Question

On January 1, 2018, the Allegheny Corporation purchased machinery for $170,000. The estimated service life of the machinery is 10 years and the estimated residual value is $5,000. The machine is expected to produce 300,000 units during its life. Required: Calculate depreciation for 2018 and 2019 using each of the following methods.

1. Straight line.

2. Sum-of-the-years'-digits.

3. Double-declining balance.

4. One hundred fifty percent declining balance.

5. Units of production (units produced in 2018, 45,000; units produced in 2019, 40,000).

Required 1

Calculate depreciation for 2018 and 2019 using straight line method

	Straight-Line Depreciation Choose Numerator: / Choose Denominator: = Annual Depreciation Expense Cost / Double the SL Rate = Depreciation Expense $165,000 / 10 = $16,500 Depreciation Expense 2018 2019

Required 2

Calculate depreciation for 2018 and 2019 using sum-of-the-years' digits.

	Sum-of-the-years' digits depreciation Depreciable Base x Rate per Year = Depreciation Expense 2018 $165,000 x 10/55 = $30,000 2019 $165,000 x 9/55 =

Required 3

Calculate depreciation for 2018 and 2019 using double-declining balance.

	Depreciation for the Period End of Period Annual Period Beginning of Period Book Value Depreciation Rate (%) Depreciation Expense Accumulated Depreciation Book Value 2018 $0 2019 $0 $0

Answer 1

Solution

Allegheny Corporation

Computation of depreciation for 2018 and 2019 under the following methods:

• Straight line method

Annual Depreciation = depreciable base x 1/useful life

Depreciable base = cost – residual value

Cost = $170,000

Residual value = 5,000

Useful life = 10 years

Depreciable base = 170,000 – 5,000 = 165,000

Depreciation = 165,000 x 1/10 = $16,500

The annual depreciation expense under the straight line method would remain constant throughout the life of the asset. Hence, annual depreciation expense for 2018 and 2019 is $16,500.

Year	Depreciation Expense
2018	$16,500
2019	$16,500

• Sum of years’ digits method:

Depreciation expense = depreciable base x 10/55

Depreciable base = cost – residual value

Cost = $170,000

Residual value = 5,000

Useful life = 10 years

Depreciable base = 170,000 – 5,000 = 165,000

Depreciation = 165,000 x 10/55 = $16,500 = $30,000

Depreciation expense for 2018 = $30,000

Depreciation expense for 2019 = 165,000 x 9/55 = $27,000

Year	Depreciable Base	x	rate per year	=	Depreciation Expense
2018	$165,000	x	10/55		$30,000
2019	$16,500	x	9/55	=	$27,000

• Double declining balance method

	Depreciation for the period			End of Period
Annual period	Beginning of period book value	Depreciation rate	Depreciation Expense	Accumulated Depreciation	Book Value
2018	$170,000	20%	$34,000	$34,000	$136,000
2019	$136,000	20%	$27,200	$61,200	$108,800

Computations –

Depreciation rate = 2 x straight line depreciation rate

= 2 x 1/10 = 20%

Depreciation for 2018 = 170,000 x20% = 34,000

Depreciation for 2019 = 136,000 x 20% = $27,200

• 150% declining balance method

	Depreciation for the period			End of Period
Annual period	Beginning of period book value	Depreciation rate	Depreciation Expense	Accumulated Depreciation	Book Value
2018	$170,000	15%	$25,500	$25,500	$144,500
2019	$144,500	15%	$21,675	$47,175	$122,875

Depreciation rate = 1.5 x straight line depreciation rate

= 1.5 x 1/10 = 15%

Depreciation for 2018 = 170,000 x15% = 25,500

Depreciation for 2019 = 144,500 x 15% = $21,675

• Units of production method

Depreciation expense = number of units x depreciation rate per unit

Depreciation rate per unit = depreciable base x 1/estimated production in units

= (170,000 – 5,000) x 1/300,000

Depreciation rate per unit = $165,000/300,000 = $0.55 per unit

Depreciation for year 2018 = 45,000 units x $0.55 per unit = $24,750

Depreciation for year 2019 = 40,000 units x $0.55 per unit = $22,000