Multiple on Invested Capital: Choosing the Denominator

A multiple is what came back divided by what went in, and the arithmetic is trivial. The bottom of that fraction is not. On Nilgiri Growth Partners Fund II, invented, at its record date at the end of Year 9 Quarter 2, the same Rs 7,20,00,00,000 reads 1.80 times, 1.50 times or 1.44 times depending on the denominator chosen. A figure quoted without its bottom cannot be checked by anybody.

A kitchen scale behaves in exactly the same awkward way as the instrument in this guide. A bag of rice goes on the scale and it reads 5. Five what? The number on the dial is real, the scale is not broken, and the reading is completely useless until the dial is known to be set to kilograms or to pounds. Nobody thinks this is a deep problem with scales. A measurement is a number plus the thing it was measured against, and half a measurement is not a small measurement. Half a measurement is not a measurement at all.

A multipleTotal value divided by money in. is a number plus the thing it was measured against, and the awkwardness is that the thing it was measured against is almost never printed beside it. Somebody says a fund is at 1.80 times. Somebody else, describing the same fund on the same afternoon, says 1.50 times. Neither of them has made an arithmetic error and neither is being dishonest. The two speakers have divided the same top by two different bottoms. Which bottoms exist, and what each of them is actually asking, is where the whole difficulty sits.

What is a multiple, and why is the bottom the whole problem?

The instrument has two parts and only two. The top is total valueDistributions received plus the reported value of what is still held., meaning everything the fund has produced so far, whether it has been paid out or not. The bottom is money in. The first divided by the second is the multiple. There is no weighting, no adjustment, no rate, no compounding and no clock. The whole operation is one division, and a school pupil could do it.

The top is settled and takes one section. The bottom is not settled at all, and every real disagreement about a multiple lives down there. Money in sounds like a single fact about a fund. It is not. There are at least three different sums of money that all honestly answer to the description money in, they are all recorded in the same fund's own books, and they differ from each other by amounts large enough to move the answer by a quarter.

Nilgiri Growth Partners Fund II is a closed-end growth and buyout fund managed by Nilgiri Alternatives Advisors Private Limited, also invented. Twelve investors and the manager together promised it Rs 5,00,00,00,000. Over eight and a half years it called Rs 4,80,00,00,000 of that, put Rs 4,00,00,00,000 of the money into nine companies, sold four of them outright and part of a fifth, wrote one off completely, and still holds five. At its record date, the end of its Year 9 Quarter 2, it had paid Rs 4,38,00,00,000 back to investors and was carrying the rest of the portfolio at Rs 2,82,00,00,000. Every figure below comes from that single invented record.

Look at the picture above for a moment before reading on. The shape of it is the argument. The top box never changes. The top box holds the same Rs 7,20,00,00,000 in all three cases, produced by the same nine companies, valued on the same day by the same people. Everything that differs between 1.80 and 1.44 differs below the rule. A multiple is not a fact about a fund's performance, it is a fact about a fund's performance measured against a stated base, and the base is a choice somebody made and may not have stated.

What goes into the top, and what does it quietly join together?

The top of the fraction is total value, and it is built by adding exactly two things. The first is every rupee the fund has actually distributed to its investors. For Nilgiri Growth Partners Fund II that is Rs 4,38,00,00,000, paid in four instalments after four sales, and it is as solid a number as exists anywhere in this subject. The money left the fund's account. The money arrived in twelve investors' accounts. A bank somewhere has a record of each transfer.

The second is the residual valueThe reported worth of unsold holdings, which is an estimate. of everything the fund still holds. For this fund that is Rs 2,82,00,00,000, being the carrying values of five companies that have not been sold to anybody: Rs 1,08,00,00,000, Rs 21,00,00,000, Rs 39,00,00,000, Rs 81,00,00,000 and Rs 33,00,00,000. Nobody has paid that Rs 2,82,00,00,000. The figure is a considered estimate, struck by an independent valuation agent and signed off, and it is still an estimate. How such an estimate is produced is covered separately and is taken as given here.

Added together they come to Rs 7,20,00,00,000. And one thing about the addition is easy to read past, and worth stopping on. The addition destroys the distinction. Once Rs 4,38,00,00,000 of cash and Rs 2,82,00,00,000 of estimate have been added into one figure, the multiple divides that single figure and prints one answer, and nothing anywhere in the output says that nearly two fifths of the top has never been sold to anybody. The instrument does not mark the join. It cannot. A fraction has no place to put that information.

