The multiple falls by the markdown times RVPI at any age; the IRR falls by far more when the fund is young, because the NAV is most of the value and there is little time to spread the loss.
Recompute the IRR with the marked-down NAV as the terminal cash flow: the answer depends almost entirely on the fund's age. On an illustrative fund, a 20 per cent NAV markdown takes the since-inception IRR from 10.1 to 0.4 per cent at year 4, a fall of 9.7 points; from 11.5 to 8.9 per cent at year 7; and from 11.1 to 10.6 per cent at year 10. The multiple is simpler: TVPI always falls by the markdown times RVPI.
Worked in full in Private Markets Performance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
This matters whenever valuations are under pressure. An investment committee told that "marks are down 20 per cent" needs to know which funds' reported returns that actually moves, and by how much, before anyone reads a quartile ranking or a carry accrual off them.
| Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Contributions | 20 | 25 | 25 | 20 | 10 | 0 | 0 | 0 | 0 | 0 | 0 |
| Distributions | 0 | 0 | 0 | 0 | 5 | 15 | 25 | 30 | 35 | 30 | 20 |
| Reported NAV | 120 | 95 | 30 |
IRR: solve Σ CFt ÷ (1 + r)t = 0, with CF at the valuation date = distribution + NAV × (1 − markdown)
TVPI change = − markdown × NAV ÷ paid-in = − markdown × RVPI
In Excel, with net cash flows in B2:L2 and the markdown in B4, replace the last flow by =distribution+NAV*(1-$B$4) and use =IRR(B2:L2), or =XIRR() with actual dates.
Step 1, the fund at year 4. Paid-in 100, distributed 5, NAV 120: TVPI 1.25 and IRR 10.1 per cent. The NAV is 96.0 per cent of the fund's total value.
Step 2, mark it down 20 per cent. NAV becomes 96.00 and TVPI 1.01, a fall of 0.24, which is 20 per cent of the RVPI of 1.20. The IRR falls to 0.4 per cent: nearly four years of return erased by one quarter's revaluation.
Step 3, repeat at years 7 and 10. At year 7 the fund has distributed 75 and holds 95.0; the same markdown cuts TVPI by 0.19 and the IRR by 2.6 points. At year 10 it has distributed 160 and holds 30.0; TVPI falls by 0.06 and the IRR by 0.5 points.
| Fund age | DPI | RVPI | NAV share of value | IRR as reported | −10% | −20% | −30% |
|---|---|---|---|---|---|---|---|
| Year 4 | 0.05 | 1.20 | 96.0% | 10.1% | 5.5% | 0.4% | −5.1% |
| Year 7 | 0.75 | 0.95 | 55.9% | 11.5% | 10.2% | 8.9% | 7.5% |
| Year 10 | 1.60 | 0.30 | 15.8% | 11.1% | 10.9% | 10.6% | 10.4% |
| Fund age | As reported | −10% | −20% | −30% |
|---|---|---|---|---|
| Year 4 | 1.25 | 1.13 | 1.01 | 0.89 |
| Year 7 | 1.70 | 1.60 | 1.51 | 1.42 |
| Year 10 | 1.90 | 1.87 | 1.84 | 1.81 |
The multiple and the rate tell different stories. In TVPI terms the year-4 and year-7 funds lose similar amounts, 0.24 and 0.19, because their RVPIs are similar. In IRR terms the young fund loses almost four times as much, because the IRR has only four years over which to spread the change in value, and most of the cash went in recently.
The more useful question for a monitoring team is the reverse: how large a markdown would take each fund below its 8 per cent hurdle, or below zero?
| Fund age | To 8% | To 0% |
|---|---|---|
| Year 4 | 4.6% | 20.8% |
| Year 7 | 26.6% | 73.7% |
| Year 10 | not reached | not reached |
At year 4 a revaluation of under 5 per cent, well inside the normal disagreement between two valuers, moves the fund across its hurdle. At year 10 the fund could write its whole NAV off and still show 8.5 per cent. This is the quantitative form of the point made in when a fund's IRR becomes meaningful: early on, the IRR is a statement about the NAV, not about the fund.
The illustration ignores carried interest. On a net basis an accrued carry provision falls with the NAV and absorbs part of the markdown, so net figures move a little less than gross ones above the carry threshold, and the accrual can reverse entirely.
The same arithmetic runs in reverse for a mark-up. A young fund that revalues one large holding upwards can add several points of IRR in a quarter, which is why a since-inception rate at year 4 should never be the basis for a re-up decision or a quartile claim on its own.
Treating a uniform markdown as a uniform hit to performance. A 20 per cent portfolio-wide revaluation costs a young fund nearly ten points of IRR and a mature fund half a point. The second mistake is reading the young fund's IRR change as information: the NAV is an estimate, and at year 4 the IRR is a magnified version of that estimate. Report the multiple and the share of value still unrealised next to the rate.
The complete measurement of the book's fund, from the cash flow series to the reporting line, is in the free workbooks for this book.
TVPI falls by the markdown multiplied by RVPI, because only the residual value is marked down. A 20 per cent markdown on a fund with an RVPI of 1.20 takes 0.24 off TVPI; on a mature fund with an RVPI of 0.30 it takes 0.06. Distributions already received are untouched, which is why DPI is the part of a multiple that cannot be revised.
Because the NAV is almost all of the value and the IRR spreads any change over very few years. At year 4 the illustrative fund's NAV is 96.0 per cent of its total value; a 4.6 per cent markdown is enough to take the IRR from 10.1 per cent to an 8 per cent hurdle, and a 20.8 per cent markdown takes it to zero.
Usually not once most of the value has been distributed. At year 10 the illustrative fund has DPI of 1.60 and NAV of 30.0; writing the whole NAV off still leaves a since-inception IRR of 8.5 per cent, above an 8 per cent hurdle. At year 7, with DPI of 0.75, a markdown of 26.6 per cent is enough.
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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