Compound annual growth rate

Measure of investment growth rate

Compound Annual Growth Rate (CAGR) is a useful measure of growth over multiple time periods. It is particularly valuable in the fields of finance and investment, where it is used to describe the geometric progression ratio that provides a constant rate of return over a time period.

Definition

CAGR is the mean annual growth rate of an investment over a specified time period longer than one year. It is calculated using the formula:

<math>\text{CAGR} = \left( \frac{V_f}{V_i} \right)^{\frac{1}{t}} - 1</math>

where:

• <math>V_f</math> is the final value,
• <math>V_i</math> is the initial value, and
• <math>t</math> is the number of years.

CAGR is a useful measure because it smooths out the effects of volatility and provides a clearer picture of an investment's performance over time.

Applications

CAGR is widely used in various fields, including:

• Finance: To compare the historical returns of investments or to project future growth rates.
• Business: To assess the growth of revenue, profits, or other key performance indicators over time.
• Economics: To evaluate the growth of economic indicators such as GDP or population.

Advantages

• Simplicity: CAGR provides a single, easy-to-understand number that summarizes the growth rate over a period.
• Comparability: It allows for the comparison of growth rates across different investments or business metrics.
• Volatility Adjustment: By smoothing out fluctuations, CAGR gives a more stable view of growth.

Limitations

• Ignores Volatility: While it smooths out volatility, it does not account for the risk or variability of returns.
• Assumes Constant Growth: CAGR assumes that growth occurs at a constant rate, which may not reflect reality.
• Not Suitable for Short Periods: It is less meaningful for periods shorter than one year.

Calculation Example

Suppose an investment grows from $1,000 to $2,000 over 3 years. The CAGR is calculated as follows:

<math>\text{CAGR} = \left( \frac{2000}{1000} \right)^{\frac{1}{3}} - 1 = 0.2599 \text{ or } 25.99\%</math>

Also see

• Annual growth rate
• Return on investment
• Net present value
• Internal rate of return