Vishal,
The most important metric in any investment is something we refer to as cash on cash return (COC). What makes RE such an excellent opportunity is that even the most un-imaginative investor is able to leverage $25,000 into a $100,000 purchase by way of a mortgage. So, let's consider a purchase of a $100,000 duplex for cash vs. 75% LTV financing.
Let's say that the 2 units in the property rent for $550/mo. each, and operating costs for the building (all costs excluding the cost of money) are $400/mo. This would leave you with $700 of NOI (net operating income). If you have no mortgage payment, this is also your CF. Thus, having purchased the building for cash, you will recover $8,400/year. This is a 8.4% return on your investment of $100,000 to buy this duplex.
Now let's say you put $25,000 and finance $75,000. At a high by today's standard 6% amortized over 30 years, your payment would be about $445/mo. This would bring your CF down to $255/mo. (NOI – Mortgage payment). This is 3,060 annually, which seems a lot lower than the $8,400 without a mortgage. However, because you only used $25,000 of your cash, the COC is actually 12.2%. Obviously this is a lot better than 8.4% return.
Now – you could use the cash flow to pay off the mortgage. Your CF would shoot up to $8,400 without a mortgage payment. But the return on your money would go down. On the other hand, you could save that cash flow and use it for a down-payment on another 3 buildings just like the first one. All things being equal, your CF would go to $255 x 4 = $1,020. You would diversify risk by having 8 rent checks instead of 2. And you would find out that there are significant benefits with respect to taxation, specifically if you don’t make too much at your day job.
This is of course overly simplified. I am just throwing numbers on paper. But this reflects my experiences as an investor very well. So, the question is - why pay off the mortgage? Hope this helps. Good luck!