Tutorial: Calculating the Graham Number
10 September 2007This post is part of a tutorial series at Dividends Matter.
My goal at Dividends Matter is “to empower individual investors to gain the knowledge, skill, and confidence required to invest in high quality, dividend paying stocks to generate steadily increasing cash flow and ensure a lifetime of successful investing.”
To that end, I want to ensure that everybody is able to do the same analysis that I perform to determine if a certain stock belongs in a portfolio of superior dividend yielding stocks.
Today, we will have a look at calculating the Graham Number.
Benjamin Graham, the father of value investing and mentor to Warren Buffett, developed rules for the defensive investor when screening for stocks. The following formula uses his principles to calculate the maximum price one should pay for the stock.
This is by far the easiest calculation to perform of my 3 valuation methods because it only has 2 inputs: current earnings per share and current book value per share. To calculate the Graham number you simply take the square root of the product of 22.5 times the earnings per share times the book value per share. In order words:
square root (22.5 X EPS X BVPS)
For example, a company has reported a current EPS of $1.30 and a current BVPS (book value per share) of $12.26. The Graham number works out to
square root (22.5 X 1.30 X 12.26) = $18.93
It is as simple as that. You now have another tool in your arsenal for creating a portfolio of superior dividend yielding stocks.
How do I use the Graham number? It is used as a gauge to determine the relative value of the stock that I am studying. First and foremost, I use my average high dividend yield model to determine my entry price. But if I have two stocks that are currently both at their average high dividend yields, I will look at the Graham number and the stock that is closest to its Graham number will seem more valued.
Please remember that my analysis is but the beginning stage of your own investment analysis. I hope that my analysis will help point you towards an interesting stock worth studying further.
Remember that in the stock market, there is a buyer for every seller. One person thinks the stock is cheap, and the other thinks that the stock is expensive. Do your own due diligence.
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on September 10th, 2007 at 8:27 am
Why does Graham choose 22.5 as his constant? Is there any reason for picking it, or was it an arbitrary choice? Does it still apply this many years later?
on September 11th, 2007 at 8:37 pm
I find your Graham number interesting and I would like to know more about how you arrived at this calculation. I have read Ben Graham for several years and believe his major focus was on Net Asset Value for establishing a purchase price for a stock. Actually he wanted to buy a stock that was selling for 66% of it’s Net Asset Value which is calculated by taking Current Assets (those things which could be converted to cash quickly)and subtracting Total Debt, then dividing the result by the number of shares outstanding. It is very difficult to find any stock selling at this level today, although there are a few. This would result in an almost “sure bet” investment. Please tell us more about how you obtained the Graham number and I will endeavor to explain how I believe Ben Graham used the NAV calculation. Thanks, Michael
on September 11th, 2007 at 9:36 pm
Michael and Jordan,
You guys are going to make me dig out the big book!
Not sure that I can do the explanation justice in the comment but I will try.
Graham believed that the price-to-earnings ratio should be no more than 15. He also believed that the price-to-book value ratio should be no more than 1.5.
However, he noted that a price-to-earnings ratio below 15 could justify a higher price-to-book value ratio.
From that, Graham proposed that - as a rule of thumb - the product of the two should not be more than 22.5 (price-to-earnings ratio of 15 x price-to-book value of 1.5).
That is where the 22.5 comes from (15 x 1.5).
on September 12th, 2007 at 1:09 pm
Got it!
Price/Earnings X Price/Book = 22.5
Price(sqr)
________________ = 22.5
Earnings X Book
Price = SquareRoot (Price x Earnings x 22.5)
Works if 22.5 is the right number and who am I to argue with Ben Graham.
Would you like me to send an example of a stock trading at 66% of it’s Net Asset Value?
on September 12th, 2007 at 8:35 pm
That is exactly right Michael.
Jordan:
You asked where the 22.5 comes from. Part of it comes from the fact that Graham believed that the price-to-earnings ratio should not be higher than 15.
Where did the 15 come from? Well, Graham wanted his portfolio to have a yield equal yield to that of a AA bond. Back then, the yield was 7.5%. The inverse of this yield is 1 divided by 7.5%. That works out to 13.3. So that was his target price-to-earnings ratio for his portfolio. I guess he rounded up to 15.
Obviously that yield is higher than is available today.
on September 13th, 2007 at 12:22 pm
Thanks for the nice explanation. As Graham’s number (22.5) was calculated considering 7.5% yield, wondering if it would be more appropriate now to increase the number to 30 instead of 22.5 for current valuation, considering 5% yield rates and P/E values working out to be 20. Your valuable comments are much appreciated.
on September 13th, 2007 at 9:30 pm
Interesting thought Debu. And your argument definitely makes sense.
I think what I might do for the next little while is put up the ‘Classical’ Graham number (using the 22.5) as well as this new modified Graham number (using the 30) just to see how it changes the analysis.
Should be interesting.
on September 16th, 2007 at 3:54 pm
Debu & average_joe
Graham’s P/E and P/B were based on 75+ years of data. If you look rolling 20 year periods the numbers are very consistent. If we inflate Graham’s number because our interest rates are 5% not 7.5% we risk following the the “pied piper” and forget what Mr. Graham was trying to tell us. Intrinsic Value of the company is what we are trying to find. If your are looking for adjustments based on current interest rates, I would suggest comparing Earnings Yield of the stock to Short Term Safe Treasuries. Earnings Yield is the inverse of the PE. A stock with a PE of 15 would have an Earnings Yield(EY) of 6.66%, a PE of 20 would give the stock an EA of 5.0% and then you could decide if the margin of the EA is enough of a cushion for you to take on the extra risk of stock ownership vs a safe US Treasury. I for one would not be willing to buy a stock with a 5% EY unless the dividend was 3% and safe.
on October 8th, 2007 at 3:02 pm
average_joe
if you are getting your data from ADVFN which Book Value figure do you use? The Book Value or the Tangible Book value?