None of that is a criticism of the measure, and none of it is a reason to distrust the multiple. The addition is exactly what the instrument was built for. A ruler does not report whether the thing measured is wet. The multiple does not report whether the value divided has been realised. Both are fine instruments, and both leave a question that the reader has to ask separately. On this fund the separate question has a locked answer: Rs 2,82,00,00,000 of the Rs 7,20,00,00,000, being 39.2 per cent of it, sits in five companies that have not been sold to anybody.

What does the first denominator, acquisition cost, leave out?

The first candidate for the bottom is acquisition costWhat the fund actually paid for the companies it bought.: the money that went into companies and nothing else. On this fund it is Rs 4,00,00,00,000, and it is the sum of nine cheques. Rs 70,00,00,000 into Sahyadri Diagnostics Private Limited, counting a later follow-on. Rs 45,00,00,000 into Konark Polymers Private Limited. Rs 60,00,00,000 into Tungabhadra Logistics Private Limited. Rs 60,00,00,000 into Bhavani Speciality Chemicals Private Limited. Rs 35,00,00,000 into Palar Foods Private Limited. Rs 30,00,00,000 into Vaigai Edutech Private Limited. Rs 30,00,00,000 into Manjira Industrial Services Private Limited. Rs 45,00,00,000 into Kaveri Renewables Private Limited. Rs 25,00,00,000 into Indravati Packaging Private Limited. The nine cheques add to Rs 4,00,00,00,000 exactly.

Rs 7,20,00,00,000 divided by Rs 4,00,00,00,000 is 1.80 times. The 1.80 times is a real reading and it answers a real question: for every rupee this manager put into a company, how many rupees of value came out? The question belongs to the choosing and the running of the nine businesses, considered apart from the vehicle that held them. Acquisition cost gives the deal-level reading.

Acquisition cost leaves out the vehicle. A fund is not a bank account with nine cheques written on it. A fund has a manager who is paid a management fee, an administrator who is paid, an auditor who is paid, an independent valuation agent who is paid, lawyers who are paid, and a set of formation costs paid before it bought anything at all. Every rupee of that came out of the same investors' pockets as the Rs 4,00,00,00,000. The acquisition cost denominator prices the nine investment decisions and prices nothing else, and pricing nothing else is exactly its use and exactly its limit.

What does the second denominator, paid in, include that cost does not?

The second candidate is paid inWhat investors actually contributed, including fees and expenses.: every rupee investors actually handed over, whatever it was subsequently spent on. On this fund it is Rs 4,80,00,00,000, drawn in seventeen separate calls across eight and a half years. Paid in is a bigger number than the cost of the companies, and it is bigger because it includes two things that never bought a share in anything.

The first is the management fee, Rs 70,20,00,000 to the record date. The fund charges 2.00 per cent a year, and the base it charges on steps down after Year 5 by the terms it always had. Across the five years of its investment period the charge was Rs 9,80,00,000 a year, being Rs 49,00,00,000 in total. From Year 6 the base became the cost of holdings not yet sold, so the charge fell to Rs 8,00,00,000, then Rs 6,40,00,000, then Rs 5,00,00,000, and then Rs 1,80,00,000 for the half of Year 9 that had run by the record date. The four later charges add to Rs 21,20,00,000, and Rs 49,00,00,000 plus Rs 21,20,00,000 is Rs 70,20,00,000.

The second is fund expenses, Rs 9,80,00,000. Rs 2,50,00,000 of that was organisational cost drawn at formation, before the fund had bought anything. The remaining Rs 7,30,00,000 is operating cost: Rs 80,00,000 a year for Years 1 to 8, Rs 40,00,000 for the elapsed half of Year 9, and a one-off Rs 50,00,000 of transaction expense on the Year 8 sell-down of the third holding. The operating cost covers the administrator, the auditor, the independent valuation agent, legal work, custody and the investor advisory committee's own costs.

Now the addition that this whole guide turns on. Rs 4,00,00,00,000 of investments, plus Rs 70,20,00,000 of fee, plus Rs 9,80,00,000 of expenses, is Rs 4,80,00,00,000 exactly. The gap between the first denominator and the second is not a rounding difference or an accounting nicety: it is Rs 80,00,00,000 of real money that real investors really handed over and that never bought a share in any company.

