Investment professionals and individual investors often need to estimate the profitability of a given investment opportunity, or to retrospectively assess the results of past endeavors. Typically this is done with the idea of comparing two or more opportunities and deciding which one to choose.

All other things being equal, the return of investment is the leading measure by which such comparisons are made. However, calculating said return is not always as trivial and there are different ways to do it.

## CAGR vs IRR vs XIRR Cheat Sheet

Different measures of return such as relative return, simple annualized return, CAGR, IRR, and XIRR apply to different investment scenarios. Each measure has its place, depending mostly on the **time to return**, as well as the **number and timings of cash flow events** in the investments to be compared, as well as the **whether the investment returns are compounding** or not.

The table below shows key differences between CAGR, IRR, and XIRR, and when to use each return measure:

Measure / Characteristics of Investments to Compare | Time to return | Cash flow events | Type of return |
---|---|---|---|

Absolute return | Same | One outflow, one inflow each | Compounding or Non-compounding |

Relative return (%) | Same | One outflow, one inflow each | Compounding or Non-compounding |

Simple Annualized Return | Different | One outflow, one inflow each | Non-compounding |

CAGR | Different | One outflow, one inflow each | Compounding |

IRR | Different | Multiple outflows and/or inflows at regular intervals | Compounding |

XIRR | Different | Multiple outflows and/or inflows at regular or irregular intervals | Compounding |

Absolute and relative return are useful if the time to return of the investments of interest is exactly the same, and there is just one outflow (the initial investment) and one inflow at the end. The type of return can be either compounding or non-compounding within the investment term.

When the time to return is different across the investment opportunities, annualized measurements are appropriate. Both CAGR and Simple annualized return work when there are only two cash flow events, one is suitable with compounding returns and the other with non-compounding ones.

When there are multiple cash flow events IRR becomes necessary, where XIRR is an extension of IRR which allows for non-periodic cash flows.

While this is a brief comparison of CAGR, IRR, XIRR, and simpler measures of profitability such as absolute return and a simple annualized return, you may find it beneficial to dig deeper into the calculation methods and assumptions behind each. Before we start discussing these advanced topics in more detail, it is useful to consider why we need them in the first place.

## What Type of Return to Calculate?

Depending on the type of investment, different types of returns are of applicable, including absolute return, relative return, periodic returns, and more complex schemes including CAGR, IRR, and XIRR among them.

For really short-term investments, one can simply compute the absolute return. For example, if you invest $10,000 and get $15,000 in a couple of days, you might as well not bother with more complex measure and just compute the absolute return which is just $15,000 – $10,000 = $5,000, or transform it into a percentage as such:

$5,000 / $10,000 x 100(%) = 0.5 x 100(%) = 50%

The above is just the “X is what percent of Y?” percentage calculation. So, **$5,000 absolute return** on an investment of $10,000 is equal to **50% relative return**. In other words, the rate of return is fifty percent.

Obviously, such investments rarely, if ever, occur in practice. Typically, a fifty percent return can be expected to take several years to achieve. Since different investments often take different amounts of time for the returns to accumulate, it is **useful to have a measure which makes investments with different time to return comparable**.

## Annualized Returns

More often than not, capital investments take years to pay back, which is why calculating the average return on a per year basis is useful to compare investments with different time spans. Say there are two investments with identical absolute return of $5,000 and relative return of 50%, but Investment A takes two years before payback day whereas Investment B takes five years before one can get said return on investment. All other things being equal, the time preference of investors dictates that one would prefer to get their return back sooner rather than later, and this is easily captured by calculating the **simple annualized rate of return** using the formula **Relative Return / Number of Years**:

- For
*Investment A*: 50% / 2 =**25%**per year ($5,000 / 2 = $2,500 per year in absolute terms) - For
*Investment B*: 50% / 5 =**10%**per year ($5,000 / 5 = $1,000 per year in absolute terms)

Note that you might also encounter the “per annum” wording, which is Latin for “per year”, and is often abbreviated as “p.a.”. Also note that returns can also be calculated on a quarterly, monthly, or even weekly basis in much the same way, though these would be less common.

The issue with simple annualized returns is that most investments do not pay in such a manner, but rather the returns are compounded year after year. This is true of stock market investments, mutual funds, certificates of deposit, and many other investment products. Such scenarios call for compound rates of return.

## When to Use Compound Annual Growth Rate (CAGR)

CAGR, short for “Compound Annual Growth Rate”, is the average rate of growth of an asset over a given period of time. It is applicable to all kinds of assets where the returns in one year get compounded into the base of calculating the return in the years following. The most simple example of this is the familiar compound interest calculation.

The basic assumption of CAGR is that there are just two cash flow events: an initial outflow – the investment event, and a final inflow where the invested sum is returned alongside a certain profit. For the same 5-year investment as discussed in the examples above, it would look like this:

Note the absence of cash flows during the investment term. While CAGR is an average rate of growth of the value of the investment on an annual basis, there are no cash flows associated with these interim periods. The calculation is therefore very simple, with the CAGR formula being:

See the “CAGR formula” section in our CAGR calculator page for details about the variables used, but it is basically just raising the relative return to the power of one divided by the number of periods. While this accounts for compounding, obviously no interim cash flows are involved.

Continuing the example with our $10,000 investment which returns $15,000 in five years time, assuming this return is achieved through yearly compounding, the compound annual growth rate of this investment would be **8.447%**, calculated simply as (15,000 / 10,000) raised to the power of (1 / 5), minus one.

