Why deal IRRs cannot be added, the three attribution lenses that work, and how a profitable deal can pull a fund's return down.
Discount each deal's cash flows at the fund's own IRR: a deal with a positive NPV at that rate lifted the IRR, a negative one dragged it down, and the NPVs add up to exactly zero. On an illustrative five-deal fund returning 14.3 per cent and 1.69x, two deals carry 84.1 per cent of the gain, and a deal that made 1.80x still pulled the IRR down, because it held its money for five years at 12.5 per cent.
Worked in full in Private Markets Performance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Every performance review ends with the same question from an investment committee: which deals made the number? The multiple answers it easily, because gains add. The IRR does not, because IRRs do not add, average or subtract, as shown in why fund IRRs cannot be averaged. You need a method that respects how the IRR is built.
| Deal | Invested | Year in | Value | Year out | Multiple | Deal IRR |
|---|---|---|---|---|---|---|
| A | 20.0 | 0 | 60.0 | 5 | 3.00x | 24.6% |
| B | 25.0 | 1 | 30.0 | 6 | 1.20x | 3.7% |
| C | 15.0 | 1 | 33.0 | 3 | 2.20x | 48.3% |
| D | 20.0 | 2 | 10.0 | 5 | 0.50x | −20.6% |
| E | 20.0 | 2 | 36.0 | 7 | 1.80x | 12.5% |
| Fund | 100.0 | 169.0 | 1.69x | 14.3% |
The fund IRR comes from the pooled flows: −20.0, −40.0, −40.0 in years 0 to 2, then 33.0, 70.0, 30.0 and 36.0 in years 3, 5, 6 and 7. It is 14.28 per cent. The simple average of the five deal IRRs is 13.7 per cent and the cost-weighted average 11.5 per cent; neither is the fund's return, and neither tells you who made it.
Lens 1: contribution to the multiple. Gains add, so each deal's gain divided by total paid-in is an exact share of the 0.69x of profit. A adds 0.40x, C 0.18x, E 0.16x, B 0.05x and D takes away 0.10x. Together they make 1 + 0.69 = 1.69x.
Lens 2: leave one out. Recompute the fund IRR without each deal. Without A the fund returns 8.7 per cent, so A is worth 5.6 points; without D it returns 18.2 per cent, so D costs 3.9. The five changes sum to 0.5 points, nowhere near 14.3, so this lens ranks deals but cannot be added up.
Lens 3: NPV at the fund IRR. Discount each deal's flows at 14.28 per cent. Because the fund's flows have an NPV of zero at its own IRR, the deal NPVs must sum to zero: positive deals beat the fund's rate, negative ones dilute it.
NPVdeal = Σ CFt ÷ (1 + fund IRR)t
Deal A: −20.0 + 60.0 ÷ 1.14285 = +10.78
In Excel, with years in A2:A9, a deal's flows in C2:C9 and the fund IRR in F1: =SUMPRODUCT(C2:C9/(1+$F$1)^A2:A9). The five results must add to zero; if they do not, a flow is missing.
| Deal | Share of gain | Fund IRR without it | IRR points it adds | NPV at 14.28% |
|---|---|---|---|---|
| A | 58.0% | 8.7% | +5.6 | +10.78 |
| B | 7.2% | 18.3% | −4.0 | −8.41 |
| C | 26.1% | 11.0% | +3.3 | +8.98 |
| D | −14.5% | 18.2% | −3.9 | −10.18 |
| E | 23.2% | 14.8% | −0.5 | −1.17 |
| Total | 100% | +0.5 | 0.00 |
Three findings a committee would not get from the deal IRR column:
C is the mirror image: the smallest cheque, a modest 18.0 of gain, and the second-largest IRR contribution, because the money came back in two years.
| Change | Deal IRR | Fund IRR | Change vs 14.3% |
|---|---|---|---|
| C exits in year 5 at the same 33.0 | 21.8% | 12.7% | −1.6 |
| C exits in year 3 at 25.0 | 29.1% | 12.4% | −1.8 |
| A exits in year 7 at the same 60.0 | 17.0% | 12.1% | −2.2 |
| E marked at 30.0 instead of 36.0 | 8.4% | 13.4% | −0.8 |
Two years of delay on A, with no change in proceeds, cost the fund 2.2 points: more than a 16.7 per cent cut in E's mark. Attribution by IRR is as much about the calendar as about value created, which is why it must always sit next to the multiple attribution, never replace it.
Ranking deals by their own IRR. On that ranking C, at 48.3 per cent, is the star and E, at 12.5, looks respectable. Both statements are true of the deals and misleading about the fund: C's IRR applies to 15.0 for two years, and E's respectable 12.5 per cent is below the fund's own 14.28, so every year it is held dilutes the result. The second mistake is presenting leave-one-out deltas as if they summed to the fund return. They summed to 0.5 points here. Only the NPV lens is additive, and it sums to zero by construction, so it explains the gap between each deal and the fund, not the level.
The same test works on a track record in a fundraising deck. Ask for deal-level flows, compute the pooled IRR, and discount each deal at it. If one or two deals carry all the positive NPV, the track record is concentrated whatever the average deal IRR says. The concentration view on the multiple side is worked in a fund's multiple without its largest investment.
Attribute the multiple by gain share, attribute the IRR by NPV at the fund's own rate, and use leave-one-out only to rank. On this fund the three lenses agree that A and C made the result, and they reveal what the deal IRR column hides: B and E, both profitable, held the IRR back. The working documents and the PME calculator that go with this book are in the free workbooks for Private Markets Performance.
Yes, whenever its own IRR is below the fund's. In the illustrative fund, deal B returned 1.20x over five years, 3.7 per cent a year, and removing it lifts the fund IRR from 14.3 to 18.3 per cent. Its NPV at the fund's 14.28 per cent is -8.41, and it costs 4.0 points of IRR, more than the 3.9 points the loss-making deal costs.
Because removing a deal changes the rate at which every other deal is weighted. In the example the five leave-one-out changes sum to 0.5 points against a fund IRR of 14.3 per cent. They are good for ranking deals, not for building an additive bridge. Use gain share for the multiple and NPV at the fund IRR for the rate.
Divide each deal's gain by the fund's total paid-in capital. The shares add exactly: in the example 0.40x, 0.18x, 0.16x, 0.05x and -0.10x make the 0.69x of profit in a 1.69x fund. This is the attribution to show for value created; the IRR attribution then shows how timing changed the rate.
This article is one calculation from Private Markets Performance. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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