Question

Depreciation by Three Methods; Partial Years

Perdue Company purchased equipment on April 1 for $32,670. The equipment was expected to have a useful life of three years, or 4,860 operating hours, and a residual value of $1,080. The equipment was used for 900 hours during Year 1, 1,700 hours in Year 2, 1,500 hours in Year 3, and 760 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) the units-of-activity method, and (c) the double-declining-balance method.

Note: FOR DECLINING BALANCE ONLY, round the multiplier to four decimal places. Then round the answer for each year to the nearest whole dollar.

a. Straight-line method

YearAmount

Year 1$

Year 2$

Year 3$

Year 4$

b. Units-of-activity method

YearAmount

Year 1$

Year 2$

Year 3$

Year 4$

c. Double-declining-balance method

YearAmount

Year 1$

Year 2$

Year 3$

Year 4$

Answer 1

Depreciation under :

1. straight line method :

Year 1 -  $7,898

Year 2 -  $10,530

Year 3 -  $10,530

Year 4 - $2,632

1. Unit activity method :

Year 1 - $5,850

Year 2 -  $11,050

Year 3 -  $9,750

Year 4 - $4,940

1. Double declining method :

Year 1 -  $16,333

Year 2 -  $10,224

Year 3 -  $3,408

Year 4 - $1,137

Explanation :

1. Depreciation under straight line method :

= (Cost of the asset - residual value )÷ life of the asset

Given , cost of the asset = $ 32,670

Life of the asset = 3 year

(i.e., 3 years = 36 months and in the year 1 used for 9 months, year 2 used for 12 months, year 3 used for 12 months, year 4 usef for 3 months)

Residual value = $1,080

Depreciation at the end of year 1 ( asset purchased on april 1 and it is used for 9 months)

= {($32,670 - $1,080)÷ 36 months} × 9 months

= $7,898

Carrying amount at the end of year 1 : $32,670 - $7898 = $24,772.

Depreciation at the end of year 2 { remaining life of the asset is 27 months(36 - 9)} :

= {($25,772 - $1,080)÷ 27 months} × 12 months

= $10,530

Carrying amount at the end of year 2 : $25,772 - $10,530 = $14,242.

Depreciation at the end of year 3 { remaining life of the asset is 15 months(27 - 12)} :

= {($14,242 - $1,080)÷ 15 months} × 12 months

= $10,530

Carrying amount at the end of year 2 : $14,242 - $10,530 = $3,712.

Depreciation at the end of year 4 { remaining life of the asset is 3 months(15 - 12)} :

= {($3,712 - $1,080)÷ 3 months} × 3 months

= $2,632

2. The depreciation amount under unit activity method:

Depreciation rate = (Cost of the asset - residual value )÷ operating hours

= ($32,670 - $1,080)÷ 4,860

= 6.5 per hour

Depreciation at the end of year 1 (asset used for 900 hours):

= Number of hours asset used × rate per hour

= 900 hours × 6.5 per hour

= $5,850

Depreciation at the end of year 2( asset used for 1700 hours) :

= 1,700 hours × 6.5 per hour

= $11,050

Depreciation at the end of year 3 ( asset used for 1,500 hours) :

= 1,500 hours × 6.5 per hour

= $9,750

Depreciation at the end of year 4(asset used for 760 hours) :

=760 hours × 6.5 per hour

= $4,940

3. Depreciation under double declining method :

Following Steps involved in the calculation of depreciation expense using Double declining method :

1. Determine the initial cost of the asset at the time of purchasing.

2. Determine the salvage value of the asset i.e. the value at which the asset can be sold or disposed of after its useful life is over.

3. Determine the useful or functional life of the asset.

4. Calculate depreciation rate i.e. 1/useful life.

5. Multiply the beginning period book value by twice the depreciation rate to find the depreciation expense.

6. Deduct the depreciation expense from the beginning value to calculate the ending period value.

Therefore by appling the above steps:

Cost of the asset = $ 32,670

Salvage Value = $ 1,080

The useful life of the asset = 3 years

Depreciation rate = 1/useful life × 100= (1/3) × 100= 33.33%

Double-declining balance formula = 2 × Cost of the asset × Depreciation rate.

Depreciation at the end of year 1 = 2 × $32,670 × 33.33% × 9/12

= $ 16, 333.3665

= $16,333 (rounded off)

Carrying amount at the end of year 1 = $ 32,670 - $16,333

= $15,337

Depreciation at the end of year 2 = 2 × $15,337 × 33.33%

= $10,223.6442

= $10,224 (rounded off)

Carrying amount at the end of year 2 = $ 15,337 - $10,224

= $5,113

Depreciation at the end of year 3 = 2 × $5,113 × 33.33%

= $3408.3258

= $3,408 (rounded off)

Carrying amount at the end of year 3 = $5,113- $3,408

= $ 1705

Depreciation at the end of year 4 = 2 × $1705 × 33.33%

= $1,136.553

= $1,137  (rounded off)