Amount needed for investment loan when you already have equity

[Todd Hanks]

After flipping several houses over the last 3.5 years, I am now wanting to get into rental property, so I bought a piece of property where I can build 7 new houses.  Since I got my contractor's license at the beginning of the year (mainly for my own real estate purposes), I will be contracting them myself.  Instead of selling, I want them to be rental properties.  My question regards the percentage down that is required and how it pertains to equity.  For easy numbers sake, if I build the houses for $100,000 and they appraise for $150,000, then I will have 33.3% equity in each property.  I have read that you have to put 20% down on the first 4 rental properties.  Does that mean that if I wanted to mortgage only the $100,000, the lender would still require me to put down 20%?  Or would the 33.3% equity (proven by new home appraisal in hand) satisfy the 20% requirement (meaning I wouldn't have to come up with much cash, if any)?  (NOTE:  I would be building the house with my cash and then wanting to get a refinance mortgage so that I could get the my invested money back and start on the next house).