That's a nice example kiddo - but I believe the rest of the details are unnecessary at this stage. The OP's question was simply to understand the major difference between a high and low PE. I believe a simple straight forward example is most effective to distill a new concept. For productive and competence purposes - if the OP is satisfied - an essay can be spared.

My example above was a back-of-the-envelope type explanation - intentionally concise for ease of understanding - as it has no mention of new capital, smoothed or adjusted earnings, off-balance sheet adjustments, etc. And the example is not wrong in itself. I think that's what wit's end is referring to as the two different versions are essentially the same given an algebraic manipulation. If we do however take these additional details into account, including new captial, then the ratio will be in error as the recent earnings need to properly reflect the injection of fresh capital in the middle of its opearting cycle. Hence, there are quite a few variations of P/E ratios - and an analyst ususally runs through a number of scenarios and sensitivity analysis, depending on the sector, before deciding on a suitable model. I've also seen some analyst use basic EPS versus diluted EPS as the denominator - which can also make P/E ratios differ.

Also, I do not (and would not) apply P/E ratios to relatively value a firm since it uses market price and accounting earnings (due diligence is a must for both as they are fickle at best) - but I understand how the ratio works. The following ratios also have the same fallacies: P/Book, P/Sales, P/Cash Flow, Dividend/P, P/Operating Earnings, P/EV - notice how all of them assume that the market is precisely right. And we know that is not true.