April 26, 2015

Benjamin Graham Intrinsic Value Formula

A Look At How the Father of Value Investing Calculated the Intrinsic Value of an Ordinary Share of Common Stock

Benjamin Graham Value Investing Allegory

Benjamin Graham, the father of value investing, recommended that intelligent investors imagine they have a business partner named Mr. Market who is manic depressive and wants to either buy your interest or sell you his every day at wildly different prices. This is probably the single most famous allegory in the history of finance. Image © Stockbyte/Thinkstock

Benjamin Graham, the rich investor, professor, and mentor to Warren Buffett, once proposed a quick back-of-the-envelope intrinsic value formula for investors to determine if their stocks were at least somewhat rationally priced.  He encouraged investors to only buy shares that passed the test and, if the market fell substantially as it is prone to do from time to time, to sit back, collect the dividends from their share of the profits, and ignore the stock price, instead acting just as you would if you owned a neighborhood pharmacy or a local hotel.

Those who follow finance know that Graham is perhaps most famous for his margin of safety concept, his allegory of Mr. Market, and the value investing strategies he used at his hedge fund, Graham Newman Corporation.

The Benjamin Graham Intrinsic Value Formula Is Incomplete But Still Useful

Benjamin Graham’s intrinsic value formula isn’t perfect.  There are several flaws in the model but for the average person who wants to try and put together a diversified portfolio of high quality blue chip stocks that will grow over time without major wipeout risk, it does have utility.

What are the shortfalls?  It doesn’t account for capital intensity, for one.  That is important.  An illustration may help you understand why I’m adamant about that belief.

Imagine that Jane and John each own a business that earns $1,000,000 per year in profit.  Jane owns an advertising agency and only has to reinvest $100,000 in capital expenditures to maintain her business, upgrading phone lines, putting in new computers, installing new furniture, and raising employee salaries.  John owns a construction equipment company that requires him to reinvest $700,000 of his earnings to grow, all of which sits in his lot rusting until it is sold.  Even though both earn a taxable profit of $1,000,000 per year, Jane has $900,000 in cash that can be spent, reinvested, or given to charity.  John only has $300,000.  Same profits, yet Jane has 3x as much cash earnings, or “owner earnings”.  You’d be foolish to think that John’s business was a bargain even if it were offered at a 40% discount to Jane’s business.

Likewise, the Benjamin Graham intrinsic value formula doesn’t quite catch risks that require wise human judgment.  A horse and buggy manufacturer would have appeared incredibly cheap on an intrinsic value basis but anyone who understood that people would switch to automobiles would have avoided owning the stock because the current earnings were doomed to collapse unless the business model changed.  You cannot just rely on the model or formula without thinking about the implications behind the figures.  The Benjamin Graham intrinsic value formula wouldn’t have caught the fatal error committed by Lehman Bros. when it borrowed short-term money to finance long-term assets, leading to its bankruptcy despite a multi-billion dollar net worth.

But it’s still useful in serving as a safety check to help you avoid using stocks as a lottery ticket and overpaying for businesses.  The biggest challenge you will have will be reigning in your optimism and avoiding overestimating future growth rates in earnings per share.  Earnings do fall from time to time.  That is the world.  You need to accept that and build it in to your valuation.

How to Calculate the Benjamin Graham Intrinsic Value Formula

Benjamin Graham argued that a “fair” price for a stock, or its intrinsic value, could be calculated as follows:

IV = EPS x (8.5 + 2g)

IV = Intrinsic Value
EPS = Diluted Earnings Per Share
8.5 = Fair Price to Earnings Ratio for No Growth Company
(This implies a 11.76% earnings yield)
G = Conservatively estimated growth in EPS for the next 7 to 10 years

The formula needs to be modified, though, because all intrinsic value calculations and formulas are based upon the opportunity cost relative to the risk-free interest rate.  Graham based his figures upon the 1962 bond rates, which aren’t the same as today’s bond rates.  So we can adjust Ben Graham’s formula as follows:

IV = EPS x (8.5 +2g) x 4.4

IV = Intrinsic Value
EPS = Diluted Earnings Per Share
8.5 = Fair Price to Earnings Ratio for No Growth Company
(This implies a 11.76% earnings yield)
G = Conservatively estimated growth in EPS for the next 7 to 10 years
4.4 = The average yield for high grade corporate bonds in 1962 when the model was introduced
Y = The Current Yield on AAA Rated Corporate Bonds

Looking at a Major Blue Chip Stock Using Ben Graham’s Formula

I wrote about Wal-Mart Stores, Inc., a few days ago in my essay on earnings yields of stocks versus yields of Treasury bonds.  Since it is fresh on many of your minds, let’s go back to it and apply Ben Graham’s formula.

Right now, the trailing twelve months earnings per share for Wal-Mart is $4.58.  If the company continues to buy back its own shares and grows its earnings at least with inflation, a 5% growth rate seems reasonable for the biggest retailer on the planet.  The current AAA bond yields are around 5.54%.  Plugging this into the formula, we get:

Step One:
IV = $4.58 x (8.5 +2*5) x 4.4

Step Two:
IV = $4.58 x (8.5 + 10) x 4.4

Step Three:
IV = $4.58 x (18.5) x 4.4

Step Four:
IV = $4.58 x 18.5 x 4.4

Step Five:
IV = 372.812

Step Six:
IV = $67.29 per share

Graham’s formula would indicate that a fair price, or the intrinsic value, of Wal-Mart’s stock is around $67.29 per share.  If you knew there was significant share dilution from stock options or convertible instruments, you’d adjust that figure appropriately.  If you expected interest rates to skyrocket, you’d lower the intrinsic value per share rate to compensate since your opportunity cost would rise.

Benjamin Graham’s Relative Intrinsic Value Formula

From here, you could calculate something called the relative intrinsic value of the stock.

RIV = IV ÷ Current Share Price

In the case of Wal-Mart, the stock trades for $53.63 so we would use that as the current share price.

RIV = $67.29 ÷ $53.63

RIV = 1.2547

In Graham’s world, anything over 1.00 is considered undervalued; the higher, the better in most cases.  Anything under 1.00 is considered overvalued and should be avoided.

Again, it’s not perfect.  But if investors had used it to measure the holdings in their portfolio, they could have avoided many of the bubbles, including the dot-com crash a decade ago.  Think of it as a preliminary screen; the companies that pass might deserve a closer look.  It’s also not going to make you rich unless you have a lot of time to compound your money and / or you are constantly adding new equity to grow the total funds working for you.  After all, if someone were 18 years old and began buying even boring blue chip stocks that were fairly or undervalued, they should retire at 65 with dignity and comfort, enjoying the fruits of their labor.

  • Daheideman

    Joshua, I know your world is full of opportunities with your operating businesses and investments, but have you decided when you are going to release your newest book on calculation of intrinsic value? I can’t wait for its release.

    • Joshua Kennon

      It’s been on the shelf for the past half a year or longer. I’d like to get back around to working on it. Last I checked, the first 105 pages were done.

      • Paarthurnax

        Any update on this? Would love to pick up a copy!

        • Eric King

          Me too! Any update Josh?

  • Muhammadrahim900

    hey joshua! i just wanted to ask regarding the intrinsic value formula that when we are calculating the current yield on AAA corporate bonds do we take the 20 year bonds??? kindly provide us with a little information on how we can get the information regarding the AAA corporate bonds……altough i know the formula for for how to calculate it i still would like it if you were to show us how you calculate the current yeild on the AAA corporate bonds. thanks!!

    • Joshua Kennon

      Bond yields are published in all major financial newspapers such as the Financial Times, The Wall Street Journal, etc. The Bloomberg Bond Yield page is especially useful. You don’t have to calculate it – it’s published. I mean, technically, you can calculate a bond’s yield or a composite of bond yields but it would be completely pointless and unnecessary.

  • Joshua Kennon

    Other than a mass deflationary event, I just don’t care about macroeconomic events except to the extent they would affect the individual profitability of the firm or asset in question.  Imagine that what you said came to pass – stocks sold off due to demographic changes and companies traded at half of their value.  Theoretically, the earnings are the same.  That means the firms could pay out 2x the dividends and buy back 2x the stock, doubling gains for stockholders.  The difference is, the gains would come from increased dividends instead of capital gains on the share price.  You’d see dividend yields of 8% or 10%.  That would be perfectly fine with me.  I don’t care how the wealth that is generated is paid to me – in cash dividends or a higher share price – just that my net worth continues to grow over time.

    If I see value, I want it.  I buy as much as I can for every dollar invested.  I figure that in the long-run, the rest will work out.  Looking at 200+ years of market data, that is the most rational course of behavior as long as you work to always avoid wipeout risk by avoiding leverage, not straining your liquidity too heavily, and not exposing yourself to foolish risks.

    • nsingh

      Good post, One question though; How do you calculate ” G = Conservatively estimated growth in EPS for the next 7 to 10 years ” ? Its subjective, What things should be considered in calculating G ? Secondly as previously questioned which AAA bond should be considered, 10, 20 or 30 year.

  • TLV

    How do you interpret the difference between this intrinsic value formula and the dividend-adjusted PEG ratio?
    For example, using the data from your article on dividend-adjusted PEG (and ignoring the bond yield factor),
    P = 38.85
    EPS = 2.05
    G = 8%
    Dividend yield = 2.6%,
    RIV comes out to 1.29, indicating the stock is under-valued, but dividend-adjusted PEG is 1.793, which would make it over-valued.

