Why a secondaries bid-ask gap often has no zone at all
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.
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.
The cash flows both sides are looking at
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
One interest, one set of projections. Both sides are looking at these four rows.
The floor and the ceiling are the same formula
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
—
Present value of the same four rows, at two different rates.
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.
Which means a discount to NAV is not a disagreement about value
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
The zone, in points of NAV. Rows: the buyer’s required return. Columns: the seller’s own rate.
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.
Reading the seller’s rate backwards from the price
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
The implied rate is the return the seller hands to the buyer.
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.
The deferred purchase price, and who actually funds it
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%
Same asset, same return, 3.94 more of headline price.
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.
Which is exactly how it fails
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 year-one distribution arrives in year three instead. Nothing else changes.
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.
What to take into the next bid
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.
The workbook behind this article
Every figure above is a live formula in the companion file for
The Private Equity Secondaries Investor, which also computes the zone matrix, the seller’s implied rate at any price, and what the deferral costs when the distribution is late. It is free, and it needs no account and
no email address.
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Does an undrawn revolver count as liquidity?67.4567 per cent of the headroom, and it leaves at a fall in annual revenue of 8.4127 per cent — not the 13.3333 per cent the board deck implies.
Does supply chain finance count as debt?66,049,315 released, and leverage of 2.7622× or 3.1362× depending on which balance the test is asked of — the second is a breach at today's EBITDA.
How do you set a minimum cash balance?Three components, 124,596,281 in total — and the double count that turns a margin of 27,403,719 into an apparent shortfall of -3,988,281.
Is a 2/10 net 60 discount worth taking?An annualised 14.8980 per cent against a revolver at 4.50 per cent — worth 5,471,890 a year, and 0.3132 turns of reported leverage.
At what wealth does a family office pay?A five-person office costs the same $2,442,000 at $100m as at $2bn. Against a tiered multi-family schedule the two curves cross exactly once.
Does the fulcrum move with enterprise value?A worked capital structure at three enterprise values. The break migrates from the first lien to the subordinated notes without a single document changing.
How many companies does a reserve pool defend?Holding pro rata to the Series D costs $14.76m per company. A $40m reserve defends 2.71 of forty — and 61 per cent of the cost is the last round.
How much room a 1.15x downside actually leaves79 basis points of margin. The leverage covenant fails first, five basis points before the coverage covenant the chapter reports on, and 4.6 per cent of EBITDA is the whole cushion.
How the GP catch-up is actually solvedMost write-ups state the catch-up formula then hardcode the answer. Set it as a solve and it moves on its own when the carry rate does.
Six ways to state the same fund's return7.12 per cent, 18.04 per cent, or 1.323 times the public market — one fund, one set of flows. The eleven-point gap is the valuation, and it is not cash.
The IRR at which a closed-ended fund merely tiesA drawdown fund advertising 13.25 per cent ties an evergreen netting 8.64. On committed rather than called capital, 78.7 per cent of the edge vanishes.
The month a remediation trigger has to be armed byMonth 8, on a one-year window and a 14-week hiring lead time. The date is 12W − L/4.33 and holds for any portfolio size — the book only changes the euros.
Two routes to the same NAVFive findings in one quarter-end close, and not one of them was a modelling error. Every one was a control that did not exist.
What a CBAM certificate buffer costs to holdCarry and protection are both linear in the buffer, so the break-even probability is identical at 5 per cent and at 30 — and 2027 costs exactly twice 2026.
What a clawback actually collateralises24 million recovers 13.20 net of tax and 7.20 is escrowed. The rule is e ≥ 1 − t, and every euro won on the tax clause lands uncollateralised.
What a co-investment programme actually saves37 basis points, and a 22.8 per cent total-loss rate erases it. At the usual per-deal cap a single failure is 37 per cent of the annual cohort.
What a diligence exercise actually recoversEighteen basis points is only the part that reaches the yield. Three of the four instruments never do, and the exercise is worth thirty-one.
What a follow-on reserve is actually worth0.019 turns under plain dilution, 0.285 under pay-to-play. The optimum is a property of the shareholders’ agreement, not of the portfolio.
What a lease mark-to-market is actually worth5,788,000 becomes 807,365 once the over-market stream, the expiry dates and the cost of re-letting are priced — and nothing at all below a 43.7 per cent renewal rate.
What a minimum payment actually does£81.53 leaves the account and £20.46 reaches the debt. On minimums alone the set clears in 258 months and repays 1.78 times what was borrowed.
What a month of delay costs in an enforcement463,000 euros of present value a month. No single error about enforcement, and no pair of errors, moves the indifference point from 58.7 cents to the 72 on the table.
What a pro rata cheque actually costsDefending costs 1.25 times the initial cheque across two rounds, not more in each — and below a 521 exit the follow-on dollars come back worth less than they cost.
What a subscription line does to the IRR20 per cent becomes 38.41 on the same asset while the multiple falls. Two dollars of interest buys 18.4 points, and the longer the line runs the cheaper each point gets.
What one point of fees actually costsOne point on the annual charge turns 738,846 into 567,961 over forty years — 23 per cent of the pot, and 2.43 of wealth lost per 1 of fee.
When the promote stops clearingCarried interest is not proportional to performance near the hurdle. It is a step function, and $2m of headroom is what stands between a promote and none.
Why refining a due diligence rubric makes it weakerThree of twelve managers carry a terminal flaw and the average approves all three. Splitting eight domains into sixteen makes it easier to hide, not harder.
This note is drawn from The Private Equity Secondaries Investor. The book is on Amazon.
If this book helped — or didn’t — a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.