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Growth rate and growth rate: definition and calculation formulas

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Growth rate - This is an increase in any studied value for one time period (usually applied to a year).

Rate of increase - this is an increase in any studied value for one time period minus 100%.

Growth rate and growth rate measured in percent and are relative values. The growth rate is always positive, the growth rate may be negative. The growth rate is equal to the growth rate minus 100%.

Now consider the calculation of the growth rate and growth rate in more detail.

Growth and growth rate calculation

For clarity, DOWNLOAD THE CALCULATION FILE, which reflects the calculation: growth rate and growth rate. Please note: on the first sheet of the book of the calculation file, the calculation is presented, and on the second sheet of the book of the calculation file is the formula for calculating the growth and growth rate.

The figure shows an example of calculating the growth rate and growth:

For clarity, the figure below shows the same example, only with open formulas:

The figure shows that the growth rate is determined by dividing Indicator 2 by Indicator 1 and multiplying by 100%. The growth rate is equal to: dividing indicator 2 by indicator 1 times 100% and minus 100%, that is, the growth rate is equal to the growth rate minus 100%.

Calculation of average growth and growth rates

The figures also show how the average growth rate and the average growth rate are calculated. To determine the average growth rate, it is necessary to add the indicators for all four periods and divide the amount received by the number of periods, that is 4. The average growth rate is calculated similarly - the sum of the growth rates for all periods is divided by the number of periods.

Calculation of basic growth rate and basic growth rate

For clarity, DOWNLOAD THE CALCULATION FILE, which reflects the calculation: basic growth rate, basic growth rate, chain growth rate, chain growth rate. Please note: on the first sheet of the book of the calculation file, the calculation is presented, and on the second sheet of the book of the calculation file is the formula for calculating the growth and growth rate.

The figure below shows the calculation of the basic rate of growth and growth (tables 2 and 3):

Baseline Growth Calculation lies in the fact that it is necessary to calculate the growth rate of all indicators. Please note that the growth (increase) of the first indicator cannot be calculated.

In the example, Indicator 1 is taken as the basic indicator, therefore, the basic growth rate or basic growth rate is calculated based on this situation, that is, when calculating the basic growth rate, Indicator 2 is divided by Indicator 1 and multiplied by 100, then Indicator 3 is divided by Indicator 1 and multiplied by 100, then divide indicator 3 by indicator 1 and multiply by 100, when calculating the base growth rate, subtract 100 from each indicator of the basic growth rate.

Calculation of chain growth rate and chain growth rate

The figure above shows the calculation of the base rate of growth and growth (tables 4 and 5).

Chain Growth Calculation lies in the fact that it is necessary to calculate the growth rate of all indicators. Please note that the growth (increase) of the first indicator cannot be calculated. In contrast to the basic growth or growth rate, the chain growth or growth rate is calculated from the current and previous indicators.

That is, the chain growth rate or chain growth rate is calculated as follows: Indicator 2 divided by Indicator 1 and multiplied by 100, then Indicator 3 divided by Indicator 2 and multiplied by 100, then Indicator 4 divided by Indicator 3 and multiplied by 100, when calculating We subtract 100 from the chain growth rate from each indicator of the chain growth rate.

In order to consolidate the information received, pay attention to the figure below, which reflects the calculation formulas: basic growth rate, basic growth rate, chain growth rate, chain growth rate:

Please note that when calculating the basic and chain indicators, the values ​​of the basic and chain growth and growth rates are equal, since when you select the first of a series as the basic indicator, they are calculated the same way.

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Growth rate

The calculation of the growth rate begins with determining a series of numbers between which you need to find a percentage. The control number is usually compared either with the previous indicator, or with the base one at the beginning of the number series. The total is expressed as a percentage.

The growth rate formula is as follows:

Growth Rate = Current / Base * 100%. If the result is more than 100%, an increase is noted. Accordingly, less than 100 is a decrease.

An example is the option to increase and reduce wages. The employee received a monthly salary: in January - 30,000, in February - 35,000. The growth rate was:

35,000 / 30,000 * 100 = 116.66. In February, relative to January, salary was 116%.

Rate of increase

The growth rate formula allows you to calculate the percentage reflection of how much the indicator has grown or decreased over a certain period. In this case, a more specific figure is visible, which makes it possible to judge the work efficiency in dynamics. That is, calculating the ratio of wages (or other characteristics) according to the growth rate formula, we will see how many percent this amount has changed.

There are two calculation options:

  1. Growth rate = current value / base value * 100% - 100%:

35 000/30 000*100%-100%=16,66%,

  1. Growth rate = (current value is the base value) / base value * 100%:

(35 000-30 000)/30 000*100%=16,66%.

