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How is the catch-up rate calculated?


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?

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.Like the example stated above it can be calculated as 0.20/0.80 = 0.25 or 25% based on 20/80 carry split.

Overall, based on a profit of 50 million, GP is entitled to 20% of performance = 10 million.

Hurdle is 8%, from 50 - 54m All goes to LP (principal plus hurdle).

From here onwards will go to GP till full catch up or a 20/80 ratio is recreated.

54 to 55 to GP - Ratio of profit is 20/80 balanced again so full catch up achieved if the profit was only 5.

From here onwards 20/80 sharing.

I think its much tricky if not full catch up but not hoping for that in exams. 

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?

1. LP get 100% contributed capital first. $50M goes back to LP.

2. $50M to distribute between LP and GP

3. LP get 8% hurdle first, $50M X 8% ==> 4M

4. 100% catch up to GP, what is the number that 80% is $4M? 4M/0.8==> 5M.  Why?  80/20 also applies to Catch up, then what is 20% of 5M==> 1$

5. So, LP get $4M and GP get $1M on the cath up. 

6. That leave 50M-$5==$45M for final spilt, LP get 0.8X45, GP get 0.2X45

Make sense?

Nice work ws. Can you elaborate what would be the calculation if the catch up were 60% instead of 100%?

let us the same example listed out by lbazer.

Since 100% catch up means GP gets $1M, then 60% catch up mean 60%X1M==$ 0.6M

So, LP gets $4M as hurdle rate, GP gets the 60% catch up $0.4M ==> $4.6M

$50-$4.6M=$45.4M available for 80/20 spilt between LP and GP.

Thanks ws.

WS, your following explanation is a bit confusing:

“ LP gets $4M as hurdle rate, GP gets the 60% catch up $0.4M ==> $4.6M”

Could you please confirm if my understanding is correct.

@60% catchup,

LP gets $0.6m extra.

So LP = $4m (Hurdle) + $0.6m (from catchup) = $4.6m

GP gets $0.4m (from catchup).

The total share available for 80/20 split between LP and GP is still $50m-$5m=$45m

but LP split: $36m+$4.6m = $40.6m

GP split: $9m + $0.4m = $9.4m

$40.6m + $9.4m = $50m