Graham Number: formula
CFI: Graham-number derivation in The Complete Guide to Trading
Graham Number: worked example
| Earnings per share | $4.00 |
|---|---|
| Book value per share | $30 |
| Current share price | $45 |
| Graham number | $52 |
| Margin of safety at the current price | 13.4% |
The formula was designed for mature, profitable industrial companies in Graham's time and fails for growth and asset-light businesses that trade far above it. It does not consider debt, competitive position or future earnings. It needs positive earnings and book value, so it cannot evaluate unprofitable firms.
Modern markets rarely offer many stocks that pass.
Graham Number: changing Earnings per share
| Earnings per share | Graham number | Margin of safety at the current price |
|---|---|---|
| $3.20 | $46 | 3.2% |
| $3.60 | $49 | 8.7% |
| $4.00 (example) | $52 | 13.4% |
| $4.40 | $54 | 17.4% |
| $4.80 | $57 | 20.9% |
Graham Number: compare input ranges
| Input | Tested from | To | Graham number: low input | Graham number: high input | Swing |
|---|---|---|---|---|---|
| Earnings per share | $3.60 | $4.40 | $49 | $54 | $5.20 (10%) |
| Book value per share | $27 | $33 | $49 | $54 | $5.20 (10%) |
| Current share price | $41 | $50 | $52 | $52 | $0.00 |
Graham Number: individual input comparisons
| Input | Value | Graham number | Margin of safety at the current price |
|---|---|---|---|
| Earnings per share | $3.20 | $46 | 3.2% |
| $3.60 | $49 | 8.7% | |
| $4.00 | $52 | 13.4% | |
| $4.40 | $54 | 17.4% | |
| $4.80 | $57 | 20.9% | |
| Book value per share | $24 | $46 | 3.2% |
| $27 | $49 | 8.7% | |
| $30 | $52 | 13.4% | |
| $33 | $54 | 17.4% | |
| $36 | $57 | 20.9% | |
| Current share price | $36 | $52 | 30.7% |
| $41 | $52 | 21.1% | |
| $45 | $52 | 13.4% | |
| $50 | $52 | 3.8% | |
| $54 | $52 | -3.9% |
Graham Number: combined input changes
| Earnings per share / Book value per share | $24 | $30 | $36 |
|---|---|---|---|
| $3.20 | $42 | $46 | $51 |
| $3.60 | $44 | $49 | $54 |
| $4.00 | $46 | $52 | $57 |
| $4.40 | $49 | $54 | $60 |
| $4.80 | $51 | $57 | $62 |
Graham Number: which assumptions move the result?
Graham Number: values and definitions
| Quantity and definition | Value used |
|---|---|
| Earnings per share | $4.00 |
| Book value per share | $30 |
| Current share price | $45 |
| Graham number | $52 |
| Margin of safety at the current price | 13.4% |
Graham Number: half and double Earnings per share
| Earnings per share | Graham number |
|---|---|
| $2.00 | $37 |
| $4.00 | $52 |
| $8.00 | $73 |
Earnings per share and book value per share should be recent and conservative: Graham advised using average earnings over several years to avoid a lucky peak. Take both from the company's filings and use the current share price for the margin of safety. The 22.5 constant comes from Benjamin Graham's criteria of a P/E of no more than 15 and a price-to-book of no more than 1.5, multiplied together.
Common error: Buying anything under the number. It ignores growth and debt, and it was built for stable industrial companies, so it screens out most modern high-growth firms by design.
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Benjamin Graham's number sets a ceiling on what a defensive investor should pay: the square root of 22.5 times earnings per share times book value per share. The 22.5 is a P/E of 15 times a price-to-book of 1.5. With $4 of earnings and $30 of book value, the ceiling is about $52, so a $45 price leaves a margin of safety near 13 percent.
Use normalized earnings, not a peak year. One unusually strong year inflates the ceiling and makes almost any price look safe.
Cross-check with the P/E ratio, PEG ratio and book value per share calculators. The dividend payout ratio and market cap pages fill in the picture on income and size. Graham's own advice was to diversify and to require a margin of safety, so the number is a starting point.
Does the Graham number work for growth stocks?
Generally not. Growth companies trade well above it because their value depends on future earnings, so the formula flags them as expensive.
What is a margin of safety?
It is the gap between the estimated value and the price you pay, meant to protect against errors in the estimate. A larger margin means more protection.
Where does 22.5 come from?
It is Benjamin Graham's maximum P/E of 15 multiplied by his maximum price-to-book of 1.5. A stock at both limits has a price equal to the square root of 22.5 times EPS times book value per share.