My results, which are not accurate as yours came up pretty close after 22 years. The ending size of your portfolio is $876K nominal, $543K real. The size of the portfolio resulting from Bengen's scheme is $
1.366M nominal, $847K real. These two portfolios are not close in value.
You designed a scheme radically different from Bengen's. Bengen assumed that one would withdraw a constant amount of money each year, in real dollars. Your scheme withdraws an amount each year that fluctuates based on the value of the portfolio.
From the way you describe your design, 4.5% + 2% for inflation, it seems that you still think that Bengen's scheme is to withdraw 4.5% of the value at the end of each year after adjusting for inflation. This is the miscommunication.
Bengen wrote (same quote as before): "
After the first year, the withdrawal rate is no longer used for computing the amount withdrawn; that will be computed instead from last year's withdrawal, plus an inflation factor." In contrast, each year you use a withdrawal rate (7%) to compute the amount withdrawn.
You direct PV to withdraw 7% of the portfolio each year, leaving 93% to grow (or shrink) over the following year. So the withdrawals can never exhaust the portfolio. However, as the portfolio shrinks in size, so will the size of the withdrawal.
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For example, suppose that the portfolio is invested in something that loses
10% of its value, no more, no less, each year. Then under your scheme, a portfolio that started with $
1M would progress as follows:
Start: $
1,000,000.
Year
1 end: $900,000.
Withdraw $63,000 (7%).
Year
1 after withdrawal: $837,000.
Year 2 end: $753,300.
WIthdraw $52,73
1 (7%) - notice that the size of the withdrawal is shrinking.
Year 2 after withdrawal: $700,569.
...
Year 22 end: $2
1,452.46
Year 22 withdrawal $
1,50
1.67
Year22 after withdrawal: $
19,950.79
I find it instructive to do calculations by hand, but in case you don't believe me,
here's PV's calculation. If you mouse over the graph to year 22, you'll see that the value is $
19,95
1 (before adjusting for inflation).
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Bengen's scheme (assume 0 inflation for simplicity, higher inflation would merely make the results worse):
Start: $
1,000,000
Year
1 end: $900,000
Withdraw: $45,000
Year
1 after withdrawal: $855,000
Year 2 end: $759,500.
Withdraw $45,000 - or more if there is inflation
Year 2 after withdrawal: $724,500.
...
Year
11 end: $50,025.36
Withdraw $45,000
Year
11 after withdrawal: $5,025.36
Year
12 end: $4,522.83
Not enough to withdraw $45,000. Portfolio is exhausted.
Again, I think that the figures above are more instructive than blindly using a calculator. But
here's PV's calculation. Mouse over year
11, and you'll find the value $5,025 (before adjusting for inflation). Obviously PV reports that the portfolio is exhausted in year
12.