CF Yield and inflation

Lets say you calculate a normalized FCF number and then a normalized FCF yield. Two questions: why do you add inflation to that number, and why do you add growth to that number.

As an example, lets say equity price is $100, Normalized FCF is $10 p/s. That gets you to a yield of 10%.

Now, why add inflation to this number. Shouldn't inflation have made its way through the income statement through higher prices, hence already be included in the earnings and FCF number?

Secondly, lets say growth is 2%. If I grow $10 p/s at 2% I come to $10.2, coming to a yield of 10.2%, not 12%.

I am clearly missing something conceptually here; I'm hoping someone can clarify this for me.

Thanks.