I regularly receive emails from readers posing questions based on my previous posts on things like how to calculate NPV, using XIRR, and other financial and Excel questions.

One of the most common questions I receive is how to calculate a compound annual growth rate 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)

CAGR = (ending amount / beginning amount)

^{(1 / # of years)}– 1Mathematically, 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 imaginary numbers

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 online financial calculators on this site to do some quick calcs and checks if you need to :)

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## Shiva

Hi! I was hoping you could explain the calculation of CAGR for a scenario in which all numbers are negative but each subsequent number is bigger than it’s preceding number (in other words, every succeeding number is getting closer to 0 but the progression hasn’t got to 0 yet)..

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