Balance method and chain substitution method. Chain Substitution Method

The method of chain substitutions is the most universal of the methods of elimination. It is used to calculate the influence of factors in all types of deterministic factor models: additive, multiplicative, multiple, and mixed (combined). This method allows you to determine the influence of individual factors on the change in the value of the effective indicator by gradually replacing the base value of each factor indicator in the volume of the effective indicator with the actual in the reporting period. For this purpose, a number of conditional values \u200b\u200bof the effective indicator are determined that take into account the change in one, then two, three, etc. factors, assuming that the others do not change. Comparison of the value of the effective indicator before and after the change in the level of one or another factor allows eliminating from the influence of all factors, except one, and determining the effect of the latter on the growth of the effective indicator.

The degree of influence of a particular indicator is revealed by sequential subtraction: the first is subtracted from the second calculation, the second is deducted from the third, and so on. In the first calculation, all quantities are planned, in the last - actual. In the case of a three-factor multiplicative model, the calculation algorithm is as follows:

Y 0 \u003d a 0 b 0 0 c 0;

Y conv. 1 \u003d a 1 ⋅ b 0 ⋅C 0 ; At a \u003d Y conv. 1 - U 0 ;

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

Y f \u003d a 1 ⋅ b 1 ⋅C 1; Y c \u003d Y f - Y conv. 2 and etc.

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

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

The absence of such equality indicates errors in the calculations.

The rule follows from this, that the number of calculations per unit is greater than the number of indicators of the calculation formula.

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

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

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

To analyze the effect on the increase in the volume of marketable products of changes in the number of employees and labor productivity of one average employee (tab. 43).

We find the missing indicators - the absolute and relative deviations of the actual values \u200b\u200bfrom the planned indicators and fill out the table. 44.

We construct a model of an effective indicator (volume of marketable products):

Output. The volume of marketable products increased by 249 thousand UAH. This growth was influenced by two factors: an increase in working time by 50 person-days contributed to an increase in output by 60 thousand UAH, an increase in labor productivity of an average employee by 0.18 thousand UAH gave an increase in output by 189 thousand UAH ( according to the calculation carried out by the method of chain substitution and the method of differences).

When using the integral method, the influence of quantitative and qualitative factors was not taken into account; the actions of factors were considered equivalent, therefore, there are deviations in the results of calculations by factors compared to calculations performed by the method of chain substitutions and the method of differences.

Task 2

Calculate the impact on the change in income from the sale of goods of the following factors: the number of employees; the number of days worked by them and the volume of production per one average employee (tab. 45).

We find the missing indicators - the absolute and relative deviations of the actual values \u200b\u200bfrom the planned indicators and fill out the table. 46.

We construct a model of an effective indicator (income from the sale of goods):

We solve the problem of factor analysis by the integral method and the method of differences:

Output. In general, income from the sale of goods increased by 3430.4 thousand UAH. This increase was influenced by the following factors: discrepancy between the actual number and the planned number per 10 people. n led to a loss of income of 912 thousand UAH; additionally worked 4 days led to an increase in revenue by 708 thousand UAH; an increase in the output of one average employee by only 20 UAH per day gave an increase in revenue by 3634.4 thousand UAH.

When using the integral method, the influence of quantitative and qualitative factors was not taken into account; the actions of factors were considered equivalent, therefore, there are deviations in the results of calculations by factors compared with calculations by the method of chain substitutions and the method of differences.

Task 3

The chief manager of the tourist company “SAM” instructed the manager of the domestic tourism department to calculate how the following factors will affect the company's income from the sale of tickets: the average cost of one ticket sold; average number of vouchers sold in one day; the number of days worked in the analyzed period (table. 47).

We find the missing indicators - the absolute and relative deviations of the actual values \u200b\u200bfrom the planned indicators and fill out the table. 48.

We construct a model of an effective indicator: x \u003d abc.

Using the chain substitution method, we obtain

We solve the problem of factor analysis by the integral method:

In general, the income from the sale of permits increased by 642.4 thousand UAH. This increase was influenced by the following factors: an increase in the average number of tickets sold in one day by 3 tickets gave an increase in sales by 501.6 thousand UAH; additionally worked 4 days gave an increase in sales volume of vouchers by 17.6 thousand UAH; with an increase in the average cost of a ticket for 50 UAH, revenue increased by 123.2 thousand UAH.

