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"...So, in words, without any numbers, that's another take.

"Thanks, however, for the numbers."


Yeah, maybe I was being too "numbery" (and too wordy?). But the explanation given by the Gardner bros. just did not make any sense to me, primarily because of the one central thesis they maintained:

"In a fully and fairly valued situation, a growth stock's price-to-earnings ratio should equal the percentage of the growth rate of its company's earnings per share."

That rule-of-thumb is simply illogical. There is no such connection between P/E and G; not per se, anyway. Ganymede97 also saw the strangeness of it:

"At the risk of being totally sophomoric, WHY? Why does Wall Street practice this concept?

"I am still trying to see why a 20% growing EPS company should trade at 20X eps to be 'fully valued'.

"Is there some simple math that might help explain the rationale?"

That query, and also the number of posts concerning how to compute it, and "Does it really work?", made it seem proper to indulge in the numbers and math:

E[i + 1] = E[i] + (a * P[i])
P[i + 1] = P[i] + E[i]

G[i] = 100*((E[i + 1] / E[i]) - 1)
= 100*(((E[i] + (a * P[i]))/E[i]) - 1)
= 100*((1 + (a * P[i]/E[i])) - 1)
= 100*a*(P[i]/E[i])

Dropping the i's, consider how this:
G = 100*a*(P/E)

compares with:
P/E = G

The whole point of the math was to demonstrate that someone made the underlying presumption of average yearly market gains of 10%. Yet, even presuming this "10% Rule", how does one make a proper choice of "a"? With a little more math, of course.

On the other hand, a company which returns 10% on its assets shall show a P/E of 10 - which is all too convenient, but, who knows, maybe that's the initial hypothesis from which the PEG had its start. Even so, we Fools must be certain of the rationale behind any idea in order to assess its soundness.
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