Question

(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.

Short answer

1. Depreciation for 2017 is $46,500 and for 2018 is $59,675
2. Depreciation for 2017 is 453,325and for 2018 is $65,768

Step-by-step solution

Meaning of Depreciation                                                                                                     

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.

(a) Computing the depreciation for the asset for 2017 and 2018 using the sum-of-the-years’-digits method.

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

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

Therefore depreciation for 2018 is $15,500 + $44,175 = $59,675

(b) Compute the depreciation for this asset for 2017 and 2018 using the double-declining-balance method

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

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

Calculating depreciation for 2018

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