HOW MUCH HOME YOU CAN AFFORD, OR QUALIFY FOR, IS NOT THE SAME AS HOW MUCH YOU SHOULD BORROW.
The Front-End Ratio
With deference to the fallout from the sub-prime/credit crisis, remember that lenders are competing for your business, so they are trying to maximize your revenue stream to them for a given level of risk. In modern banking, originating lenders barely wait for your revenue stream of payments. Mortgages are packaged up into pools, thereby spreading the risk/return over hundreds of mortgages, which can then be cut into slices (or tranches), and sold to investors as bonds or investments. The originating lenders get a "cut" on this sale; investors assume an insured risk of poorly performing loans, and use the revenue stream as income and compensation for holding the risk. Everyone makes money, and you are the source of this revenue stream. The higher the interest rate for a given level of risk, the higher the value your mortgage contributes to the pool, and the higher the price the lender can sell investments in the pool in secondary markets. (In practice, its not so "perfect," but these are the basic dynamics). Lenders (and investors) seek to maximize revenue while minimizing risk.
Traditionally, there are two simple ratios lenders look at when deciding how much risk they are willing to take for the anticipated revenue stream of your payments. We will look at those numbers from the perspective of both the lender and the borrower.
The first is called your debt ratio, or more technically your front-end ratio. It is easy. Your front end ratio is the proportion of your gross income that you spend on your core housing expenses:
Front-End Ratio = PITI Expenses / Gross Income
"PITI Expenses" are core expenses relevant to the loan and collateral itself: Principal + Interest + Taxes + Insurance. Just take your mortgage payment (principal + interest), add to that property taxes and monthly insurance (both mortgage insurance [PMI], if required, and home owner insurance) and divide it by your gross monthly income. Your gross income is your income before taxes. Most companies take out tax payments from your pay check before you even get the check, so your gross income is the answer to the question "How much do I make?"; it is not the amount you actually take home each month (your "net").
Many times home insurance premiums and property taxes are added as part of your monthly payment to the mortgage servicer. The servicer accrues the insurance and tax payments in an escrow account and pays them for you when they are due. So often your front-end ratio is simply the mortgage bill you will see each month divided by your monthly gross income (annual income divided by 12).
Lenders differ on what is an acceptable ratio, but usually it is between 0.25 and 0.38. Bottom line: lenders will limit your core housing cost (Principal + Interest + Taxes + Insurance or PITI) to approximately 1/4 to 1/3 of your gross (before tax) income. Lenders differ on exactly what limits they use—those willing to lend you more and accept the risk of your increased indebtedness in return for greater interest payments will use a higher ratio, while those more conservative will use a lower ratio.
If your qualifying income is $60,000 annually, then your monthly gross income is $60,000 / 12 = $5,000 month. Thus a front-end ratio sets a monthly limit at somewhere between $1,250 (for a 0.25 front-end ratio) to $1,900 (for a 0.38 front-end ratio) per month:
Low Front-End Ratio = $1,250 / $5,000 = 0.25
High Front-End Ratio = $1,900 / $5,000 = 0.38
Insurance and taxes are not trivial. Home owners' insurance can run $500 - $1,500/yr, or about $100/month. If you finance more than 80% of the home's value (i.e., put less than 20% down), you will be required to pay mortgage insurance (so-called PMI). This can cost approximately 1/2 point (1/2 of 1%), or $50 - $150/month. Property taxes vary greatly; a rule of thumb is to budget 2% of the house's value per year. A $200,000 home would be $4,000 per year or $333 added to each month's payment. Just these basic expenses could easily add $500/month to the basic principal + interest payments.
The Back-End Ratio
The second ratio lenders often look at is called your household ratio or back-end ratio. This is also easy. Your back-end ratio is just like the front-end, except now we include your other monthly debt. This ratio should not exceed 0.36 to 0.40:
Back-End Ratio = (PITI Expenses + debt) / Gross Income
Lenders will look at both ratios and limit you by the lesser of the two.
Notice that the maximum front-end and back-end ratios are similar—about 0.4 or 40%. So if you carry credit card debt, auto debt, school loans or other debt, your back-end ratio may really limit you, even if you earn more than someone who is debt-free. For example, compare someone who makes $60,000/yr and is debt free with someone who makes $72,000/yr but owes $1,000/month in other debt. Both people gross $60,000 after debt payments. The back-end ratio for the first person sets a ceiling of $2,000 a month for housing:
Back-End Ratio = ($2,000 + $0 debt) / ($60,000/12) = 0.4
where 0.4 is the highest back-end ratio the lender will allow. The person who makes $72,000—and grosses the same $60,000 after paying $1,000/month in other debt—has a lower ceiling of $1,400:
Back-End Ratio = ($1,400 + $1,000 debt) / ($72,000/12) = 0.4.
So even though the second person earns 20% more, and even though both people have the same $60,000/yr after subtracting for servicing their debt, the second person is limited to much smaller monthly payments.
Carrying debt hurts you.
The difference between $2,000/mth and $1,400/mth is substantial in terms of the house you can buy, so carrying credit card or auto or other debt hurts your eligibility for a mortgage, even if you make more and have the equivalent income after serving the debt.
Is this fair? Lenders realize that if your total indebtedness exceeds 40% of your gross income, things start getting tight. The risk of default increases. So it does not matter if you are in debt because of a big house, or a relatively low income, or credit cards: they will not lend you money for a mortgage (or alternatively will charge you higher interest to cover their higher risk) if your total indebtedness exceeds 40%.
If lenders get nervous at front and back-end ratios approaching 0.4, that's a hint that ratios that high are truly associated with increased risk. And they are. Similarly, if ratios approaching 0.25 are at the low end—meaning virtually no lender would not consider lending if your ratio was below that, then this too is a simple signal that core housing expenses of approximately 1/4 of your gross income are considered reasonable for a broad swath of the population. And, indeed, they are. So how much house can one afford (as opposed to how much will they lend me)? Ideally, target your 15-year PITI at about 1/4 of your gross. If that is too tight, then target your 30-year PITI at the 1/4 lower bound and work an upper-limit budget on your 15-year PITI. Remember, houses are like little black holes for maintenance costs, repairs, utilities, cable, phone, internet, improvements, what-nots and forget-me-nots—none of them included in the above ratios—so being conservative on the core expense ratios is wise.