Chapter 10, Problem 3PB

(a)

To determine

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

Explanation of Solution

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.

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

2014:

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)

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

2015:

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)

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

2016:

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)

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

2017:

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)

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

Therefore, the amount of depreciation ending December 31 by straight-line method for 2014 is $8,400, 2015: $33,600, 2016: $33,600, and 2017: $25,200.

(b)

To determine

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

Explanation of Solution

Determine the 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)
2014	1,350	$8.40	$11,340
2015	4,200	$8.40	$35,280
2016	3,650	$8.40	$30,660
2017	2,800	$8.40	$23,520

Table (1)

Working note (1):

Determine the 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.

$\begin{array}{c}\text{Depreciation rate}\text{=}\left(\frac{\text{Cost}-\text{Residual}\text{value}}{\text{Estimated}\text{useful life}}\right)\\ =\left(\frac{\$108,000-\$7,200}{12,000\text{hours}}\right)\\ =\frac{\$100,800}{12,000}\\ =\$8.40\text{per hour}\end{array}$

Therefore, the amounts of depreciation for three years ending December 31 by units-of-activity method are 2014: $11,340, 2015: $35,280, 2016: $30,660, and 2017: $23,520.

(c)

To determine

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

Explanation of Solution

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

2014:

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)

$\begin{array}{c}\text{Depreciable}\text{Expense}\text{=}\left(\text{Purchase}\text{Price}\times \frac{2}{\text{Useful life}}\right)\times \left(\frac{\text{Number of months used}}{12}\right)\\ =\left(\$108,000\times \frac{2}{3}\right)\times \left(\frac{3}{12}\right)\\ =\$18,000\end{array}$

2015:

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)

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

2016:

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)

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

2017:

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

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 2017 would be $\$2,800(\$10,000-\$7,200)$.

Therefore, the amounts of depreciation for four years ending December 31 by double-declining-balance method are 2014: $18,000, 2015: $60,000, 2016: $20,000, and 2017: $2,800.