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Private equity funds - economics, the waterfall, and the arithmetic of performance

PME and the subscription-line effect

The same LP cash flows measured four ways against a public index, and then restated as though a capital call facility of a stated length had bridged the drawdowns. The point of the second half is short: deferring a capital call does not change what the fund earned, and it moves the reported IRR anyway. Every input is encoded in the URL. All arithmetic runs in the browser; the page makes no network request.

Facility and index assumptions

Every rate above is an input you set, labelled as an assumption. Nothing on this page is a market-terms survey, a measured index return, or a benchmark for anything. The waterfall terms are used only to re-run the distribution split when the facility changes contributed capital.

Cash-flow schedule

Time is years from the first closing and is used directly in every IRR. Investment portion is the part of the call that buys an asset, which is what a facility bridges; the remainder is fees and expenses. Gross proceeds are before carry and are used to re-run the waterfall when the facility changes paid-in capital. LP distribution is net of carry and is what the PME methods use.

PeriodTime, yrsCapital callof which investmentLP distributionGross proceedsIndex level
11119.30105.00.00.0107.0000
22110.50100.00.00.0114.4900
33110.50100.00.00.0122.5043
4490.5080.00.00.0131.0796
5550.5040.0110.0110.0140.2552
666.200.030.030.0150.0730
775.300.0310.0310.0160.5781
883.800.0197.144225.0171.8186
992.300.0136.636180.0183.8459
10101.100.064.2280.0196.7151

IRR with and without the facility

The two IRR paths

Each curve is the net present value of the LP's own cash flows at every discount rate. The IRR is where a curve crosses zero. The facility moves the crossing without moving the money the fund made.

Cumulative capital called

The calls the facility moves

Public market equivalent

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The formulas

Notation. PIC is paid-in or contributed capital, D cumulative distributions to LPs, NAVT the terminal net asset value, It the level of the public index at time t, T the terminal date and lambda the PME+ scaling factor. A flow is restated into terminal-date money by multiplying it by I_T / I_t.

Kaplan-Schoar, KS-PME. A wealth ratio, not a rate: KS-PME = (FV(distributions) + NAV_T) / FV(contributions) where each flow is future-valued at the index to T. Above 1.00 the fund produced more terminal wealth than the index would have on the same cash-flow timing. It answers how much, never at what rate.

Long-Nickels, LN-PME. The rate the index would have returned on this cash-flow schedule. Take the fund's own contributions and distributions and replace the terminal value with the index portfolio's residual, PME NAV = FV(contributions) - FV(distributions), then solve for the IRR. When distributions future-valued at the index exceed contributions future-valued at the index, that residual is negative - a short position in the index - and the resulting rate is unstable or undefined. That is the method's known weakness and this page flags it rather than hiding it.

PME+. The same idea with distributions scaled by a single factor so the index portfolio ends at exactly the fund's own NAV: lambda = (FV(contributions) - NAV_T) / FV(distributions), then the IRR of the contributions against lambda-scaled distributions plus NAVT at T. It cannot produce a negative index NAV, which is why it exists.

Direct Alpha. The annualised excess return itself rather than a spread between two rates. Restate every fund cash flow into terminal-date money at the index, then take the IRR of the restated vector on its original dates. For a constant index return i the result combines exactly: (1 + i) * (1 + Direct Alpha) - 1 = fund net IRR. That identity is shown on the page as a check.

The subscription facility. A capital call facility borrows against LP commitments so the manager can fund an investment now and call the capital later. A call of amount A due at time t becomes a call of A * (1 + r)^(m/12) at time t + m/12, where m is the facility length in months and r its all-in rate. Three things then follow, and they do not point the same way.

First, paid-in capital rises by the facility interest, because the interest is a fund expense drawn from the LPs. Second, gross proceeds do not change at all - the assets earned what they earned - so gross MOIC is identical before and after. Third, because return of capital is larger, fund profit is smaller, so carried interest falls and LP distributions rise by the carry on the interest. Net DPI and TVPI therefore fall, since the denominator grows faster than the numerator. And the IRR rises, because every call has been pushed later while every distribution has stayed where it was.

A higher IRR alongside an unchanged gross multiple and a lower net multiple is the whole of the effect. It is arithmetic, not performance. Any comparison of IRRs between funds is a comparison of facility usage as much as of investing, unless the facility is disclosed and adjusted for.

IRR. The IRR is the rate r solving 0 = sum over flows of amount / (1 + r)^t with t in years, solved numerically by bisection over r on the actual dated cash-flow vector - not from a multiple. Where the vector changes sign more than once the equation can have several solutions and the page says so; where it never changes sign there is none, and the page says that too.

URL parameters

ParameterMeaningDefault
callsLP capital calls by period, earliest first, comma separatedthe reference schedule
distsLP distributions by period, net of carry, aligned to callsthe reference schedule
navTerminal net asset value at the final period0
indexEither a comma-separated series of index levels starting at period zero, or a single decimal fraction treated as a constant annual total return0.07
facilityLength of the capital call facility in months. 0 for none0
facilityRateAll-in cost of the facility as a decimal annual rate0.06
facilityScopeall or investmentall
investOptional. Investment portion of each call, used by facilityScope=investmentthe reference schedule
grossOptional. Gross realisation proceeds by period, used to re-run the waterfall when the facility changes paid-in capitalthe reference schedule
hurdle, carry, catchupOptional. Waterfall terms for that re-run0.08, 0.2, 1
timesOptional. Time in years for each period, if not annual year ends1,2,3,...

A constant 7 percent index:
https://pe-finance.wiki/calc/pme/?calls=119.3,110.5,110.5,90.5,50.5,6.2,5.3,3.8,2.3,1.1&dists=0,0,0,0,110,30,310,197.144,136.636,64.22&index=0.07

The same fund with a 12-month facility bridging the investment drawdowns:
https://pe-finance.wiki/calc/pme/?calls=119.3,110.5,110.5,90.5,50.5,6.2,5.3,3.8,2.3,1.1&dists=0,0,0,0,110,30,310,197.144,136.636,64.22&index=0.07&facility=12&facilityRate=0.06&facilityScope=investment

The simplest check that the index restatement is right - 100 called at period 1, 130 returned at period 2:
https://pe-finance.wiki/calc/pme/?calls=100,0&dists=0,130&nav=0&index=0.07
KS-PME is (130 / 1.07^2) / (100 / 1.07) = 1.2150 and Direct Alpha is 130 / 107 - 1 = 21.4953 percent.

What this model leaves out

On the PME side it ignores dividend treatment and index total-return construction, currency, the choice of index and its survivorship, cash-flow timing inside a period, and the fact that a public index has daily liquidity while a fund does not. On the facility side it ignores commitment and unused-line fees, upfront and arrangement costs, borrowing-base limits and advance rates, the LPA's cap on facility length and size, clean-down provisions, the possibility that the facility funds distributions rather than investments, and any effect on the fund's own return other than the interest cost. It also assumes the facility interest is borne by the fund and therefore by the LPs.

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Reference information only. Not legal, tax, or investment advice. Fund documents vary materially between managers, vehicles and jurisdictions; the structures described here are common patterns rather than the terms of any particular fund, and every figure is derived from a single illustrative reference fund whose inputs are stated. Consult counsel.

Reviewed 2026-08-27. Text and data under CC BY 4.0. See also the distribution waterfall calculator.