Three computable deductions sit between the discount quoted in the memo and the discount received in the deal.
On a reported net asset value of €38.5 million offered at 82 per cent — a price of €31.57 million — an 18 per cent headline discount is worth 9.18 per cent. Unsmoothing the appraisal removes 3.58 points, because the reported number stands 4.36 per cent above spot value. The unfunded commitment, funded at par, removes 1.41 points. Management fees to term remove 3.84 points. The three deductions come to 8.82 points, or 49 per cent of the headline.
Worked in full in The Real Estate Secondaries Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The offer is 82 per cent of a reported net asset value of €38.5 million: a price of €31.57 million, and a memo that calls it an 18 per cent discount. Nothing that follows changes the price. What changes is the number the price is a percentage of.
Each correction replaces the reported net asset value with something closer to what is actually being acquired. The appraisal is replaced by spot value. Spot value is grossed up by the unfunded commitment that will be wired at par. The management fees the interest still owes to the end of the fund's life are taken off the value acquired. Three replacements, three defensible discounts, one price.
| Measured against | Value | Price or outlay | Discount |
|---|---|---|---|
| Reported net asset value | €38.50 m | €31.57 m | 18.00% |
| Spot value, once the appraisal is unsmoothed | €36.89 m | €31.57 m | 14.42% |
| Spot value plus the unfunded commitment | €40.89 m | €35.57 m | 13.01% |
| The same, less the fees to term | — | — | 9.18% |
The distance between the top line and the bottom line is 8.82 points — 49 per cent of the headline. It is not a market view and it is not bad luck. A buyer who prices every interest off the headline makes the same error, in the same direction, on every trade, and overpays by the amount of the smoothing every time.
A valuer anchors on the previous appraisal and moves it as far as the evidence supports and no further. Write that down and it inverts. If the reported return in a quarter is a blend of this quarter's true return and last quarter's reported return, with α the share of new information absorbed, then the true return is recoverable from the reported series and α alone.
α is unobservable, so the useful output is a range rather than a point. The same offer, priced across it:
| α | Appraisal above spot | Real discount at 82 per cent of net asset value |
|---|---|---|
| 0.25 | 9.07% | 10.56% |
| 0.30 | 6.93% | 12.32% |
| 0.40 | 4.36% | 14.42% |
| 0.50 | 2.87% | 15.65% |
| 0.70 | 1.21% | 17.01% |
| 1.00 | 0.00% | 18.00% |
Two things come out of that table. Across the assumptions a committee would accept without argument, the real discount runs from about 11 per cent to 18 per cent. And there is a threshold: below α = 0.1315, an 18 per cent discount to the appraisal buys no discount to value at all. An appraiser absorbing less than about 13 per cent of new information each quarter is an appraiser whose number a buyer is paying spot for.
The interest carries €4.0 million of unfunded commitment against €38.5 million of reported net asset value — a ratio of 10.4 per cent. That money is wired at par into whatever the manager buys with it. No secondary discount applies to it. The headline discount is therefore scaled by the share of the total outlay that is already invested, a factor of 0.906 here, which turns 18 per cent into 16.31 per cent before any other correction and into 13.01 per cent once spot value replaces the reported one.
The formula inverts, and the inversion is what to carry. For an 18 per cent headline to be worth only 10 per cent effective, the unfunded commitment would have to be €30.8 million — 80 per cent of net asset value. An interest whose unfunded is smaller than about four-fifths of its net asset value keeps most of its headline. An interest early in its investment period, where unfunded can exceed net asset value outright, is being sold at a discount that barely exists.
The fee to term is the largest single deduction and the most mechanical. The fund charges 1.25 per cent a year on drawn capital of €46.0 million, or €0.575 million a year, with 3.5 years to the stated term. Discounted at 12 per cent, the annuity factor is 2.729 and the present value of the obligation is €1.57 million — 3.84 points of discount consumed before anything happens to a building.
That deduction deserves an argument rather than a reflex. The fee buys work: leasing, capital expenditure, refinancing, sale. Deduct it, because it is certain and computable, but do not pretend the offsetting value is zero. State the test instead. The manager must create €1.57 million of value beyond what a passive owner would achieve, in present value, for the fee to be free. That is 3.8 per cent of the value being acquired, and it is a question with a yes or a no.
Put all four discounts in the memo and let the committee see which one is being voted on. Then check the corrected number by a second route rather than trusting it alone: rebuilding the value from estimated rental values, non-recoverable ratios, exit yields and capital expenditure to stabilise gives an independent estimate, and on this portfolio the two roads landed 0.87 per cent apart. Neither would carry a committee on its own.
Finally, order the work by what moves the answer. The whole unsmoothing argument is worth 3.58 points here. Twenty-five basis points on the exit yields is worth 7.79 per cent of the value of the interest, because debt sits between gross asset value and the interest and amplifies everything. Correct the headline first, because the error is systematic and free to remove. Then spend the remaining time on the yields.
Treat the reported return as a blend of the true return and the previous reported return, with α the share of new information absorbed each quarter, then invert it. At α = 0.40 the appraisal on this fund stands 4.36 per cent above spot value, turning a reported €38.5 million into €36.89 million.
Yes, because unfunded money is wired at par and carries no discount. With €4.0 million of unfunded against €38.5 million of net asset value, the scaling factor is 0.906 and an 18 per cent headline becomes 16.31 per cent. Only an unfunded commitment above 80 per cent of net asset value halves the headline.
Compute them as an annuity. At 1.25 per cent a year on €46.0 million of drawn capital, with 3.5 years to term and a 12 per cent discount rate, the annuity factor is 2.729 and the present value is €1.57 million. That is 3.84 points of discount, and the largest of the three deductions.
This article is one calculation from The Real Estate 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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