How to calculate the percentage of the plan. Relative value of the planned task and the fulfillment of the plan

Relative value of the planned target(planned target indicator) is the ratio of the planned level of the indicator to its level achieved in the previous period (or in the period considered as the base one).

The relative value of the planned task characterizes the prospects for the development of the phenomenon
OVTR = planned level for the future (next) period / actual level of the current (previous) period

Example: in 2007 the number of employees was 120 people. in 2008, it was planned to reduce production and bring the number to 100 people.
Solution:
OVTR =(100/120) *100% = 83.3% - 100% = -16.7%.
The company planned to reduce the number of personnel by 16.7%.

Relative value of plan execution

Relative value of plan execution(plan implementation indicator) characterizes the degree of implementation of the plan.
TFR = actual level of the current period / plan of the current period

Example: in 2007 the number of employees was 120 people. in 2008, it was planned to reduce production and bring the number to 100 people. But the number of employees for the year increased to 130 people in a year.
Solution:
ROVP \u003d (130 / 100) * 100% \u003d 130% - 100% \u003d 30%.
The actual number of employees exceeded the planned level by 30%.

There is a relationship between and the relative value of the plan task and the relative value of the implementation of the plan, expressed in the formula: OVVP = OVD / OVPV

Example: the company planned to reduce the cost by 6%. The actual decrease compared to the previous year was 4%. How was the cost reduction plan implemented?
Solution:
ATS \u003d (96 / 100) * 100% \u003d 96% - 100% \u003d - 4%
OVTR \u003d (94 / 100) * 100% \u003d 94% - 100% \u003d - 6%
RWP = 96% / 94% = 102.1% - 100% = -2.1% the actual level exceeded the planned one by 2.1%.

Example: an insurance company in 1997 entered into contracts in the amount of 500 thousand rubles. In 1998, she intends to conclude contracts for the amount of 510 thousand rubles. The relative value of the target will be equal to 102% (510 / 500).

Suppose the influence of various factors led to the fact that in 1998 the insurance company concluded expensive deals in the amount of 400 thousand rubles. In this case, the relative value of the execution fee will be equal to 78.4% (400/510).

The relative values ​​of the dynamics, the planned task and the fulfillment of the plan are related by the following relationship.

The implementation of the plan is an indicator that is very often used not so much in statistics as in the economy of an organization. The thing is that the analysis of the implementation of planned actions is the most important part of the analysis of sales revenue, productivity, cost and a number of other important indicators of the enterprise. But to help calculate the level of implementation of the plan, and more often overfulfillment or underfulfillment helps the relative value of the plan.

As already noted, the three relative values ​​are interconnected. They are combined into a common block of mutually complementary relative values. The relationship formula in this case looks like this: ATS = OVPV x OVVP, but we will talk about this in more detail in the third part.

So, Relative value of plan execution , we will call it for short OVVP . In some textbooks, in particular Shmoylova's Theory of Statistics, this relative value has a slightly different name. Relative plan completion rate , well, the essence of the calculation itself and its principle, of course, will not change.

The relative value of the implementation of the plan shows how many times the actual level is more or less than planned. That is, by calculating this relative value, we can find out whether the plan is overfulfilled or underfulfilled, and what is the percentage of this process.
Similar to the calculation of the plan target, the execution of the plan is calculated based on two indicators. However, there is a fundamental difference here; for the calculation, indicators of the same period of time are used (in the planned task, these were two different periods). Included in the calculation:
Upl - the planned level for the current year.
Uf.t.g. - the actual level of the current year.

Calculation of the relative value of the implementation of the plan (RTI)

We will calculate the fulfillment of the plan, as well as the percentage of fulfillment and the percentage of overfulfillment, using similar formulas, as in the calculation of the planned target.
1. Coefficient form- characterizes how many times the actual value for the current period exceeds the planned indicator for the current period.

3. Growth rate form allows you to determine by what percentage the plan is overfulfilled or underfulfilled.

We will carry out calculations using the indicated formulas and analyze the results obtained.

Example. The output in 2015 actually amounted to 157 million rubles, while the planned figure for the same period was 150 million rubles. Determine the relative value of the plan, the percentage of the plan and the percentage of overfulfillment of the underfulfillment of the plan.

