Compound annual growth rate
Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry or sector . CAGR is equivalent to the more generic exponential growth rate when the exponential growth interval is one year. Formula. CAGR is defined as: where formula_2 is the initial value, formula_3 is the end value, and formula_4 is the number of years. Actual or normalized values may be used for calculation as long as they retain the same mathematical proportion. Example. In this example, we will compute the CAGR over a three-year period. Assume that the year-end revenues of a business over a three-year period, formula_5, have been: Therefore, to calculate the CAGR of the revenues over the  three-year period spanning the "end" of 2004 to the "end" of 2007 is: Note that this is a smoothed growth rate per year. This rate of growth would take you to the ending value, from the starting value, in the number of years given, if growth had been at the same rate every year. Verification: Multiply the initial value (2004 year-end revenue) by (1 + CAGR) three times (because we calculated for 3 years). The product will equal the year-end revenue for 2007. This shows the compound growth rate: For "n" = 3: For comparison: In contrast  to CAGR, you cannot obtain formula_3 by multiplying the initial value, formula_2, three times by (1 + AMR) (unless all annual growth rates are the same). Applications. These are some of the common CAGR applications: