Perdue Company purchased equipment on April 1 for $38,880. The equipment was expected to have a useful life of three years, or 5,400 operating hours, and a residual value of $1,080. The equipment was used for 1,000 hours during Year 1, 1,900 hours in Year 2, 1,600 hours in Year 3, and 900 hours in Year 4.

Required:

Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by (a) the straight-line method, (b) units-of-activity method, and (c) the double-declining-balance method.

See explanation section.

Explanation:

Requirement 1

We know,

Depreciation expense under the straight-line method = (Cost price - residual value) ÷ useful life

The depreciation expense under the straight-line method remains same in every year.

December 31, Year 1 - depreciation expense = ($38,880 - $1,080) ÷ 3 years.

Depreciation expense = ($37,800 ÷ 3)

Depreciation expense = $12,600

Depreciation expense for year 1 = $12,600 × 9 ÷ 12

Depreciation expense for year 1 = $9,450

Requirement 2

The depreciation expense under the straight-line method remains the same every year.

Year 2 depreciation expense = ($38,880 - $1,080) ÷ 3 years = $12,600

Year 3 depreciation expense = ($38,880 - $1,080) ÷ 3 years = $12,600

Year 4 depreciation expense = ($38,880 - $1,080) ÷ 3 years = $12,600

The equipment will be dissolved after 4 year with a residual value of $1,080.

Requirement 3

The depreciation expense under units-of-activity method = [(Cost price - residual value) ÷ Total operating hours] × usage during the period.

Given,

Cost price = $38,880

residual value = $1,080

Total operating hours =  5,400

Putting the values into the formula, we can get

Depreciation expense rate = ($38,880 - $1,080) ÷  5,400

Depreciation expense rate = $37,800 ÷ 5,400

Depreciation expense rate = $7 per hour.

Depreciation expense for year 1 = $7 per hour × 1,000

Depreciation expense for year 1 = $7,000

Requirement 4

We get from requirement 3

Depreciation expense rate = $7 per hour.

Year 2 Depreciation expense = $7 per hour.

Depreciation expense for year 2 = $7 per hour × 1,900 hour.

Depreciation expense for year 2 = $13,300 hour.

Year 3 Depreciation expense = $7 per hour.

Depreciation expense year 3 = $7 per hour ×  1,600 hour.

Depreciation expense year 3 = $11,200 hour.

Year 4 Depreciation expense = $7 per hour.

Depreciation expense year 4 = $7 per hour ×  900 hour.

Depreciation expense year 4 = $6,300 hour.

Requirement 5

Depreciation rate under the double-declining-balance method = (100% ÷ useful life) ÷ 2

Depreciation rate = (100% ÷ 3 years) × 2

Depreciation rate = 66.67%

Depreciation expense for year 1 = cost price × depreciation rate

Given,

cost price = $38,880

depreciation rate = 66.67%

Putting the values into the formula, we can get

Depreciation expense for year 1 = cost price × depreciation rate

Depreciation expense for year 1 = $38,880 × 66.67%

Depreciation expense for year 1 = $25,921

Requirement 6

In double-declining-balance method, depreciation expense is decreasing.

Book value of year 1 after depreciation = Cost price - year 1 depreciation expense =  $38,880 - $25,921 = $12,959

Depreciation expense for year 2 = Book value of year 1 × depreciation rate.

Depreciation expense for year 2 = ($12,959 × 66.67%) = $8,640

Book value of year 2 after depreciation = Book value of year 1 - Depreciation expense for year 2 = $12,959 - $8,640 = $4,319

Depreciation expense for year 3 = Book value of year 2 × depreciation rate.

Depreciation expense for year 3 = $4,319 × 66.67% = $2,879.50

Book value of year 3 after depreciation = Book value of year 2 - Depreciation expense for year 3 = $4,319 - $2,879.50 = $1,439.5

Depreciation expense for year 4 = Book value of year 3 × depreciation rate.

Depreciation expense for year 4 = $1,439.5 × 66.67% = $960

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answer; by looking at total product,marginal product,and changes in both after changes in inputs