When using the integral method, the influence of quantitative and qualitative factors was not taken into account; the actions of factors were considered equivalent, therefore, there are deviations in the results of calculations by factors compared with calculations carried out by the method of chain substitutions and the method of differences.

Task 4

We construct a model of an effective indicator:

We solve the problem by the method of absolute differences:

Output. Profit from sales in the reporting period increased compared to the base by 14,000 UAH. This increase was influenced by three factors:

due to growth in sales of products by 2000 UAH, profit increased by 14000 UAH;

with an increase in unit price from 25 to 26 UAH, profit increased by 32,000 UAH;

an increase in the unit cost of production by 1 UAH resulted in a loss of profit by 32,000 UAH.

Task 5

Calculate how the revenue from the sale of goods will change, taking into account changes in factors associated with the use of the material and technical base: the number of jobs, work shifts, days worked per year, the volume of output per shift per shift. In the calculations, use the method of the correction factor (table. 50).

We find the missing indicators - the absolute and relative deviations of the actual values \u200b\u200bfrom the planned indicators and fill out the table. 51.

We construct a model of an effective indicator (retail turnover):

We calculate the amount of revenue from the sale of goods according to plan and, in fact, we will enter the data in table. 51:

0,242 + 0,689 + 0,329 + 3,333 = 4,593.

Calculate the correction factor (K):

Using the correction factor, we calculate the full influence of factors on the effective indicator. We assume that all factors affect the effective indicator in the same way, i.e., when calculating, it is not necessary to observe the sequence of replacement of factors.

Since the conditional influence of factors is not equal to the deviation of the effective indicator (the volume of retail turnover), it is necessary to calculate their full impact on the indicator being studied.

We find the full influence of factors on the effective indicator taking into account the correction factor:

Output. The planned revenue from the sale of goods exceeded 4.64%. Over the plan, goods sold for 2540.4 thousand UAH. Four factors influenced this increase:

with an increase in the number of jobs per place, revenue increased by 133.588 thousand UAH;

an increase in the number of work shifts by 0.01 resulted in revenue growth of 381.419 thousand UAH;

an increase in working time by one day gave an increase in revenue by 181.927 thousand UAH;

with an increase in output at one workplace per day by 0.01 thousand UAH, revenue increased by 1843.526 thousand UAH.

Task 6

We find the missing indicators - the absolute and relative deviations of the actual values \u200b\u200bfrom the planned indicators and fill out the table. 53.

We calculate the average base price of the goods:

according to plan:

Output. The average planned price per 1 kg of goods sold was 81.7 kopecks, and the actual price was 84.8 kopecks, that is, increased by 3.1 kopecks. The impact of changes in the structure of trade:

the average price per 1 kg of goods is due to a change in the structure of trade.

Task 7

Determine the volume of sales of goods for the analyzed period, using the data in table. 54.

To determine the volume of sales of goods for the period we use the formula of commodity balance:

where Y is the markdown.

The model of the effective indicator (P) is additive. In this case, goods are not discounted.

Using this formula, we find the sale of goods for the base and reporting periods and fill out the table. 55:

Output. To solve the problem, an additive model is built on the basis of the commodity balance formula. To determine the influence of factors on the effective indicator, the method of chain substitutions is used.

The calculations established: underfulfillment of the plan in terms of sales of goods for 527 thousand UAH due to the action of the following factors:

an increase in stocks of goods at the beginning of the period by 9 thousand UAH and a decrease in them at the end of the period by 34 thousand UAH led to an increase in sales by 43 thousand UAH;

a decrease in the receipt of goods for the period by 560 thousand UAH and an increase in their disposal by 10 thousand UAH led to a decrease in sales by 570 thousand UAH.

This problem can also be solved by direct counting (according to the absolute deviation of the factors of the commodity balance, taking into account the additive model and the signs in it).

Task 8

Percentage method

The manager of the economic department of the store “SONY” was instructed to calculate how, for the analyzed period, the average frequency of delivery of household appliances is affected by the frequency of delivery of certain types of equipment and the structure of their delivery. The initial data for the calculation are given in table. 56.

