If it's a DSCR loan, you could get up to 80% LTV if the property qualifies.

To qualify for a loan, focus on having a credit score of at least 620 (or 580 for FHA loans), keeping your total monthly debt under 43% of your income, and saving enough for a down payment and closing costs—about 5-10% of the home's price in total.

Look into a DSCR, Debt Service Coverage Ratio, loan where the rental income can be used to qualify the cash out refinance instead of your personal income.To Your Success! 

If you go that route, ensure to use a Qualified Intermediary to handle the sale/purchase otherwise there will be no 1031 exchange. 

Underwriting guidelines are more strict than on residential loans, and buyers who might qualify for a condo loan sometimes cannot qualify for an individual tenancy in common loan.

Rev Proc 2008-16 does create a safe harbor for your investment intent at 2 years of investment use coupled with  some other qualifiers.  

In our area we have 3 different HUD agencies that provide vouchers to qualifying tenants.  

This will not qualify for 1031 Exchange treatment under the present structure and "use." 

End result here is that whether or not the new property was eligible for a 1031 exchange you were investing inside a qualified retirement account. 

For example, would a temporary work visa qualify?