The accepted belief is that you are going to buy a property near fair market value so to bring the loan-to-value (LTV) down to a safe level, most banks require 20% down regardless of the purchase price. That’s why you hear banks say that they will fund up to 80% of the lower of appraisal value or purchase price.
In our opinion, if you can buy a property below 70% of the fair market value (like many of our investors routinely do at foreclosure auctions, short-sales, etc), the equity is sufficient enough so we may not require any cash down. Our lending objective is to make safe loans and down payments are just one component to accomplish that goal; purchase price is another of equal importance.
Do some research to find yourself a local, established and trusted private lender. Then start hunting for great deals!