4% is very optimistic; early retirees usually aim for 3%, and even models with that withdrawal rate fail over long enough time periods. You'd want it to be well-funded enough that there's no question it could commit to the payouts indefinitely (so that people don't act more conservatively than they would knowing it might fail). On top of that are costs of administration and study.

The number I ended up with was actually around $600M, and I figured might as well round up.