Given: Solution:
Upl 2015 - 150 million rubles. OVVP = 157 / 150 = 1.047

UV 2015 - 157 million rubles. % VP \u003d 1.047 x 100% \u003d 104.7%

Define:Δ% VP \u003d 104.% - 100% \u003d + 4.7%
ROVVP, %VP, Δ%VP
Thus, we get:
- The relative value of the implementation of the plan was 1.047, that is, the actual indicator exceeds the planned one by 1.047 times.
— The plan was fulfilled by 104.7%.
— The plan was exceeded by 4.7%.

It should be said that when calculating the growth rate, the resulting data can be negative , that is, there will be an underfulfillment of the plan.

As already noted, this relative value is a whole complex with two other relative values, you can view the link, and features.

The planning process is an integral part of any success. The presence of goals specified in indicators allows you to control the movement of a person or organization in a certain direction, gives clarity to the activity. This allows you to quickly move to effective action. However, an equally important condition for achieving success is the ability to control the results of their activities. A person should have a good idea of ​​what stage he is at and how much more he has to do. This article will tell you how to calculate the percentage of the plan completed.

Why do you need to count

There are many areas of human activity, the results of which can be accurately quantified. In order to carry out their activities effectively, to get the maximum benefit from their actions, they resort to planning. The presence of specific goals allows you to adhere to exactly those indicators under which the activity makes sense.

A prime example in this case is budget planning. In order for the organization to remain profitable and receive the funds necessary for development, indicators of income and expenses are developed. The implementation of the plan is a guarantee of the successful development of the company.

In order to properly build their activities and achieve these indicators in a timely manner, it is necessary to imagine at what stage the organization is in relation to this goal. It is for a clear positioning of a person or organization on the path to achieving results that the calculation of the percentage of the plan is applied. It allows you to properly build your activities so that all the necessary indicators are achieved just in time.

How to calculate the execution of the plan

When it comes to how to calculate the percentage of the plan, it means the ratio of its two components: those indicators that have been achieved and those that need to be achieved. In sales, this is the total number of purchases made by customers in relation to the total planned sales volume. When planning a budget, this is the amount of money earned at the moment in relation to the amount of finance that needs to be earned over a certain period of time.

Thus, to determine the percentage of completion of the plan, it is necessary to find the quotient of the results achieved at the moment and those planned for a certain date, and then multiply the resulting number by 100.

PVP \u003d TR / ZR * 100

• PVP - the percentage of the plan;
• TR - current results;
• ZR - planned results.

For example, a real estate agency plans to hand over 28 apartments this month. At the moment, 6 are rented. So, the percentage of the organization's plan at the current time is 21. It is this information that serves as the basis for intensifying the company's further activities and searching for new tenants.

PVP = 6 / 28 * 100 = 21.428

Conclusion

In most areas of activity in which results are clearly quantifiable, a person or organization resorts to planning values, the achievement of which is a necessary condition for ensuring successful development. This operation is applied in the field of sales, economic activities of large organizations, small projects, ordinary families, as well as in many other areas. Achieving the planned indicators requires a clear positioning along the entire path towards them. It is for the purpose of exercising control over the approximation to the plan that the formula for the percentage of the plan is used.

Creating a sales plan is an important procedure for every company. The sales plan is the basis for the formation of the entire planning system at the enterprise, because other components of planning directly depend on the sales plan (purchase plan, production plan, cost plan, personnel plan, etc.)

Chinese folk wisdom says:

If you don't know where you are going, how will you know that you have come?

Having determined the direction of movement, we understand how we can implement and what will be required on the way to our goals.

We want to note right away that it is not possible to fully disclose the topic of planning at an enterprise within the framework of this article, because. This question is quite voluminous in content. A lot of good literature is devoted to this topic. We will only touch on the most important aspects of planning.

Let's take a step-by-step look at how a sales plan is formed in any enterprise.

How to prepare for a sales plan?

Planning starts with input. If your company has been on the market for more than a year, then you have statistics for the previous period. If a company is just starting out, then it can rely on the statistics of the work of existing companies whose activities are suitable for a particular market segment, of course, if such information is available.

Let's assume that we have data. After analyzing the figures with reference to months, we can assume the presence or absence of seasonality in this type of activity.

Let's consider how the cell values ​​are obtained. In line Sales 2013 columns 1-12 contains information on sales of goods for each month of 2013 in rubles. In column Total contains the total sales for the entire year.

