Fine-tuning pays back by shortening the prompt
A fine-tuned model usually costs more per token at inference. It wins when it removes enough prompt — instructions, examples, format specifications — to more than offset that premium.
If it does not shorten the prompt, it is unlikely to pay for itself on cost. It may still be worth it for consistency, but that is a quality argument.
Try the cheaper options first
A better prompt, then few-shot examples, then retrieval. Fine-tuning is the last resort and the slowest to iterate on, because every change means another training run.
It is also a poor way to add knowledge. Facts belong in retrieval, where they can be updated; fine-tuning is for format, tone and consistency at volume.