Determine the volume of delivery of household appliances to the store “SONY”, respectively, according to plan and in fact:

3200 + 4200 + 1800 + 1890 + 2150 + 450 = 13690; 3500 + 3800 + 2150 + 1500 + 2600 + 300 = 13850.

in fact: 20 · 25 \u003d 500; 25.27 \u003d 675; 1016 \u003d 160;

19 \u003d 247; 10 · 2 \u003d 20;

according to the intermediate calculation: 22 · 25 \u003d 550; 30.27 \u003d 810;

16 \u003d 224; 1611 \u003d 176; 2519 \u003d 475;

We divide the resulting percentage numbers by 100 and get the average frequency of delivery of household appliances to the store (effective indicator):

according to plan: 2287: 100 \u003d 22.87; in fact: 1734: 100 \u003d 17.34; with the planned frequency of delivery and the actual structure of delivery:

2265: 100 \u003d 22.65. 4. We calculate the influence of factors on the change in the average frequency of delivery:

17.34 - 22.87 \u003d -5.53, including due to changes in factors of the structure of the delivery of household appliances:

22.65 - 22.87 \u003d -0.22, due to changes in factors of the frequency of delivery for certain types of household appliances:

17.34 - 22.65 \u003d -5.31. The calculation results are listed in table. 57.

Output. Calculations of the manager of the store “SONY” showed that the average frequency of delivery of household appliances increased by 5.53 days (from 22.87 to 17.34). This change in the effective indicator (average frequency of delivery) is due to the action of the following factors:

The change in the frequency of delivery for certain types of households led to an increase in the average frequency of delivery by 5.31 days (17.34 - 22.65);

Due to changes in the structure of delivery of household appliances to the store, the effective indicator increased by 0.22 days (22.65 - 22.87).

Task 9

Multiple model

Based on the tab. 58 data that characterize the use of objects of labor in the enterprise, to do the following:

Analyze the obtained indicators using the method of chain substitutions and the method of differences, determine the impact on the change in output in the reporting period compared with the planned and previous period of the following factors:

a change in the number of labor objects used in production;

change in material consumption.

To conclude.

We find the missing indicators (material consumption - labor costs per hryvnia of marketable products in kopecks; the absolute and relative deviations of actual values \u200b\u200bfrom the values \u200b\u200bof the previous period and planned indicators. Fill out the generalized table. 59.

We construct a model of an effective indicator (material consumption):

where In - the cost of labor for production; A - marketable products.

As you can see, our model is multiple, that is, the dependence of the effective indicator on factors is expressed as a private division.

We will conduct a factor analysis of changes in the effective indicator by comparing the actual data for the reporting period with the data of the previous period using the chain setting method;

- change in material consumption due to factor B;

The increase in the cost of labor for the production of commodity products due to factor A;

We carry out a factor analysis of changes in the effective indicator by comparing the actual data for the reporting period with the planned data using the chain setting method:

change in the effective indicator due to factor B;

Change in the effective indicator due to factor A;

The actual material consumption for the reporting period relative to the previous one increased by 2.37 kopecks. (from 62.952664 to 65.3266 kopecks). This indicates an increase in the cost of labor for the production of marketable products for the reporting period. This increase is due to the influence of two factors:

the costs of labor for the production of marketable products increased by 340 UAH (from 2260 to 2600 UAH), or by 15%. The increase in costs gave an increase in material consumption by 9.47075 kopecks;

an increase in the output of marketable products by 390 UAH (from 3590 to 3980 UAH), or by 10%, reduced the consumption of materials by 7.09676 kopecks.

The actual material consumption in the reporting period decreased by 0.349 kopecks. regarding the planned indicators (from 65.67 to 65.3266 kopecks). The decrease in the share of costs in manufactured products is due to the action of two factors:

The costs of labor for the production of commodity products increased by 170 UAH (from 2430 planned to 2600 UAH actually received). Due to increased costs, material consumption increased by 4.94364 kopecks. in one hryvnia spent on production;

An increase in the production of commercial products by 240 UAH (from 3,700 to 3,980 UAH) led to a decrease in the share of material consumption in manufactured products by 4.5946 kopecks.

Task 10

Delphi Method

Perform a comprehensive assessment of the totality of the studied objects and a comparative analysis of economic activity using the Delphi method.

We find the maximum value for each indicator studied and select it in the source data matrix (Table 60).

