How much does quarterly compounding add to a preferred return?

The compounding clause is worth millions on paper and nothing at all in most outcomes. The band where it bites can be computed.

Julian R. Sterling · from Private Equity Real Estate

Quarterly compounding turns an 8 per cent preferred return into an effective 8.24 per cent a year. On a $100M commitment called in three tranches, the accrued pref at year 10 is $63.08M compounded annually and $65.45M compounded quarterly: $2.37M, or 3.8 per cent, more. That difference only reaches the LP if the fund ends inside the catch-up zone, here between $163.08M and $181.82M of distributions.

Worked in full in Private Equity Real Estate by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →

The assumptions

Private Equity Real Estate states the rule: the 8 per cent pref is calculated on invested capital, compounded, accruing from the date each dollar is actually called, not from fund inception. Its example is an LP that commits $100M and is called for $30M in year 2, $40M in year 4 and $30M in year 5. The chapter adds that quarterly compounding is now more common in modern LPAs. Below, the accrual is measured at year 10 and, to isolate the convention, the fund is assumed to make one terminal distribution then. The waterfall is European, with a 100 per cent catch-up to a 20 per cent carry.

The three calls
Tranche	Called	Call year	Years accruing to year 10
First deal	$30M	2	8
Second deal	$40M	4	6
Third deal	$30M	5	5
Total	$100M

The calculation, step by step

Annual: pref = called × ((1 + 8%)^years − 1)

Quarterly: pref = called × ((1 + 8%/4)^{4 × years} − 1)

First tranche, quarterly: $30M × (1.02³² − 1) = $26.54M

Excel: =Called*((1+Rate/m)^(m*Years)-1), with m = 1, 4 or 12

Each tranche runs from its own call date. Summing the three gives the accrued pref under each convention.

Accrued 8 per cent pref at year 10, by tranche and compounding convention
Convention	$30M, 8 yrs	$40M, 6 yrs	$30M, 5 yrs	Total	Effective rate
Simple, no compounding	$19.20M	$19.20M	$12.00M	$50.40M	8.00%
Annual	$25.53M	$23.47M	$14.08M	$63.08M	8.00%
Quarterly	$26.54M	$24.34M	$14.58M	$65.45M	8.24%
Monthly	$26.77M	$24.54M	$14.70M	$66.01M	8.30%

Quarterly adds $2.37M to the annual figure, 3.76 per cent of it. Monthly adds $2.93M. The far larger term is compounding itself: annual compounding is worth $12.68M more than simple interest on the same schedule. And ignoring the call dates altogether, accruing 8 per cent on the full $100M from year 0, would give $115.89M, overstating the pref by 83.7 per cent. That is the error the time-weighted rule exists to prevent.

Where the $2.37M actually lands

A larger pref does not change total profit. It changes the hurdle the fund must clear before the GP is paid, and how far the catch-up has to run. With a 100 per cent catch-up to 20 per cent, the catch-up is complete once the GP has received pref × 20 / 80.

Hurdle = capital + pref: $163.08M annual, $165.45M quarterly

Catch-up complete = capital + pref / (1 − 20%): $178.85M annual, $181.82M quarterly

GP carry at year 10 by total distributions, under each convention
Distributions	GP, annual	GP, quarterly	Kept by the LP	GP share of profit, quarterly
$150M	$0.00M	$0.00M	$0.00M	0.0%
$164M	$0.92M	$0.00M	$0.92M	0.0%
$170M	$6.92M	$4.55M	$2.37M	6.5%
$180M	$16.00M	$14.55M	$1.45M	18.2%
$200M	$20.00M	$20.00M	$0.00M	20.0%

Below the hurdle the GP gets nothing either way. Above full catch-up, at 1.82x and beyond, the GP has 20 per cent of profit under both conventions and the compounding clause is worth nothing. Between the two, every dollar of extra pref is a dollar moved from the GP to the LP, up to the full $2.37M. The convention is a clause about mediocre outcomes: it matters most to the fund that returns around 1.65x to 1.79x.

The common mistake

The first mistake is to model the pref on committed capital, or from the first close, rather than tranche by tranche from each call date. The second is to model annual compounding when the LPA says quarterly, or the reverse, and then reconcile a waterfall that is off by millions. The third is to read the clause as a headline cost to the GP. On a fund that does well it costs nothing, because the catch-up gives it all back; on a fund that ends near the hurdle it decides whether the GP is paid at all. For how the catch-up itself is solved, see how the GP catch-up is actually solved.

Distributions made before year 10 reduce the balance on which the pref compounds, so a real fund's figures will be lower than these. The convention gap scales with the balance outstanding and the time it is outstanding.

Takeaway

Accrue the pref per tranche from its call date; never on the commitment.
Read the compounding frequency in the LPA: quarterly at 8 per cent is an effective 8.24 per cent.
Locate the band where it matters: from the hurdle to the end of the catch-up, here 1.63x to 1.82x.
Above full catch-up the convention changes nothing; below the hurdle it changes nothing either.

The three-tranche pref, both waterfalls of the chapter and the clawback between them are live in the free workbook for this book, so a different call schedule or measurement year reprices the table. The binary nature of the hurdle is worked in when the promote stops clearing.

Questions readers ask

What is the effective rate of an 8% preferred return compounded quarterly?

(1 + 0.08/4)^4 minus 1, or 8.24 per cent a year. Monthly compounding gives 8.30 per cent. On a $100M commitment called in three tranches and measured at year 10, quarterly compounding adds $2.37M to the accrued pref compared with annual.

Does the preferred return accrue on committed or called capital?

On called capital, from the date each tranche is drawn. Accruing 8 per cent on the full $100M commitment from year 0 would give $115.89M by year 10 instead of $63.08M on the actual calls, an overstatement of 83.7 per cent.

When does the pref compounding convention change the GP's carry?

Only between the hurdle and the end of the catch-up. With a 100 per cent catch-up to 20 per cent carry, that band runs from $163.08M to $181.82M of distributions in the worked case. Above it the GP receives 20 per cent of profit under either convention.

Read the whole case

The time-weighted pref is worked in the Chapters 11 and 12 waterfall workbook of Private Equity Real Estate. 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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Also on this site

How the GP catch-up is actually solvedThe catch-up is an equation, not a number: C / (pref + C) = carry rate. Worked on a $160m distribution, at three carry rates.
When the promote stops clearing: the hurdle as a binary thresholdA fund clears its catch-up by $2m. Move the winners from 1.8x to 1.7x and the promote does not shrink by a fifth. It goes to zero.
European versus American waterfall: what the clawback is really worthThe American order pays the GP early and leaves a $9M clawback, 16% of what was banked. What it is worth depends on who owes it.
Core vs value-add vs opportunistic real estate: what are the returns net of fees?Net of fees and promote, core earns 6.56%, value-add 12.02% and opportunistic 15.15%. The 12.50-point gross spread shrinks to 8.59.
How much does 70% LTV amplify real estate equity returns?At 70% LTV a value move reaches equity times 1/(1-LTV), 3.33x: a 10% rise is +33.3% on equity, a 10% fall -33.3%, and a 30% fall wipes it out.
Mezzanine vs preferred equity: which costs the sponsor more?On $15M over a three-year build, 11% mezzanine costs $5.51M and 9% pref $4.43M. If mezz cuts senior leverage, pref stays cheaper up to 11.96%.

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