The cash flows
Aman puts ₹25,000 into a flexi-cap fund on 5 January each year from 2022 to 2024, then checks the folio on 22 September 2026. It is worth ₹1,15,000. He has not redeemed anything yet, so that last number is treated as a redeem — “if I sold today, this is the inflow.”
| Date | Type | Amount |
|---|---|---|
| 5 Jan 2022 | Invest | −₹25,000 |
| 5 Jan 2023 | Invest | −₹25,000 |
| 5 Jan 2024 | Invest | −₹25,000 |
| 22 Sep 2026 | Current value | +₹1,15,000 |
Invested: ₹75,000. Returned / value: ₹1,15,000. Net:₹40,000 over 4.72 years.
The equation
Let t be years from 5 Jan 2022, using actual days ÷ 365. XIRR is the rate r that solves:
−25000 / (1+r)0 − 25000 / (1+r)t₂ − 25000 / (1+r)t₃ + 115000 / (1+r)t₄ = 0
That left-hand side is the net present value (NPV) of the folio at rate r. We want the r that drives NPV to zero.
Guess, then correct — Newton–Raphson
Excel and XirrRupee start near 10% and walk downhill. You can see the same path by evaluating NPV at a few nearby rates:
| Trial rate | NPV of Aman’s flows | Meaning |
|---|---|---|
| 8% | +₹10,421 | Too cheap — the folio is worth more than an 8% hurdle. |
| 10% | +₹4,983 | Still a bit cheap. |
| 12% | +₹144 | Almost there. |
| 12.06% | ₹0 | XIRR. Newton lands here in four iterations. |
| 14% | −₹4,167 | Too expensive — that hurdle overstates the return. |
Each Newton step is r ← r − NPV(r) / NPV′(r). If the derivative vanishes or the walk jumps below −100%, XirrRupee bisects the bracket instead. Aman’s folio never needs that fallback.
Why “CAGR on the pile” is 9.49%
If you ignore dates and compute (115000 / 75000)1/4.72 − 1 you get9.49%. That pretends all ₹75,000 arrived on 5 Jan 2022. The 2023 and 2024 cheques did not. XIRR at 12.06% is the honest personal rate. The gap is the whole point of an XIRR calculator — see XIRR vs CAGR.
The longer sample (Priya)
The home-page Load sample button uses a noisier folio: ₹8,000 on the 5th for 24 months, a ₹50,000 lump on 12 Mar 2023, a ₹30,000 partial redeem on 18 Aug 2024, and a ₹2,85,000 value on 22 Sep 2026. Invested ₹2,42,000, inflows ₹3,15,000, XIRR10.19% p.a. Naive CAGR on that pile is 7.35%. Same lesson, more rows.
Type Aman’s four lines into the xirr calculator — or paste them as CSV — and you should land on 12.06%. If you do not, check the signs first.