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

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

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

Topic 3. Characteristics of traditional factorial techniques economic analysis

Chain substitution method

This method is used in cases where two or more factors are included in the model for calculating a generalizing (resultative) indicator and the relationship between them is functional in nature.

The essence of the chain substitution method:

1) Consistently replace the basic factors with actual ones and recalculate the general indicator after each substitution. The first substitution is always basic, and the last is always factual. Therefore, the number of substitutions is always one more than the number of factors included in the model for calculating the general indicator.

2) In order to quantify the influence of a factor, it is necessary to subtract the general indicator obtained in the previous calculation from the general indicator obtained in the subsequent calculation.

The disadvantage of the chain substitution method is that the quantitative assessment of the influence of factors strongly depends on the sequence of substitutions.

In order to avoid this drawback it is necessary:

First replace quantitative (extensive) factors, and then qualitative (intensive);

If there are several quantitative factors, then those that are least dependent on the subsequent ones are replaced first.

Example. Assess the influence of labor factors on changes in production volume at an industrial enterprise.

Table 2 - Assessment of the influence of the main factors on changes in product output in an industrial enterprise

Indicators	Last year	Reporting year	Changes (+/-)	Substitutions	Quantitative assessment of the influence of factors

1.Volume of production (thousand rubles)	157,1	144,2	- 12,9	157,1	103,15	104,4	110,2	144,2	-12,9
2. Average number of workers			-1						-53,95
3.Average number of days worked by one worker per year									+ 1,25
4.Average number of hours. worked by 1 worker per day	7,2	7,6	0,4	7,2	7,2	7,2	7,6	7,6	+5,8
5. Product output per 1 man-hour worked (item 1/item 2item 3item 4), thousand rubles.	0,029	0,038	0,009	0,029	0,029	0,029	0,029	0,038	+34

The data presented in Table 2 show that the volume of production in the reporting year compared to the previous year decreased by 12.9 thousand rubles. This is mainly due to a decrease in the number of employees per person, so due to the influence of this factor, production output decreased by 53.95 thousand rubles.

Due to an increase in the number of working days by 3 days, product output increased by 1.25 thousand rubles, and due to an increase in the duration of the working day by 0.4 hours, the volume of production increased by 5.8 thousand rubles. Due to more effective use labor resources Product output increased by 34 thousand rubles.

Thus, the main factor in reducing production output at an industrial enterprise is the lack of personnel.

Absolute difference method

This method is a derivative of the method of chain substitutions and is used in cases where only two factors (or several) are included in the model for calculating the general indicator and the relationship between them is necessarily multiplicative. If two factors are included in the model for calculating a general indicator, one of these factors must be qualitative and the other quantitative.

The essence of the absolute difference method:

1). In order to assess the influence of a quantitative factor on the change in the general indicator, it is necessary to multiply the change in the quantitative factor by the basic qualitative factor;

2). In order to assess the influence of a qualitative factor on the change in the general indicator, it is necessary to multiply the change in the qualitative factor by the actual quantitative factor.

Example. Based on the data provided, it is necessary to determine the influence of the main factors on the change in the fund wages.

The data given in Table 3 shows that general fund wages increased in the reporting year compared to last year by 3.4 thousand rubles.

Table 3 - Assessment of the influence of the main factors on the change in the wage fund industrial enterprise

This increase is mainly due to an increase in the average annual salary of one employee by 2.32 thousand rubles; due to the influence of this factor, the total wage fund increased by 13.92 thousand rubles.

By reducing the number of personnel per person, the wage fund. fees decreased by 10.4 thousand rubles.

The method of absolute differences can also be used if there are several factors included in the model for calculating the general indicator, but the relationship between them is necessarily multiplicative.

Let us evaluate the influence of labor factors on changes in production volume (Table 3) using the method of absolute differences.

Change in product output due to reduction in personnel numbers:

∆VP ∆h = (-1) *247 * 7.2 * 0.029 = -51.57 thousand rub.

Change in output due to an increase in the number of working days worked by one worker per year:

∆VP ∆d = 2 * (+3) * 7.2 * 0.029 = +1.25 thousand rub.