Our calculation formulas:

Wed sale = total / 12 months

Coef. seasonality \u003d Amount per month / Avg. sale

Sales growth in % = ((Prod. 2014 / Prod. 2013) - 1) * 100

Wed coefficient seasonality = (Seasonal factor 2013 + Seasonal factor 2014) / 2

With the naked eye, we see that the first three months of the year in 2013 and 2014 are not the most successful for this type of product, because. values Coef. seasonality

We would like to draw your attention to the fact that the number of units sold in 2014 increased by 10.3% compared to 2013, while the amount of revenue increased by only 9.8%. This fact tells us that the difference of 0.5% was compensated by the profit of the enterprise. It is necessary to carefully monitor this proportion in order to prevent a significant decrease in marginality both for the product and for the company as a whole.

In our case, only two years of information is used. This is not enough for a qualitative analysis, because within these time periods (2013, 2014) there could be managerial and operational miscalculations that affected the final result. It is better to take statistics for more than 3 years. The more data for analysis, the smaller the final error in the calculations.

To fully calculate the sales plan, we need to get the following numbers:

• Market size in the sector of your company;
• Market share of your company;
• The volume of increasing the range and (or) quality of products;
• Purchase price of products;
• The average market price of products;
• Percentage of your company's sales growth (coefficient);
• Average company expenses per month;
• inflation rate;
• The percentage of devaluation of the national currency.

Market size it is quite difficult to calculate, because Not all companies disclose information about their sales. You can order an analytical note from Rosstat, but the quality of the information provided will be very difficult to verify and will have to be trusted. Let's take the value Market volume = 25,000 rubles.

Having received the approximate volume of the market, you determine by a simple calculation Market share occupied by your company:

Market share in % = (Total sales in rubles for 2014 / Market volume) * 100 = (8560 / 25000) * 100 = 34.24%

The volume of assortment increase and (or) product quality we will consider as part of the calculation of the sales plan.

Let's take the value Middle Purchase price for Products 1 = 1.5 rubles

Let's take the value of the Average market price for the Products 1 = 6.2 rubles

Company Growth Percentage we will determine as part of the sales plan calculation.

For the convenience of calculations, we will analyze one nomenclature position within the framework of this article. In the future, you can combine information into item groups and then combine all the received data into a single sales plan. When calculating, we accept the fact that all costs of the enterprise (variable and fixed) are distributed in proportion to the sales volume of the nomenclature unit.

Wed expenses per month per unit products = ((Unit sales per year / Total sales per year) * Total cost per year) / 12

It is necessary to raise your company's data on average costs per month in order to determine the required margin per unit of production. We will assume that you have already found this number and take the value of Cp. expenses per month (variables + constants) = 550 rubles.

Now let's talk about the work schedule.

After seven years of studying people, we have identified several main postulates:

• During the working day, you can productively make calls for no more than 2 (very rarely 4) hours.
• On the basis of human biorhythms, it is possible to draw up days on which it is better for a manager to do paperwork than to call, because. damage from violence against himself will affect his long recovery.
• Be sure to hold planning meetings every morning, where the head of the department. sales will encourage employees and inspire to accomplishment (without threatening or criticizing). Within the framework of these meetings, positive and negative cases in the company are considered. Conducted training calls to clients.
• Every day, you must devote at least 1 hour to training according to a pre-created program.
• Every day you need to devote at least 2 hours to business correspondence with clients.
• At least once a week, the head of the sales department should devote time to work on bugs with each sales manager in his department (at least an hour).
• According to a pre-developed individual program, face-to-face meetings with clients should be held (this depends on the specifics). It is important for people to have live communication, because it helps a lot in developing sales skills and helps to expand personal contacts.
• All planned activities and information received should be entered into a system that will help to centralize all data and allow you to quickly retrieve the necessary data. For this purpose, a CRM system is best suited.

Using the Bitrix 24 CRM system as an example, we will look at how you can calculate a sales plan for a manager.

The functionality of Bitrix 24 is quite extensive and allows you to solve a lot of questions that arise both for the head of the sales department and for an ordinary manager.

