The seller's side of a secondary sale, measured on the allocation that has been working for a decade.
Measure the discount against the whole programme, not against the NAV sold. An investor who sells a 143 residual at a 30 per cent discount loses 42.90, but on a ten-year, 600 allocation whose terminal value is 1,445.08 the annual return falls only from 9.19 to 8.86 per cent: 33 basis points a year. The shortcut is discount times the residual's share of terminal value, divided by the years, times one plus the return.
Worked in full in Alternative Investments by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A 30 per cent discount sounds like a 30 per cent loss, and on the line item it is. But an investor deciding whether to sell a tail-end fund interest is not choosing between two NAVs; it is choosing between two outcomes for an allocation that has been working for a decade. By year 10 most of the money has come back as distributions and been reinvested. The residual is a small share of what the allocation is worth, so a large discount on it is a small cost on the allocation's return. The same arithmetic run on a young fund gives the opposite answer.
An illustrative foundation sets aside 600 for a private equity commitment of 600. Uncalled capital and distributions are held in a listed equity index until the fund needs them, so the allocation, or sleeve, is the fund plus that index account. Flows are at the start of each year.
| Year | Calls | Distributions | Index return | Index account, end of year |
|---|---|---|---|---|
| 1 | 90 | 0 | 12.4% | 573.24 |
| 2 | 150 | 0 | 8.1% | 457.52 |
| 3 | 138 | 29 | -6.7% | 325.17 |
| 4 | 120 | 86 | 18.3% | 344.46 |
| 5 | 66 | 143 | 9.6% | 461.92 |
| 6 | 0 | 152 | 2.4% | 628.65 |
| 7 | 0 | 133 | 14.1% | 869.04 |
| 8 | 0 | 95 | -11.2% | 856.07 |
| 9 | 0 | 86 | 21.7% | 1,146.50 |
| 10 | 0 | 67 | 7.3% | 1,302.08 |
| Total | 564 | 791 |
At the end of year 10 the fund still holds a residual NAV of 143. The sleeve's terminal value is the index account plus the residual: 1,302.08 + 143 = 1,445.08.
Sleeve return, residual at NAV: (1,445.08 / 600)1/10 − 1 = 9.19%.
Residual sold at a 30% discount: proceeds = 143 × 0.70 = 100.10; terminal value = 1,302.08 + 100.10 = 1,402.18; return = (1,402.18 / 600)1/10 − 1 = 8.86%.
Cost: 9.19 − 8.86 = 0.33 points a year.
Shortcut: discount × residual share of terminal value / years = 30% × 9.90% / 10 = 0.30 points; multiplied by 1 + r for the compounding it leaves out, 0.32. Close enough for a first read.
In Excel: =((Liquid+NAV*(1-Disc))/Sleeve)^(1/Years)-1, against the same formula with Disc at zero.
The residual is 9.90 per cent of the sleeve's terminal value, and that one ratio carries the answer. The 42.90 given up is real money, but it is 42.90 out of 1,445.08 at the end of a ten-year compounding period, so it costs a third of a point a year.
| Discount | Proceeds | Given up | Terminal value | Sleeve return | Cost, basis points a year |
|---|---|---|---|---|---|
| 0% | 143.00 | 0.00 | 1,445.08 | 9.19% | 0 |
| 10% | 128.70 | 14.30 | 1,430.78 | 9.08% | 11 |
| 20% | 114.40 | 28.60 | 1,416.48 | 8.97% | 22 |
| 30% | 100.10 | 42.90 | 1,402.18 | 8.86% | 33 |
| 50% | 71.50 | 71.50 | 1,373.58 | 8.64% | 55 |
| 100% | 0.00 | 143.00 | 1,302.08 | 8.06% | 113 |
Even giving the residual away leaves the sleeve at 8.06 per cent, 0.92 points above the index's own 7.13 per cent a year. On this programme the residual does not decide whether private equity beat public markets; the 791 already distributed and reinvested did. The other side of the trade looks very different. A buyer paying 100.10 for 143 earns 26.84 per cent a year if the residual is realised in 1.5 years, and 12.62 per cent if it takes three. The seller's 33 basis points and the buyer's 26.84 per cent are the same 42.90 seen through two denominators.
On a young programme the conclusion reverses. Take a four-year-old 600 allocation worth 750, of which 450 is residual NAV, 60.00 per cent of the total. It returns 5.74 per cent a year at NAV; selling the residual at 30 per cent off gives up 135.00 and drops the return to 0.62. The cost is 5.12 points a year, 15.6 times the mature case, for the same discount.
Treating the discount as the cost. An investment committee that refuses every bid below 85 per cent of NAV is applying one rule to two very different decisions: on a tail-end interest the discount barely touches the programme's return, while on a young interest a smaller discount can wipe out years of performance. The second mistake is the reverse: comparing the buyer's IRR with the seller's lost return and concluding that the seller was robbed. Short holding periods inflate the buyer's rate; the seller's cost is measured over ten years.
The cost of a secondary discount to the seller is roughly the discount times the residual's share of the allocation's terminal value, spread over the years the allocation ran: 33 basis points a year for 30 per cent off a residual worth 9.90 per cent of the total, and over 5 points on a young fund. The sleeve, both idle-capital policies and the exit table are live in the free workbook for this case. For the buyer's side of the same trade, see why the same secondary discount gives such different IRRs.
Compute the allocation's annual return with the residual at NAV and again with the discounted proceeds, and take the difference. In the worked case a 30 per cent discount on a 143 residual changes the terminal value from 1,445.08 to 1,402.18 and the ten-year return from 9.19 to 8.86 per cent.
Discount times the residual's share of the allocation's terminal value, divided by the number of years, times one plus the return. For a 30 per cent discount on a residual that is 9.90 per cent of terminal value over ten years, that gives about 0.32 points against an exact 0.33.
When the residual is a large share of the allocation and the holding period is short. On a four-year-old allocation worth 750 with 450 of residual NAV, a 30 per cent discount cuts the annual return from 5.74 to 0.62 per cent, a cost of 5.12 points.
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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