What Is CAGR? A Complete Guide To Compound Annual Growth Rate

An infographic that explains what the Compound Annual Growth Rate is, how to calculate it, how to use CAGR for investment decisions, and what the limitations of CAGR are.

There are numerous ways to evaluate investment performance. Compound Annual Growth Rate (CAGR) and the total return on investment are some of the most effective methods. The concept of CAGR is pretty straightforward and can provide a good measure of an investment return from various assets. These assets can include bonds, stocks, stock market indexes, real estate, gold, etc. The Compound Annual Growth Rate can actually be used to evaluate anything that changes over time, not just investment performance.

The Compound Annual Growth Rate is the average rate of return of an investment, over a certain number of years, from its beginning balance to its ending balance, assuming that profits will be reinvested annually.

CAGR provides investors with valuable information when comparing or evaluating the historical returns of particular assets.

What Is CAGR?

CAGR or Compound Annual Growth Rate is a mathematical formula that calculates the average growth of an investment. It is calculated over a specific period of time on an annually compounded basis. Compounding means that you reinvest profits at the end of each year within that specified time period. The CAGR smoothes out the actual growth rate as if the growth happened steadily each year over that time period. In other words, it shows a hypothetical constant growth rate from the starting value of an investment to its ending value. It essentially provides an average return rate to show investors how much their investment has grown by the end of an investment period.

Investors can use CAGR to compare the historical performance of different investments with each other. An example would be the assessment of a stock’s performance.

In addition to being a tool for measuring an investment’s past performance, CAGR can also be used to help an investor determine how much to invest in the present to reach a certain investment goal over time.

How To Calculate Compound Average Growth Rate

CAGR shows the consistent growth rate of an investment over a specific period of time. However, it should be noted that It assumes that returns are compounded at the same rate each year and that it does not consider any deviation or variability of returns.

The mathematical formula calculates the Compound Annual Growth Rate as a percentage of the annual compounded growth rate. To calculate it, you take the ending value of the investment, divide it by the beginning value of the investment, raise it to the power of the reciprocal of the time duration of the investment, and then you subtract 1. To get CAGR as a percentage, you’d multiple this value by 100%.

CAGR FORMULA

CAGR FORMULA
Where:
EV = Ending Value of the investment
BV = Beginning value of the investment
n = number of years 

Example of CAGR Calculation

CAGR calculates the historical return on investment at the end of the period on an annually compounded basis. 

Scenario:
Company X invests $2000 in an asset fund in the first year for a period of 4 years.
The year-end value in each year is:
year 1: $3,000
year 2: $4,500
year 3: $4,000
year 4: $6,000

The CAGR of the investment is 31.61%

The tables above and below show how the CAGR smooths out the volatility of the fund’s performance and provides a more realistic idea of how the fund may perform in the future.

Year-end value growth table for CAGR (Note: these are fictional numbers, CAGR smoothens the return)

Year 0: $2,000
Year 1: $2,632
Year 2: $3,464
Year 3: $4,559
Year 4: $6,000

If you’re looking for a compound interest calculator, you can find one here https://cagrcalculator.net/.

What Compound Average Growth Rate Can Tell You?

The Compound Annual Growth Rate is not an exact return rate but a representation of the rate at which the investment would grow if it grows by the same rate each year, and the profits are reinvested on an annual basis. 

While this type of measurement does not reflect the reality of investment scenarios, it can smoothen returns. Hence, it is easy to comprehend and is useful when comparing different companies’ investment returns and measures against one another. This can reveal the company’s strengths and weaknesses and tell you how well a company stacks up against its competition. 

It is also beneficial when growth rates have been inconsistent and have fluctuated considerably as CAGR smoothens the return rate. This will help in comparing past performance between different investments. It also shows you that one year of negative returns can significantly impact the CAGR and that it can take several years to make up the loss to reach your target CAGR.

For example, you buy a stock for $1,000. At the end of year 1, that stock’s price falls to $500. Then at the end of year 2, it increases to $1,500. The CAGR, in this case, is 22.47%. However, because the stock price dropped by 50% (from $1,000 to $500) by the end of year 1, in year 2, the stock price has to increase by 200% (from $500 to $1,500) to get a CAGR of 22.47%.

What Are the Limitations of CAGR?

