# What is the 'Compound Annual Growth Rate - CAGR

CaseX - Inventor Steven D. Cabouli.

## What is the 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year.

To calculate compound annual growth rate, divide the value of an investment at the end of the period in question by its value at the beginning of that period, raise the result to the power of one divided by the period length, and subtract one from the subsequent result.

This can be written as follows:

CAGR can also be calculated using Investopedia's own Compound Annual Growth Rate Calculator.

## BREAKING DOWN 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially an imaginary number that describes the rate at which an investment would have grown if it had grown at a steady rate, which virtually never happens in reality. You can think of CAGR as a way to smooth out an investment’s returns so that they may be more easily understood.

Don't worry if this concept is still fuzzy to you – CAGR is one of those terms best explained through example. Suppose you invested \$10,000 in a portfolio on Jan 1, 2005. Unsurprisingly, your portfolio would likely grow at an inconsistent rate. Let us assume that by Jan 1, 2006, your portfolio had grown to \$13,000. Let us also assume that it then grew to \$14,000 by the same time in 2007, and spiked during that year, ending up at \$19,500 by Jan 1, 2008.

To calculate the CAGR of your portfolio from the period from Jan 1, 2005 to Jan 1, 2008, you would divide the final value of your portfolio by the portfolio’s initial value (\$19,500 / \$10,000 = 1.95). Next, you would  raise the result to the power of 1 divided by the number of years (1 / 3 = 1/3 or 0.3333). Finally, you would subtract 1 from the resulting value.

Doing the math, you would calculate:

[(19,500 / 10,000)^(1 / 3)] – 1

= (1.95 ^ 0.3333) – 1

= 1.2493 – 1

= 0.2493, or 24.93%.

Thus, the compound annual growth rate of your three-year investment is equal to 24.93%, representing the smoothed annualized gain you earned over your investment time horizon.

## Uses of the Compound Annual Growth Rate (CAGR)

CAGR is a relatively simple metric, since it merely measures the average rate of an investment’s growth over a variable period of time. Because of this simplicity, this metric is a flexible one and thus has a variety of uses.

Most simply, CAGR can be used to calculate the average growth of a single investment. Because of market volatility, the year-to-year growth of an investment may be difficult to interpret. For example, an investment may increase in value by 8% in one year, decrease in value by 2% the following year and increase in value by 5% in the next. With inconsistent annual growth, CAGR may be used to give a broader picture of an investment’s progress.

CAGR may also be used to compare investments of different types with one another. For example, suppose in 2010 you put \$10,000 into a savings account with a fixed annual interest rate of 1%, growing to a value of \$10,100 in 2011, \$10,201 in 2012 and \$10,303.01 in 2013. Say that in 2010, you wanted to pursue other investment options but, fearing market volatility, you only invested \$5,000 this time, into a portfolio with a varying growth rate. Suppose that the portfolio grew in value to \$5,114 in 2011, dropped to a value of \$5,098 in 2012 and grew to \$5,437 in 2013. Although the portfolio grew at an inconsistent rate and even lost value in 2012, the investment’s CAGR between 2010 and 2013 was 2.83% ((5,437/5,000)^(1/3) - 1 = 1.0874^0.3333 – 1 = 1.0283 – 1 = 0.0283 = 2.83%), substantially higher than the interest rate of the savings account. The portfolio, then, proved to be the more profitable investment.

CAGR can also be used to track the performance of various business measures of one or multiple companies alongside one another. For example, over a five-year period Big-Sale Stores’ market share CAGR may be 1.82% but its customer satisfaction CAGR over the same period might be -0.58%. In this way, comparing the CAGRs of measures within a single company may reveal that company’s strengths and weaknesses. However, comparing those CAGRs with those tracking the same measures in other companies may help situate this data within the scope of the market. For example, Big-Sale’s customer satisfaction CAGR might not seem so low if compared with SuperFast Cable’s customer satisfaction CAGR of -6.31% during the same period.

For more on the Compound Annual Growth Rate (CAGR), see: Compound Annual Growth Rate: What You Should Know.

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