(Depreciation Computations—SYD, DDB—Partial Periods) Judds Company purchased a new plant asset on April 1, 2017, at a cost of \(711,000. It was estimated to have a service life of 20 years and a salvage value of \)60,000. Judds’ accounting period is the calendar year.

Instructions

1. Compute the depreciation for this asset for 2017 and 2018 using the sum-of-the-years’-digits method.
2. Compute the depreciation for this asset for 2017 and 2018 using the double-declining-balance method.

The term "depreciation" refers to the process of diminishing the book value of fixed assets over time.Shrinkage is calculated using the cost of the assets used in the company rather than the market worth of the assets.

Calculating the sum of years’ digit value

$$\begin{gathered} \mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{year's}}\mathbf{}\mathbf{\text{digits}}\mathbf{=}\frac{\mathbf{\text{n}}\left(\text{n}+1\right)}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{20}\left(20+1\right)}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{210} \end{gathered}$$

Calculating depreciation for 2017

$$\begin{gathered} \mathbf{\text{Deprecaition}}\mathbf{=}\left(\text{Plant}\text{asset}\text{cost}-\text{Salvage}\text{value}\right)\mathbf{\times }\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}}{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}\mathbf{}\mathbf{\text{in}}\mathbf{}\mathbf{\text{a}}\mathbf{}\mathbf{\text{year}}}\mathbf{\times }\frac{\mathbf{\text{Service}}\mathbf{}\mathbf{\text{life}}}{\mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{year's}}\mathbf{}\mathbf{\text{digit}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$711,000-\$60,000\right)\mathbf{\times }\frac{\mathbf{9}}{\mathbf{12}}\mathbf{\times }\frac{\mathbf{20}}{\mathbf{210}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{651}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{9}}{\mathbf{12}}\mathbf{\times }\frac{\mathbf{20}}{\mathbf{210}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{46}\mathbf{,}\mathbf{500} \end{gathered}$$

Calculating depreciation for 2018 for the first 3 month

$$\begin{gathered} \mathbf{\text{Deprecaition}}\mathbf{=}\left(\text{Plant}\text{asset}\text{cost}-\text{Salvage}\text{value}\right)\mathbf{\times }\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}}{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}\mathbf{}\mathbf{\text{in}}\mathbf{}\mathbf{\text{a}}\mathbf{}\mathbf{\text{year}}}\mathbf{\times }\frac{\mathbf{\text{Service}}\mathbf{}\mathbf{\text{life}}}{\mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{year's}}\mathbf{}\mathbf{\text{digit}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$711,000-\$60,000\right)\mathbf{\times }\frac{\mathbf{3}}{\mathbf{12}}\mathbf{\times }\frac{\mathbf{20}}{\mathbf{210}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{651}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{3}}{\mathbf{12}}\mathbf{\times }\frac{\mathbf{20}}{\mathbf{210}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{15}\mathbf{,}\mathbf{500} \end{gathered}$$

Calculating depreciation for 2018 for the first next 9 months

$$\begin{gathered} \mathbf{\text{Deprecaition}}\mathbf{=}\left(\text{Plant}\text{asset}\text{cost}-\text{Salvage}\text{value}\right)\mathbf{\times }\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}}{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{month}}\mathbf{}\mathbf{\text{in}}\mathbf{}\mathbf{\text{a}}\mathbf{}\mathbf{\text{year}}}\mathbf{\times }\frac{\mathbf{\text{Service}}\mathbf{}\mathbf{\text{life}}}{\mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{year's}}\mathbf{}\mathbf{\text{digit}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$711,000-\$60,000\right)\mathbf{\times }\frac{\mathbf{9}}{\mathbf{12}}\mathbf{\times }\frac{\mathbf{19}}{\mathbf{210}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{651}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{9}}{\mathbf{12}}\mathbf{\times }\frac{\mathbf{19}}{\mathbf{210}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{44}\mathbf{,}\mathbf{175} \end{gathered}$$

Calculating double declining percentage

$$\begin{gathered} \mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{depreciation}}\mathbf{}\mathbf{\text{percentage}}\mathbf{=}\frac{\mathbf{\text{100\%}}}{\mathbf{\text{Useful}}\mathbf{}\mathbf{\text{life}}}\mathbf{\times }\mathbf{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{100}\mathbf{\%}}{\mathbf{20}}\mathbf{\times }\mathbf{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{10}\mathbf{\%} \end{gathered}$$

Calculating depreciation for 2017

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\mathbf{\text{Plant}}\mathbf{}\mathbf{\text{asset}}\mathbf{}\mathbf{\text{cost}}\mathbf{\times }\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{months}}}{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{months}}\mathbf{}\mathbf{\text{in}}\mathbf{}\mathbf{\text{a}}\mathbf{}\mathbf{\text{year}}}\mathbf{\times }\mathbf{\text{Depreciation}}\mathbf{ }\mathbf{\text{rate}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{711}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{9}}{\mathbf{12}}\mathbf{\times }\mathbf{10}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{711}\mathbf{,}\mathbf{000}\mathbf{\times }\frac{\mathbf{9}}{\mathbf{12}}\mathbf{\times }\frac{\mathbf{10}}{\mathbf{100}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{53}\mathbf{,}\mathbf{325} \end{gathered}$$

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\left(\text{Plant}\text{asset}\text{cost}-\text{Depreciation} \text{for}2017\right)\mathbf{\times }\mathbf{\text{Depreciation}}\mathbf{ }\mathbf{\text{rate}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$711,000-\$53,325\right)\mathbf{\times }\mathbf{10}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{657}\mathbf{,}\mathbf{675}\mathbf{\times }\frac{\mathbf{10}}{\mathbf{100}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{65}\mathbf{,}\mathbf{768} \end{gathered}$$