Say you own 1 share. It's trading for $20. Tomorrow the company pays $2 dividend. Then your share is worth $18 and you have $2 cash as well.
Alternatively, if you're buying the share, you're willing to pay $20 for it today but only $18 tomorrow, because you know that you won't be getting a $2 dividend if you buy it.
If you take future dividend payments into account, you also need to discount them. If you think that (discounted future dividends) > (stock price), that's a signal for you to buy. If enough investors reason this way, the price will rise until (discounted future dividends) ~~ (stock price).
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.
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.
Say you own 1 share. It's trading for $20. Tomorrow the company pays $2 dividend. Then your share is worth $18 and you have $2 cash as well.
Alternatively, if you're buying the share, you're willing to pay $20 for it today but only $18 tomorrow, because you know that you won't be getting a $2 dividend if you buy it.
If you take future dividend payments into account, you also need to discount them. If you think that (discounted future dividends) > (stock price), that's a signal for you to buy. If enough investors reason this way, the price will rise until (discounted future dividends) ~~ (stock price).