Question
XYZ Company purchased a new piece of equipment on January 1, 2022. The following information relates...
XYZ Company purchased a new piece of equipment on January 1, 2022. The following information relates to the equipment purchased: Purchase price .............. ? Residual value .............. ? Life ........................ 8 years Using the straight-line depreciation method, the equipment's book value at December 31, 2025 would be $82,700. Using the double-declining balance depreciation method, the depreciation expense recorded on the equipment in 2023 would be $30,000. Calculate the residual value assigned to this piece of equipment.
Answers
a)Double declining depreciation rate = 2 /useful life
= 2/8
= .25 or 25%
We have to make reverse working under double declining depreciation method to compute cost /Book value at purchase date.Let the purchase cost /book value at beginning of 2022 be"X" so depreciation expense for 2022 = X *.25 =.25X
Purchase cost -Depreciation expense for 2022 = Book value at end of 2022
X -.25X = 120000
.75X =120000
X =120000/.75
= 160000
Year Depreciation expense Book value at beginning/purchase cost 2023 30000 30000/.25 = 120000 2022 160000*.25=40000 160000 Purchase price = 160000
b)Under straight line method:
Book value at end of Dec 31,2025 =Cost - Accumulated depreciation over 4 years [1Jan2022-31Dec 2025]
82700 = 160000- Accumulated depreciation over 4 years
Accumulated depreciation over 4 years = 160000-82700
= 77300
or depreciation expense per year = 77300/4 = 19325
Depreciation expense per year =[cost -residual value /useful life
19325= [160000-residual value]/8
19325*8 = [160000-residual value]
[160000-residual value] = 154600
Residual value =160000-154600
= 5400
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