The calculator
Weighting last year at 80% and a 5.25% target at 5.0% returns starts at $52,500 and ends at $42,786, with the collar binding in 0 of 30 years.
The rule Yale actually publishes
Next spend = (prior weight) × last spend × (1 + inflation) + (1 − prior weight) × target rate × market value. Yale publishes the weights as 80 / 20, with a 5.25% long-term target rate, and then holds the answer between 4.0% and 6.5% of fair value. Those are the defaults above. The smoothing is the point: a university cannot move its operating budget 20% because the endowment had one bad year, and neither can a household that has already retired.
One difference worth stating plainly. Yale applies the target rate to the endowment's market value from an earlier year, which smooths the result a second time. This calculator applies it to the current value, because that is the number a household can look up today. On a long horizon the gap is small; in the year of a crash the lagged version cuts less.
Working one year by hand
A $1,000,000 portfolio at the 5.25% target spends $52,500 in year one. Say the portfolio ends the year at $900,000 after that withdrawal and a flat market, and inflation ran 2%. Last year's spending indexes to $53,550, and 80% of that is $42,840. The market leg is 20% × 5.25% × $900,000, or $9,450. The blend is $52,290, which is 5.8% of $900,000 and sits inside the 4.0% to 6.5% collar, so that is what you spend. A pure percent-of-balance rule would have paid $47,250 instead, a 10% pay cut in one year.
Assumptions
No fees, no taxes, one withdrawal a year taken at the start. Set the floor or the cap to 0 to see the unconstrained 80/20 blend. The Yale endowment spending guide is the long form. Compare with Vanguard dynamic spending, which clamps the year-to-year change instead of blending levels, and with Guyton-Klinger guardrails, which leaves spending alone until a rail trips.