Can you help me analyze a refi?

[Cory Melious]

Hey y'all

I'd love some input on a refi I'm currently doing. 

Here's the skinny - 

Bought a fixer upper 1 yr ago for $60k. It was assessed at $85k. I know that's not a good gauge of value, but it's what I had at the time. 

I've put $28k in repairs, spent $13k on Mortgage payments (thats down payment, mortgage and interest combined), and some other expenses like placement fee's, etc. 

All in I'm at $51k expenses. Now I'm refinancing (long story short I was privately financed by the former owner at 6% and he was charging me $500/mo....250 principal, and 250 interest, so I needed to finance with a bank and wanted to lock into a lower rate since they are shooting for the stars right now). 

I had initially wanted to refinance at $55k (enough to pay off the remainder of the mortgage and cover the closing costs). 

BUT

After the appraisal came in at $105k...I decided to refinance at $73.5k to pull out some of my cash. 

Heres the main questions---

They are charging me a higher rate now to do a cash out refi instead of traditional refi (i guess, idk how they're different)...to the tune of about $3k. SO, doing a cash out refi I will be sacrificing about $3k to pull out $15k. 

Is it worth it?? Am I missing something?

Cory