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#1
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Is there a mathematical relationship between the expected growth rate and PE ratio?
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#2
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Yes. You pay a higher PE for stock A than stock B because you expect increasing earnings per share over time from stock A. The detailed valuation is done by DCF, two simpler models are Graham's formula or the (brain dead) PEG ratio.
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#3
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Pretty much when discounting the earning (if treating them as a perpetuity) you do a 2 stage growth model (or multi stage growth if you want). This means for the first 5 years you expect high growth you subtract that rate of growth from the discount rate
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