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Capital Asset Pricing Model (CAPM) & Discounted Cash Flow (DCF)

Why does the Capital Asset Pricing Model (CAPM) give a different result than Discounted Cash Flow (DCF)? Please fully explain this as I understand both CAPM and DCF, but am not sure how to put it into words.

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Capital asset pricing models are mathematical formulas designed to quantify the trade-off between risk and return. Methods based on the CAPM are sometimes referred to as "risk premium" methods because the model provides an estimate of the risk premium associated with investing in specific issues of common stock. Therefore, CAPM based on the estimated market performance and the risk free rate, which are both ...

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"Discounted Cash Flow Method is one standard way of determining the cost of equity. This method assumes that a firm's current stock price is equal to the present (that is, discounted) value of all expected future dividends from the investment."