Graham number vs market price
By Jude Wallis
The Graham number is a ceiling built from two accounting figures. With $2 of earnings per share and $20 of book value per share it is $30. The market price is what buyers are paying: $42 here, a P/E of 21 and an earnings yield of 4.76 percent. One is a rule, the other is a fact.
| Graham number | Market price | |
|---|---|---|
| Where it comes from | Two lines from the accounts, one from the income statement and one from the balance sheet. | The order book, second by second. |
| This company | $30, from $2 of EPS and $20 of book value. | $42, which is 40 percent above that ceiling. |
| What moves it | New accounts, four times a year at most. | Anything, including nothing. |
| The constant inside it | 22.5, which is a P/E of 15 times a price to book of 1.5. | None. At $42 the P/E alone is 21. |
| What it ignores | Growth, brands, patents and anything else not on the balance sheet. | Nothing, which is also the problem: it prices moods as well as facts. |
| How to read the pair | A screen. Below it means worth a look, not worth buying. | The number you would actually pay, and the one the earnings yield is measured against. |
On this page
The 22.5 is two rules multiplied
Benjamin Graham's defensive screen wanted a price no higher than 15 times earnings and no higher than 1.5 times book value. Multiply those limits and you get 22.5, which is why the formula is the square root of 22.5 times EPS times book value per share. With $2 and $20 the product inside the root is 900, and the square root of 900 is $30.
That is a ceiling on the pair of ratios taken together, not on either separately. A company can sit above 15 times earnings and still pass, if book value is high enough to pull the product back under the line. The Graham number calculator works it out from the two inputs.
The market price is not trying to be the Graham number
At $42 the shares trade at 21 times the $2 of earnings, which is an earnings yield of 4.76 percent. The gap to $30 is not evidence of a mistake. It is the market paying for something the formula cannot see: growth, a brand, a licence, a balance sheet full of assets carried at cost from decades ago.
This matters most for companies whose value is not on the balance sheet at all. Software firms and service businesses can hold almost no book value and still earn well, and the Graham number will call them expensive at any price. Book value per share is an accounting figure, and book value is where its limits are set out.
Using the pair
Read the Graham number as a screen and the price as the decision. A stock below the ceiling has passed one filter built from two conservative ratios, and nothing more. A stock above it, like this one at 40 percent over, is telling you the case rests on something the accounts do not carry. The earnings yield calculator puts the price back in return terms, and how the margin of safety works covers the discipline the ceiling belongs to. This is educational material, not financial advice.
Worked examples
The ceiling on \$2 of earnings and \$20 of book value
A company earns $2 a share and carries $20 of book value a share. What is its Graham number?
- Multiply the constant by both inputs: 22.5 times 2 times 20 gives a product of 900.
- Take the square root of 900, which is $30.
The Graham number is $30 a share. Above that price the pair of ratios breaches Graham's defensive limits.
The same company at a \$42 price
The shares trade at $42 while earning $2. What does the price say on its own terms?
- Price over earnings is 42 divided by 2, a P/E of 21.
- Turn that upside down and the earnings yield is 4.76 percent.
At $42 the market pays 21 times earnings for a 4.76 percent earnings yield, well past the 15 times the Graham ceiling allows.
Common questions
Does a price above the Graham number mean the stock is overvalued?
It means it fails a conservative screen built from two accounting figures. That is a starting point, not a verdict.
Why 22.5?
It is 15 times 1.5: Graham's maximum price to earnings multiplied by his maximum price to book.
What happens with negative earnings?
The product goes negative and the square root has no real value, so the screen simply does not apply.
Is this financial advice?
No. It is educational material about a valuation screen and the price it is compared with.
Keep reading
This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.