Is Equity necessary?

[Tony Szymczak]

I am VERY new, which will likely be obvious by my question :). I am looking to "buy and hold", and am reading that you "make your money when you buy" a home, i.e. buy a home that is a deal because it will come with equity in it. But let's say I instead overpay by $10k for a home, but through deal analysis even with overpaying it is still going to net me a 15% annual return on my investment after all expenses. Other than if I needed to sell in the first few years, my brain still wants to think this is a good investment because of the good ROI. Can someone point out the error in my thinking? Thanks in advance, and take it easy on the new guy!