    • Paarthurnax

      I’ve had the same question of sorts lately. I’ve been collecting a list of stocks to further study/watch and have been working on calculating their IV with the formula you showed above, as well as finding each stocks APEG, and other bench-marks such as dividends = to T-bond, Lynch’s EPS to P/E requirements, etc. And I’ve found what looks like a good pick with some of the criteria, while not fitting in by others (or perhaps my math was off).
      Could you shed some more light on if you’ve ever experienced this sort of outcome while looking at a stock? Do you feel the IV outweighs the APEG, or is it all a part of your criteria a stock must past? I’m assuming it’s a by-case scenario but would appreciate some further insight, thanks for the great post.

  • Flash

    I agree with the other two previous posts there are other variables that go into deciphering which corporate bond to select. Which criteria is it that you select from when selecting your Corporate AAA bond?

  • Anon

    Thank you for posting this. Keep up the good work.

  • Bryin

    Perhaps the greatest article every written in history of the stock market. Given the basis is Mr. Graham, this is hardly surprising. Since most of the USA is lazy and not prone to pick the “Intelligent Investor” writing this article does a great service for many people.

  • kelseynealon

    Hello Joshua,

    Might I ask why you divide the whole formula by the current AAA Corporate Bond rate? Shouldn’t you just replace the 4.4% with 5.54? For example, IV = ($4.58 x 18.5 x 5.54) instead of IV = (($4.58 x 18.5 x 4.4 )/ 5.54)?

    • http://www.joshuakennon.com/ Joshua Kennon

      First, keep in mind that the formula in question has limited utility. With a little bit of inversion, it allows you to roughly estimate, in a rational world, whether the growth rate other investors say they are assuming is mathematically consistent with the current stock price were you to demand a satisfactory return relative to one of your next best options, in this case, high-grade corporate bonds.

      The “reasonable” base earnings yield, with is the inverse of the 8.5 multiple he used (here, 11.76%) is determined by a real spread over that a competing, “safer” benchmark. Graham used it at a time when corporate bond yields were 4.4%. That means unless corporate bond yields are always 4.4%, his formula cannot, by definition, make sense. You’d have to change the 8.5x multiple figure to come up with a better number.

      You could do that. Graham implied the earnings yield should be at least 7.36% above and beyond the corporate bond yield, so you can go back to the time period and figure out the inflation rate + tax rate to see what kind of real return he was expecting, then make an adjustment for today’s conditions. Given the limited utility of this particular formula in the real world, it’s probably not worth the effort (which would take all of 2 or 3 minutes) but it’s still a possibility were you curious. Today, for example, dividend income is taxed more favorably than interest income so you’d need to make an adjustment for differentials in net after-tax cash flows. It’s, again, probably not worth the effort.

      Regardless, we have to somehow approximate this grossly oversimplified tool to account for shifts in the bond yield without changing the 8.5 figure if we just want to flip over an envelope. The simplest way to do this is to add a product on the end, expressed as a number (4.4) corresponding with the bond yield, then divide the whole thing by the current bond yield expressed as a number (5.54, in this case when the post was written). This has the effect of changing the intrinsic value answer by a proportional amount to the change in the bond yield from the time when he wrote the formula. (This is normally nonsensical due to the way exponential growth works – a small change means big ultimate differences but, again, this is a grossly approximate first-glance tool.)

      If you don’t do this, the numerical relationships stop making sense. It wouldn’t tell you anything particularly useful because it would ignore real world opportunity cost.

      It might be easier to walk you through an example.

      Let’s say that corporate bond yields had skyrocketed to 15%. We have a business with $10 earnings per share and a 10% growth rate.

      Using Graham’s original formula, intrinsic value might approximate $185 per share. ($10 x (18.5) = $185). That is, if investors say they expect a 10% growth rate, profits are $10 per share, and the stock price is $185, the market value matches up with their expectations without being too out of line, all else equal.

      If we, instead, adjust it to account for changes in the bond yield, we would slap his original bond yield on the end, then make the current bond yield the divisor, and get $146.93. ([$10 x 18.5 x 4.4] / 5.54]). That is because the stock is relatively less attractive when this post was written, and you could earn 5.54% by parking your money in bonds, than it was in his time, when you could only earn 4.4% parking your money in bonds. That means, due to opportunity cost, if the stock were trading at $185, it would have to grow at more than 10% if you were to generate a mediocre rate of return on it compared to your hurdle rate.

      If you did what you suggest, the numbers become meaningless. Give it a try and see.

      Again, this is an extreme approximation tool; a sort of first pass way to see if something weird is going on with a business or if people have become too optimistic or pessimistic in general. People use it, or treat it as gospel, because it’s easy. It’s dangerous to take that approach. To actually value the firm, you’d need to dig into the financial statements and discount cash flows. I’ve written about my preferred method here.