Negative cash flow vs $65k-$75k?? I'd definitely sell it. Not only are you negative cash flow but any major repair, bad tenant or vacancy is going to dig you deeper. Then I'd take the money and put it toward a better investment.
I like the idea of doing the refi to create positive cash flow. With the option of that refi today, while rates are still low, to me negative cash flow is off the table. That 65k could also go a long way into a new investment that could give you higher ROI, but that will require work to find, close, and manage that new property. You could combine the two strategies with a cash-out refi to get some cash but keep it in positive cash-flow. Without more details about the property, the market, and your long-term goals, it's hard to say what the best option for you is.
I say refi into 30 year with today's rates then get a home equity line to use for other investments. With a HELOC you only pay interest on what you use and typically the appraisal is covered by the lender. With it being non-owner occupied and assuming your DTI can cover the proposed new debt (which really shouldn't be a problem considering the rental income and the amazing new cash flow) I suspect you'll be able to get a 70% LTV line on it which can be used for capital improvements and/or new investments. I know Wells offers a HELOC that grows annually as values increase and principle decreases. 4% ish is cheap money man. In 10 or 20 years that house will be worth way more with usable equity, a fixed low rate and rents will have increased.
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