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Interesting question. Given that you're usually using the yield on the 10yr on a nominal basis, I'd assume that CAPM would return a nominal cost of equity.

Additionally, if CAPM returned a real rate, then in our calculation of WACC we would want to provide real, not nominal, returns to debt investors as well in order to have them on the same basis. Given that we typically just look at after tax cost of debt as it currently stands (or comps as they stand), we're looking at cost of debt that isn't adjusted for inflation. This would imply that cost of equity is on a nominal basis as well.

 

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