Benjamin Graham

Chapter 11 – Security Analysis for the Lay Investor: General Approach

Summary and Discussion – Chapter 11 – Security Analysis for the Lay Investor: General Approach
Notes on The Intelligent Investor by Benjamin Graham
Notes by Jason Fernando
Created January 9th, 2014
Last updated July 29th, 2015
Reference document: Graham, Benjamin, and Jason Zweig. The Intelligent Investor. Rev. ed. New York: HarperBusiness Essentials, 2003.

50-Word Recap

  • Ideally, the math used for security analysis should be clear and uncomplicated. This promotes accountability; with simple algebra, it is easy to understand one’s reasoning process. Conversely, questionable assumptions can easily be obscured within more complex math.
  • A number of mathematical tools have been invented to aid in securities analysis.

What is security analysis?

“The security analyst deals with the past, the present, and the future of any given security issue. He describes the business; he summarizes its operating results and financial position; he sets forth its strong and weak points, its possibilities and risks; he estimates its future earning power under various assumptions, or as a “best guess.” He makes elaborate comparisons of various companies, or of the same company at various times. Finally, he expresses an opinion as to the safety of the issue, if it is a bond or investment-grade preferred stock, or as to its attractiveness as a purchase, if it is a common stock.” [1]

In somewhat simpler terms:

“The security analyst develops and applies standards of safety by which we can conclude whether a given bond or preferred stock may be termed sound enough to justify purchase for investment. These standards relate primarily to past average earnings, but they are concerned also with capital structure, working capital, asset values, and other matters.” [2]

In doing so, a key insight to be kept at hand is the following:

“…[T]he more dependent the valuation [of a given company] becomes on anticipations of the future—and the less it is tied to a figure demonstrated by past performance—the more vulnerable it becomes to possible miscalculation and serious error.”

Similarly, modes of inferring the value of a company which rely heavily on advanced mathematics should be treated with skepticism if not outright suspicion. As noted by Jason Zweig in his footnote to page 282, Graham says as much in the Appendix to The Intelligent Investor:

“Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw therefrom. In forty-four years of Wall Street experience and study I have never seen dependable calculations made about common-stock values, or related investment policies, that went beyond simple arithmetic or the most elementary algebra. Whenever calculus is brought in, or higher algebra, you could take it as a warning signal that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment.” [3]

Having laid down this introduction, Graham moves on to the meat of Chapter 11, which is intended to introduce “the non-professional investor” with an understanding of the basic concepts of security analysis, thereby equipping him “to distinguish between superficial and sound analysis.” Central to this understanding are “two basic questions”: “What are the primary tests of safety of a corporate bond or preferred stock? What are the chief factors entering into the valuation of a common stock?” [4]

Bond Analysis

“The chief criterion used for corporate bonds is the number of times that total interest charges have been covered by available earnings for some years in the past. In the case of preferred stocks, it is the number of times that bond interest and preferred dividends combined have been covered.” [5]

Graham elaborates on this criterion through a table (table 11-1 on page 284) in which he recommends “Minimum Ratio[s] of Earnings to Total Fixed Charges”. Let’s begin by examining this in relation to corporate bonds.

The logic of Graham’s “Minimum Ratio” is fundamentally simple: A corporate bond is more secure if the corporation issuing the bond has significantly higher earnings than are required to pay the expenses associated with the bond. Today, the “Ratio of Earnings to Total Fixed Charges” is generally referred to as the “Fixed-Charge Coverage Ratio”. It is calculated by adding the company’s pre-tax earnings to its pre-tax fixed charges and then dividing that number by the sum of its pre-tax fixed charges and in its interest payments. Rewritten as an equation, we can calculate the Fixed-Charge Coverage Ratio as follows:

Fixed-charge coverage ratio

In this equation, the acronym “EBIT” stands for “Earnings Before Interest and Tax”. It is calculated through the following equation: [6]


The term “fixed charges” refers to expenses which recur on a regular, predictable basis. Examples of fixed charges include property leases, salaries, or utility payments such as electricity or gas costs. The “interest” in the equation pertains to the interest paid by the company on its outstanding debts, such as corporate bonds or business loans. For example, if Company A has EBIT of $1 million, fixed charges before tax of $200,000, and interest payments of $75,000, then its Fixed-Charge Coverage Ratio is calculated as follows:

Fixed-charge coverage ratio completed

What this number (4.36) means is that Company A can afford to cover its fixed charges 4.36 times over. The higher this number, the more capable is the company of handling the interest burden of its debts, and the more secure its bonds can be said to be. The same logic is applied with respect to preferred shares. However, in the case of preferred shares the “Total Fixed Charges” number refers to the dividends paid out to preferred shareholders. More detail on this below.

