How to Use the Graham Number to Value Stocks

The Graham Number is a valuation metric developed by Benjamin Graham, who's widely considered the "father of value investing." This approach provides investors with a quick way to estimate a stock's intrinsic value based on its earnings per share (EPS) and book value per share (BVPS). The Graham Number can be particularly useful for value investors seeking stocks with a margin of safety, especially in stable sectors like utilities, consumer staples, and industrials.

This article explains Graham's method and formula, including how to calculate and interpret the output. We'll walk through a detailed example using a real-world company to illustrate the process, with a free Excel template included. Additionally, we'll discuss the limitations and practical applications of this valuation technique.

Graham Number Explained

The Graham Number originates from Benjamin Graham's foundational 1949 value investing book, "The Intelligent Investor." This valuation metric stems from Graham's principle of investing with a margin of safety, referring to the practice of purchasing securities at a significant discount to their intrinsic value to provide a buffer against errors in analysis and/or unforeseen market declines.

The Graham Number represents the maximum price a defensive investor should pay for a stock to consider it undervalued. Graham defines "defensive investors" as those who primarily seek to avoid "serious mistakes or losses" while also aiming for "adequate, though unsensational, results." Therefore, this metric helps these risk-averse investors identify stable, undervalued stocks that offer a margin of safety.

This valuation metric considers two fundamental metrics: earnings per share (EPS) and book value per share (BVPS). By incorporating both earnings and asset value, the Graham Number aims to provide a more comprehensive estimate of a stock's intrinsic value than using either metric alone.

The Graham Number's flexibility allows it to assess stocks across various sectors, adjusting for industry-specific characteristics. For example, companies in capital-intensive sectors like manufacturing may require higher asset figures, while those in service-oriented sectors like technology may need higher earning figures.

However, the Graham Number has limitations, including its reliance on historical data and its potential to undervalue growth stocks. Additionally, the fixed multiples used in the Graham Number formula may be outdated, as they were based on market observations from the mid-20th century. We'll discuss these drawbacks and others in more detail in the final section of this article.

Graham Number Formula

The Graham Number, although not explicitly proposed by Benjamin Graham himself, is derived from principles outlined in Chapter 14 of his book "The Intelligent Investor." Investors developed this formula based on Graham's stock selection criteria for defensive investors.

Graham provided a list of seven rules for selecting defensive stocks in his book. The Graham Number specifically draws from rules #6 and #7:

1. Adequate Size of the Enterprise: Not less than $100 million of annual sales for an industrial company and, not less than $50 million of total assets for a public utility.
2. A Sufficiently Strong Financial Condition: For industrial companies, current assets should be at least twice current liabilities. Also, long-term debt should not exceed the net current assets (or "working capital"). For public utilities the debt should not exceed twice the stock equity (at book value).
3. Earnings Stability: Some earnings for the common stock in each of the past 10 years.
4. Dividend Record: Uninterrupted payments for at least the past 20 years.
5. Earnings Growth: A minimum increase of at least one-third in per-share earnings in the past 10 years using three-year averages at the beginning and end.
6. Moderate Price/Earnings Ratio: Current price should not be more than 15 times average earnings of the past three years.
7. Moderate Ratio of Price to Assets: Current price should not be more than 1½ times the book value. However, a multiplier of earnings below 15 could justify a correspondingly higher multiplier of assets. As a rule of thumb we suggest that the product of the multiplier times the ratio of price to book value should not exceed 22.5 (This figure corresponds to 15 times earnings and 1½ times book value. It would admit an issue selling at only 9 times earnings and 2.5 time asset value, etc.)

— Benjamin Graham in "The Intelligent Investor," Chapter 14 (pg. 348-349)

The formula derived from Graham's principles for the Graham Number is shown below:

Graham Number = √(22.5 × EPS × BVPS)

where:

• EPS (Earnings Per Share): EPS is calculated as a company's net profit divided by the number of outstanding shares of its common stock. It can also be found in the income statement.
• BVPS (Book Value Per Share): BVPS is the ratio of equity available to common shareholders divided by the number of outstanding shares. This figure represents the minimum value of a company's equity and measures the book value of a firm on a per-share basis.

