Summary :
I - WHAT IS GRAHAM's FORMULA ?

A - A FEW IMPLICATIONS OF GRAHAM'S FORMULA
1 - Price Earning Ratio (P/E) as a function of future growth (G)
2 - Implicit Growth derived from price and earnings.

II - HOW IS GRAHAM's FORMULA APPLIED ON INVESTINVALUE.COM ?

Benjamin Graham describes a formula he used to value stocks in the 11th chapter of the “Intelligent Investor”.(whole text here) :

"Most of the writing of security analysts on formal appraisals relates to the valuation of growth stocks. Our study of the various methods has led us to suggest a foreshortened and quite simple formula for the valuation of growth stocks, which is intended to produce figures fairly close to those resulting from the more refined mathematical calculations.

Our formula is :

Intrinsic Value = Current Earnings x (8.5 + 2 x Expected Annual Growth Rate)

The growth figure should be that expected over the next seven to ten years."

Example n°1 : A stock is trading at 120$. Its current earnings are 8$ per share. The annual growth rate over the next 7 to 10 years should be around 7%. The Intrinsic Value is = 8 *( 8.5 + 2 * 7) = 180 $. The Margin of Safety is : (180 - 120) / 180 = 33%.

Example n°2 : the same stock is still trading at 120$, but its earnings are revised to 9$ per share and the annual long term growth rate should now be around 8%. The Intrinsic Value becomes = 9 *( 8.5 + 2 * 8) = 220.5. The Margin of Safety is : (220.5 - 120) / 220.5 = 56%.

Example n°3 : the same stock is trading at 120$, its earnings are 5.5$ per share, the annual growth rate around 6.5%.
The Intrinsic Value is = 5.5 *( 8.5 + 2 * 6.5) = 118. The Margin of Safety is : (118 - 120) / 118 = -1%.

A - A FEW IMPLICATIONS OF GRAHAM'S FORMULA

1 - Price Earning Ratio (P/E) as a function of future growth (G)

If we assume that Intrinsic Value = Price, then Graham's Formula is equivalent to : Price / Earnings = 8.5 + 2 x G.

In other words, the P/E for a no-growth company (G = 0) should be around 8.5.


2 - Implicit Growth derived from price and earnings.

From the fomula above, a P/E can be linked to G this way : G = (P/E - 8.5) / 2.

or graphically :




Example : If a stock is trading at 100$ and has earnings of 5$, then we have : G = ( P/E - 8.5 ) / 2 = (100/5 - 8.5) / 2 = (20-8.5)/2 = 11.5 / 2 = 5.75%.


B - HOW TO ESTIMATE LONG TERM GROWTH ?

Estimating long term growth over the next seven to ten years as required by Benjamin Graham is a key point. Unfortunately, what is certain about future growth is that it is unpredictable. Yet, a few techniques are available :

- dividing earnings current earnings by earnings ten years ago and assuming that past growth will reflect future.
- dividing average earnings on last three years by average 3 years earnings ten years ago
- estimating future growth by fundamentals from the balance sheet
- linear regression or log-linear regressions : this is the one chosen on Investinvalue.com.
- you can also try this one : here

A good study of the different ways of estimating growth (... and much more...) is available on Pr. Aswath Damodaran website : here


C - COMPARING GRAHAM's FORMULA WITH DISCOUNTED CASH FLOW METHOD ?


A good website to compare valuation methods is MoneyChimp : here

GRAHAM'S FORMULA / DCF SIMULATOR : With this simulator (click HERE) you can compare the fair value given by a two-stage discounted cash flows model with the fair value of Graham's Formula.


D - GRAHAM'S FORMULA LIMITATIONS

Concerning Future Growth Rate :

Investinvalue.com utilizes a linear regression of past 10 years earnings to determine growth rates : the last ten years may or may not reflect the future growth rate. Competitive landscapes change, capital structures change, and hence earnings growth rates will be affected.

Concerning the level of Current E.P.S. :

- earnings may be bloated or understated depending on accounting choices.
- cyclical businesses in the late stages of an economy will have a very high earnings base that is used as the basis of the valuation.
- Balance sheet leverage is also not considered in the valuation.
- Businesses that are currently loss-making are worth zero in this analysis.

What follows is taken from an excellent blog : http://valuediscipline.blogspot.com/

" This raises another important reminder. Valuation is an incredibly imprecise art. In some ways, the development of the spreadsheet was one of the most dangerous inventions of the twentieth century. Extrapolating data into the hereafter without consideration of its reasonableness, without consideration of competitive advantage periods, and without considering something other than linear growth has often provided ridiculous results.

Though elegant spreadsheet models may create an illusion of precision, their complexities do not necessarily suggest greater accuracy than the Graham model. I do prefer free cash flow based valuation models but like every model, the valuation is entirely dependent on the input assumptions. Man have I gotten a lot of those wrong over time, but the spreadsheet sure looked impressive.

I think the website is definitely worth a look and a spin. You may or may not agree with the valuation it accords your stock, but at least it should make you think about the reasonableness of your assumptions. If it achieves that, it's a great site."


E - BACK TESTING GRAHAM'S FORMULA

GRAHAM's formula has been applied to S&P500 index since 1940. The datas come from Professor Robert J. Shiller (Yale University).

1 - Estimating Earnings Long term Growth : the "G" parameter

Our estimation of earnings long term growth rate is based on a linear regression of the past ten years earnings per share.

For example, consider Citigroup's Historical earnings on this chart.

The linear regression on the past ten years earnings (orange bars) looks like this (red line) :

The prospective linear regression for the next year is the red line.

Long term growth is estimated by dividing next years earnings (estimated by regression) by current year earnings ; here, long term growth rate estimation is 4.79 / 4.48 - 1 = 6.91%

2 - Applying GRAHAM's FORMULA

In the example above :

Current Earnings Per Share = EPS = 4.48

Long Term Growth Rate = G = 6.91

Intrinsic Value = V = EPS * (8.5 + 2 * G ) = 4.48 * (8.5 + 2 * 6.91) = 100 dollars.