Yet Graham’s recommendations are more rigorous than this cursory explanation would imply. His “Minimum “Coverage”” table, here reproduced from page 284, offers advice as to which ratios are appropriate (before and after taxes) for different kinds of companies and over different time-frames:

Minimum Ratio of Earnings to Total Fixed Charges

(For “Investment-grade [corporate] Bonds”) [7]

Type of enterprise Average of Past 7 Years Alternative: Measured by “Poorest Year” Average of Past 7 Years Alternative: Measured by “Poorest Year”
Public-utility operating company 4 times 3 times 2.65 times 2.10 times
Railroad 5 4 3.20 2.65
Industrial 7 5 4.30 3.20
Retail concern 5 4 3.20 2.65

As for preferred shares, Graham adds the following:

“The same minimum figures as above are required to be shown by the ratio of earnings before income taxes to the sum of fixed charges plus twice preferred dividends… The inclusion of twice the preferred dividends allows for the fact that preferred dividends are not income-tax deductible, whereas interest charges are so deductible.” [8]

Graham notes that “In addition to the earnings-coverage test [described above], a number of others are generally applied.” [9] These include:

I. “Size of Enterprise. There is a minimum standard in terms of volume of business for a corporation… and of population for a municipality.”

II. “Stock/Equity Ratio. This is the ratio of the market price of the [corporation] to the total face amount of the debt [owed by that corporation]… This factor includes the market’s appraisal of the future prospects of the enterprise.”

III. “Property Value. The asset values, as shown on the balance sheet or as appraised, were formerly considered the chief security and protection for a bond issue. Experience has shown that in most cases safety resides in the earning power, and if this is deficient the assets lose most of their reputed value. Asset values, however, retain importance as a separate test of ample security for bonds and preferred stocks in three enterprise groups: public utilities (because rates may depend largely on the property investment), real-estate concerns, and investment companies.” [10]

Graham goes on to say that while the above means of assessing the safety of bonds and preferred shares are by no means foolproof, they nonetheless go a long way toward reducing the risk of malinvestment. [11]

Common Stock Analysis

“The ideal form of common-stock analysis leads to a valuation of the issue which can be compared with the current price to determine whether or not the security is an attractive purchase. This valuation, in turn, would ordinarily be found by estimating the average earnings over a period of years in the future and then multiplying that estimate by an appropriate “capitalization factor.”” [12]

Estimating average (future) earnings:

“The now-standard procedure for estimating future earning power starts with average past data for physical volume, prices received, and operating margin. Future sales in dollars are then projected on the basis of assumptions as to the amount of change in volume and price level over the previous base. These estimates, in turn, are grounded first on general economic forecasts of gross national product, and then on special calculations applicable to the industry and company in question.” [13]

[Elaborating on the above is a topic for another time!]

Factors Affecting the Capitalization Rate

Let’s imagine you are presented with two companies which each have a market capitalization of $40,000,000. Does it logically follow that both those companies are worth $40,000,000? Not necessarily. How, then, might you estimate the fair value of these companies? Graham lists five criteria, with words of caution for each.