While CAGR is a highly useful metric, it is important to be aware of its limitations. Investors can end up making wrong decisions if they don’t consider these restrictions. Here are some of the limitations of Compound Annual Growth Rate calculations.

It ignores volatility – The CAGR’s biggest limitation is that it does not take volatility and risk into account. Instead, it calculates an average growth rate over a period of time. CAGR only compares the final value of an investment over a time period to its initial value. It does not show any extreme jumps or dips in the value of an investment. Furthermore, it does not measure what happened to an investment in a particular year.

Returns on most investments vary over time except for maturity bonds and deposits. A stock can jump 30% one year because of some potential technological advancement and fall the next year if that technological advancement does not materialize. CAGR smoothens out the volatility of the stock’s performance. As a result it provides a more realistic picture of how the stock may perform in the future.

Fund managers sometimes promote their funds by advertising the fund’s CAGR for the periods it made the most money. By intentionally excluding the years for which the returns are low, they make the investment look better than it is.

For example, take a fund with a starting value of $10,000 in 2000, $7,000 in 2001, $4,000 in 2002, $8,000 in 2003, and $13,000 in 2004. The investment company advertises that the CAGR of this fund was 48.12% over the past three years. This is technically correct because it grew from $4,000 to $13,000 in 3 years. However, they fail to mention that the fund’s CAGR of the last 5 years was only 5.39% as its beginning value was $10,000 and its ending value was $13,000.

It is not guaranteed return – CAGR is based on historical data and is not a guarantee that future returns will be the same. Even though the growth rate has been good in the past, it might go down in the future. The shorter the duration used in the analysis, the less likely the CAGR will meet its target rate.

It only considers the initial investment – CAGR is only appropriate for lump sum investments. It does not suit investments like Systematic Investment Plans (SIPs). SIPs allow investors to invest small amounts periodically instead of one big lump sum. CAGR does not consider investments made at different intervals and only accounts for the beginning value in its calculation. It does not consider the funds added to or withdrawn from a portfolio over the specified period.

Short timeframes will be less accurate – The CAGR is affected in a big way by the time period analyzed. There are many factors that contribute to an investment’s return during a particular year. The returns in one year can easily be an outlier to the norm. To get a better picture of statistical probability, you should look at the average over a longer period of time. Furthermore, it is a good idea to calculate CAGR over various periods to see if there is a statistical difference.

Using CAGR for Investment Decisions

The CAGR formula can help investors devise methods to estimate future profits and evaluate past returns. The formula can be tweaked to determine the present or future value of an investment and calculate the return’s hurdle rate. For example, if an investor has an amount to invest today and knows how much he needs his investment to be worth after a few years, he can calculate how much the return rate has to be to reach that desired return in that time period. This can also help the investor determine the ideal amount to invest to reach his/her financial goals.

CAGR is also very valuable when comparing different investments with each other. For example, if an investor placed an amount in a savings account with a fixed interest rate for 5 years and the same amount into a mutual fund, the comparison could be difficult because the fund’s return rate will be different every year. Comparing the Compound Annual Growth Rates of both investments will give the investor a clear picture of the fund’s past performance, which helps the investor decide which investment will be more profitable.

The Compound Annual Growth Rate is often used as a tool for assessing a stock’s performance over a time period in the past. Once calculated, investors can use it to compare that stock’s performance against other individual stocks or against the performance of stock indexes and other investment benchmarks.

The Compound Annual Growth Rate can be beneficial to an investor who is planning to invest in a mutual fund as it can help gauge the fund’s performance by making it easier to see the fund’s annual growth rate. However, besides CAGR, other measurements should be used as well to evaluate a fund’s performance. Total Return and Internal Rate of Return (IRR) are other beneficial metrics for mutual fund performance evaluation. 

It is essential when you’re using CAGR to compare investments to make sure that you are comparing apples with apples. It is important to note that two investments can have the same CAGR, but one can be a better investment. For example, remember that risk is not considered in the Compound Annual Growth Rate. So, if 2 investments have the same growth rate, but one is extremely volatile, and the other investment is very stable, the investment that is not volatile is the better one.