An alternative formula of the Graham Number, which is equivalent to the original, is shown below:

Graham Number = √(15 × 1.5 × (Net Income / Shares Outstanding) × (Shareholders' Equity / Shares Outstanding))

where:

• Net Income: Company's total earnings after all expenses and taxes.
• Shares Outstanding: Total number of a company's shares held by all of its shareholders.
• Shareholders' Equity: Company's total assets minus its total liabilities, representing the net value of the company.

This formula is equivalent because EPS is net income divided by the number of shares outstanding, and book value is another term for shareholders' equity.

In either case, the square root in the formulas is used to find the geometric mean between the maximum price based on earnings and the maximum price based on book value. The geometric mean, unlike the arithmetic mean (average), provides a balanced measure that gives equal weight to both factors, ensuring neither earnings nor book value dominates the final valuation.

To apply the Graham Number formula effectively, two key conditions must be met (as specified by Graham):

1. The price-to-earnings (P/E) ratio (what Graham defines as the "multiplier") should be less than 15x.
2. The price-to-book (P/B) ratio should be less than 1.5x.

Note that the "22.5" factor in the formula represents the product of the maximum possible ratios (15 × 1.5 = 22.5).

If you don't follow the criteria for the P/E and P/B ratios, the Graham Number may overestimate a stock's intrinsic value, leading to potential investments in overvalued stocks.

Once the Graham Number is calculated, the resulting value represents the maximum price an investor should pay for the stock according to Graham's criteria. This value can be used to assess the stock's potential valuation:

• Current Market Price < Graham Number: Potentially undervalued
• Current Market Price = Graham Number: Fairly valued
• Current Market Price > Graham Number: Potentially overvalued

Lastly, it's important to note that Graham recommended using an average EPS figure rather than a single year's earnings to obtain a more reliable Graham Number.

Here's Graham discussing why EPS can be potentially flawed:

"The more seriously investors take the per-share earnings figures as published, the more necessary it is for them to be on their guard against accounting factors of one kind and another that may impair the true comparability of the numbers. We have mentioned three sorts of these factors: the use of special charges, which may never be reflected in the per-share earnings, the reduction in the normal income-tax deduction by reason of past losses, and the dilution factor implicit in the existence of substantial amounts of convertible securities or warrants. A fourth item that has had a significant effect on reported earnings in the past is the method of treating depreciation— chiefly as between the "straight-line" and the "accelerated" schedules."

— Benjamin Graham in "The Intelligent Investor," Chapter 12 (pg. 316)

Related: Why Earnings Per Share (EPS) is Flawed in Stock Analysis

Next, here's Graham explaining why averaging EPS over a period of time is recommended for analysis purposes:

"In former times analysts and investors paid considerable attention to the average earnings over a fairly long period in the past— usually from seven to ten years. This "mean figure" was useful for ironing out the frequent ups and downs of the business cycle, and it was thought to give a better idea of the company's earning power than the results of the latest year alone. One important advantage of such an averaging process is that it will solve the problem of what to do about nearly all the special charges and credits. They should be included in the average earnings. For certainly most of these losses and gains represent apart of the company's operating history."

— Benjamin Graham in "The Intelligent Investor," Chapter 12 (pg. 319)

Thus, by averaging the EPS figure in the Graham Number formula, investors can mitigate the impact of various accounting manipulations and treatments of depreciation, thereby providing a more stable basis for valuation.

Price to Graham Number

The Price to Graham Number Ratio compares a stock's current market price to its calculated Graham Number, offering a quick assessment of potential under- or overvaluation based on Graham's conservative principles.

The Price to Graham Number Ratio formula is shown below:

Price to Graham Number Ratio = Current Stock Price / √(22.5 × EPS × BVPS)

Investor's can interpret the output of this ratio as follows:

• Ratio < 1: Potentially undervalued. The stock price is below the maximum price a defensive investor should pay according to Graham's criteria.
• Ratio = 1: Fairly valued, based on the Graham number.
• Ratio > 1: Potentially overvalued. The stock price exceeds the maximum price a defensive investor should pay according to Graham's criteria.

For example, if a stock has a current market price of $50 and a calculated Graham Number of $40, the Price to Graham Number Ratio would be 1.25x (50 / 40 = 1.25x). This suggests that the stock might be overvalued by 25% according to Graham's criteria.

