Articles

How is the weighted average multiple in a Level 3 table calculated?

The fair value note's weighted average weights by equity, so sales and leverage move it as much as marks do.

Julian R. Sterling · from How to Read a Private Fund's Financial Statements

In most private fund accounts the weighted average in the Level 3 inputs table is weighted by each investment's fair value: Σ (fair value × multiple) ÷ Σ fair value. On an illustrative five-company portfolio worth 252.0 that gives 10.59x, against a simple average of 9.50x and an aggregate multiple of 9.51x. Because the weights are equity values, the figure moves with sales and leverage as much as with marks: selling one company at its carrying value takes it to 8.98x with no mark changed.

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 quantitative table in the fair value note lists, for each valuation technique, the unobservable input, its range and usually a weighted average. Readers treat the weighted average as the fund's valuation multiple and compare it year on year. It is a useful number once you know what it weights, and a misleading one if you do not.

The portfolio

Five illustrative Level 3 investments valued on EV/EBITDA comparables. Millions.

Company	EBITDA	Multiple	EV	Net debt	Equity	Fund stake	Fair value
Alder	20.0	13.5x	270.0	120.0	150.0	60%	90.0
Birch	15.0	10.0x	150.0	60.0	90.0	70%	63.0
Cedar	25.0	8.0x	200.0	130.0	70.0	50%	35.0
Damson	10.0	9.0x	90.0	30.0	60.0	80%	48.0
Elm	30.0	7.0x	210.0	170.0	40.0	40%	16.0
Fund							252.0

The note would print: market comparables, EV/EBITDA multiple, range 7.0x to 13.5x, weighted average 10.59x. Everything else in the table above is what the note does not show.

The calculation, step by step

The aggregate is the multiple at which the fund is effectively paying for its share of the portfolio's EBITDA. It is more than a turn below the reported 10.59x, because Alder, the most expensive company, also has the largest equity value and carries 35.7 per cent of the fair value. Elm, the cheapest and most indebted, carries 6.3 per cent although it has the largest EBITDA. A high multiple on the same debt leaves more equity, so weighting by fair value leans towards the expensive companies.

The result: what moves the number

Four events and what each does to NAV and to the reported weighted average.

Event	Fair value after	Weighted average	Change
Opening	252.0	10.59x	0.00
Alder sold at its carrying value	162.0	8.98x	−1.62
Alder marked down one turn	240.0	10.12x	−0.47
Elm marked down one turn	240.0	10.75x	+0.16
Every company down half a turn	224.5	10.22x	−0.37

Three readings follow.

• A sale looks like a markdown. Selling Alder at 90.0, exactly its mark, cuts the weighted average by 1.62 turns. A reader comparing years sees an aggressive write-down where there was none.
• A markdown can raise the average. Taking one turn off Elm costs 12.0 of fair value, 75.0 per cent of the position, because Elm's equity is thin. The same cut shrinks Elm's weight, so the average rises to 10.75x. Taking one turn off Alder costs the same 12.0, 13.3 per cent of that position, and moves the average down by 0.47.
• A real, broad markdown understates itself. Half a turn off every company cuts NAV by 10.9 per cent, but the average falls by only 0.37 because the weights move with the marks. At opening weights the like-for-like fall is the full 0.50.

The like-for-like test. Reweight this year's multiples by last year's fair values, over the companies held at both dates. If that figure is unchanged and the reported one fell, the move came from the composition of the portfolio, not from the marks. With Alder sold and nothing remarked, the like-for-like average of the four remaining companies is 8.98x at both dates.

What to ask for

The note gives one range and one average, and the range is set by its two extremes. To use the figure, ask the manager for three things: the basis of the weighting, in words; the weighted average recomputed on last year's holdings; and EBITDA and net debt by company, which turn a multiple into an equity sensitivity. The last is what the NAV sensitivity to one turn of EBITDA multiple needs, and the movements in the same Level 3 balance are read in the Level 3 roll-forward.

The common mistake

Reading a lower weighted average multiple as more conservative valuation. In this portfolio the figure fell by 1.62 turns with no company remarked, and rose by 0.16 when a company was written down by three quarters. The weighted average describes the mix of what the fund holds at the reporting date, weighted by equity; it is not an index of how hard the marks were pushed.

Takeaway

Recompute the weighted average yourself from the schedule of investments, weighting by fair value, and set it beside the simple average and a like-for-like figure before drawing any conclusion. A reporting pack with every note tied to the statements is in the free workbooks for How to Read a Private Fund's Financial Statements.

Questions readers ask

What does the weighted average in a Level 3 unobservable inputs table mean?

It is the average of the input, here the EV/EBITDA multiple, across the investments valued with that technique, usually weighted by each investment's fair value. In the illustrative fund it is 2,669.0 divided by 252.0, or 10.59x. Because fair value is equity value, highly levered companies get little weight even when they are large businesses.

Why did a fund's weighted average multiple fall if nothing was written down?

Because the weights changed. Selling the highest-multiple company at exactly its carrying value removes 35.7 per cent of the weight at 13.5x, and the average falls from 10.59x to 8.98x. Reweighting the remaining multiples at last year's fair values shows the same 8.98x, which confirms the move is composition, not valuation.

Can a markdown increase the weighted average multiple?

Yes. Cutting one turn off a thinly capitalised company destroys most of its equity and so most of its weight. In the example, Elm loses 12.0 of fair value, 75.0 per cent of the position, and the weighted average rises from 10.59x to 10.75x even though NAV fell by 4.8 per cent.

Also on this site

• How much does one turn of EBITDA multiple move a PE fund's NAV?Ownership times each company's EBITDA, summed. At a weighted 11.1x, one turn moves an illustrative fund's NAV by 18.6%, not the 9.3% the average multiple suggests.
• How do you read a Level 3 fair value roll-forward?Split the unrealised line: minus 31,600 is 22,700 of reversal on exits and 8,900 of markdown on what is still held, minus 2.47 per cent.
• What is a fund's multiple without its largest investment?Take the largest position out of the schedule of investments and recompute. A portfolio at 1.37x falls to 0.96x: one holding carries 110.1 per cent of the gain.
• How does a blocker's deferred tax liability change a fund's NAV?It is the tax rate times the built-in gain, so it moves with value: on a 180.0 asset with a 24.0 liability, a 10% fall costs the fund 13.5, not 18.0.
• How is a fund's income allocated between the GP and the LPs?By capital before carry, then carry to the LPs alone: on a 13,600 result a 2% GP gets 272, LPs 10,478 after 2,850 of carry, and the GP's share drifts to 2.02%.
• How much of a private credit fund's income is PIK?PIK from the cash flow statement over total income: 14,400 of 96,000 is 15.00%, and NII coverage of 110.38% falls to 72.69% in cash.

Reading guide: private equity and private markets → · All 1614 articles →

If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.