Change in output due to an increase in the number of hours. worked by 1 worker per day:

∆VP ∆hour = 2 * 250 * (+0.4) * 0.029 = +5.8 thousand rub.

Change in product output due to increased efficiency in the use of labor resources:

∆VP ∆pr = 2 * 250 * 7.6 * (+0.009) = +34.2 thousand rub.

Relative difference method

The method of relative differences, like the method of absolute differences, is used to measure the influence of factors on the growth of an effective indicator only in multiplicative models and combined types

y = (a-b) c.

It is much simpler than chained substitutions, which makes it very effective under certain circumstances. This applies, first of all, to those cases when the source data contains previously determined relative deviations of factor indicators in percentages or coefficients.

Let us consider the methodology for calculating the influence of factors in this way for multiplicative models such as y = a b c. First you need to calculate the relative deviations of factor indicators:

Then the deviation of 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 basic value of the effective indicator by the relative increase in the first factor, expressed as a percentage, and divide the result by 100.

To calculate the influence of the second factor, you need to add to the basic value of the effective indicator the change due to the first factor and then multiply the resulting amount by the relative increase in the second factor in percentage and divide the result by 100. The influence of the third factor is determined in the same way: you need to add to the basic value of the effective indicator its increase due to the first and second factors and the resulting amount multiplied by the relative increase of the third factor, etc.

The advantage of this method is that when using it it is not necessary to calculate the value of factor indicators. It is enough to have data on the growth rates (percentage of plan fulfillment) of factors for the analyzed period.

Thus, the results of calculations obtained using this method are the same as when using the chain substitution and absolute difference methods, but the number of computational procedures is reduced. This makes it convenient to use the method of relative differences in cases where it is necessary to calculate the influence of a large set of factors.

Example. Assess the impact of average wages and average number personnel to change the wage fund of the enterprise under study

Table 4 - Quantitative assessment of the influence of the main factors on the change in the wage fund of the enterprise under study

To determine the influence of each factor, the relative deviations of factor indicators are first calculated as follows:

The change in the general indicator due to each factor is determined as follows:

The data in Table 4 shows that the wage fund changed by 3.5 thousand rubles compared to last year, which is due to the influence of the following factors:

Due to an increase in wages by 2.32 thousand rubles. the wage fund increased by 16.24 thousand rubles;

The reduction in the number of personnel per person led to a decrease in the wage fund by 12.72 thousand rubles.

Index method

Along with the considered methods of chain substitution, absolute differences and relative differences index method is based on elimination, that is, excluding the impact on the value of the performance indicator of all factors except one. This method is used in cases where it is necessary to determine the influence of prices, rates and tariffs on changes in the general indicator.

The indices are effective tool comparative economic analysis. The index is statistical indicator, which is the ratio of two states of any attribute. Using indices, comparisons are made with the plan, in dynamics, in space. An index is called simple (particular, individual) if the characteristic under study is taken without taking into account its connection with other characteristics of the phenomena being studied. A simple index looks like:

Where p 0 and p 1- compared states of the characteristic.

The index is called analytical (general, aggregate), if the characteristic being studied is not taken in isolation, but in connection with other characteristics. An analytical index always consists of two components: the indexed attribute p (the one whose dynamics are being studied) and the weight attribute q. Using weights, the dynamics of a complex economic phenomenon, the individual elements of which are incommensurable, are measured.

Where q 0 u q 1- weight sign.

Simple and analytical indices complement each other.

The index method is one of the most powerful, informative and widespread tools of economic analysis in all its aspects: from analysis of the activities of individual economic units to macroeconomic studies of national economies.

Example. Determine the impact of price and changes in the quantity of goods sold on sales volume in a trading organization.

1. In order to determine the impact of price on changes in total sales volume, it is necessary to subtract the sales volume in comparable prices from the sales volume in the reporting year.

This follows from the calculation of the general price index:

I p = ∑p 1 q 1 / ∑p 0 q 1 = ∑p 1 q 1 / (∑p 1 q 1 /i p); i p = p 1 /p 0 – individual. price index.

Change in total sales volume due to the price factor: ∆О ∆ p = ∑p 1 q 1 - ∑p 1 q 1 /i p.

