Houses are a little bit different in that a house often is worth more than you paid for it, and unless you got one of those negative amortization loans it's almost certainly worth more than the outstanding mortgage balance. In the traditional sense, then, you're in the black: disposing the asset will more than erase any associated liability.
The traditional way of looking at things defines an asset as something that you can convert to cash. A liability is money that you're committed to paying at some point. House, car, boat, home furnishings, etc. are assets. Mortgage loans, student loans, credit card balances and such are liabilities. If you add up the assets and subtract the liabilities, you obtain a number called "Net Worth"--the amount of money you'd get if you sold everything and paid off all of your debts. Not surprisingly, a very large number of people--even "successful" people--in the United States have a negative net worth.
Net worth is a nice pretty number to figure out, but it's almost meaningless. It's a fictional number that's usually based on over-valued assets and unreasonable assumptions. And it's a worthless number because you can't spend your net worth. In most cases, the best you can do is borrow against it.
A more realistic way of viewing things, popularized by Robert T. Kiyosaki's book Rich Dad Poor Dad
By this definition the only asset that most of us have is our daily job. Your house, even if you have it paid off, is a liability. Why? Because it still costs you money every month for taxes and insurance. Your car is a liability, requiring a loan payment, insurance, gas, registration, and maintenance. Almost anything you buy is a liability, or at best neither--that is, it costs you nothing to maintain.
The trick to getting ahead is to increase your assets and reduce your liabilities. Most of us increase our assets by putting our money in savings accounts, certificates of deposit, or mutual funds that invest in dividend paying stocks. Rental property is another popular asset in which to invest, but remember that by our definition it's only an asset if the monthly income from rents, plus any tax advantages, is more than the monthly outlay for the property. The equity you're building in the property with each payment doesn't count because it's not money going into your pocket.
I'll be the first to admit that this isn't the most sophisticated way to look at things, and that any second year accounting student could poke holes in some of the reasoning. Many people will dismiss it as being too conservative and short-sighted because it doesn't take appreciation into account. But that's okay. I've seen all too many people with high net worth figures work their way through bankruptcy court because their cash flow situation became untenable. I'd rather maintain a positive cash flow and treat any asset appreciation (in the traditional sense) as a bonus.
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