The value of each indicator from the source data matrix is \u200b\u200bdivided by the maximum value of the studied indicator. For example, according to the degree of fulfillment of the turnover plan 102.5: 113 \u003d 0.907, etc.

We add the results of the calculations to the coordinate matrix (Table 61).

The value of each indicator in the coordinate matrix is \u200b\u200bsquared and the data obtained is entered into the matrix of squares (Table 62).

The squared data for each indicator are summarized by row, i.e., for each enterprise studied. For example, for enterprise A: 0.823 + 0.542 + 0.781+ 1.0 + 0.859 \u003d 4.005, etc.

In the matrix of squares (Table 62), each enterprise was awarded a prize according to the sum of the points, however, the significance of the used evaluation indicators was not taken into account here (all of them were considered equivalent).

To clarify the results of awarding the prize, we will use an expert assessment of the significance of each indicator taken for calculations and fill out the table. 63.

Reference. To assess the significance of the indicator, experts use a five-point scale:

Income from the sale of goods 4.5

Net profit 5

Labor productivity of employees 4 Return on assets of fixed assets 2

Working capital turnover 3

Weigh the data from the matrix of squares according to the scoring of each indicator and summarize the data obtained for each enterprise studied (by row). For example, for enterprise A: 0.823 ⋅ 4.5 + 0.542 ⋅ 5 + 0.781 ⋅ 4 + 1 ⋅ 2 + 0.859 ⋅ 3 \u003d 14.115, etc.

Compare the prizes calculated without expert evaluation of indicators with the prizes calculated taking into account the expert evaluation, and fill out the table. 64.

Output. To conduct a comparative assessment of seven enterprises, five evaluation indicators were used. Calculations carried out using the method of mathematical analysis showed that a more accurate distribution of places was given by the Delphi method, which takes into account the significance of indicators used for a comparative assessment of enterprises.

Task 11

The method of integrated assessment of enterprises. Place Sum Method and Distance Method

In the table. 65 shows the source data characterizing the economic activities of enterprises. Using these indicators, calculate the integral indicator of a comprehensive assessment of the enterprise. Based on this information, rank the enterprises and choose the best.

We will rank the enterprises and fill out the table. 66. For example, in terms of gross income, the first place will be taken by enterprise 4 with the maximum dynamics of revenue growth (115.2%); in terms of the dynamics of the level of distribution costs, the first place will be taken by enterprise 3, which has a dynamics of decrease in the level (93%).

The first place was shared by enterprises 4 and 5, which scored an equal number of points (21 points each), the second place was taken by company 6 (24 points), etc.

Using the digital values \u200b\u200bof the indicators given in table. 65, we will solve the problem by the method of distance to the standard for enterprise 1:

Similarly, we calculate the distance to the standard for the other five enterprises and fill out the table. 67.

Output. The smallest deviation of the indicators of enterprises from the standard has enterprise 4, which rightfully took first place.

Y0 \u003d a0? B0? Co;

Ysl. 1 \u003d a1? B0? C0 ; Ata \u003d Ysl. 1 - U0;

Y.sub.2 \u003d a1? B1? C0; Yb \u003d Ysl. 2 - Ysl. 1;

Yph \u003d a1? B1? C1; Ys \u003d Yf - Ysl. 2 and etc.

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

Ya + Yb + Ys \u003d Yf - Y0.

The absence of such equality indicates errors in the calculations.

The rule follows from this, that the number of calculations per unit is greater than the number of indicators of the calculation formula.

FEDERAL AGENCY FOR EDUCATION OF THE RUSSIAN FEDERATION

ST. PETERSBURG STATE UNIVERSITY

SERVICE AND ECONOMY

INSTITUTE OF REGIONAL ECONOMICS AND MANAGEMENT

TEST

subject: "ECONOMIC ANALYSIS OF THE ENTERPRISE'S ACTIVITY IN THE FIELD OF SERVICE"

Completed by a student of 3 courses

specialties 080507.65 (061100)

distance learning

Kuzmina Veronika Valentinovna

ST. PETERSBURG

Task number 1 …………………………………………………………………………… 3

Task number 2 …………………………………………………………………………… 5

Task number 3 …………………………………………………………………………… 7

Task number 4 ………………………………………………………………………… ... 11

Assignment No. 5 ...................................................... 13

Exercise 1

1. State the main theoretical aspects of the topic.

Subject: Chain Substitution Method.

