Compound Annual Growth Rate - CAGR

Compounded Annual Growth rate (CAGR) is a business and investing specific term for the smoothed annualized gain of an investment over a given time period. CAGR is not an accounting term, but remains widely used, particularly in growth industries or to compare the growth rates of two investments because CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. CAGR is often used to describe the growth over a period of time of some element of the business, for example revenue, units delivered, registered users, etc.


the formula is 

Let’s understand it with an example.

Year =>	0	1	2	3	4	5	6
Growth Rate in the year		20%	-8%	11%	-5%	35%	5%
Value of Investment	100.00	120.00	110.40	122.54	116.42	157.16	165.02

The CAGR will be calculated based on the evidence that an investment of Rs. 100.00 turned out to be Rs. 165.02 in 6years.
The CAGR will be (165.02/100) ^ (1/6) – 1 = 0.0871 = 8.71%
This means if the investment grows at 8.71% for 6 years, value of Rs. 100 will be Rs. 165.

Uses of CAGR:
CAGR is a very useful number. It is used to measure the rate of almost every parameters that changes over time in a non-linear fashion. Some of them can be measuring GDP of a nation, investment in risky assets such as equity or equity based funds where the returns are non-linear, or growth in highways in terms of length in kilometre. The uses of CAGR are humongous. In our case, we will focus on CAGR with respect to investment in the market.

Let’s look at some of the uses and advantages of CAGR.

1.    It is useful in measuring the change in parameters which follow non-linear pattern. This is the reason we usually see the use of CAGR in earning growth, revenue growth, and EPS growth and many more parameters.

2.    It cuts through the noise and expresses returns in nice and convenient format. CAGR is very useful number as this eliminates the volatility of different investment and provides a figure that is understandable.  Take the above mentioned example, how will you know what that investment meant. Imagine a stock broker or a bank agent coming to you and showing you the data of last 6 years with the returns, what will you infer? Instead of the data, if the bank agent shows you the number CAGR of 8.71%, you can easily understand the value of investment and decide accordingly.

3.    CAGR helps in comparing investment across the spectrum.Take the same example, if the broker or bank agent shows you the details and not CAGR, you will not be able to tell whether this investment is better than investment in high grade bond (say L&T corporate bond). However, once you know the CAGR, it is easier to compare the bond rate of L&T and decide where to invest. Of course, there are other factors like volatility which also play a part in your decision but more on this later). In the same way, CAGR can be used to compare return on two or more stocks, mutual funds, portfolios, or any financial instrument.

Disadvantages of CAGR:
There are some pitfalls of CAGR too which should not be ignored. Remember, CAGR eliminates volatility from the picture and presents a number which is convenient to us. In reality, things are different.
First, most of the investors, while looking at CAGR forget the volatility part. The underlying assumption is that the investment will give a return of x% (in the example, 8.71%), year after year. This is not correct. The investor should keep the volatility factor in mind.

Second, the CAGR is calculated on past data. The past data may not truly represent the expected future growth. This may mislead investors. For example, the CAGR of inflation in India from 2000 to 2008 may be about 4%-5%. If an analyst would have projected in 2008, the expected inflation rate in 2009-2012, the data would have been completely misleading. We know that inflation in last 2 years is in double digit.
Third, timing is crucial in CAGR. As shown in above example on inflation, the time between 2000 and 2008 is not a right predictor of future inflation.

Lastly, we have to also consider the duration in which the CAGR is calculated. A too short duration can give you misleading picture because of business cycle. For example, if we invest in infrastructure mutual fund based on last 3 years data (especially if these 3 years were booming), our expectation will not be met. At the same time, too long duration will make the CAGR invalid for any expected projection in future. For example, if we take 30 years CAGR for Walkman business of Sony Corp and project the same going forward, our projection will be wrong because the times have changed and the sale of Walkman is dwindling.

source: wikipedia , investopedia