• The CRM system has a database of contacts, which is presented in the form of Companies and Contacts (individuals). This database is well protected from theft by unscrupulous employees. Your employees, changing the status of the Company, will systematically create an up-to-date picture of all your customers. So you can quickly analyze all stages of customer relationships, filter out those who require special treatment right now.
• IP-telephony is built into this CRM system and your employees can make calls to customers directly from the program. In this case, (if required) all call records will be saved and you can listen to them directly from the history of communication with the client.
• The system has the entities Lead (contacting the company or going to the company's website in order to clarify any issues) and Deal. These entities allow you to systematize the entire flow of information on each contact with the company or track all the stages of a transaction with your customers.
• The system has the Tasks functionality that will help transfer information from management to employees and between employees to perform any actions aimed at concluding a deal, conducting a deal or others. This functionality also allows you to make temporary measurements of the execution of the task. This is especially valuable in service companies where pricing is based on time.
• An email client is built into the Bitrix 24 CRM system and now all incoming and outgoing important letters will be in one place. You can not ignore the most important functionality - automatic analysis of the content of the letter in order to determine the person responsible for its execution.

This is only a small list of the functionality of the Bitrix 24 CRM system, which allows you to calculate the sales plan of a manager within a working day.

More information about the functionality of modern CRM-systems can be found in the section of the site "CRM Capabilities" .

Monitoring the implementation of the sales plan

You have made a sales plan. They distributed it among the managers. Now it is necessary to control the implementation of all activities. The sales plan is not only numbers in the table. This is a whole list of activities and tasks that need to be completed in order to get the coveted figures in the report at the end of the reporting period.

It's good when all your employees are independent and conscious, in terms of work, people. If you have not very experienced or negligent employees, then constant monitoring is necessary. You can control all activities and the achievement of goals in different ways:

• Hold permanent meetings;
• Force employees to prepare reports;
• Call and clarify matters by phone;
• Write letters or require employees to send them to you;
• Constantly generate reports in accounting programs such as 1C;
• Keep paper journals, etc.

Most of the methods I have listed are morally and professionally obsolete. It takes a huge amount of time to carry out such methods of monitoring the implementation of the sales plan, which means that the employee’s working time is reduced to achieve the plan, i.e. using such methods, you will inevitably not help, on the contrary, even interfere with the achievement of your financial goals. I propose to consider in detail what, at present, there are tools for monitoring the implementation of the sales plan.

Failure to fulfill the sales plan

Failure to meet the sales plan is a serious nuisance for any company. It is better to predict such an event than to deal with its consequences. Let's use the Bitrix 24 CRM system as an example, let's look at how you can predict the failure of the sales plan in your company. Bitrix 24 has a very good tool - "Company Pulse". With it, you can monitor activity (creating tasks, calls, chat messages, transactions, etc.) in the system for different periods of time.

The first and rather approximate harbinger of this event is the low activity of users in the CRM system. If everything is done a little bit or just nothing is done, then you must figure out why this is happening.

The next Important report in the Bitrix 24 system is "Completed by managers". This report shows the number of phone calls made (assuming calls were made through the system or events of the "Call" type were created), emails created, appointments made. This information for the head of the sales department is simply priceless.

Let's try to analyze this report. Let's imagine that Vasily Petrov, Petr Skvortsov, Sergey Voronov are new sales managers who are currently being trained in the company. Of course, for them, the zero values ​​​​of calls made, letters sent and tasks completed are normal. They have not yet been admitted to full-fledged work and you should not worry about their work.

Olga Belova is on sick leave and for her, too, low activity is quite natural. Nikolai Drozd is the leader in the number of actions performed in the system. At first glance, everything is fine with him, but you need to take a closer look. Why doesn't he have any incoming emails? Also, the head of the sales department should be alerted by only one scheduled meeting for the reporting period, when, according to the plan, he should have 3 meetings scheduled.

To Ivan Rudov, in general, a lot of questions arise. Here, either the fact of non-use of the CRM system, or a frank disregard for their job responsibilities, is obvious.

As we can see, such a simple report gives serious food for thought for both the head of the sales department and the head of the company.

This is only a small part of all the reports that are available in the Bitrix 24 CRM system.

Let's talk about the reasons for not meeting the sales plan.

Analyzing hundreds of employees for more than seven years, we came to an unequivocal conclusion - most people do not do what they really want to do in life. This is the real scourge of our modern society. Naturally, in this situation, one should not expect great productivity from such specialists. If every day a person forces himself to perform a function that he does not like, then the results will not be very impressive. CRM-systems will help to reveal most of the hidden facts, and much will become clear to you, as a leader, even at the implementation stage, because there are employees who furiously prove that such a system will greatly complicate the work and will only interfere. This is our experience. Not all of them are bad workers. It often happens that people do not fully understand the essence of the issue and simply draw hasty conclusions.

