91Ó°ÊÓ

In financial accounting, depreciation could be a strategy for spreading out the cost of tangible resources over their functional lives. Essentially, it is the disintegration of the value of an asset, which happens over time due to continuous use and abrasion of the asset.

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\frac{\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Useful}}\mathbf{}\mathbf{\text{life}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{315}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{15}\mathbf{,}\mathbf{000}}{\mathbf{10}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{30}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{per}}\mathbf{}\mathbf{\text{unit}}\mathbf{=}\frac{\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Estimated}}\mathbf{}\mathbf{\text{production}}}\mathbf{×}\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{units}}\mathbf{}\mathbf{\text{produced}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{315}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{15}\mathbf{,}\mathbf{000}}{\mathbf{240}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{\text{units}}}\mathbf{×}\mathbf{25}\mathbf{,}\mathbf{500} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{31}\mathbf{,}\mathbf{875} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{per}}\mathbf{}\mathbf{\text{unit}}\mathbf{=}\frac{\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Estimated}}\mathbf{}\mathbf{\text{working}}\mathbf{}\mathbf{\text{hour}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{315}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{15}\mathbf{,}\mathbf{000}}{\mathbf{25}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{\text{hours}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{12}\mathbf{}\mathbf{\text{per}}\mathbf{}\mathbf{\text{hour}} \end{gathered}$$

Therefore depreciation under the working hour is $31,800

Working notes:

Working notes:

$$\begin{gathered} \mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{year's}}\mathbf{}\mathbf{\text{digits}}\mathbf{=}\frac{\mathbf{\text{n}}\left(\text{n}+1\right)}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{10}\left(10+1\right)}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{55} \end{gathered}$$

Therefore, depreciation under the sum-of-the-years’-digits method is $50,909

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{rate}}\mathbf{×}\mathbf{\text{Book}}\mathbf{}\mathbf{\text{value}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{×}\mathbf{\text{Time}}\mathbf{}\mathbf{\text{period}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{20}\mathbf{\%}\mathbf{×}\mathbf{\$}\mathbf{315}\mathbf{,}\mathbf{000}\mathbf{×}\frac{\mathbf{4}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{21}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\mathbf{\text{Book}}\mathbf{}\mathbf{\text{value}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\left(\text{Book} \text{value}×\text{Depreciation}\text{rate}\right)\mathbf{×}\mathbf{\text{Deprecaition}}\mathbf{ }\mathbf{\text{rate}}\mathbf{×}\mathbf{\text{Time}}\mathbf{}\mathbf{\text{period}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{315}\mathbf{,}\mathbf{000}\mathbf{-}\left(315,000×20\%\right)\mathbf{×}\mathbf{20}\mathbf{\%}\mathbf{×}\frac{\mathbf{8}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{315}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{63}\mathbf{,}\mathbf{000}\mathbf{×}\frac{\mathbf{20}}{\mathbf{100}}\mathbf{×}\frac{\mathbf{8}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{33}\mathbf{,}\mathbf{000} \end{gathered}$$

Therefore, depreciation under the Double Declining-balance method is $54,600