 # The problem with extending a trend forever

The Draft Coyote Valley Fiscal Report has a problem with extending a trend line indefinitely. It says that housing prices will increase at a rate of 3% above inflation indefinitely, for 50-60 years. This results in a similar increase in property tax receipts, which is then used to claim that Coyote will result in a fiscal surplus for San Jose.

However, the report makes no prediction for increases in median household income. Fortunately, we found useful data here: income rose 10% over 10 years, or slightly less than 1% annually. You might see the problem already – if income increases more slowly than a major expense – housing – that expense can’t keep increasing at the same level indefinitely.

I need to find someone more versed in Excel than I am, but I tried to calculate how it would turn out. Assume average housing costs of 33% of income, which is probably reasonable for San Jose. To simplify numbers, assume an average household income of \$100,000, increasing 1% annually, and housing costs of \$33,000, increasing 3% annually.

End of Year 1: housing costs \$33,990, income is \$101,000 and housing now is 33.65% of household income. Interesting. Let’s do that for 10 more years:

(calculations show costs of housing if it increases 3% above inflation each year for ten years)

Year 1: 33 + (33 * .03) = 33.99
33.99 + (33.99 * .03) = 35.0097
35.0097 + (35.0097 * .03) = 36.059991
36.059991 + (36.059991 * .03) = 37.1417907
37.1417907 + (37.1417907 * .03) = 38.2560444
38.2560444 + (38.2560444 * .03) = 39.4037257
39.4037257 + (39.4037257 * .03) = 40.5858375
40.5858375 + (40.5858375 * .03) = 41.8034126
41.8034126 + (41.8034126 * .03) = 43.057515
43.057515 + (43.057515 * .03) = 44.3492405
Year 11: 44.3492405 + (44.3492405 * .03) = 45.6797177

At year 11, divide \$45,679.7177 by \$112,000 (should be very close to household income appreciating 1% annually), and you get housing costing 40.79% of income, up from 33% ten years earlier. And the fiscal report thinks this can continue for 60 years. I think it can’t – I don’t even know if it could continue for eleven years.

-Brian

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