I dont understand in the Distribution Waterfall Schweser examples why the catch up rates are calculated as the 25% of LP preferred rates. I saw this 25% in two different problems.

This is the problem:

Year1: LP Contributes 50mill. Hurdle is 8%, catch-up is full (100%) and carry split is 80/20. Year2: Investment is sold for 100mill

LP Ending Balance: -50(Cont) + 50 (ROC) - 4 (50*8% hurdle) + 36 (residual after deducting Catch up) = 40 GP Ending Balance: 1mill (catch up → .25*4 (hurdle) + 9 (20% residual amount because of carry) = 10

Can someone explain where the value of catch up cost come from?

So we can say that if Catch-up rate is 100% then, catch-up for GP is the split ratio (0.2/0.8)*hurdle earned by LP (if there is enough money in the fund). Am I right?