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each passing year, the price according to our formula will never actually reach zero. This
does not entirely agree with common sense. At a certain point, the car will either become
worthless, or it will be considered a collectible and increase in value. This is not a problem,
though. We did not claim that the price will actually drop by exactly 15% each year. The
15% a year figure is an estimate and a prediction, based on what has happened to the prices
of similar cars in the past. If it is based on reliable data, we have reason to expect it to agree
reasonably well with what will actually happen, but we should not take it too literally. It
would be no surprise at all if the car’s value in 5 years actually turns out to be an even
$10,000, or $10,995, or some other value in the same general neighborhood instead of the
predicted $10,386. Likewise, we should not be too surprised if the car’s value after 20 years
is $500 or nothing instead of the $20,387(0.85)^20 $907.24 that the formula predicts.
When we calculate depreciation in this way, assuming that each year’s depreciation is
a set percent of a decreasing value, the amount of annual depreciation decreases with each
passing year. For this reason, this is often referred to as declining balance depreciation. As
we will see next, this is not the only way to do it.Straight-Line Depreciation
As we have suggested in the previous discussion, declining balance depreciation is often a
very reasonable way to project the actual market price of something. There is another very
commonly used method for calculating depreciation, though. With straight-line deprecia-
tion we assume that the price declines by the same dollar amount (not the same percent)
each year.
In order to determine the amount of this annual price decline, we fi rst must determine the
period of time over which we expect the depreciation to occur. This is often termed the item’s
useful life. We then determine the total amount that the price is to decline over the course of
the item’s useful life. In some cases, that amount is the entire original value of the item; once
it reaches the end of its useful life, we consider its value to be zero. For example, a computer
that has reached the end of its usefulness has little if any value, and in fact old computers are
of so little value that they can be hard to get rid of. In other cases, though, we assume that
at the end of its useful life the item still has some salvage value, called its residual value or
salvage value. A 15-year old car may be basically worthless as a vehicle, but it may still have
some value for parts or scrap metal, and can probably still be sold to a salvage yard for a few
hundred dollars even if it doesn’t run.
Once we have determined the useful life and salvage value, we then calculate the total
amount of depreciation to be taken and divide this by the useful life. This gives the amount
the price will decrease each year. We call this amount the rate of (straight-line) deprecia-
tion, or the (straight-line) depreciation rate. The value of the item after a period of time
calculated from this rate is called the item’s depreciated value.
Before trying to make a formula out of this, let’s illustrate the idea with an example.Example 8.4.3 The Cotswold Real Estate Agency purchased a computer for $2,000.
The useful life of the computer is 5 years. The computer is assumed to have no salvage
value. Find (a) the straight-line depreciation rate, (b) the depreciated value of the
computer after 3 years, and (c) the depreciated value after 7 years.The computer will lose its full $2,000 initial value in 5 years, and since it loses the same
amount each year, the depreciation rate is $2,000/5 $400 per year.If the computer’s value drops by $400 per year for 3 years, that means it will be worth
$2,000 3($400) $2,000 $1,200 $800 at the end of the 3 years.Since the computer’s useful life is 5 years, from that time on it has a value of zero. So at 7 years,
the depreciated value would be $0.It may not be necessary to have a formula for straight-line depreciation, since any other
problem of this type will be done in pretty much the same way. Nonetheless, we can sum
this up with formulas:8.4 Depreciation 365