MOIC vs IRR: A Multiple Against a Rate of Return

A multiple counts how many rupees came back for each rupee put in. A rate of return counts how fast. Nilgiri Growth Partners Fund II, invented, read 1.50 times and 8.3 per cent at its record date, and between its Year 8 year end and that date the multiple fell from 1.51 while the rate fell from 8.7 per cent, for two entirely different reasons.

Two numbers get quoted about a private fund more often than any others, and a reader who has met both usually assumes they are two views of the same thing, one coarse and one precise. The two are not two views of one thing. A multiple and a rate of return answer two different questions, and the whole of the difference between them is a single input that one of them contains and the other does not. The multiple has no time in it and the rate of return is made of nothing else. Every disagreement the two of them will ever have follows from that one sentence.

Start with something concrete. Suppose a cousin borrows Rs 2,00,000 from a household to fit out a small tailoring shop, and one day hands back Rs 3,00,000. The household has received one and a half rupees for every rupee it put in. The one and a half is complete, it is checkable, and it is true whether the money came back after eleven months or after eleven years. Now the second question. Was that eleven months or eleven years? The first sentence cannot answer it. A count of rupees per rupee was never trying to. A number that is silent about time is not a worse number, it is a number about a different subject.

Nilgiri Growth Partners Fund II, invented, supplies every figure below. Its record date is the end of its Year 9 Q2, and that date sits 8.50 years after its final close. At that date it had drawn Rs 4,80,00,00,000 from its investors, had sent back Rs 4,38,00,00,000 in cash, and still held five companies carried at Rs 2,82,00,00,000 that nobody has bought. Every figure below belongs to that fund at a date on its own clock, and its record stops at that record date.

What does a multiple count, and what does a rate of return count?

One line each.

A multiple on invested capitalHow many rupees came back for each rupee put in, with no time in it., or MOIC, is a division. The division puts everything the investor has got, plus everything the investor is still holding, over everything the investor has put in, and reports the answer as a number of times. On Nilgiri Growth Partners Fund II, invented, at its record date, that division is Rs 7,20,00,00,000 over Rs 4,80,00,00,000. The answer is 1.5000 times. The multiple used below is total value to paid inThe multiple on capital paid in, which is the one used throughout this guide.. The three denominators a multiple can be divided by are covered separately, so the denominatorWhat a multiple divides by, which can rise without anything being lost. here is named once and left alone. Taken as given from that separate treatment, the same invented fund at the same record date reads 0.9125 on cash returned and 0.5875 on value still held, and 1.5000 on the two together.

An internal rate of returnThe dated return on the fund's own cash flows, assumed known here., or IRR, is not a division of that kind at all. An internal rate of return works on a list of dated amounts. Every rupee that left an investor and every rupee that came back carries the quarter it moved in, and the answer is a percentage per year that reconciles the whole dated list. On Nilgiri Growth Partners Fund II, invented, at its record date, the fund's own record reads plus 8.3 per cent since inceptionMeasured from the fund's own final close rather than over a single year., measured across the 8.50 years from its final close.

The arithmetic that produces a rate of return is settled elsewhere and is used below without being explained, derived or run. Every percentage below is read off the locked record of one invented fund and attributed to it, and not one of them is worked out in the prose, in a picture or in the moving part further down. The build of either instrument is not the subject. The subject is what each one measures, where the two of them disagree, and why.

What is taken as known here?

Several ideas are taken as settled here, and it is worth naming them.

The definition of an internal rate of return, how it is set up, why a list of dated amounts has one at all and how a machine finds it, are all covered separately and used below without further explanation. Setting those aside leaves room for the comparison itself. Where the two part company is the only thing worth saying about the pair.

Three other things are also taken as settled. The three different denominators a multiple can be divided by, and the discipline of saying which one is meant, are covered separately, so the denominator here is named once and not argued about again. The shape a private fund's value traces across its whole life, year by year, belongs to a separate treatment, and exactly two points of that shape are drawn here: Nilgiri Growth Partners Fund II's Year 8 year end and its record date at Year 9 Q2. And how the carrying value of an unsold holding is arrived at, and by whom, is a third separate subject, taken as given here.

