Graham Number Calculator

What is the Graham Number?

The Graham Number is a conservative equity valuation metric designed to establish the maximum purchase price a defensive value investor should consider paying for a share of common stock. Formulated from the investment principles of Benjamin Graham, widely regarded as the dean of Wall Street and mentor to Warren Buffett, the metric establishes an intrinsic price ceiling derived strictly from hard accounting fundamentals: trailing corporate earnings and tangible book value.

In his seminal 1949 treatise The Intelligent Investor and co-authored textbook Security Analysis, Graham argued that sound equity investing requires an uncompromising margin of safety. Rather than attempting to forecast volatile future growth rates, defensive investors screen for established businesses whose market price does not exceed a prudent multiple of their current earnings power and tangible assets. By combining your per-share profitability from the earnings per share calculator with the net asset base from the book value per share calculator, the Graham Number provides an objective, mathematical cap that guards against paying speculative premiums.

The Graham Number formula and derivation

The standard mathematical formula for the Graham Number is expressed as:

Where:

• EPS (Earnings Per Share): The net profit earned by the company for each outstanding share of common stock over the trailing twelve months (TTM).
• BVPS (Book Value Per Share): Common shareholders' equity (total assets minus total liabilities and preferred claims) divided by total shares outstanding.
• 22.5 (The Graham Multiplier): The mathematical product of Graham's two foundational valuation benchmarks.

Why 22.5 is the benchmark multiplier

Graham laid down two explicit valuation constraints for defensive portfolios:

1. A stock should not trade at a price-to-earnings (P/E) ratio greater than 15.0 times its three-year average earnings.
2. A stock should not trade at a price-to-book (P/B) ratio greater than 1.5 times its recorded net asset value.

Graham recognized that an exceptional bargain on book value could justify a slightly higher earnings multiple, and vice versa. He therefore permitted the product of the two ratios to serve as the overall test. Because P/E is defined as Price / EPS and P/B is defined as Price / BVPS, multiplying the two ratios yields:

Solving this inequality for Price gives the maximum allowable purchase price:

Interpreting the calculation and Margin of Safety

Once calculated, the Graham Number acts as a clear benchmark against the current market price of the stock:

• Undervalued (Market Price < Graham Number): When the market price trades at a discount to the Graham Number, the stock satisfies Graham's defensive price threshold. A discount greater than 10% indicates an attractive valuation buffer.
• Fairly Valued: When the market price trades within a narrow band (typically within 10%) of the calculated ceiling, the stock is valued in line with its fundamental asset and earnings base.
• Overvalued (Market Price > Graham Number): When the market price exceeds the Graham Number, investors are paying a premium above Graham's joint P/E and P/B limits. While common in fast-growing sectors, it violates defensive criteria.

The Margin of Safety quantifies this discount as a percentage of the intrinsic ceiling:

A positive percentage indicates the degree of downside protection, giving investors room for error if earnings contract or economic conditions deteriorate. To project how annual earnings compound over multi-year horizons, compare historical performance using our CAGR calculator, or analyze intrinsic cash flows across future periods with the discounted cash flow calculator.

Published worked example

Consider an industrial manufacturing company with trailing twelve-month Earnings Per Share (EPS) of $5.00 and Book Value Per Share (BVPS) of $30.00. The stock currently trades on the open market at $45.00 per share.

1. Multiply the Graham multiplier by EPS and BVPS: 22.5 × $5.00 × $30.00 = 3,375.00.
2. Compute the square root: √3,375.00 = $58.09 per share. This represents the fair value cap.
3. Calculate the Margin of Safety: (($58.09 - $45.00) / $58.09) × 100% = +22.53%.
4. Evaluate market multiples: P/E = $45.00 / $5.00 = 9.00, and P/B = $45.00 / $30.00 = 1.50. Their product is 9.00 × 1.50 = 13.50, well beneath the 22.50 maximum.

Because the current price of $45.00 trades well below the $58.09 ceiling with a 22.53% margin of safety, the stock qualifies as an undervalued defensive candidate under Benjamin Graham's rules.

When to use and when to avoid the Graham Number

The Graham Number was formulated during an era dominated by tangible industrial assets, railways, and heavy manufacturing. Understanding its structural strengths and practical boundaries ensures you apply it effectively:

• Best suited for: Capital-intensive, asset-heavy enterprises such as industrial equipment manufacturers, traditional utilities, consumer staples, and mature financial holding companies where historical balance sheets accurately mirror productive capacity.
• Unsuitable for high-growth and asset-light firms: Modern software, biotechnology, and platform companies generate enterprise value primarily from intangible assets, patented algorithms, and network effects that do not appear on traditional balance sheets. These companies frequently trade at multiples that far exceed 22.5 despite strong underlying economics.
• Requires positive earnings and book value: If a company posts negative EPS or negative shareholder equity, the radicand becomes negative, making the formula mathematically undefined. The metric is explicitly restricted to profitable businesses with intact equity bases.

Frequently asked questions