CAGR is defined for exactly one shape of investment: money goes in once, and comes out once. The moment there’s a third cash flow - a second SIP instalment, a partial withdrawal, a top-up - CAGR has nothing to compute; the number most apps show for that kind of history is actually XIRR, which finds the single rate that discounts every cash flow, in and out, to a total of zero.

That equation has a property CAGR’s never has: it doesn’t always have a unique solution. By Descartes’ Rule of Signs, an equation like this can have as many valid positive roots as the number of times the cash flow sequence changes sign. Money in, then money out, changes sign once - so a plain lump-sum-in, lump-sum-out CAGR is always unique. Add a withdrawal followed by a reinvestment, and the sequence changes sign twice. The equation can then genuinely balance to zero at two different rates, not one.

Here is an exact case, computed rather than assumed:

Solve for the rate that discounts these three cash flows to zero, and two answers work: 25% and 400%. Both are exact - plug either one back into the equation and it balances precisely.

Net present value of the cash flow above, plotted against every possible discount rate. The curve crosses zero at 25% and again at 400% - both are valid XIRR solutions for the identical cash flows.

Nothing in the maths says one of those rates is the real answer and the other a mistake. Excel’s XIRR function, and most apps built on the same logic, resolve this by starting from a guess and walking toward the nearest root - so which number gets displayed depends on the solver’s starting point and search path, not on which rate is more “correct.” A different tool, or the same tool given a different starting guess, can return a different number for the identical cash flow history, and both would be right.

This isn’t confined to textbook cash flows either. Any real portfolio with a SIP, a partial withdrawal at some point, and continued investing afterward has exactly this sign-changing shape. Most such histories still only have one real solution in practice - multiple valid roots are the exception, not the rule. But there is no way to tell which case you’re in just by looking at the single number an app displays.

None of this makes XIRR the wrong tool - it is still the only measure that can even be defined for a cash flow history CAGR can’t handle. It means the figure on screen is the output of a numerical search, not an algebraic certainty, and for cash flows that change direction more than once, there may quietly be more than one number that is equally right.

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