The Waterfall: Watching Four Tiers Fill as the Total Moves

One number decides which tier a distributed rupee lands in, and the number is how much the fund has distributed in total since it began. Nilgiri Growth Partners Fund II, invented, has three boundaries written into its own contract, at Rs 4,80,00,00,000, Rs 7,09,98,27,451 and Rs 7,67,47,84,313. Below the first of them the manager receives nothing at all, at any setting.

A water tanker arrives in a lane and fills four drums standing in a row. The rule the lane has agreed is that no drum is touched until the one before it is full to the brim. Drum one belongs to the households that paid for the water. Drum two also belongs to them. Drum three is the driver's, and drum four is shared. On a day when only two drums are filled, the driver goes home with nothing. The rule says so, and nobody in the lane thinks an injustice has occurred. A distribution waterfall is that rule written at greater length, and the only thing that decides how many drums are full is how much water arrived. This calculator is the tap. One number moves, the running total the fund has paid out, and the four tiers fill in order.

What does the control actually move?

One number, and no other. The control moves the total distributableThe running total a fund has paid out to its investors since it began, counted from the first payment onwards and never reset.. The total distributable is the cumulative amount Nilgiri Growth Partners Fund II, invented, has paid out since it began. Everything else on the screen is held where the fund's own contract fixes it: capital drawn of Rs 4,80,00,00,000, an accrued preferred return of Rs 2,29,98,27,451, a catch-up at 100 per cent to the manager, carried interest at 20.0 per cent, and a whole-of-fund ordering. The Rs 4,80,00,00,000 drawn, the 8.0 per cent rate, the 100 per cent catch-up and the 20.0 per cent carried interest are one invented fund's contracted terms, and none of them is usual, typical or expected of anything.

The arithmetic of a waterfall is often taught as a list of four sentences, and a list conceals a proportion. Reading that the manager takes 20 per cent says nothing about how much of the plausible range of outcomes pays the manager 20 per cent of nothing, and on this fund's terms that range is most of it. A number that can be moved is the only honest way to see that.

Moving the control is arithmetic on a formula that was written down before any of these numbers existed. A setting of the control is therefore a statement about that formula and never a claim that this invented fund will reach the total shown. Nilgiri Growth Partners Fund II has distributed Rs 4,38,00,00,000 and that is the only figure on the scale that has actually happened.

Where are this fund's three boundaries, and what changes at each?

A boundaryA running total at which one tier finishes and the next one starts taking the money. is a cumulative rupee figure at which one tier stops taking money and the next one starts. Nilgiri Growth Partners Fund II, invented, has three of them, and all three are arithmetic on figures its own records already carry rather than percentages anybody has to interpret.

The three boundaries cut the range into four regions, and the widths are the lesson. Between nil and Rs 7,09,98,27,451 the manager of Nilgiri Growth Partners Fund II, invented, receives not one rupee, and that stretch is 78.9 per cent of a scale running to Rs 9,00,00,00,000. The catch-up region, where the manager is being paid and the investors are not, is Rs 57,49,56,863 wide. On the same scale that width is 6.4 per cent. Region one alone is 53.3 per cent.

Why is the first region so much wider than the other three?

Picture the whole range as a nine metre rule laid along a table. Return of capitalTier 1, which runs until the investor class has back the whole amount the fund called from it, whatever that money was spent on. takes the first four metres and eighty centimetres of it. Everything else in the contract, the preferred return, the catch-up and the split, shares what is left. The width of region one is not an accident of this fund's terms but the whole meaning of Tier 1: the investor class gets back every rupee the fund ever called, and nothing about profit is discussed until it has.

The width of region one is set by what was drawn, not by what was invested, and on Nilgiri Growth Partners Fund II, invented, those two figures are Rs 4,80,00,00,000 and Rs 4,00,00,00,000. The Rs 4,80,00,00,000 is made of Rs 4,00,00,00,000 that bought nine holdings, Rs 70,20,00,000 of management fee and Rs 9,80,00,000 of fund expenses to the record date. The Rs 4,00,00,00,000, the Rs 70,20,00,000 and the Rs 9,80,00,000 add to Rs 4,80,00,00,000 exactly. Every one of those rupees left an investor's bank account, so every one of them has to come back before the boundary is crossed.

Think of an autorickshaw bought on hire purchase. The finance company advanced the whole amount, including the rupees that paid the dealer's handling charge and the first year's insurance, and it counts the whole amount as owed. Nobody deducts the handling charge on the ground that it did not buy any part of the vehicle. Tier 1 counts the same way, and so Rs 80,00,00,000 of fee and expenses sits inside the first boundary rather than beside it.

What fills between Rs 4,80,00,00,000 and Rs 7,09,98,27,451?

