Compound annual growth rate

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.

In practice, CAGR calculations are often performed in Microsoft Excel. A convenient built-in function is =RRI(nper, pv, fv), where nper represents the number of periods, pv denotes the present value (initial investment), and fv represents the future value (final value of the investment). The RRI function (Return Rate on Investment) returns the equivalent constant interest rate per period, effectively matching the CAGR when applied over a specified period.{{cite web |title=How to Calculate CAGR in Excel

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.

References

References

1. (3 December 2010). "The Handbook of Traditional and Alternative Investment Vehicles: Investment Characteristics and Strategies". John Wiley & Sons.
2. root. "Compound Annual Growth Rate (CAGR) Definition {{!}} Investopedia".
3. Emily Chan. (27 November 2012). "Harvard Business School Confidential: Secrets of Success". John Wiley & Sons.
4. (January 11, 2008). "How is average annual growth calculated?". Bureau of Economic Analysis.
5. "Compound Annual Growth Rate CAGR: Summary and Forum".
6. (January 11, 2008). "How is average annual growth calculated?". Bureau of Economic Analysis.