The future earnings have huge uncertainty to them. A company with a $50 stock price might have $5 per share worth of cash in the bank, (which is something you can actually observe.) The other $45 represents expected future earnings. If the stock pays out a 50c dividend, the stock now has $4.50 per share in the bank and the $45 expected future value is unchanged.

Either you're stupid, or there's a misunderstanding. Probably the latter. Let me try again. Assume that δ is the discount factor (δ = 1 / (1 + r)), P is price, and D_i is the dividend in year i.

Before dividend:

  P = D_0 + δ D_1 + δ^2 D_2 + δ^3 D_3 + ...

After dividend:

  P = δ D_1 + δ^2 D_2 + δ^3 D_3 + ...

When calculating the value of an annuity, all that matters is your number of periods, the amount, and your discount rate. This is why an annuity appreciation chart over time is continuous.

This comment would be better without the gratuitous namecalling.

Sorry, I get very (too) emotional when someone is wrong with math...