Once all of that is set aside, a question about measurement remains, and it is not a question about arithmetic. Two instruments are pointed at one fund on one afternoon. The two return different numbers. A reader has to know what each number is a number about before either of them is any use.

Why does a multiple not know what day anything happened?

Because there is nowhere in the division for a date to go. In the left panel above there is a number on top, a number underneath, and a line between them. A date is not an ingredient of that operation. Every rupee in the numerator could be shuffled into any quarter at all and the figure printed underneath would not twitch.

The blindness to dates is easiest to see inside a single fund rather than in the abstract. Here is Nilgiri Growth Partners Fund II, invented, and four of the positions it has sold or partly sold, laid on its own clock. Every span below is derived from one clock convention, so the convention is worth stating once. Time is counted from the fund's own final close, and Year n Q m sits at n minus one, plus a quarter of a year for each quarter m. So the end of Year 1 Q1 is 0.25 years after final close, the end of Year 8 Q4 is 8.00 years, and the record date at the end of Year 9 Q2 is 8.50 years. Every holding period below is that subtraction and nothing more.

Read the four bars twice. The first time, ignore the lengths and look only at the multiples. Ignoring the lengths is what a multiple itself does. The second time, look only at the lengths. Holding 1 and holding 3 occupied exactly the same 5.75 years of this fund's life. Equal speed produced unequal amounts: one returned 2.90 times and the other 2.50 times. Holding 2 sat for 4.75 years and returned 1.40 times, while the sold slice of holding 9 sat for 3.00 years and returned 2.20 times, so the shorter hold produced the larger amount. A span is not one of the things a multiple is made of, so neither of those two facts is visible in a multiple.

There is a second blindness, and it is the one people forget. A multiple is indifferent to order as well as to speed. The four bars above start in four different quarters and finish in four different quarters, and the fund-level multiple would be exactly what it is if all four had been bought on one morning and sold on one afternoon, so long as the same rupees changed hands. Money back early and money back late give the same multiple. Money back in the sequence the fund actually managed and money back in the reverse sequence give the same multiple. There is no ordering information anywhere in a division of one total by another total, and there never was.

The blindness is a genuine strength and not a defect. Because it has no dates in it, a multiple is almost impossible to argue with. Two people can dispute what a company is worth, but nobody disputes what a division is. A multiple is the figure that can be handed across a table and agreed in a second, and agreement in a second is worth something in a subject area where almost nothing else is agreed at all.

Why is a rate of return nothing but timing?

Because the date column is the thing it eats. Hand the second instrument the ledger from the right panel above, and it will use every rupee once and every quarter once. Take the same rupees and shift one of them two years earlier, changing nothing about the amount, and the answer changes. The change is not a quirk to be worked around. A rate of return exists to register exactly that shift.

Go back to the tailoring shop for a moment, and put a second household beside the first. Both lent Rs 2,00,000. Both got back Rs 3,00,000. Both can say, truthfully, that one and a half rupees came back for each rupee out. One of them waited eleven months and the other waited eleven years. Every household in that street would call those two different outcomes. Of the two instruments, only the one that reads the dates agrees with them. The other one has no opinion, because it was never asked.

The blindness runs the other way too, and it is the half people skip. A rate carries no size, so a rate of return says nothing about whether the total that came back was large. A tiny sum handled quickly and an enormous sum handled at the same speed produce the same percentage, and there is no size information anywhere inside it. So the reader who has only the rate knows how fast a fund's money moved and does not know how much of it there was. The reader who has only the multiple knows how much and does not know how fast. Both readers are missing exactly the thing the other one has.

The consequence is worth stating bluntly. Neither of these two is a fuller version of the other, and neither is the more honest number. They are not competing estimates of one quantity where one is coarse and one is refined. The multiple and the rate are two measurements of two different properties of the same object, in the way that the weight of a parcel and the distance it travelled are two measurements of the same journey. A courier who quotes only the weight has not given a rough version of the distance.

What did this fund read on one afternoon, and did the two agree?

Here is Nilgiri Growth Partners Fund II, invented, at the end of its Year 9 Q2. The record date sits 8.50 years after its final close, the fund's own locked record stops there, and every reading below is what that record shows on that day.