2. In order to assess the impact of the physical volume of goods sold on changes in total sales volume, it is necessary to subtract the base sales volume from the sales volume at comparable prices.

The essence of factor analysis in economics

Definition 1

Factor analysis is a type of economic analysis that studies the influence of specific factors on economic indicators. Main types of factor analysis: deterministic and stochastic analysis.

The basis of deterministic analysis is the methodology for studying the influence of those factors that have a functional relationship with the general indicator.

In stochastic factor analysis, the influence of those factors that have a probabilistic relationship with the general indicator is studied, i.e. correlation.

The efficiency of an enterprise is influenced by many factors. They can be classified into internal, which depend on the activities of a given company, and external, which do not depend on a given enterprise.

The methods used in factor analysis can also vary. Deterministic factor analysis uses:

Chain substitution method;
Method of absolute and relative differences;
Index method;
Balance method;
Integral method;
Logarithmic method, etc.

Stochastic analysis uses:

Correlation method;
Regression method;
Cluster analysis method;
Dispersion method, etc.

The greatest completeness and depth of analytical research, the greatest accuracy of results is ensured through the use of economic and mathematical methods. These methods have a great advantage over statistical and traditional methods, since they allow a more accurate and detailed calculation of the influence of individual factors on the value of economic indicators, and they also help solve some analytical problems.

Relative difference method

Note 1

The method of relative differences is used in deterministic factor analysis to assess the influence of a specific factor on the growth of performance indicators. The most important advantage of the method under consideration is its simplicity. However, it can only be used in multiplicative and multiplicative-additive factor models.

The basis this method constitutes the elimination method. Elimination means eliminating the impact of other factors, i.e. all other factors become static. Main idea method is an independent change in all factors. First, the base value of one factor changes to the reporting value, while the other factors are static, and then the second, third, etc. change.

To calculate the magnitude of the impact of the first factor on the effective one, you should multiply the basic value of the effective indicator by the relative increase in the first factor in % and divide by 100. To calculate the degree of influence of the second factor, you need to add the basic value of the effective indicator and its increase from the first factor, and the resulting multiply the amount by the relative increase in the next factor, etc.

When using this method, the order of factors in the model and, consequently, the sequence of changes in their values is of great importance, since this determines the quantitative assessment of the influence of each individual factor.

Using the method of relative differences involves the use of a correctly constructed deterministic factor model and adherence to a certain order in the arrangement of factors.

Factors can be both quantitative and qualitative. Qualitative factors reflect the internal properties, signs and characteristics of the objects under study. For example, labor productivity, milk fat content, product quality. Quantitative factors characterize the quantitative certainty of a phenomenon. Quantitative factors have both cost and natural expression. Quantitative factors can characterize the volumes of production and sales of goods, and the value of such factors can be expressed both in money and in pieces, etc.

If during the analysis there are several quantitative and qualitative indicators, then first of all the magnitude of factors that are at the first level of subordination changes, and then at a lower one.

Factors of the first level are factors that directly influence the performance indicator, and factors that indirectly affect the performance indicator belong to a lower level (second, third, etc.)

The calculation algorithm using the relative difference method is presented in Figure 1.

The sum of the quantities $∆X_A$, $∆X_B$ must be identical to the difference between $X_1$ and $X_0$.

Example of using the relative difference method

Let's consider using the relative difference method on specific example. The volume of production for the year depends on the average annual number of workers (N) and the average annual output per worker (B). A two-factor multiplicative model is built, in which the number of workers is a quantitative factor, so it is in first place, and production is a qualitative factor, and is located behind the quantitative one.

$OP = H V$

All data that will be used is presented in the table (Figure 2).

At the first step, the relative increase in factors is calculated (Figure 3).

Figure 3. Calculation of the relative increase in factors. Author24 - online exchange of student work

At the second step, the degree of influence of the first factor on the performance indicator is determined (Fig. 4)

Figure 4. Calculation of the degree of influence of a factor. Author24 - online exchange of student work

From the data obtained it follows that with an increase average annual number workers by 2 people, production volume will increase by 400 thousand rubles.

