Waterfall and carried interest math

Key takeaways

• A whole-fund (European) waterfall returns all contributed capital and the full preferred return before any carry, while a deal-by-deal (American) waterfall can pay carry on an early winner before the fund as a whole has returned capital.
• With interim distributions, the preferred return is tracked as a hurdle account that compounds contributions at the hurdle rate and subtracts distributions.
• The catch-up tier size is pref x carry / (g - carry), where g is the GP's share of catch-up distributions: pref / 4 at 100% and pref / 3 at 80% for 20% carry.
• Once the catch-up completes, the catch-up rate does not change total carry; it matters when proceeds stop inside the catch-up zone, where in the downside case Fund W's GP earns $4.34m at 100% but $3.47m at 80%.
• Under the deal-by-deal structure Fund W's GP takes $12.0m of carry in year 3 against a whole-fund entitlement of $8.4m, so a clawback of $3.6m is due, and LP net IRR is lower even after it is repaid.
• A hard hurdle pays carry only on profits above the hurdle, cutting Fund W's carry from $8.4m to $3.27m, and a GP commitment normally earns returns but pays no carry.

The four tiers and the two structures

A standard private equity waterfall has four tiers, applied in order to each distribution. Tier 1, return of capital: LPs receive distributions until they have recovered their contributed capital. Tier 2, preferred return: LPs receive distributions until they have earned the hurdle rate, commonly 8 percent a year compounded, on that capital for the time it was outstanding. Tier 3, catch-up: the GP receives all or most of the next distributions until it has received its carry percentage of all profit distributed so far. Tier 4, split: everything after that is divided, typically 80 percent to LPs and 20 percent to the GP.

The two structures apply these tiers to different pools. In a whole-fund waterfall, often called European, the tiers run on the fund's cumulative cash flows: capital means all capital contributed to the fund, so no carry is paid until the LPs have recovered all of it plus the pref. In a deal-by-deal waterfall, often called American, the tiers run separately on each realized investment, usually with some protection for losses on other deals. The GP can therefore receive carry from a successful early exit while other investments are still held or have lost money.

The names are conventions, not geography. Many US funds use whole-fund waterfalls, and the terms of any particular fund are whatever its LPA says. In this topic, as in the rest of the track, contributions include only invested capital so the carry arithmetic stands out; fees and expenses would simply add to contributed capital in tier 1.

Fund W: the facts

Fund W is a hypothetical $100m fund with two investments. Deal A costs $40m at year 0 and is sold at the end of year 3 for $100m, an early winner. Deal B costs $60m at year 1 and is sold at the end of year 6 for $42m, a later loser. The LPs contribute exactly the cost of each deal on the day it is made. The fund distributes all proceeds as they are received.

Terms: 8 percent preferred return compounded annually from each contribution date, 20 percent carried interest, and a catch-up. The whole fund makes $142m on $100m, a $42m profit, a 1.42x gross multiple and a gross IRR of 11.6 percent.

The hurdle account

When capital goes in on different dates and comes out in pieces, the cleanest way to track the preferred return is a hurdle account. It starts at zero. Each contribution is added. At each date the balance grows at the hurdle rate for the time elapsed. Each distribution paid to LPs in tiers 1 and 2 is subtracted. When the balance reaches zero, the LPs have received their capital and their compounded pref, and tier 3 can begin. The pref paid in dollars is total tier 1 and tier 2 distributions minus contributed capital.

For Fund W, by year 3 the account holds $120.37m. The $100m from Deal A is not enough to clear it. All $100m returns capital (tier 1), and $20.37m of hurdle remains. That balance keeps compounding until year 6, when it has grown to $25.66m.

Whole-fund waterfall with a 100% catch-up

With a 100 percent catch-up, every dollar after the pref goes to the GP until the GP holds 20 percent of all profit distributed. Profit distributed at that point is the pref plus the catch-up itself, so the catch-up C must satisfy C = 0.20 x (pref + C), which gives C = pref / 4. Any remaining proceeds then split 80/20.

For Fund W the year 3 distribution is entirely tier 1. The year 6 distribution runs through tiers 2, 3 and 4.

An 80% catch-up, and when the rate matters

Some LPAs give the GP only part of each catch-up dollar, commonly 80 percent, with the other 20 percent going to the LPs. The catch-up then takes longer to complete: the tier is pref / 3 in size rather than pref / 4. If proceeds are large enough to complete it, the total carry is identical to the full catch-up case, because in both cases the GP ends with 20 percent of total profit. What changes is how the distributions inside the tiers are divided.

The rate matters when proceeds run out inside the catch-up zone, which is the case for funds that only just clear their hurdle. There the LPs keep 20 percent of every catch-up dollar, and the GP's carry falls below 20 percent of profit. The downside case below cuts Deal B's proceeds from $42m to $30m.

The deal-by-deal waterfall

Under a deal-by-deal waterfall the tiers run on each realized deal. When Deal A is sold at year 3, the LPs receive Deal A's $40m cost and an 8 percent compounded pref on that $40m for three years; the GP then catches up and the remainder splits 80/20. Deal B, still held at cost, does not enter the calculation. Many deal-by-deal LPAs add protection by requiring that realized losses and write-downs on other deals also be returned before carry on a winner, but Deal B has no realized loss or write-down at year 3, so the protection would not bite here.

When Deal B is sold at year 6 for less than its cost, the LPs receive all $42m and the GP receives nothing. The GP keeps the carry it took on Deal A, unless a clawback applies.

Clawback

A clawback provision requires the GP to return carry it received in excess of what it would have been entitled to on the fund's cumulative results. It is typically tested at the end of the fund's life, sometimes also at interim dates. The amount is the carry actually received minus the carry due under a whole-fund calculation of the final outcome. The clawback repays the dollars but, unless the LPA says otherwise, without interest, so the LPs still bear the timing cost shown in the table above.

Clawbacks carry credit risk. The carry has usually been paid out to individual members of the GP's team, who have paid tax on it. Most LPAs therefore cap the clawback at the carry received net of taxes paid or deemed paid, and many support it with an escrow of part of each carry payment or with guarantees from the GP's principals. The net-of-tax cap means that in a bad enough outcome the LPs do not recover all of the excess.

Hard versus soft hurdles, and the GP commitment

Everything above uses a soft hurdle: once the LPs have their pref, the catch-up lets the GP recover carry on all profit, including the part below the hurdle. A hard hurdle has no catch-up. The GP receives carry only on profits above the hurdle amount, and the pref is effectively a deduction from the carry base. Soft hurdles with a catch-up are the more familiar structure in private equity; a hard hurdle is a term an LP with negotiating leverage may seek.

The GP commitment is the capital the GP and its principals invest in their own fund, usually expressed as a small percentage of total commitments and set in the LPA. It aligns incentives because the GP loses its own money when the fund loses. The GP's own capital normally participates pro rata in returns but pays no management fee and no carry. So the GP's total economics are its pro rata share of fund results plus carry on the LPs' share only.