The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


9.1 Sales Taxes


Sales taxes are taxes imposed on retail sales. In the United States, sales taxes are imposed
by state and/or local governments. Businesses are generally required to calculate and collect
these taxes on the sales that they make, and then forward what they collect to the appro-
priate government tax collection agency. This places some mathematical and accounting
responsibilities on businesses; a business needs to make sure that sales taxes are calculated
and collected correctly at point of sale, and that the business’s overall tax collections are
reported and paid correctly to the government.
As of this writing, state sales taxes are in place in 45 states, plus the District of Columbia.
Only Alaska, Delaware, Montana, New Hampshire, and Oregon do not impose state sales
taxes. There is a great deal of diversity, though, in both tax rates and in the types of sales
on which these taxes are collected. In some areas, purchases of things like food, clothing,
or prescription and/or over the counter drugs may be exempt from sales taxes, or may be
taxed at a lower rate than other purchases. For example, in much of North Carolina the
general sales tax rate is 7.0%, but a 2.5% rate applies for groceries. Different rates may
also be charged on other types of sales, such as utility bills, gasoline, hotel rooms, hybrid
cars, home improvement services, or any other sort of sale that lawmakers deem fit for a
different rate. Furthermore, regardless of the type of item sold, sales made to government
agencies and nonprofit organizations may be exempt from sales taxes, regardless of the
item purchased.
Each state sets its own sales tax rates, and so naturally rates differ from one state to
another. Matters can be further complicated by sales taxes imposed by a county or city,
meaning that the sales tax rate differ from one location to another within the same state.
For example, the general state sales tax rate in New York is 4%, but the actual rate in effect
in that state ranges from 7% to 9^3 ⁄^8 %, depending on the additional sales tax imposed by
local governments.
When different levels of government impose taxes on the same purchases, each rate is a
percent of the price before taxes. This differs from series discounts (or series markups). We
saw in Chapter 8 that a 5% discount followed by a 3% discount is not the same as an 8%
discount. This is because the first discount is a percent of the original price, and the second
is a percent of the already discounted price. The situation is different with sales tax rates:
since both rates are a percent of the same thing, the overall sales tax rate can be calculated
by adding the two rates.

Example 9.1.1 If the state sales tax rate is 4.5% and the local sales tax rate is
3.75%, what is the overall sales tax rate?

The overall rate is 4.5%  3.75%  8.25%.

At this time, there is no national sales tax in the United States, though the idea of a
national sales tax has often been proposed as an alternative to the current income tax sys-
tem. Advocates of a national sales tax often use the term consumption tax to emphasize
the claim that collecting taxes on purchases rather than income would encourage savings
over spending. Many other countries have a national value-added tax, which functions
in much the same way as a sales tax. While we are unlikely to see a national sales tax in
the near term in the United States, it is possible that such a tax may eventually come into
place.^1
Because sales taxes are a state or local tax, matters become interesting with mail order
or Internet sales. If a Pennsylvania resident buys merchandise over the Internet from a
company in California, which state collects the sales tax? In general a merchant is not
required to collect tax on sales made to an out-of-state customer, unless the merchant has
a business presence (such as a retail store) of some sort in that state. If the merchant in

(^1) This would have an interesting effect on retirement plans. Withdrawals from Roth IRAs (discussed in Chapter 7) are
not subject to income tax. Things that you buy with money from a Roth IRA, though, are not immune from sales taxes.
9.1 Sales Taxes 377

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