What it means
A company's revenue grew from $10 million to $20 million over five years. It did not grow by 20% a year (which would give $24.9 million) nor by 100% over five years divided by five; it grew at a compound rate of about 14.9% a year, because each year's growth built on the previous year's larger base.
CAGR is that rate. The measure exists because growth compounds and simple averages mislead.
Revenue that grows 50% one year and falls 50% the next has an average annual change of zero but has actually fallen 25% (from 100 to 150 to 75). CAGR, calculated from the endpoints, gives the true annualised result: minus 13.4% a year over two years.
For any series with variable growth, CAGR is the rate that a smooth series would have needed to reach the same end. Its uses are wide.
Investment returns are quoted as CAGR (an investment that grew from $1,000 to $2,000 in ten years returned 7.2% a year). Company growth is described by CAGR (revenue CAGR of 12% over five years).
Market forecasts are expressed as CAGR (a market expected to grow at 8% a year to a given size). Targets are set as CAGR (double revenue in five years means a 14.9% CAGR).
Comparisons between companies or periods of different lengths use CAGR to put them on a common annual basis. The limitations follow from the arithmetic.
CAGR uses only the first and last values, so a series that rose steadily and one that collapsed and recovered to the same endpoint show the same CAGR; investors and analysts look at the year-by-year figures as well. The start and end points can be chosen to flatter: measuring from a bad year to a good one produces a high CAGR that the trend does not support.
CAGR assumes reinvestment or compounding, which is right for growth and investment returns but not for some cash flow measures. And a CAGR over a short period (two or three years) can be dominated by one unusual year.
Related measures address some of these. The year-on-year growth series shows the path.
A regression trend rate fits a line to all the points rather than the endpoints. The internal rate of return generalises CAGR to series with intermediate cash flows.
Rolling CAGRs (five-year CAGR measured each year) show whether growth is accelerating or slowing. In practice, CAGR is quoted with its period and its endpoints, and a careful reader checks whether those endpoints are representative and asks for the intervening years.
In practice
Real-world examples.
Example
An analyst reports that a retailer's revenue CAGR over ten years was 6.5%, while its profit CAGR was 2.1%, showing margin erosion.
Example
A market research firm forecasts a 9% CAGR for a product category, implying the market will grow 54% in five years.
Example
A pension fund reports a 7.4% CAGR on its assets over twenty years, against a target of inflation plus 4%.
Think of it
“CAGR is like calculating the steady speed needed to drive from A to B on time, even if you actually drove faster or slower at different points.
Formula
Calculation
CAGR = (Ending value / Starting value) to the power of (1 / Number of years) minus 1
Number of years = Ending year minus Starting year (for annual data), or exact years as a fraction for other periods
Ending value implied by a CAGR = Starting value x (1 + CAGR) to the power of Years
Years to reach a target = ln(Target / Start) / ln(1 + CAGR)
Worked example 1, revenue growth. A company's revenue: year 0 $24,000,000; year 1 $27,500,000; year 2 $26,800,000; year 3 $31,900,000; year 4 $38,200,000; year 5 $42,600,000.
- CAGR over 5 years = ($42,600,000 / $24,000,000) to the power of (1/5) minus 1 = 1.775 to the power 0.2 minus 1 = 1.1216 minus 1 = 12.2%
- Check: $24,000,000 x 1.122 to the power 5 = $24,000,000 x 1.777 = $42,650,000, close to the actual $42,600,000
- Year-on-year growth: 14.6%, minus 2.5%, 19.0%, 19.7%, 11.5%. The CAGR of 12.2% summarises a path that included a decline and two years near 20%
- Endpoint sensitivity: measured from year 1 to year 5 (4 years): ($42,600,000 / $27,500,000) to the power 0.25 minus 1 = 1.549 to the power 0.25 minus 1 = 11.6%. From year 2 (a dip) to year 5 (3 years): ($42,600,000 / $26,800,000) to the power (1/3) minus 1 = 1.590 to the power 0.333 minus 1 = 16.7%. A presentation choosing year 2 as the base would show a growth rate a third higher than the five-year figure
Worked example 2, investment return. An investor put $50,000 into a fund on 1 January and it was worth $83,000 six and a half years later.
- CAGR = ($83,000 / $50,000) to the power (1/6.5) minus 1 = 1.66 to the power 0.1538 minus 1 = 1.0810 minus 1 = 8.1% a year
- Comparison: a bond returning 5% a year over the same period would have grown $50,000 to $50,000 x 1.05 to the power 6.5 = $68,650. The fund outperformed by 3.1 points a year, or $14,350 in total
Worked example 3, target setting. A company with revenue of $80,000,000 sets a target of $150,000,000 in five years.
- Required CAGR = ($150,000,000 / $80,000,000) to the power 0.2 minus 1 = 1.875 to the power 0.2 minus 1 = 1.134 minus 1 = 13.4% a year
- If the company grows at 10% a year instead: after 5 years, $80,000,000 x 1.611 = $128,900,000, short by $21,100,000
- Years needed at 10% to reach $150,000,000: ln(1.875) / ln(1.10) = 0.6286 / 0.0953 = 6.6 years
Worked example 4, the average trap. A start-up's customer count: 1,000, then 3,000 (up 200%), then 2,400 (down 20%), then 3,600 (up 50%). Average of the annual growth rates = (200% minus 20% + 50%) / 3 = 76.7%. CAGR = (3,600 / 1,000) to the power (1/3) minus 1 = 3.6 to the power 0.333 minus 1 = 1.533 minus 1 = 53.3%. The simple average overstates the compound rate by 23 points; the CAGR is the rate that actually gets from 1,000 to 3,600 in three years.Case study
Seen in the real world.
A company seeking investment presented a slide showing "revenue CAGR of 34%" over three years. The investor's analyst asked for the annual figures: revenue had been $4,000,000, $3,200,000, $6,500,000 and $9,600,000. The CAGR was correct as calculated from year 0 to year 3.
But year 0 had been a year of disruption when a major customer was lost, year 1 had fallen further, and the "growth" from $4,000,000 to $9,600,000 included the recovery of the lost customer in year 2. Measured from the company's pre-disruption revenue of $6,000,000 two years before year 0, the five-year CAGR was 9.9%.
The analyst also noted that year 3 included $1,500,000 of one-off project revenue; on a recurring basis, year 3 was $8,100,000 and the three-year CAGR from year 0 was 26.5%, or from the pre-disruption base, 6.2%. The investor priced the business on a sustainable growth rate of 8% to 10%, less than a third of the headline, and the company's founder, shown the analysis, agreed that the slide had told the truth about two dates and nothing about the business.
Watch out
Common mistakes.
- Averaging annual growth rates instead of calculating the compound rate, which overstates growth for any volatile series.
- Choosing a trough as the start point or a peak as the end point, which produces a CAGR that the underlying trend does not support.
- Quoting a CAGR without the period or the annual figures, which hides volatility and the path.
Questions
People also ask.
What is the difference between CAGR and average annual growth?
Average annual growth is the arithmetic mean of each year's percentage change; it ignores compounding and overstates the true rate for volatile series. CAGR is the geometric rate that connects the endpoints and represents the true annualised growth.
How many years should a CAGR cover?
Enough to smooth unusual years, typically three to five for company metrics and five to ten for investment returns. Short-period CAGRs are dominated by single years.
Can CAGR be negative?
Yes: if the ending value is below the starting value, the CAGR is negative, representing the compound annual rate of decline.
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