You generally have addressed the three factors correctly, except for this: Leverage does not increase the inherent returns of an investment, but rather increases the risk of those returns.
Actually it does increase the rate of return, but he did not calculate the rate of return right because he was using different comparison types. It also does increase the risk associated with those returns. In fact risk and rate of return go hand in hand. On a more risky asset, you will always expect better returns. What this points to is the difference in ROI and ROE. ROI = Return On Investment. ROE = Return On Equity. In the scenario, The equity is the price of the house, the investment is your down payment and the sum of monthly payments (discounted by time). In the scenario above, if the purchase was cash (no mortgage), the results would roughly be
ROE = 4%
ROI = 4%
With the mortgage as described, the numbers end up being:
ROE = 4%
ROI = 20% because only the down was the invested capital considered. The monthly payment was omitted, which is also invested capital.
There is one problem here. The amount for payments on the mortgage are offset against the rent it displaces. The comparison shown is not appropriate for this scenario. You want to compare return on the $80,000 when invested (rent scenario) vs the gain in owning the house (buy scenario). Doing this, you can balance out the monthly rent vs mortgage payment. You would have to get 20% or better return on $80,000 to make renting match buying. Less than 20% return on $80,000 would mean buying is better, greater than 20% return means renting is better (of course not taking into account taxes on gains).
In terms of leverage increasing returns on investment, look into something known as ‘carry trade’ and spreads. Leverage gains you when the growth rate of the asset is higher than the interest rate you are paying on the loan for the asset. If it is the other way around, you are sucking wind.
