Rebuilding the sensitivity the Level 3 note leaves out, from fair value, ownership, multiple and net debt, and why leverage doubles it.
One turn of EV/EBITDA moves each holding by the fund's share of that company's EBITDA, and because the companies carry debt, the equity moves about twice as much as the multiple. On an illustrative buyout fund with 300.0 of net assets and portfolio companies at a weighted 11.1x, one turn is worth 55.8, or 18.6 per cent of NAV, not the 9.3 per cent that dividing by the average multiple suggests.
Worked in full in How to Read a Private Fund's Financial Statements by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The Level 3 note in a private fund's financial statements tells you the valuation technique, the multiples used, their range and a weighted average. It rarely tells you what happens to the NAV if those multiples are wrong by one turn, which is the question every investor asks when public comparables reprice. The answer can be rebuilt from three columns.
| Company | Fund ownership | Fair value to fund | EV/EBITDA used | Net debt (100%) |
|---|---|---|---|---|
| Alder | 80% | 96.0 | 11.0x | 130.0 |
| Birch | 60% | 54.0 | 9.0x | 90.0 |
| Cedar | 100% | 70.0 | 12.5x | 55.0 |
| Dunmore | 50% | 40.0 | 8.0x | 80.0 |
| Elm | 70% | 50.0 | 14.0x | 40.0 |
| Investments | 310.0 | 11.09x |
Fair value and, often, ownership come from the schedule of investments; the multiples from the Level 3 note or the valuation report; net debt from the quarterly portfolio company reports, which most investors receive even when the audited statements do not repeat it. Other net liabilities of 10.0 bring net assets to 300.0. The Level 3 note would show a range of 8.0x to 14.0x and a fair-value-weighted average of 11.09x.
Step 1: gross up each holding to 100 per cent equity. Divide the fund's fair value by its ownership. Alder: 96.0 ÷ 0.80 = 120.0.
Step 2: add net debt to get enterprise value, then back out EBITDA. Alder: 120.0 + 130.0 = 250.0 of EV, and 250.0 ÷ 11.0 = 22.73 of EBITDA.
Step 3: one turn is one year of EBITDA, times the fund's share. Alder: 22.73 × 0.80 = 18.18, which is 18.9 per cent of its 96.0 fair value.
ΔFair value per turn = ownership × (fair value ÷ ownership + net debt) ÷ multiple
As a share of equity: 1 ÷ (multiple × equity ÷ EV)
In Excel, with ownership in B, fair value in C, multiple in D and net debt in E: =B2*(C2/B2+E2)/D2 for each row, then =SUM(F2:F6)/NAV.
| Company | EV (100%) | EBITDA | Net debt / EV | One turn to fund | % of its fair value | Naive 1 ÷ multiple |
|---|---|---|---|---|---|---|
| Alder | 250.0 | 22.7 | 52% | 18.2 | 18.9% | 9.1% |
| Birch | 180.0 | 20.0 | 50% | 12.0 | 22.2% | 11.1% |
| Cedar | 125.0 | 10.0 | 44% | 10.0 | 14.3% | 8.0% |
| Dunmore | 160.0 | 20.0 | 50% | 10.0 | 25.0% | 12.5% |
| Elm | 111.4 | 8.0 | 36% | 5.6 | 11.1% | 7.1% |
| Fund | 55.8 | 18.0% |
One turn across the portfolio moves the investments by 55.8, 18.0 per cent of their fair value and 18.6 per cent of NAV. The naive reading of the Level 3 note, 310.0 ÷ 11.09 = 28.0, or 9.3 per cent of NAV, understates it by a factor of 1.99.
The factor is leverage. On a look-through basis the fund owns 591.0 of enterprise value financed with 281.0 of net debt, 47.5 per cent, so equity is 0.525 of EV. One turn at a look-through 10.60x is 9.4 per cent of EV and 1 ÷ (10.60 × 0.525) = 18.0 per cent of equity. The most levered holdings move most: Dunmore, at 8.0x, the cheapest multiple in the book, loses 25.0 per cent of its value per turn because half its EV is debt.
| Scenario | Change | NAV | % of NAV |
|---|---|---|---|
| Multiples +1 turn | +55.8 | 355.8 | +18.6% |
| Multiples −1 turn | −55.8 | 244.2 | −18.6% |
| Multiples −2 turns | −111.5 | 188.5 | −37.2% |
| EBITDA −10%, multiples unchanged | −59.1 | 240.9 | −19.7% |
| EBITDA −10% and −1 turn | −109.3 | 190.7 | −36.4% |
A 10 per cent fall in earnings costs more than a turn of multiple here, because a 10 per cent EBITDA fall is 1.1 turns at the average multiple. Two turns down would halve Dunmore's equity, from 40.0 to 20.0 for the fund, and the losses are not linear beyond that: equity cannot fall below zero, so the most levered names stop contributing once they are wiped out.
These are gross figures, before the general partner's carried interest. If the fund carries an accrued carry liability, a fall in the portfolio first reduces that accrual, so the limited partners' share of NAV moves by less than 18.6 per cent until the accrual is exhausted.
Dividing by the weighted average multiple in the Level 3 note and calling the result the sensitivity. That treats the fair value as enterprise value. The multiple applies to EV; the fund owns equity, which is EV minus debt. The thinner the equity, the larger the move, and the weighted average multiple says nothing about how thin it is. Ask for net debt by company, or read it from the portfolio reports, before reading any sensitivity.
Gross up each holding, add its net debt, back out EBITDA and multiply by ownership. On this fund one turn is 55.8, 18.6 per cent of NAV, almost double the 9.3 per cent the averages suggest. The roll-forward that shows how marks moved in the year is in how to read a Level 3 fair value roll-forward, and the full reporting pack with its reconciliations is in the free workbooks for this book.
Because the multiple applies to enterprise value and the fund owns equity, which is EV less net debt. The change in equity per turn is 1 / (multiple x equity / EV). At a look-through 10.60x with equity at 0.525 of EV, that is 18.0 per cent of the equity, against 9.4 per cent of the EV.
The most levered, not the most expensive. In the illustrative fund, Dunmore at 8.0x, the lowest multiple, loses 25.0 per cent of its fair value per turn because net debt is half its EV. Elm at 14.0x, the highest, loses 11.1 per cent, because its net debt is only 36 per cent of EV.
Yes. When the fund carries an accrued carry liability, a fall in portfolio value first reduces the accrual, so the limited partners' share of NAV falls by less than the gross 18.6 per cent until the accrual is used up. On the way up, the accrual takes part of every gain once the hurdle is cleared.
This article is one calculation from How to Read a Private Fund's Financial Statements. 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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