How much is the property tax? In Calfornia, we pay 1% per year.

That doesn't seem bad, except that property values are very high. You can't get a tear-down in Palo Alto for under $2 million. If you buy a house that costs 5 times your income -- say someone earning $200,000 per year buying a $1 million house -- then that is equivalent to 5 percentage points additional income tax. On top of 42% federal, 13.2% state, 9% sales, and other taxes, it's part of my view that we're past 70% top marginal rate now.

The other way to look at taxes is in present value. At 1% interest rate, the value of a 1% payment is $1.00. What that means: Suppose you bought a $1,000,000 house. It's going to cost you $10,000 in property taxes per year. Let's set up an account that will pay your property taxes. If you get 1% interest on that account, you need to put $1,000,000 in the account!

A 1% property tax at a 1% interest rate is equivalent to a 100% tax on houses. That $1,000,000 house is really going to cost you $2,000,000!

There is a general paradox here: The top two things our politicians say they want to encourage are jobs and homeownership. Jobs are perhaps the most highly taxed economic activity in the economy, and by this calculation houses come in a close second.

(California also assesses a 1% personal property tax, on top of a sales tax, for anything they can prove you own, which usually means boats and airplanes. That too is an additional 100% tax.)

The second lesson, the value of wealth taxes depends sensitively on the interest rate, as I'm sure some of you are chomping at the bit to point out. If the interest rate is 2%, then the tax rate is "only" 1/0.02 = 50%. If the interest rate is 5%, then the tax rate is 1/0.05 = 20%. I suspect these taxes were put in place in a time of higher interest ares and nobody is really thinking about the effect of lower rates.

Similarly, suppose the government puts in a 1% per year wealth tax. If wealth generates a 5% rate of return, then the 1% wealth tax is the same thing as a 20% one-time confiscation of value*. If wealth generates a 1% rate of return, a 1% wealth tax is a 100% confiscation of value**. Mercifully, our income tax system taxes the rate of return, not the principal, and avoids this conundrum. Others do not.

What is the right rate? We can have a lot of fun with that one. The current 30 year TIPS (inflation indexed) rate is 1.19%. The 30 year nominal Treasury rate is 2.97%. In California, under Proposition 13, you pay 1% of the actual purchase price per year, but that quantity never increases. (This fact results in the paradox of extremely high property taxes on new purchasers, older people staying in huge old houses, and low property tax revenues.) So you might say that the nominal rate applies.

In Illinois, you pay a percentage of assessed value, which is usually a good deal lower than the actual value. (It also leads to a fun game of fighting over what the assessed value is. No surprise some of Illinois' most powerful politicians are also lawyers whose firms argue property assessment cases. ) That means however that the real interest rate matters.

But in both cases, we need to use the after-tax rate. If you put your money in a 30 year treasury (or a long-term bond fund that keeps a long maturity), you pay taxes on the interest. If your marginal tax rate (federal + state + local) is 50%, that means you only get half the interest. So that 3% nominal yield is really a 1.5% nominal yield, and the Californian should use a 1.5% rate, resulting in a 1/0.015 = 66% tax rate.

The tax treatment of TIPS is more complicated. (Really, inflation protected bonds are a great idea, but did the Treasury have to screw up the tax treatment so thoroughly?) You pay taxes on the nominal interest payments, and also on increases in principal value. This causes an accounting mess that I don't want to get into here, but as a rough guide, if you are in a 50% marginal tax bracket, then you need to buy $200 worth of TIPS to generate a $1.00 after-tax stream. So, if you live in a state where property tax assessments rise over time, we're really talking about 2 x 1/0.01 = 200% tax rate on the initial assessed value.

Now, house prices rise more than inflation. That argues for an even higher present value of taxes.

On the other hand, you're not going to keep your house forever. But you will sell it, and the price reflects the property tax. On one extreme, if there is no house supply, then the price reflects the full property tax. Without property tax, you could sell it for double the current value. Then these calculations are right. That's a good approximation for Palo Alto. If house supply is flat, then the house price equals construction costs, and we need to cut off these present values at your horizon for owning the house.

The back of my envelope is full.

I'm not very good at taxes, so I welcome comments and corrections on this. Also if it's all standard stuff, send a pointer to the source.

*sum_j=0^inf (0.05 - 0.01)/(1.05)^j = 0.04/0.05 = 0.80 = (1-0.20) x sum_j=0^inf 0.05 / (1.05)^j

**sum_j=0^inf (0.01 - 0.01)/(1.01)^j = 0 = (1-1) x sum_j=0^inf 0.01 / (1.01)^j

*Update: *Thanks to several commenters who point out that California property tax rises at the lesser of inflation or 2%. This means that the lower real interest rate is the right discount rate, not the higher nominal interest rate.