The Bitrix 24 CRM system is an excellent tool for identifying signs of non-fulfillment of the sales plan even at the early stages, while you still have the opportunity to adjust the final results, but it does not solve all problems. Only an integrated approach will allow you to bring your company to a new qualitative level of work.

Sales increase plan

Let's move on to the final part of our article. We told you how to prepare for the sales plan, how to calculate the sales plan for the year and break it down by months and managers. Showed the tools that will help implement the plan and monitor its implementation. Now let's talk about the technology to increase sales.

To increase sales, you need to follow the following strategy:

• Make sure that all employees of the sales department correspond in their moral and professional qualities to the position of a sales manager. Ideally, they should just love their job. Only with such an attitude to work can outstanding results be achieved.
• All employees must receive ongoing training in sales and communication skills. To do this, classes are held as part of daily morning planning meetings and third-party sales trainers are invited to the company. The learning process must be continuous, because. in the modern world, methods become obsolete very quickly due to the rapid penetration into the masses. It's a good idea to involve psychologists in the company in order to help the sales staff overcome internal barriers and complexes.
• It is necessary to get rid of the constant criticism of employees. If you are sure that professionals work for you, then you need to help them, and not constantly "kick". Forcing the situation, you only worsen the results and contribute to the development of a negative mood in the team. If only “random” people work for you, who came by acquaintance or just passed by, then you need to blame the one who hired them, i.e. all questions to yourself. If you are unable to understand people, then we advise you to turn to professionals. Saving on recruitment, you only lose money and time of employees who will be forced to train newcomers.
• Don't skimp on motivating your sales staff. If a person works qualitatively, then he should earn appropriately. There is an old adage: "Greed begets poverty." It is better to develop a motivation system together with employees. So it will take root better and be more effective. Non-material motivation is no less important than material. Praise, sometimes, is more necessary than a coin.
• It is necessary to get rid of the postulate: "There are no irreplaceable people." This is a very vicious practice - to fire a person at the first conflicts. Enormous sums are spent on recruiting, training and growing an employee, which will pay off only if the employee has been working for at least two years. According to our calculations, in manufacturing enterprises and companies in science-intensive industries, the payback period generally reaches five years. Try to calculate how much a sales employee costs you.
• Use CRM systems in your work, because the level of customer service increases significantly, because employees will understand that they are being controlled and will make fewer mistakes and negligence.
• Let employees feel needed. Show concern for them. Collective events should be held regularly, and it is desirable if there are informal ones among them.
• Don't set overly high sales targets. They greatly demotivate employees and encourage them to leave.

To increase sales, you must perform the following tactics:

• A plan is developed for the number of calls for the manager per day, week, month, etc.;
• A plan is being developed for the number of meetings with clients;
• A plan is being developed for the number of sent commercial offers, letters, etc.;
• A system of continuous training of employees is being developed;
• A plan is developed to regularly call all customers;
• Exemplary scripts for communication between employees and potential clients are being developed;
• The logic of phone calls is being developed (not to be confused with scripts). How many times to call, at what time, after how much to call back;
• Introduced into the company and regularly used CRM-system;
• All tasks and instructions for employees are transferred to the CRM system;
• It is necessary to start writing telephone conversations of employees to work on mistakes or resolve conflict situations;
• Regularly (every day, every two or three days) it is necessary to hold planning meetings, which should not be confused with the "morning of the archery execution." They should be as comfortable as possible and charge with positive;

Practice #1.

Average values.

Exercise 1.

Task 2. Indicators of financial performance and tax burden of commercial banks in the region for the reporting year.

It is required to determine the average values ​​of all features presented in the table.

Task 3.

There is data on wages at the enterprise for the month:

the average salary and the number of certain categories of workers are known (columns 1 and gr. 2);

the average wages of certain categories of workers and the share of workers of these categories in the total number of employees of the enterprise are known (columns 1 and gr. 4);

the average salary and wage fund of certain categories of workers are known (column 1 and gr. 3);

the number and wage fund are known (column 2 and gr.3).

METHODOLOGICAL INSTRUCTIONS

Exercise 1. Data on the work of two organizations are presented:

In the example under consideration, the unit of the population is one enterprise, therefore, among the signs presented in the table, the planned and actual volume of output are primary. Therefore, to calculate the average value of each of these features, it is required to apply the form of a simple average.

