Chapter 9, Problem 9.3BPR

1(A)

To determine

Methods of Depreciation: Depreciation refers to the reduction in the monetary value of a fixed asset due to its wear and tear, or obsolescence. It is a method of distributing the cost of the fixed assets over its estimated useful life.

The three methods of depreciation are:

• Straight-line method: Under the straight-line method of depreciation, the same amount of depreciation is allocated every year over the estimated useful life of an asset.
• Units-of-activity method: In this method of depreciation, the amount of depreciation is charged based on the unit of production each year.
• Double-declining balance method (Accelerated method): In this method of depreciation, the diminishing value of the asset is taken into consideration for determining the depreciation for the succeeding years.

To determine: the amount of depreciation for four years ending December 31 by straight-line method.

Explanation of Solution

Determinethe amount of depreciation for four years ending December 31 by straight-line method.

Year 1:

Cost of the equipment= $108,000

Residual value of the equipment = $7,200

Estimated Useful life of the equipment = 3 years

Number of months equipment used =3 months (October 1-December 31)

$\begin{array}{c}\text{Depreciable Expense}=\left[\begin{array}{l}\frac{\text{Cost}-\text{Residual value}}{\text{Estimated}\text{useful}\text{life}}\times \\ \frac{\text{Number}\text{of}\text{months}\text{used}}{12}\end{array}\right]\\ \text{= }\frac{\text{\$108,000 – \$7,200}}{3\text{years}}\times \frac{3}{12}\\ \text{=}\frac{\$100,800}{3}\times \frac{3}{12}\\ =\$8,400\end{array}$

Year 2:

Cost of the equipment= $108,000

Residual value of the equipment = $7,200

Estimated Useful life of the equipment = 3 years

Number of months equipment used =12 months (January 1-Deccember 31)

$\begin{array}{c}\text{Depreciable Expense}=\left[\begin{array}{l}\frac{\text{Cost}-\text{Residual value}}{\text{Estimated}\text{useful}\text{life}}\times \\ \frac{\text{Number}\text{of}\text{months}\text{used}}{12}\end{array}\right]\\ \text{= }\frac{\text{\$108,000 – \$7,200}}{3\text{years}}\times \frac{12}{12}\\ \text{=}\frac{\$100,800}{3}\times \frac{12}{12}\\ =\$33,600\end{array}$

Year 3:

Cost of the equipment= $108,000

Residual value of the equipment = $7,200

Estimated Useful life of the equipment = 3 years

Number of months equipment used =12 months (January 1-Deccember 31)

$\begin{array}{c}\text{Depreciable Expense}=\left[\begin{array}{l}\frac{\text{Cost}-\text{Residual value}}{\text{Estimated}\text{useful}\text{life}}\times \\ \frac{\text{Number}\text{of}\text{months}\text{used}}{12}\end{array}\right]\\ \text{= }\frac{\text{\$108,000 – \$7,200}}{3\text{years}}\times \frac{12}{12}\\ \text{=}\frac{\$100,800}{3}\times \frac{12}{12}\\ =\$33,600\end{array}$

Year 4:

Cost of the equipment= $108,000

Residual value of the equipment = $7,200

Estimated Useful life of the equipment = 3 years

Number of months equipment used =9 months (January 1-September 30)

$\begin{array}{c}\text{Depreciable Expense}=\left[\begin{array}{l}\frac{\text{Cost}-\text{Residual value}}{\text{Estimated}\text{useful}\text{life}}\times \\ \frac{\text{Number}\text{of}\text{months}\text{used}}{12}\end{array}\right]\\ \text{= }\frac{\text{\$108,000 – \$7,200}}{3\text{years}}\times \frac{9}{12}\\ \text{=}\frac{\$100,800}{3}\times \frac{9}{12}\\ =\$25,200\end{array}$

Conclusion

Therefore, the amount of depreciation ending December 31 by straight-line method for Year 1 is $8,400, Year 2: $33,600, Year 3: $33,600, and Year 4: $25,200.

(B)

To determine

the amount of depreciation for four years ending December 31 by units-of-activity method.

Explanation of Solution

Determinethe amount of depreciation for four years ending December 31 by units-of-activity method.

