Compound Annual Growth Rate

The compound annual growth rate (CAGR) measures the annual change in earnings, an investment, or some other financial amount. The compound annual growth rate assumes the initial amount grows at the same rate every year. The compound annual growth rate also assumes each annual increment compounds during the period measured. For example, suppose an investor buys stock that costs $2,000 in year 1 and sells it two years later for $3,000. The total return is 50% ($3,000/$2,000); but the annual return is not 25%, because $2,000 X 125% X 125% = $3,125. The compound annual growth rate finds the answer using the formula
((Ending Value) /(Beginning Value))^(1/Number of years)-1. The compound annual growth rate in this example would thus be ((3,000) /(2,000))^(1/2) -1 = (1.5^0.5)-1=22.47%. (Easy-to-use calculators for the compound annual growth rate are on the Internet.) The compound annual growth rate thus smoothes the rate of growth. Indeed, a major drawback of the compound annual growth rate is that it says nothing about volatility. But for making growth comparisons over time, the compound annual growth rate is extremely useful.