Impact on refi of NOI changes

[Ben Jess]

Have an opportunity to purchase a property with rents below market value: property is 2 multi, 300k listed, rooms currently yield $1930 in total, NOI 13k

After raising rents (one Aug '23, other immediately), NOI jumps to $31k

So planning to do a mortgage then a re-fi based on the higher NOI.

My question is this:

1. How long do mortgage lenders want to see that NOI being higher before they are prepared to base a valuation on it? I cannot imagine I could go to the bank a day after and say "appraise my property based on my rent increase yesterday"

2. I know things work a little differently sub-4 unit buildings. I've also heard that mortgage company will look at what market rents are and take a view on that, rather than literally multiplying rent x cap rate to arrive at a valuation. So let's play that out. Let's say I want to get as bigger mortgage as possible as I want to put down as little as possible. Say I get the property for $350k. Bank says NOI should really be $31k for this neighborhood, which at a 6.5 cap rate is $476k. So they value the property at $476k. But I made (and had the offer accepted at $350k. How would I go to the back and say - "I know I offered $350k, but lucky me, it's worth far more, i'd like a mortgage for $476k. Is that realistic?

3. I also have read that "banks don't really use NOI" for apt complexes less than 4 bed. In which case. Is there much in the "game" of trying to boost NOI and refinance on NOI * Cap Rate, or is it just the case of getting one single mortgage and it's the art of trying to simply negotiate with the seller to get a good deal in the first place?

Thanks