Graham number formula: how to calculate it and what it tells you

The formula and where 22.5 comes from

Graham number = √(22.5 × EPS × BVPS)

In The Intelligent Investor, Benjamin Graham told defensive investors to pay no more than 15 times average earnings and no more than 1.5 times book value. He allowed a lower P/E to justify a higher price-to-book, as long as the product of the two stayed at or below 15 × 1.5 = 22.5. Graham never wrote down the square-root formula himself. It is that rule of thumb solved for the highest acceptable price: if price ÷ EPS × price ÷ BVPS = 22.5, then price = √(22.5 × EPS × BVPS).

The inputs: EPS and book value per share

EPS is net income divided by the shares outstanding. Graham used the average of the last three years, not one year, so a single good year cannot inflate the result. Use diluted EPS if the company has many options or convertibles. Book value per share (BVPS) is shareholders' equity divided by the shares outstanding. A more conservative version uses tangible book value, which leaves out goodwill and other intangible assets.

Worked example: Graham number and net-net test for three stocks

Price, EPS, book value and the balance sheet figures are inputs. The three companies are fictional. Each formula is copied across the three columns, the list shows column B.

Worked example: Graham number and net-net test for three stocks

	A	B	C	D
1	Per share ($)	Alder Foods	Brook Software	Corran Tools
2	Share price	38.00	120.00	6.10
3	Earnings per share (EPS)	3.10	4.20	0.55
4	Book value per share (BVPS)	24.50	15.00	14.20
5	Graham number	41.34	37.65	13.26
6	Margin of safety vs Graham number	8.1%	-218.7%	54.0%
7	P/E × P/B (limit 22.5)	19.0	228.6	4.8
8	Price below Graham number?	Yes	No	Yes
9
10	Net-net test	Alder Foods	Brook Software	Corran Tools
11	Current assets ($m)	900.0	2,400.0	310.0
12	Total liabilities ($m)	1,100.0	1,600.0	120.0
13	Shares outstanding (m)	60.0	150.0	20.0
14	NCAV per share ($)	-3.33	5.33	9.50
15	Net-net buy limit (2/3 of NCAV)	-2.22	3.56	6.33
16	Price at or below the limit?	No	No	Yes

This guide is educational, not investment advice. A stock that passes a screen still needs a close look at the business, its debt and the reasons it is cheap.

Reading the three results

• Alder Foods, a steady food producer: Graham number $41.34, price $38. It passes, with a margin of safety of 8.1%. A pass, but not a wide one.
• Brook Software: Graham number $37.65, price $120. The price is more than three times the ceiling. That says more about the formula than about the business: software companies earn high returns on little book capital and grow, and the Graham number gives no credit for either.
• Corran Tools: Graham number $13.26, price $6.10, a margin of safety of 54.0%. Very cheap on paper, which usually means the market has doubts. Find out why before you buy.

The shortcut: P/E × P/B of 22.5 or less

Because the formula comes from Graham's rule, a stock trades below its Graham number exactly when P/E × P/B is below 22.5. Alder Foods: 12.3 × 1.55 = 19.0, a pass. Brook Software: 228.6, far above. Corran Tools: 4.8. This version is handy in a screener, where P/E and P/B are often ready-made columns.

Graham's net-net test (NCAV)

A net-net is Graham's deepest bargain: a stock priced below what would be left for shareholders if the company collected its current assets and paid every liability, valuing factories, brands and everything else at zero.

NCAV per share = (current assets − total liabilities) ÷ shares outstanding

Graham bought only below two-thirds of NCAV. Corran Tools has NCAV of $9.50 per share, a buy limit of $6.33, and trades at $6.10: it qualifies. Brook Software's limit is $3.56, far below its price, and Alder Foods has negative NCAV because its liabilities exceed its current assets, which is normal for a company with large plants. Net-nets are rare today and are mostly small, unloved companies, often with a real problem. The screen finds candidates, not investments.

Margin of safety

The margin of safety is the gap between a value estimate and the price: =1-price/value. Graham's point was that every value estimate can be wrong, so you only buy when the price is well below it. The Graham number is a ceiling for a conservative investor, not an estimate of what the business is worth. For that, combine it with an intrinsic value from a discounted cash flow model, as in how to build a DCF model in Excel, and set your buy price with a margin below that value.

Limits of the Graham number

• It ignores growth, return on equity and debt. A highly indebted company can pass easily.
• It does not work with negative EPS or negative book value: the square root of a negative number returns #NUM! in Excel. The test simply does not apply.
• Share buybacks and write-offs reduce book value, which lowers the Graham number of many good companies.
• Do not confuse it with Graham's growth formula, value = EPS × (8.5 + 2g), which is a different, much more generous estimate.

Common mistakes

• Forgetting the square root. =22.5*B3*B4 gives 1,709 for Alder Foods instead of $41.34.
• Using 15 instead of 22.5. 22.5 is the product of Graham's two limits, 15 × earnings and 1.5 × book value.
• Applying it to loss-making companies. Negative EPS or book value gives #NUM!. The test is meant for stable, profitable firms.
• Using one unusually good year. Graham averaged earnings over several years. A peak year makes almost any stock look cheap.
• Subtracting only current liabilities for NCAV. That is working capital. NCAV subtracts all liabilities, including long-term debt.
• Treating a pass as a buy signal. Cheap stocks are often cheap for a reason. The Graham number is a screen, not a valuation.