Chapter 6, Problem 10E

a.

To determine

Compute the depreciation expense for each of the five 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.

Compute the depreciation expense for five years, using double-declining-balance depreciation.

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)$
2014	0.40	47,000	18,800
2015	0.40	28,200	11,280
2016	0.40	16,920	6,768
2017	0.40	10,152	3,152
2018	0.40	7,000	0

Table (1)

Note:

Book value:

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

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

Determine the depreciation rate applied each year.

Useful life = 5 years

$\begin{array}{c}\text{Depreciation rate = }\frac{\text{100\%}}{\text{4 years}}\text{ × 2}\\ \text{= 40\%}\text{or }\text{.40}\end{array}$                                       

Compute depreciation expense on 2017:

$\begin{array}{c}\text{Depreciation on 2017}=\left(\begin{array}{l}\text{Asset cost–Residual value}-\\ \text{Accumulated depreciation in 2016}\end{array}\right)\\ =\text{\$47,000–\$7,000–}\left(\text{\$18,800+\$11,280+\$6,768}\right)\\ =\$40,000-\$36,848\\ =\$3,152\end{array}$

Hence, the depreciation expenses for each of the five years, using double-declining-balance depreciation are $18,800, $11,280, $6,768, $3,152 and $0 respectively.

b.

To determine

Compute the depreciation expense for each of the five 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 five years, using units-of-production depreciation:

Date	Depreciation per unit (A)	Number of copies (B)	Depreciation expense (in $)$\left(\left(\text{C}\right)=\left(\text{A}\right)\times \left(\text{B}\right)\right)$
2014	$0.02	560,000	11,200
2015	$0.02	490,000	9,800
2016	$0.02	430,000	8,600
2017	$0.02	350,000	7,000
2018	$0.02	210,000	3,400

Table (2)

Compute depreciation per unit:

$\begin{array}{c}\text{Depreciation per unit =}\frac{\text{ Asset cost – Residual value}}{\text{Estimated units of total production}}\\ \text{=}\frac{\text{\$47,000–\$7,000}}{2,000,000\text{copies}}\\ \text{=}\frac{\text{\$40,000}}{2,000,000\text{copies}}\\ \text{= \$0}\text{.02}\end{array}$

Compute depreciation expense on 2018:

$\begin{array}{c}\text{Depreciation on 2018}=\left(\begin{array}{l}\text{Asset cost–Residual value}-\\ \text{Accumulated depreciation in 2017}\end{array}\right)\\ =\text{\$47,000–\$7,000–}\left(\text{\$11,200+\$9,800+\$8,600+\$7,000}\right)\\ =\$40,000-\$36,600\\ =\$3,400\end{array}$

Hence, the depreciation expenses for each of the five years, using units-of-production depreciation are $11,200, $9,800, $8,600,$7,000 and $3,400 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 copier under double-declining balance depreciation is as follows:

Particulars	$	$
Consideration received		7,600
Less: Book value:
Cost of the copier	47,000
Accumulated depreciation	(40,000)	(7,000)
Gain on sale of copier		$ 600

Table (3)

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

Particulars	$	$
Consideration received		7,600
Less: Book value:
Cost of the copier	47,000
Accumulated depreciation	(40,000)	(7,000)
Gain on sale of copier		$ 600

Table (4)

Working Note 1: Calculate the accumulated depreciation under double-declining-balance depreciation.

$\begin{array}{c}\text{Accumulated depreciation=}\left(\text{Total amount of depreciation from 2014 to }2018\right)\\ =\left(\$18,800+\$11,280+\$6,768+\$3,152+\$0\right)\\ =\$40,000\end{array}$

Working Note 2: Calculate the accumulated depreciation under units-of-production depreciation.

$\begin{array}{c}\text{Accumulated depreciation=}\left(\text{Total amount of depreciation from 2014 to }2018\right)\\ =\left(\$11,200+\$9,800+\$8,600+\$7,000+\$3,400\right)\\ =\$40,000\end{array}$

Conclusion

Hence, the gain from the sale of the asset under double-declining-balance depreciation and units-of-production depreciation are the same amount of $600.