Amortization based withdrawal with arbitrary income/spending
Concept of Amortization-Based Withdrawal
Amortization-Based Withdrawal (ABW), also called Variable Percentage Withdrawal (VPW), is a retirement spending method. Unlike the 4% rule, ABW is not a historical observation, but a calculation: given your current balance, years remaining, assumed growth rate, and optional final value, it tells you what you can withdraw for that year.
At its core, it is just the standard time-value-of-money payment formula. You can calculate it in a spreadsheet, financial calculator, or even a mortgage calculator (the 'payment' is the withdrawal amount).
Success is not measured in percent of times running out of money - if you can live on the prescribed withdrawal amount, you will never run out of money. Instead, you see what ABW's withdraw numbers are based on your assumptions and see if you can live on that.
Simple example
With $1.2M, 30 years, 0% real growth, and $0 ending value, ABW gives a withdrawal of $40,000/year. So far, that's easy. And note it's adaptive; if you receive an extra $100k at age 70, withdrawals rise by $5,000/year for the remaining 20 years (Scenario B). If life expectancy later increases by, say, 3 years, withdrawals fall to spread the remaining balance over the longer period (Scenario C).
Future income and spending
The point of this post is to show we can add real-world complexity to ABW to account for many changes.
Future income (Social Security, e.g.), can be handled by creating a temporary "virtual income" stream before the real income begins. Calculate its present value, set that aside conceptually, and run ABW on the remaining portfolio. Until real income starts, spending is the ABW base amount plus virtual income (Scenario D).
Quick note that ABW works with non-zero return assumptions, which we've only used for simplicity's sake. For example, Scenario E has 5% real growth allowing for higher withdrawals. But let's go back to 0% for simplicity.
Temporary income (say for a fixed term) can be modeled by adding an offsetting negative virtual income stream after the income ends: Scenario F.
Future spending works the same way, but in reverse: treat it as negative income. That allows fixed spending blocks as seen in Scenario G. And by adding multiple income or spending streams we can get ramps (Scenario H) and non-linear spending patterns (Scenario I). This all comes about from layering PMT functions on top of each other - nothing too complex.
Bottom line
ABW can be extended to handle future income, temporary income, future spending, and year-by-year spending adjustments to work with arbitrary spending needs.
The general idea is:
- Future income = present-value asset
- Future spending = present-value liability
- ABW applies to the remaining flexible portfolio
Here is a combined example with $1.2M, a future income stream, and a spending-smile adjustment. Since the example assumes 0% real growth, total portfolio-funded spending equals exactly the original $1.2M.
Of course this is not a full retirement plan. You'll need to come up with a conservative enough expected return to handle market volatility and sequence-of-returns risk, and RMD's may present an issue like with all plans. But it is a useful framework for turning a portfolio, future income, and planned spending into a year-by-year withdrawal plan to start with, and adapt with.
I have shared my Google Sheets spreadsheet: go to File → Make a copy to edit.
