A secondary sale converts the whole residual value into distributions at once, so DPI jumps by the price and TVPI falls by the discount times RVPI; the real cost is the return the buyer earns on the cash flows you hand over.
Yes, and by a lot: a secondary sale turns the whole residual value into a distribution on the closing date, so DPI rises by the price over paid-in capital while TVPI falls by the discount times RVPI. On an illustrative interest with an RVPI of 0.900, a sale at 85 per cent of NAV lifts DPI from 0.600 to 1.365 and cuts TVPI from 1.500 to 1.365. The true cost is not the 0.135 of TVPI but the return the buyer earns on the cash flows sold: 17.30 per cent a year, against 10.22 per cent if they were bought at NAV.
Worked in full in The Private Equity Secondaries Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The LP and the fund are illustrative. The commitment is fully called, so no unfunded commitment passes to the buyer, and the LP's expected cash flows from holding are its own forecast, which a buyer will discount at its own target return.
| Item | Value |
|---|---|
| Paid-in capital | 50.0 |
| Distributions to date | 30.0 |
| Reported NAV | 45.0 |
| DPI / RVPI / TVPI | 0.600 / 0.900 / 1.500 |
| Expected return on NAV if held, multiple | 1.30x |
| Timing of the 58.50 expected back, years 1 to 4 | 15 / 25 / 30 / 30% |
| Offered price, % of NAV | 85.0% |
Price = 45.0 × 85.0% = 38.25
DPI after = (30.0 + 38.25) / 50.0 = 1.365, up 0.765
RVPI after = 0, so TVPI after = DPI = 1.365, down 0.135
In general: ΔDPI = (1 − d) × RVPI = 0.85 × 0.900 = 0.765; ΔTVPI = −d × RVPI = −0.15 × 0.900 = −0.135
The DPI jump is mechanical: it is the price, expressed per unit of paid-in capital. It says nothing about value, and it is the same jump whether the fund's companies are excellent or poor. The TVPI fall is the discount, 6.75 of NAV, expressed the same way. Both are defined in how to calculate TVPI, DPI and RVPI.
The 0.135 of TVPI understates the cost, because the LP is also giving up the growth it expected on the NAV. If held, the 45.0 of NAV is expected to return 58.50, paid 8.78, 14.62, 17.55 and 17.55 over years 1 to 4. That makes the final TVPI 1.770, so the sale leaves the LP 0.405 below its expected outcome, or 20.25 of cash.
Return on NAV if held = IRR(−45.0, 8.78, 14.62, 17.55, 17.55) = 10.22%
Implied cost of selling = IRR(−38.25, 8.78, 14.62, 17.55, 17.55) = 17.30%
In Excel: =IRR(B2:B6) with the price, negative, in B2 and the forecast flows below it.
The 17.30 per cent is the rate at which the LP is effectively borrowing against its own interest: it receives 38.25 today and gives up 58.50 over a weighted life of 2.75 years. Whether that is expensive depends on what the cash is for. If it rebalances an over-allocated programme or funds a commitment expected to earn more, selling can be right. If it only improves the DPI line in a report, it is a costly way to buy a number.
| Price, % of NAV | Price | DPI after | TVPI after | TVPI given up | Implied annual cost |
|---|---|---|---|---|---|
| 80% | 36.00 | 1.320 | 1.320 | 0.180 | 20.12% |
| 85% | 38.25 | 1.365 | 1.365 | 0.135 | 17.30% |
| 90% | 40.50 | 1.410 | 1.410 | 0.090 | 14.74% |
| 95% | 42.75 | 1.455 | 1.455 | 0.045 | 12.39% |
| 100% | 45.00 | 1.500 | 1.500 | 0.000 | 10.22% |
Even at par, selling costs 10.22 per cent a year, the return the NAV was expected to earn. Each 5 points of discount adds roughly 2.2 to 2.8 points of annual cost, and DPI changes by only 0.045 between neighbouring rows. The DPI an LP reports after a sale differs by 0.135 between 80 and 95 per cent; the annual cost it accepted differs by almost eight points, 20.12 against 12.39 per cent.
The implied cost depends on the forecast. If the LP believes the NAV is overstated, or the cash flows will arrive later, the true cost of selling is lower than these figures. That is the seller's version of the buyer's underwriting, and it should be done before a price is accepted, not after.
A sale at a discount raises DPI by (1 − d) × RVPI and lowers TVPI by d × RVPI. At 85 per cent of a 45.0 NAV, DPI goes from 0.600 to 1.365 and TVPI from 1.500 to 1.365, while the cash flows sold earn the buyer 17.30 per cent a year. The deal model that projects distributions and splits a buyer's return between discount and appreciation, the other side of this trade, is in the free workbooks for this book.
TVPI falls by the discount times RVPI, because unrealised value becomes cash at less than its carrying amount. With an RVPI of 0.900, a 15 per cent discount costs 0.135 of TVPI, from 1.500 to 1.365. Against the expected outcome of holding, 1.770, the gap is 0.405, or 20.25 of cash: the buyer's expected profit, made of the 6.75 discount and the 13.50 of growth expected on NAV.
The internal rate of return the buyer earns on the cash flows sold. A 45 NAV expected to return 58.50 over four years earns 10.22 per cent a year if bought at NAV. Sold at 85 per cent, 38.25, the same flows give the buyer 17.30 per cent; at 80 per cent, 20.12 per cent. Selling is cheap only if the seller's own use of the cash beats that rate.
No. DPI measures cash returned, not value created. An LP that sells at 85 per cent of NAV shows a DPI of 1.365 against 0.600 before the sale, but its TVPI has fallen and its final multiple is 0.405 below holding. Read DPI after a sale beside TVPI and the sale price, never alone.
This article is one calculation from The Private Equity Secondaries Investor. 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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