Rago Company takes a full year’s depreciation expense in the
year of an asset’s acquisition, and no depreciation expense in the
year of disposition. Data relating to one of Rago’s depreciable
assets at December 31, year 5, are as follows:

Acquisition year Year 2

Cost $110,000

Residual value 20,000

Accumulated depreciation 72,000

Estimated useful life 5 years

Using the same depreciation method as used in year 2, year 3, and
year 4, how much depreciation expense should Rago record in
year 5 for this asset?

(a) The requirement is to calculate the amount of
depreciation expense to be recorded in year 5. After three years
(year 2-year 4), accumulated depreciation is $72,000. Therefore,
the method that was used was the sum-of-the-years’ digits (SYD)
method. Using this method, after three years the balance in accumulated
depreciation would be 12/15 of the depreciable base
(5/15 + 4/15 + 3/15). The depreciable base is the cost
($110,000) less the residual value ($20,000), or $90,000. Thus,
using the SYD method, accumulated depreciation at 12/31/Y4
would be $72,000 ($90,000 × 12/15), which matches the
amount given in the problem. Year 5 depreciation expense, using
the SYD method is $12,000 ($90,000 × 2/15).