At the third step, the sequential consideration of the model factors continues (Fig. 5)

According to the data obtained, we can conclude that by increasing the average annual output of one worker, the volume of production increased by 810 thousand rubles.

At the fourth step, the calculations are checked (Figure 6).

Thus, the calculations performed are correct.

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

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

The first four methods are based on the elimination method. Eliminate means to eliminate, reject, exclude the influence of all factors on the value of the effective indicator, except one. This method is based on 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 us to determine the influence of each factor on the value of the indicator under study separately.

The most universal of them 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 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 the change 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.

Let's look at the procedure for using this method using 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 (GW). We have a two-factor multiplicative model: VP = CR X GV.

Calculation algorithm using the chain substitution method for this model:

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

The third indicator differs from the second 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 increased labor productivity, the volume of gross output increased by 48,000 million rubles. (240,000 - 192,000).

Thus, exceeding the plan for 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 shown in table. 6.2.

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

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

The production plan as a whole was exceeded by RUB 80,000 million. (240,000 - 160,000), including due to changes:

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 changes in quantitative and then qualitative indicators. If there are several quantitative and several 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 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 scheme 5.2, 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, accordingly, the order of their research.

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.

We looked at an example of calculating the influence of factors on the growth of a performance indicator in multiplicative models.

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

Where FO- capital productivity; VP -gross output; OPF - average annual cost of fixed production assets.

Methodology for calculating the influence of factors in mixed models:

a) Multiplicative-additive type P = V.P.P (C - WITH)

Where P- the amount of profit from product sales; V.P.P - volume of product sales; C - selling price; C is the cost per unit of production;

The influence of factors is calculated in a similar way using other deterministic mixed-type models.

Separately, it is necessary to dwell on the methodology for determining the influence structural factor to increase the performance indicator using this method. For example, revenue from product sales (IN) depends not only on 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 are sold at higher prices, increases, then revenue will increase due to this, and vice versa. The factor 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 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 product sales due to changes in its structure (Table 6.3.).

The table shows that due to the increase specific gravity of second-grade products in the total volume of its sales, revenue decreased by 10 million rubles. (655 - 665). This is an unused reserve of the enterprise.

6.2. Index method

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, you can identify the impact various factors to change the level of performance indicators in multiplicative and multiple models.

For example, let's take the cost index commercial products:

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

To establish how the cost of marketable products has changed due to the quantity of products produced and due to prices, you need to calculate the physical volume index Iq and price index 1 p:

In our example, the volume of gross output can be represented as the product of the number of workers and their average annual output. Therefore, the gross output index 1ch will be equal to the product of the number of workers index lchr and average annual production index 1st Guards:

If we subtract the denominator from the numerator of the above formulas, we obtain absolute increases in gross output as a whole and due to each factor separately, i.e. the same results as the chain substitution method.

6.3. Absolute difference method

The essence, purpose and scope of application of the method of absolute differences. The procedure and algorithms for calculating the influence of factors in this way

Way absolute differences is one of the elimination modifications. Like the chain substitution method, it is used to calculate the influence of factors on the growth of a performance indicator in deterministic analysis, but only in multiplicative and multiplicative-additive models: Y= (a -b)With and Y = a(b- With). And although its use is limited, due to its simplicity it is widely used in ACD. This method is used especially effectively if the source data already contains absolute deviations in factor indicators.

When using it, the magnitude of the influence of factors is calculated by multiplying the absolute increase of the factor under study by the base (planned) value of the factors that are to the right of it, and by the actual value of the factors located to the left of it in the model.

Let's consider the calculation algorithm for multiplicative factor model of the type Y= a x b x c x d. There are planned and actual values for each factor indicator, as well as their absolute deviations:

We determine the change in the value of the effective indicator due to each factor:

As can be seen from the above diagram, the calculation is based on the sequential replacement of the planned values of factor indicators with their deviations, and then with the actual level of these indicators.

Let us consider the methodology for calculating the influence of factors in this way for a four-factor multiplicative model of gross output:

Thus, the absolute difference method gives the same results as the chain substitution method. Here it is also necessary to ensure that the algebraic sum of the increase in the effective indicator due to individual factors is equal to its total increase.

