I imagine most loan due diligence will ask you whether the tenant is current or not. I don't see a difference in delaying the eviction process.
File for eviction today. Get the process started. Maybe this will get your tenant into gear to pay. Right now, you're not getting the income, eviction or no eviction...so do yourself a favor and file.
File for eviction now. It should have no impact on loan application.
As long as the eviction is at one of the houses that is not being refinanced, you'll be fine. Ultimately, that is why they take 75% of rent. They know you're going to have collection/turnover times like that but that its not permanent.
I don't think I've ever been asked in over 70+ refi's if any of my houses had collection issues or evictions. I actually completed a refi not too long ago where I had just evicted the tenant and got them out of the house about a week before the appraisal. :-)
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