There are a few numbers in the equations that can alter your returns, but here's a sample calculation.
Purchase price $350k. 20% down ($70k) + $280k new mortgage. For the example lets say the mortgage is fixed interest @ 3.5%, 5 year term (60 monthly payments) and 25 year amortization.
After 5 years of mortgage payments you will have paid ~$39k in principal + ~$45k in interest.
After 10 years the payments of principal & interest are comparable at ~$84k each.
If you held for 5 years and had ~$39k principal pay down = ~$5571/year. $5571/$70,000 = 7.96% annual (return on initial down payment).
If you held for 10 years and had ~$84k principal pay down = ~$8400/year. $8400/$70,000 = 12% annual (return on down payment.)
These returns are based on zero net new investment over the 5 or 10 year holding period (repairs & maintenance, renovations etc.)
This portion is only based on mortgage pay down and has nothing to do with monthly cashflow or vacancy rates.
There are other costs to consider as well (such as Realtor & legal fees when its time to sell), repairs/maintenance, but this should give you an idea of how the several % return on initial investment could be calculated assuming no property appreciation over time.