Is it possible to Cash Out Refinance without closing costs?

[Victor Mondragon]

I live in Texas and am working  on using the equity in my home to get a loan and construct a garage apartment to rent out and try my hand at land-lording. 

I understand that most banks like to use this formula: (Value of home - amount owed) .8

I have enough equity in the home to where 80% of the difference in value minus balance is sufficient to fund my construction project. 

All 3 banks I have approached have given me the same type of offer:

1. We'll offer you a cash out refinance where you pay us ~$4000 in closing costs and we'll refinance your entire loan and offer you a good interest rate 3.875%

2. We'll offer you a Home Equity Loan with 3% closing costs (on the total amount of  your loan) and a not so good interest rate of 5.49%

I'm very inexperienced in the loan industry.  Is there a way to do a cash out refinance without having to pay the hefty closing costs?