In an earlier post, I exposed the math of mortages in layman’s terms.  Mortgages calculations are done using the formula for calculating Net Present Value, meaning the value today of money dished out tomorrow in recurring payments to the bank.  However, there is more than just the pure interest rate of a mortgage involved in buying a home.

The economy does not stand still for the few decades it takes you to pay off your mortgage.  Inflation means that your a dollar today will be worth less tomorrow, as the price of goods and services generally increases over time.  Plus, property takes effort (and money) to keep up.  There are property taxes, condo fees, maintenance costs, and utilities to pay.  Things that you, as a renter, have never before heard or worried about.

The assumptions

Here is a link to download the Excel file for these calculations.

To do any sort of estimate, certain assumptions have to be made.  For the following calculations, here are our assumptions:

Obviously in a volatile market, these assumptions will not be reliable.  For that reason and others, we need to set limits on how far into the future we predict given these shaky assumptions.  Shorter-term predictions are more likely to hold water.

The lost decade

Here is the 10-year cash flow resulting from these assumptions:

Given the declining real estate market for the first two years (the “property appreciation rate” row), coupled with inflation (assumed to be a steady 3% in the initial variables), we’re predicting that selling the property within the first 10 years will be a loss.  Although the nominal value of the property (the “property value” row) exceeds the buying price in year 5, selling it would still lead to a loss.  This is because the nominal property value does not take into account the time value of money.

The cost of goods and services increases every year, meaning that a dollar today is more valuable than a dollar tomorrow.  This is the definition of inflation – things cost more in the future.  So even though the property value exceeds its buying price in 5 years doesn’t mean it’s necessarily worth more in terms of today’s dollar value.  In fact, if we assume 3% inflation, even with the real estate market on the rebound after 2 years of negative gains, the value of the property in terms of today’s dollars (the “present value of property” row) at the end of year 5 is still only $443,000.

So if we were to sell it, even after 10 years, we’d be taking a loss (an 11.24% loss to be exact, as shown in the “return on investment” row). In fact, with this model, it’s not until year 13 that we would be able to sell the property with anything resembling a profit.

Another thing to notice is that this model shows that our yearly expenses (the “cash outlay” row) for a property costing $500,000 are significantly more than our current rental situations.  The first year requires $88,000 due to all the costs of buying (equivalent to $7,333 per month).  Subsequent years hover around the mid-$50’s (equivalent to about $4,600 per month) for the first ten years.   To keep costs near what they are today would require purchasing a property closer to $300,000.

The second decade

The second decade sees the property start to gain positive value.

You can see that by year 13, the property’s present value, meaning its value in terms of today’s dollars, is worth $500,567, about what we paid for it.  So selling it at this point would break even.  However, this break-even point does not factor in all the fees and operating costs we would have put into the property during the first 12 years of ownership (all the stuff in red).  Those expenses, if counted, would still lead to a loss for several more years.

So after the second decade, we can optimistically be said to have barely broken even.

The third decade

In the third decade of ownership, when we’re in our mid-60’s, we see some real gains.  Assuming steady inflation of 3% and steady real-estate appreciation of 5% (very shaky assumptions), we are no longer working for our home, but our home is working for us.

At the end of 30 years, we are full owners of the property, having paid off the private loan in year 10, and the mortgage in year 30.  Things are starting to look up.  If we were to sell the property at the end of this decade, we would have made a modest profit of (38%, or $194,000 in present dollars), and have had a place to live for 30 years.

Of course, the years after the 30th year, assuming the world is not overrun by vegan environmentalists with the sane people living in yurts by that time, would be the most valuable in which to hold onto the property….

Conclusions

If my calculations are at all in the right order, then we cannot afford to buy anything more than $300,000 if we want to keep our monthly outlays similar to what they are today in our rental situations.  If you plug in “$300,000″ in the “property cost” assumption, you’ll see that our cash outlays would average around $35,000 for the first bunch of years, which is not a major change from today.   If we assume a “property cost” of $500,000, then we get into cash outlays higher than $55,000, which require significantly more commitment.

Most questionable of my assumptions are the inflation and appreciation rates.

Another important factor is the “private loan” repayment.  I currently have the assumption that we borrow $200,000 from private investors and repay it within 10 years at 3% (to keep up with inflation).  If we get rid of the private loan and take out a bigger mortgage instead, then our cash outlay actually becomes more manageable, and might allow us to cover a more expensive property, albeit at a higher overall interest rate.  If you change the “private loan amount’ field, you’ll see the changes appear in the “cash outlay” row.

So we need to determine whether the assumptions and calculations are believable.