Year	Number of Hours (A)	Depreciable Rate (B) (1)	Depreciation Expense (A×B)
Year 1	1,350	$8.40	$11,340
Year 2	4,200	$8.40	$35,280
Year 4	3,650	$8.40	$30,660
Year 4	2,800	$8.40	$23,520

Table (1)

Working note:

Determinethe depreciable rate of the equipment.

Cost of the equipment= $108,000

Residual value of the equipment = $7,200

Estimated Useful life of the equipment = 12,000 operating hours.

$\begin{array}{c}\text{Depreciation}\text{rate =}\frac{\text{Cost}-\text{Residual}\text{Value}}{\text{Estimated}\text{useful}\text{life}}\\ =\frac{\$108,000-\$7,200}{12,000\text{hours}}\\ =\frac{\$100,800}{12,000\text{hours}}\\ =\$8.40perhour\end{array}$ (1)

Conclusion

Therefore, the amounts of depreciation for three years ending December 31 by units-of-activity method are Year 1: $11,340, Year 2: $35,280, Year 3: $30,660, and Year 4: $23,520.

(C)

To determine

the amount of depreciation for four years ending December 31 by double-declining-balance method.

Explanation of Solution

:

Determinethe amount of depreciation for four years ending December 31 by double-declining-balance method.

Year 1:

Cost of the equipment= $108,000

Estimated Useful life of the equipment = 3 years

Number of months equipment used =3 months (October 1-December 31)

$\begin{array}{c}\text{Depreciation}\text{expense}\text{= }\left[\begin{array}{l}\text{Purchase}\text{Price}\times \frac{2}{\text{Useful}\text{life}}\\ \times \frac{\text{Number}\text{of}\text{months}\text{used}}{12}\end{array}\right]\\ =\$108,000\times \frac{2}{3}\times \frac{3}{12}\\ =\$18,000\end{array}$

Year 2:

Cost of the equipment= $108,000

Accumulated Depreciation=$18,000

Estimated Useful life of the equipment = 3 years

Number of months equipment used =12 months (January 1-December 31)

$\begin{array}{c}\text{Depreciation}\text{expense = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Cost}-\\ \text{Accumulated}\\ \text{Depreciation}\end{array}\right)\times \frac{2}{\text{Useful}\text{life}}\\ \times \frac{\text{Number}\text{of}\text{months}\text{used}}{12}\end{array}\right]\\ =\left(\$108,000-\$18,000\right)\times \frac{2}{3}\times \frac{12}{12}\\ =\$90,000\times \frac{2}{3}\\ =\$60,000\end{array}$

Year 3:

Cost of the equipment= $108,000

Accumulated Depreciation= $\$78,000(\$18,000+\$60,000)$

Estimated Useful life of the equipment = 3 years

Number of months equipment used =12 months (January 1-December 31)

$\begin{array}{c}\text{Depreciation}\text{expense = }\left[\begin{array}{l}\left(\begin{array}{l}\text{Cost}-\\ \text{Accumulated}\\ \text{Depreciation}\end{array}\right)\times \frac{2}{\text{Useful}\text{life}}\\ \times \frac{\text{Number}\text{of}\text{months}\text{used}}{12}\end{array}\right]\\ =\left(\$108,000-\$78,000\right)\times \frac{2}{3}\times \frac{12}{12}\\ =\$30,000\times \frac{2}{3}\\ =\$20,000\end{array}$

Year 4:

$\begin{array}{c}\text{Depreciation}\text{expense = Cost}-\text{Accumulated}\text{Depreciation}\\ =\$108,000-\left(\$18,000+\$60,000+\$20,000\right)\\ =\$108,000-\$98,000\\ =\$10,000\end{array}$

Notes:

Accumulated depreciation is the sum total of the previous years’ depreciation expense.

The depreciation expense should not exceed the residual value of $7,200. Thus, it should be adjusted to make the book value of the equipment (cost less accumulated depreciation) equal to its residual value.  Thus, the depreciation expense for Year 4 would be $\$2,800\left(\$10,000-\$7,200\right)$.

Conclusion

Therefore, the amounts of depreciation for four years ending December 31 by double-declining-balance method are Year 1: $18,000, Year 2: $60,000, Year 3: $20,000, and Year 4: $2,800