When one calculate the real invetment return (incorporating inflation), one often replaces the nominal return R by
R  i
or, more correctly, by (R  i) / (1+i) ... where i is the annual inflation rate.
For example, a nominal return of 8% means R = 0.08.
Incorporating a 3% inflation rate means i = 0.03 so, the real return (in terms of buying power) can be estimated
by 0.08  0.03 = 0.05 or 5% or (more correctly) (0.08  0.03) / (1+0.03) = 0.0485 or 4.85%.
When calculating the value of your portfolio with annual withdrawals increasing with inflation, we can do this:
 Let P_{1}, P_{2}, P_{3}, etc. be the portfolio values after year 1, 2, 3, etc. with a starting portfolio of p_{0}.
 Let R_{1}, R_{2}, R_{3}, ... and I_{1}, I_{2}, I_{3}, ... be the nominal returns and inflation rates during years 1, 2, 3, ...
 Then the withdrawals at the end of years 1, 2, 3 ... are W_{0}(1+I_{1}), W_{0}(1+I_{1})(1+I_{2}), W_{0}(1+I_{1})(1+I_{2})(1+I_{3}) where W_{0} is the initial withdrawal.
 At the end of years 1, 2, 3, ... the portfolio values are:
 [1] P_{1} = p_{0}(1+R_{1})  W_{0}(1+I_{1})
so P_{1}/(1+I_{1}) = p_{0}(1+r_{1})  W_{0} where (1+r_{1}) = (1+R_{1}) / (1+I_{1})
Let p_{1} = P_{1}/(1+I_{1}) which is then the first year portfolio "in today's dollars".
Note too, that we can solve (1+r_{1}) = (1+R_{1}) / (1+I_{1}) to get the "inflation reduced" or real return as r_{1} = (R_{1}  I_{1})/(1+R_{1}).
Hence, [1] can be rewritten:
[1A] p_{1} = p_{0}(1+r_{1})  W_{0}
 [2] P_{2} = P_{1}(1+R_{2})  W_{0}(1+I_{1})(1+I_{2})
so P_{2}/(1+I_{1})(1+I_{2}) = p_{1}(1+r_{2})  W_{0} where (1+r_{2}) = (1+R_{2}) / (1+I_{2})
Letting p_{2} = P_{2}/(1+I_{1})(1+I_{2}) again in "in today's dollars", we rewrite [2] as:
[2A] p_{2} = p_{1}(1+r_{2})  W_{0}
 [2] P_{3} = P_{2}(1+R_{3})  W_{0}(1+I_{1})(1+I_{2})(1+I_{3})
so ...
>Yeah, I get the idea. So?
The point I'm making is that, in determining the value of your portfolio in today's dollars, you can use the real, inflation reduced return
and assume a constant withdrawal amount.
>Constant withdrawal amount? That's W_{0}, right?
Right. So, if you're picking random nominal returns R, just change each random selection
to (R  i) / (1+i) and withdraw a constant amount.
>And do you have a spreadsheet for that?
No, of course not! However, here's an example of what I mean
The 20 years of annual returns are selected from a lognormal distribution with Mean Return of 8% and Standard Deviation 15% and an
assumed annual inflation of 3% and the initial withdrawal rate is 4%.
When one portfolio is reduced to $0, so is the other


