Once it is paid off, open a LOC to have access to that equity and repeat it.

Would those ultimately affect the Cash on Cash ROI? 

ROI/COC infinity.Repeat - Since you have no money in the deal, you will want to repeat the process and scale your investment portfolio.Traditional Rental      Buy - Purchase the property with 20% down.Rehab - Only minor rehab if any.Rental - Select a tenant and rent the unit at market rent  Refinance - Not necessary since the purchase included financing. 

You do want to be at market value, but you also don't want to lose monthly income due to vacancy. 3%-5% increase is pretty common and you can repeat it yearly.

Cash-Out Refi and Repeat.

But, ARV itself, is not affected by closing costs, profit is.A loaf of bread costs $3.50 and is taxed at 8% does that then mean the loaf of bread is worth $3.22?

Also, does anyone know if it will affect rentals in any way?

in order to not repeat myself, I will say, I have talked to a couple lenders, and one suggested the conv-95 loan. which would be owner occupied, for at least 90 days, and isn't that much more expensive to start out, but you do get a few extra equity points. 

@Isaac Bazek-Buy, Rehab, Rent, Refinance, Repeat by David Greene (RE)-Real Estate Investing Gone Bad by Phil Pustejovsky (RE)-Investing in Real Estate by Gary Eldred (RE)-Quit Like a Millionaire by Kristy Shen (FI)-Playing with FIRE by Scott Rieckens (FI)-I Will Teach You to be Rich by Ramit Sethi (FI)-The One Thing by Gary Keller (Inspiration)-Am I Being Too Subtle by Sam Zell (Bio)-Shoe Dog by Phil Knight (Bio)-The Big Short by Michael Lewis (Business)-Liar's Poker by Michael Lewis (Business)

From my understanding,  BRRRRing is paying out cash on a distressed property through a private lender or with hard money loans at a huge discount from market price, rehabbing, renting out, cash out refi to AFV of 65-70% of cash in which is then used to pay back the private lender or hard money, and used to repeat.