Re:Calculus in SaaS
by ZephyrBlu on Friday September 25, 2020 @08:14PM
(#24595348)
> If y = 10x where y = ARR and x = time in months, then after two months ARR = $20. After 12 months, ARR = $120 (assuming we start from $0 of ARR)
I don't think this makes sense, because the time is in months yet you're calculating a yearly value. Time should be in years, because otherwise you're calculating forecasted values.
> So at the end of a year, the business has grown from $0 to $120 in ARR. But what is the recognized revenue? The complex answer is that it's the integral of 10x from 0 to 12 months
(Recognized revenue = $720 in this example)
Again, this doesn't make sense due to the fact that your calculated ARR values are forecasted.
If your projected ARR has grown throughout the year, it's intuitive that your recognized revenue must be lower than your ARR.
It's not possible to recognize $720 in revenue when your ARR is only $120, it should be $60.
I think the issue here is using ARR, since ARR grows quadratically given a linear increase in MRR. This math would make sense if you used MRR instead, or modelled actual ARR instead of forecasted ARR.
I don't think this makes sense, because the time is in months yet you're calculating a yearly value. Time should be in years, because otherwise you're calculating forecasted values.
> So at the end of a year, the business has grown from $0 to $120 in ARR. But what is the recognized revenue? The complex answer is that it's the integral of 10x from 0 to 12 months
(Recognized revenue = $720 in this example)
Again, this doesn't make sense due to the fact that your calculated ARR values are forecasted.
If your projected ARR has grown throughout the year, it's intuitive that your recognized revenue must be lower than your ARR.
It's not possible to recognize $720 in revenue when your ARR is only $120, it should be $60.
I think the issue here is using ARR, since ARR grows quadratically given a linear increase in MRR. This math would make sense if you used MRR instead, or modelled actual ARR instead of forecasted ARR.