Compound growth rate

A simple average of monthly changes misleads. Growth of 50 per cent one month and a fall of 33 per cent the next averages out to a gain, yet the business ends where it began. The compound rate gives the single steady rate that matches what actually happened.

It also shows the power of consistency. A modest rate held every month beats a spike followed by a flat stretch, because every period grows from a larger base. As a rough guide, 7 per cent a month doubles a figure in about ten months.

• Measure over consistent periods, usually months.
• Use the compounding formula, not a simple average.
• Keep one-off jumps, such as a single large contract, separate from the repeatable rate.
• Track the rate over a rolling window of several months to see whether it is holding, rising or slipping.
• Set targets as a rate to sustain, such as 5 per cent a month, instead of one total to hit once.

Growth compounds when each period's gain is added to a base that already includes earlier gains. The formula is: end value divided by start value, raised to the power of one over the number of periods, minus one. Revenue that goes from 10,000 to 15,000 over six months has grown by about 7 per cent a month on a compound basis, because 1.07 multiplied by itself six times gives roughly 1.5.

When the period is a month, the figure is often called compound monthly growth rate. Over years it is the compound annual growth rate, or CAGR.

• Projecting a high early rate far into the future. Rates fall as a base grows.
• Using too short a window. Two months can say nothing about the trend.
• Applying it to a metric that can be zero or negative.