Cost of Equity (WACC) vs. Cost of Stock (Merger Model)

I was wondering why the cost of equity for WACC is calculated using CAPM but the cost of stock in a merger model is used by inverting the P/E ratio. I don't understand why these costs are different. Any insight would be appreciated.

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good question hope someone will be able to correct me if i'm wrong but the one given by the CAPM is the average (for a certain period- cf how much historical data you've used to make it) best opportunity cost you were able to get on the market given a certain level of sensitivity to market risk (beta). This means that in order for this company'sb stock[/b] to add value given all the equity in stock market & the actual risk free rate and it's beta it must beat this CAPM Re. it does not mean that the company actually did beat it. (P/E)^-1 = Earnings/Market Cap ~~ Yield on that security - this is what the stock has been actually doing (if u calculate ur P/E ratio using historical data)

 
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