When shopping for mortgages, the obvious question is: which set of mortgage options will cost me the least? This turns out to be a fairly complicated question to answer. The difficultly in giving a concrete answers rests in the fact the certain assumptions have to be made in order to calculate long-run mortgage/housing cost. Below, I list the important variables involved in calculating mortgage/housing costs. The variables in bold are not known a priori when one buys a house, and the parenthetical values are the values assumed for our analysis.
So, the process for calculating future value cost of owning a home (financed with a mortgage), is simply a function of all of these variables. Fortunately many of the variables are known (to a large degree). However, two variables must be estimated in order to calculate costs: the rate at which the purchase property will appreciate and the rate at which any other investment assets will appreciate (return on investment; ROI).
- Known Variables
- Closing Cost (4% of purchase price)
- Home Insurance Rate (0.46% of home value)
- Tax Rate (1.35% of home value)
- Cost of Sale (6% of selling price)
- Mortgage Term
- Points (0% of mortgage loan)
- Interest Rate (4.8%)
- Down Payment
- Purchase Price ($100,000)
- Unknown Variables
- Home Appreciation
- Investment Appreciation
As an estimate for ROI consider that the average ROI on US stocks over long periods of time varies from 8%-12%. On the other hand, house appreciation has only sustained an approximately 3% return over long periods of time. There are notable exceptions like high-demand urban areas where home appreciation approaches 8%. Interestingly, as we will show in a subsequent post, the choice of mortgage is completely independent of the house appreciation rate, but is highly dependent to the non-home ROI.
Below are several plots for various ROIs and mortgage options. Two general conclusions can be drawn from these plots:
- When the ROI (i.e. the opportunuity cost of money sunk in a house) is high, You want to keep as much money as possible and put as little into paying off your house as possible.
- When the ROI on alternative investments is low, it also makes sense to pay off your home as quickly as possible.
By high ROI, we mean and ROI that exceeds the mortgage rate. The plots show, that for high ROI, even after the short-term mortgage has been paid off, the opportunity cost of having all that capital sunk in a house far out paces the cost of additional payment.