I. General Long-Term Prospects. [14] Be wary, however, of a) the fact that the long-term prospects of any business or sector are notoriously difficult to predict; and b) that the consensus view of market “experts” is highly unreliable and frequently prone to irrational exuberance. [15]

II. Management. [16] There’s not doubt that unusually competent management can lead to unusually impressive performance. However, it is equally true that a) quality management is difficult to identify before the results of that management have materialized in the form of increased business growth/profits; and b) once these results have materialized the price of the company’s shares are all but assured to rise shortly thereafter as other market participants respond to the company’s impressive performance. Consequently, assessing the value of a company on the basis of its management is impractical. Moreover, there is a risk of overestimating a company’s value by way of this method, particularly in instances where the management in question has become universally praised. Such perceptions are prone, again, to irrationally exuberant responses (and thus irrationally high prices). Of course, the same phenomenon can occur in the opposite direction—irrational selling of a company’s stock due to the perceived incompetence of its management—in which case a desirable buying opportunity may present itself.

III. Financial Strength and Capital Structure. [17] Graham here refers to the relative balance between common shares, preferred shares, and outstanding debts held on the corporation’s balance sheet. He notes that, in comparing two corporations (of the same industry) with identical earnings per share, it makes sense to favour that corporation which has less in the way of “bank loans and senior securities.” The term “senior securities” here refers to outstanding bonds and preferred shares; they are “senior” because such claims receive priority over common stocks in the event of bankruptcy. Thus the ideal “Capital Structure” consists of “a lot of surplus cash and nothing ahead of [meaning, senior to] the common [stock]”.

IV. Dividend Record. [18] “One of the most persuasive tests of high quality is an uninterrupted record of dividend payments going back over many years. We think that a record of continuous dividend payments for the last 20 years or more is an important plus factor in the company’s quality rating. Indeed the defensive investor might be justified in limiting his purchases to those meeting this test.” This makes sense; after all, companies which are capable of maintaining dividend payments to their shareholders over a period of two decades or more are far more likely to be skilled at navigating the vicissitudes of economic cycles and business trends than are counterparts without such a sterling dividend record. Some investors go a step further, insisting that companies must also have increased their dividend payments consistently for each of those years. Such companies are compiled into indexes, upon which index funds are based: a popular example being the Dividend Aristocrats Index. Such an extreme qualification may not in fact be advisable, however. Companies which aspire to remain on such indexes may be pressured into increasing their dividend payments even under conditions where doing so is harmful to the business as a whole. For example, Company A may be pressured into increasing dividends in lieu of investing in new equipment, personnel, share repurchases, etc. purely due to their desire to remain on the Aristocrats index (or others like it). Such a move may be in the best long-term interest of the company, but it may also not be.

V. Current Dividend Rate. [19] What percentage of its earnings should a company pay out in dividends? This is a difficult question to answer. In Graham’s time, it was customary for corporations to pay out approximately two-thirds of their earnings in dividends. However, this figure has since dropped significantly, with a recent report by FactSet pinning the number at 31.5% for the S&P 500. [20]

Capitalization Rates for Growth Stocks

How ought one estimate the fair value of a growth stock? Graham offers the following “foreshortened and quite simple formula for the valuation of growth stocks”:

Graham Formula

Before we move any further, it is critical that the reader understand the above formula should not be taken seriously at face value! This segment of Graham’s Investor is widely misunderstood. This formula does not yield an accurate picture of a company’s “true value”; all that it does is provide an estimate of what the market expects the company’s future growth to be. Graham is not saying that the number produced by the equation is accurate; it is intended only to give you an impression of what other market participants are expecting. Graham explains this in footnote 7 of page 295 (relegated to the Endnotes in the “Revised Edition” on which these notes are based), where he states: “Note that we do not suggest that this formula gives the “true value” of a growth stock, but only that it approximates the results of the more elaborate calculations in vogue.” What Graham’s saying is that this formula allows you to get into the mindset of other investors with respect to their growth expectations; it is by no means suggested that you should necessarily adopt that mindset yourself.

Having said this, let’s get to know this formula (known colloquially as the “Graham Formula”) by applying it to a real-life company—and one of my favourites—IBM. Let’s start by rephrasing the above formula in simpler terms:

Graham Formula simplified Where:
“IV” = The implied value of the company. [21]“EPS” = The company’s current diluted earnings per share.“8.5” = The price-to-earnings ratio of a company with 0% EPS growth. [22]“g” = A conservative estimate of the company’s average annual EPS growth over the next 7 to 10 years.

