I developed this model independently in the 1970's while a management consultant.  Eventually, it was published in the Financial Analyst's Journal ("The P/B-ROE Valuation Model,", Financial Analyst's Journal, Jan/Feb 1984, pp.3-11) and much later provided the basis for much of Chapter 12 in my 1999 book, Investing By The Numbers.  Several institutional investors have adopted it, but it remains little used in comparison with other valuation approaches.  I recommend a simplified version of it here, not so much as a definitive valuation, but as a broad-based tool for surveying an industry and zeroing in on interesting cases. -- Jarrod Wilcox

This is the world's simplest valuation model more complicated than a ratio!  It is based on the general notion that there is a roughly linear relationship between a company's expected return on equity and the log of the ratio of it's stock price to its book value. It's empirical usefulness rests on an approximate correspondence between current return on equity and expected return on equity.  For that reason, it is best used to model possible fair values within a relatively homogeneous industry where technology stories don't overly affect expectations. In practice, the relationship is somewhat S-shaped for companies with extremely high profitability and extremely large losses, because extreme recent profitability levels are not expected to continue very long.

We can use the fact that a stock is much above the normal fair value in that industry given its particular level of profitability as an indication that the market believes relative profitability will increase in the future.  If it is much below, the market thinks relative profitability will decline.  Note that we do not conclude that such stocks are mispriced.  Cheap stocks are usually cheap for a good reason.  But not always.  And so the measure is a way to focus attention within an industry on a small number of stocks that are "interesting."

Here is the way it should be calculated. (You might go further by working out diluted earnings if options were exercised, making your own adjustments to book value and earnings, and so on.  But this is not a good practice unless you are truly expert, because you will tend to inject biases.)

First calculate return on equity (ROE) as the ratio of the last 12 month's earnings per share to book value per share.  Use GAAP reported earnings, not the pro forma version companies like to publish to get rid of unpleasant events.  As book value, use common equity from the balance sheet.  Do not use various alternative ROE measures that exclude negative earnings or include analyst estimates of the future.

Second, calculate or obtain common equity per share.  This is book value.  There is enormous prejudice against book value, apparently taught in MBA courses.  However, the basis for it is almost entirely mistaken.  Book value is original owner's capital plus the accumulation of retained earnings.  The errors it contains because of inflation or good will are similarly present in earnings.  Now divide price per share by book value per share to get PB.

What we want is to do the equivalent of plotting each stock's PB and ROE on semi-log graph paper, with PB on the log scale.  The following chart is for the computer industry as categorized by Value Line, as of October 25, 2002.  Only stocks with ROE greater than -0.2 and less than 0.5 have been plotted, so as to reduce the noise from stocks that where current ROE is clearly not predictive.

On the figure above, with PB on a logarithmic scale, we see that the computer industry leader Dell is far more profitable and more highly priced than others, but the pricing relative to a linear relationship is not excessive if we expect relative profitability to continue. The slope of the relationship, if we are using the natural log of PB (ln(PB) in EXCEL), measures the time horizon over which relative differences in profitability are expected to continue.  In the case of the computer industry, this is on the order of 6+ years.

How would we use such a chart?  One approach is to look for "buy" candidates on the "underbelly" of the relationship.  Usually they are there for a good reason, but sometimes you can find a stock that seems to have been overlooked or for whom the market seems to have over-reacted to current bad news.  "Sell" candidates may be generated for further investigation by looking on the upper edge of the relationship.  Again, these are mostly expensive for a good reason, but sometimes study will produce a picture of an overwrought market fad.

The preceding approach looks for the all too rare places where we might discover something the market hasn't reflected.  We can also use the fact that most of the rest of the time the market knows more than we do.  Suppose we owned Qwest in October 2002 but had read no newspapers in the last year.  Sometimes the PB-ROE chart will show a stock so far off from normal valuation that you know a large write-off must be expected.

In the chart above, the mainline spectrum (to paraphrase astronomy) runs from CCI (Crown Castle Intl) at the lower left up to VZ (Verizon) on the right.  Q (Qwest) lies far below, signifying an expectation of a catastrophe not apparent in past financials.  The lesson is that relative valuation based on accounting data is a good place to start, but is dangerous if used for blind screening.