Calculation of growth (including CAGR) may look trivial, but it is not. Growth is intuitive and works well when both the numbers involved are positive. But things change when negative numbers come into the picture which happens quite often with financial measures. Let’s explain this through an example.
Suppose we are looking at EPS growth (CAGR) in last 3 years. Let’s call today’s EPS as EPS-0 and EPS 3 years ago as EPS-3.
Everything is fine if both EPS-0 and EPS-3 are positive. We can calculate a meaningful CAGR number using our standard CAGR calculation:
CAGR = [EPS-0/EPS-3]^(1/3)-1
But if either of them is negative, we run into problems. Generally, we run into problems if starting number (in our case EPS-3) is negative but when dealing with CAGR, we encounter problems when even the ending number (EPS-0) is negative.
A lazy approach to handle this would be to simply ignore growth calculation (set it to NA) when we encounter this problem.
However, growth is an important metric and contains a lot of information and should not be ignored. For example, if a stock’s EPS goes from -10/share to +2/share, that is growth. Even going from -10/share to -5/share is growth (becoming less negative). Ignoring this would mean the loss of valuable information.
Therefore, we have a modified version of growth and CAGR calculation which we use for financial metrics. When both starting and ending numbers are positive, it works in the same way as traditional CAGR calculation.
However, if either of the 2 numbers are negative, it tries to calculate a “meaningful” number approximating the “rate” of growth.
This method does have limitations. For cases when starting number (EPS-3) is negative and ending number (EPS-0) is positive, it still sets the growth to NA. This is a significant limitation because this is the most important scenario (company going from negative to positive EPS).
However, we get some very unstable and explosive results if we use our modified CAGR formula in this scenario. Further, the results do not accurately capture the true magnitude of growth. And hence for the sake of prudence (even at the cost of throwing away information), we have decided to keep growth as NA in this scenario.
But we are working on a more stable solution for scenarios where starting number (EPS-3) is negative and ending number (EPS-0) is positive. Our aim is to create a formula that can accurately capture the rate of change when a variable goes from negative to positive.