The Price to Graham Number Ratio offers two key advantages over using the Graham Number alone:

• Relative Valuation Measure: The ratio provides a standardized way to compare the degree of potential over- or undervaluation across different stocks, even if their Graham Numbers differ significantly.
• Market Sentiment Insight: The ratio reflects the current market price relative to the maximum price determined by Graham's criteria. This comparison can potentially indicate investor sentiment or growth expectations beyond the historical financial data used in the Graham Number calculation.

Although a high (or low) Price to Graham Number Ratio doesn't necessarily indicate a poor (or attractive) investment, as it may reflect growth prospects or qualitative factors not captured by this metric, the ratio can be used to compare similar companies and better evaluate investor sentiment or implied market growth expectations.

Graham Number Example

To demonstrate how to apply the Graham Number to determine a company's implied valuation, we'll use Under Armour (UA) as our example company. Under Armour is a global manufacturer and distributor of performance apparel, footwear, and accessories.

Besides being an established company with positive earnings and book value, Under Armour currently has a price-to-earnings (P/E) ratio of 13.41x and a price-to-book (P/B) ratio of 1.45x. Both of these ratios are below Graham's recommended maximum values of 15x and 1.5x respectively, making Under Armour a suitable case study for this valuation method.

Here are the steps investors can follow to calculate the Graham Number for any company, as explained in greater detail in the following sections:

• Step #1: Calculate or Find Earnings Per Share (EPS)
• Step #2: Calculate or Find Book Value Per Share (BVPS)
• Step #3: Calculate the Graham Number Formula and Interpret the Results

Step #1: Calculate or Find Earnings Per Share (EPS)

Earnings per share (EPS) measures a company's profitability on a per-share basis. There are two types of EPS: basic and diluted, as defined below:

• Basic EPS: The company's net income divided by the number of outstanding common shares. This measure assumes no dilution from convertible securities or stock options.
• Diluted EPS: The company's net income divided by the total number of outstanding shares, including all convertible securities. This provides a more conservative estimate of earnings per share.

While Graham didn't explicitly specify which to use, we'll focus on diluted EPS as it provides a more conservative estimate by accounting for all potential shares that could be issued.

You can find EPS figures on stock market data sites or at the bottom of a company's income statement. Diluted EPS can also be calculated using the following formula:

Diluted EPS = Net Income / Weighted Average Diluted Shares Outstanding

Here's Under Armour's income statement with its net income, EPS figures, and weighted average common shares outstanding outlined:

As you can see, Under Armour reported diluted EPS of $0.52 in FY 2024, which can also be calculated by completing the diluted EPS formula, as shown below:

Diluted EPS [UA; FY 2024] = $232,042K / 451,011K --> $0.52

Thus, Under Armour earned $0.52 per share in FY 2024, considering all potential dilutive securities.

To align with Graham's conservative approach, we'll use a normalized EPS figure rather than the single-year result. This method involves averaging EPS over several years, which helps smooth out short-term fluctuations and reduces the impact of potential accounting manipulations.

Here's a visual of Under Armour's diluted EPS over the last 10 years:

Under Armour's recent financial history includes some significant anomalies. In FY 2020, the COVID-19 pandemic caused widespread operational challenges, including store closures and supply chain disruptions. Additionally, in FY 2022, Under Armour changed its fiscal year-end from December 31st to March 31st, resulting in a transition period rather than a full fiscal year.

To account for these unusual circumstances and provide a more accurate representation of Under Armour's normalized business operations, we'll calculate the average EPS over the 10-year period, excluding FY 2020 and FY 2022. This approach results in an adjusted average EPS of $0.40, which we'll use in our Graham Number calculation as a more stable indicator of the company's long-term earnings power.

Step #2: Calculate or Find Book Value Per Share (BVPS)

Book value per share (BVPS) represents the net asset value of a company on a per-share basis. This figure can be found on stock market data sites or calculated using the following formula:

BVPS = Shareholders' Equity / Total Shares Outstanding

Here's Under Armour's balance sheet with shareholders' equity outlined:

As you can see, Under Armour reported total shareholder's equity of $2,153,286K in FY 2024.

