Welcome to the world of bank loans! There is not secret sauce, especially on a value-add deal like you're describing. The under writing doesn't carry for a 1.25 DSCR which (at the moment) is the golden rule for banks and commercial hard money lenders.
First off- $4.5M for 48 units and 50% are vacant is not a steal, unless this property is located in a downtown area and you have a contact with a developer who will pay 2X to build a high rise. $93k/unit for 50% vacancy doesn't carry hardly any debt, hence why they are capping you at $500k. It's about NOI and DSCR.
If you're confident in your UW and the numbers do make sense, I would recommend a seller carry deal. That's the only way this would work for you and the seller unless a cash buyer comes along which is unlikely at $93k/door. It can be a simple one page contract b/w you too at an agreed upon rate. I would pay I/O for 5 yrs, and then ri-fi but you HAVE to hit your pro-forma to execute this plan.
Simple trick- NOI/Cap Rate will tell you the worth. Use the actual NOI, not the pro-forma b/c that is how the property is ACTUALLY performing. Something like this, if I had to guess is an 7.5-10% CAP rate market if 50% is vacant. Don't use some compressed 5% cap rat, you'll lose money if you do. Be conservative on all aspects
Now go take over the world!
