Compound annual growth rate

Compound annual growth rate (CAGR) is a business and investing specific term for the smoothed annualized gain of an investment over a given time period.^{[1]} CAGR is not an accounting term, but remains widely used, particularly in growth industries or to compare the growth rates of two investments because CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. CAGR is often used to describe the growth over a period of time of some element of the business, for example revenue, units delivered, registered users, etc.
Contents
Formula
 V(t_{0}) : start value, V(t_{n}) : finish value, t_{n} − t_{0} : number of years.
 Actual or normalized values may be used for calculation as long as they retain the same mathematical proportion.
 The CAGR can also be calculated as the geometric mean of 1 plus each year's return (i.e. +3% becomes 1.03 and 2% becomes 0.98), minus 1.^{[2]}
Example
Suppose the revenues of a company for four years, V(t) in above formula, have been:
Year 2004 2005 2006 2007 Revenues 100 115 150 200  t_{n} − t_{0} = 2007  2004 = 3
Then the CAGR of revenues over the threeyear period from the end of 2004 to the end of 2007 is:
Verification:If you multiply the initial value by (1 + CAGR) three times (because we calculated for 3 years) you will get exactly the final value again. This is:
For n = 3:
For comparison: the Arithmetic Mean Return (AMR) would be the sum of annual revenue changes (compared with the previous year) divided by number of years, or:
In contrast to CAGR, you cannot obtain V(t_{n}) by multiplying the initial value, V(t_{0}), three times by (1 + AMR) (unless all annual growth rates are the same). the Arithmetic Return (AR) or simple return would be the ending value minus beginning value divided by the beginning value:
Applications
These are some of the common CAGR applications:
 Calculating and communicating the average returns of investment funds^{[3]}
 Demonstrating and comparing the performance of investment advisors^{[3]}
 Comparing the historical returns of stocks with bonds or with a savings account^{[3]}
 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 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.
References
See also
Categories: Actuarial science
 Basic financial concepts
 Money
Wikimedia Foundation. 2010.
Look at other dictionaries:
compound annual growth rate — Annual return calculated based on each year s previous balances where each previous balance includes both the original principal and all interest accrued from prior years. Best defined by example. Bloomberg Financial Dictionary If you invest $100 … Financial and business terms
Compound Annual Growth Rate  CAGR — The year over year growth rate of an investment over a specified period of time. The compound annual growth rate is calculated by taking the nth root of the total percentage growth rate, where n is the number of years in the period being… … Investment dictionary
growth rate — compound annual growth rate for the number of full fiscal years shown. If there is a negative or zero value for the first or last year, the growth is N.M. (not meaningful). Bloomberg Financial Dictionary * * * growth rate ˈgrowth rate noun… … Financial and business terms
Growth rate — may refer to:*Exponential growth, a growth rate classification *Compound annual growth rate or CAGR, a measure of financial growth *Economic growth, the increase in value of the goods and services produced by an economy *Growth rate (group… … Wikipedia
compound growth rate — See: compound annual growth rate * * * compound growth rate compound growth rate ➔ growth rate * * * compound growth rate UK US noun [C] (also compounded growth rate, ABBREVIATION CGR, also … Financial and business terms
compound annual return — See: compound annual growth rate … Financial and business terms
Growth rates — Compound annual growth rate for the number of full fiscal years shown. If there is a negative or zero value for the first or last year, the growth is NM (not meaningful). The New York Times Financial Glossary … Financial and business terms
growth rates — compound annual growth rate for the number of full fiscal years shown. If there is a negative or zero value for the first or last year, the growth is N.M. (not meaningful). Bloomberg Financial Dictionary … Financial and business terms
Rate of return — In finance, rate of return (ROR), also known as return on investment (ROI), rate of profit or sometimes just return, is the ratio of money gained or lost (whether realized or unrealized) on an investment relative to the amount of money invested.… … Wikipedia
Compound Return — The rate of return, usually expressed as a percentage, that represents the cumulative effect that a series of gains or losses have on an original amount of capital over a period of time. Compound returns are usually expressed in annual terms,… … Investment dictionary