Thursday, August 28, 2008

Price to rent comparison info

This is kinda a PSA post, along the lines of the rent vs buy calculation. Lots of people have been clamoring about house prices getting back to normal, and although that's happening, they are far from there yet. Many people are confused as to where they should be, and there are lots of useful guidelines (3x annual household income, etc.), and here's another one:

A useful metric for calculating when prices are equivalent to rent amounts.

If the total ownership amount (mortgage + taxes + insurance + HOA + upkeep) minus the amount going into principle is equal to the rent, the price is about "right". The rationale is that if you were renting, you could be saving the principle amount in a bank account, and be accumulating just as much "equity" as the person paying a higher cost to own. For a 30-year mortgage, about 1/4 of the payment is principle during the first 10 years or so, and it's about $6.32/month per 1K borrowed (for a 6.5% mortgage).

So say you have a condo which would rent for $2000/month, and has $400/month HOA. If we assume $100/month for insurance, $100/month for upkeep, and 2% taxes, we could compute the "right" price 'p' relative to rent 'r':

***** Edit: charles pointed out my math is wrong; interestingly the "right" prices are even lower with the correct numbers. Numbers corrected below. *****

p * 0.00632 + p * 0.00167 + 100 + 400 + 100 - (0.25 * p * 0.00632) = r
p * 0.006416 + 600 = r
p * 0.006416 = r - 600
p = (r - 600) * 156

So with r = 2000, the "right" price should be ~$218,000.

For a house, the calculations are similar; figure $200 for insurance and upkeep instead (no HOA though), and you get:
p = (r - 400) * 156

With r = 2000, the "right" price would be a higher ~$250,000.

Note: Down payments are not included because then you'd also have to include lost opportunity cost on the down payment amount, which works out to be roughly equivalent to assuming 100% financing as far as the ratio goes.

Feel free to use this metric the next time someone tells you a property is affordable, and/or reasonably priced. This is above the amount that intelligent investors will buy property, but it's close enough to be a good measure for when prices are "right".


  1. This is a great post. Something like it should be required reading for anyone borrowing large amts of money.

    I got a slightly different equation when I solve it:
    p*(0.00632+0.00167-0.25*0.0632)+600 = r.
    I don't get p * 0.00578 + 600 = r
    Instead I get p*0.00641600 + 600 = r.
    p = (r-600)*156.

    I'm inclined to model the problem just using 6.5% and not taking into account principal. The monthly payment includes some principal, and then you adjust for the by subtracting 25% of the 1st 10 years of payment. My inclination would be to say:
    This gives me p = (r-600)*141. That's an even lower valuation.

    There's no exact answer, as far as I know. Any of these formulas is a good rule of thumb. Most properties in my area in Madison, WI, which is supposedly flyover country free from speculative mania, are overvalued compared to any formula I can come up with.

  2. I think your initial formula is correct; my math seems off. Which is funny, cause it makes the principle "value" even smaller than my approximation.

    As for the "flyover" areas, I think the bubble probably affected everyone some, although certainly more in the more expensive areas (eg: LA, where I am). Every proclamation I have heard about some area being immune from the bubble has either been proven wrong, or I would expect to be proven wrong. To say otherwise would be to imply there were areas of the country where nobody was trying to make a quick buck, and that's one thing which seems to be ubiquitous in America.