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How do you calculate the discount on a portfolio of LP interests?

A portfolio sale is priced line by line and quoted as one number. Only the NAV-weighted discount says what fraction of reported value is paid.

Julian R. Sterling · from The Real Estate Secondaries Investor

The discount on a portfolio of LP interests is one minus total price over total NAV, which weights each fund by its NAV. On an illustrative €100.0 million portfolio of five real estate fund interests bought for €78.05 million, the portfolio discount is 21.95 per cent, not the 27.00 per cent simple average of the five line discounts. Strip out the smallest, deepest-discounted line and the remaining four trade at 19.95 per cent.

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 →

Portfolio sales are priced line by line and quoted as one number. That number gets compared with market surveys, with the seller's reserve and with the next deal, so how it is computed matters. There are at least four ways to express the same price, and only one of them answers the question "what fraction of NAV am I paying".

The assumptions

Five interests sold as one lot, reference-date NAVs, € million. All figures illustrative.

Fund	NAV	Line discount	Price	Unfunded
Core-plus fund, Germany	40.0	15%	34.00	5.0
Logistics value-add	25.0	20%	20.00	2.0
Office core, Paris	15.0	25%	11.25	0.0
Residential development	12.0	30%	8.40	6.0
Retail fund in extension	8.0	45%	4.40	1.0
Portfolio	100.0		78.05	14.0

The calculation, step by step

Each line is priced first, on its own adjusted value: 85 per cent of NAV for the core-plus fund, 55 per cent for the retail fund in extension. The prices add to €78.05 million against €100.0 million of NAV. The buyer is paying 78.05 per cent of reported value, so the discount is 21.95 per cent.

The simple average of 15, 20, 25, 30 and 45 per cent is 27.00 per cent. It gives the €8.0 million retail line the same weight as the €40.0 million core-plus line, so it overstates the discount by 5.05 points. It is the figure most likely to end up in an investment memo because it is the one a spreadsheet produces when someone averages a column.

The same price, four ways.

Measure	Discount	What it answers
NAV-weighted (total price over total NAV)	21.95%	What fraction of reported value is paid
Simple average of line discounts	27.00%	Nothing; ignores size
Price-weighted average	21.03%	Understates: weights cheap lines less
On exposure (price plus unfunded over NAV plus unfunded)	19.25%	Discount on total capital at risk

The result: what the tail does to the number

The retail fund in extension is 8 per cent of NAV but €3.60 million of the €21.95 million discount in euros, 16.4 per cent of it. Remove it and the remaining four lines cost €73.65 million for €92.0 million of NAV, a discount of 19.95 per cent. The tail adds 2.00 points to the headline on its own.

That matters in two directions. A seller who insists on selling the whole lot is reporting a 21.95 per cent discount when the quality part of the book went at 19.95. A buyer reporting its entry discount to its own investors should say which number it is quoting, because a tail line priced near zero inflates the headline without creating any value: the buyer paid little because it expects to receive little.

The discount on exposure, 19.25 per cent, includes the €14.0 million of unfunded commitments, which the buyer will fund at par. It is the right base for sizing what the buyer has at risk, and the wrong one for comparing with a market survey quoted on NAV. How the unfunded changes the economics of a single interest is worked in what an 18 per cent discount to NAV actually buys.

What if the tail line is priced differently?

Portfolio price and discount as the retail line's discount moves, other lines unchanged, € million.

Retail line discount	Portfolio price	Portfolio discount
35%	78.85	21.15%
45%	78.05	21.95%
55%	77.25	22.75%
100% (nil price)	73.65	26.35%

Each 10 points on the tail moves the portfolio by 0.80 points; one point on the core-plus line moves it by 0.40, five times as much as one point on the tail at 0.08. Negotiating time is best spent on the large lines, which is where most of the euros of discount sit.

The common mistake

The common mistake is averaging line discounts. The second is mixing NAV dates: if the core-plus fund's NAV is a quarter older than the others, its line discount is measured against a stale base, and the portfolio discount inherits the error in proportion to its 40 per cent weight. Roll every NAV to the same reference date before adding them up, and deduct debt and deferred tax consistently, as in the GAV to NAV calculation.

A useful check: the NAV-weighted discount must equal the sum of each line's weight times its discount. Here 40 per cent at 15, 25 per cent at 20, 15 per cent at 25, 12 per cent at 30 and 8 per cent at 45 give 21.95 per cent, the same figure as 1 − 78.05 ÷ 100.0. If the two routes disagree, a NAV or a price has been typed in twice or at a different date.

Takeaway

Portfolio discount = 1 − total price ÷ total NAV: 21.95 per cent here, against a 27.00 per cent simple average and 19.95 per cent without the tail line. Quote the NAV-weighted figure, show the ex-tail figure beside it, and state the unfunded separately. The free workbook for this case prices a five-line portfolio on each line's adjusted value and finds the weakest line itself.

Questions readers ask

Should you average line discounts to get a portfolio discount?

No. A simple average gives a small line the same weight as a large one. On five interests with €100.0 million of NAV, line discounts of 15 to 45 per cent average 27.00 per cent, but the buyer pays €78.05 million, a NAV-weighted discount of 21.95 per cent. Weight by NAV, or divide total price by total NAV.

How much does a tail-end fund change a secondary portfolio discount?

In proportion to its NAV weight times its excess discount. A retail fund in extension at 8 per cent of NAV and a 45 per cent discount adds 2.00 points: the other four lines trade at 19.95 per cent and the whole lot at 21.95. Priced at nil, the same line takes the headline to 26.35 per cent.

Should unfunded commitments be included in a secondary discount?

Quote it both ways, clearly labelled. The buyer funds the unfunded at par, so adding €14.0 million to both price and NAV dilutes the discount from 21.95 to 19.25 per cent. The exposure figure sizes capital at risk; the NAV figure is the one market surveys and sellers compare.

Also on this site

• What does an 18 per cent discount to net asset value actually buy?An 18 per cent discount to a real estate fund's reported net asset value is worth 9.18 per cent once the appraisal, unfunded and fees are corrected.
• How do you get from GAV to NAV in a real estate fund?Deduct debt, liabilities and deferred tax from gross assets: €525.0m becomes a €261.0m NAV, so at 50% LTV each 1% move in GAV moves NAV 1.92%.
• Why do tail-end secondaries trade at deeper discounts?Fund costs do not shrink with NAV. On 40 of NAV, fees, 0.60 of fixed expenses and carry take 6.6 points: a 15% buyer pays 78.6% of NAV, not 85.1.
• How much cap rate expansion does a secondary discount absorb?Less than it looks once the fund is geared. A 15% discount to NAV at 48% LTV absorbs a 40.5 bp rise in valuation yields, not the 88 bp an unlevered view suggests.
• How do you unsmooth appraisal-based real estate returns?Subtract (1 minus alpha) times last quarter's reported return and divide by alpha. At alpha 0.40, volatility rises from 2.46 to 3.83 per cent.
• What is a real estate fund interest worth in wind-down?Discount the disposal plan, not the NAV: a 19.20m interest in a geared fund selling three assets over three years is worth 13.99m at 13%, 72.9% of NAV.

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