Private Equity puzzles, solved step by step

About 1.52x. The buyer pays 85 for the NAV today and 20 more when the unfunded commitment is drawn, 105 in all. It receives 130 when the NAV realises at 1.3x and 30 when the drawn 20 returns 1.5x, 160 in all. 160 over 105 is 1.52x, roughly 15% a year if the money went out at the start and came back at year three. At full NAV the same deal would be 1.33x.

Why does the unfunded commitment belong in the sum at all?

Think of taking over a friend's gym membership halfway through. You pay him something for the months already paid up, but you also inherit the remaining monthly instalments, and in return you get every month of the membership that is left. Buying an LP interest transfers both the assets already in the fund and the obligation to fund the rest of the commitment, so the cheque you write today is only part of what the position costs. Here the buyer pays 85 now and 20 later, and the unfunded commitmentThe part of an LP commitment that the fund has not yet called. The buyer of the interest takes over the obligation to pay it when called. is money the buyer must find whether or not it wants to.

What are the numbers, line by line?

Money out: 85% of 100 is 85, plus 20 when it is drawn, so 105. Money in: the existing NAV of 100 grows 1.3x to 130, and the 20 of new capital earns 1.5x, which is 30, so 160. 160 over 105 is 1.52x, and the discount is what lifts it, because at full NAV the cost would be 120 and the multiple only 1.33x. Note that the 15-point discount is 15% of NAV but only 12.5% of the 120 of total exposure. Quoting the discount on NAV alone makes a secondary look cheaper than it is when a lot of the commitment is still to be drawn.

What does the simple version leave out?

Timing, mostly. The 20 is drawn after the purchase and the 160 arrives in pieces, so the 15% figure is only a placeholder for an IRR that depends on when each call and distribution lands. A later draw raises the IRR because less money is out for less time, which is one reason secondary buyers like interests with a large unfunded tail: the headline discount applies to a small NAV and the rest of the exposure is priced at cost. Say that out loud, then say what else is missing: the GP's management fee on the commitment, transfer costs and the fact that 1.3x and 1.5x are assumptions, not knowledge.

Management receives about 29.5, roughly 5.9x its money. The preference compounds to 400 x 1.12^5 = 704.9 and is paid first. That leaves 295.1 for the ordinary shares, and management's 10% is 29.5. The sponsor gets 970.5 on 445, about 2.18x. The structure gears management's small cheque on the ordinary hard.

Why does management do so much better than the sponsor on the same deal?

Imagine two friends buy a flat for Rs 50 lakh. One lends Rs 45 lakh at a fixed rate; both put a little cash in for the ownership. When the flat sells, the loan and its interest are repaid first and whatever is left belongs to the owners. If the price rises, the owners' small stake multiplies; the lender just gets the fixed rate. The preference share is the lender here: it takes a fixed 12% a year first, so all of the upside above that sits on the thin layer of ordinary equity where management's 10% lives. This is called sweet equityOrdinary shares sold to management at the same price as the sponsor, made valuable because most of the sponsor money sits in a senior preference instrument..

What happens to management if the deal goes less well?

Run it at different exits. Because the preference keeps compounding whether the business grows or not, management's payout swings from nothing to many times its money over a narrow range of exit values. The table shows management's cheque and multiple at four exit values.

Sponsors measure this with the envy ratioThe price per 1% of ordinary equity paid by the sponsor, counting all its money, divided by the price per 1% paid by management.. The sponsor pays 445 for 90%, about 4.94 per point; management pays 5 for 10%, 0.5 per point, an envy ratio of about 9.9x. The limitation: the sums assume no leaver clauses, ratchets or management loan notes, all of which change who gets what in a real deal.

The GP receives about 30.7, all of it from the catch-up, which is 6.1% of the profit. LPs first get their 1,000 back, then the 8% compounding preferred return: 1,000 x (1.08^5 - 1) = 469.3. That leaves 30.7. A full catch-up sends 100% of the next distributions to the GP until it holds 20% of profit, which would take 117.3, so the money runs out inside that tier.

What order does the money flow in?

Think of a restaurant partnership where the investor gets her money back first, then an 8% a year return on it, and only then does the chef share in the profit. A waterfall pays in tiers: capital back, then the preferred returnThe minimum return LPs receive before the GP shares in profit, often 8% a year, here compounding., then the GP's catch-up, then the 80/20 split, and each tier must fill before the next one starts. Here capital takes 1,000, the preferred return takes 469.3, and only 30.7 is left to flow further.

Why does the GP's share jump so fast just above the hurdle?

Because inside the catch-up tier every extra unit goes to the GP. Between 1,469 and 1,587 of proceeds, each additional 1 of exit value adds 1 to carry, so the GP's share climbs from zero to 20% across a band of only 117. Above 1,587 the split settles at 80/20 and stays there.

This is why secondaries buyers and LPs model carry near the hurdle so carefully. A fund sitting just above its hurdle has a GP with a strong incentive to push value up through that band, and a buyer of the LP interest must remember that much of the next gain goes to the GP. The limitation: real waterfalls run on dated cash flows, often deal by deal, with clawbacks; a single drawdown and exit is the clean case.

Both end at 20 of carry, but deal-by-deal pays 40 in year 2 and needs a 20 clawback in year 4. Deal-by-deal pays 20% of A's 200 profit as soon as A exits. When B is written off, fund profit is only 100, so the manager owes 20 back. Whole-fund returns all 200 of capital first, then pays 20% of the 100 profit: 20, with nothing to settle.

What is the difference between the two waterfalls?

Picture a salesperson paid commission on each sale as it closes, against one paid at year end on the year's net result. The first gets paid for the good deals before the bad ones show up. A deal-by-deal waterfall pays carry on each exit as it happens; a whole-fund waterfallA distribution order in which investors get back all contributed capital across the fund, plus any hurdle, before the manager receives any carry. pays carry only after investors have their capital back across the entire fund. The final entitlement is the same here; the timing is not.

Why does the clawback matter so much to investors?

The clawbackA promise by the manager to return carry it was paid early if the fund as a whole ends up earning less than the carry assumed. is only as good as the manager's ability to pay. By year 4 the 40 has been distributed to individual partners and often taxed, so recovering 20 can mean chasing people, not a fund account. That is why investors negotiate escrows that hold back part of early carry, or prefer whole-fund terms altogether. The manager, meanwhile, has had an extra 20 for two years for free.

One honest caveat: whole-fund here still pays in year 2, because the 300 from A is enough to return both deals' capital. Had A returned only 200, the fund would have made no profit and whole-fund would never have paid carry, while deal-by-deal would have paid 20 on A's 100 of profit and then had to claw all of it back.