Can anyone pls explain how does catch up clause work through an example with hurdle rate

i just cant get my head around it i feel lost

there’s another exam CAIA (Chartered Alternative Investment Analyst or some such) some people take as well as CFA, and this topic was discussed in the forum at this site for that exam
How is the catch-up rate calculated?

@Ibazer gives a 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

@WS1 gives the best solution

  1. Year 1: Original cost was $50M
    Year 2: Investment sold for $100M, profit $50M
    To date: LP $0M, GP $0M, balance $100M

  2. First the LP get 100% of their contributed capital back,
    so they get $50M
    To date: LP $50M, GP $0M, balance $50M

  3. Next the LP get their 8% hurdle,
    so they get 8% of the original $50M cost which is $4M
    To date: LP $54M, GP $0M, balance $46M

  4. Next the GP has to catch up. 100% catch up to GP
    The split was supposed to be 80/20 and so far the LP has received $4M profit, so the LP will receive $1M for catch up (so the first $5M of profit has been split 80/20 or $4M to LP and $1M to GP)
    To date: LP $54M, GP $1M, balance $45M

  5. The balance of $45M is also split 80:20 so $36M to LP and $9M to GP
    To date: LP $90M, GP $10M, balance $0M

  6. LP get $90M total:
    $50M (return of original capital), $4M (8% hurdle), $36M (80% of profit left after hurdle and catch up)

  7. GP gets $10M total:
    $1M (100% catch up of 8% hurdle), $9M (20% of profit after hurdle and catch up)

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