Question

(Depreciation Computations—SL, SYD, DDB) Deluxe Ezra Company purchases equipment on January 1, Year 1, at a cost of \(469,000. The asset is expected to have a service life of 12 years and a salvage value of \)40,000.

Instructions

1. Compute the amount of depreciation for each of Years 1 through 3 using the straight-line depreciation method.
2. Compute the amount of depreciation for each of Years 1 through 3 using the sum-of-the-years’-digits method.
3. Compute the amount of depreciation for each of Years 1 through 3 using the double-declining-balance method. (In performing your calculations, round constant percentage to the nearest one-hundredth of a point and round answers to the nearest dollar.)

Short answer

1. Straight-line depreciation = $35,750
2. Depreciation for Year 1,2 and 3 is $66,000,$60500 and $55,000

3. Depreciation for Year 1, 2 and 3 is $390,818, $65,149 and $54,289

Step-by-step solution

Meaning of Straight-Line Depreciation

Straight-line depreciation is the simplest way to assess depreciation over time.By allocating identical amounts to the asset's accounting periods over its useful life, it makes the asset's expense predictable along with smoothing net income.

(a) Computing the amount of depreciation for each of Years 1 through 3 using the straight-line depreciation method

Straight-line method depreciation for each of Years 1 through 3 =$35,750

Working notes:

Calculating the amount of depreciation

$$\begin{gathered} \mathbf{\text{Straight}}\mathbf{}\mathbf{\text{line}}\mathbf{}\mathbf{\text{depreciation}}\mathbf{=}\frac{\mathbf{\text{Equipment}}\mathbf{}\mathbf{\text{cost}}\mathbf{-}\mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Service}}\mathbf{}\mathbf{\text{life}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{469}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{40}\mathbf{,}\mathbf{000}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{429}\mathbf{,}\mathbf{000}}{\mathbf{12}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{35}\mathbf{,}\mathbf{750} \end{gathered}$$

(b) Computing the amount of depreciation for each of Years 1 through 3 using the sum-of-the-years’-digits method

Calculating the sum of years’ digit

$$\begin{gathered} \mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{years}}\mathbf{}\mathbf{\text{digit}}\mathbf{=}\frac{\mathbf{\text{Service}}\mathbf{}\mathbf{\text{life}}\mathbf{\times }\left(\text{Service}\text{life}+1\right)}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{12}\mathbf{\times }\mathbf{13}}{\mathbf{2}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{78} \end{gathered}$$

Calculating depreciation for Year 1

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{years}}}{\mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{years}}}\mathbf{\times }\left(\text{Asset}\text{value}-\text{Salvage}\text{value}\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{12}}{\mathbf{78}}\mathbf{\times }\left(\$469,000-\$40,000\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{12}}{\mathbf{78}}\mathbf{\times }\mathbf{\$}\mathbf{429}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{66}\mathbf{,}\mathbf{000} \end{gathered}$$

Calculating depreciation for Year 2

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{years}}}{\mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{years}}}\mathbf{\times }\left(\text{Asset}\text{value}-\text{Salvage}\text{value}\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{11}}{\mathbf{78}}\mathbf{\times }\left(\$469,000-\$40,000\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{11}}{\mathbf{78}}\mathbf{\times }\mathbf{\$}\mathbf{429}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{60}\mathbf{,}\mathbf{500} \end{gathered}$$

Calculating depreciation for Year 3

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\frac{\mathbf{\text{Number}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{years}}}{\mathbf{\text{Sum}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{years}}}\mathbf{\times }\left(\text{Asset}\text{value}-\text{Salvage}\text{value}\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{10}}{\mathbf{78}}\mathbf{\times }\left(\$469,000-\$40,000\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{10}}{\mathbf{78}}\mathbf{\times }\mathbf{\$}\mathbf{429}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{000} \end{gathered}$$

(c) Computing the amount of depreciation for each of Years 1 through 3 using the double-declining-balance method

Calculating double-declining-balance rate

$$\begin{gathered} \mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{balace}}\mathbf{}\mathbf{\text{method}}\mathbf{}\mathbf{\text{rate}}\mathbf{=}\frac{\mathbf{\text{Total}}\mathbf{}\mathbf{\text{percenatge}}}{\mathbf{\text{Years}}}\mathbf{\times }\mathbf{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{100}\mathbf{\%}}{\mathbf{12}}\mathbf{\times }\mathbf{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{16}\mathbf{.}\mathbf{67}\mathbf{\%} \end{gathered}$$

Calculating depreciation for Year 1

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\mathbf{\text{Equipment}}\mathbf{}\mathbf{\text{value}}\mathbf{\times }\mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{balance}}\mathbf{}\mathbf{\text{method}}\mathbf{}\mathbf{\text{rate}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{469}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{16}\mathbf{.}\mathbf{67}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{78}\mathbf{,}\mathbf{182} \end{gathered}$$

Calculating the book value of the asset after one year

$$\begin{gathered} \mathbf{\text{Book}}\mathbf{}\mathbf{\text{value}}\mathbf{=}\mathbf{\text{Equipment}}\mathbf{}\mathbf{\text{cost}}\mathbf{-}\mathbf{\text{Depreciation}}\mathbf{}\mathbf{\text{of}}\mathbf{ }\mathbf{\text{Year}}\mathbf{}\mathbf{1} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{469}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{78}\mathbf{,}\mathbf{182} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{390}\mathbf{,}\mathbf{818} \end{gathered}$$

Calculating depreciation for Year 2

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\left(\text{Equipment}\text{cost}-\text{Depreciation}\text{of}\text{Year}1\right)\mathbf{\times }\mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{rate}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$469,000-\$78,182\right)\mathbf{\times }\mathbf{16}\mathbf{.}\mathbf{67}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{390}\mathbf{,}\mathbf{818}\mathbf{\times }\mathbf{16}\mathbf{.}\mathbf{67}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{65}\mathbf{,}\mathbf{149} \end{gathered}$$

Calculating depreciation for Year 3

$$\begin{gathered} \mathbf{\text{Depreciation}}\mathbf{=}\left(\text{Equipment}\text{cost}-\text{Depreciation}\text{of}\text{Year}1-\text{Depreciation}\text{of}\text{Year}2\right)\mathbf{\times }\mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{rate}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\left(\$469,000-\$78,182-\$65,149\right)\mathbf{\times }\mathbf{16}\mathbf{.}\mathbf{67}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{325}\mathbf{,}\mathbf{65}\mathbf{\times }\mathbf{16}\mathbf{.}\mathbf{67}\mathbf{\%} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{54}\mathbf{,}\mathbf{289} \end{gathered}$$