A private equity fund called Rs 30, 30 and 25 crore in years 0 to 2, distributed Rs 40, 60 and 70 crore in years 4 to 6, and holds Rs 20 crore of NAV at year 6. Compute TVPI, DPI, IRR and a public market equivalent, and judge the fund.

A strong fund on every measure: TVPI 2.24x, DPI 2.00x, IRR about 20.5% and a public market equivalent of 1.53. Investors paid in Rs 85 crore and have Rs 170 crore back in cash plus Rs 20 crore of NAV. Most of the value is already realised, so the result does not rest on the manager's own marks, and it returned about 1.53 times what the same cash flows would have earned in the index.

Always divide by money actually paid in, Rs 85 crore, not the Rs 100 crore committed. TVPITotal value to paid-in: distributions plus remaining NAV, divided by capital called. is (170 + 20) / 85, 2.24 times; DPIDistributions to paid-in: cash returned divided by capital called. The realised part of TVPI. is 170 / 85, 2.00 times; the residual, NAV over paid-in, is only 0.24 times. That last number matters: a fund whose value is mostly cash in hand has proved its result, while one whose value is mostly NAV is still asking you to trust its marks.

The multiples ignore time; the IRR does not. Solving for the rate that sets the net cash flows, minus 30, minus 30, minus 25, zero, plus 40, plus 60 and plus 90 including NAV, to zero gives an IRR of about 20.5% a year. The cash pattern draws the familiar J-curveThe shape of cumulative cash flows in a private fund: negative in the early years as capital is called and fees paid, rising as investments are sold.: investors are Rs 85 crore down by year 2 and do not break even until year 5. It is like planting a mango orchard: years of spending before the first harvest.

A plain comparison of the fund's IRR with the index's return is unfair, because the fund's money went in and out on its own dates. The public market equivalentA comparison that invests and withdraws the fund cash flows in a public index on the same dates, so timing is matched. fixes that. Kaplan and Schoar's version, published in 2005, divides every call and every distribution by the index level on its date, and compares the totals. Distributions plus final NAV, index-adjusted, are 1.53 times the index-adjusted calls: investors got 53% more than the same timing in the index would have given. The index itself rose from 100 to 165, about 8.7% a year.

Yes, and for three reasons that support each other. The money multiple is high, most of it is already cash, and it beat the index with timing matched. Say the limits: one fund is a small sample, the comparison should also be made against funds of the same vintage year, which a database would provide, and the Rs 15 crore never called was committed capital that investors had to keep ready, earning little, which the IRR does not see.