Chapter 9, Problem 9.2BPR

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 four years ending December 31 by straight-line method.

Explanation of Solution

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

Year	Depreciation Expense (1)
2015	$71,250
2016	$71,250
2017	$71,250
2018	$71,250
Total	$285,000

Table (1)

Working note:

Compute depreciable expense under straight line method.

Cost of the equipment= $320,000

Residual value of the equipment = $35,000.

Estimated Useful life of the equipment = 4 years

$\begin{array}{c}\text{Depreciation expense =}\frac{\text{ Cost }-\text{Residual}\text{value}}{\text{Estimated useful life}}\\ \text{=}\frac{\text{ \$320,000 }-\text{\$35,000}}{\text{4 Years}}\\ =\frac{\text{ \$}285,00\text{0}}{\text{4 Years}}\\ =\$71,250\end{array}$ (1)

Conclusion

Therefore, the amount of depreciation for four years ending December 31 by straight-line method is $71,250.

(b)

To 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) (2)	Depreciation Expense (A×B)
2015	7,200	$14.25	$102,600
2016	6,400	$14.25	$91,200
2017	4,400	$14.25	$62,700
2018	2,000	$14.25	$28,500
Total			$285,000

Table (2)

Working notes:

Determine the depreciable rate of the equipment.

Cost of the equipment= $320,000

Residual value of the equipment = $35,000.

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

$\begin{array}{c}\text{Depreciation expense =}\frac{\text{ Cost }-\text{Residual}\text{value}}{\text{Estimated useful life}}\\ \text{=}\frac{\text{ \$320,000 }-\text{\$35,000}}{\text{20,000 Hours}}\\ =\frac{\text{ \$}285,00\text{0}}{\text{20,000 Hours}}\\ =\$14.25\text{ Per hour}\end{array}$ (2)

Conclusion

Therefore, the amount of depreciation for four years ending December 31 by units-of-activity method are 2015: $102,600, 2016: $91,200, 2017: $62,700, and 2018: $28,500.

(c)

To determine

the amount of depreciation for four year 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.

Year	Depreciable Expense
2015	$160,000 (3)
2016	$80,000 (4)
2017	$40,000 (5)
2018	$5,000 (6)
Total	$285,000

Table (3)

Working notes:

Compute depreciable expense for 2015.

$\begin{array}{c}\text{Depreciation expense = Purchase price}\times \frac{\text{2}}{\text{Useful life}}\\ \text{ = \$320,000}\times \frac{\text{2}}{4}\\ =\$160,000\end{array}$ (3)

Compute depreciable expense for 2016.

$\begin{array}{c}\text{Depreciation expense =}\left[\begin{array}{l}\left(\begin{array}{l}\text{Cost}-\\ \text{Accumulated depreciation}\end{array}\right)\\ \times \frac{\text{2}}{\text{Useful life}}\end{array}\right]\\ \text{ = }\left[\left(\begin{array}{l}\text{\$320,000}-\\ \$160,000\end{array}\right)\times \frac{\text{2}}{\text{4}}\right]\\ =\left(\$160,000\times \frac{\text{2}}{\text{4}}\right)\\ =\$80,000\end{array}$ (4)

Compute depreciable expense for 2017.

$\begin{array}{c}\text{Depreciation expense =}\left[\begin{array}{l}\left(\begin{array}{l}\text{Cost}-\\ \text{Accumulated depreciation}\end{array}\right)\\ \times \frac{\text{2}}{\text{Useful life}}\end{array}\right]\\ \text{ = }\left[\left\{\text{\$320,000}-\left(\$160,000+\$80,000\right)\right\}\times \frac{\text{2}}{\text{4}}\right]\\ =\left(\$80,000\times \frac{\text{2}}{\text{4}}\right)\\ =\$40,000\end{array}$ (5)

Compute depreciable expense for 2018.

$\begin{array}{c}\text{Depreciation expense =}\left(\begin{array}{l}\text{Cost}-\\ \text{Accumulated depreciation}\end{array}\right)\\ \text{ = }\$320,000-\left(\begin{array}{l}\$160,000+\\ \$80,000+\$40,000\end{array}\right)\\ =\$320,000-\$280,000\\ =\$40,000\end{array}$

Note (6):

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

Since the depreciation expense should not exceed the residual value of $35,000. 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 2018 would be $\text{\$5,000 (\$40,000 - \$35,000)}$.

Conclusion

Therefore, the amount of depreciation for four years ending December 31 by double-declining-balance method are 2015: $160,000, 2016: $80,000, 2017: $40,000, and 2018: $5,000.

2.

To determine

the method that yields the highest depreciation expense for 2015.

Explanation of Solution

The method that yields the highest depreciation expense for 2015 is double-declining-balance method that is, $160,000.

3.

To determine

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

Explanation of Solution

As calculated above, the total depreciation expense under three method for the four-year life of the equipment is same, that is, $285,000. Thus, it cannot be determined.