The last two rows are the whole argument in two lines. One instrument looked at that fund on that afternoon and said one and a half. The other looked at the same fund on the same afternoon and said eight point three. Both are correct. Neither is a rounding of the other. The two figures were built from different information, one from two totals and the other from a dated list. No arithmetic turns 1.5000 into 8.3, and none turns 8.3 back.

A reader who wants both properties of that fund has to look at both readings. There is no shortcut where one of them stands in for the other, and a fund quoting a single figure has left out precisely the thing the missing figure was invented to carry. Reading both is the rule, and the rule is worth having in mind before the two falls arrive.

Why did two readings fall at once for two unrelated reasons?

Two quarters before the record date, at its Year 8 year end, Nilgiri Growth Partners Fund II, invented, read 1.51 times and plus 8.7 per cent. At the record date it read 1.50 times and plus 8.3 per cent. Both readings went down. The two dates are the only points of that fund's year by year record drawn here, and the full year by year shape is covered separately.

The obvious reading of two simultaneous falls is that something went wrong in between. It did not. Across those two quarters this fund sold nothing, wrote nothing down, revalued nothing and lost nothing. The value of everything it still held was Rs 2,82,00,00,000 at the Year 8 year end and Rs 2,82,00,00,000 at the record date, the same five companies at the same carrying values. The two falls have two separate causes, neither of them is an event in any portfolio company, and neither of them is a loss.

The fall from 1.51 to 1.50: a larger denominator and nothing else

At the Year 8 year end the investors of this fund had paid in Rs 4,77,80,00,000. At the record date they had paid in Rs 4,80,00,00,000. The difference is Rs 2,20,00,000, and it is the seventeenth and last capital call this fund made, drawn at its Year 9 Q1 to meet the management fee and fund expenses. The call is the entire story.

Watch what a capital call does to a division. A call adds to the bottom of it. The money that came in went straight back out to pay a fee and some expenses and never became value in a company, so the top of the division, the Rs 7,20,00,00,000 of cash returned plus value still held, did not move at all. So the same numerator was divided by a bigger denominator, and the answer got smaller. Rs 7,20,00,00,000 over Rs 4,77,80,00,000 is 1.5069, and 1.5069 prints as 1.51. Rs 7,20,00,00,000 over Rs 4,80,00,00,000 is 1.5000, and 1.5000 prints as 1.50.

The third strip does something honest that looks like a trick, and it is worth a sentence of its own. At the true scale of the second strip, the Rs 2,20,00,000 that was called is about three pixels wide. Widening the bar to make it look bigger would have been a lie about the size of the move. Magnifying a named slice of the same scale, saying by how much and labelling it, keeps the size honest and still makes the move visible. A move worth teaching can be genuinely small, and the answer is to magnify it and say so rather than to inflate it or to leave it out.

The fall from 8.7 to 8.3 per cent: two more quarters and nothing else

Now the second fall, on the same fund, over the same two quarters. The recorded reading went from plus 8.7 per cent at the Year 8 year end to plus 8.3 per cent at the record date. The second fall has nothing whatever to do with the Rs 2,20,00,000 call. The second instrument does not have a denominator in that sense, so the denominator cannot be the cause. The fall happened because the calendar advanced.

The picture is worth holding on to. On the Year 8 year end this fund's dated list ran 8.00 years from its final close, and it ended with Rs 2,82,00,00,000 of value that had not been sold, entering the list as a terminal valueThe carrying value treated as a final flow when a rate of return is computed. on that date. Two quarters later the identical Rs 2,82,00,00,000, being the identical five companies at the identical carrying values, sits at the end of a list that now runs 8.50 years. The same amount of value, reached later.

An instrument built out of dates responds to the calendar even when nobody does anything, and that is exactly what it was designed to do. A holding that is worth what it was worth two quarters ago has, in the language of the second instrument, gone two quarters without earning anything. A flat holding is not an accusation and not a write-down. The arithmetic is responding to the one input it has.

Is either fall a loss, and how would a reader tell?

