A fund's cash flows are dated, irregular, and multi-directional, calls out, distributions in, at whatever dates the GP and the market dictate. The right tool is the Internal Rate of Return (IRR) you built in M3.01, generalized to irregular dates: XIRR, the rate r that sets the net present value of every dated cash flow to zero, discounting each flow by the exact year-fraction from the first cash flow's date (NPV(r) = Σ CFᵢ / (1+r)^tᵢ, tᵢ in years, Actual/365). This is a dollar-weighted return: it is sensitive to the size and timing of every cash flow, which is exactly right for a vehicle where the GP, not the LP: decides when capital moves. Contrast this with the time-weighted return you compute for a liquid public portfolio in AA1.03, a measure deliberately insensitive to cash-flow timing, because a public-market client, not the manager, usually controls when money moves in and out. The two answer genuinely different questions and are not interchangeable: IRR tells you what the GP actually delivered on capital under the GP's own timing control; a time-weighted return would credit or blame the GP for timing decisions that, in a fund structure, are the GP's own calls to make.
There is no closed-form solution for IRR on an arbitrary schedule; it is solved by iteration, narrowing a bracket until the NPV crosses zero. That is exactly the "hand XIRR" this branch's law (R3) requires you to be able to reproduce: pick two rates that give NPV of opposite sign, take the midpoint, recompute NPV, and keep halving the bracket (bisection) until it is tight enough. Worked Example 3 walks this by hand, eight halvings deep, against Cascadia's actual net-to-LP cash flows, and ties the result to a Python scipy.optimize.brentq solve to within five basis points.
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Why can a fund's net IRR look better than it is?
Two further IRR subtleties, both real and both testable. First, the reinvestment-rate critique: IRR implicitly assumes every interim distribution is reinvested at the same rate as the IRR itself, an assumption with no basis in fact for an LP who simply banks a distribution rather than immediately redeploying it at, say, 25%. A very high IRR on a fund that returned capital quickly is, to a degree, an artifact of this assumption, which is one reason MOIC/TVPI is always read alongside IRR, never as a substitute for it (Worked Example 4 makes this vivid with a clean, two-cash-flow example). Second, the subscription-line effect: most modern funds (Konkan included, see Worked Example 1) draw on a short-term bank facility, a subscription line of credit, secured against the LPs' unfunded commitments, to fund a closing quickly, then call LP capital afterward to repay the facility. This is standard, LPA-permitted practice (explicitly compatible with a Category II AIF's "no leverage except for operational/temporary needs" rule), but it mechanically shortens the LP's own effective holding period relative to a schedule with no such facility, which inflates the reported net IRR without changing DPI or TVPI at all. ILPA has specifically flagged this as a transparency issue, recommending GPs disclose both a subscription-line-adjusted and an unadjusted ("capital-call") IRR side by side, know to ask which one you are looking at.