Cash out refinance question

[Mike Emokpae]

I am under contract on a new home that will become my primary residence.  I was initially going to use the proceeds of the sale from my current primary residence to repay myself my down payment (currently coming out of my personal cash reserves) and for renovations on the new home.  

The thought just occurred to me today - instead of selling my current home, can I do a cash out refinance on the home, keep it as a rental, and use the remaining cash to repay my down payment and renovations on the new home?  I am expecting ~$100k in equity after closing and fees from the sale of my current home.  Is this possible?  If it is possible, is it a good idea, assuming the rental rates in my area and all other financial analyses involved with turning my home into a single-family home rental works out?  

Thank you all for your help with this!