# How to calculate average growth when it's negative?

We have annual reports for company's revenue and can calculate annual growth as $$yg = {y_{i+1} \over y_i}$$.

And then we can calculate the average monthly growth as $$mg = ({y_{i+1} \over y_i})^{1 \over 12}$$.

So for reports 2000-12 $1m and 2001-12$2m the average monthly growth would be 1.06.

But how calculate monthly growth when the revenue became negative?

For reports 2000-12 revenue = $1m and 2001-12 revenue =$-1m?

P.S.

I need it for simple prediction. For example 2000-12 $1m and 2001-12$2m the revenue in 2002-02 could be predicted as $$2 \times 1.06^2 = 2.25$$

• Why not the same formulas? You'll have ratios smaller than one (because $y_{i+1}<y_i$), and that should be fine.
– user239203
Commented Jun 4, 2020 at 22:07
• Revenue is negative, earnings are negative, or revenue growth is negative? Commented Jun 5, 2020 at 1:14
• @DougM the revenue became negative 2001 revenue = $1M, 2002 revenue =$-1M Commented Jun 5, 2020 at 4:07

An example for negative growth rate: $$y_0=100, y_1=80$$

The growth rate from $$t=0$$ to $$t=1$$ is $$g_{01}=\frac{80}{100}-1=0.8-1=-0.2$$

So you can use the formula for growth rate no matter whether the growth rate is positive or negative:

$$g_{t,t+1}=\frac{y_{t+1}}{y_t}-1$$

Btw, the growth factor $$1+g_{01}$$ is still positive $$1-0.2=0.8$$

To apply the formula for the growth rate you need a meaningful zero point. That means that the values are ratio scaled. If $$y_t$$ is can be negative as well, then a growth rate cannot be determined.

• Thanks, but I meant - the revenue itself is negative (the net revenue could be negative even if the gross revenue is positive). So in this example it would be $y_0=100$ and $y_1=-80$ Commented Jun 4, 2020 at 22:51
• @AlexeyPetrushin I´ve made an edit. Commented Jun 4, 2020 at 23:07
• I see, thanks. I don't know how to find a proper zero point, maybe I'm not forming the question properly. May I ask you to take a look at this slightly different explanation of the issue? stats.stackexchange.com/questions/470440/… Commented Jun 4, 2020 at 23:27
• @AlexeyPetrushin To the iproblem here: Maybe you should compare net revenues only or the gross revenues only. It seems not a good idea to compare net and gross revenues. I´ve to admit that I´m not good in solving recurrence equations. But I´m pretty sure that someone else can help you. Commented Jun 4, 2020 at 23:37
• Thanks anyway :). To be clear - I'm not comparing net to gross. I'm only talking about the net. But it can change the sign, could be that one year it's positive and the next became negative. Commented Jun 5, 2020 at 0:11