Numbers every analyst uses
Percentages, growth and CAGR
Measure growth correctly: period growth, compound annual growth, and percentage points versus percent.
Learning objectives
- Calculate period-over-period growth
- Calculate a compound annual growth rate (CAGR) and explain why averaging growth rates misleads
- Distinguish a percentage-point change from a percent change
Results announcements, investor presentations and analyst reports are full of growth figures: revenue up 12%, margin up 150 basis points, five-year CAGR of 9%. Most of the errors in them come from three simple slips: the wrong base, the wrong number of years, and confusing percentage points with percent.
Getting these right is the first thing reviewers check, and the easiest way to lose credibility if you get them wrong.
Growth = (Current − Prior) ÷ Prior = Current ÷ Prior − 1
CAGR = (End value ÷ Start value)^(1 ÷ n) − 1
- n
- number of years *between* the start and end values: 2020 to 2024 is 4 years, not 5
- CAGR
- the constant yearly rate that turns the start value into the end value
Where the formula comes from. If something grows at a constant rate g for n years, it ends at Start × (1 + g)ⁿ. CAGR simply solves that equation for g: divide the end by the start to get the total growth factor, then take the n-th root to spread it evenly across the years. It answers the question "what steady rate would have got us from there to here?"
How practitioners use it. Suppose a fictional pharmacy chain, Dawa Pharmacies, grew revenue from SAR 40m in 2019 to SAR 58m in 2024. That is 5 years of growth, so CAGR = (58 ÷ 40)^(1/5) − 1 = 7.7% a year. An analyst can now compare it with the market's growth, with competitors' CAGRs over the same years, or with management's plan, and can run it forward: at the same rate, revenue would reach about SAR 72.5m three years later.
Its limits. CAGR depends entirely on the two end points. Starting from a weak year (a pandemic dip, say) flatters it, ending on one depresses it, so check which years were chosen and why. It hides the path between them: steady growth and a wild ride can share the same CAGR. And it cannot be calculated when the start value is zero or negative, as with a loss-making year's profit.
Data
| Actual | CAGR −13.4% | Average 0% | |
|---|---|---|---|
| Year 0 | 100 | 100 | 100 |
| Year 1 | 150 | 87 | 100 |
| Year 2 | 75 | 75 | 100 |
The CAGR line ignores the bumpy route but lands exactly on the actual end value of 75. Compounding the simple average of 0% instead predicts an end value of 100, hiding the 25% the investor actually lost.
Percentage points vs percent
When a rate changes, there are two ways to describe it. If a margin rises from 12% to 15%:
- it rose by 3 percentage points (15% − 12%), and
- it rose by 25% in relative terms (15% ÷ 12% − 1).
Both are correct, but they are not interchangeable. Analysts often use basis points (1 bp = 0.01 percentage point), so the same change is 300 bp.
Calculate
A company's net margin improved from 8% to 10%. By what percent did the margin increase (relative change, not percentage points)?
Calculate
Rawdah Home Retail Co. (a fictional retailer used later in the platform) reported revenue of SAR 1,240.0m in FY2023, 1,386.0m in FY2024 and 1,497.0m in FY2025. What is its revenue CAGR from FY2023 to FY2025?
Check your understanding
A shop's sales rise 10% one year and fall 10% the next. Compared with where they started, sales are now:
Challenge: growth analysis of a fictional start-up
Revenue (SAR thousands) for five years is in row 2. Calculate each year's growth (C3:F3), the number of years of growth from the year headers (B5), the simple average of the growth rates (B6) and the CAGR (B7). Then show what each rate implies for 2024 revenue starting from 2020 (B8 and B9) and compare with the actual figure in F2. Finally, measure the change in operating margin in percentage points (B13) and in relative terms (B14).
| A | B | C | D | E | F | |
|---|---|---|---|---|---|---|
| 1 | Year | 2020 | 2021 | 2022 | 2023 | 2024 |
| 2 | Revenue (SAR k) | 500 | 850 | 680 | 1,020 | 1,122 |
| 3 | Growth vs prior year | |||||
| 4 | ||||||
| 5 | Number of years of growth (n) | |||||
| 6 | Average of yearly growth rates | |||||
| 7 | CAGR | |||||
| 8 | 2024 revenue implied by the average | |||||
| 9 | 2024 revenue implied by CAGR | |||||
| 10 | ||||||
| 11 | Operating margin, 2020 | 6.0% | ||||
| 12 | Operating margin, 2024 | 9.0% | ||||
| 13 | Change in margin (percentage points) | |||||
| 14 | Change in margin (relative %) |
You're learning as a guest — exercises are checked, but progress isn't saved. Create a free account to keep it.