Compound annual growth rate

Compound annual growth rate (CAGR) is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period. CAGR smoothes the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of various data values, such as revenue growth of companies, or of economic values, over time.

Origin of CAGR

Compound interest is an idea used in the CAGR formula that dates back to ancient times when compounding was practiced by the Babylonians and Egyptians. However, it was not until after the 1950s that people began using a specialized term, “compound annual growth rate,” widely across various forms of financial studies, especially with the emergence of increased importance on evaluating investment performances. Although the exact date when this term originated is unknown, its incorporation signified a rising demand for uniform techniques in assessing investment return evolution across different periods.

Equation

For annual values, CAGR is defined as:

$\mathrm {CAGR} (t_{0},t_{n})=\left({\frac {V(t_{n})}{V(t_{0})}}\right)^{\frac {1}{t_{n}-t_{0}}}-1$

where $V(t_{0})$ is the initial value, $V(t_{n})$ is the end value, and $t_{n}-t_{0}$ is the number of years.

CAGR can also be used to calculate mean annualized growth rates on quarterly or monthly values. The numerator of the exponent would be the value of 4 in the case of quarterly, and 12 in the case of monthly, with the denominator being the number of corresponding periods involved.

CAGR Calculator

The CAGR calculator is an online tool created for ease in working out the compound annual growth rate with respect to investments or financial metrics. It enables users to calculate the CAGR by instantly providing them with the two endpoint values, as well as the number of years between these two data points. The tool is very beneficial especially to investors and analysts, because through it, they can find out how well stocks, mutual funds, and other assets have performed on an average annual basis, factoring in compounding over a given period, without having to apply any formulas on their own.

Applications

These are some of the common CAGR applications:

• Calculating and communicating the mean 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.
• Calculating mean annualized growth rates of economic data, such as gross domestic product, over annual, quarterly or monthly time intervals.

See also

• Annual growth %
• Arithmetic mean
• Average annual return
• Continuous compounding
• Geometric mean
• Exponential growth
• Internal Rate of Return