The Compound Annual Growth Rate explained.

The Compound Annual Growth Rate (CAGR) measures the average annual growth of an investment over a given period. CAGR is a helpful tool for investors because it measures investment growth (or decline) over time. This can be a useful way to measure against a benchmark if you have one.

It can be used in a lot of other ways to determine the compounded annual rate of return for anything that can rise and fall over a period. The CAGR is not a true rate of return, it is rather used as a quick representation of the investment over a period of time, “ironing out” all the bumps, rises and falls and providing a fairly accurate average to review. Think of it as way to disguise all the volatility and give you the number you need at the end of the day so you can determine, am I up or am I down.

It does not consider taking out profits or adding in fresh capital. It assumed it is all reinvested and compounded over that period. It is a hypothetical growth rate assuming that the rise or fall occurred evenly at the same rate over each individual period. It also makes it easier to compare different investments or measure the performance of a specific investment. 

I use the CAGR more when I am conducting Quantitative analysis and valuing a business, especially against another business. I find it helpful to look at a business and look back over the past 5+ years to see how that company has performed. It gives me a very quick look at the CAGR of the metric I am measuring. It is helpful when looking at Growth companies.

What is the Compound Annual Growth Rate Formula?

• CAGR = (EndV ÷ StartV)^1÷t -1
• *V = Value
• *t = Time Period
• Year 0 is excluded when counting the time period as only the compounding years must be counted. 
• To convert the final number into a percentage % multiply it by 100.

How to use the Compound Annual Growth Rate?

Let us work out a few different sets of examples to provide an idea on how you can also implement this tool. Whilst Excel can determine this rather quickly, I find I use it on the go or when an opportunity surfaces, I have a quick calculation to see what the CAGR rate is. I find I use this quite often when evaluating all forms of investments, both current and new prospects. Using the reverse engineered CAGR is also a good way to look at the end result of a desired investment and what the compounded average rate needs to be in order to get there.

It can also be very useful in working out other formulas like Future Growth Rates based on the past CAGR when doing our forecasting and modelling. If a CAGR over the last 10 years has been 20% it can be helpful determining what a reasonable rate of growth can be when working on a DCF. It just gives us a good base to start with.

Below are some examples of how we can use this formula. There are of course many areas it can be used for. I typically use it measuring the annual growth and measuring past performance on areas like sales revenue, operating margin and even to determine if a company has a MOAT by looking at a sustained CAGR of higher-than-average ROC.

Measuring CAGR on Portfolio Returns

Let’s use an example of an investment portfolio and measuring the CAGR after a decade of Investment. We want to see how we measure against a benchmark or how we stacked up against the greats. We started in the year 2010 and we stopped Investing in 2019.

Our starting year = 2010 with a 15% return. Our final year is 2019 with a 47% return. It is over a 9-year period as we never include the Starting year. The first year provides the starting point and the years after provide the periods you evaluate for growth.

The years compounded will be between 2011-2019. The formula will be:

(47÷15)^(1÷9) -1 = 0.1353 x 100 = 13.53%

Measuring CAGR on Earnings Per Share

Using the CAGR on certain metrics like the EPS can help us visualise how the company has performed over a certain period. When evaluating business against one another, I will compare a potential idea against other competitors or other Investment opportunities. If I am conducting deep research and there appears to be reasonable growth, I then compare it to other businesses within the same industry to determine if it is in fact growing at a higher rate, if yes it leads me to the next stage of the investment process, why?

Let’s compare 3 companies and their EPS (Earnings Per Share) over a 5-year period. This is not exhaustive valuation, nor does it tell me anything except the company is growing and at an annual rate that may warrant further investigation. (It tells me nothing about the intrinsic value of the company).

Year/EPS	Company A	Company B	Company C
2018 (Starting Value)	0.13	14	4.98
2019	0.32	30	9.55
2020	0.67	21	10.21
2021	0.29	36	11.01
2022	0.59	41	9.89
2023 (Final Value)	0.61	21	11.07
CAGR = %	36.23%	8.44%	17.32%

The formulas are below to show exactly how it was worked out.

Company A = (0.61÷0.13)^(1÷5) -1 x 100 = 36.23%

Company B = (21÷14)^(1÷5) -1 x 100 = 8.44%

Company C = (11.07÷4.98)^(1÷5) -1 x 100 = 17.32%

It is best to compare apples to apples when evaluating companies like this. Of course we can use this to look at industries and how it stacks up, however finding a company with a high CAGR and comparing it against competitors in that industry is a great way to identify a company doing something different. We can take Company A and ask the questions, why is this company able to sustain a higher CAGR than it’s peers? This moves us into investigating the company further.

How to reverse the Compound Annual Growth Rate?

Using a reverse CAGR is a way to determine what rate of annual return you likely need to achieve to get to a desired future amount. Let us assume we want to achieve a $1,000,000 retirement fund in 20 years. We have $100,000 to start investing now, what is the rate of return we need to achieve to reach our desired goal in the time frame?

We simply reverse engineer the CAGR and rearrange the present value and the future value equation. It would look like the below.

Required Return = ($1,000,000÷$100,000)^(1÷20) -1 x 100 = 12.20%

So we would need to generate a 12.20% annual rate of return to turn $100,000 into $1,000,000 in the 20 year period. (You can also use the Investment Calculator provided to make it easier).

A quick way to measure declining growth.

The CAGR is quite useful when we are evaluating a business and looking at the growth rate over set periods of time. If we find a company that has a CAGR over a 15-year period of 20%, that looks amazing, however if we take the past 5 years it may only show a 7% CAGR which reflects a declining growth rate.

We can take this further and use the CAGR to measure sales figures, earnings per share and determine if a long-term investment is growing at the same rate in the past. A rising or declining CAGR can reflect a business entering a different life cycle from early stage to maturing or declining.

In Summary…

The CAGR is especially useful for comparing investments with different holding periods or where returns vary from year to year. It is best used for multiple years. It can give a false sense of return over shorter time periods.

The CAGR formula is not a perfect tool, it is a simple way to look at performance over a certain time. I find it most useful when using a minimum of 5 years when inputting time periods. Fund managers will often use their latest results to entice new investors with the most recent performance figures, be careful to do your due diligence.

If we are measuring growth metrics, such as the CAGR of sales revenue or gross margin in small caps it is best to include all the data available to get a realistic CAGR and full account of the business operations.