Chapter 11, Problem 11.3E

1.

To determine

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 following is the formula to calculate the depreciation.

$\text{Depreciation cost = }\frac{\text{Cost of the asset-Salvage value}}{\text{Estimated useful life of the asset}}$

To Calculate: The depreciation amount for the year 2016, and 2017 using straight-line method.

Explanation of Solution

Calculate depreciation using Straight-Line Method:

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.

$\text{Depreciation expense = }\frac{\text{Cost of the asset-Salvage value}}{\text{Estimated useful life of the asset}}$

Calculate the depreciation expense for the year 2016.

$\begin{array}{c}\text{Depreciation expense for 2016= }\left(\begin{array}{l}\text{Depreciation expense for the year }\\ \times \frac{\text{Number of months in 2016 }}{\text{Number of months in a year}}\end{array}\right)\\ =\$11,000\times \frac{3}{12}\\ =\$2,750\text{per}\text{year}\end{array}$

Calculate the depreciation expense for the year 2017.

$\begin{array}{c}\text{Depreciation expense for 2017 = }\left(\begin{array}{l}\text{Depreciation expense for the year }\\ \times \frac{\text{Number of months in 2017 }}{\text{Number of months in a year}}\end{array}\right)\\ =\$11,000\times \frac{12}{12}\\ =\$11,000\text{per}\text{year}\end{array}$

Working Note:

Calculate the depreciation expense.

$\begin{array}{c}\text{Depreciation = }\frac{\text{Cost of the Asset }-\text{ Residual value}}{\text{Estimated Useful Life of the Asset}}\\ =\frac{\$115,000-\$5,000}{10\text{years}}\\ =\frac{\$110,000}{\text{10 years}}\\ =\$11,000\text{per}\text{year}\end{array}$

Conclusion

Thus, the depreciation expense for the year 2016, and 2017 as per straight line method is $2,750, and $11,000 respectively.

2.

To determine

To Calculate: The depreciation amount for the year 2016, and 2017 using sum-of-the years’ digits method.

Explanation of Solution

Sum-of- the-years’ digits method:

Sum-of-the years’ digits method determines the depreciation expense by multiplying the depreciable base and declining fraction.

Calculate the depreciation expense using sum-of-years’ digits method.

Calculate the depreciation expense for the year 2016.

Year	Depreciable Base(2)  ($)		Depreciation rate per year		Number of months the asset is in service		Depreciation ($)
2016	110,000	$\times$	$\frac{10}{55}$	$\times$	$\frac{3}{12}$	=	5,000

Table (1)

Calculate the depreciation expense for the year 2017.

Year	Depreciable Base(2)  ($)		Depreciation rate per year		Number of months the asset is in service		Depreciation ($)
2017	110,000	$\times$	$\frac{10}{55}$	$\times$	$\frac{9}{12}$	=	15,000
	110,000	$\times$	$\frac{9}{55}$	$\times$	$\frac{3}{12}$	=	4,500
Total							19,500

Table (2)

Working notes:

1. Calculate the sum of the digits

$\begin{array}{c}\text{Sum-of-the-digits}=\frac{\text{n}\times \left(\text{n}+1\right)}{2}\\ =\frac{10\times \left(10+1\right)}{2}\\ =\frac{10\times 11}{2}\\ =55\end{array}$ (1)

2. Calculate the value of depreciable base

$\begin{array}{c}\text{Depreciable base = Cost of the Asset }-\text{ Residual value}\\ =\$33,000-\$3,000\\ =\$30,000\end{array}$ (2)

Conclusion

Thus, the depreciation expense as per sum-of-the-years’ digits method for the year 2016 and 2017 is$5,000, and $19,500 respectively.

3.

To determine

To Calculate: The depreciation amount for the year 2016, and 2017 using double-declining balance method.

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.

Calculate the depreciation expense using Double-declining-balance method.

Calculate the depreciation expense for the year 2016.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning book value }\\ \text{× Depreciation rate}\\ \times \frac{\text{Number of months}}{\text{12}}\end{array}\right)\\ =\$115,000\times \frac{20}{100}\times \frac{3}{12}\\ =\$5,750\end{array}$ (3)

Working Note:

Determine the depreciation rate applied each year.

Useful life = 10 years

$\begin{array}{c}\text{Depreciation rate = }\frac{\text{100\%}}{\text{10 years}}\text{ × 2}\\ \text{= 20\%}\end{array}$

Note: Use 100% to represent depreciation in percentage. Multiply the depreciation rate by 2 as it is a double-declining method. 

Calculate the depreciation expense for the year 2017.

$\begin{array}{c}\text{Depreciation for 2019}=\left(\begin{array}{l}\left(\begin{array}{l}\text{Beginning book value }\\ \text{– Depreciation for 2018 (3)}\end{array}\right)\\ \times \text{Depreciation rate}\end{array}\right)\\ =\left(\left(\$115,000-\$5,750\right)\times \frac{20}{100}\right)\\ =\$21,850\end{array}$

Conclusion

Thus, the depreciation expense as per double declining balance method for the year 2016 and 2017 is$5,750, and$21,850 respectively.

4.

To determine

To Calculate: The depreciation amount for the year 2016, and 2017 using one hundred fifty percent declining balance method.

Explanation of Solution

One hundred fifty 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 one and half times the rate of the straight-line depreciation.

Calculate the depreciation expense using One hundred fifty declining-balance method.

Calculate the depreciation expense for the year 2016.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning book value × Depreciation rate}\\ \text{× }\frac{\text{3}}{\text{12}}\end{array}\right)\\ =\$115,000\times \frac{15}{100}\times \frac{3}{12}\\ =\$4,313\end{array}$ (4)

Calculate the depreciation expense for the year 2017.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning book value – }\\ \text{Depreciation charged in first year (4) }\end{array}\right)\text{× Depreciation rate}\\ =\left(\$115,000–\$4,313\right)\times \frac{15}{100}\\ =\$16,603\end{array}$

Conclusion

Thus, the depreciation expense as per one hundred fifty percent declining balance method for the year 2016 and 2017 is$4,313, and $16,603respectively.

5.

To determine

To Calculate: The depreciation amount for the year 2016, and 2017 using unit-of-production method.

Explanation of Solution

Unit-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.

Calculate the depreciation expense using Unit-of-production method.

Calculate the depreciation expense for the year 2016.

$\begin{array}{c}\text{Depreciation Expense}=\text{Depreciation per unit}\times \text{Usage}\\ \text{Depreciation Expense}=\text{Depreciation per unit}\times \text{Usage}\\ \text{= \$0}\text{.50}\times \text{\$10,000 units}\\ \text{= \$5,000}\end{array}$

Determine the depreciation expense for the year 2017.

$\begin{array}{c}\text{Depreciation Expense}=\text{Depreciation per unit}\times \text{Usage}\\ \text{= \$0}\text{.50 }\left(\text{From 5}\right)\times \text{\$25,00 units}\\ \text{= \$12,500}\end{array}$

Working Note:

Determine the depreciation per unit.

$\begin{array}{c}\text{Depreciation per unit}=\frac{\text{Cost}-\text{Residual value}}{\text{Estmated units of usefule life}}\\ \text{Depreciation per mile}=\frac{\text{Cost}-\text{Residual value}}{\text{Estmated units of usefule life}}\\ =\frac{\$115,000-\$5,000}{220,000\text{miles}}\\ =\$.50\text{per mile depreciation}\text{rate}\end{array}$ (5)

Conclusion

Thus, the depreciation expense as per units-of-production method for the year 2016 and 2017 is $5,000, and$12,500 respectively.