What actually moves the answer
Sixteen months is a real answer, and for a lot of companies it is the wrong side of the line. That is the useful part of doing the arithmetic rather than quoting a percentage: it shows you which assumption you are really betting on.
Volume dominates everything else. The build cost barely moves with ticket volume; the saving moves with it almost linearly. Run the same model at 12,000 tickets a month and the gross saving becomes €10,584, the running cost rises only to about €1,067, and payback falls to roughly month 5. Same system, same deflection rate, entirely different decision.
Deflection rate matters less than people expect. Moving deflection from 45% to 60% at 4,000 tickets pulls payback in from about month 16 to about month 11. Tripling the volume pulls it in to month 5. Teams spend their energy on the wrong variable here, and vendors encourage it, because deflection rate is the number that appears on the slide.
Handle time is where the estimate usually breaks. The tickets an AI deflects most easily are the short ones. If your 7-minute average is dragged up by complex cases the system will not touch, the saving is on a shorter ticket than the average implies — which is why the assumption above says median, not mean, and why we sample the deflected set rather than trusting the aggregate.
If the honest version of this model does not clear your threshold, that is the answer, and it is cheaper to find here than in month nine of a build. We would rather show you this arithmetic on a call than a case study.