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a quick question about the DDM

I have a quick question about the DDM dividend discount model.

Do we need to assume that the capital gain growth rate is the same as the dividend growth rate? and why ?

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GGM implies that the constant growth rate, g, is the same and applies to both dividends and the intrinsic stock value, holding and the payout ratio constant. But since capital gains involves appreciation in the market price (which could be different from the intrinsic value), I don’t think we should assume the capital gain growth rate to be the same.