# CAGR – Compound Annual Growth Rate

CAGR is the acronym for  Compound Annual Growth Rate . In Portuguese, we can translate the term to Compound Annual Growth Rate.

This rate is responsible for calculating the return necessary for an investment to move from an initial balance to a certain final balance. For this, the basic premise is to consider that the profits for a period were constant and reapplied in each period to understand the growth of the applied capital.

In other words, it is an indicator used by economists, analysts and investors to carry out the profitability analysis and, in this way, to understand the forecast of return over a certain period.

## What is the role of the CAGR?

First of all, it must be made clear that the CAGR calculation (we will see below) does not bring the true rate of return on an investment.

As you saw in the definition of the concept, it is assumed that there is a constant growth rate and that the profits generated are always invested again at the end of each year of the analysis.

You don’t even have to be a financial market expert to know that there are no constant rates in reality. You can make an investment and, for example, have yields of 5%, 10% and 8% in three consecutive years.

The calculation will smooth these returns, assuming that the average value for that period is repeated each year.

The main objective is to establish an easier comparison with other investment options. This is because, with this constant premise, it demonstrates what the average return on investment needs to be to obtain a certain result.

## What is the formula for calculating the CAGR?

The CAGR calculation takes into account the following formula:

Where:

FV = Final Investment
Value VI = Initial Investment Value
n = number of years of investment

In a simplified way, everything consists of dividing the final value of your investment by the initial value and raising it to the division of one by the period (in years). Finally, just subtract 1 from the result and multiply by 100 to find the percentage return.

This formula is only for understanding since, currently, there are several ways to find the result in an automated way via spreadsheets and calculators.

### Practical example and implications

So that the formula and the concept are clearer in terms of understanding, let’s take an example.

Suppose that you have made an investment of R \$ 10,000.00 and that, after three years, the amount has reached the level of R \$ 13,800.00. Applying these values ​​in the formula we saw earlier, you would find the result of 11.33%.

This allows an analyst to make his assessments of other investments in a simplified comparison, since the return is smoothed to 11.33% regardless of the different performance in each year.

Looking at other returns and drawing conclusions is easier that way.

## Problems and limitations of the CAGR

Like all calculations, the CAGR brings a numerical and therefore cold representation of an investment. Only numbers and not qualitative aspects enter here, which in itself is a limitation.

However, this is still not the biggest problem, but the smoothing of returns, which simply ignores much of the reality, especially the volatility and volatility of investments.

If you take this result we found from our 11.33% investment and compare it with some fixed income asset, you may find it very advantageous to continue with it. However, the account does not address the volatility and high risk of this option.

In addition, when comparing investment with risk versus fixed income, the error of considering a past rate of return as constant for the future is incurred. And, as we know, past profitability does not guarantee future profitability.

In any case, it is still another analysis tool for financial assets. The problem lies in using it in isolation, without also considering other factors in decision making.