Chapter 6, Problem 26P

a.

To determine

Calculate the depreciation expense for each of the five years, assuming the use of straight-line depreciation.

Explanation of Solution

Straight-line Depreciation:

Under the straight-line method of depreciation, the same amount of depreciation is allocated every year over the estimated useful life of an asset. The formula to calculate the depreciation cost of the asset using the residual value is shown as below:

$\text{Depreciation = }\frac{\left(\text{Cost of the asset}-\text{Residual value}\right)}{\text{Estimated useful life of the asset}}$

Calculate the depreciation expense for each of the five years using straight-line depreciation as follows.

Date	Depreciable Cost (in $) (A) (W.N. 1)	Depreciation Rate (B)	Depreciation expense (in $)$\left(\left(\text{C}\right)=\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Year 1	35,000	1/5	7,000
Year 2	35,000	1/5	7,000
Year 3	35,000	1/5	7,000
Year 4	35,000	1/5	7,000
Year 5	35,000	1/5	7,000

Table (1)

Working note 1:

Calculate the depreciable cost.

$\begin{array}{c}\text{Depreciable cost=Cost of the asset}-\text{Residual value}\\ \text{=\$40,000}-\$5,000\\ =\$35,000\end{array}$

Conclusion

Hence, the depreciation expense for each of the five years under straight-line depreciation is $7,000.

b.

To determine

Calculate the depreciation expense for each of the five years, assuming the use of 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:

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

Calculate the depreciation expense for each of the five years using double-declining-balance depreciation as follows.

Date	Double-Declining-Balance Depreciation Rate (A) (W.N. 2)	Book Value (Refer note) (in $) (B)	Depreciation expense (in $)$\left(\left(\text{C}\right)=\left(\text{A}\right)\times \left(\text{B}\right)\right)$
Year 1	0.40	40,000	16,000
Year 2	0.40	24,000	9,600
Year 3	0.40	14,400	5,760
Year 4	0.40	8,640	3,456
Year 5	0.40	5,184	(W. N. 3) 184

Table (2)

Working note 2:

Determine the depreciation rate applied each year.

Useful life = 5 years

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

Working note 3:

Compute depreciation expense on Year 5.

$\begin{array}{c}\text{Depreciation on Year 5}=\left(\begin{array}{l}\text{Asset cost–Residual value}-\\ \text{Accumulated depreciation in Year 4}\end{array}\right)\\ =\text{\$40,000–\$5,000–}\left(\text{\$16,000+\$9,600+\$5,760+\$3,456}\right)\\ =\$35,000-\$34,8166\\ =\$184\end{array}$

Conclusion

Hence, the depreciation expense for each of the five years using double-declining-balance depreciation are $16,000, $9,600, $5,760, $3,456, and $184 respectively.

c.

To determine

Identify whether the choice of one depreciation method over another would produce a different amount of cash flow for any year and discuss its reason.

Explanation of Solution

Statement of cash flows:

This statement reports all the cash transactions which are responsible for inflow and outflow of cash, and result of these transactions is reported as ending balance of cash at the end of reported period.

Cash flows from operating activities:

These refer to the cash received or cash paid in day-to-day operating activities of a company.  In this direct method, cash flow from operating activities is computed by using all cash receipts and cash payments during the year.

Identify whether the choice of one depreciation method over another would produce a different amount of cash flow for any year and discuss its reason as follows:

Depreciation is a non-cash expense. It is added to net income while preparing the statement of cash flows under the indirect method. Due to this, the cash flow is not affected. However, there will be differences in the taxable income and the tax paid amount, when different depreciation methods are used for the tax purposes.

Hence, the choice of one depreciation method over another would produce a different amount of cash flow for the year.

d.

To determine

Compute the amount of gain or loss on sale of the computer system using each depreciation method.

Explanation of Solution

Compute the amount of gain or loss on sale of the computer system using each depreciation method as follows:

Straight line method:

$\begin{array}{c}\text{Gain = Sale price–Book value of the computer system}\\ \text{=\$15,000}-\$12,000\\ =\$3,000\end{array}$

Double declining method:

$\begin{array}{c}\text{Gain = Sale price–Book value of the computer system}\\ \text{=\$15,000}-\$5,184\\ =\$9,816\end{array}$

Working note 4:

Calculate book value of the computer system.

$\begin{array}{c}\text{Book value of computer system}=\left\{\begin{array}{l}\text{Cost of computer system}–\\ \text{Accumulated depreciation }\left(\text{Refer requirement}\text{a}\right)\end{array}\right\}\\ =\text{\$40,000 –}\left(\$7,000\times 4\text{years}\right)\\ =\text{\$40,000}-\$28,000\\ =\$12,000\end{array}$

Working note 5:

Calculate book value of the computer system.

$\begin{array}{c}\text{Book value of computer system}=\left\{\begin{array}{l}\text{Cost of computer system}–\\ \text{Accumulated depreciation }\left(\text{Refer requirement}\text{b}\right)\end{array}\right\}\\ =\text{\$40,000 –}\left(\$16,000+\$9,600+\$5,760+\$3,456\right)\\ =\text{\$40,000}-\$34,816\\ =\$5,184\end{array}$

Conclusion

Hence, the amount of gain on sale of the computer system using straight-line depreciation method, and double-declining-balance depreciation method are $3,000, and $9,816 respectively.