XIRR is often treated as the be-all and end-all metric for quantifying an investment’s performance. I used to utilize this metric all the time to compare the performance of MFs I had invested in. I took it for granted by treating it as a black-box for years.

One fine day, I decided to check its concrete definition.

XIRR of a given cashflow time-series data, is defined as value of r, the rate of discounting, such that NPV is 0.

The formula for NPV was quite abstruse.

$NPV = \sum_{i = 0}^{n - 1} \frac{P_{i}}{(1 + r)^{\frac{t_{i} - t_{0}}{\Delta T}}}$

Ignorance was truly a bliss. I relied on it quite a lot and not having an intuition made me a bit uncomfortable.

If something is so ubiquitous, it can’t be hard to understand. I resorted to searching on YouTube, Google, etc, to find out what does XIRR really represent. Most sources simply plugged in the Excel function and others quoted jargon like discounting, cashflow decay, etc.

Luckily, I could derive XIRR using nothing but first principles. I didn’t find any source explaining the intuition, so here is one :)


Alice invested ₹100 and today its value is ₹180. Bob invested ₹100 and today its value is ₹150.

Since $80 > 50$, Alice’s portfolio performed better.

Now suppose, Alice invested ₹200 and today its value is ₹250. Bob invested ₹100 and today its value is ₹150.

Who did it better?

Alice’s investment increased by 25% and Bob’s by 50%.

This might make Bob look like Buffet but we forgot to account for one thing - time.

Suppose it took Bob 2 years to get 50% return and it took Alice 1 year to get 25% return, how do we evaluate their portfolio performance?

Compound interest enters the room.

Suppose both of their investments were compounding using a hypothetical rate, we could simply compare this rate.

$250 = 200 * (1 + \frac{r_{alice}}{100}) ^ {1} \implies r_{alice} = 25\%$

$150 = 100 * (1 + \frac{r_{bob}}{100}) ^ {2} \implies r_{bob} = 22.47\%$

So, Alice had the upper hand. This “hypothetical compound interest rate” is termed as CAGR.

Now, we enter the realm of XIRR/IRR1.

Suppose, today were 2022-01-01. The assumption that Alice’s investment went from ₹200 to ₹250 in 1 year and Bob’s investment went from ₹100 to ₹150 in 2 years, is intact. Assume that the investing timeline were as follows.

Person Date Amount invested
Bob 2020-01-01 ₹10
Bob 2021-06-01 ₹90
Alice 2021-01-01 ₹190
Alice 2021-06-01 ₹10

Again, let’s assume for each person, there exists a “hypothetical compound interest rate”.

For Alice, ₹190 was invested for 1 year and ₹10 for half a year.

$250 = 190 * (1 + \frac{r_{alice}}{100}) ^ {1} + 10 * (1 + \frac{r_{alice}}{100}) ^ {0.5}$

$\implies r_{alice} = 25.59\%$

For Bob, ₹10 was invested for 2 years and ₹90 for half a year.

$150 = 10 * (1 + \frac{r_{bob}}{100}) ^ {2} + 90 * (1 + \frac{r_{bob}}{100}) ^ {0.5}$

$\implies r_{bob} = 74.99\%$

Bob is the ultimate champion!

This “hypothetical compound interest rate” is XIRR. This computation that we did, if you rearrange the terms, we get the scary NPV formula. Would you look at that!

In short, XIRR is the “hypothetical compound interest rate” at which your portfolio grows. This accounts for random amounts invested at random time intervals.




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  1. IRR is a subset of XIRR. IRR is used for recurring, periodic investments of equal amount. XIRR is generalized and hence more popular. ↩