Calculating stock or investment returns: the difference between ROI and IRR

Whether you are investing in the stock market or a business project, you need to understand rates of return. Stock gurus talk about things like ROI and IRR, but what do they mean? I’ll go through the logic of each method and explain why IRR is my preferred choice.

Rate of return (ROR, or more commonly called ROI)

ROI is the simplest return measure and also the most often quoted. ROI is defined as the percentage increase or decrease of an investment over a period of time. This method gives an idea of how much an investment is growing or declining.

Here’s an example. Imagine an investment started at $1,000 and grew to $1,100 by the end of the year. In this case, the ROI is equal to the percentage increase of 10 percent.

In general, you can calculate the ROI once you know:

1. The starting investment value (C₀)
2. The ending investment value (C₁)

The general formula is:

One thing you might notice is the ROI formula doesn’t include a time component. Mathematically, we would have gotten the same ROI had the investment taken place over 1 day, 1 month, 1 year, or even 10 years. This is why the ROI is usually stated with a time period, like “a 10 percent daily return” or “a 10 percent annual return.”

There are two reasons the ROI is useful.

First, ROI gives a quick assessment of investment performance, and it helps that ROI can be computed mentally.

Second, ROI is useful when comparing two investments over the same time period. If one mutual fund had an annual ROI of 15 percent compared to another that had 10 percent, you could conclude the first performed better.

Unfortunately, there are two fatal flaws with the simple rate of return method.

First, it does not allow you to compare investments over different time periods. Suppose you were trying to compare two investments, one that had a 5 percent return over 1 month versus another that had a 50 percent return over 1 year. Which is better? It is not easy to draw conclusions.

Second, what if you invested in several increments? Suppose you invested $100 monthly for one year and ended up at $1,300. What would you investment return have been over that time period?

These two issues are realistic concerns for the individual investor. And then there are other issues like taxes and dividends. How do you figure out investment performance then?

A more flexible framework is needed and this is where IRR comes in. While the IRR is mathematically more complicated, understanding it is vital for tracking investment return.

Internal rate of return (IRR, also called yield or APY)

I bet you are already familiar with IRR because it is given a special name when quoted on products like CDs or savings account. The IRR is called the APY, the annualized percentage yield.

IRR is a more sophisticated return measure and is widely used in the finance world for valuations. IRR is the annualized compound rate which can be earned on invested money, also known as the yield. IRR takes into account the investment growth but unlike ROI it also accounts for the timing of the cash flows.

Some examples are: a 5 percent monthly return is an IRR of about 80 percent. Making 12 monthly investments of $100 that accumulate to $1,300 is an IRR of about 15 percent.

How can you calculate those figures? In theory, one could go to the math formula and try to solve a complicated polynomial. The calculating complexity is probably one reason the IRR was not as widely quoted.

Nowadays, calculating the IRR has been made easy because of numerical methods. We can calculate IRR in spreadsheets fairly easily. The specific function is “XIRR” in Open Office Calc, Google Documents spreadsheet, and Microsoft Excel (*I think this requires the Analysis Toolpak add-in).

Calculating IRR is done by creating a time series of cash flows. One column is a listing of all the dates of cash flows-including investments, dividends, taxes, etc. The other column is the numerical values of those events. The IRR can then be calculated using the “XIRR” function in a spreadsheet with the appropriate ranges. Here are some examples of calculating IRR.

Example 1: converting monthly to annualized yield

Suppose you invested $1,000 on January 1, 2008 and got back $1,050 on February 1, 2008. What is the annualized yield of this investment (ignoring taxes, etc)?

Here is the IRR calculation:

Note that cash outflows (buying) are negative and cash inflows (selling) are positive.

Example 2: monthly investments

Suppose you invested $100 on the first of each month during 2007 and got back $1,300 at the end of the calendar year. What is the annualized yield of this investment (ignoring taxes, etc)?

Here is the IRR calculation:

Example 3: buying and selling

IRR is flexible enough to handle even harder problems. Take the example of buying and selling during the year.

Suppose you invested $100 on January 1, 2008, sold for $90 on June 1, 2008. You later bought back $100 on July 1, 2008 and then sold for $150 at the year end. What would the annualized investment return be here?

This situation can be solved using the IRR method:

Example 4: adding in taxes, dividends

The real beauty is IRR can measure performance with realistic factors like taxes and dividends. I’ve made up numbers in the next example of dividends and taxes. You can modify them for your actual performance.

Suppose you invested $100 on January 1, 2008, received a $3 dividend on June 1, 2008. You sold at the year end for $105 but had to pay taxes of $1 for the dividend and capital gains. What is your net annualized yield?

Here is the IRR calculation:

I hope these examples give you can idea of the flexibility of the IRR. It’s okay if you still have questions about how to calculate it. Just ask any of your competent friends with economics or accounting degrees and they should be able to run the numbers.

In summary, the IRR is harder to compute but it gives a more accurate picture. Plus, in some cases it is the only way to figure out the return. For my money, I focus on the IRR.

(optional) Math of IRR:

In general, you can calculate the ROI once you know:

1. The cash flows of the investment (C₀, C₁, …)
2. The time elapsed in years after the first cash flow (t₁, t₂ …) where (t₀=0)

The IRR is the value (or values) that solve the following equation:

The IRR cannot always be solved analytically so we rely on numerical methods, like financial calculators or spreadsheets.

Related articles on the web

Tracking your success–a nice article from fool.com on why IRR is the appropriate metric

How to calculate your return on investment–a step by step explanation from Fat Pitch Financial on how to get IRR…plus a free spreadsheet

Disclaimer: This explanation is for educational and recreational purposes only. Every attempt has been made to make the article accurate for the time of writing. Do your own research or consult a professional before making an investment decision.