I know we've beaten this topic to death, but I want to make sure I understand the math. Due to a homestead exemption, I have a fairly low property tax rate (0.5%). If I'm using the wrong formula, then I made a worse financial decision when I bought than I thought I had, and I want to know it so I can deal with it.
Here is my derivation of rent/buy cost equivalence:
At a safe withdrawal rate SWR, renting requires principal P = 12*rent/SWR.
If purchasing a house of cost C out of P, part of P must cover the house, and part must cover annual expenses. If the annual expense ratio is E (typically property tax, maintenance, and insurance), then annual expenses are E*C, and E*C/SWR must be set aside to pay for expenses. This leaves P-E*C/SWR to buy the house. To come out ahead, the house must cost less than this amount.
C < P-E*C/SWR
C*(1+E/SWR) < 12*rent/SWR
C < 12*rent/SWR/(1+E/SWR)
C < 12*rent/(SWR+E)
Double-checking this, if E were 0%, then you just have to spend less than P to buy the house and come out ahead. If E were the same as the SWR, then C must be less than P/2 in order to leave P/2 to pay expenses, which are E*C<E*P/2=SWR*P/2.
Critiques, other perspectives, general advice, etc., are welcome. Many thanks for your help.