### Growth Calculation with negative numbers

Once in a while, you face a situation wherein growth % is to be calculated – where one of the number is negative. Here’s quick approach and my thoughts.

Ideal approach used to calculate the growth is

Approach 1: (Current Number / Old Number) -1

Few people follow the approach of differential, like

Approach 2: (Current Number – Old Number) / Old Number

Both are good to use as long as both the numbers are positive. Let’s take a quick example:

Scenario 1: Say Previous quarter profit was at 100 and current quarter profit is at 120 – growth in profit would be calculated at 20% using either of the formula.

Approach 1: (Current Number / Old Number) -1 = (120 / 100) -1 = 0.2 or 20%
Approach 2: (Current Number – Old Number) / Old Number = (120 – 100)/100 = 0.2 or 20%

Scenario 2: Assume that current quarter there is a loss of 20 and previous quarter was profit of 100, in this case outcome would be as follows:

Approach 1: (Current Number / Old Number) -1 = (-20 / 100) -1 = -1.2 or -120%
Approach 2: (Current Number – Old Number) / Old Number = (-20 – 100)/100 = -1.2 or -120%

Which basically means, profit is negative 120% compared to previous quarter

Scenario 3: Now considering you move to next quarter, where in you have profit again, say, 50. So previous quarter is -20. How do you calculate growth? Let’s try following standard approach:

Approach 1: (Current Number / Old Number) -1 = (50 / -20) -1 = -3.5 or -350%
Approach 2: (Current Number – Old Number) / Old Number = (50  – negative 20)/-20 = -3.5 or -350%

As you can see – this absolutely doesn’t make any sense. Where in positive movement in growth is shown as negative growth %.

Alternate Approach

Few people follow the approach of converting negative number to positive  while calculating (in excel using ABS or Absolute formulae). But this approach ends up showing the number, which is quite mis-guiding in itself.

Approach 1: (Current Number / Old Number) -1 = (50 / 20) -1 = 1.5 or 150%, here negative number of previous quarter is converted as positive to compute the growth.

As you can see, the outcome of 150% is quite mis-leading in such cases.

Personally, I feel to keep the Growth % as “nm” or not meaningful when the base is negative.

How do you approach to such situation?