What is compound annual growth rate?

Definition

Compound annual growth rate is the smoothed average yearly growth rate across several periods, often shortened to CAGR. On the books, this is a reading of a starting amount and an ending amount a few years apart, not an account and not a posted line.

Where it shows up

P&L: Related to the smoothed average yearly growth in a result across several years.

Balance Sheet: Related to the same smoothed growth in a balance when that is the base.

Cash flow: Related to the same smoothed growth in cash when that is the base.

See also: Year-Over-Year Growth · Revenue · Trailing Twelve Months

You will not find this rate as a line on the Income Statement. It is calculated from revenue or another result at two year-ends, then stated as one yearly percent.

The Balance Sheet can be the base when the question is about an asset or equity balance. The method is the same: start value, end value, and the number of years between them.

Cash can be the base too. The reading is still a smoothed yearly percent, not a cash-flow line.

Owners use it when a single year-over-year jump would mislead. One fat year and one thin year still collapse into one average rate.

A budget may cite a target CAGR. That is a plan number; the calculated rate on actuals is what happened.

How it works

Pick a starting amount and an ending amount a few years later. Count the years of growth between those two points.

Year 1 to year 4 is three years of growth, not four. Divide the end by the start, raise that ratio to 1 divided by the number of years, then subtract 1.

A language school that grows from $50,000 of tuition in year 1 to $80,000 in year 4 has a ratio of 80,000 divided by 50,000, which is 1.6. Raise 1.6 to 1/3, subtract 1, and the smoothed yearly rate is about 17 percent.

That 17 percent is not any single year's actual change. Year 2 might have jumped 30 percent and year 4 only 5 percent; CAGR still reports the one rate that would turn $50,000 into $80,000 if every year grew the same.

The formula does not care about the path in between. It only uses the start, the end, and the years.

If the start is zero, the rate is not defined. State the dollar change instead.

A run rate annualizes one recent period. CAGR uses several years of actuals and smooths them.

Net income can use the same math. The method does not change: end divided by start, raised to 1 over years, minus 1.

The general ledger already holds the yearly totals. You are reading issued years, not posting a journal entry.

Example

A language school recorded $50,000 of tuition in year 1 and $80,000 in year 4. Three years of growth sit between those two year-ends.

80,000 divided by 50,000 is 1.6. 1.6 to the power of one-third, minus 1, is about 17 percent, and that 17 percent is the compound annual growth rate.

If year 2 was $70,000 and year 3 was $72,000, those middle years do not enter the formula. The smoothed rate still uses only $50,000 and $80,000.

If the owner had compared only year 3 to year 4, that single pair would be year-over-year growth, not CAGR. CAGR is the multi-year average, not one jump.

The same 17 percent can be checked forward. $50,000 grown at 17 percent a year for three years lands near $80,000, which is the point of the smoothing.

Common mix-ups

Compound annual growth rate is not year-over-year growth. Year-over-year growth is one period versus the same period a year earlier; CAGR is the smoothed yearly rate across several years.

Compound annual growth rate is not a run rate. A run rate annualizes a recent month or quarter; CAGR uses a start year and an end year.

Compound annual growth rate is not a forecast. A forecast is an updated projection; CAGR describes growth that already happened, unless someone is using it as a target.

Related terms

• Year-Over-Year Growth: The change versus the same period a year earlier.
• Revenue: The total value of goods and services the business earned in a period.
• Trailing Twelve Months: The most recent twelve months of results, regardless of fiscal year.
• Forecast: An updated projection of where the numbers are actually heading.
• Run Rate: Annualizing a recent period's results as a rough forward estimate.
• Annual Recurring Revenue: Monthly recurring revenue expressed on a yearly basis.
• Budget: The approved plan of revenue and spending for a coming period.
• Net Income: What is left from revenue after every expense, including interest and taxes, is subtracted.