Region two, and it belongs entirely to the investor class. The preferred returnA rate that accrues to the investor class and stands ahead of the manager in the order of payments, whether or not any cash has arrived to pay it. on Nilgiri Growth Partners Fund II, invented, is contracted at 8.0 per cent a year compounded annually, and by the record date it had accrued to Rs 2,29,98,27,451 without one rupee of it having been paid. Anywhere inside this region the control shows Tier 1 full, Tier 2 partly full, and Tiers 3 and 4 empty.

An accrual never received is a strange thing to hold in mind, so here is the everyday version. A recurring deposit keeps crediting interest whether or not the holder goes to the counter. The credit is real, it is written in the passbook, and it stands ahead of the holder in the queue for the branch's money. Region two is that credit, and its width of Rs 2,29,98,27,451 is why the second boundary sits at 1.48 times what the investors paid in rather than at 1.00 times. Rs 7,09,98,27,451 divided by Rs 4,80,00,00,000 is 1.4791.

Where does the catch-up finish, and what does the manager hold on the way there?

The catch-upTier 3, which pays the manager and nobody else until the manager holds its contracted fraction of everything paid above return of capital. is region three, it is Rs 57,49,56,863 wide, and it is the only stretch of the whole range where the investor class receives nothing while the manager receives everything. Region three runs from Rs 7,09,98,27,451 to Rs 7,67,47,84,313 and is by a long way the narrowest region on the rule.

A reader checking this with a calculator deserves two arithmetic notes. First, the catch-up on this fund is a quarter of the preferred return, and a quarter of Rs 2,29,98,27,451 is Rs 57,49,56,862 and seventy five paise. The catch-up is written above as Rs 57,49,56,863 and the boundary as Rs 7,67,47,84,313, so adding the two written figures gives a total one rupee above the written boundary. There is no error there and no missing rupee: one number is rounded up, the other rounded down, and both are the same seventy five paise. The control below works in paise so that the four tiers add back to the total exactly at every setting, and it rounds only for display.

Second, the manager's share of profit inside region three is not 20 per cent and is not fixed. The share starts at nil at Rs 7,09,98,27,451 and rises steeply to 20.0 per cent at the far end. Every setting inside this narrow band gives a different answer. The region is worth sliding through slowly rather than reading about.

Why is the manager's share exactly 20.0 per cent above the last boundary?

Because of one line of algebra that holds for every preferred return, and once it is seen the shape of the whole thing falls into place. With C for the capital drawn, P for the preferred return accrued and D for the total distributed: above the third boundary the manager holds the catch-up of 0.25P plus 20 per cent of Tier 4, and Tier 4 is D less C less 1.25P. So the manager holds 0.25P plus 0.20 multiplied by the quantity D less C less 1.25P. The expansion of that is 0.25P plus 0.20D less 0.20C less 0.25P.

The two quarter-P terms cancel, leaving 0.20 multiplied by the quantity D less C. Whatever P happens to be, the manager holds exactly 20 per cent of the profit above the capital drawn. Check it on this fund at two settings. At Rs 8,00,00,00,000 the profitHere, everything distributed above the capital drawn, so the total less Rs 4,80,00,00,000 and nothing else. is Rs 3,20,00,00,000 and the manager holds Rs 64,00,00,000. At Rs 9,00,00,00,000 the profit is Rs 4,20,00,00,000 and the manager holds Rs 84,00,00,000. Both are 20.0 per cent to four decimal places.

The Rs 64,00,00,000 and the Rs 84,00,00,000 carry a property that is easy to miss. Neither of them depends on the Rs 2,29,98,27,451 at all. If that accrual were recomputed tomorrow at a different figure, the two boundaries would move and the readings inside region three would move with them, and the manager would still hold Rs 64,00,00,000 at Rs 8,00,00,00,000 and Rs 84,00,00,000 at Rs 9,00,00,00,000. The preferred return changes when the manager is paid and whether it is paid, never how much it ends with once region four is reached.

Where does this fund actually sit on that scale today?

At Rs 4,38,00,00,000, inside region one, with every other tier empty. Nilgiri Growth Partners Fund II, invented, has distributed that amount across four payments to its record date at the end of its Year 9 Quarter 2, against Rs 4,80,00,00,000 drawn. The fund is Rs 42,00,00,000 short of finishing Tier 1 after eight and a half years, its investors stand at 0.91 times what they paid in, and its manager has been paid no carried interest at all.

The most useful single number here is the distance from where the fund stands to where the manager's first rupee sits, and on this fund that distance is Rs 2,71,98,27,451. Rs 7,09,98,27,451 less Rs 4,38,00,00,000 gives it. Of that distance, Rs 42,00,00,000 is capital still owed and the remaining Rs 2,29,98,27,451 is accrued preferencePreferred return that has built up on the fund's own convention and has not been paid to anybody. that has never been paid. The fund would have to distribute more than it has already distributed, again, before the second boundary came into view.

What would selling the whole remaining portfolio at its carrying value do?