We can now complete the BVPS formula for Under Armour, using the company's total diluted shares outstanding found in the previous step:

BVPS [UA; FY 2024] = $2,153,286K / 451,011K --> $4.77

This BVPS of $4.77 means that each share of Under Armour stock is supported by $4.77 in net assets. Net assets, which are the company’s total assets minus its total liabilities, represent the shareholders' claim on the company’s resources.

Step #3: Calculate the Graham Number Formula and Interpret the Results

In this final step, we'll calculate the Graham Number, which will provide us with an estimate of Under Armour's maximum fair value according to Graham's conservative criteria.

Let's apply the Graham Number formula using our averaged EPS of $0.40 and current BVPS of $4.77:

Graham Number [UA; FY 2024] = √(22.5 × $0.40 × $4.77) --> $6.54

The Graham Number suggests a maximum fair value of $6.54 for Under Armour stock. Compared to the current stock price of ~$6.53, this indicates that the stock is fairly valued (or at most, slightly overvalued) according to Graham's criteria.

To further quantify this valuation, we can calculate the Price to Graham Number Ratio:

Price to Graham Number Ratio [UA; FY 2024] = $6.53 / $6.54 --> 1.00x

This ratio of 1.00x suggests that Under Armour's stock is trading at almost exactly its Graham Number value. In practical terms, this means that based on Graham's conservative valuation method, Under Armour's current stock price aligns closely with its estimated intrinsic value. Comparing this ratio to those of Under Armour's competitors can also provide insights into relative industry valuation.

Limitations of Graham Number

The Graham Number, while a potentially useful valuation metric for stable, mature companies in traditional industries, has several important limitations that should be considered when applying this method:

• Limited Scope of Analysis: The Graham Number ignores fundamental factors such as management quality, competitive landscape, industry characteristics, and major shareholders. It also overlooks key financial metrics like free cash flow, EBITDA margin, and return on equity (ROE). This narrow focus can lead to an incomplete assessment of a company's true value and potential.
• Reliance on Positive Metrics: The formula requires positive earnings per share (EPS) and book value per share (BVPS). This limitation means it's not applicable to companies with negative earnings or book values, which are common in certain stages of a business lifecycle or in specific industries. As a result, the Graham Number may overlook potentially valuable investment opportunities in emerging or restructuring companies.
• Lack of Growth Consideration: The Graham Number does not factor in a company's growth prospects or potential for future expansion. This limitation can lead to undervaluing rapidly growing businesses that may derive significant worth from their growth potential rather than current earnings or book value.
• Ineffective for Intangible-Heavy Companies: As markets have evolved, the Graham Number has become less relevant for technology-driven companies and businesses with low tangible asset reliance. It struggles to capture the value of companies in knowledge-based economies, where intellectual property and other intangible assets often constitute a significant portion of a company's worth.
• Oversimplification of Valuation: By reducing a company's valuation to a single number, the Graham Number risks oversimplifying the investment decision-making process. This approach may lead investors to overlook other critical factors that contribute to a company's overall value and future prospects.
• Outdated Assumptions: The Graham Number uses fixed multiples (P/E of 15x and P/B of 1.5x) that may not reflect current market conditions or industry-specific valuations. These assumptions were based on Graham's observations from the mid-20th century and may not account for changes in the modern economy.

The Graham Number, while providing a potentially useful quick valuation estimate for established companies in traditional sectors such as utilities, manufacturing, and consumer goods, should not be used in isolation. Instead, investors should incorporate it into a broader investment strategy to improve decision-making.

The Bottom Line

The Graham Number is a valuation metric developed by Benjamin Graham to determine a stock's maximum fair value. It combines earnings per share and book value per share in a formula that provides a quick estimate of a stock's intrinsic value.

This metric may be beneficial for evaluating stable, mature companies in traditional industries, helping identify potentially undervalued stocks that meet Graham's criteria for defensive investing.

However, the Graham Number has limitations. It relies on positive earnings and book value, limiting its applicability to profitable companies with tangible assets. Additionally, the Graham Number is based on Graham's observations from the mid-20th century, using fixed multiples that may not reflect the current market environment.

Investors should use the Graham Number as part of a broader analysis, combining it with other valuation methods and fundamental analysis. This approach allows for a more comprehensive assessment of a stock's true value and investment potential.