The sum of the planned output of all

Average volume planned by enterprises

output = ______________________________________ ;

Number of enterprises

Similarly:

The sum of the actual output of all

Average volume of actual enterprises

output = ______________________________________;

Number of enterprises

The next feature in the table - the percentage of plan completion - is a relative value calculated by the formula:

Percent Actual output (F)

plan execution (B) = ______________________________________
.

Production plan (P)

The average value of the percentage of plan completion can be represented as a ratio of generalized values ​​of the same features, each of which will cover the entire set of units under study.

Total actual volume

Average percentage of products of all enterprises

execution = _________________________
.

plan for the total output of all

set of enterprises according to the plan

enterprises .

Since, as already noted, the unit of the population in our example is one enterprise, the output of one worker is a secondary feature. Hence, to calculate the average value of production, it is required to apply the weighted average formula. The following ratios are the starting points for such a calculation.

Total actual volume

The actual production of the enterprise ( )

production of one = _________________________________.

working ( ) Number of workers of the enterprise ( )

In accordance with the above method for determining the average value of a secondary feature, we can write:

Actual output

Average actual output produced by two enterprises

one worker = ________________________________

Number of workers of two enterprises

;

To determine the average output of one worker, it is necessary to first calculate the number of workers employed at each enterprise. In accordance with the initial data, this is possible by the formula
. Having carried out the necessary substitution, we obtain the following expression for the desired average, which corresponds to the form of the harmonic weighted average.

.

Substituting the numerical values ​​into the formula, we get:

The basis for calculating the average values ​​of a secondary attribute (relative values) is the initial ratio of attributes that determine the logical formula of the averaged relative indicator. For each indicator used in economic analysis, only one initial ratio can be compiled to calculate the average. If, for example, it is required to calculate the average size of a bank deposit, then the initial ratio will be as follows:

The amount of all deposits (thousand rubles)

ISS \u003d __________________________. (2.20)

Number of deposits

If it is necessary to determine the average interest rate on loans issued for the same period, then the following initial ratio will be required:

Total amount of interest payments (on an annual basis, thousand rubles)

ISS \u003d ________________________________________________________. (2.21)

Total amount of loans granted (thousand rubles)

To calculate the average wages of employees of the enterprise, it is necessary to divide the total wage fund by the number of employees.

In the case when one of the final indicators is unknown, the calculation of the average is made on the basis of the initial data on the value of the averaged secondary attribute for each individual unit of the population and the attribute associated with it - the weight. Thus, the average of the secondary feature has the form of a weighted average. If the values ​​of the denominator of the original ratio are known, but the values ​​of the numerator are not known, then the average is calculated using the arithmetic mean formula. If the values ​​of the numerator of the original ratio are known, but the values ​​of the denominator are not known, then the average is calculated using the harmonic mean formula.

For example, to compare the level of tax burden and the financial condition of credit institutions, the following data is used (Table 2.4)

Task 2. Indicators of financial performance and tax burden of commercial banks in the region for the reporting year.

It is required to determine the average values ​​of all features presented in the table.

In the example under consideration, the aggregate unit is one bank, therefore, among the features presented in the table, the primary ones are the profit and equity of banks. Therefore, to calculate the average value of each of these features, it is required to apply the form of a simple average.

The amount of profit received by all banks

Average size (P)

profit received by banks = ______________________________________ ;

for the reporting period Number of banks (n)

=186910.25 thousand rubles.

The amount of own funds of all banks

Average volume of own

Bank funds (F)

for the reporting period = ______________________________________;

Number of banks (n)

=1346926.25 thousand rubles

The next sign in the table - return on capital is a relative value calculated by the formula:

Profit received by the bank (P) Profitability

Capital (B) = ______________________________________
.

Bank equity value (F)

The average value of the percentage of profitability can be represented as a ratio of generalized values ​​of the same features, each of which will cover the entire set of units under study.

The total amount of profit,

received by all banks

Average percentage

return on equity = _________________________
;

Amount of own funds

all banks

13,88%.

To calculate the average value of the tax burden, it is required to apply the weighted average formula. The following ratios are the starting points for such a calculation:

Tax payments

on capital = _________________________________.

Bank equity value (F)

Tax payments (N)

on assets \u003d Value of the bank's assets (A)

In accordance with the above method for determining the average value of a secondary feature, one can write down:

;

To determine the average tax burden on capital, it is necessary to first calculate the amount of tax payments for each bank. In accordance with the initial data, this is possible using the formula:
.