Neither of them is, and there is a short test that settles it without needing anybody's opinion. The test is two questions, plus one that keeps the pair honest.

The first question is whether the bottom of the division rose. If a fund called more capital in the period, then the multiple was pushed downwards by that call alone, whatever else happened. The second question is whether time passed. The question sounds facetious until one notices how many notes about a fund's numbers never mention it. If more quarters have gone by and the value at the end of the list has not grown, the recorded rate is pushed downwards by that alone. The third question is the check on the other two: was any holding marked down? If the answer is no, then the value at the top of the division did not shrink, and both falls are fully explained by the first two answers.

Notice how much work the third question does. A fund could easily have called capital, watched two quarters pass and also written a company down, and then both readings would have fallen for a mixture of reasons. Without the third question, yes and yes would be a description rather than an explanation. The reason this invented fund is worth teaching from is that its third answer is a clean no: Rs 2,82,00,00,000 at the Year 8 year end and Rs 2,82,00,00,000 at the record date, the same five companies at the same carrying values. That makes it a controlled case, where each fall has exactly one cause and the two causes do not touch.

The test has a limit worth naming. Three questions cannot decide whether a fund is doing well. Three questions attribute a movement to its arithmetic, and a reader who sees two numbers go down then knows which of the possible stories is consistent with the record in front of them.

What happens if one distribution moves and nothing else does?

Everything so far has compared two dates. The cleanest demonstration of the difference between the two instruments does something else: it holds one date still and moves a single payment.

Here is the setup, and it is a counterfactualA deliberate what-if on a locked record, labelled as one wherever it appears., labelled as one every time it appears. Nilgiri Growth Partners Fund II, invented, sold holding 1 and distributed the Rs 2,03,00,00,000 of proceeds to its investors at its Year 7 Q3. The Year 7 Q3 distribution is a fact about the fund. Now take that single distribution and imagine it falling in a different quarter, anywhere from the fund's Year 6 Q1 to its Year 8 Q4. The span offered is eleven quarters of movement and two and three quarter years of it. Hold everything else exactly where the record puts it: all seventeen capital calls, the other three distributions, and the Rs 2,82,00,00,000 of value that is still held. Nothing about any company changes. Nothing about any amount changes. Only the quarter one payment lands in.

Work out what each instrument does with that. The multiple divides Rs 7,20,00,00,000 by Rs 4,80,00,00,000. Moving a payment does not change how much it was, so neither of those two totals has moved. So the multiple reads 1.5000 times at every single one of the twelve settings, and it is not approximately 1.5000, it is the identical division twelve times over. The second instrument reads the quarter, so it reads something different at every setting. On this fund's own locked record the reading runs from plus 9.1 per cent when the payment is placed at Year 6 Q1 down to plus 7.7 per cent when it is placed at Year 8 Q4, passing through the recorded plus 8.3 per cent at Year 7 Q3 where the payment actually fell.

Two lines, one picture, one lesson. The flat line is not an approximation and the sloping line is not noise. A spread of 1.4 points, produced by nothing at all except when the cash arrived, sitting on top of a total value that never moved by a single rupee, is the entire difference between the two instruments rendered as a shape. The shape of those two lines is the thing to carry away.

Two guardrails before the control below. First, every setting sits inside this fund's own recorded life, and none of them is later than its record date. Second, the eleven settings that are not Year 7 Q3 are not claims about the fund. The other eleven are a labelled what-if run on a locked record, and the recorded readings they produce are read from that record rather than worked out here.

How does each one cope with value nobody has bought?

Now the uncomfortable part, and it is the reason the pair should never be treated as a safe number and a risky one.

Nilgiri Growth Partners Fund II, invented, still holds five companies at the record date, carried at Rs 2,82,00,00,000 between them. The carried figure is not cash. Nobody has paid it. The figure is a carrying value struck by a process that is covered separately, and until somebody signs a cheque it stays an estimate. Rs 4,38,00,00,000 of this fund's total value has actually been received by its investors and Rs 2,82,00,00,000 has not, and the split between realised and unrealised value is covered separately and taken as given here.

