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.

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	Depreciation Expense (1)
Year 1	$71,250
Year 2	$71,250
Year 3	$71,250
Year 4	$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

$\begin{array}{c}\text{Depreciable Expense}=\frac{\text{Cost}-\text{Residual value}}{\text{Estimated}\text{useful}\text{life}}\\ \text{= }\frac{\text{\$320,000 – \$35,000}}{4\text{years}}\\ \text{=}\frac{\$285,000}{3}\\ =\$71,250\end{array}$ (1)

Conclusion

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

1(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) (2)	Depreciation Expense (A×B)
Year 1	7,200	$14.25	$102,600
Year 2	6,400	$14.25	$91,200
Year 3	4,400	$14.25	$62,700
Year 4	2,000	$14.25	$28,500
Total			$285,000

Table (2)

Working notes:

Determinethe 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.

$\begin{array}{c}\text{Depreciation}\text{rate =}\frac{\text{Cost}-\text{Residual}\text{Value}}{\text{Estimated}\text{useful}\text{life}}\\ =\frac{\$320,000-\$35,000}{20,000\text{hours}}\\ =\frac{\$285,000}{20,000\text{hours}}\\ =\$14.25perhour\end{array}$ (2)

Conclusion

Therefore, the amount of depreciation for four years ending December 31 by units-of-activity method are Year 1: $102,600, Year 2: $91,200, Year 3: $62,700, and Year 4: $28,500.

1(c)

To determine

the amount of depreciation for four year 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	Depreciable Expense
Year 1	$160,000 (3)
Year 2	$80,000 (4)
Year 3	$40,000 (5)
Year 4	$5,000 (6)
Total	$285,000

Table (3)

Working notes:

Compute depreciable expense for Year 1.

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

Compute depreciable expense for Year 2.

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

Compute depreciable expense for Year 3.

$\begin{array}{c}\text{Depreciation}\text{expense = }\left(\begin{array}{l}\text{Cost}-\\ \text{Accumulated}\\ \text{Depreciation}\end{array}\right)\times \frac{2}{\text{Useful}\text{life}}\\ =\left[\$320,000-\left(\$160,000+\$80,000\right)\right]\times \frac{2}{4}\\ =\left(\$320,000-\$240,000\right)\times \frac{2}{4}\\ =\$80,000\times \frac{2}{4}\\ =\$40,000\end{array}$ (5)

Compute depreciable expense for Year 4.

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

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 Year 4 would be $\$5,000\left(\$40,000-\$35,000\right)$.

Conclusion

Therefore, the amount of depreciation for four years ending December 31 by double-declining-balance method are Year 1: $160,000, Year 2: $80,000, Year 3: $40,000, and Year 4: $5,000.

2.

To determine

the method that yields the highest depreciation expense for Year 1.

Explanation of Solution

The method that yields the highest depreciation expense for Year 1 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