Compounding Engines and Price Volatility

I view companies as compounding engines.

Quality companies  have consistently high returns on equity.  They have this special ability to use their retained earnings to increase their equity base, which they can then use to generate even more earnings in the future, and so on.  I don't give any consideration to low quality companies, that is, that don't have consistent and high returns on equity, so pour moi, and long term value investors alike, it holds that companies are compounding engines.



Companies choose how much of their earnings to retain, and how much to pay out to their shareholders as dividends.  Companies that have high returns on equity, can generally manage their retained-earnings capital more effectively than their shareholders, almost by definition, because that are at or near the top of the return-on-equity ladder.  Therefore, it makes sense for quality companies to retain a high proportion of their earnings.

Interestingly, these compounding engines sell for prices that vary widely.  Even the same engine varies quite a lot in price over a period of years, and also within a given financial year.  Generally, of course, the price of these compounding engines rise over time, but within that trend, there is certainly a lot of volatility.

Let's say that every 5 years, shares in a quality company go on sale for half price.  By waiting for the sale, as opposed to purchasing "now", I will be able to buy twice as many shares.  Logically, then, I will receive twice the dividends from my shares, and so I will have twice as much cash for my next purchase.

Now, in next purchase, I will of course by the more shares in the same quality company, and of course I will wait until they are on sale again - probably in about 5 years.  Thus, I will have twice as much cash, and again by them on sale, such that I have 4 times the number of shares that I would otherwise have had if I had not waiting for the sale.

Five years later, I will have 8 times the portfolio value than I otherwise would have, and 40 years later, I would have 256 times.

There's an obvious mathematical mistake in the above.  Over 40 years, the answer isn't really 256 times.  My question for the reader is:

• What is the real answer?
• Does that convince you that it is worth waiting for?