A distribution waterfall decides, contractually, who gets each dollar a private fund returns —
and in what order. This models the full four-tier structure against a real-shaped mid-market
buyout book: return of capital → compounding preferred return → GP catch-up → residual
carry split. Move the terms and every tier, every LP allocation and both structures
recompute. The preferred return is accrued on unreturned capital by date, not approximated,
because the pref is path-dependent and the shortcut is wrong by real money.