Both calculation methods are identical. A negative mathematical result indicates a decrease in the indicator for the period under consideration. In our example, the employee wage in February was 16.66% higher than in January.

How to calculate growth rate: formula

This term shows the change in the value of any economic or statistical indicator in the current period to its initial value (which is the base) for a certain time period. It is measured in percentage or ratios.

For example, when comparing the volume of output of goods at the end of the year (for example, in the value of 100,000 rubles) to the indicator of volume at the beginning of the year (70,000 rubles), the growth rate is found by the ratio of the final value to the initial one: 100,000 / 70,000 = 1,428. The growth index in the example was 1.429. This means that at the end of the year the output amounted to 142.9%.

How to calculate the percentage growth rate - formula:

TP = Pt / Pb x 100%,

where pto and Pb - indicators of the values ​​of the current and base periods.

The growth rate shows the intensity of changes in a process with respect to its initial (base) value. The result of the calculations is one of three options:

TP is more than 100%, therefore, the final value increased in comparison with the initial, i.e. there is an increase in the indicator,

TP = 100%, i.e. there were no changes either up or down - the indicator remained unchanged,

TR is less than 100%, which means that the analyzed indicator decreased by the beginning of the period.

Here are examples of how to calculate the percentage growth rate for each calculation option by combining the source data in a table:

Volume of issue in thousand rubles

This growth rate is called basic, since the comparison base for periods remains unchanged - an indicator at the beginning of the period. If the comparative base changes, and the growth rate is calculated by the ratio of the current value to the previous (and not the base), then this indicator will be chain.

How to calculate chain growth

Consider an example of calculating the basic and chain growth rates:

Period

Volume in thousand rubles

% Growth rate

basic

chain

Chain growth rates characterize the saturation of changes in levels from quarter to quarter, while the base ones reflect it as a whole for the entire time interval (the indicator of the 1st quarter is the comparison base).

Comparing the indicators in the above example, it can be noted that a number of values ​​calculated at the beginning of the period have a lower amplitude of oscillations than chain indicators, the calculations of which are tied not to the beginning of the year, but to each previous quarter.

How to calculate growth rates

In addition to calculating growth rates, it is customary to calculate growth rates. These values ​​are also basic and chain. The basic increase is defined as the ratio of the difference between the indicators of the current and base periods to the value of the base period according to the formula:

The chain growth is calculated as the difference between the current and previous indicators divided by the growth rate of the previous period:

A simpler calculation method is the formula: ∆ ТР = ТР - 100%, where the calculated indicators of the growth rate are reduced by 100%, i.e., the initial value. The growth rate indicator, in contrast to the growth rates, can have a negative value, since the growth (or decrease) rate shows the dynamics of the indicator, and the growth rate indicates what kind they are.

Continuing the example, we calculate the increase in volumes in the periods under consideration:

Growth and growth formulas: basic, chain and medium

Growth and growth rates can be found in several ways, depending on the purpose of the calculation. The formulas for obtaining the basic, chain and average growth and growth rates are distinguished.

Basic growth and growth rate shows the ratio of the selected indicator of the series to the indicator adopted as the main (calculation base). Usually it is at the beginning of a row. The formulas for the calculation are as follows:

  • Growth rate (B) = Selected indicator / Base indicator * 100%,
  • Growth Rate (B) = Selected indicator / Base indicator * 100% -100.

Chain growth and growth rate shows the change in the indicator in the dynamics of the chain. That is, the difference in each subsequent indicator in time to the previous one. The formulas look like this:

  • Growth rate (C) = Selected indicator / Previous indicator * 100%,
  • Growth rate (C) = Selected indicator / Previous indicator * 100% -100.

There is a correlation between the chain and basic growth rates. The ratio of the total division of the current indicator to the base to the total division of the previous indicator to the base is equal to the chain growth rate.

Average growth and growth rate used to determine the average value of changes in indicators for the year or other reporting period. In order to determine this value, you need to determine the geometric mean of all indicators in the period or find by determining the ratio of the final value to the initial:

  • Average growth rate
  • Average growth rate = average growth rate - 100.

The nuances of computing

The formulas presented are very similar and can cause confusion and confusion. To do this, we explain the following:

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  • growth rate shows how many percent is one number from another,
  • the growth rate shows how many percent one number increased or decreased relative to another,
  • growth rate cannot be negative, growth rate - maybe
  • the growth rate can be calculated based on the growth rate, the reverse order is not allowed.

In economic practice, the growth indicator is more often used, since it more clearly reflects the dynamics of changes.

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