The method of chain substitutions is to determine a number of intermediate values \u200b\u200bof the effective indicator by successively replacing the basic values \u200b\u200bof factors with reporting ones. This method is based on elimination. Eliminating means eliminating, eliminating the influence of all factors on the value of the effective indicator, except for one. It is assumed that all factors change independently of each other, i.e. first, one factor changes, and all the others remain unchanged, then two change when the others remain unchanged, etc.

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

The advantages of this method: versatility of use; simplicity of calculations.

The disadvantage of this method is that, depending on the selected order of factor replacement, the results of factor decomposition have different meanings. This is due to the fact that as a result of applying this method, an indecomposable residue is formed, which is added to the magnitude of the influence of the last factor. In practice, the accuracy of factor estimates is neglected, highlighting the relative importance of the influence of a factor. However, there are certain rules that determine the sequence of substitution:

If there are quantitative and qualitative indicators in the factor model, the change in quantitative factors is considered first;

if the model is represented by several quantitative and qualitative indicators, then first of all the influence of factors of the first order, then the second, etc. is determined.

Under the quantitative factors in the analysis, we understand those that express the quantitative certainty of phenomena and can be obtained by direct accounting (the number of workers, machines, raw materials, etc.).

Qualitative factors determine the internal qualities, signs and characteristics of the phenomena studied (labor productivity, product quality, average working day, etc.).

1. The daily income.

2. Revenue from the sale of services for the month.

3. The weighted average occupancy rate of the hotel.

4. The average price of a room per day.

a) 12 * 210 \u003d 2520 cu (one hundred %)

2520 cu \u003d 100%

x \u003d 25.0%, then x \u003d (2520 * 25.0) / 100% \u003d 630 cu

b) 28 * 145 \u003d 4060 c.u. (one hundred %)

4060 c.u. \u003d 100%

x \u003d 65.0%, then x \u003d (4060 * 65.0) / 100% \u003d 2639 cu

So, the daily income of the hotel:

If the average month consists of 30 days, then sales revenue per month will be calculated as follows:

(25.0 + 65.0) / 2 = 45 %

(210 + 145) / 2 \u003d 177.5 c.u.

5. Conclusion.

Having made the calculations, we obtained the following results:

1. The daily income of the hotel is 3269 cu;

2. Revenues from sales of services for the month 98070 cu;

3. The weighted average occupancy rate of the hotel is 45%;

4. The average price of a room per day is 177.5 cu

Having received these results, we can say that an increase in the occupancy rate of the hotel, to a greater extent deluxe rooms, is required. The hotel occupancy can be increased by the device of class 2 rooms.

The relative change in sales revenue.

The absolute change in sales revenue.

The structure of services for each period.

Absolute and relative change in the share of each type of service.

2. Build a pie chart of the structure of services for 2002 and 2003

3. Make a conclusion about the changes.

- absolute change in sales revenue.

840.0 – 850.3 = - 10.3

- the relative change in sales revenue.

x \u003d - 10.3, then x \u003d (- 10.3 * 100) / 840.0 \u003d - 1.23%

- the structure of services for each period.

For the year 2002:

Payment for accommodation:

If 850.3 \u003d 100%, then 811.9 \u003d x, then

x \u003d (811.9 * 100) /850.3 \u003d 95.5%

Communication services:

If 850.3 \u003d 100%, then 33.0 \u003d x, then

x \u003d (33.0 * 100) /850.3 \u003d 3.9%

Other services:

If 850.3 \u003d 100%, then 5.4 \u003d x, then

x \u003d (5.4 * 100) /850.3 \u003d 0.6%

For 2003:

Payment for accommodation:

If 840.0 \u003d 100%, then 785.7 \u003d x, then

x \u003d (785.7 * 100) /840.0 \u003d 93.5%

Communication services:

If 840.0 \u003d 100%, then 44.0 \u003d x, then

x \u003d (44.0 * 100) /840.0 \u003d 5.2%

Other services:

If 840.0 \u003d 100%, then 10.3 \u003d x, then

x \u003d (10.3 * 100) /840.0 \u003d 1.3%

- absolute and relative change in the share of each type of service.