Rs 7,20,00,00,000 divided by Rs 4,80,00,00,000 is 1.50 times. The 1.50 times is the reading an investor of this fund sees on its own quarterly capital account statement, and the reason is simple: the statement records what that investor contributed, and what an investor contributed includes its share of the fee and the expenses. Investor 1 of this fund, a domestic life insurance company, committed Rs 1,00,00,00,000 and has contributed Rs 96,00,00,000. Its distributions received are Rs 87,60,00,000 and its share of the residual value is Rs 56,40,00,000, so its total value is Rs 1,44,00,00,000 against Rs 96,00,00,000 contributed. Every investor of this fund is drawn strictly in proportion and no side letter moves any investor's economics, so Rs 1,44,00,00,000 over Rs 96,00,00,000 is 1.50 times, exactly the fund's own figure.

What does the third denominator, commitment, measure instead?

The third candidate is the commitmentWhat investors agreed to contribute, called or not. itself: what everybody promised, whether the fund ever asked for it or not. For this fund that is Rs 5,00,00,00,000, being Rs 4,90,00,00,000 across twelve investors plus the manager's own Rs 10,00,00,000. Rs 7,20,00,00,000 divided by Rs 5,00,00,00,000 is 1.44 times.

The difference between this and the second reading is Rs 20,00,00,000, being Rs 5,00,00,00,000 promised less Rs 4,80,00,00,000 called. The Rs 20,00,00,000 was never asked for. The money sat where the investors kept it, doing whatever they had it doing, and at the record date it was still sitting there. Whether that fact should be inside the measurement is a genuine question with two defensible answers. The question is a real one: an investor who promised Rs 1,00,00,00,000 to this fund had to keep Rs 1,00,00,00,000 available to it, not Rs 96,00,00,000, and the commitment denominator is the only one of the three measured against that promise.

Now for a trap that has been found repeatedly in this subject, and it is worth slowing down for. There are two different unfunded figures on this fund and they are five times apart. The fund's unfunded commitment is Rs 20,00,00,000, and investor 1's own unfunded commitment is Rs 4,00,00,000, and both are correct at their own level. Correctness at two levels at once is precisely why the confusion survives review. Investor 1 holds 20.0 per cent of the fund, so its share of the fund's Rs 20,00,00,000 is one fifth of it. Deriving it on paper keeps the confusion from forming: investor 1 promised Rs 1,00,00,00,000 and has contributed Rs 96,00,00,000, so it still owes Rs 4,00,00,000. Either figure, written anywhere, should name the level in the same sentence.

How can the same fund on the same day read 1.80, 1.50 and 1.44 times?

Put the three side by side and the answer is entirely mechanical. The denominatorThe bottom of the fraction, and the choice that decides the answer. grows from Rs 4,00,00,00,000 to Rs 4,80,00,00,000 to Rs 5,00,00,00,000 while the numerator sits still at Rs 7,20,00,00,000, and a fraction with a fixed top and a growing bottom gets smaller. A fixed top over a growing bottom is the whole of the mechanism. There is nothing clever in it and nothing hidden.

Each of the three is answering a different question, and each answers its own question well.

The first asks: what did the nine investment decisions produce, judged on their own? Answer, 1.80 times. The second asks: what did the people who funded this vehicle get back for what they put in? Answer, 1.50 times. The third asks: what did the vehicle produce against the whole promise that was made available to it? Answer, 1.44 times. There is no such thing as the multiple. None of the three is it, and a reader who insists on one is asking for a number nobody can supply.

Which addition checks whether a multiple has been quoted correctly?

There is a check that costs nothing and catches the commonest error in this whole area, and it is worth learning as a reflex. A fund's numbers usually arrive as three figures rather than one: the headline multiple, the share of the denominator that has come back as cash, and the share of the denominator still sitting in unsold holdings. On this fund those three are 1.50, 0.9125 and 0.5875.

The cash share is Rs 4,38,00,00,000 divided by Rs 4,80,00,00,000, or 0.9125. The unsold share is Rs 2,82,00,00,000 divided by the same Rs 4,80,00,00,000, or 0.5875. Add them: 0.9125 plus 0.5875 is 1.5000, exactly, with no rounding anywhere. The two shares have the same bottom and their tops add to the numerator, so the addition has to come out. The tie is not a coincidence and it is not an approximation. If the two shares do not add to the headline, one of the four numbers is wrong, and the most likely fault is that one of the shares was taken against a different bottom from the other.

