The Mathematics of Money

(Darren Dugan) #1

402 Chapter 9 Taxes


In this example we can see that rounding provides a bit more than the tax levy would have
called for. In proportion to the overall tax levy, the difference is not all that large; however,
if this is too large of an error, the only recourse is to carry the rate out to more decimal
places.

Comparing Tax Rates


Comparing tax rates can be a tricky matter, because two different localities may use different
assessment practices. For example, suppose that the real estate tax rate in the City of East-
ville is $31.75 per thousand, while in the City of Westville the real estate tax rate is only
$18.34 per thousand. Obviously, real estate taxes are lower in Westville, right? Despite
appearances, we can’t immediately tell from this information which city’s taxes are lower.
Even though Westville’s rate is lower, it may be that properties in Westville are assessed
at a higher rate.

Example 9.3.6 The real estate tax rate in Eastville is $31.75 per thousand, and
properties are assessed at 50%. In Westville, the tax rate is $18.34 per thousand, and
properties are fully assessed. Which city has the higher property taxes?

To be able to make an “apples to apples” comparison, we will calculate the total tax owed on
properties of equal actual value in each community. For convenience, let’s use a $100,000
market value (any value could be used equally well).

In Eastville, we would expect a $100,000 property to be assessed at (50%)($100,000) 
$50,000. The tax rate would then be (50 thousands)($31.75 per thousand)  $1,587.50.

In Westville, we would expect a $100,000 property to be assessed at $100,000. The tax rate
would then be (100 thousands)($18.34 per thousand)  $1,834.00.

Realistically speaking, the tax rate in Westville is actually higher than in Eastville.

Tax rates can be misleading in comparing property taxes from year to year as well. Sup-
pose that next year Westville lowers the tax rate to $18.00 per thousand. Good news for
Westville’s taxpayers, right?

Example 9.3.7 In 2007 the tax rate in Westville was $18.34 per thousand. In 2008,
thanks to a strong real estate market, properties in Westville increase in value by 10%
on average. The tax assessor kept up on this, and the assessed values also grew at the
same rate, allowing the city to lower the tax rate to $18.00 per thousand. How much
did property taxes drop between 2007 and 2008?

In Example 9.3.5 we calculated that the 2007 property tax on a $100,000 house in Westville
would have been $1,834.00.

On the basis of the average increase in assessed value, that $100,000 house would have
increased in assessed value by 10%, so its 2008 assessed value would be $100,000(1.10) 
$110,000. The 2008 property tax would be (110 thousands)($18.00 per thousand) 
$1,980.00.

How much did the property tax drop? It didn’t! In fact, we can divide $,1980/$1,834 
1.0796 and see that, realistically speaking, property taxes actually increased by 7.96%!

Naturally, local politicians running for re-election will still want to talk about the decreas-
ing tax rate.

Special Property Tax Rates


In some areas different types of property may be assessed at different rates. Residential
property may be taxed at a higher, or lower, rate than commercial or agricultural property.
Businesses may be offered special breaks on property taxes as an incentive to locate in a
community, or reduced tax rates may be offered for veterans or senior citizens. Other prop-
erties (such as churches, schools, or hospitals) may be exempted from them altogether.
Free download pdf