Compound Annual Growth Rate

The compound annual growth rate (CAGR) measures the constant annual rate at which an initial value would have grown to reach a final value over a multi-year period, assuming annual compounding. It is a smoothed, geometric growth rate, not the arithmetic average of the actual yearly growth rates. Therefore, it does not imply that the variable grew at that rate in every year.

Calculation

If the initial value is Vi, the final value is Vf, and the period is n years, CAGR = [(Vf/Vi)^(1/n) - 1] × 100. The calculation uses the two endpoint values and the number of compounding periods.

• A value rising from 100 to 121 in two years has a CAGR of 10 per cent, because 100 × 1.10 × 1.10 = 121.
• CAGR incorporates the compounding effect, unlike a simple division of total percentage growth by the number of years.

Interpretation and uses

CAGR enables comparison of growth over periods of different lengths. It is commonly applied to GDP, income, investment, production, sales and population, provided the underlying series and measurement basis are comparable.

• CAGR may describe nominal or real growth depending on whether the data are measured at current or constant prices.
• It provides a single summary rate for the entire period and therefore makes long-term trends easier to communicate.

Limitations

CAGR depends only on the initial value, final value and duration. It conceals year-to-year volatility, intermediate declines and changes in the growth path.

• Two series can have the same CAGR despite having very different annual fluctuations.
• CAGR is a historical summary and does not by itself establish causation or predict future growth.
• Comparisons can mislead if base years, price measures, definitions or time periods differ.