The same check works on the other two denominators too, and working everywhere is the proof that the property belongs to the arithmetic rather than to this particular fund. Against cost: Rs 4,38,00,00,000 over Rs 4,00,00,00,000 is 1.095, Rs 2,82,00,00,000 over Rs 4,00,00,00,000 is 0.705, and 1.095 plus 0.705 is 1.80. Against commitment: 0.876 plus 0.564 is 1.44. Mixing never works. The cash share against cost and the unsold share against paid in give 1.095 plus 0.5875, or 1.6825, and 1.6825 is not any of this fund's three multiples. A single mismatch of that kind is how a mixed pair announces itself.

What happens to the reading as the nine holdings are added one at a time?

So far the nine companies have been treated as one lump of Rs 4,00,00,00,000. The nine companies were not bought as a lump. Nine purchases were made one at a time across four and a half years, and the multiple on cost computed after each purchase gives nine different numbers, every one of them correct on the day it was struck. The control below walks through them in the order the fund actually entered.

Watch what the first holding does to the reading, and watch what the rest of the portfolio then does to it. Sahyadri Diagnostics Private Limited cost Rs 70,00,00,000 and produced Rs 2,03,00,00,000, so after one holding the cumulative reading on cost is 2.90 times. By the time all nine are in, the same instrument on the same fund on the same day reads 1.80 times. Nothing went wrong to move 2.90 down to 1.80: eight more holdings simply joined the denominator, and the reading is the average it always was.

What can a multiple never show, however carefully it is built?

Everything so far has been about getting the bottom right. Now for the limit that survives even when the bottom is perfectly right. The limit is not a defect in anybody's arithmetic but a property of the instrument.

There is a small and precise demonstration of that inside this fund's own record, and it is worth having because it looks at first like a loss and is not one. At its Year 8 year end the fund's multiple on paid in was 1.51 times, and at its record date two quarters later it was 1.50 times. Nothing was sold in between, nothing was written down, and no holding was revalued at all. Rs 2,20,00,000 more was drawn from investors in Year 9 Quarter 1 and nothing came back. The top of the fraction stood still at Rs 7,20,00,00,000 while the bottom grew from Rs 4,77,80,00,000 to Rs 4,80,00,00,000, and the reading fell. A denominator moved, and the denominator was the only thing that moved.

How does somebody reading a fund's numbers actually use all this?

Picture the person this matters to most, and it is not a professor. The person is somebody at a fund of funds, an institution that has put money into other people's private funds and now has to describe what happened to a board that will not read a footnote. Investor 5 of this fund is exactly that: a fund of funds holding Rs 50,00,00,000 of the Rs 5,00,00,00,000 committed. Once a quarter somebody there opens a capital account statement and has to turn it into two sentences.

The routine that person follows is short and mechanical. First, they find the denominator before they read the headline. A headline read first is a headline that has already lodged. Second, they run the addition: distributed share plus unsold share against the printed multiple, and if the three do not tie they stop and ask. A mismatch means one of the four numbers came from somewhere else. Third, they split the numerator. The statement adds cash and estimate into one figure and the board will hear the whole of it as money. On this fund that split is Rs 4,38,00,00,000 received against Rs 2,82,00,00,000 estimated, and saying it out loud takes four seconds and changes what the board understands.

The same discipline is what makes a comparison between two funds honest, and it is also why so many comparisons are not. Two funds quoted at 1.80 and 1.50 may be identically placed and differently described. Meera Sathe, invented, who chairs the investor advisory committee of this fund and represents its largest investor, is in the position of reading numbers produced by somebody else about a vehicle she cannot sell out of, and the only leverage she has is asking what the bottom was. The single question that does more work than any other in this subject is four words long: divided by what, exactly.

One more use, and it belongs to anybody who has ever had a number quoted at them anywhere. The habit generalises completely. A shop that says it doubled its money means something different depending on whether the rent and the wages were in the denominator. A household comparing what a plot of land did against what a deposit did is choosing bottoms whether it knows it or not. The private fund case is simply the one where the three candidate bottoms are all written down, all in the same document, and all separated by amounts big enough to notice.