The web is full of articles on buy-vs-rent or "pay down the mortgage" vs. invest, but most authors seem very confused by the large number of variables. And almost no one talks about the benefits of not paying rent.
If I bought a 0K property with cash and if living there saved me K in rent per year, wouldn’t that be equivalent to a 12% return on investment (modified of course by all the other variables like interest deductions I’d get if I financed; property tax and maintenance costs; the fact that rent is paid post income tax, etc.)
If I’m in the middle of paying off my home, does my equity pay me back in the same way? or is the saved-rent benefit irrelevant till the day my payments end?
Does anyone know where to find a complete list of all of the variables involved (and maybe a calculator?)
Does anyone know where I can find something written on this subject by a qualified economist/mathematician?

the value of money invested in own home; is the rent saved equivalent to a dividend.
and the increase in the value of own home,is the bonus got on the value of money invested.
Your math is way off.
There are numerous online calculators that will perform this comparison for you, Yahoo’s calculator appears to be a fairly good one.
It’s clear that your point about saving $12k per year in rent is valid. The problem is that your other point about "modified of course by all the other variables…" is also valid and in fact requires such a large correction that the other factors could easily overwhelm the $12k in saved rent. What if, for example, you need to cash in some stock market investments to pay cash for your $100k house and you discover years later that you could have averaged 20% per year by retaining your stocks. Just by correcting for the so-called "opportunity cost" of not having money available for other investments would cause you to go from a $12k profit to a $8k loss. Furthermore, these calculators require so much input of things that can’t possibly be known ahead of time, future inflation rates and home price appreciation among them. Back during the housing bubble many investors used wildly optimistic assumptions about home price appreciation to justify buying over renting no matter what the cost. Now, of course, home prices are starting to near bottom, so perhaps people are being unduly pessimistic about the chances for future appreciation.
So use the calculators for what they’re worth, but keep in mind that they are at best just a reasonable estimate. Probably your best bet is to look at a house through the eyes of a prospective landlord. If you imagine buying the property in order to rent it out and can produce numbers that show a positive monthly cash flow, then the chances are excellent that buying will be a good decision.
your math is off. first of all that 100 grand has to come from somewhere and real estate nororiously has one of the worst long term returns of any asset group.second of all you cant buy anything other than a trailer in a trailer park for 100 grand where i live and after 20 years of living in it no one will want to buy it from you. now, also, surely there will be other expenses involved in buying that home such as condo fees and property taxes that you have not had to pay before, diminishing your return. if you are in the middle of paying off your home you are finally putting some decent equity into your home and not just paying interest like you do at the beginning of a mortgage. i think that owning your own home is very important and everyone should do it but its not as cut and dry as you have tried to make it here.
-johnny wadd
Sorry but your logic is deeply flawed…
You assumed you ‘saved’ $12k per year by not renting. But you lost the economic buying power of the $100k you put down to buy the property. You overlook maintenance and property taxes.
A more realistic assumption is that you may have been able to rent for less than the $12k per year you cite here. That is why you have to perform a lease/buy decision before buying.
Had you saved the difference and invested it you likely would have come out ahead during most investment cycles since the 1930′s. The problem of course is most are not disciplined enough to save and invest the difference.
Housing is really a cost. Not an investment. For most people it is a great way to build equity because of the forced savings aspects of it. But numerous studies have shown that the return on residential real estate after factoring in all costs returns less than the 1 year Treasury bill.
BUT for most folks it is a positive return over their lifetime. It builds stable communities and provides a taxbase for schools. For that reason the US has favored it with interest deductions to help provide a tax incentive.