# Hypothetical Mean

Commentary from an Actuarial and Economic Perspective

## Housing and Gas Prices: Calculating the Impact

James Hamilton’s thoughts on the link between housing and gas prices  reminded me of a rough back-of-the-envelop calculation I did when buying my own home four years ago.

My wife and I bought a home in central Little Rock, with a 10 mile daily (roundtrip) commute.  We paid a premium for the proximity to downtown.  We both place a high value on family time, and likely would have paid this premium regardless.  However, a motivating factor was the possible increase in gas prices.

Little Rock is surrounded by commute communities:  Conway, Sherwood, Cabot, Benton, Maumelle, etc.  I assumed that an alternative housing arrangement would result in an additional 60 miles of driving, for roughly 200 days of work.  Under those assumptions, commuting would add 10,000 miles per year.  Assuming an average of 30 miles per gallon, that’s \$333 per year for gasoline alone.

If you further assume an average expected residency of 20 years and a 3% discount rate, then a \$1 increase in gas prices translates into more than \$5,000 of added cost to the commuters.  That’s \$5000 of potential appreciation for homes like mine.

That’s one reason I’m not disappointed by the rise in the price of gas.

Notes on assumptions:
* The 20 year residency may be too high.  If you assume a 10 year residency, the gain drops to \$3,000 in present value.

* The days per year assumption is rather low for a full-time employee; I’m implicitly hedging the assumptions against work-at-home opportunities that may become more of a norm in the future.

* A 3% discount rate is a bit low, but it’s roughly the after-tax interest rate for our fixed-rate mortgage.  A 1% increase in that discount rate reduces the potential price appreciation by about \$400 (out of the initial \$5000 estimate).