Cost of equity and fair share price growth: at cost of equity?

I am used to using cost of equity in DCF valuation etc. However, from a perspective of an investor in public equity markets: does cost of equity of, say 10%, imply that the justified growth for that share price should be 10%? So, if the share price is USD 10 today, the price should be USD 11 in one year? That is of course assuming the market values that share correctly (i.e. its intrinsic price is indeed USD 10 today). 

Is the above a correct way of thinking about this? Would be grateful for any input from you guys. 

 

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