# CAGR (compound annual growth rate)

Compound annual growth rate (CAGR) is an average growth rate over a period of several years. It is a geometric average of annual growth rates:

CAGR = (ending value ÷starting value)1/(number of years - 1

If a company had sales of £10m in 2005 and £15m in 2010 then the CAGR of its sales is: (15 ÷10)1/5 - 1 = .084 = 8.4%

If percentage growth rates are used it is important to remember to add one to each of them before calculating the geometric average. For example, the CAGR over two years of 10% one year and 20% the next is (1.1 ×1.2)1/2 - 1.

Although no historical data is a substitute for a forecast, the CAGR over a number of years (typically the last five) is a better indication of a trend than a single year's growth which may be atypically good or bad.

CAGR should be used because arithmetic averaging of growth numbers gives incorrect results. For example, if a company's sales rose from £10m in year one to £15m in year two and then fell back to £10m in year three, then there has been a 50% increase (year-on-year) followed by a 33% decrease (year-on-year). Adding these up would give 17% and therefore an arithmetic mean of 8.5%, whereas it is obvious that the average growth has been 0%. A geometric average gives the correct answer.