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.