Exactly what Chad said
And I would add one small distinction that the CFA exam may try to throw in as a curveball.
There are two types of hurdle rates, soft and hard. Unless they say soft hurdle rate, assume it’s a hard hurdle rate. A hard hurdle rate works exactly like the math above and it’s the usual case.
But if the question throws the word “soft hurdle” in there, just realize in this niche case there is a key distinction. With a soft hurdle rate, if the PE firm “clears” the hurdle rate (return > hurdle rate), then in this specific case the manager will be paid their succcess fee (carried interest or the “carry”) based on the “entire” year’s return here.
So for a hard hurdle rate (most all typical cases) the manager would get 20% success fee paid against the 5% return in excess of the hurdle rate.
For a soft hurdle rate (never assume this as the case unless they use “soft” in the problem wording), you ask if the return (15%) cleared the hurdle rate (10%)… and if it does clear it, then the manager is paid a success fee equal to 20% of the entire 15% return.
Keep an eye out for tricky wording, but unless you see “soft hurdle” then assume the math is for a hard hurdle rate.
Cheers - good luck on your exam - you got this