Start from a unit of business meaning rather than from tokens. Cost per resolved ticket, per document processed, per user per month. That number can be compared against the value of the thing it replaces, and it survives a change of model or provider in a way that a token estimate does not.
Model three volumes: the pilot, the realistic first year, and the scenario where it works better than expected. The third is the one that matters, because AI systems that deliver get used more, and a cost model that only works at pilot volume is a problem waiting for success to trigger it.
Put the sensitivities in explicitly. Which assumption, if wrong, changes the answer? Usually it is request volume or the proportion needing an expensive model, and stating that lets a finance function interrogate the model properly instead of accepting or rejecting a single number.
Then compare deployment models on the same footing. A hosted estimate that omits migration and governance overhead against a self-hosted estimate that omits operator time is not a comparison. The business case page sets out both sides in full.