What is Compounded Annual Growth Rate( CAGR)?

Introduction:

The decision of investing is very critical. Albert Einstein once said that compounding is the eighth wonder of the world. Now how would one measure the compounding effect? With the help of CAGR, we can calculate the average growth at which our portfolio is increasing in value during a period of time. We can also predict what the future value of today’s investment could be using the CAGR. Let’s get right into it!

Table of Contents:

  1. What is CAGR?
  2. Formula and Calculation of CAGR
  3. Example of how to use CAGR
  4. Importance of CAGR
  5. Disadvantages of CAGR
  6. Conclusion

What is CAGR?

CAGR stands for Compound Annual Growth Rate. It is the measure of the annual growth of the investment over time with the compounding effect taken into account during the investment period. It is one of the most popular and most accurate ways to calculate the approximate returns of the assets and portfolios over time [1]. For example, HDFC Bank has delivered a profit growth of 20.40% over the past 5 years. This means that the average growth of profit was at 20.40%. CAGR is often associated with specific parameters which indicate the performance of a company over a fixed period, such as sales, revenue, earnings, etc. [2]

The formula of CAGR is [3]:

Where CAGR   = compound annual growth rate

Vbegin = beginning value

Vfinal   = final value

t            = time in years

Example of how to use CAGR:

Imagine you have invested $10,000 in a portfolio. The return for 3 years is outlined below [1]:

Year Average Returns Portfolio value
1 30% $13,000
2 7.69% $14,000
3 35.71% $19,000

As you can see, the returns for every year are not constant. By using the formula, the CAGR can be calculated as follows:

The CAGR of 23.86% over the 3-year investment can assist the investor in comparing alternatives for his capital or making forecasts of future values. Furthermore, he can even predict what his returns are going to be after a few years.

Let us look at another example where the CAGR is known to us, and we have to calculate the future value. Say, you have invested $5,000 in a stock mutual fund with an average CAGR of 26% and you want to find out your approximate returns after 10 years. According to the formula, the final value will be,

After solving this, the value of the return after 10 years will be approximately $50,428.

Importance of CAGR:

CAGR is one of the most popular variables used to determine the profitability of an investment. One of CAGR’s advantages over an average rate of return is that it is not influenced by percentage changes that may yield misleading results. For example, look at the following example [3]:

Year Amount Return
0 $1,000
1 $1,250 25%
2 $937.5 -25%

This example shows that the value of the portfolio increased by 25% to $1,250. The following year, the returns dropped down by 25% and the final value of the portfolio is $937.5. Even though the average returns are 0%, there is a loss of $62.5. By using these values, the CAGR comes out to be -3%. Hence the CAGR is more accurate than the average returns.

Disadvantages of CAGR:

There are a few disadvantages of CAGR as well. The most important limitation of CAGR is that it calculates a smoothed rate of growth over a period, Hence, it ignores volatility and implies that the growth during that time was steady. Also, CAGR does not account for when an investor adds or withdraws funds from his portfolio. Another disadvantage of CAGR is that it only represents past growth, and the investor cannot assume that the CAGR will be the insame in the future as well. [3]

A third limitation of CAGR is its representation. Say that an investment fund was worth $10,000 in 2016, $7,100 in 2017, $4,400 in 2018, $8,100 in 2019, and $12,600 in 2020. In 2021, the fund manager will represent that the CAGR was a whopping 42.01% over the past 3 years but when it comes to the CAGR over the past 5 years, it is only 4.73%. [1]

Quick Method to Calculate Value Doubling

A simple method to check how many years the value of an investment will double is to divide 74 by the rate of growth. For example, if your annual growth rate CAGR is 4% in a savings account, then 74/4= 18.5 number of years is what it will take the money to double. Similarly, if the compound annual growth rate is instead 20%, then approximately the money doubles in 3 years.

This simple mental math calculation can be very helpful while taking investment decisions.

Conclusion:

CAGR is a very useful method to calculate the growth rate of an investment . It can be used to evaluate the past returns or predict the future returns of your investments. However, remember that CAGR works suitably only for lumpsum investments. Investors can analyze investment alternatives by comparing their CAGRs from identical periods. Also a direct conclusion worth noticing is that higher the return, higher the future value. So if you kept you capital in a savings account with a 4% annual return, versus a 12% rate every year in a mutual fund portfolio then the value will be higher with the higher rate of return.

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