The three fund multiples computed from one call and distribution schedule, with the DPI path year by year and what a write-down of the residual does.
All three divide by paid-in capital, the money the fund has actually called: DPI is cumulative distributions over paid-in, RVPI is remaining net asset value over paid-in, and TVPI is their sum. On the Thornbury programme, 564 called, 791 distributed and 143 still held give DPI 1.4025x, RVPI 0.2535x and TVPI 1.6560x. 84.7 per cent of the multiple is already cash.
Worked in full in Alternative Investments by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
These are the first three numbers on every private fund report and the ones limited partners quote to each other. They are easy to compute; what is easy to miss is what each one leaves out, and which of them can still change.
Thornbury is the illustrative foundation in the book: it committed 600 to a buyout fund, which called capital over five years and distributed over eight. Net asset value at the end of Year 10, the residual still to be realised, is 143.
| Year | Called | Distributed | Cumulative paid in | Cumulative distributed | DPI |
|---|---|---|---|---|---|
| Year 1 | 90 | 0 | 90 | 0 | 0.0000 |
| Year 2 | 150 | 0 | 240 | 0 | 0.0000 |
| Year 3 | 138 | 29 | 378 | 29 | 0.0767 |
| Year 4 | 120 | 86 | 498 | 115 | 0.2309 |
| Year 5 | 66 | 143 | 564 | 258 | 0.4574 |
| Year 6 | 0 | 152 | 564 | 410 | 0.7270 |
| Year 7 | 0 | 133 | 564 | 543 | 0.9628 |
| Year 8 | 0 | 95 | 564 | 638 | 1.1312 |
| Year 9 | 0 | 86 | 564 | 724 | 1.2837 |
| Year 10 | 0 | 67 | 564 | 791 | 1.4025 |
DPI = cumulative distributions ÷ paid-in capital = 791 ÷ 564 = 1.4025x
RVPI = residual net asset value ÷ paid-in capital = 143 ÷ 564 = 0.2535x
TVPI = (cumulative distributions + residual NAV) ÷ paid-in capital = 934 ÷ 564 = 1.6560x
Check: DPI + RVPI = TVPI, 1.4025 + 0.2535 = 1.6560. In Excel, with paid-in in B1, distributions in B2 and NAV in B3: =B2/B1, =B3/B1, =(B2+B3)/B1.
Paid-in capital is everything the investor has wired to the fund, including the part used to pay management fees, because these are net multiples measured from the investor's side. Distributions are net of carried interest. Thornbury's 564 of paid-in is 94 per cent of the 600 commitment (a PIC ratio of 0.9400); the other 36 was never called.
The same three ratios are sometimes quoted gross, before fees and carried interest, in a manager's deal-level track record. Those are portfolio multiples, not investor multiples, and they are normally higher. When two figures for the same fund disagree, the first question is which side of the fee line each one sits on.
TVPI says the fund has turned 564 into 934, a gain of 370. DPI says how much of that is in the bank: 791 has come back, more than the 564 put in, so the investor's cash is already repaid with a profit whatever happens to the residual. RVPI is the part that is still a valuation.
The DPI column above is the programme's life in one line. It is zero for two years, reaches 0.4574 when the last capital is called in Year 5, and crosses 1.00x in Year 8. Until then a TVPI above 1.00 was partly a promise. A young fund with a TVPI of 1.6 and a DPI of 0.2 is a very different asset from this one, though the headline multiple is the same.
Only RVPI can still move. Writing the 143 down shows how much of the result depends on it.
| Write-down | Residual | RVPI | TVPI | Net IRR |
|---|---|---|---|---|
| 0% | 143.0 | 0.2535 | 1.6560 | 13.2935% |
| 10% | 128.7 | 0.2282 | 1.6307 | 12.9879% |
| 20% | 114.4 | 0.2028 | 1.6053 | 12.6745% |
| 30% | 100.1 | 0.1775 | 1.5800 | 12.3530% |
| 50% | 71.5 | 0.1268 | 1.5293 | 11.6834% |
| 100% | 0.0 | 0.0000 | 1.4025 | 9.8247% |
Even if the residual were worth nothing, the TVPI would fall only to the DPI, 1.4025x, and the IRR to 9.8247 per cent. At this stage of the fund's life the valuation decides a quarter of a turn of multiple, not whether the investment worked.
Dividing by the commitment. (791 + 143) ÷ 600 = 1.5567x, not 1.6560x. Value over commitment is a legitimate figure for an investor sizing a programme, since the whole 600 had to be held ready, but it is not TVPI, and mixing the two across funds with different call ratios makes the comparison meaningless.
Reading a multiple as a rate. 1.6560x over ten years is 5.17 per cent a year if all the money had been out for the whole decade. It was not: the capital went out over five years and came back from Year 3, which is why the IRR on the same flows is 13.2935 per cent. A multiple has no clock. The conversion for a given holding period is in MOIC to IRR by holding period.
Treating DPI as the realised return. DPI includes the return of capital as well as the profit. A DPI of 0.9628 in Year 7 means the investor had not yet got all its money back, not that it had earned 96 per cent.
Compute all three on paid-in capital, check that DPI plus RVPI equals TVPI, and read DPI first: it is the only one of the three that cannot be revised. Then ask what share of the TVPI is still a valuation, here 15.3 per cent, and how the IRR moves if it is marked down. The free cash-flow engine workbook for this case computes the multiples and the J-curve from the same schedule. For what the investor earned on the whole 600 set aside, see how much of the IRR reaches the investor.
DPI counts only cash returned to investors; TVPI adds the fund's remaining net asset value. On 564 paid in, 791 distributed and 143 still held, DPI is 1.4025x and TVPI 1.6560x. The difference, RVPI of 0.2535x, is a valuation that can still change, which is why investors read DPI first in a mature fund.
On paid-in capital, the amount actually called. Here that is 564 of a 600 commitment, giving a TVPI of 1.6560x. Dividing by the commitment gives 1.5567x, which is a useful figure for an investor that held the whole commitment ready, but it is not TVPI and should not be compared with one.
It depends on the fund's age. A DPI above 1.00x means investors have their money back; this illustrative fund crossed that line in Year 8 and reached 1.4025x by Year 10. Early in a fund's life a low DPI is normal: Thornbury's was 0.4574x at Year 5, when all capital had just been called.
This article is one calculation from Alternative Investments. 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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