Why IRR and CAGR Give Different Answers for the Same DCA Plan
You run a backtest, see an annualized return, work it out yourself with a compound growth formula, and get a completely different number. Neither calculation is broken. They are measuring different things, and only one of them is appropriate for a plan with ongoing contributions.
#Start with an example that looks wrong
Here are two ways of putting $70,000 into VOO over the last decade, taken from the lump sum versus DCA comparison.
| Plan | Invested | Final value | Ann. return |
|---|---|---|---|
| All $70,000 invested on day oneVOO | $70,000 | $295,929 | +15.51% |
| $10,000 up front plus $500 a monthVOO | $70,000 | $178,251 | +15.74% |
The lump sum ended about $112,000 richer. And yet its annualized return is lower: 15.29 percent against 15.75 percent. More money, worse rate.
That is not a contradiction, and it is the clearest illustration of what these numbers actually measure. The lump sum had all $70,000 invested for the full ten years. The contribution plan’s final $500 was invested for about a month. Per dollar, per year, the contribution plan earned a slightly better rate. In total dollars it earned far less, because far fewer of its dollar-years were available to compound.
#What CAGR actually measures
Compound annual growth rate answers a narrow question: if a single amount grew from A to B over N years at a constant rate, what rate was that? The formula is straightforward.
Notice what it requires: one beginning value and one ending value. It has no way to represent money that arrived partway through. For a lump sum held untouched, CAGR is exactly right and is what fund fact sheets report.
For a contribution plan, it has no valid input. If you feed it your total contributions as the beginning value, you are pretending $70,000 was present on day one when most of it arrived years later. That systematically understates the rate, sometimes severely.
#Where the naive calculation goes wrong
Suppose you contribute $500 a month for ten years, $60,000 total, and finish with $100,000. The tempting calculation treats $60,000 as the starting value:
This is wrong, and not by a small margin. You never had $60,000 invested for ten years. On average, each dollar was invested for roughly five years, not ten. The money that arrived in year nine had one year to work, not the full decade.
Correcting for that timing typically pushes the real annualized rate meaningfully higher. Getting that right is precisely what IRR does.
#What IRR does instead
Internal rate of return treats the plan as what it is: a series of dated cash flows. Each contribution is an outflow on a specific date. The final portfolio value is a single inflow at the end. IRR finds the single annual rate at which all of those, discounted back to the start, sum to zero.
Every dollar is credited for exactly the time it was actually invested. A contribution made in month one compounds for the full period; one made in the final month barely compounds at all. Both are counted correctly.
There is no closed-form solution, so it has to be solved numerically. This calculator uses Newton-Raphson, iterating until the discounted cash flows sum to approximately zero. The methodology page covers the implementation, including the convergence guards.
#Which one you should use
- Comparing funds:use the fund’s published CAGR or total return. That is the correct measure for a single amount held over a period, and it is what makes two funds comparable on equal footing.
- Evaluating your own plan: use IRR. It is the only figure that correctly handles contributions arriving over time, which is what an actual investing plan looks like.
- Comparing two plans against each other: look at both. As the table above shows, the higher IRR and the larger ending balance can belong to different plans, and which one matters depends on whether you are asking about rate or about dollars.
#Why this site reports IRR
The column labeled “Ann. Return” throughout this site is IRR, not simple CAGR. For the tool’s primary use, backtesting a recurring contribution plan, it is the only defensible choice. Reporting a naive CAGR against total contributions would understate nearly every result and would be actively misleading for plans that ramp up over time.
It also means the number here will not match a fund’s published annualized return, and it should not. Those describe a lump sum held for the whole period. Yours describes your actual contribution schedule.
#A caveat worth knowing
IRR assumes intermediate cash flows can be reinvested at the same rate the calculation produces, which is an idealization. It can also behave unusually with cash flows that change sign repeatedly, though a standard contribution plan, all outflows followed by one inflow, has a single unambiguous solution.
For the plans this tool models, IRR is well behaved and is the right measure. It is worth knowing the assumption exists, particularly if you are comparing against figures produced somewhere else that may be using a different method entirely.