Engineering Economic Analysis

344 DEPRECIATION

The straight-line (SL) method is often used for intangible property. Veronica's finn

bought a patent in April that was not acquired as part of acquiring a business. She paid

$6800 for this patent and must use the straight-line method to depreciate it over 17 years

with no salvage value. The annual depreciation is $400 (=$6800/17). Since the patent Was

purchased in April, the deduction must be prorated over the 9 months of ownership. This

year the deduction is $300 (=$400 x 9/12), and then next year she can begin taking the

full $400 per year.

Sum-of- Years'-Digits Depreciation

Another method for allocating an asset's costminussalvage valueoverits depreciable life

is called sum-of-years'-digits (SOYD) depreciation. This method results in larger-than-

straight-line depreciation charges during an asset's early years and smaller charges as the

asset nears the end of its depreciablelife. Each year, the depreciationcharge equals a fraction

of the total amount to be depreciated(B- S).The denominator of the fraction is the sum of

the years' digits. For example, if the depreciable life is 5 years, 1 + 2 + 3 + 4 + 5 = 15=

SOYD. Then 5/15,4/15,3/15,2/15, and 1/15 are the fractions from Year 1 to Year 5.

Each year the depreciation charge shrinks by 1/15 ofB- S. Because this change is the

same every year, SOYD depreciation can be modeled as an arithmetic gradient, G. The

equations can also be written as:

(

Sum-of-years' -digits

)

depreciation charge for =

any year

(

Remaining depreciable life

)

at beginning of year (Total amount depreciated)

(

Sum of years' digits

for total depreciable life)

dt-_ N~~~~- t+ 1(B_S) (11-3)

where dt=depreciation charge in any yeart

N=number of years in depreciable life

SOYD=sum of years' digits, calculated asN(N + 1)/2=SOYD

B=cost of the asset made ready for use

S=estimated salvage value after depreciable life

Compute the SOYD depreciation schedule for the situation in Example 11.2.

Cost of the asset,B

Depreciable life, in years,N

Salvage value, S

$900

5

$70

SOlUTIQ,~;

--..- - - -- - -

'

s

5

OYD _ ~ >&6

~=15

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