They are engineering those returns by over raising equity.  

But then raise their rent an extra $50/month for this at their next lease renewal.

Kind of like raising earthworms or Ostriches for skin care oil.  

If you do, use a prepaid card that you don't mind being attached to your account.

You raise the rent a bit each year and that is your cash flow. 

Thank you for your advice, Jason.I agree, A cash-out refinance is indeed a viable solution to my problem.My main concern, however, is the tight timeframe I'm dealing with rather than the availability of funds per see.With an additional three months, I could potentially refinance my other properties to raise the necessary capital.

If you wanted the tenant out, why did you only raise their rent to $1k below market?

Also, don't dismiss paying for capital raising.

However, there’s no set rule on how long you must hold the home as an investment before converting it to your primary residence, but it’s generally advisable to rent it out for at least a year to avoid raising any IRS concerns.

Especially if you're a first-time portfolio buyer, these online platforms can help you raise capital from multiple investors.Work with an experienced commercial real estate broker.