(Depreciation Computations—Five Methods, Partial Periods) Muggsy Bogues Company purchased equipment for \(212,000 on October 1, 2017. It is estimated that the equipment will have a useful life of 8 years and a salvage value of \)12,000. Estimated production is 40,000 units and estimated working hours are 20,000. During 2017, Bogues uses the equipment for 525 hours and the equipment produces 1,000 units.

Instructions

Compute depreciation expense under each of the following methods. Bogues is on a calendar-year basis ending December 31.

1. Straight-line method for 2017.
2. Activity method (units of output) for 2017.
3. Activity method (working hours) for 2017.
4. Sum-of-the-years’-digits method for 2019.
5. Double-declining-balance method for 2018.

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.

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

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

Therefore total depreciation under the activity method is:

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

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

Therefore total depreciation under the activity method is:

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

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

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

Calculating double-declining depreciation rate

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

Calculating depreciation for 2017

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

Calculating depreciation for 2018

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

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