Price a tail-end interest on its net distributions, with the fund's costs in absolute amounts, and a large part of the discount turns out to be structure.
Because the costs of a fund do not shrink as fast as its NAV. On an illustrative tail-end fund with 40 of NAV left, a 1 per cent fee on remaining cost, 0.60 a year of fixed expenses and 20 per cent carry on further gains, a buyer requiring 15 per cent can pay 78.6 per cent of NAV. The same assets with no costs are worth 85.1. Of the 21.4 point discount, 6.6 points are drag, and half of that is the fixed expenses alone.
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 →
Tail-end interests, positions in funds past their tenth year with a handful of companies left, are often explained as cheap because nobody wants them: small tickets, little information, a manager with no reason to engage. All true, and all hard to price. The part that can be priced is the cost line. A fund that was built to run 400 of assets keeps its administrator, auditor, legal counsel and reporting cycle when 40 remain, and the buyer inherits its share of every one of them.
| Input | Value |
|---|---|
| Remaining NAV, net of accrued carry | 40 |
| Remaining invested cost (fee base) | 32 |
| Management fee in the extension, on remaining cost | 1.0% |
| Fixed fund expenses a year until wind-up | 0.60 |
| Carry on further gains (hurdle and catch-up already cleared) | 20% |
| Gross growth of the remaining assets a year | 6% |
| Run-off: equal shares of the remaining assets sold each year | 3 years |
| Buyer's required return | 15% |
In the first year the fee is 0.32 and the expenses 0.60, a combined 0.92, which is 2.30 per cent of NAV. The expenses alone are 1.50 per cent of NAV. The same 0.60 in a fund with 300 of NAV would be 0.20 per cent and nobody would model it.
Grow the assets at 6 per cent, sell a third of what remains in year 1, half in year 2 and the rest in year 3. From each year's proceeds deduct the fee on the cost still held, the fixed expenses and carry at 20 per cent of the gain over the opening NAV, allocated pro rata to proceeds.
| Year | Proceeds | Fee | Expenses | Carry | Net distribution |
|---|---|---|---|---|---|
| 1 | 14.13 | 0.32 | 0.60 | 0.31 | 12.90 |
| 2 | 14.98 | 0.21 | 0.60 | 0.33 | 13.84 |
| 3 | 15.88 | 0.11 | 0.60 | 0.35 | 14.82 |
| Total | 44.99 | 0.64 | 1.80 | 1.00 | 41.56 |
Look at the columns, not the totals. The fee falls as the cost base is realised. The carry rises gently with the proceeds. The expenses do not move: by year 3 they are 0.60 against 15.88 of proceeds, and they would be the same 0.60 if the last company took another two years to sell.
Price = PV at the required return of the net distributions
Gross of costs: PV of 14.13, 14.98, 15.88 = 34.06, or 85.1% of NAV.
Net of costs: PV of 12.90, 13.84, 14.82 = 31.42, or 78.6% of NAV.
In Excel: =NPV(15%, C2:C4)/40. Cost drag = 85.1 − 78.6 = 6.6 points.
The 14.9 point discount on the gross stream is the ordinary price of buying assets growing at 6 per cent with money that needs 15. The extra 6.6 points is what the fund's structure costs. Split by adding each cost in turn: the fee is 1.3 points, the fixed expenses 3.4 and the carry 1.9. The largest single item is the one that appears in no fee table.
Put the identical slice of assets inside a fund with 300 of NAV, same fee rate, same 0.60 of expenses, and the expense drag falls from 3.4 points to 0.5. The net price rises to 81.5 per cent. Same companies, same manager, three points of price explained by the size of the fund around them.
| Run-off | Price gross of costs | Price net of costs | Cost drag, points | Total costs paid |
|---|---|---|---|---|
| 2 years | 88.6% | 83.6% | 4.9 | 2.41 |
| 3 years | 85.1% | 78.6% | 6.6 | 3.44 |
| 4 years | 81.9% | 73.8% | 8.1 | 4.47 |
| 5 years | 78.8% | 69.5% | 9.4 | 5.52 |
Every extra year costs four to five points of net price, and roughly a third of that is cost drag rather than time value. That is why tail-end buyers spend their diligence on the exit timetable of the last few companies and on whether the manager will agree to cut expenses or wind the fund up early. Each year of extension is another 0.60 of expenses plus a year of fees.
Where the "tail-end discount" comes from: on these inputs a 21.4 point discount is 14.9 points of required return against asset growth and 6.6 points of structure. Neither is a sign of distress. A seller who reads the discount as the market's view of the companies is reading the wrong number.
The common mistake is to price the tail-end interest from the reported NAV and the asset outlook alone, as if the gross stream were what the buyer receives. Paying the gross price of 34.06 for the net distributions earns 10.4 per cent, not 15. The second mistake is to treat fund expenses as a percentage of NAV taken from the fund's mid-life accounts. At 0.20 per cent they are noise; at 1.50 per cent of a 40 NAV they are the biggest cost in the deal.
On a tail-end interest, model the costs in absolute amounts, not as rates: the fee on the remaining cost base, every fixed expense until the fund is wound up, and carry on the gains still to come. Then price the net stream at the required return and stress the run-off by a year or two. The deal model in the free workbooks for this book projects distributions and stresses delay in the same way. For the effect of timing on the return from a given discount, see why the same secondary discount gives different IRRs.
The sale of an interest in a fund late in its life, typically past year ten, with a few companies left and most capital returned. In the illustrative case a fund of 400 has 40 of NAV left and expects to sell it over three years, which a 15 per cent buyer prices at 78.6 per cent of NAV.
They are fixed in amount, so they grow as a share of a shrinking NAV. In the worked case 0.60 a year is 1.50 per cent of a 40 NAV and costs 3.4 points of price over a three-year run-off. In a fund with 300 of NAV the same expenses cost 0.5 points.
In the worked case each extra year cuts the price by four to five points of NAV at a 15 per cent required return. Stretching the run-off from three to five years moves the price from 78.6 to 69.5 per cent, and the cost drag from 6.6 to 9.4 points.
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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