Question on Equity

[Eric Mass]

So I've been pondering on a certain topic and want to make sure I understand it in its entirety. Let's say for instance, I come across a property for say $15,000. It needs another $10-15k in rehabbing. Once completed, the ARV is 65k. If I'm able to pay those cost (the property, closing cost, rehab, etc.) in cash in the beginning, how am I able to get the equity out of the house from the ARV if there is no mortgage? Or should I not pay those cost off in cash? Thank you in advance and much love.