While this may work for simple textbook scenarios, most real-world applications involve multiple cash flows. For example, buying a house and selling it later with a profit may look like a case for applying CAGR, however if you want to be accurate you should account for house maintenance, taxes, and other expenses, as well as the rent income if the property is being rented during the investment period. More complex scenarios such as investing in a company, purchasing stocks or bonds, and so on almost always include interim cash flows such as dividend payments, interest rate payments, and so on, and not just the appreciation of the investment or capital asset.

## When to Use Internal Rate of Return (IRR)

When there are periodic cash flows, e.g. annual interest being accrued or charged, annual or quarterly dividends being paid out, monthly withdrawals or contributions, etc. these need to be taken into account, including the timing of their occurrence. In such cases, CAGR cannot capture these flows and so IRR is the correct profitability metric to compute.

Another way to understand IRR is that it is the **compound annual growth rate adjusted for the cash flows, accounting for their amount, direction, and timing**. Due to the time value of money, earlier **cash flows need to be weighed more heavily than later cash flows** which is exactly what an IRR calculation does. This logic is factored in a net present value calculation and also IRR, given that the latter is simply the return rate at which the NPV of an investment equals zero.

The NPV formula with regular cash flow intervals is:

and IRR is just solving the above equation for *r* with NPV equal to zero. Note that unlike CAGR, the IRR formula is not analytical and uses iterative summation to account for the cash flows. The IRR equation when applied to a single cash outflow followed by a single cash inflow can be shown to be equivalent to the CAGR formula.

**So, CAGR and IRR are exactly the same when the interim cash flows all equal zero.** The internal rate of return of our example $10,000 investment calculated with zero cash flows in years one through four equals **8.447%** (see this IRR calculation), which is exactly the investment’s compound annual growth rate.

If the interim cash flows are non-zero, IRR will typically be greater than the CAGR if the earlier flows are positive, reflecting the fact that getting money out quicker is preferred by investors. In this example IRR calculation the rate of return is over **12%**, despite the net cash flow (absolute return) being exactly $5,000, and the relative return being exactly 50%, just like in the original example. This is due to the significant inflows happening in the years before the term of the investment, namely: $1,900, $2,150, $1650, $2,200 at the end of years 1-4, and a final inflow of $7,100 at the end of year five, as plotted below:

The above example shows why it would be **inappropriate to use CAGR when there are more than two cash flows and the adequate measure of returns in such cases is the IRR**.

## When to Use Extended Internal Rate of Return (XIRR)

XIRR can be viewed as an extension of IRR calculations for cases when the cash flows associated with an investment are **irregular**. Remember that an assumption of the IRR formula is that cash flow events occur at fixed time intervals. There are no such restrictions with XIRR’s more complex formula which involves solving the following equation for *r* with NPV fixed at zero.

Therefore, XIRR differs from IRR only in its allowance for non-periodic investment cash flows. Note that XIRR is an annualized rate by the above formula, but it can also be adopted for quarterly, monthly or weekly rates of return by substituting 365 with the appropriate number of days.

**Viewed from a different angle, a XIRR calculation is the most generic type of compound annual growth rate calculation.** IRR is a simplified version of the XIRR formula in which the timing is given in number of years (or other periods) whereas CAGR can be viewed as an IRR calculation with a single cash outflow and a single cash inflow event.

So, XIRR and IRR will give the same output if the intervals between cash flows are regular. CAGR, IRR, and XIRR will all result in the same annualized rate of return if there are only two cash flow events: an outflow followed by an inflow after some number of years. This was shown in the example above where CAGR, IRR, and XIRR are all equal to 8.447% if there are no interim flows of money.

## A Recap on CAGR, IRR, and XIRR

Compound annual growth rate, annualized internal rate of return and the annualized extended internal rate of return can all be viewed as **simplifications of XIRR tailored to specific scenarios**.

**XIRR**, being the most general method, is applicable for comparing compounding return investments with:

- the same of different term (holding period)
- presence or absence of cash flows of varying size
- periodic or non-periodic cash flows

In all this, XIRR calculations take into account the time preference of investors.

**IRR** is a simplification of XIRR in which only periodic cash flows are allowed.

**CAGR **is a further simplification in which just a single inflow (investment event) and a single outflow (cash out event) are allowed.

With CAGR being so simple, it barely leaves place for the time value of money, except for when it takes into account the total duration of the investment period. CAGR is therefore mostly useful when comparing things like mutual fund or investment strategy performance. IRR and especially XIRR find a greater number of practical applications due to their allowance of multiple cash flows.

That said, all of these methods suffer from a common limitation which is that they are not accounting for the riskiness of an investment or business project. In other words, they are useful in isolation only when “all else is equal”, which is a reflection of the fact that the return of an investment represents only one part of the picture when considering whether to undertake it or not, in comparison with other possible uses of the same capital.

If you’ve found this comparison of CAGR, IRR, and XIRR, the exploration of their differences and similarities and how they can be applied to investing useful, make sure to share it by also citing the source.

An applied statistician, data analyst, and optimizer by calling, Georgi has expertise in web analytics, statistics, design of experiments, and business risk management. He covers a variety of topics where mathematical models and statistics are useful. Georgi is also the author of “Statistical Methods in Online A/B Testing”.