A worked example: one cash flow series, two calculators
Take a real ₹6,00,000 investment made on 2022-01-01, followed by four annual inflows of ₹1,80,000 each on 2023-01-01, 2024-01-01, 2025-01-01, and 2026-01-01 — ₹7,20,000 total received back. Fed into the payback period formula (which only needs the amounts, not the dates), this series recovers in 3.33 years. Fed into the XIRR formula (which uses the signed amounts and the actual dates), the same series produces an annualized return of 7.71%. Same underlying money, two different real answers.
The formula: why payback period only needs the amounts
Payback period tracks cumulative cash flow against the ₹6,00,000 investment: ₹1,80,000 after year 1, ₹3,60,000 after year 2, ₹5,40,000 after year 3 — still ₹60,000 short — and ₹7,20,000 after year 4. That ₹60,000 shortfall divided by the ₹1,80,000 received during year 4 gives a fraction of 0.33, landing the payback period at 3 + 0.33 = 3.33. Dates never enter the calculation — it only cares how many periods' worth of cash flow it takes to add up to the investment.
The formula: why XIRR needs both the sign and the date
XIRR takes the same amounts but with the investment entered as −₹6,00,000 and each inflow as +₹1,80,000, matched to its actual date, then searches by bisection for the annualized rate that discounts all five dated cash flows to a net present value of zero. Because the four inflows are spread from one to four years after the investment, discounting them back to 2022-01-01 at the found 7.71% rate — each divided by 1.0771 raised to the power of its own years-elapsed — nets to zero, which is what makes 7.71% the answer rather than the simpler 20% total-gain-on-investment figure.
Why the two answers are both correct and both incomplete alone
3.33 years and 7.71% are not competing estimates of the same thing — they answer different questions about the identical ₹6,00,000-in, ₹7,20,000-out series. Payback period says nothing about how good a 7.71% annualized return is, and XIRR says nothing about how long the capital was actually tied up before any of it came back. An investor comparing two opportunities with the same payback period but different cash flow timing would see that difference show up only in XIRR — and one with the same XIRR but a slower payback would carry more time risk that XIRR alone doesn't surface.