Let's consider the algorithm for calculating factors in this way in mixed models type V = (a - b)With. For example, let’s take the factor model of profit from product sales, which was already used in the previous paragraph:

P = VRP(C - WITH).

Increase in profit due to changes in product sales volume:

selling prices:

production costs:

Calculation of the influence of a structural factor using this method is carried out as follows:

As can be seen from table. 6.4, due to changes in the sales structure, the average price for 1 ton of milk decreased by 40 thousand rubles, and for the entire actual volume of product sales, less profit was received by 10 million rubles. (40 thousand rubles x 250 tons).

6.4. Relative difference method

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

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

Let us consider the methodology for calculating the influence of factors in this way for multiplicative models of type V = A X IN X WITH. 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 basic (planned) value of the effective indicator by the relative increase in the first factor, expressed as a percentage, and divide the result by 100.

To calculate the influence of the second factor, you need to add the change in it 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 as a percentage and divide the result by 100.

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

Let us consolidate the considered methodology using the example given in Table. 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 necessary to calculate the influence of a large set of factors (8-10 or more). Unlike previous methods, the number of calculations is significantly reduced.

A variation of this method is acceptance of percentage differences. Let's consider the method of calculating the influence of factors using it 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 exceeding the plan for the number of workers HR%:

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 plan fulfillment for the total number of days worked by all workers D% and percentage of plan completion average number workers HR%:

The absolute increase in gross output due to changes 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 plan completion for the total number of hours worked by all workers t% and the total number of days they worked D%:

To calculate the influence of average hourly output on changes in the volume of gross output, the difference between the percentage of plan fulfillment for gross output is necessary VP% and the percentage of plan completion for 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 using it it is not necessary to calculate the level of factor indicators. It is enough to have data on the percentage of plan fulfillment for gross output, the number of workers and the number of days and hours they worked for the analyzed period.

6.5. Method of proportional division and equity participation

The essence, purpose and scope of application of the method of proportional division. The procedure and algorithms for calculating the influence of factors in this way.

In a number of cases, to determine the magnitude of the influence of factors on the growth of a performance indicator, it can be used method of proportional division. This applies to those cases when we are dealing with additive models like V = Xi and multiple additive type

In the first case, when we have a single-level model of type V= A + b+ s. the calculation is carried out as follows:

For example, the level of profitability decreased by 8% due to an increase in the enterprise’s capital by 200 million rubles. At the same time, the value of fixed capital increased by 250 million rubles, and working capital decreased by 50 million rubles. This means that, due to the first factor, the level of profitability decreased, and due to the second, it increased:

The calculation method for mixed models is somewhat more complicated. The relationship of factors in the combined model is shown in Fig. 6.1.

When known INd, VP And W, and also Yb, then to determine Yd, Y n, Ym you can use the method of proportional division, which is based on the proportional distribution of the increase in the effective indicator Y due to a change in the factor IN between second level factors D, N And M according to the magnitude of their growth. The proportionality of this distribution is achieved by determining a constant coefficient for all factors, which shows the amount of change in the effective indicator Y due to a change in the factor IN per unit.

Coefficient value (TO) is defined as follows:

Multiplying this coefficient by the absolute deviation IN due to the corresponding factor, we find the change in the effective indicator:

For example, the cost of 1 tkm increased by 180 rubles due to a decrease in the average annual production of a car. It is known that the average annual production of a car has decreased due to:

a) above-planned machine downtime -5000 tkm

b) above-plan idle runs -4000 tkm

c) incomplete use of carrying capacity -3000 tkm

Total - 12000 tkm

From here you can determine the change in cost under the influence of second-level factors:

To solve this type of problem, you can also use the equity method. First, the share of each factor in the total amount of their increases is determined, which is then multiplied by the total increase in the effective indicator (Table 6.5):

There are many similar examples of the use of this method in ACD, as you can see in the process of studying the industry analysis course economic activity enterprises.

6.6. Integral method in the analysis of economic activity

The main disadvantages of the elimination method. The problem of decomposition of additional growth from the interaction of factors between them. The essence of the integral method and the scope of its application. Algorithms for calculating the influence of factors in different models in an integral way.

