No finance person has ever approved a migration. They have approved a reduction in something they can already feel: an outage that costs a day of revenue, an audit finding that has to be closed, a vendor contract that renews in March at a worse rate. The work is the same either way. The framing decides whether it gets funded.
So I stopped presenting infrastructure work as infrastructure. I present the exposure. Here is what breaks, here is roughly how often it has broken in the last year, here is what one occurrence cost us in people and money. Then the proposal, with a number attached, and what remains exposed even after we do it.
The last part is what earns trust. Someone who tells you what their plan does not fix is someone whose estimate you can believe. Every conversation I have lost was one where I oversold the coverage and had to walk it back a quarter later.