Question

The cost of equipment purchased by Sheffield, Inc., on June 1, 2020, is $100,800. It is estimated that the machine will have a $8,400 salvage value at the end of its service life. Its service life is estimated at 7 years, its total working hours are estimated at 46,200, and its total production is estimated at 660,000 units. During 2020, the machine was operated 7,080 hours and produced 64,900 units. During 2021, the machine was operated 6,490 hours and produced 56,600 units. Compute depreciation expense on the machine for the year ending December 31, 2020, and the year ending December 31, 2021, using the following methods. (Round depreciation per unit to 2 decimal places, e.g. 15.25 and final answers to 0 decimal places, e.g. 45,892.) 2020 2021 (a) Straight-line $ $ (b) Units-of-output $ $ (c) Working hours $ $ (d) Sum-of-the-years'-digits $ $ (e) Double-declining-balance (twice the straight-line rate) $ $

Answer 1

Computation of Depreciation expenses for the Year 2020 & 2021:

(a) Straight Line Method:

With the straight-line depreciation method, the value of an asset is reduced uniformly over each period until it reaches its salvage value. Straight-line depreciation is the most commonly used and straightforward depreciation method for allocating the cost of a capital asset. It is calculated by simply dividing the cost of an asset, less its salvage value, by the useful life of the asset.

Particulars		Equipment
		$
Purchase Price	A	100,800
Estimated Salvage value	B	8,400
Value to be depreciated in its useful life	C=A-B	92,400
Useful Life of Asset (in Years)	D	7
Depreciation value per year as per SLM	E=C/D	13,200

As in the year 2020, the equipment has been used only for 7 months i.e. from 1 June to 31 Dec, depreciation expense = $13,200*7 months/12months = $7,700

Depreciation expense for the Year 2021 = $13,200

(b) Units of output method:

The term units-of-output depreciation refers to one of several methods of allocating the cost of an asset over its expected lifetime. The units-of-output depreciation method is based on the assumption the asset will output a fixed number of units over its lifetime; therefore, the depreciation expense in a given accounting period is directly related to the asset's output in that same accounting period.

Units-of-Output Depreciation = (Cost of Asset - Residual Value) / Total Units of Output

Units-of-Output Depreciation = ($100,800-$8,400)/660,000 units = $0.14 per unit

Depreciation Expense = Units of Output Depreciation x Units Produced

Therefore, depreciation expense for the Year 2020 = $0.14 * 64,900 units = $9,086

Therefore, depreciation expense for the Year 2021 = $0.14 * 56,600 units = $7,924

(c) Working Hours Method:

Under this method, hourly rate of depreciation is calculated. The cost of the asset (less residual value if any) is divided by the estimated working hours. The actual depreciate for any given period depends upon the working hours during that year.

Working Hour Depreciation = (Cost of Asset - Residual Value) / Total expected working hours

Hours of Output Depreciation = ($100,800-$8,400)/46,200 units = $2 per hour.

Depreciation Expense = Units of Output Depreciation x working hours

Therefore, depreciation expense for the Year 2020 = $2* 7,080 units = $14,160.

Therefore, depreciation expense for the Year 2021 = $2 * 6,490 units = $12,980.

(d) Sum of years digit method:

The sum of years' digits method is a form of accelerated depreciation that is based on the assumption that the productivity of the asset decreases with the passage of time. Under this method, a fraction is computed by dividing the remaining useful life of the asset on a particular date by the sum of the year's digits.

Sum of years = 7+6+5+4+3+2+1 = 28

Depreciation amount = Remaining useful life at the start/Sum of years of useful life * Depreciable Value

Depreciation expense for the full Year 2020 = (7/28)*(100,800-8,400) = $23,100

But the asset was used only for 7 months, therefore depreciation for Year 2020 = $23100*7 Months/12 months = $13,475.

Useful life of asset remaining at the start of Year 2021 = 6 years & 5 months = 6.4167 Years

Depreciation expense for the Year 2021 = (6.4167/28)*(100,800-8,400) = $21,175

(e) Double-declining-balance Method:

The double-declining balance depreciation method is an accelerated depreciation method that counts as an expense more rapidly when compared to straight-line depreciation that uses the same amount of depreciation each year over an asset's useful life.

Double Declining rate = (100/Useful life)*2 = (100/7)*2 = 28.5714%

Double Declining Depreciation = Net Book Value at the beginning of year * Double Declining rate

Depreciation expense for the full Year 2020 = $100,800*28.5714% = $28,800

But the asset was used only for 7 months, therefore depreciation for Year 2020 = $28,800*7 Months/12 months = $16,800.

Net Book value at the beginning of Year 2021 = $100,800 - $16,800 = $84,000.

Depreciation expense for the Year 2021 = $84,000*28.5714% = $24,000