A discount to NAV is earned once and spread over the hold, so duration, not the headline percentage, decides the return.
Because a discount to NAV is a one-off gain, and an IRR spreads it over the years until the cash comes back. A 12 per cent discount on a portfolio growing 8 per cent a year gives 22.7 per cent if the NAV is realised in one year and 10.8 per cent if it takes five. To hold a 15 per cent IRR, the discount has to widen from 6.1 points at one year to 26.9 points at five.
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 →
Secondary prices are quoted as a percentage of NAV, which invites comparison across deals as if the percentage were the return. It is not. Two interests bought at the same 88 can produce returns that differ by more than ten points, depending only on how long the fund takes to sell its companies. Duration is the input that converts a discount into a rate, and it is the one the seller's pricing deck says least about.
| Input | Value |
|---|---|
| Reported NAV | 100 |
| Price paid (a 12 per cent discount) | 88 |
| Annual growth in the underlying NAV | 8% |
| Buyer's target IRR | 15% |
If the NAV grows at g and is realised in full after t years, the cash returned is NAV × (1 + g)t and the IRR has a closed form.
IRR = (1 + g) × (NAV ÷ price)1/t − 1
At three years: 1.08 × (100 ÷ 88)1/3 − 1 = 12.7%. In Excel: =(1+B4)*(B2/B3)^(1/B5)-1.
The formula separates the two engines. The growth term is earned every year. The discount term, 100 ÷ 88 or 1.136x, is earned once and divided by the years.
Invert the formula. For a target IRR of r, the price that delivers it is the future value discounted back at r:
Price for target = NAV × ((1 + g) ÷ (1 + r))t
At five years: 100 × (1.08 ÷ 1.15)5 = 73.1, a discount of 26.9 per cent. In Excel: =B2*((1+B4)/(1+B6))^B5.
| Years to realisation | Cash returned | Multiple | IRR at 88 | Discount alone, IRR | Price for 15% | Discount needed |
|---|---|---|---|---|---|---|
| 1 | 108.0 | 1.23x | 22.7% | 13.64% | 93.9 | 6.1% |
| 2 | 116.6 | 1.33x | 15.1% | 6.60% | 88.2 | 11.8% |
| 3 | 126.0 | 1.43x | 12.7% | 4.35% | 82.8 | 17.2% |
| 4 | 136.0 | 1.55x | 11.5% | 3.25% | 77.8 | 22.2% |
| 5 | 146.9 | 1.67x | 10.8% | 2.59% | 73.1 | 26.9% |
| 6 | 158.7 | 1.80x | 10.3% | 2.15% | 68.6 | 31.4% |
Three things stand out. The multiple rises with duration while the IRR falls, so a buyer screening on multiple prefers exactly the deals a buyer screening on IRR should avoid. The discount alone, with no growth at all, is worth 13.64 per cent over one year and 2.59 per cent a year over five. And each extra year of duration costs roughly five to six points of discount at this target: the gap between 8 per cent growth and a 15 per cent target has to be bought, year after year, at the entry price.
The break-even holding period: at 88 the deal clears 15 per cent only if the NAV comes back within two years (15.1 per cent). A buyer that underwrites two years and gets three earns 12.7 per cent. The price did not change; the deal did.
A fund sells companies over several years. Spread the same portfolio over five annual distributions, each a share of the NAV still held and still growing at 8 per cent, and the cash comes back as 21.6, 23.3, 25.2, 27.2 and 29.4, a total of 126.7 and a 1.44x multiple. The IRR at 88 is 12.8 per cent, and the price for 15 per cent is 83.2, a 16.8 per cent discount.
The weighted average life of that profile is 3.15 years, and the answers sit almost exactly on the three-year row of the table (12.7 per cent and 17.2 points). That is the practical shortcut: compute the weighted average life of the projected distributions, read the IRR and the required discount off the bullet formula at that life, then confirm with a full IRR on the cash flows.
The common mistake is comparing discounts across deals without comparing durations. A 12 per cent discount on a fund with two years of life left and a 20 per cent discount on a fund with five years left look like a cheap deal and a cheaper one. At 8 per cent growth, the first returns 15.1 per cent and the second needs 26.9 points of discount just to reach the same 15. The deeper discount is the worse price. The same error runs the other way when the exits slip: a deal priced on a three-year life that takes five has lost the equivalent of nearly ten points of entry discount (17.2 against 26.9) without anyone renegotiating anything.
Never state a secondary discount without its duration. Convert the projected distributions into a weighted average life, and price the discount per year of that life rather than per deal. The deal model in the free workbooks for this book carries the duration table and the stress on delay. To see how much of a projected IRR is the discount and how much is the portfolio, read how much of a secondary return comes from the discount.
It depends on duration and NAV growth. With growth of 8 per cent a year, the price is NAV times (1.08 / 1.15) to the power of the years: 93.9 for one year, 82.8 for three, 73.1 for five. That is a 6.1, 17.2 or 26.9 per cent discount for the same target return.
Because NAV keeps growing while the one-off discount is spread over more years. At a price of 88, the multiple climbs from 1.23x at one year to 1.67x at five, while the IRR falls from 22.7 to 10.8 per cent. Screening on multiple favours exactly the long-dated deals an IRR target penalises.
Compute the weighted average life of the projected distributions and use the bullet formula at that life. A five-year spread with a weighted average life of 3.15 years gives 12.8 per cent at 88, against 12.7 per cent for a three-year bullet. Confirm with a full IRR.
Chapter 8 of The Private Equity Secondaries Investor sets out the duration table this calculation extends. 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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