A queue pays the reported net asset value on the dealing date, not today's, and after a fall in values that number still has to come down.
A unit in a one-year redemption queue is worth the reported net asset value it will be paid at, which is still falling, plus the income received while waiting, discounted at your opportunity cost. With the appraisal 6.0 per cent above spot, a 4.0 per cent income yield and a 10.0 per cent cost of capital, the queue is worth 89.99 per 100 of reported value, so a secondary bid up to a 10.01 per cent discount is the better exit. The naive answer, discounting today's net asset value for a year, says 5.32.
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 →
When an open-ended real estate fund gates, an investor who has asked for redemption faces two exits. Wait in the queue and be paid, eventually, at the reported net asset value on the dealing date. Or sell the units to a secondary buyer today at a discount to the current reported net asset value. The buyer's bid is a firm number. The queue looks like par with a delay, and that is the mistake.
The queue pays the net asset value on the day it pays, not today's. When the appraisal stands above spot value, as it does after a fall in values, the reported number still has to come down, and the redeeming investor is paid after it has. Pricing the queue therefore needs three things: the gap between appraisal and spot, how fast the appraiser closes it, and what your money earns elsewhere.
| Input | Value |
|---|---|
| Reported net asset value per unit | 100 |
| Appraisal above spot value | 6.0% |
| α, share of the remaining gap closed each quarter | 0.40 |
| Income yield on spot value, paid quarterly | 4.0% |
| Spot capital growth while queued | 0.0% |
| Opportunity cost of capital | 10.0% |
| Queue length | 4 quarters |
Spot value today: S = NAV / (1 + gap) = 100 / 1.06 = 94.34. The appraisal premium is 5.66.
Reported value at payment: NAVT = S × (1 + g)T + 5.66 × (1 − α)quarters
Value of waiting: PV = Σ incomeq / (1 + k)q/4 + NAVT / (1 + k)T
Break-even discount: 1 − PV / NAV
In Excel, with the quarter number in column A, the appraisal premium in B1, α in B2 and the cost of capital in B3: =$B$1*(1-$B$2)^A5 for the gap left, and =(1+$B$3)^(-A5/4) for the discount factor.
Each quarter the appraiser closes 40 per cent of what remains, so 0.60 of the gap survives each quarter and 12.96 per cent of it survives four. The quarter by quarter path:
| Quarter | Spot value | Gap left | Reported value | Income | Discount factor |
|---|---|---|---|---|---|
| Q1 | 94.34 | 3.40 | 97.74 | 0.94 | 0.9765 |
| Q2 | 94.34 | 2.04 | 96.38 | 0.94 | 0.9535 |
| Q3 | 94.34 | 1.22 | 95.56 | 0.94 | 0.9310 |
| Q4 | 94.34 | 0.73 | 95.07 | 0.94 | 0.9091 |
The queue pays 95.07 at the end of the year, not 100. Discounted at 10.0 per cent, that payment is worth 86.43 today. The four income receipts add 3.56. The value of staying in the queue is 89.99.
| Approach | Value of waiting | Break-even discount |
|---|---|---|
| Naive: today's net asset value in a year, income on 100 | 94.68 | 5.32% |
| Correct: the reported value at payment, income on spot | 89.99 | 10.01% |
Any secondary bid above 89.99, a discount narrower than 10.01 per cent, beats the queue. The naive approach would tell the same investor to refuse a bid at a 7 or 8 per cent discount, and wait to be paid at a number that is already on its way down. The difference, 4.69 points, is the appraisal premium the queue does not deliver plus the income that is earned on spot value rather than on the reported figure.
A slower appraiser helps the redeeming investor. At α = 0.25 the queue pays 96.13 rather than 95.07, because more of the stale premium is still in the price on the dealing date, and the break-even discount falls to 9.05 per cent. That premium is paid by the investors who stay. It is the dilution a dealing-date valuation transfers, and the reason managers apply swing prices or redemption discounts when appraisals lag.
| Queue length | 8% cost | 10% cost | 12% cost |
|---|---|---|---|
| 2 quarters | 5.43 | 6.29 | 7.12 |
| 4 quarters | 8.37 | 10.01 | 11.60 |
| 8 quarters | 12.11 | 15.16 | 18.06 |
| 12 quarters | 15.09 | 19.38 | 23.38 |
Length dominates. Once the appraisal has caught up, after about a year here, each further year in the queue is pure time value net of income, and at a 10.0 per cent cost against 4.0 per cent of income that is worth several points of discount a year. A three-year queue justifies selling at 19.38 per cent below reported value.
| Appraisal above spot | Spot flat | Spot falling 4.0% a year |
|---|---|---|
| 0.0% | 5.32 | 9.05 |
| 3.0% | 7.74 | 11.36 |
| 6.0% | 10.01 | 13.53 |
| 10.0% | 12.86 | 16.25 |
Two forces stack. The appraisal gap is a fall already incurred but not yet reported; spot growth is a fall still to come. A seller who believes values have further to go should accept a wider discount, and a buyer should demand one, for the same reason.
Treating the queue as par with a delay. It is a payment at a future reported value, and the two diverge exactly when queues form, after values have fallen and before appraisals have caught up. Estimate the gap first: unsmoothing the reported series gives both the premium and the speed at which it closes. Then estimate the queue length honestly. A gate paying a fixed share of net asset value each quarter, as in how long it takes to exit a gated semi-liquid fund, rarely clears in the four quarters the first notice implies.
Price the queue as a cash flow, not as a percentage of today's net asset value. With a 6.0 per cent appraisal premium and a one-year wait, a 10.01 per cent discount is the break-even, nearly twice the naive answer. Every extra year moves it by several points. The sell-or-roll decision and the redemption queue are both modelled in the free workbook for this case, with the queue length and the appraisal gap as inputs.
Compare the bid with the present value of waiting: the reported net asset value you will be paid at, plus income, discounted at your cost of capital. In the illustrative case a one-year queue is worth 89.99 per 100, so a bid at any discount narrower than 10.01 per cent is the better exit.
Because it pays at the reported value on the dealing date. After a fall, the appraisal lags spot and keeps falling while you wait. With a 6.0 per cent premium closing at 40 per cent a quarter, a unit reported at 100 today is paid at 95.07 a year later, before any discounting.
A great deal. At a 10.0 per cent cost of capital and 4.0 per cent income, the break-even discount is 6.29 per cent for two quarters, 10.01 for four, 15.16 for eight and 19.38 for twelve, because each year in the queue costs time value net of income once the appraisal has caught up.
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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