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 ?

GGM implies that the constant growth rate, g, is the same and applies to both dividends and the intrinsic stock value, holding r 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.