Private Equity puzzles, solved step by step

The LPs earn 1.56x net. The 850 invested at 2.0x returns 1,700. LP profit is 1,700 less the 1,000 they paid in, fees included, which is 700. Carry at 20% of 700 is 140, so LPs receive 1,560 on 1,000. Fees cost 0.30x and carry 0.14x, so a 2.0x gross fund delivers 1.56x.

Why do fees and carry need separate treatment?

Think of a farmer who hands a contractor 100 kilos of seed. The contractor keeps 15 kilos as a fee and sows 85, then takes a fifth of whatever extra grain the harvest brings. Fees shrink the base that gets invested, while carry takes a share of the profit after the LPs have their money back. They hit at different points, so they cannot simply be added as percentages, and trying to do it in one step is where most answers go wrong.

So run it in order. Fees of 150 mean only 850 reaches companies. At 2.0x, 850 becomes 1,700. LPs paid in 1,000 in total, fees included, so the profit is 700. Carry at 20% of 700 is 140. The LPs receive 1,700 less 140, which is 1,560, a net multiple of 1.56x.

How big is the gap between gross and net, really?

Measured as a multiple, fees and carry take 0.44x off 2.0x, just over a fifth. Measured as profit, the gap is far larger: the LPs keep 560 of what would have been 1,000 of gross profit had every rupee been invested at 2.0x, so fees and carry together take 44% of the gain. That framing is why LPs negotiate hard over the fee base and the fee step-down after the investment period. A fee that looks small as an annual percentage of committed capital takes a large share of the profit over a ten-year life.

What has the simple version left out?

Two things worth naming. Most funds pay carry only after LPs earn a hurdleA minimum return, often expressed as an annual rate, that LPs must receive before the GP earns carried interest. and then let the GP catch up; at a 2.0x outcome a full catch-up still leaves the GP with 20% of all profit, so the answer here holds. Timing is the bigger omission: net IRR falls further than net multiple, because fees are paid early and proceeds arrive late. Recycling of proceeds and fee offsets from portfolio companies would also change the figure.

Carry of 50 is paid, and a 10% LP that sells receives 45. The transfer is a sale at 500 against a cost of 250, so the old fund books a profit of 250 and the GP takes 20% of it, 50. The remaining 450 belongs to the old fund's LPs; a 10% holder gets 45 in cash. The GP earns that carry at a price it helped set, which is the conflict LPs examine.

What is a continuation vehicle, in plain terms?

Picture a shopkeeper who manages a shop for a group of owners and is paid a share of the profit when the shop is sold. Instead of selling to an outsider, he sets up a new group, with some new owners and some old ones, and sells the shop to that group. A continuation vehicleA new fund, managed by the same GP, that buys one or more assets from the GP’s older fund so they can be held for longer. is the same GP selling an asset from its old fund to a new fund it also manages, so existing LPs can take cash or roll into the new vehicle. To the old fund the transfer is a sale, so its carry is calculated as though the asset had been sold.

Why does the transfer price matter so much?

Because the GP is on both sides of it. A higher price raises the carry the GP collects today; a lower price makes the new vehicle, which the GP also manages and earns carry from, a cheaper purchase. At 450, carry falls to 40 and old LPs get 410; at 550, carry is 60 and they get 490. Each 10 of price moves carry by 2 and the selling LPs by 8. That is why these deals usually rely on a third-party lead buyer setting the price and a fairness opinion, so the number is tested by someone without the conflict.

What has the simple version left out?

Carry in most funds is calculated across the whole fund, not deal by deal. If the old fund has losses elsewhere, or has not yet returned LP capital and the hurdle, the crystallised carry could be lower or held back in escrow. Transaction costs, a discount to NAV and the GP rolling part of its carry into the new vehicle all change the cash figures. Name those three, then give 50 and 45 as the answer on the question's terms.

The manager receives 160 of carry. Investors first get 1,000 of capital and 469.3 of preferred return, 8% compounded for five years. The manager then takes 100% of the next 117.3 as catch-up. The last 213.3 splits 80/20. Manager's total: 117.3 plus 42.7, which is 160, exactly 20% of the 800 profit.

What order does the money flow in?

A distribution waterfallThe agreed order in which a fund pays out cash: capital back, then the preferred return, then catch-up, then the profit split. pays tier by tier, like a row of glasses being filled in turn: the next glass gets nothing until the one before is full. Capital comes back first, then the hurdle, then the catch-up, and only then the 80/20 split. Compounding 1,000 at 8% for five years gives 1,469.3, so the preferred return is 469.3.

How big is the catch-up, and why does it end at 20% of all profit?

The catch-up runs until the manager holds 20% of everything distributed above capital. Investors already hold 469.3 of profit, so the manager needs c where c equals 20% of 469.3 plus c. That solves to a quarter of the preferred return, 117.3, after which every rupee splits 80/20 and the manager's share of total profit stays at exactly 20%. There was enough money to finish the catch-up, so the answer is simply 20% of 800.

Say the shortcut, then show the tiers as proof. If the fund had returned only 1,500, the catch-up would not complete: after the hurdle only 30.7 would be left, all of it to the manager, and carry would fall well short of 20% of the 500 profit.