91Ó°ÊÓ

Depreciation can be stated as the decline in the value of an asset over a useful period.All fixed assets depreciate over time, except for land whose value increases with the passage of time. Among the various methods of depreciation, straight-line depreciation is considered to be the simplest and error-free method.

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\frac{\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset - Salvage}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Useful}}\mathbf{}\mathbf{\text{life}}}\mathbf{×}\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}\mathbf{}\mathbf{\text{used}}}{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}\mathbf{}\mathbf{\text{in}}\mathbf{}\mathbf{\text{a}}\mathbf{}\mathbf{\text{year}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{212}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{12}\mathbf{,}\mathbf{000}}{\mathbf{8}}\mathbf{×}\frac{\mathbf{3}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{200}\mathbf{,}\mathbf{000}}{\mathbf{8}}\mathbf{×}\frac{\mathbf{3}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{6}\mathbf{,}\mathbf{250} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{per}}\mathbf{}\mathbf{\text{unit}}\mathbf{=}\frac{\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Estimated}}\mathbf{}\mathbf{\text{production}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{212}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{12}\mathbf{,}\mathbf{000}}{\mathbf{40}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{\text{units}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{}\mathbf{\text{per}}\mathbf{}\mathbf{\text{unit}} \end{gathered}$$

Therefore total depreciation under the activity method is:

role="math" $$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\mathbf{\text{Total}}\mathbf{ }\mathbf{\text{units}}\mathbf{×}\mathbf{\text{Per}}\mathbf{}\mathbf{\text{unit}}\mathbf{}\mathbf{\text{price}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{×}\mathbf{\$}\mathbf{5} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{000} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{per}}\mathbf{}\mathbf{\text{unit}}\mathbf{=}\frac{\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Estimated}}\mathbf{}\mathbf{\text{working}}\mathbf{}\mathbf{\text{hours}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{212}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{12}\mathbf{,}\mathbf{000}}{\mathbf{20}\mathbf{,}\mathbf{000}\mathbf{}\mathbf{\text{hours}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{10}\mathbf{}\mathbf{\text{per}}\mathbf{}\mathbf{\text{hour}} \end{gathered}$$

Therefore total depreciation under the activity method is:

localid="1660288200619" $$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\mathbf{\text{Total}}\mathbf{ }\mathbf{\text{units}}\mathbf{×}\mathbf{\text{Per}}\mathbf{}\mathbf{\text{unit}}\mathbf{}\mathbf{\text{price}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1525}\mathbf{×}\mathbf{\$}\mathbf{10} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{250} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{yaer's}}\mathbf{}\mathbf{\text{digits}}\mathbf{=}\frac{\mathbf{\text{n}}\mathbf{(}\mathbf{\text{n}}\mathbf{+}\mathbf{1}\mathbf{)}}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{8}\mathbf{(}\mathbf{8}\mathbf{+}\mathbf{1}\mathbf{)}}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{36} \end{gathered}$$

Therefore, depreciation under the sum-of-the-years digit method is $37,500

Calculating double-declining depreciation rate

$$\begin{gathered} \mathbf{\text{Deprecaition}}\mathbf{=}\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{year}}}{\mathbf{\text{Useful}}\mathbf{}\mathbf{\text{life}}}\mathbf{×}\mathbf{2}\mathbf{×}\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{1}}{\mathbf{8}}\mathbf{×}\mathbf{2}\mathbf{×}\mathbf{100} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{25}\mathbf{\%} \end{gathered}$$

Calculating depreciation for 2017

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\mathbf{\text{Equipment}}\mathbf{}\mathbf{\text{cost}}\mathbf{×}\mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{rate}}\mathbf{×}\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}\mathbf{}\mathbf{\text{used}}}{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}\mathbf{}\mathbf{\text{in}}\mathbf{}\mathbf{\text{a}}\mathbf{}\mathbf{\text{year}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{212}\mathbf{,}\mathbf{000}\mathbf{×}\frac{\mathbf{25}}{\mathbf{100}}\mathbf{×}\frac{\mathbf{3}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{13}\mathbf{,}\mathbf{250} \end{gathered}$$

Calculating depreciation for 2018

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\left(\text{Equipment}\text{cost}-\text{Depreciation}\text{for}2017\right)\mathbf{×}\mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{rate}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$212,000-\$13,250\right)\mathbf{×}\frac{\mathbf{25}}{\mathbf{100}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{49}\mathbf{,}\mathbf{688} \end{gathered}$$

Therefore, depreciation under the double-declining-balance method for 2018 is $49,688.