Cash Out Refi Question

[Joshua Levine]

Hi guys, I'm a newb.  Trying to understand the numbers on a cash out refinance while also explaining it to my wife so she can understand it as well.

So let's say I find a home I want to buy.  Home stats

Purchase Price - $60,000

Down Payment - $12,000 (20%)

Initial Loan Amount - $48,000

Closing Costs- $5000

Repairs - $35,000 (using cash for repairs)

Total all In costs = $52,000

ARV- $150000

I then want to go to the bank and do a cash out refinance (75% LTV which by my numbers would be $112,500 and my equity in the home would be $37,500).

$37,500 - $7,500 = $30,000

Does this mean the bank would give me a check for $30,000?  Am I missing something here or do I have it about right? Thank you.