# Compound Annual Growth Rate (CAGR)

## What is Compound Annual Growth Rate (CAGR)?

Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry or sector.

CAGR is equivalent to the more generic exponential growth rate when the exponential growth interval is one year.

Compound annual growth rate (CAGR) is the metric that allows an investor to compare the return rates of their investments over a given time period. In simpler terms, the compound annual growth rate removes the volatility a stock might experience.

CAGR tells you the annual growth the stock had as if it had grown steadily over the course of those same years. It’s important to remember that if you are calculating for multiple years, the returns are reinvested throughout the desired period.

Compound annual growth rate can be used to analyze past investments in order to compare the performance of them. You can also use it to try and forecast the expected future returns on prospective investments.

## Compound Annual Growth Rate Formula

The compound annual growth rate formula requires only the ending value of the investment, the beginning value, and the number of compounding years to calculate. It is achieved by dividing the ending value by the beginning value and raising that figure to the inverse number of years before subtracting it by one.

Where:

• EV – Ending Value
• BV – Beginning Value
• N – Number of Compounding Periods

The name of the variables may change slightly, but the meaning behind them stays the same. For this article, we will use investment ending and beginning balance but you might see it referred to as ending (EV) and beginning value (BV) or simply ending (EB) and beginning balance (BB).

When thinking about these variables to evaluate past investments, use the actual numbers from the stock investment. You can plug them into the number of periods. This means that if you originally spent \$100 on 3 shares and, as of today, the shares are worth \$45 each, the ending balance would be \$135. This will allow you to see which of your investments have performed better historically.

If your goal is to try and predict a future return, then you would put the desired theoretical investment ending balance and the actual current stock price into the formula. For the number of periods, you would substitute the desired length of time. You can then compare the compound annual growth rate for that stock’s past performance to the predicted compound annual growth rate to see if the number is a realistic projection.

### What is the difference between simple growth rate and compound annual growth rate?

The simple growth rate formula is used to determine the percentage increase of a value within a particular period of time, which is usually the same as the whole investment period (e.g., three years, ten months, etc.) In other words, a simple growth rate says how much an investment is going to yield within its time horizon.

On the other hand, the compound annual growth rate reflects the average rate of return that is required for an investment to grow from its initial balance to its final balance within the particular period on a yearly basis. In the case of CAGR, it doesn’t matter what is the time horizon of the investment. Note that unlike the simple growth rate, the compound annual growth rate enables you to compare investments with different time horizons.

## Compound Annual Growth Rate Example

### Example 1

Let’s do a few examples to show the versatility of the compound growth rate. The first 2 investments that you want to evaluate are stocks’ that have been in your portfolio for a few years now. You’ve had one investment for 4 years with the starting balance of \$625 and the end balance of \$890. The other investment you’ve had for 7 years and had a starting balance of \$400 and the end balance of \$945.

First, we’ll break it down to identify the meaning and value of the different variables in this problem. Then, for each, we can apply the values to our variables and calculate the compound annual growth rate. Now let’s use our formula: compound annual growth rate = ((investment ending balance / investment beginning balance) (1/n)) – 1

#### Investment A

• Investment ending balance = \$890
• Investment beginning balance = \$625
• Number of periods = 4

In this case, the compound annual growth rate would be 0.0924 or 9.24%.

#### Investment B

• Investment ending balance = \$945
• Investment beginning balance = \$400
• Number of periods = 7

In this case, the compound annual growth rate would be 0.1307 or 13.07%. In this example of analyzing past performance investment b has a higher rate of return annually.

### Example 2

Now let’s do an example where we are looking to predict the future growth of these same two investments. To do this we will need to choose the amount that we want the ending balance to be. To keep things simple let’s say that we want both of our investments to have the ending balance of \$2000 and we want them to reach that amount in 6 more years.

Let’s break down the new variable values for each investment.

#### Investment A

• Investment ending balance = \$2000
• Investment beginning balance = \$890
• Number of periods = 6

In this case, the compound annual growth rate would be 0.1445 or 14.45%.

#### Investment B

• Investment ending balance = \$2000
• Investment beginning balance = \$945
• Number of periods = 6

In this case, the CAGR would be 0.1331 or 13.31%. Looking at these numbers you can predict that investment B will reach \$2000 in six years with a much higher degree of confidence since the compound annual growth rate is fairly close to the historic number.

Remember that since this is just a prediction there is no guarantee that investment won’t have a higher return rate as the market is volatile.

## Compound Annual Growth Rate Analysis

The compound annual growth rate formula is a great tool for investors when they want to analyze the return rate of their investments. Because it smooths the performance of the investment over time, it allows for comparison between various investments over the course of time, as well as predicting future investment value.

This can be especially essential when an investor needs to determine which of their investments are performing well and which are not. This means that emotion can be more easily removed from the decision process of buying and selling an investment.

## Applications

These are some of the common CAGR applications:

• Calculating and communicating the average returns of investment funds
• Demonstrating and comparing the performance of investment advisors
• Comparing the historical returns of stocks with bonds or with a savings account
• Forecasting future values based on the CAGR of a data series (you find future values by multiplying the last datum of the series by (1 + CAGR) as many times as years required). As with every forecasting method, this method has a calculation error associated.
• Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, market share, costs, customer satisfaction, and performance.

## Compound Annual Growth Rate Conclusion

• The compound annual growth rate measures how much cash is generated from a business’s everyday operating activities and processes over a specific length of time.
• It can be used to analyze past investment performance or to try and predict future investment performance.
• The formula for CAGR requires three variable variables: investment ending balance, investment beginning balance, number of compounding periods