The first step is to obtain the EPS and “g” variables. The first of these, EPS (“earnings per share”) can be easily obtained from the company’s most recent annual report. [23] A convenient place to look for this figure is in the “Financial Highlights” section, near the beginning of the annual report:

IBM Financial Highlights

The portion of this screenshot we are interested in is the row “Assuming dilution”, under the heading “Earnings per share of common stock”. On the right-hand side, we see that the diluted EPS for 2012 was $14.37. As the name suggests, this figure means that, over the course of 2012, IBM earned the equivalent of $14.37 for every one of their shares.

What about “g”? Let’s start by determining what IBM’s average annual EPS growth has been over the past 10 years. Then, we can make a conservative estimate of what its average annual EPS growth will be over the next 10 years. The following figures are derived from IBM’s annual reports for the years 2003 through 2012. IBM’s financial reports are publicly available online at

The first step is to simply look up the diluted EPS figures for each of the past 10 years.Diluted EPS by Year Next, we determine the annual diluted EPS growth for each of these years.EPS by Year Increase

From here, we can take the average per-year EPS growth from these past 10 years:

Average of EPS growth from the past 10 years

What we find is that, over the past 10 years, IBM has been growing its diluted EPS at an average annual rate of 17.81%.

So, now that we know what IBM’s average annual EPS growth has been over the past 10 years, we can proceed to conservatively estimate what IBM’s average annual EPS growth will be over the next 10 years. There are many convoluted ways of doing this, but I prefer to stick as much as possible with straightforward methods whose logic is transparent and easy to understand.

One simple and effective way of conservatively estimating future EPS growth is by applying a “margin of safety” to the average past EPS growth (17.81%). For example, a margin of safety of 50% would mean an estimated future annual EPS growth (over the next 10 years) that is 50% of the average annual EPS growth over the past 10 years:

Margin of Safety

With this last step completed, we now have both the values (“EPS” and “g”) needed to fill in the Graham Formula. Let’s apply them to arrive at the “implied value” (“IV”) of IBM:

Implied Value Calculation

What this number (392.92) tells you is that, according to this formula, IBM’s shares have a current (c. Feb. 4th 2014) implied value of $392.92 per share. Currently, IBM’s shares are trading for $174.54 per share, implying that they are approximately 44% undervalued.

The question of whether or not it would make sense to purchase shares in IBM at this price depends in part on how much of an additional margin of safety you desire. For example, an investor with a margin of safety requirement of 50% would not be satisfied with this share price, while an investor with a margin of safety requirement that is less or equal to 44% would be satisfied. Of course, formulae such as this so-called “Graham Formula” should never be relied upon in isolation in making such investment decisions. Indeed, as noted above, this particular formula should not be relied upon to accurately estimate the intrinsic value of companies at all; it is more a gauge of market sentiment (“implied value”) than a valuation tool per se.

Before we move on from our discussion of this formula, it is worth noting that the “Graham Formula” has been interpreted and modified by more recent investors. For example, Joshua Kennon has offered a modified version which takes into account the “opportunity cost” [24] associated with the investment in question. These modifications consist of first multiplying the equation by the interest rate paid on high-grade corporate bonds at the time in which Graham wrote the equation. [25] Having done so, we then divide the whole equation by the interest rate paid on high-grade corporate bonds today. This expanded “Graham Formula” thus reads:

Implied Value Calculation continued Where “Y” = the current interest rate paid on “AAA”-rated corporate bonds.

We can find the current interest rate for “AAA”-rated corporate bonds by referring to an online database such as Yahoo! Finance. Alternatively, we can do so by referring to an index of “AAA”-rated corporate bonds, such as the popular Moody’s Seasoned AAA Corporate Bond Yield. For this article, I’ll take the second approach. At the time of writing, this yields an interest rate of 4.49%.

Plugging in our values from IBM, and adding this figure of 4.49% as our “Y” variable, we can now work through the formula as follows:

Implied Value Calculation completed

As we can see, this method yields an “implied value” for IBM of $385.05 per share. This is a slightly smaller figure than the $392.92 figure yielded by the original “Graham Formula”. What this difference in implied values tells us is that IBM’s shares appear slightly less attractive when the opportunity cost of alternative investment in high-grade bonds is taken into consideration.

