The floor and the ceiling are one formula run twice. At equal required returns the zone is exactly zero, and a buyer cannot widen it by underwriting harder.
A limited partnership interest is offered at 88 against a reported net asset value of 100. The seller discounts its own fund at 10 per cent; the buyer needs 15. The usual account of this trade is that the two sides disagree about value and meet somewhere in the middle. They do not disagree about value at all. On these projections there is no price that satisfies both of them, and the gap is 11.02 points of 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 →
Every write-up of secondary pricing repeats the same sentence: a deal clears where the buyer’s ceiling and the seller’s floor overlap, and the art is to infer the floor. Almost none of them computes either one. Computing both takes four rows and settles a question that is usually left to instinct.
One interest in one fund. The manager projects 130 of value over four years, net of a small remaining call in year one. Assume — this is the point of the exercise — that buyer and seller agree on every figure.
| Year | Distributions | Capital called | Net to the holder |
|---|---|---|---|
| 1 | 20 | 2 | 18 |
| 2 | 30 | — | 30 |
| 3 | 40 | — | 40 |
| 4 | 40 | — | 40 |
| Total | 130 | 2 | 128 |
The seller’s floor is what the interest is worth if it keeps it: the present value of those four rows at the seller’s own cost of capital. The buyer’s ceiling is the most it can pay and still earn its hurdle: the present value of the same four rows at the buyer’s rate. That is not two models. It is one model run twice.
| Value | As a discount to NAV | |
|---|---|---|
| Seller’s floor — hold and receive the cash | 98.53 | 1.5% |
| Buyer’s ceiling — pay this and earn 15%% | 87.51 | 12.5% |
| The zone between them | -11.02 | — |
The floor is above the ceiling. At these two rates there is no overlap, no zone, and no price that satisfies both parties — and yet the deal is being offered at 88, which is 10.53 points below the seller’s own floor. Something other than valuation is closing that gap.
Run the identity out and the consequence is immediate. If the floor and the ceiling are the same present value at two rates, then at equal required returns the zone is exactly zero — not small, zero — and it is negative whenever the buyer wants more than the seller requires, which is the ordinary case. The discount a secondary trades at is the price of a difference in required return, plus whatever the seller’s motivation is worth. It is not a view on the assets.
| Buyer’s hurdle | 6% | 8% | 10% | 12% | 15% | 18% | 20% |
|---|---|---|---|---|---|---|---|
| 10% | -10.42 | -5.01 | 0.00 | +4.65 | +11.02 | +16.75 | +20.26 |
| 12% | -15.07 | -9.66 | -4.65 | 0.00 | +6.37 | +12.10 | +15.61 |
| 15% | -21.44 | -16.03 | -11.02 | -6.37 | 0.00 | +5.73 | +9.24 |
| 18% | -27.17 | -21.76 | -16.75 | -12.10 | -5.73 | 0.00 | +3.50 |
| 20% | -30.68 | -25.27 | -20.26 | -15.61 | -9.24 | -3.50 | 0.00 |
| 25% | -38.49 | -33.08 | -28.07 | -23.42 | -17.04 | -11.31 | -7.81 |
Read the diagonal: every cell where the two rates are equal is exactly zero. Then read the shape. The zone opens only to the right of the diagonal — that is, only when the seller’s own rate is higher than the buyer’s. A buyer cannot widen it by underwriting harder, discounting more carefully, or building a better bottom-up NAV. It widens when the seller’s cost of capital rises.
Three things practitioners assert without deriving fall straight out of that shape. Stress favours buyers because stress raises the seller’s own rate, which is the only axis that opens the zone. Proprietary deals clear tighter because an unmarketed seller has a motivation the price has to compensate. And near-harvest funds trade closer to par because a short duration shrinks the present-value gap between any two rates.
You will never be told the seller’s discount rate. You can read what it is implicitly accepting off the price it takes, which turns a judgement about motivation into a number you can bid against.
| Price the seller accepts | Rate it is implicitly accepting | Against its own 10% | Reading |
|---|---|---|---|
| 98 | 10.22% | 0.22% | above what a 15% buyer can pay |
| 95 | 11.50% | 1.50% | above what a 15% buyer can pay |
| 92 | 12.85% | 2.85% | above what a 15% buyer can pay |
| 88 | 14.76% | 4.76% | above what a 15% buyer can pay |
| 85 | 16.27% | 6.27% | a buyer at 15% can pay this |
| 82 | 17.88% | 7.88% | a buyer at 15% can pay this |
At 88 the seller is handing the buyer 14.76% a year against its own 10 per cent. That is a concession of 4.76% points of annual return, and it is the measurable form of the sentence “a motivated seller has a lower, softer floor”. If the seller has no visible reason to concede that much, the projections are the thing to re-underwrite, not the price.
A deferral is usually explained as a way to pay more without earning less, which sounds like a free lunch and is treated as one. It is worth being exact about the size and the mechanism. Defer one third of the price by a single year at no interest, hold the buyer’s return constant, and the headline price it can bid rises from 88 to 91.94.
| All cash | One third deferred by a year | |
|---|---|---|
| Headline price | 88.00 | 91.94 |
| Paid at closing | 88.00 | 61.29 |
| Paid a year later | — | 30.65 |
| The fund’s own year-one distribution | — | 18.00 |
| Out of the buyer’s pocket, in total | 88.00 | 73.94 |
| Return to the buyer | 14.76% | 14.76% |
3.94 points of headline price, in a market where a competitive gap is one or two. And look at where the money comes from: the deferred cheque is 30.65, the fund’s own year-one distribution is 18.00, so the fund itself covers 58.7% of it. The buyer never finds a second cheque. This is not leverage on the asset — it is the fund’s own cash, arriving before the payment is due.
If the extra points were bought with a distribution, then the risk being taken is not “will the assets perform” but “will that particular distribution arrive before that particular cheque is due”. Let the year-one distribution slip to year three — same companies, same manager, same total value, only later — and the two structures do not suffer equally.
| Return | Cost of the slip | |
|---|---|---|
| All cash, at 88 | 13.10% | -1.66% |
| Deferred, at 91.94 | 12.91% | -1.85% |
The deferred buyer loses more. It paid a higher headline price for a timing assumption, and when the timing fails the points stay paid while the cash does not arrive. The difference is small here because the slip is modest; it widens with the size of the deferral and with the length of the delay, and neither is inside the buyer’s control.
The discipline that follows is narrow and worth stating plainly: use structure to enhance the return on an asset you are confident in, never to reach a return you could not otherwise justify. A deferral that makes an 11-point gap disappear on paper has not closed the gap. It has moved it onto a distribution date.
Three things. First, compute both sides of the trade before pricing it — the floor and the ceiling are the same four rows at two rates, which takes a minute and tells you whether a zone exists at all. Second, if no zone exists at your hurdle and the seller’s plausible rate, stop treating the negotiation as a valuation argument and start pricing the seller’s motivation, because that is the only thing that can close it. Third, if you are offered structure, ask which distribution funds it and what happens if that distribution is late.
None of this requires a proprietary model. It requires running the same present value twice and reading the difference as what it is.
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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