Question

(Depreciation—Conceptual Understanding) Rembrandt Company acquired a plant asset at the beginning of Year 1. The asset has an estimated service life of 5 years. An employee has prepared depreciation schedules for this asset using three different methods to compare the results of using one method with the results of using other methods. You are to assume that the following schedules have been correctly prepared for this asset using (1) the straight-line method, (2) the sum-of-the years’-digits method, and (3) the double-declining-balance method.

Year	Straight-Line	Sum-of-the Years’-Digits	Double-Declining Balance
1	\( 9,000	\) 15,000	\(20,000
2	9,000	12,000	12,000
3	9,000	9,000	7,200
4	9,000	6,000	4,320
5	9,000	3,000	1,480
Total	\)45,000	\(45,000	\)45,000

Instructions

Answer the following questions.

1. What is the cost of the asset being depreciated?
2. What amount, if any, was used in the depreciation calculations for the salvage value for this asset?
3. Which method will produce the highest charge to income in Year 1?
4. Which method will produce the highest charge to income in Year 4?
5. Which method will produce the highest book value for the asset at the end of Year 3?
6. If the asset is sold at the end of Year 3, which method would yield the highest gain (or lowest loss) on disposal of the asset?

Short answer

1. Cost of asset =$50,000
2. Salvage value = $5,000
3. Double declining balance method
4. Straight-line method
5. Depreciation is $23,000, $14,000 and $10,800
6. Double declining balance method

Step-by-step solution

Meaning of Depreciation

Depreciation is a branch of accounting that deals with systematically spreading or dividing the cost or other principal value of a fixed assetover its expected useful life by charging regular expenses or revenues.

(a) Explaining the cost of the asset being depreciated

If there is any salvage value and the quantity is unknown (as is the case here), the cost must be calculated using the double-declining balance method's data.

Determining the percentage of double declining balance

$$\begin{gathered} \mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{Balance}}\mathbf{=}\frac{\mathbf{\text{Total}}\mathbf{}\mathbf{\text{percentage}}}{\mathbf{\text{Service}}\mathbf{}\mathbf{\text{life}}}\mathbf{\times }\mathbf{\text{Double}}\mathbf{}\mathbf{\text{times}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{100}\mathbf{\%}}{\mathbf{5}}\mathbf{\times }\mathbf{2} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{40}\mathbf{\%} \end{gathered}$$

Calculating the Cost of asset

$$\begin{gathered} \mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{=}\frac{\mathbf{\text{Declining}}\mathbf{}\mathbf{\text{balance}}\mathbf{}\mathbf{\text{value}}}{\mathbf{\text{Declining}}\mathbf{}\mathbf{\text{balance}}\mathbf{}\mathbf{\text{percentage}}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{000}}{\mathbf{40}\mathbf{\%}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{\mathbf{\$}\mathbf{20}\mathbf{,}\mathbf{000}}{\mathbf{.}\mathbf{40}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000} \end{gathered}$$

(b) Determining the amount, if any, was used in the depreciation calculations for the salvage value for the asset

There is a Salvage value of $5,000 for the asset used by the Rembrandt Company whose estimated service life is 5 years.

Working notes:

$$\begin{gathered} \mathbf{\text{Salvage}}\mathbf{}\mathbf{\text{value}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\mathbf{\text{Total}}\mathbf{}\mathbf{\text{depreciation}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{45}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{5}\mathbf{,}\mathbf{000} \end{gathered}$$

(c) Explaining the method that will produce the highest charge to income in Year 1 

The highest charge to income for Year 1 will be yielded by the double-declining balance method.

In double declining balance depreciation, the existing depreciation approach is doubled. Deferring income taxes to later years permits the company to devalue settled resources more intensely during its early years.

(d) Explaining the method that will produce the highest charge to income in Year 4

The highest charge to income for Year 4 will be yielded by the straight-line method.

The most typical approach for recognizing a fixed asset's carrying value over time is to use straight-line depreciation. When there is no precise pattern to how assets will be used over time, this is used.

(e) Explaining the method that will produce the highest book value for the asset at the end of Year 3

The straight-line technique, which delivers the lowest accumulated depreciation at the conclusion of Year 3, is the method that produces the greatest book value at the end of Year 3.

Computation of Straight-line depreciation for Year 3

$$\begin{gathered} \mathbf{\text{Straight}}\mathbf{}\mathbf{\text{line}}\mathbf{}\mathbf{\text{depreciation}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\left(\text{Sum}\text{of}\text{depreciation}\text{for}\text{year}1,2,\text{and}3\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\left(\$9,000+\$9,000+9,000\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{27}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{23}\mathbf{,}\mathbf{000} \end{gathered}$$

Computation of Sum-of-the Years’-Digits for Year 3

$$\begin{gathered} \mathbf{\text{Sum}}\mathbf{ }\mathbf{\text{of}}\mathbf{}\mathbf{\text{the}}\mathbf{}\mathbf{\text{year}}\mathbf{}\mathbf{\text{digit}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\left(\text{Sum}\text{of}\text{depreciation}\text{for}\text{year}1,2,\text{and}3\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\left(\$15,000+\$12,000+9,000\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{36}\mathbf{,}\mathbf{000} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{14}\mathbf{,}\mathbf{000} \end{gathered}$$

Computation of Double-Declining Balance for Year 3

$$\begin{gathered} \mathbf{\text{Double}}\mathbf{}\mathbf{\text{declining}}\mathbf{}\mathbf{\text{balance}}\mathbf{=}\mathbf{\text{Cost}}\mathbf{}\mathbf{\text{of}}\mathbf{}\mathbf{\text{asset}}\mathbf{-}\left(\text{Sum}\text{of}\text{depreciation}\text{for}\text{year}1,2,\text{and}3\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\left(\$20,000+\$12,000+7,200\right) \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{50}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{\$}\mathbf{39}\mathbf{,}\mathbf{200} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{\$}\mathbf{10}\mathbf{,}\mathbf{800} \end{gathered}$$

(f) Explaining the method would yield the highest gain (or lowest loss) on the disposal of the asset

The technique with the lowest book value at the end of Year 3 will generate the highest gain (or lowest loss) if the asset is sold at the end of Year 3, which in this case is the double-declining balance approach.