I will close this section by repeating Graham’s warning concerning the use of this and other such formulas:

Warning: This material is supplied for illustrative purposes only, and because of the inescapable necessity in security analysis to project the future growth rate for most companies studied. Let the reader not be mislead into thinking that such projections have any high degree of reliability or, conversely, that future prices can be counted on to behave accordingly…” [26]

Or better still, as Warren Buffet aptly put it, “Beware of geeks bearing formulas.” [27]

Industry Analysis

In theory, a fruitful way to gain valuable insight into the future prospects of a given company would be to study the general prospects of their industry. In practice, however, such studies often have limited practical value because such industry-wide information is often already part of the “received wisdom” of market participants (and therefore often reflected in current market prices). [28]

The desire to gain a superior understanding of a company’s prospects by studying its industry is especially strong with respect to companies in emerging technology sectors. Who among us would not have loved to buy marquee technology companies like Google and Apple (or, for that matter, IBM) when they were first listed on the stock exchange? Yet for every technology success story, there are very many stories of failure. Moreover, since it is rare for failed companies to receive significant media attention, our memories are disproportionately skewed in favour of those very few giants who have achieved extraordinary success. For every Sidney Crosby there are tens of thousands of athletes who are never drafted to the NHL. Drafting Crosby to your team is like winning the lottery, but the odds of this happening are also like winning the lottery (well, not quite, but you get the point).

The alternative to investing in this manner consists of “sticking closely to the limits of value set by sober calculations resting on actual results.” [29] The disadvantage of this method is that “[one] must be prepared for the later contemplation of golden opportunities foregone.” The advantage of this method is that it works.

A Two-Part Appraisal Process

“Let us return for a moment to the idea of valuation or appraisal of a common stock… We suggest that analysts work out first what we call the “past-performance value,” which is based solely on the past record. This would indicate what the stock would be worth… if it is assumed that its relative past performance will continue unchanged in the future… The second part of the analysis should consider to what extent the value based solely on past performance should be modified because of new conditions expected in the future.” [30]

Distilling this paragraph, Graham’s “Two-Part Appraisal” consists of:

  1. Determining the stock’s “past-performance value”;
  2. Modifying the past-performance value based on “conditions expected in the future.”

What does this look like in practice? Graham expands on such appraisals in subsequent chapters.


At the time of publication, Jason Fernando held shares in one of the securities mentioned in this article. Specifically, he held shares in IBM (“International Business Machines Corporation”). He does not intend to trade any of these shares within 48 hours of publication.


[1] 281.
[2] 281.
[3] 570.
[4] 282-283.
[5] 282.
[6] See:
[7] 284.
[8] 284.
[9] 285.
[10] 285.
[11] 285-287.
[12] 288.
[13] 288.
[14] 291.
[15] 291.
[16] 293.
[17] 293.
[18] 294.
[19] 294.
[20] See:
[21] The terminology here is worth noting. In most articles written about this formula, the “IV” is taken to mean “intrinsic value”. This term (intrinsic value) is in fact the phrase used by Graham; the term I have chosen to use (implied value) is a substitution. The reason I have made this change is that many people are misled by Graham’s use of the term “intrinsic value” in this formula. As discussed in the previous section, this formula is in fact not intended to be used to ascertain the true (or “intrinsic”) value of a company. Instead, it is intended to give one an impression of the value which is superficially implied by currently available information (namely, EPS figures and “g”). Consequently, it seems to me that the phrase “implied value” is less likely to mislead investors than the traditional term “intrinsic value”.
[22] This figure of 8.5 is an estimate made by Benjamin Graham. Investors should feel free to modify this number if they feel they have good reason to substitute it for another.
[23] This report is freely available on IBM’s website, at
[24] Investopedia defines opportunity cost as “The cost of an alternative that must be forgone in order to pursue a certain action” ( They also provide a helpful video which illustrates the concept with examples (
[25] Kennon pins this year at 1962, but I am not sure where this figure stems from (
[26] 297-298
[27] See: This letter is a must-read for all current and future investors.
[28] 298.
[29] 299.
[30] 300.