If an asset is purchased for $10,000, and has an estimated life of 6 years, and
ID: 2755408 • Letter: I
Question
If an asset is purchased for $10,000, and has an estimated life of 6 years, and it costs $2,000 to install the asset, and it is not expected to have any salvage value after its six year useful life, how much will the depreciation be in the fourth year recorded on the income statement if the organization used straight-line depreciation? How much will the accumulated depreciation be for that asset on the balance sheet? If the organization uses an accelerated depreciation method such as Sum-of-the-years’ digit, will the depreciation in the fourth year be higher or lower than it would be using the straight line method? Will the accumulated depreciation be higher or lower after the fourth year than it would be using the straight line method?
Explanation / Answer
Cost of Asset = $10,000 + $2,000 = $12,000
The Depreciation in the fourth year using staight-line depreciation method = $12,000 / 6 = $2,000
(As in straight-line depreciation method, a fixed amount is charged as depreciation in the books of accounts through out the life of the asset.)
Book Value of the asset at the begining of the fourth year = $12,000 - $6,000 (i.e. total depreciated amount in three years) = $6,000
Accumulated depreciation of the asset at the begining of the fourth year = Cost of asset - Book Value of asset
= $12,000 - $6,000 = $6,000
Sum-of-the-years’ digit:
SYD = n (n + 1) / 2, where n = estimated life
SYD = 6 *(6 + 1) /2 =21
Year
Remaining useful life
Applicable Percentage
Annual Depreciation
1
6
6/21 = 28.57%
$12,000 * 28.57% = $3,428.57
2
5
5/21 = 23.80%
$12,000 * 23.80% = $2,857.14
3
4
4/21 = 19.05%
$12,000 * 19.04% = $2,286
4
3
3/21 = 14.28%
$12,000 * 14.28% = $1,714.28
5
2
2/21 = 9.53%
$12,000 * 9.52% = $1,143.60
6
1
1/21 = 4.77%
$12,000 * 4.76% = $572.40
Total
21
100%
$12,000
So, the depreciation in the fourth year will be lower than it would be using the straight line method.
The accumulated depreciation after the fourth year would be higher that it would be using straight line method.
Year
Remaining useful life
Applicable Percentage
Annual Depreciation
1
6
6/21 = 28.57%
$12,000 * 28.57% = $3,428.57
2
5
5/21 = 23.80%
$12,000 * 23.80% = $2,857.14
3
4
4/21 = 19.05%
$12,000 * 19.04% = $2,286
4
3
3/21 = 14.28%
$12,000 * 14.28% = $1,714.28
5
2
2/21 = 9.53%
$12,000 * 9.52% = $1,143.60
6
1
1/21 = 4.77%
$12,000 * 4.76% = $572.40
Total
21
100%
$12,000
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