How much of a benefit to BRRR purchasing with cash?

[Eric James]

I'm using the BRRR strategy and trying to figure out how much of an advantage it would be for me to purchase with cash, and then cashout refi after renovations are complete. My alternative is financing with a local bank, that will finance the purchase as well as repair costs (as long as the ARV of the property appraises well) for 20% down.

If I buy with cash I would be able to purchase 1, or possibly 2, properties at a time (I'd be limited by my capital).  If I use financing I could probably manage 4-5 at a time (at various stages of completion).

So, I'm trying to decide how much of an advantage it would be for me to be able to give sellers cash offers and quick closings.  Can anyone provide input on how much of an advantage this might be?  Is there any way to quantify how much of a discount I might be able to purchase properties at if offering the cash/quick closing terms?