Also, make sure you know what time period the Compound Annual Growth Rate is for. For example, the CAGRs for investment A and investment B are 50%. However, the specified time period for investment A is 20 years and the specified time period for investment B is 2 years. Investment A is definitely the preferred investment as it has an average 50% return rate for 20 years instead of the same return rate for a lot shorter period of only 2 years for investment B.

CAGR Versus Average Annual Growth Rate

The Average Annual Growth Rate (AAGR) measures the average increase in the value of an investment or asset over a period of a year. It is calculated by taking the sum of the average growth rates in a specified number of periods, divided by the total number of periods. 

Let’s use a previous example again:

Scenario:
Company X invests $2000 in an asset fund in the first year for a period of 4 years.
The year-end value in each year is:
year 1: $3,000
year 2: $4,500
year 3: $2,000
year 4: $6,000

The CAGR of the investment is 31.61% (6000/2000) to the 1/4th power minus 1.

year 1 growth: 50%
year 2 growth: 50%
year 3 growth: - 55.5%
year 4 growth: 200%

The AAGR for this example is (50% + 50% – 55.5% + 200%) / 4 = 61.11%

The AAGR helps determine long-term trends. It measures the average return rate or growth of an investment over a series of equally spaced time periods. It does not take into account the investment’s overall risk or periodic compounding. Furthermore, it does not account for the timing of returns. In some cases, it can be misleading because it can overestimate the growth of an investment.

For example, add year 5 to the scenario above. Year 5 shows a year-end value of $2,000. The percentage growth rate for Year 5 is – 66.7% (from $6,000 to $2,000). 

The resulting AAGR would be (50% + 50% – 55.5% + 200% – 66.7%) / 5 = 35.6%%.

However, this investment’s return is 0% because the beginning value is $2,000, and the ending value is still $2,000.  The CAGR, in this case, is = 0

Depending on the situation, it may be more useful to calculate the CAGR. The CAGR smooths out an investment’s returns and diminishes the effect of the volatility of periodic returns. 

CAGR Versus Internal Rate of Return

Compound Average Grwoth Rate and Internal Rate of Return (IRR) are two important financial metrics used for calculating investment returns. While CAGR measures the return rate of an investment over time and only considers the initial investment (beginning value) and one ending value, IRR calculates the performance more complexly. The IRR calculation includes multiple cash inflows and outflows to calculate the return on investment.

IRR involves complex calculations and is often used for complicated projects and investments with multiple inflows and outflows. A mathematical calculator, accounting software, or Excel is necessary for IRR calculations. In contrast, the Compound Average Growth Rate is a straightforward calculation that can often be done manually.

CAGR Versus Absolute Return

Many people look at their investment returns in absolute terms. Absolute Returns show the percentage of your investment growth over the entire investment duration, however long that may be. 

Example:
Investor X put $20,000 in a mutual fund in 2000
The value of the investment is $35,000 in 2020 
Absolute Return = 75%, CAGR = 2.84%

In absolute terms, investor X has a 75% return on his investment. While initially, this might sound good, it does not give you the full picture because it does not consider the 20-year time frame. The Compound Annual Growth Rate is only 2.84%, which is not very impressive. 

As an investor, it is important to know how well your investments have performed on average per year. CAGR can be very helpful in such a situation. The example shows the Compound Annual Growth Rate will give you a better picture of the return on investments than the Absolute Return.

Conclusion

The CAGR is a simple yet valuable measure to evaluate different investment options. It analyzes an investment’s performance over a period of time. However, it is important to realize that it doesn’t take volatility and risk into account. Besides, It cannot be used in situations where investments and withdrawals are made at different intervals. It only takes the beginning and ending value of the investment into consideration.

Besides using CAGR to measure and compare investment performance, you should use other methods such as fundamental and technical analyses. Also, make sure when comparing one investment with another that you are comparing apples to apples, not only in terms of the investment type but also regarding the investment duration.

Vikram R
Vikram Raghavan is a value investor, technologist, and Finexy co-founder. In addition to stock market investing, Vik also invests and advises startups on growth marketing and product management. Vik's work is focused on themes of marketplaces, micro-entrepreneurship, marketing automation, and user growth. Previously, Vikram led product and growth teams at Overstock.com, focusing on efforts across acquisition, new user experience, churn, and notifications/email. He holds an MBA in Finance from Temple University and a B.S. in Computer Information Systems and Finance from Bemidji State University.