The Mathematics of Money

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

(The slight difference between the 10th year value in the table and the residual value we

stated is due to rounding of the straight-line depreciation rate.)

This steady decrease is clearly different from what we saw with percent depreciation.

To make it easier to compare the two, let’s look at the car’s values under the two different

depreciation methods side by side:

Year Percent Straight Line

Start $23,407.00 $23,407.00

1 $19,895.95 $21,527.12

2 $16,911.56 $19,647.24

3 $14,374.83 $17,767.36

4 $12,218.61 $15,887.48

5 $10,385.82 $14,007.60

6 $8,827.95 $12,127.72

7 $7,503.76 $10,247.84

8 $6,378.20 $8,367.96

9 $5,421.47 $6,488.08

10 $4,608.25 $4,608.20

We can also illustrate this comparison with a graph (which also illustrates where the name

straight-line depreciation comes from), as seen in Figure 8.1.

While both methods reflect the same reality—that the value of the car is declining with

time—there are some significant differences in the values that they predict. The most sig-

nificant difference between the two lies in how the value declines with each method. With

percent (declining balance) depreciation, the value takes heavier hits in the early years, and

then the rate of decline slows down. In contrast, the graph shows where straight-line depre-

ciation gets its name; the depreciated value declines by the same steady amount each year,

reflected by the steady, straight-line graph. Given that we concluded in our prior discussion

that it is realistic to expect a faster drop in value in the early years, this should raise the

question of why we bother with straight-line depreciation as an alternative.

One advantage of straight-line depreciation is that it is easier to calculate with pencil

and paper. That may not be such a big deal today, but in the past this mattered much more,

giving the straight-line method a foothold. A second reason is that even though the percent

method gives a more realistic estimate of actual market value for most items, this is not

necessarily always true. For some items the straight-line method may be the more realistic

choice. Straight-line depreciation might give a more realistic estimate of the value of a cop-

per mine that contains $500 million worth of copper and can produce a steady $25 million

FIGURE 8.1

Straight-Line Versus

Percent Depreciation

$0

$5,000

$10,000

$15,000

$20,000

$25,000

Depreciated value

Time

Percent Straight line

8.4 Depreciation 367