Should I refinance out of FHA to get rid of PMI?

[Mark P.]

So I am at a crossroads right now and would like some feedback. Currently, I rent a place out with a FHA mortgage t 3.75% owing $182k on the loan for a place I bought in 2011 for $205k. I pay $2100/year in PMI and recently got the house appraised at $230k, which brings my LTV to 80%. I live in Southern California and would like to buy something here, but my rental is appreciating and I'm not sure I want to sell just yet.

I was recently quoted 4.125% to refinance, but I would need to come out of pocket $10k plus closing costs ($4k). 

Does this make sense to refinance to give myself the ability to buy FHA in CA with little money down, then sell when the time is right to pay down the principal? or do I keep going?