First, take your monthly amount of rent. Let's say $3000 for a round number.
Then, you need to subtract something to represent the maintenance (for a coop), or common charges + property taxes (for a condo) that you might be paying. This amount varies a great deal based on the size of the property that you are looking at. Common amounts are $500-$800 for a one bedroom or $800 - $1000 for a two bedroom, and go up from there.
Let's say we're looking at a one-bedroom and want to be conservative, so we'll take $800 as the number. $3000-$800=$2200. Notice we didn't include insurance. This is because homeowners policies are not a very big jump from renters insurance policies, so we'll assume that cost remains the same. (If you don't have a renter's insurance policy, you should seriously consider getting one up - your belongings are not covered by the landlord's insurance policy if they are stolen or destroyed).
So we have a principal and interest payment of $2200. Now, we look at the current interest rates. Your bank's website can provide those to you. Keep in mind two things: 1) interest rates change daily and 2) when the economy is good, interest rates tend to move up. So if you are doing this exercise for a future purchase six months from now, you might want to add .25%-.5% just to be safe. (of course you can always buy the interest rate back down if you have the cash and the desire).
At the moment I am writing this, I just clicked over to the Bankrate.com website. Bankrate is an independent web site that publishes information about mortgage rates across many banks and regions of the US. Keep in mind that New York rates may be different from the national average. Coop loan rates are usually higher, as are condo loans, though somewhat less so. Indeed, Bankrate gives me a range of 3.97%-4.89%, while the national average is listed as 4.29%.
Let's again be conservative and use 4.75% as our rate. Now, we flip over to http://www.realestate-calc.com/Mortgage_Calculators/Mortgage_Amortization.asp, where we find a nicely laid out table of the cost per $1000 borrowed. Scroll down to 4.75 in the first column, then slide your finger over to the 30-year column (all the way to the right). The number is $5.22. That means for every $1000 you borrow at 4.75% interest rate, your monthly payment is $5.22 for a 30 year self-amortizing loan (meaning when you hit the last payment of the 30 year loan, you have paid off the loan).
Ok, so now we take your monthly rent payment less allowance for monthly maintenance fees (remember that? $3000-$800=$2200), and we divide $2200 by $5.22. So in other words, we are seeing how many thousands of dollars we can service with the $2200 we already pay. The answer? 421.456. Just multiply that by $1000 (or move the decimal over 3 places) and you'll get $421,456, which is the amount of mortgage you can carry, plus maintenance charges and (if condo) property taxes.
Now let's take that one step further. You generally need a 20% down payment to get a mortgage. Most coops require that at least 20% be put down. Condos might only require 10% (some coops do as well, but banks have become more stringent since 2008 and it's harder to get a 90% mortgage on a coop than it once was).
The amount of mortgage that we figured, $421,456, represents 80% of the total cost of the property that you can purchase. This is the maximum loan to value ratio (or LTV) that most loans allow. Dividing that number by four tells us what 20% of the total price must be. Answer: $105,364.
To get 100% of potential purchase price, we multiply that number by five. (because 5 x 20% = 100%). So $105,364 x 5 = $526,820.
So, the total purchase price that you can likely afford while still keeping a similar housing payment to what you pay in rent is $526,820. This assumes a down payment of $105,364 (the 20% number we calculated earlier).
In the hottest parts of Manhattan, this will get you a studio or a small one bedroom. In northern Manhattan, this will get you even a two bedroom. Even in Brooklyn, you can score a very nicely sized one bedroom or even two bedroom depending on area (though probably not in Williamsburg, alas). So if you feel you can't afford to buy, think again. You can afford to buy if you can afford to rent at Manhattan's prices.