368 Chapter 8 Mathematics of Pricing
worth per year. After 1 year, $475 million worth remains; after 2 years, $450 million is
left, and so on. (This of course assumes no change in the market price for copper and no
signifi cant changes in operating costs.)
By far the greatest reason to consider the straight-line method, though, is this: depre-
ciation is used not only as a way of assessing the actual fair market value of an item. In
business, depreciation is also used for accounting purposes, and often those purposes call
for straight-line depreciation. Accountants use depreciation to match a business’s cost of
purchasing an item with the revenues that are produced by using that item. A thorough
explanation of this lies beyond the scope of this book, but a simple example will illustrate
the basic idea.
The Cotswold Real Estate Agency in Example 8.4.3 paid $2,000 for a computer.
This is a business expense, and so when the agency sets out to calculate its profi t for the
year, the cost of this computer should be taken into account, just as the agency would
take into account its offi ce rent or electric bill. But there is a very important difference
between the computer and the offi ce rent or electric bill. The offi ce rent and electric
bill are expenses for business costs incurred entirely for that year, but the expense of
the computer is for a piece of equipment that will be useful for years to come. There is
something not quite right about attributing the entire cost of the computer to this year’s
business expenses. If, as we assumed, the computer has a useful life of fi ve years, then
only 1/5 of its cost really is attributable to the current year (assuming that the computer
was in use for the full year; if it was only in use for part of the year, the fraction would
be even smaller).Example 8.4.5 Suppose that Cotswold Real Estate put its computer into use 7 months
before the end of 2007. For straight-line depreciation, how much depreciation for the
computer should be attributed to 2007? How much for 2008?The depreciation amount is $400 per year. In 2007, the computer was in use for 7/12 of the
year, so the company should count (7/12)($400) $233.33 worth of the computer’s cost
as an expense for 2007.In 2008, the computer will be in use for the full year, so the depreciation would be
$400.As far as accounting for business expenses is concerned, then, $233.33 of the purchase
price is attributable to 2007, and the remaining $1,788.67 remains an expense for future
years. Looked at this way, the depreciated value of the computer is not intended to refl ect
its actual value if sold. Instead, the depreciated value represents the amount of money spent
for it that is yet to be counted as an expense against the business’s income.
Before moving on, let’s try one more example of this type.Example 8.4.6 Suppose that a retailer buys fi xtures for $14,835. The useful life is
12 years, and the residual value is $1,500. If the fi xtures are put into use 5 months
before the end of 2007, determine the depreciated value of the fi xtures at the end of
2007 and at the end of 2008.First, we determine the annual depreciation amount:D ___IV UL SV
$14,835 $1,500
_____ 12 $1,111.25
In the fi rst year, the retailer would take 5/12 of a full year’s depreciation, or (5/12)($1,111.25)
$463.02.So at the end of 2007, the depreciated value is $14,835 $463.02 $14,371.98. In
2008, a full year’s depreciation would be taken, so the end-of-year depreciated value is
$14,371.98 $1,111.25 $13,260.73.The use of depreciation in accounting has some interesting side effects. It may be to a compa-
ny’s benefi t to make its expenses seem as large as possible to minimize the amount of income
taxes it will have to pay. The useful life of an item may be estimated very aggressively low
to allow the business to use as much depreciation as possible as soon as possible. Even if
Cotswold Realty really expects its computer to be useful for 5 or more years, they may prefer