The evolution of any business depends on several factors that come into play for achieving objectives. These various factors are evaluated through the calculation of the rate of evolution. This value thus represents an indicator expressing the evolution between two data points from various fields. How is it calculated? What is its purpose? The following article provides answers to these different questions.
What is the rate of evolution?
Also known as the percentage of evolution, the rate of evolution is a mathematical calculation that allows for the assessment of the difference between an initial value and a final one. It thus enables an ideal and precise analysis of different data in order to draw summaries.
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The rate of evolution calculation is done using the following formula: Te = [(VF-VI) / VI] x 100. The abbreviations VI, VF, and Te specifically refer to Initial Value, Final Value, and Rate of Evolution. It should be noted that the result of this calculation is expressed as a percentage.
In cases where the result of the rate of evolution is positive, it is preceded by a + sign. However, when it is negative, the result exceeds 100%, indicating that the final value is different from the initial one.
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For example, considering a company that achieved savings of 2000 euros in the first year and 2200 euros in the second year, the percentage of evolution would be: [(2200-2000) /2000] x 100. This would yield a 10% rate of evolution for this company after one year.
How are different rates of evolution calculated?
In addition to the standard rate of evolution, there is also the reciprocal rate of evolution, the index of initial value relative to the final value, and the average rate of evolution. These different percentages of evolution allow for a more precise tracking of the company’s progress.
The reciprocal rate of evolution
Unlike the standard rate of evolution, the reciprocal rate of evolution has an inverse multiplier coefficient. Its calculation is done using the following formula: Te’= [(VI – VF) / VF] x 100.
Using the same example as the rate of evolution, we obtain:
Te’ = [(2000 -2200) /2200]x100. The reciprocal rate of evolution for this company is -9.09%. It can be observed from this calculation that the difference between the percentage of evolution and the reciprocal percentage of evolution is not significant. However, it remains important.
The average rate of evolution
The average rate of evolution represents the average of several cumulative evolution rates over a given period. For example, if we consider a quantity Q that has undergone successive evolutions of 5%, 10%, 15%, 12%, and 20% (over a given period), we obtain a new quantity K = (1+0.05) x (1+0.10) x (1+0.12) x (1+0.15) x (1+0.20) x Q
K= 1.785 x Q
It follows that the coefficient is 4.14 and the overall rate of evolution is 89.25%. Thus, the average evolution percentage corresponds to the average of the 5 rates. To obtain it, we do: K= (1+tm) x (1+tm) x (1+tm) x (1+tm) x (1+tm) x Q
K= (1+tm)5x Q
By taking (1+tm)5, we get: (1+tm)5= K/Q
Thus, 1+tm= (K/Q)1/5
And if we replace Q with its initial value, we have: 1+tm= [(1.785xK)/K]1/5
1+tm= 1.122
Then tm= 0.122. Estimated as a percentage, this gives 12.2%.
It should be noted that the average rate of evolution in business is used to obtain the difference between the monthly rate and the annual rate.
The index of initial value relative to the final value
The value index allows for a more ideal comparison between the results of calculations. Its calculation is done as follows: I= 100 x (VF/VI).
Considering (t) as the rate of evolution of the initial value VI relative to the final value VF, we have: I = 100 x (1+t)
If we take the same values as above, we have: I = 100 x (2200/2000)
This gives 110.
The index of 2200 compared to 2000 is therefore 110.
While the calculation of the rate of evolution from 2000 to 2200 gives 0.1, the index calculation will therefore be: I = 100 (1+0.1) = 110.
This means that an index of 110 corresponds to an increase of 10%. Thus, we can say that the rate of evolution is 10%.