Selling the whole remaining portfolio at carrying value would put the control at Rs 7,20,00,00,000, and that setting is worth trying because it is the one every reader reaches for. Nilgiri Growth Partners Fund II, invented, has distributed Rs 4,38,00,00,000 and carries its remaining holdings at Rs 2,82,00,00,000 at the record date. The Rs 4,38,00,00,000 distributed and the Rs 2,82,00,00,000 still held add to Rs 7,20,00,00,000. The sum is 1.50 times the Rs 4,80,00,00,000 paid in. At that setting Tier 1 is full at Rs 4,80,00,00,000, Tier 2 is full at Rs 2,29,98,27,451, Tier 3 holds Rs 10,01,72,549 and Tier 4 is empty.

The manager would hold Rs 10,01,72,549 there. Because the catch-up has barely started, that figure is 4.2 per cent of the Rs 2,40,00,00,000 of profit and not 20 per cent. Another Rs 80,00,00,000 on the control takes it to Rs 8,00,00,00,000 and the answer becomes Rs 64,00,00,000, being exactly 20.0 per cent. Two settings a tenth of the range apart, and the manager's share of profit between them goes from a twenty fourth of the profit to a fifth of it. An unfinished catch-up looks like that from the outside, and no list of tiers will ever show it.

The Rs 7,20,00,00,000 reading is arithmetic performed on carrying values for nine holdings, three of which have been sold and six of which have not. A carrying value is not a sale price and not an offer anybody has made, and no holding is bound to realise the figure written against it. How those carrying values were arrived at is covered separately.

Where does the Rs 2,29,98,27,451 preferred return figure come from?

Not from the contract, and the difference is the whole point. The term Nilgiri Growth Partners Fund II, invented, has written down is a rate: 8.0 per cent a year, compounded annually, accruing on unreturned capital together with unpaid accrued preference, with every distribution applied first to unreturned capital and only then to the preference. The Rs 2,29,98,27,451 is what that rate has accrued to on this fund's own seventeen drawdowns and four distributions by the record date at the end of its Year 9 Quarter 2, and not one rupee of it has been paid.

The gap between a rate and a rupee figure is why the second boundary is a computed number that moves with time rather than a term anybody negotiated. The accrual at this fund's last cash event, drawdown 17, was Rs 2,66,79,97,473, and the whole balance then accreted a further quarter of a year to the record date, adding Rs 5,18,29,978. Every day that passes without a distribution moves the second and third boundaries further to the right. No property of the whole instrument is more counterintuitive.

Why does a fund at 1.50 times paid in still pay its manager nothing?

A fund standing at 1.50 times paid in while its manager is owed nothing breaks most people's intuition about the whole instrument, and the reading is worth sitting with rather than skimming. Two statements about Nilgiri Growth Partners Fund II, invented, at the end of its Year 9 Quarter 2 are both completely true at the same moment, and they point in opposite directions.

The household version makes it concrete. A household lives in a flat worth Rs 90,00,000 with a loan of Rs 60,00,000 outstanding and Rs 5,000 in the bank. Its net worth is Rs 30,00,000 and its cash is Rs 5,000, and both figures are true. The electricity bill is paid out of the second one. Nobody settles a bill with a valuation, and no waterfall pays a tier out of a carrying value.

Draw the same fact as a length and it stops being paradoxical. The fund's total value clears its Tier 1 boundary by Rs 2,40,00,00,000, and its cash falls short of the same boundary by Rs 42,00,00,000. Rs 7,20,00,00,000 against Rs 4,80,00,00,000 is the first comparison and Rs 4,38,00,00,000 against Rs 4,80,00,00,000 is the second, and the waterfall makes only the second one.

What does somebody actually do with a control like this?

More people read a waterfall than write one, and the reading is a job rather than a judgement. Somebody in a monitoring team inside an institution that has committed to several funds, an analyst covering such an institution, an auditor checking a distribution notice against a trust deed, and a student who will do one of those in a few years. Every one of them can build the three boundaries for any fund from figures the fund already reports, and none of it needs an opinion about the manager.

Take the capital drawn from the capital account statement. Take the cumulative distributions from the same statement. Take the preferred return rate and the catch-up percentage from the fund's own documents, and take the accrual, if the fund publishes one, from the distribution notice. The four inputs give the first boundary directly, the second by addition and the third by adding a quarter of the accrual, and where the fund sits between them is then a single comparison. On Nilgiri Growth Partners Fund II, invented, that comparison says Rs 4,38,00,00,000 against a first boundary of Rs 4,80,00,00,000, and the answer to whether any carried interest can currently be paid is a plain no by Rs 42,00,00,000.

The one input that will not be on any statement is the accrual, and that is the one worth asking about. The accrual is a computed figure, it moves with the calendar, and two people computing it on different day-count assumptions will disagree. Ask which convention the fund uses, ask what date the figure accretes to, and check whether distributions are applied to capital first or to preference first. The three questions decide the second boundary, and the second boundary decides everything about when anybody gets paid.