Mechanics Of Price Increase Of Growth Stocks At New Earning Announcement - Please Critique

Hi there, 

A bit ashamed to say that I am still a bit confused how growth stocks actually produce their returns for their shareholders over time. More specifically the actual mechanics of it. Please bear with me:

Let's say you buy one stock of a tech company today at t=0 at a rather high 1yr forward P/E ratio. Now fast forward one year to t+1. Suppose the earnings announced at t+1 are exactly those implied by 1yr forward P/E ratio a year ago at t=0.

At t+1 we realized one year of earnings. The remaining future earnings are unchanged minus what we just realized at t+1. Basic algebra tells me that stock price should appreciate by the difference in value of all discounted future earnings at t=0 and t+1. 

If we look at classic DCF valuation, in % terms that difference is the discount rate or cost of equity. That stock's market price should appreciate by the cost of equity of that tech firm = risk-free rate + beta x equity risk premium.

If the above is how it works, then the actual rate of stock price appreciation is in steady state its required rate of return, or cost of equity. Then, unless cost of equity for growth stocks is higher relative to value stocks, growth stocks should not necessarily appreciate in value faster than value stocks. 

Of course in real life there is one more important factor at play. Earning expectations themselves fluctuate, some times wildly, as well as perception of how risky a given stock (or how high its beta) is.  

But overall, is my thinking correct?