Chapter 9, Problem 9.2APR

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.

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

Explanation of Solution

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

Year	Depreciation Expense (1)
2014	$28,000
2015	$28,000
2016	$28,000
Total	$84,000

Table (1)

Working note:

Compute depreciation expense under straight line method.

Cost of the equipment= $90,000

Residual value of the equipment = $6,000.

Estimated Useful life of the equipment = 3 years

$\begin{array}{c}\text{Depreciation}\text{Expense}\text{=}\frac{\text{Cost}\text{-}\text{Residual}\text{Value}}{\text{Estimated}\text{useful}\text{life}}\\ \text{=}\frac{\text{\$90,000}\text{-}\text{\$6,000}}{\text{3}\text{years}}\\ \text{=}\frac{\text{\$84,000}}{\text{3}\text{years}}\\ \text{=}\text{\$28,000}\end{array}$ (1)

Conclusion

Therefore, the amount of depreciation for three years ending December 31 by straight-line method is $28,000.

(b)

To determine

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

Explanation of Solution

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

Year	Number of Hours (A)	Depreciation Rate (B) (2)	Depreciation Expense (A×B)
2014	8,900	$4.20	$37,380
2015	7,100	$4.20	$29,820
2016	4,000	$4.20	$16,800
Total			$84,000

Table (2)

Working notes:

Determine the depreciation rate of the equipment.

Cost of the equipment= $90,000

Residual value of the equipment = $6,000.

Estimated Useful life of the equipment = 20,000 operating hours.

$\begin{array}{c}\text{Depreciation}\text{Expense}\text{=}\frac{\text{Cost}\text{-}\text{Residual}\text{Value}}{\text{Estimated}\text{useful}\text{life}}\\ \text{=}\frac{\text{\$90,000}\text{-}\text{\$6,000}}{\text{20,000}\text{hours}}\\ \text{=}\frac{\text{\$84,000}}{\text{20,000}\text{hours}}\\ \text{=}\text{\$4}\text{.2}\text{per hour}\end{array}$ (2)

Conclusion

Therefore, the amount of depreciation for three years ending December 31 by units-of-activity method are 2014: $37,380, 2015: $29,820, and 2016: $16,800.

(c)

To determine

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

Explanation of Solution

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

Year	Depreciation Expense
2014	$60,000(3)
2015	$20,000 (4)
2016	$4,000(5)
Total	$84,000

Table (3)

Working notes:

Compute depreciation expense for 2014.

$\begin{array}{c}\text{Double-declining-balance}\text{rate =}\text{Purchase}\text{Price}\text{×}\frac{\text{2}}{\text{Estimated}\text{useful}\text{life}}\\ \text{=\$90,000×}\frac{\text{2}}{\text{3}\text{years}}\\ \text{=\$60,000}\end{array}$ (3)

Compute depreciation expense for 2015.

$\begin{array}{c}\begin{array}{l}\text{Depreciation}\text{for}\\ \text{the}\text{2015}\text{year }\end{array}]\text{= }\left(\text{Cost-Accumulated}\text{depreciation}\right)\text{× }\left(\frac{\text{2}}{\text{Useful life}}\right)\\ \text{=}\left(\text{\$90,000-\$60,000}\right)\text{×}\frac{\text{2}}{\text{3}}\\ \text{=\$30,000×}\frac{\text{2}}{\text{3}}\\ \text{=\$20,000}\end{array}$ (4)

Compute depreciation expense for 2016.

$\begin{array}{c}\begin{array}{l}\text{Depreciation}\text{for}\\ \text{the}\text{2016}\text{year }\end{array}]\text{= }\left(\text{Cost-Accumulated}\text{depreciation}\text{-}\text{Residual}\text{Value}\right)\\ \text{=}\left\{\text{\$90,000}\text{-}\left(\text{\$60,000}\text{+}\text{\$20,000}\text{+}\text{6,000}\right)\right\}\\ \text{=\$90,000}\text{-}\text{\$86,000}\\ \text{=\$4,000}\end{array}$

Note (5):

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

Since the depreciation expense should not exceed the residual value of $6,000. Thus, it should be adjusted to make the book value of the equipment (cost less accumulated depreciation) equal to its residual value.

Conclusion

Therefore, the amount of depreciation for three years ending December 31 by double-declining-balance method are 2014: $48,000, 2015: $16,000, and 2016: $4,000.

2.

To determine

the method that yields the highest depreciation expense for 2014.

Explanation of Solution

The method that yields the highest depreciation expense for 2014 is double-declining-balance method that is, $60,000.

3.

To determine

the method that yields the most depreciation over the three-year life of the equipment.

Explanation of Solution

As calculated above, the total depreciation expense under three method for the three-year life of the equipment is same, that is, $84,000. Thus, it cannot be determined.