Chapter 6, Problem 10E

a.

To determine

Compute the depreciation expense for each of the four years, using double-declining-balance depreciation.

Explanation of Solution

Double-declining-balance method:

It is an accelerated method of depreciation under which the depreciation declines in each successive year until the value of asset becomes zero. Under this method, the book value (original cost less accumulated depreciation) of the long-term asset is decreased by a fixed rate. It is double the rate of the straight-line depreciation.

Book value:

The amount of acquisition cost of less accumulated depreciation as on a particular date is referred to as book value.

Formula for book value:

$\text{Book value = }\left\{\begin{array}{l}\text{Acquisition cost–}\\ \text{Accumulated depreciation}\end{array}\right\}$

Accumulated depreciation:

The total amount of depreciation expense deducted, from the time asset acquired till date, as reported in the account as on a particular date, is referred to as accumulated depreciation.

Formula for accumulated depreciation:

$\text{Accumulated depreciation = }\left\{\begin{array}{l}\text{Depreciation expense in the previous years}+\\ \text{Depreciation in current year}\end{array}\right\}$

Compute the depreciation expense for four years, using double-declining-balance depreciation as follows.

Date	Double-Declining-Balance Depreciation Rate (A)	Book Value (Refer note) (in $) (B)	Depreciation expense (in $)$\left(\left(\text{C}\right)=\left(\text{A}\right)\times \left(\text{B}\right)\right)$
2018	0.50	38,000	19,000
2019	0.50	19,000	9,500
2020	0.50	9,500	4,750
2021	0.50	4,750	1,250 (W.N.1)

Table (1)

Working note 1:

Compute depreciation expense on 2021.

$\begin{array}{c}\text{Depreciation on 2021}=\left(\begin{array}{l}\text{Asset cost}–\text{Residual value}-\\ \text{Accumulated depreciation in 2018}\end{array}\right)\\ =\text{\$38,00}0–\text{\$3,500}–\left(\text{\$19,000}+\text{\$9,500}+\text{\$4,750}\right)\\ =\$34,500-\$33,250\\ =\$1,250\end{array}$

Note:

Determine the depreciation rate applied each year.

Useful life = 4 years

$\begin{array}{c}\text{Depreciation rate = }\frac{\text{100\%}}{\text{4 years}}\text{ × 2}\\ \text{= 50\%}\text{or }\text{.50}\end{array}$

Conclusion

Hence, the depreciation expenses for each of the four years, using double-declining-balance depreciation are $19,000, $9,500, $4,750, and $1,250 respectively.

b.

To determine

Compute the depreciation expense for each of the four years, using units-of-production depreciation.

Explanation of Solution

Units-of-production method:

Under this method of depreciation, the depreciation expense is calculated on the basis of units produced in a year. This method is suitable when a company has fluctuating productive rate.

Compute the depreciation expense for each of the four years, using units-of-production depreciation as follows.

Date	Depreciation per unit (A)	Number of pages (B)	Depreciation expense (in $)$\left(\left(\text{C}\right)=\left(\text{A}\right)\times \left(\text{B}\right)\right)$
2018	$0.023	390,000	8,970
2019	$0.023	410,000	9,430
2020	$0.023	420,000	9,660
2021	$0.023	300,000	6,440 (W.N 3)

Table (2)

Working note 2:

Compute depreciation per unit.

$\begin{array}{c}\text{Depreciation per unit =}\frac{\text{ Asset cost – Residual value}}{\text{Estimated units of total production}}\\ \text{=}\frac{\text{\$38,000–\$3,500}}{1,500,000\text{pages}}\\ \text{=}\frac{\text{\$34,500}}{1,500,000\text{pages}}\\ \text{= \$0}\text{.023}\end{array}$

Working note 3:

Compute depreciation expense on 2021.

$\begin{array}{c}\text{Depreciation on 2021}=\left(\begin{array}{l}\text{Asset cost–Residual value}-\\ \text{Accumulated depreciation in 2018}\end{array}\right)\\ =\text{\$38,000–\$3,500–}\left(\text{\$8,970+\$9,430+\$9,660}\right)\\ =\$34,500-\$28,060\\ =\$6,440\end{array}$

Conclusion

Hence, the depreciation expenses for each of the four years, using units-of-production depreciation are $8,970, $9,430, $9,660, and $6,440 respectively.

c.

To determine

Calculate the gain or loss from the sale of the asset under each of the depreciation methods.

Explanation of Solution

A schedule to calculate the gain or loss on the sale of the printer under double-declining balance depreciation is as follows:

Particulars	$	$
Consideration received		1,650
Less: Book value:
Cost of the printer	38,000
Accumulated depreciation (W.N. 4)	(34,500	(3,500)
Gain on sale of printer		$ (1,850)

Table (3)

A schedule to calculate the gain or loss on the sale of the printer under units-of-production depreciation is as follows:

Particulars	$	$
Consideration received		1,650
Less: Book value:
Cost of the printer	38,000
Accumulated depreciation (W.N. 5)	(34,500	(3,500)
Gain on sale of printer		$ (1,850)

Table (4)

Working notes 4:

Calculate the accumulated depreciation under double-declining-balance depreciation.

$\begin{array}{c}\text{Accumulated depreciation=}\left(\text{Total amount of depreciation from 2018 to 2021}\right)\\ =\left(\$19,000+\$9,500+\$4,750+\$1,250\right)\\ =\$34,500\end{array}$

Working notes 5:

Calculate the accumulated depreciation under units-of-production depreciation.

$\begin{array}{c}\text{Accumulated depreciation=}\left(\text{Total amount of depreciation from 2018 to 2021}\right)\\ =\left(\$8,970+\$9,430+\$9,660+\$6,440\right)\\ =\$34,500\end{array}$

Conclusion

Hence, the loss from the sale of the asset under double-declining-balance depreciation and units-of-production depreciation are the same amount of $1,850.