Each of the two instruments has to put that estimate somewhere, and both of the places are uncomfortable in a useful way. Both of them count it, and neither of them can be quoted as the number that avoids it. The multiple counts it in the top of the division, where Rs 2,82,00,00,000 of the Rs 7,20,00,00,000 has never been sold. The second instrument counts it as the final flow the dated list ends with, standing in for a sale that has not happened, placed at 8.50 years. Same estimate, two doorways.

The estimate matters most on exactly the kind of fund this one is: nine years old, six quarters of contracted term still to run, and five positions unsold. A reader who reaches for the multiple because a percentage feels slippery has not escaped anything, and a reader who reaches for the percentage because a multiple feels crude has not escaped anything either. The estimate is inside both. A reader can ask how much of the stated total has actually been received. On this fund the answer is Rs 4,38,00,00,000 out of Rs 7,20,00,00,000, and both figures should be read knowing it.

What goes wrong when only one of the two is quoted?

Who actually reads the pair, and what do they do with it?

Almost nobody meets these two figures as an exercise. Readers meet the pair inside a document somebody has to act on, and the shape of that document is worth seeing.

Start with the person on the investor advisory committee. Meera Sathe, invented, chairs the investor advisory committee of Nilgiri Growth Partners Fund II, invented, and represents the largest of its twelve investors. When a quarterly pack arrives showing a multiple that has barely moved and a rate that has slipped, her job is not to decide whether that is good. Her job is to establish which of the two moved for which reason and whether the third question, the one about mark-downs, answers no. If it answers no, she has a period in which the arithmetic did what arithmetic does. If it answers yes, she has a different conversation to have, and the two figures no longer separate cleanly.

Now the analyst inside an institution that has committed money to a number of such vehicles. The analyst is not being asked which fund is doing well. Ranking funds is a different exercise with different tools. The analyst is being asked to describe what happened. The two figures together let a period be described as a movement with a cause, and either figure alone lets it be described only as a movement. Writing that a fund's total value multiple was 1.50 times at 8.50 years since final close, and saying both halves of that sentence, is more work than writing 1.50 times, and it is the difference between a description somebody can check and a number somebody has to trust.

Then there is the person furthest from any of it, whose retirement money sits inside an institution that has committed to vehicles like this one and who will never see a capital account statement. The same distinction governs every long, illiquid holding that reader will ever have an interest in, so it reaches even somebody who never sees a capital account statement. How much came back and how long it took are always two questions, and any product, statement or summary that answers only one of them has left the other one open. A household that has put money into a chit fund, a plot of land or a cousin's shop is in exactly the same position with much smaller numbers.

One last practical note, and it is the one that generalises furthest. Where the two figures disagree about direction, that disagreement is information rather than a contradiction to be resolved. A multiple that rises while a rate falls says that more value arrived but arrived late. A multiple that holds still while a rate falls says that nothing arrived and time passed anyway. Nilgiri Growth Partners Fund II shows roughly that across its last two quarters. Neither sentence is available from one figure.

How should the pair be read together?

Three habits, and they are all consequences of one sentence that has already been said several times: the multiple has no time in it and the rate of return is made of nothing else.

The first habit is to refuse a single figure. If a document gives one, the honest reading is that a question has been left unanswered rather than that the fund has been described. Ask for the other one, and if it is not available, say in writing that it is not available rather than treating the figure in hand as the whole picture.

The second habit is to attach the period to the multiple every single time, in the same sentence. Nilgiri Growth Partners Fund II, invented, stood at 1.50 times at 8.50 years after its final close. The added span carries what 1.50 times by itself cannot, and it costs six words. A reader who has the span in front of them stops expecting a multiple to contain it, and the four holdings on the timeline above then look unsurprising rather than confusing.

The third habit is to attach the amount to the rate. A percentage on a fund that has returned Rs 4,38,00,00,000 in cash and a percentage on a fund that has returned almost nothing are not the same statement, and the rate itself does not say which one is in front of the reader. Naming what has actually been received alongside the percentage is the mirror image of naming the period alongside the multiple.

Neither of the two is better and neither is more honest, because they are not answers to the same question. A reader who wants both properties of a fund looks at both figures. Reading both is the entire rule, and everything above is the demonstration that the rule is necessary.