Absolute change:

a) payment for accommodation

785.7 – 811.9 = - 26.2

b) communication services

44.0 – 33.0 = 11

c) other services

10.3 – 5.4 = 4.9

Relative change:

a) payment for accommodation

x \u003d - 26.2, then x \u003d (- 26.2 * 100) / 785.7 \u003d - 3.33%

b) communication services

x \u003d 11, then x \u003d (11 * 100) / 44.0 \u003d 25%

c) other services

x \u003d 4.9, then x \u003d (4.9 * 100) / 10.3 \u003d 47.57%

2. Build a pie chart of the structure of services for 2002 and 2003

For the year 2002 :

For 2003 :

3. Make a conclusion about the changes.

Calculating the absolute change, we see that sales revenue in 2003 was 10.3 thousand rubles. less than in 2002.

Calculating the relative change in the volume of sales revenue, we received that the revenue in 2003 decreased by 1.23%.

In 2002, the proceeds from payment of accommodation amounted to 95.5%, from the payment of communication services 3.9%, and other services accounted for 0.6% of revenue. In 2003, the proceeds from payment of accommodation amounted to 93.5%, i.e. 2 percent lower than in 2002; communication services makes up 5.2% of revenue, which is 1.3% higher than in 2002. Other services account for 1.3%, which is also higher than the 2002 figure by 0.7%.

The calculation of the absolute and relative changes in the share of services showed that in 2002 the payment for accommodation exceeded the payment for accommodation in 2003, and communication services and other services in 2003 exceeded the corresponding figures for 2002.

Task 4

3. Draw conclusions.

1. Build a factor model and determine its type.

Building a factor model – this is the first stage of deterministic analysis.

The dependence of revenue on sales in the reporting year can be described using the additive model:

OB1 \u003d OP1 + KU1 ;

OB1 \u003d 720 + 260 \u003d 980 (thousand rubles),

where RV is the volume of revenue;

OP payment for accommodation;

KU utilities.

Then the effect of payment of accommodation on the change in the volume of revenue is calculated by the formula:

OP1 - OP2 = 720 – 550 \u003d 170 (thousand rubles)

And the impact of utility bills on the change in revenue is calculated using the formula:

KU1 - KU2 = 260 – 330 = – 70 (thousand rubles)

The dependence of revenue on sales in the base year can be determined by the formula:

OB2 \u003d OP2 + KU2;

OB2 \u003d 550 + 330 \u003d 880 (thousand rubles)

The impact of changes in indicators on revenue:

OB1 - OB2 = 980 – 880 \u003d 100 (thousand rubles)

3. To conclude.

The increase in revenue was positively affected by an increase in living expenses by 170 thousand rubles. and a negative impact had a decrease in utility bills by 70 thousand rubles. The combined effect of two factors led to an increase in revenue by 100 thousand rubles.

Task 5

1. Build a factor model and determine its type.

Chain Substitution Method

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

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

The first four methods are based on the elimination method. Eliminating means eliminating, rejecting, eliminating the influence of all factors on the value of the effective indicator, except for one. This method proceeds from the fact that all factors change independently of one another: at first one changes, and all the others remain unchanged, then two, then three, etc., change, while the others remain unchanged. This allows you to determine the influence of each factor on the value of the studied indicator 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 the change in the value of the effective indicator by gradually replacing the base value of each factor indicator in the volume of the effective indicator with the actual in the reporting period. For this purpose, a number of conditional values \u200b\u200bof the effective indicator are determined that take into account the change in one, then two, three, etc. factors, assuming that the others do not change. Comparison of the value of the effective indicator before and after the change in the level of one or another factor allows eliminating from the influence of all factors except one, and determining the effect of the latter on the growth of the effective indicator.

The application of this method will be considered in the following example (table. 6.1).

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

Chain substitution algorithm for this model:

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

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

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

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

b) increase labor productivity + 48,000 million rubles.

Total +80,000 million rubles.

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

The absence of such equality indicates errors in the calculations.

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

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

The source data for solving the problem are given in table 6.1:

The production plan as a whole has been exceeded by 80,000 million rubles. (240000 - 160,000), including due to changes:

a) the number of workers

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

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

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

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

where DOF - capital productivity; VP gross output; OPF - the average annual value of fixed assets.

Methodology for calculating the influence of factors in mixed models:

a) Multiplicative-additive type P = VPP (C - FROM)

where P - the amount of profit from product sales; VPP - volume of sales; C - selling price; C is the unit cost of production;