This equation can be shortened with summation notation. Just in case you never had to deal with this in school, the funny looking "E" thing means "take the sum of...", the little t=1 below the summation sign means "starting from 1" and the infinity up the top means "...and continuing on until you reach infinity", the t in the equation itself then stands in for all the values of t from 1 to infinity, and you add them all up.
For example if you assume that dividends are going to increase at a constant rate for ever, the equation becomes very simple. D0 is today's dividend yield, D1 is next year's dividend yield, k is still the required rate of return and g is the rate of growth. If growth is zero, that is this is just a steady dividend that will never increase, then the value of this stock is the dividend divided by your rate of return. If the growth rate is not zero, then the share is worth next year's dividend divided by the rate of return minus the growth rate. It isn't that difficult when you understand the notation.
So you could use this to estimate the value of a growth stock that you think is going to have a few great years and then slow down a bit to grow at a more normal rate of growth.
Well this is all fine, but dividends are subject to the vagaries of dividend policy by management and anyway if we are going to consider ourselves as owners of the business we'd be wanting to look at earnings instead of just dividends. Putting this into the one-stage model where D=E(1-b) where D is the dividend per share, E is earnings per share, and b is the earnings retention rate (or 1-b is the dividend payout ratio) we get the following:
I know to many people here these equations will look horrendous, but they can be programmed into a computer or programmable calculator easily enough and then it all just becomes a matter of plugging growth rates or PERs or cash flows in to figure out what is a fair price for a security. Excel has most of these functions built in among its financial functions.
You can plug growth rates into this formula and get prices, or you can plug in prices and work out growth rates (tricky, but a computer can solve it easily enough). This is why you often hear comments about a stock having a certain growth rate "built in". Expensive growth stocks already reflect a very rosy future, when you work out the k's and the g's for the stock you'll find that either the market may already have a high rate of growth factored into the equation, and the corresponding rate of growth, g, will be pretty dull.