Calculating CAGR (compound annual growth rate) when the beginning value is negative

Corporate finance, Personal finance

I regularly receive emails from readers posing questions based on my previous posts on things like , , and other financial and Excel questions.

One of the most common questions I receive is how to calculate a when the beginning value is negative.

The basic answer is that you can’t. Why?

Let’s look at the formula for calculating CAGR:


CAGR = (ending amount / beginning amount)(1 / # of years) – 1

Mathematically, because you’re taking a root of a number, if you have a negative beginning amount and a positive ending amount, you’d be taking the root of a negative number. Unless you have an odd # of years, you can’t compute this mathematically without going into

Even if you do happen to have (or force) a negative # of years, the result will also be a negative growth rate, which also doesn’t make sense in terms of what’s going on.

The best way to deal with situations where you have a negative initial value is to just footnote it and calculate CAGR based on the first positive initial value you have. So, for example, if you had a project that lost $500 in year 2003, then gained $100 in year 2004, and ended in year 2007 with $500, you might write the following:

    Revenues grew from $100 to $500 during the period from 2004-2007 (CAGR of 71%). Note that this excludes the initial 2003 year, when the project lost $500.

Remember, your goal is to present an accurate picture of what’s going on. That almost always means using a few more words to reflect and explain reality rather than just provide a single, calculated figure.

As a reminder, you can also always use the on this site to do some quick calcs and checks if you need to :)

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