I'm sure somewhere there is a calculator that does this, but I haven't seen it. A quick figuring of how much a house returns as an investment would be the amount saved on rent as a % of the invested value.
e.g. If rent costs $1750 per month, and taxes/insurance/maintenance for a purchased home end up at $750/month then buying the house netted $12,000/year. for a $200k house that would be 6% yield. This is with zero house appreciation. So that would be if you are buying the house outright.
The nice thing is that that ROI is independent of where you get the money from. So if you financed with a mortgage for 100% of value, and with an interest rate of less than 6% (real, not nominal) then you are getting more out of the investment than the bank. If, on the other hand, your interest rate is higher, or if the house price is much higher, then that may not work out short term.
Investing otherwise is a tricky figure, but your return with mortgage roughly works out as the difference. The problem comes with the "what are you doing with the money otherwise" question. Rent is not an investment. If rent and mortgage are equivalent then mortgage wins (if the above is positive) though it may take a few years to offset closing costs. If rent is less, then you would need to only look at return on the difference and compare the total values not just percents.
This is a valuation that ignores inflation and appreciation. If the house is appreciating and/or if rents are inflating, than the numbers shift more toward buying. If the house is falling in value or we have deflation in rents, then it shifts away. A generally safe assumption would be to add 2% for inflation. Appreciation is a non-factor to me as it only factors in upon selling and is likely eaten up by a subsequent purchase.
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