How the deposit affects cash flow

[Matt Donley]

I hear so much about how important it is to have positive cash flow when analyzing a property to buy and hold. What I don't hear is how the deposit you put down on a property affects the cash flow (by directly affecting the amount of money you need to borrow), and how that should affect your analysis. 

For example, let's say I have $20,000 to buy a $100,000 property, but can qualify for a low interest FHA loan that only requires a 3.5% down payment ($3,500). Since my mortgage payment will be relatively high, let's say this causes my analysis to show a negative cash flow.

On the other hand, imagine if I had chosen to put the entire $20,000 as down payment. My mortgage  payment would be lower, so let's say it's enough to provide me with positive cash flow. 

So what's the difference? Should I turn down the deal just because I plan on only putting 3.5% down, just so I can keep extra cash on hand? Why does the deal suddenly get better when I tie that $20,000 as equity into the house? Whether my $20k is in cash, or is tied up in equity, why should that affect my decision based off of the cash flow rule?

What if I was paying 100% cash for the property? Of course the property is going to cash flow better than if it had a mortgage. But the deal may actually be terrible if you calculate it with a mortgage. 

What am I missing here?