Delusional Investing: Price to Book ratio and Return on Equity

Following on from my look at the Price to Earnings ratio, and in a similar vein to my post on subsequent rates of return, I'd now like to take a look at P/B ratios and ROE. The mechanics of the numbers are fairly straight forward.

The Price to Book ratio is the price that you pay for the book value of the company - the book value being the net (booked) value of their assets - or in really simplistic terms - how much money they have in the bank, assuming no liabilities. So, if they have $100,000 in assets and you pay $200,000 for the company, you are paying a price to book value of 2:1.

The Return on Equity is simply how efficient the company is at making a profit. If they use the $100,000 to generate $15,000 profit, they have an ROE of 15%. Not bad.

These two metrics are linked though the P/E ratio.

But before that, some Value Investing history. The original value investor, Benjamin Graham, looked for (good) value in low P/B ratios - ie, below 1. The theory should be obvious. If you are paying $50,000 for a company that has $100,000 in the bank, you'll tend to do well.

The art, of course, was differentiating between "book" value, and real value. For example, some companies (e.g. railroads) purchased lots of real estate. Over time, the real value of these properties increased - some times many times over, however the value on the companies balance sheets (book value) never changed. To continue the example, let's say the $100,000 of company money was not all cash in the bank, but was made up of $50,000 cash and $50,000 real estate. But let's also say that that real estate was purchased 20 years ago, and could be conservatively valued today at $500,000. All of a sudden, a price of $300,000, or a book value of 3:1, doesn't seem so expensive.

Warren Buffet learned this P/B trick off Graham, but then took it to another level. By focusing his "value" portfolio on companies with a high ROE, he got a double whammy - cheap companies that were very efficient and would continue to grow over time. The actual business feature that led to the high ROE was what buffet called a "durable competitive advantage".

OK. History lesson over. Lets take a look at the interplay between the P/B ratio and ROE. I said above that the two were linked through the P/E ratio. Let's take a look this.

Market Price / Book Value => P/B ratio
Profit / Book Value => ROE
Market Price / Profit => P/E ratio

Hence my conclusion about the two components of P/E being cheapness (P/B ratio) and growth (ROE).

Going back to our example of our $100,000 company (book value) that earns an ROE of 15%. Let's also assume that, as an investor, our target rate of return is 15%. Clearly, if we pay par value (P/B = 1) for this company (or part thereof), then we achieve our desired rate of return.

If, however, ROE of the company is only 7.5%, then, to achieve our desired rate of return of 15% we would need to purchase this company at a discount, to compensate for it's slower growth. Clearly, if we purchase this company for only $50,000, then we achieve our desired rate of return of 15%.

Hold the phone. Not so fast. We achieve an initial rate of return of 15%, ($7,500 / $50,000), but the following year we would achieve a rate of return of 16.125% ($8,625 / $50,000) because the company is still achieving 7.5% ROE on it's compounding capital ($100,000 x 1.075^n). This is discussed in more detail here.

The interplay between cheapness (P/B ratio) and growth (R/E) is delicate, and needs to be modeled in a spreadsheet to be able to see the interplay a little more clearly. I'll save this for another post. However, I'll leave you with the Buffet quote: