Charlottesquare wrote: the value of a share is the discounted sum of its dividends to infinity
Change that to cashflows and you might have a point. Valuing a share like a perpetual bond, which is basically what you are saying, doesn't allow for capital growth nor future capital distributions, which of course would not apply to a perpetual bond.
Again, are those dividends growing or stagnant? Covered or not? There are so many other variables.
Also infinity is rather too long a time. The difference in valuations between, say, 50 year and 100 year bonds is trivial, indicating that when you go out more than a few decades it doesn't really affect anything.
And imputing a dividend to a stock like Berkshire Hathaway, let alone Amazon or FaceBook, will take you nowhere close to its actual valuation, which I would take as a sign of a fundamental flaw in the method. Since the market takes more into accounts than just dividends, so should a valuation model. I'm afraid it just isn't that easy, otherwise we'd all do it