A private foundation looks like a small endowment and behaves like a different animal, for two reasons that are both legal rather than financial.
What is the payout requirement, and what return does it demand?
The first is that its payout is a floor set outside the institution. A United States private non-operating foundation must distribute a minimum share of the fair market value of its non-charitable-use assets each year, conventionally 5%, with qualifying administrative expenses counting inside that figure and a carry-forward mechanism for excess distributions. (The 5% minimum and the excise tax on net investment income sit in the Internal Revenue Code at sections 4942 and 4940; the excise rate was set at a flat 1.39% by the Taxpayer Certainty and Disaster Tax Relief Act of 2019. Check both against the current Code text and the foundation's own tax counsel before using them; the excise rate in particular has changed twice in living memory.)
The return requirement that follows has one trap in it. The additive shortcut, payout plus fee plus inflation, omits the excise tax, and the excise tax resists being tacked on at the end: it is charged on the investment income the portfolio produces, so it depends on the return being solved for. The correct statement is a one-line equation:
R - [ payout + fee + excise x (R - fee) ] = inflationWorked Example 3 solves it, and the excise tax turns out to add only about ten basis points. The shortcut is nearly right and wrong for an instructive reason, which is that every cost stack with a rate charged on income rather than on assets has this shape.
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How does a foundation's horizon differ from an endowment's?
The second legal difference is the horizon, and it is subtler. A charter may permit a foundation to spend down, and many modern ones are drafted to require it, which converts a perpetual institution into a finite one: a fund with a stated twenty-year life has no business holding a twenty-five-year illiquidity premium. Even a perpetual foundation has a shorter effective horizon than an endowment, because the statutory floor keeps paying whatever the portfolio does, so a decade of poor returns cannot be recovered by underspending. Worked Example 3 prices that too, and the headline is that one percentage point of realised return moves the foundation's half-life from thirty-three years to sixty-two.