Question

On October 1, 2018, the Allegheny Corporation purchased machinery for $245,000. The estimated service life of the machinery is 10 years and the estimated residual value is $3,000. The machine is expected to produce 440,000 units during its life. Required: Calculate depreciation for 2018 and 2019 using each of the following methods. Partial-year depreciation is calculated based on the number of months the asset is in service. 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, 22,000; units produced in 2019, 37,000).

Answer 1

Solution

Allegheny Company

1. Straight line method

• Depreciation expense = depreciable base x 1/useful life

Depreciable base = cost – residual value

Cost = $245,000

Residual value = $3,000

Useful life = 10 years
depreciable base = 245,000 – 3,000 = $242,000

Annual Depreciation expense = 242,000 x 1/10 = $24,200

Depreciation for 2018 (Oct 1 – Dec 31) = 24,200 x 3/12 = $6,050

The annual depreciation expense under straight line method would remain constant throughout the life of the asset.

Hence, depreciation expense for all the ten years = $24,200

Depreciation expense for Year 2019 = $24,200

Book value = cost – accumulated depreciation

End of Year 2018 = 245,000 – 6,050 = $238,950

Year 2019 = 245,000 – 30,250 = $214,750

1. Sum of years’ digits:

Depreciation expense = (remaining useful life of asset)/sum of the years’ digits x depreciable base

Useful life = 10

Cost = $245,000

Residual value = $3,000

Depreciable base = 245,000 – 3,000 = $242,000

Depreciation expense, Year 1 2018 -

Sum of the years’ digits for 10 years = 55

Remaining useful life for 2018 = 10

Depreciation expense (Oct – Dec) = (10/55) x 242,000 x 3/12 = $11,000

Book value at EoY 2018 = 245,000 – 11,000 = $234,000

Depreciation expense, Year 2, 2019 –

Sum of the years’ digits for 10 years = 55

Remaining useful life for 2018 = 9

Depreciation expense = (9/55) x 242,000 = $39,600

Book value at EoY 2018 = 245,000 –(11,000 + 39,600) = $194,400

1. Double-declining balance method:

Depreciation expense Year 1 = cost x double declining depreciation rate

Double declining rate = 2 x straight line depreciation rate

Straight line depreciation rate = 1/useful life = 1/10 = 10%

Double declining rate = 2 x 10% = 20%

Depreciation expense for other years = book value x double declining rate

Depreciation expense, Year 1, 2018 (Oct – Dec) = 245,000 x 20% x 3/12= $12,250

Book value = cost – accumulated depreciation

Book value, End of Year 1, 2018 = 245,000 – 12,250 = $232,750

Depreciation expense, Year 2, 2019 = 232,750 x 20% = $46,550

Acc. Dep = 12,250 + 46,550 = $58,800

BV EOY 2 = 245,000 – 46,550 = $198,450

1. 150% declining balance method:

Depreciation expense Year 1 = cost x 150% declining depreciation rate

Double declining rate = 150% x straight line depreciation rate

Straight line depreciation rate = 1/useful life = 1/10 = 10%

Double declining rate = 150% x 10% = 15%

Depreciation expense for other years = book value x 15% declining rate

Depreciation expense, Year 1, 2018 (Oct – Dec) = 245,000 x 15% x 3/12= $9,188

Book value = cost – accumulated depreciation

Book value, End of Year 1, 2018 = 245,000 – 9,188 = $235,812

Depreciation expense, Year 2, 2019 = 235,812 x 15% = $35,372

Acc. Dep = 9,188 + 35,372 = $44,560

BV EOY 2 = 245,000 – 44,560 = $200,440

1. Units of production method:

Depreciation expense = depreciation rate per unit x expected annual production

Depreciation rate per unit = depreciable base/estimated productive life

Depreciable base = Depreciable base = cost – residual value

Cost = $245,000

Residual value = $3,000
depreciable base = 245,000 – 3,000 = $242,000

Estimated productive life = 440,000 units

Depreciation rate per unit = $242,000/440,000 units = $0.55

Depreciation expense, Year 1 = $0.55 x 22,000 units = $12,100

Depreciation expense, Year 2 = $0.55 x 37,000 units = $20,350