Question

Would firm value be the same for a valuation in real terms discounted at a real WACC, to that if the valuation was changed to nominal using a flat inflation rate discounted at a nomial WACC? If not why?

Answer 1

i think it should be same provided that conditions satisfies is
1+R = (i+r)(1+i)
R = Nominal Rate
r = Real Rate
i = Inflation

Answer 2

If you are consequent with the calculations, it should be.
Because the greater the cashflows get from inflation you are deducting it in the nominal WACC, and vice versa.

if cash flow get bigger = 100*(1+i) , 100*(1+i)^2... and discounting it by the nominal rate, you can see it will be 0 effect.

Answer 3

both the value will be same provided value is calculated for t=0