Equity in the Property

[Blake Norman]

I need clarification on a subject that my friend and I were discussing earlier today. I have heard about this concept of various episodes of the BP podcast. Please feel free to offer any input that may be relevant.

If I buy a house for $80,000, and it is valued at $120,000, do I have $40,000 equity in that property? If so, can I draw that $40,000 in cash from the lender to use to purchase another property?

Does a house need to appraised at $120,000 for it to be "valued" at $120,000? Is the appraisal what sets the value of the house?

I hope these questions are clear. Please let me know if I need to clarify any of these questions or statements. Thank you in advance!