Why do we use CAPM model to calculate cost of equity but also expected returns?

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I still can’t wrap my head around why expected returns, which is what CAPM calculates, is supposed to be equal to cost of equity, which is also what CAPM seems to calculate. I haven’t found a clear explanation that directly addresses the relation between the two. Help?

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Think of it as an opportunity cost – what returns am I expecting given a certain risk profile? That is essentially my “cost” as I need to earn that at least that return on my equity or else it’s going to be an NPV negative investment.