Machinery was purchased on January 1 for $73,500.00. The machinery has an estimated life of seven years and an estimated salvage value of $9,000. Double-declining-balance depreciation for the second year would be (round calculations to the nearest dollar):

a.$16,000
b.$15,000
c.$14,500
d.$14,000

The correct answer is:

$15,000 (b.)

Explanation:

Depreciation in accounting is a cost allocation method, which refers to how much the value of an asset has been used up, assets that are depreciating helps companies earn revenues from the asset, while expensing a portion of its cost each year the asset is in use, and this is taken into account to properly determine the profit gotten.

In calculation of the depreciation of an asset, the straight-line depreciation refers to a uniform allocation of the depreciation of an asset over the useful life of the asset, while an accelerated depreciation allows for greater deductions in the early years of the useful life of an asset as compared to its later years. Double-decline-balance depreciation is a type of accelerated depreciation method. Here, the depreciation rate (reciprocal of the useful life) of an asset is doubled, and it is applied to the book value for the remaining useful life of the asset. Mathematically, this is shown as:

Double-decline-balance formula = 2 × cost of asset × depreciation rate

where:

Cost of asset = $73,500

useful life = 7 years

salvage value = $9,000

Depreciation rate = (1 ÷ useful life) × 100 = (1 ÷ 7) × 100 = 14.2857% or

Therefore,

Year 1 = 2 × cost of asset × depreciation rate

= (2 × depreciation rate ) × cost of asset.

2 × depreciation rate = 2 × 14.2857% = 28.57% = 28.57 ÷ 100 = 0.2857

∴ Year 1 = 0.2857 × 73,500 = $20,999

Cost of asset after year 1 depreciation = 73,500 - 20,999 = $52,501

Year 2 = (2 × depreciation rate ) × cost of asset.

where cost of asset for year 2 = $52,501

∴ Year 2 depreciation = 0.2857 × 52,501 = 14,999.5 = $15,000 ( to the nearest dollar)

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