BRRRR vs fix & flip strategies

[Elizabeth Justice]

My husband and I are in the option period of our first deal.  The house needs a lot of work, but nothing major came back on the inspection that we weren't aware of.  So after several offers it looks like we may finally close on a deal (yay!).  Because we don't have much cash, our plan is to rehab and sell it to build capital.  The numbers are:

ARV = 150K

Purchase = 72K

Rehab = 22K

Profit after closing costs, holding costs, loan costs = 29K (but I expect unexpected expense to lower that a little)

I'm interested in the BRRRR method, but my understanding is we could only refi for for 105K, or 70% of ARV. Our expenses of house (72K)+rehab(22K)+closing costs(1440)+loan costs(10K)+holding costs(3K) are almost 109K. So we would have to bring cash to the table for the refi.

So how do you make the BRRRR method work when you don't have a lot of cash and don't want to raid your 401K? Do you have to negotiate lower with this in mind, or do I have some assumptions wrong?