@Ryan Dalton, you are not alone in thinking that just paying off properties results in greater cash flow, so why wouldn't people do that instead of leverage (I get this question a lot).
If you talk to most REI's, they will talk about leveraging your money as one benefit of REI vs. other investment vehicles. I always try to break it down this way: remember the 5 ways to make money in real estate, understand how leveraging your money can help you make more money, and understand how holding a mortgage lets you pay off a loan with money from the future (which, due to inflation, is worth less).
5 Ways to make money in REI
1. Equity capture at time of purchase (buy low, buy distressed and value-add, etc.)
2. Equity appreciation (year by year, your property value may go up in value)
3. Cash Flow (so far, the bulk of this thread is only talking about this)
4. Tax benefits (interest is deductible, depreciation is deductible = many investments can net you income but you end up paying $0 in taxes due to the many deductions available)
5. Principal pay down.
So let's go back to the illustration of buying a $100k house and paying it off, cash flow of $10k per year (your example said $1k/mo which equals $12k/year, but let's go with $10k for ease of calculation). You already did some calculations, I'll go with your numbers and you already admit that if you can leverage and pay only 10% on 10 properties, your cash flow is greater than the single, paid-off property even when factoring in property management.
But the story doesn't end there. Let's say you buy your properties well, and capture at least $2k in equity per property by negotiating the price down (very conservative # and you can easily do better than this). 10 leveraged properties = $20k extra earned equity vs. $2k earned for 1 paid-off property.
Let's also say the average yearly appreciation is 2% (again, pretty conservative #). 10 leveraged properties = $20k extra equity per year vs. only $2k for 1 paid-off property.
You will likely be paying taxes on 1 paid-off property because you are no longer deducting interest, which is a pretty big expense. If you had 10 properties, you could easily be getting a net tax deduction (instead of paying taxes) due to the multitude of tax benefits (besides interest and depreciation, you have flexibility to value-add to properties gain additional tax deductions).
Finally, you will have 10 people paying off your mortgage vs. 0 people (your 1 property is paid-off already, remember? And who paid for that property? You did. Who is paying for the 10 leveraged properties? Your tenants.).
That is the power of leveraging. You are easily looking at an additional $50k or so in the first year.
One final note, Brandon or Jay mentioned in another thread (or podcast?) about the power of leveraging (taking out a mortgage) which allows you to use future money to pay for your mortgage. Let's say you took out a $100k mortgage today and paid $10k down. You will pay off the $90k over the next 30 years on a 30-year fixed. In 2045, your mortgage payment will remain the same, but due to inflation, how much do you think everything else costs? In 1986, you could get a Honda Accord for around $9k. Today, 30 years later, a new Honda Accord costs $24k. Yet, if you took out a mortgage in 1986, you would be paying it off in 2016 with the exact same payment using 1986 dollars. No matter how much inflation the economy undergoes, on a traditional, fixed mortgage, your payment never changes. You are using future (devalued) money to allow you to buy a property in the present.