Compute the depreciation and book value each year of a machine that costs $67,000 topurchase and $3,000 to install with an 8-year life. Use the sum-of-years-digits method.

                                          Depreciation                      Book Value

                                              for year                             after year

                                                  $                                           $

Year 1 -                                   15,556                                 54,444

Year 2                                     13,611                                   40,833                                  

Year 3                                     11.667                                   29,667

Year 4                                      9,722                                   19,444

Year 5                                      7,778                                    11,667

Year 6                                      5,833                                     5,833

Year 7                                       3,889                                     1,944

Year 8                                       1,944                                           0

Explanation:

Computation of yearly depreciation using sum of the years method

Cost of equipment                                                                $ 67,000

Installation cost                                                                     $   3,000

Depreciable cost                                                                  $ 70,000

In a sum of the years method the mo of years are summed up and then depreciation  is applied with the highest number first.

Sum of the years = (1+2+3+4+5+6+7+8) = 36

Depreciable basis                                                                 $  70,000

Depreciation for year 1 = 8/36* 70,000                               $ (15,556)

Book value after year 1                                                          $ 54,444

Depreciation for year 2 = 7/36* 70,000                               $ (13,611)

Book value after year 2                                                          $ 40,833

Depreciation for year 3 = 6/36* 70,000                               $  (11,667)

Book value after year 3                                                          $ 29,667

Depreciation for year 4 = 5/36* 70,000                               $  ( 9.722)

Book value after year 4                                                          $ 19,444

Depreciation for year 5 = 4/36* 70,000                               $   (7,778)

Book value after year 5                                                        $    11,667

Depreciation for year 6 = 3/36* 70,000                               $   (5,833)

Book value after year 6                                                        $    5,883

Depreciation for year 7 = 4/36* 70,000                               $   (3,889)

Book value after year 7                                                        $    1,944

Depreciation for year 8 = 1/36* 70,000                               $   (1,944)

Book value after year 8                                                        $    0

Year 1: Depreciation expense = $15,556

Year 2: Depreciation expense = $13,611

Year 3: Depreciation expense = $11,667

Year 4: Depreciation expense = $9,722

Year 5: Depreciation expense = $7,778

Year 6: Depreciation expense = $5,833

Year 7: Depreciation expense = $3,889

Year 8: Depreciation expense = $1,944

Explanation:

Step 1: Calculation of machine depreciable cost

Depreciable cost of machine =  $67,000 + $3,000 = $70,000

Step 2: Calculation of sum of the year's digit

Sum of the year's digit = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) = 36

Step 3: Computation of depreciation

The following formula will be used:

Depreciation expenses = (Remaining useful asset life ÷ Sum of the year's digit) × machine depreciable cost

Net book value for the current year = Net book value for the previous year - Depreciation expenses for the current year

The calculation now proceeds as follows:

Machine depreciable cost = $70,000

Year 1: Depreciation expense = [(8 ÷ 36) × 70,000) = $15,556

Year 1: Net book value = $70,000 - $15,556  = $54,444

Year 2: Depreciation expense = [(7 ÷ 36) × 70,000) = $13,611

Year 2: Net book value = $54,444  - $13,611   = $40,833

Year 3: Depreciation expense = [(6 ÷ 36) × 70,000) = $11,667

Year 3: Net book value = $40,833  - $11,667   = $29,667

Year 4: Depreciation expense = [(5 ÷ 36) × 70,000) = $9,722

Year 4: Net book value = $29,667  - $9,722 = $19,444

Year 5: Depreciation expense = [(4 ÷ 36) × 70,000) = $7,778

Year 5: Net book value = $19,444 - $7,778 = $11,667

Year 6: Depreciation expense = [(3 ÷ 36) × 70,000) = $5,833

Year 6: Net book value = $11,667 - $5,833  = $5,833

Year 7: Depreciation expense = [(2 ÷ 36) × 70,000) = $3,889

Year 7: Net book value = $5,833 - $3,889  = $1,944

Year 8: Depreciation expense = [(1 ÷ 36) × 70,000) = $1,944

Year 8: Net book value = $1,944 - $1,944  =  $0

It can be seen that the asset becomes fully depreciated and its value become zero after year 8.

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