The actual answer to this is - it depends. It doesnt always increase intrensic value because of the dividend displacement of earnings - which you alluded to. It just depends on the size of the increase and the relative growth rates.
I have run across a few questions about this when studying. Each time they are either:
If a firm increases dividend payout then the most likely effect on the stocks intrensic value/fundamental P/E ratio is: A) Goes up B) goes down C) cannot determine. Obviously in this case the answer would be you cannot determine. There is no blanket rule due to the dividend displacement of earnings.
If a firm increases its dividend payout ratio while holding other factors constant then the most likely effect on the stocks intrensic value/fundamental P/E ratio is: A) Goes up B) goes down C) cannot determine. Obviously in this case the answer would be A - assuming all else is held constant.
There is also some questions that put numbers to it in which you would be able to calculate the effect of the increase in payout ratio. I think for exam purposes they would be specific on what point they are trying to get at and what concept they are trying to test (knowing dividend displacement of earnings vs. knowing how to use constant growth model/fundamental p/e model).