Would you install HVAC for existing tenants from previous owner?

[Roy C.]

I am inheriting tenants from the previous owner. The property needs new HVAC system which would cost about $4-5k. The existing heating system is at least few decades old, and it sounds pretty rough when it turns on.  My plan is to honor the existing lease which ends in April and not renew lease so that I can renovate the property. So far, I am leaning toward the idea of not installing new HVAC system until existing tenants vacate the property, and I would probably have to eat up the cost of repairing the existing heating system throughout this winter. I feel like trusting someone who I didn't vetted/screened with $4-5k capital investment sounds like a financial disaster. 

What do you guys think? If you are in my shoes, would you install new HVAC system for existing tenants from the previous owner?