Graham Number Calculator
From EPS and book value per share, estimate the price ceiling for a defensive investor via the Graham number: √(22.5 × EPS × BVPS).
Input Data
Results
At a glance:The Graham number = √(22.5 × EPS × BVPS), Benjamin Graham's valuation for a defensive investor's price ceiling. 22.5 = P/E cap 15 × P/B cap 1.5 — his rule that price must satisfy both conservative limits. When price is below the Graham number, by his standard it has a margin of safety (reasonable buy zone); above, it is expensive. It blends earnings (P/E) and assets (P/B) into one threshold, best for asset-heavy, steadily profitable traditional value stocks; it ignores growth and is unsuitable for high-growth or asset-light firms.
Formula
Graham number = √(22.5 × EPS × BVPS).
22.5 = 15 (P/E cap) × 1.5 (P/B cap).
$$\text{Graham} = \sqrt{22.5 \times EPS \times BVPS}$$$$22.5 = 15_{(P/E)} \times 1.5_{(P/B)}$$How to Use
- Enter trailing-12-month EPS.
- Enter book value per share (BVPS).
- View the Graham number and compare with the current price.
Graham number at various EPS and BVPS
| EPS | BVPS | Graham number |
|---|---|---|
| HK$1.50 | HK$12 | HK$20.12 |
| HK$3.00 | HK$20 | HK$36.74 |
| HK$5.00 | HK$15 | HK$41.08 |
| HK$2.00 | HK$40 | HK$42.43 |
| HK$4.00 | HK$25 | HK$47.43 |
EPS and BVPS both raise the ceiling. Because the formula multiplies then square-roots, earnings and assets can substitute: EPS 5/BVPS 15 (≈41.08) ≈ EPS 2/BVPS 40 (≈42.43) — Graham wants neither overpriced earnings without assets nor weak-earning assets.
Case Studies
Case 1: Screening a traditional value stock
A HK manufacturing stock: EPS = HK$3, BVPS = HK$20 over 12 months. Graham number = √(22.5 × 3 × 20) = √1,350 ≈ HK$36.74.
If the price is HK$30 (< 36.74), by Graham's conservative standard it is cheap with a margin of safety — a candidate for further study; at HK$45 it lacks protection.
But the investor knows: the Graham number is only a screen; after passing, still check earnings sustainability, debt and industry outlook to avoid a value trap (cheap but worsening fundamentals).
Case 2: An asset-heavy bank stock
A large bank: EPS = HK$4.5, BVPS = HK$30 → Graham number = √(22.5 × 4.5 × 30) = √3,037.5 ≈ HK$55.11.
Banks are asset-heavy with relatively stable earnings, fitting the Graham premise. If price HK$48 < 55.11, valuation looks reasonable.
But the investor notes: the Graham number ignores growth and bank-specific asset quality, provisions and capital rules, so treat it as a valuation floor, then combine with P/B, ROE and asset-quality metrics — do not be misled by a single number.
FAQ
Where does 22.5 come from?
From Graham's two rules for defensive investors: P/E should not exceed 15, and P/B should not exceed 1.5. He combined 15 × 1.5 = 22.5 as a single coefficient. So the Graham number merges the earnings side (P/E 15) and the assets side (P/B 1.5) into one threshold. When price equals the Graham number, the product of P/E and P/B is exactly 22.5 — the safety ceiling he deemed acceptable.
Is a price below the Graham number always a buy?
No. It is only a conservative initial screen — passing means valuation looks cheap with a margin of safety, but you still need full fundamental analysis. A low price can be a value trap — reflecting deteriorating fundamentals and falling earnings, not a market mispricing. Also the Graham number ignores growth and may over-penalise quality growth stocks. So use it to narrow the universe, but decide with industry outlook, financial health and earnings sustainability.
For which companies is it unsuitable?
It is unfriendly to high-growth and asset-light firms. Tech, internet and brand-consumer companies derive value mainly from intangibles (patents, brands, users) and future growth; their BVPS is often low, so the Graham number yields a very low 'fair price', severely undervaluing them. Also firms with negative or distorted EPS break the formula. It fits traditional value stocks with tangible assets and stable earnings (utilities, manufacturing, banks); for growth stocks use growth-aware valuation.
Graham number vs dividend discount model (DDM)?
Very different angles. The Graham number is relative/asset-side: using EPS and BVPS with conservative 15× P/E and 1.5× P/B caps, it gives a defensive buy price, ignoring growth. DDM (Gordon growth) is absolute/cash-flow: discounting future dividends at a perpetual growth rate to intrinsic value, extremely sensitive to growth assumptions. They complement: the Graham number quickly screens 'asset- and earnings-cheap' candidates; DDM/DCF then verifies cash-flow generation.
What if EPS or BVPS is negative?
If EPS or BVPS is negative, 22.5 × EPS × BVPS can go negative, and the square root is undefined in reals — the Graham number cannot be computed (this calculator requires both non-negative). That actually reflects its design intent: it only suits steadily profitable firms with positive net assets. A loss-making or insolvent firm fails Graham's defensive-investor criteria; do not force the formula — instead review financial health and prospects, or use other tools.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.