Having carried out the necessary substitution, we obtain the following expression for the desired average, which corresponds to the form of the weighted arithmetic average.

*100=4,31 %;

;

To determine the average tax burden on assets, it is necessary to first calculate the value of assets for each bank. In accordance with the initial data, this is possible according to the formula:
.

Having carried out the necessary substitution, we obtain the following expression for the desired mean, which corresponds to the form of the harmonic weighted mean:

=0,96%.

In some cases, the weights can be presented as relative values ​​of the structure (in percentages or fractions of a unit). Then the formula for the arithmetic weighted average will look like:

(2.12)

Where
- the share of each group in the total number of population units (frequency). If the frequencies are expressed in fractions (coefficients), then
and the arithmetic mean formula is simplified:
.

Consider methods for calculating the average value.

1. Determine the average volume of output at the enterprise.

This is a primary feature, therefore, we will use a simple arithmetic average:

2. Determine the average labor productivity. In this case, the initial data for calculating the PT may be different.

PT is a secondary symptom.

In order to choose the right formula for averaging a secondary feature, it is necessary to compose the initial ratio of the average(ISS), which reflects the logical formula of the average indicator.

For our example, the ISS looks like this:

To find the average value of the PT, it is necessary to find the quotient of the division of the final calculations for VP and NZ for two enterprises:

- this form of calculation of the average is called the aggregate or implicit average (because the individual values ​​of the averaged feature are not explicitly present).

Consider 2) the case.

Now the denominator is unknown in the ISS - CZ, but for each enterprise it can be found by expressing from the ISS:

, i.e. f-lu avg.harm.vzv., where in quality. weight favors VP

3) Now in the ISS the numerator is unknown - VP, then

Substituting this expression into the AIS to calculate the average PT, we get:

this is f-la cf.ar.vzv., where the weight is yav. CHZ

Task 3.

There is data on wages at the enterprise for the month:

Data on remuneration of certain categories of employees of the enterprise

In order to summarize data on the wages of employees of certain categories, it is necessary to calculate the average wage level for the enterprise as a whole. The initial information for calculating the average wage can be different:

the average salary and the number of certain categories of workers are known (columns 1 and gr. 2);

the average wages of certain categories of workers and the share of workers of these categories in the total number of employees of the enterprise are known (columns 1 and gr. 4);

the average salary and wage fund of certain categories of workers are known (column 1 and gr. 3);

(gr.2 and gr.3)

In order to choose the right formula for calculating the average wage, we compose the initial ratio of the average(ISS), reflecting the essence of the averaged feature, its logical content. The initial ratio for finding the average wage will look like this:

Obviously, knowing two elements from the ISS, you can always find the value of the third.

To find the average level of wages at the enterprise, it is necessary to find the quotient from dividing the final calculations by wage funds and the number of employees in four selected categories:

Let's consider how this formula will be transformed depending on the nature of the initial information.

In the first case, when there are data on average wages and the number of employees of certain categories, the numerator is not known in the EIS, i.e. the size of the payroll. For each category of workers, the wage fund can be defined as

Substituting the expression for F into the formula for finding the average wage , we get the formula arithmetic mean weighted. The role of the sign-weight is performed by the number of employees:

Let's calculate the average salary for our example:

The average salary at the enterprise is 17,845 thousand rubles.

Let us consider the second case, when not the absolute numbers of employees of certain categories are known, but their relative values ​​- specific weights (shares) in the total number of employees of the enterprise ( d=H/∑H). In this case, the formula for the arithmetic weighted average will take the form:

If d are specific weights expressed as fractions ( ∑ d= 1),

If d– specific weights in percent ( ∑ d= 100%).

Let's use the second formula.

In the third case, the average wage at the enterprise must be determined on the basis of data on average wages and payroll funds for certain categories of workers. Now the denominator is not known in the ISS - the number of employees, but for certain categories it can be found using the formula:

.

Substituting this expression into the formula for calculating the average wage, we obtain the formula average harmonic weighted:

,

where the wage fund acts as the weight.

The average salary for the enterprise, calculated by the harmonic mean formula, will be:

In the fourth case, when data on the number and wage funds of certain categories of workers are known, i.e. both the numerator and denominator of the AIS are known, the calculation of the average wage for the enterprise comes down to substituting the data into the original formula:

This formula for calculating the average value is called aggregate average or implicit average, since the individual values ​​of the averaged feature are not explicitly present in the calculation.