Question

(Depreciation Computations—Five Methods) Jon Seceda Furnace Corp. purchased machinery for \(315,000 on May 1, 2017. It is estimated that it will have a useful life of 10 years, salvage value of \)15,000, production of 240,000 units, and working hours of 25,000. During 2018, Seceda Corp. uses the machinery for 2,650 hours, and the machinery produces 25,500 units.

Instructions

From the information given, compute the depreciation charge for 2018 under each of the following methods. (Round to the nearest dollar.)

1. Straight-line.
2. Units-of-output.
3. Working hours.
4. Sum-of-the-years’-digits.
5. Declining-balance (use 20% as the annual rate)

Short answer

1. Depreciation = $30,000
2. Depreciation = $31,875
3. Depreciation = $31,800
4. Depreciation = $21,000
5. Depreciation = $54,600

Step-by-step solution

Meaning of Depreciation Methods                                                                               

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.

(a) Computing depreciation using the Straight-line method 

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

(b) Computing depreciation using the Units-of-output method

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

(c) Computing depreciation using the Working hour method

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

Therefore depreciation under the working hour is $31,800

Working notes:

(d) Computing depreciation using Sum-of-the-years’-digits

Year	Depreciation base	Depreciation factor	Calculation	Depreciation expression in $
2017	300,000			18,181.82
2018	300,000			32,727.24
				50,909.09

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

(e) Computing depreciation using the Declining-balance method

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

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

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