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 P1, P2, P3, etc. be the portfolio values after year 1, 2, 3, etc. with a starting portfolio of p0.
- Let R1, R2, R3, ... and I1, I2, I3, ... be the nominal returns and inflation rates during years 1, 2, 3, ...
- Then the withdrawals at the end of years 1, 2, 3 ... are W0(1+I1), W0(1+I1)(1+I2), W0(1+I1)(1+I2)(1+I3) where W0 is the initial withdrawal.
- At the end of years 1, 2, 3, ... the portfolio values are:
>Yeah, I get the idea. So?
-  P1 = p0(1+R1) - W0(1+I1)
so P1/(1+I1) = p0(1+r1) - W0 where (1+r1) = (1+R1) / (1+I1)
Let p1 = P1/(1+I1) which is then the first year portfolio "in today's dollars".
Note too, that we can solve (1+r1) = (1+R1) / (1+I1) to get the "inflation reduced" or real return as r1 = (R1 - I1)/(1+R1).
Hence,  can be rewritten:
[1A] p1 = p0(1+r1) - W0
-  P2 = P1(1+R2) - W0(1+I1)(1+I2)
so P2/(1+I1)(1+I2) = p1(1+r2) - W0 where (1+r2) = (1+R2) / (1+I2)
Letting p2 = P2/(1+I1)(1+I2) again in "in today's dollars", we rewrite  as:
[2A] p2 = p1(1+r2) - W0
-  P3 = P2(1+R3) - W0(1+I1)(1+I2)(1+I3)
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 W0, 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