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.
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.
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.
| Period | Time, yrs | Capital call | of which investment | LP distribution | Gross proceeds | Index level | |
|---|---|---|---|---|---|---|---|
| 1 | 1 | 119.30 | 105.0 | 0.0 | 0.0 | 107.0000 | |
| 2 | 2 | 110.50 | 100.0 | 0.0 | 0.0 | 114.4900 | |
| 3 | 3 | 110.50 | 100.0 | 0.0 | 0.0 | 122.5043 | |
| 4 | 4 | 90.50 | 80.0 | 0.0 | 0.0 | 131.0796 | |
| 5 | 5 | 50.50 | 40.0 | 110.0 | 110.0 | 140.2552 | |
| 6 | 6 | 6.20 | 0.0 | 30.0 | 30.0 | 150.0730 | |
| 7 | 7 | 5.30 | 0.0 | 310.0 | 310.0 | 160.5781 | |
| 8 | 8 | 3.80 | 0.0 | 197.144 | 225.0 | 171.8186 | |
| 9 | 9 | 2.30 | 0.0 | 136.636 | 180.0 | 183.8459 | |
| 10 | 10 | 1.10 | 0.0 | 64.22 | 80.0 | 196.7151 |
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.
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.
| Parameter | Meaning | Default |
|---|---|---|
calls | LP capital calls by period, earliest first, comma separated | the reference schedule |
dists | LP distributions by period, net of carry, aligned to calls | the reference schedule |
nav | Terminal net asset value at the final period | 0 |
index | Either a comma-separated series of index levels starting at period zero, or a single decimal fraction treated as a constant annual total return | 0.07 |
facility | Length of the capital call facility in months. 0 for none | 0 |
facilityRate | All-in cost of the facility as a decimal annual rate | 0.06 |
facilityScope | all or investment | all |
invest | Optional. Investment portion of each call, used by facilityScope=investment | the reference schedule |
gross | Optional. Gross realisation proceeds by period, used to re-run the waterfall when the facility changes paid-in capital | the reference schedule |
hurdle, carry, catchup | Optional. Waterfall terms for that re-run | 0.08, 0.2, 1 |
times | Optional. Time in years for each period, if not annual year ends | 1,2,3,... |
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.
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.