91Ó°ÊÓ

Depreciation is a branch of accounting that deals with systematically spreading or dividing the cost or other principal value of a fixed assetover its expected useful life by charging regular expenses or revenues.

If there is any salvage value and the quantity is unknown (as is the case here), the cost must be calculated using the double-declining balance method's data.

Determining the percentage of double declining balance

$$\begin{gathered} \mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{Balance}}\mathbf{=}\frac{\mathbf{\text{Total}}\mathbf{}\mathbf{\text{percentage}}}{\mathbf{\text{Service}}\mathbf{}\mathbf{\text{life}}}\mathbf{×}\mathbf{\text{Double}}\mathbf{}\mathbf{\text{times}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{100}\mathbf{\%}}{\mathbf{5}}\mathbf{×}\mathbf{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{40}\mathbf{\%} \end{gathered}$$

Calculating the Cost of asset

$$\begin{gathered} \mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{=}\frac{\mathbf{\text{Declining}}\mathbf{}\mathbf{\text{balance}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Declining}}\mathbf{}\mathbf{\text{balance}}\mathbf{}\mathbf{\text{percentage}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{000}}{\mathbf{40}\mathbf{\%}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{000}}{\mathbf{.}\mathbf{40}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000} \end{gathered}$$

There is a Salvage value of $5,000 for the asset used by the Rembrandt Company whose estimated service life is 5 years.

Working notes:

$$\begin{gathered} \mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\mathbf{\text{Total}}\mathbf{}\mathbf{\text{depreciation}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{000} \end{gathered}$$

The highest charge to income for Year 1 will be yielded by the double-declining balance method.

In double declining balance depreciation, the existing depreciation approach is doubled. Deferring income taxes to later years permits the company to devalue settled resources more intensely during its early years.

The highest charge to income for Year 4 will be yielded by the straight-line method.

The most typical approach for recognizing a fixed asset's carrying value over time is to use straight-line depreciation. When there is no precise pattern to how assets will be used over time, this is used.

The straight-line technique, which delivers the lowest accumulated depreciation at the conclusion of Year 3, is the method that produces the greatest book value at the end of Year 3.

Computation of Straight-line depreciation for Year 3

$$\begin{gathered} \mathbf{\text{Straight}}\mathbf{}\mathbf{\text{line}}\mathbf{}\mathbf{\text{depreciation}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\left(\text{Sum}\text{of}\text{depreciation}\text{for}\text{year}1,2,\text{and}3\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\left(\$9,000+\$9,000+9,000\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{27}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{23}\mathbf{,}\mathbf{000} \end{gathered}$$

Computation of Sum-of-the Years’-Digits for Year 3

$$\begin{gathered} \mathbf{\text{Sum}}\mathbf{ }\mathbf{\text{of}}\mathbf{}\mathbf{\text{the}}\mathbf{}\mathbf{\text{year}}\mathbf{}\mathbf{\text{digit}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\left(\text{Sum}\text{of}\text{depreciation}\text{for}\text{year}1,2,\text{and}3\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\left(\$15,000+\$12,000+9,000\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{36}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{14}\mathbf{,}\mathbf{000} \end{gathered}$$

Computation of Double-Declining Balance for Year 3

$$\begin{gathered} \mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{balance}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\left(\text{Sum}\text{of}\text{depreciation}\text{for}\text{year}1,2,\text{and}3\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\left(\$20,000+\$12,000+7,200\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{39}\mathbf{,}\mathbf{200} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{800} \end{gathered}$$

The technique with the lowest book value at the end of Year 3 will generate the highest gain (or lowest loss) if the asset is sold at the end of Year 3, which in this case is the double-declining balance approach.