Elimination as a method of deterministic factor analysis has a significant drawback. When using it, it is assumed that the factors change independently of each other. In fact, they change together, are interconnected, and from this interaction an additional increase in the effective indicator is obtained, which, when using elimination methods, is added to one of the factors, usually the last one. In this regard, the magnitude of the influence of factors on the change in the performance indicator changes depending on the place in which one or another factor is placed in a deterministic model.

Let's look at this using the example given in table. 6.1. According to the data presented in it, the number of workers at the enterprise increased by 20%, labor productivity - by 25%, and the volume of gross output - by 50%. This means that 5% (50 - 20 - 25), or 8000 million rubles. gross output is an additional increase from the interaction of both factors.

When we calculate the conditional volume of gross output, based on the actual number of workers and the planned level of labor productivity, then all additional growth from the interaction of two factors is attributed to quality factor- change in labor productivity:

If, when calculating the conditional volume of gross output, we take the planned number of workers and the actual level of labor productivity, then the entire additional increase in gross output relates to quantitative factor, which we change secondly:

We will show a graphical solution to the problem in different versions (Fig. 6.2).

In the first calculation option, the conditional indicator has the form: VP conv = CHRF X GV pl, in the second – VP cond = CR pl X GVf.

Accordingly, deviations due to each factor in the first case

in the second

On the graphs, these deviations correspond to different rectangles, since with different substitution options the amount of additional increase in the effective indicator is equal to the rectangle ABCD, refers in the first case to the magnitude of the influence of annual output, and in the second, to the magnitude of the influence of the number of workers. As a result, the magnitude of the influence of one factor is exaggerated, and the other is understated, which causes ambiguity in assessing the influence of factors, especially in cases where the additional increase is quite significant, as in our example.

To get rid of this drawback, deterministic factor analysis uses integral method, which is used to measure the influence of factors in multiplicative, multiple and mixed models of multiple additive form

The use of this method makes it possible to obtain more accurate results for calculating the influence of factors compared to methods of chain substitution, absolute and relative differences, and to avoid ambiguous assessment of the influence of factors because in this case the results do not depend on the location of factors in the model, but an additional increase in the effective indicator, which formed from the interaction of factors, is divided equally between them.

At first glance, it may seem that to distribute the additional increase it is enough to take half of it or a part corresponding to the number of factors. But this is most often difficult to do, since factors can act in different directions. Therefore, in the integral method, certain formulas are used. Here are the main ones for different models.

The logarithm method is used to measure the influence of factors in multiplicative models. In this case, the calculation result, as with integration, does not depend on the location of the factors in the model and, compared to the integral method, even higher calculation accuracy is ensured. If, during integration, the additional increase from the interaction of factors is distributed equally between them, then using logarithm, the result of the joint action of factors is distributed in proportion to the share of the isolated influence of each factor on the level of the performance indicator. This is its advantage, and its disadvantage is the limited scope of application.

Unlike the integral method, when taking logarithms, not absolute increases in indicators are used, but indices of their growth (decrease).

Mathematically, this method is described as follows. Let us assume that the effective indicator can be represented as a product of three factors: f = xyz. Taking logarithms of both sides of the equality, we get

Considering that the same relationship between the indices of changes in indicators remains as between the indicators themselves, we will replace their absolute values with indices:

It follows from the formulas that the total increase in the effective indicator is distributed among the factors in proportion to the ratio of the logarithms of the factor indices to the logarithm of the index of the effective indicator. And it does not matter which logarithm is used - natural or decimal.

Using the data from table. 6.1, we calculate the increase in gross output due to the number of workers (CR), number of days worked by one worker per year (D) And average daily output (DV) according to the factor model:

By comparing the obtained results of calculating the influence of factors using different methods using this factor model, one can be convinced of the advantage of the logarithm method. This is reflected in the relative simplicity of calculations and increased accuracy of calculations.

Having considered the main techniques of deterministic factor analysis and the scope of their application, the results can be systematized in the form of the following matrix:

Knowledge of the essence of these techniques, the scope of their application, calculation procedures - necessary condition qualified conduct of quantitative research.