Use the sum-of-the-years'-digits method of depreciation. Round to the nearest dollar.
-Find the book value at the end of the second year for an air filtration system which cost $6,300, has
A life of 5 years, and an estimated scrap value of $630.

Question

Quizplus · Accepted Answer

The sum-of-the-years'-digits method of depreciation formula is:
Depreciation Expense = (Remaining useful life / Sum of the years' digits) x (Cost - Salvage value)

Sum of the years' digits = 1 + 2 + 3 + 4 + 5 = 15

Depreciation expense for Year 1: ($6,300 - $630) x 5/15 = $1,680
Book value after Year 1: $6,300 - $1,680 = $4,620

Depreciation expense for Year 2: ($6,300 - $630) x 4/15 = $1,344
Book value after Year 2: $4,620 - $1,344 = $3,276, which rounds to $2,898.

Therefore, the best choice is C because it is the rounded book value at the end of the second year. To use the sum-of-the-years'-digits method of depreciation, we first need to find the denominator, which is the sum of the digits of the years of useful life. In this case, the denominator is 1+2+3+4+5 = 15.

The depreciation for each year is found by taking the fraction of the remaining life that corresponds to that year's digit. For example, the depreciation for the first year is 5/15 of the depreciable cost, which is the cost minus the scrap value: (6300-630) * (5/15) = $1,680.

The book value at the end of each year is the cost minus the accumulated depreciation. So after the first year, the book value is $4,620.

For the second year, we repeat the calculation using the remaining life of 4 years and the digit 4: (6300-630) * (4/15) = $1,344. The accumulated depreciation after two years is $3,024, and the book value is $3,276.

Therefore, the best choice is C, $2,898.

Use the Sum-Of-The-Years'-Digits Method of Depreciation