Chapter 11, Problem 11.3E

Depreciation methods; partial periods

• LO11–2

[This is a variation of Exercise 11–2 modified to focus on depreciation for partial years.]

On October 1, 2018, the Allegheny Corporation purchased machinery for $115,000. The estimated service life of the machinery is 10 years and the estimated residual value is $5,000. The machine is expected to produce 220,000 units during its life.

Required:

Calculate depreciation for 2018 and 2019 using each of the following methods. Partial-year depreciation is calculated based on the number of months the asset is in service. Round all computations to the nearest dollar.

1. Straight line

2. Sum-of-the-years’-digits

3. Double-declining balance

4. One hundred fifty percent declining balance

5. Units of production (units produced in 2018, 10,000; units produced in 2019, 25,000)

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 2018, and 2019 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 2018.

$\begin{array}{c}\text{Depreciation expense for 2018= }\left(\begin{array}{l}\text{Depreciation expense for the year }\\ \times \frac{\text{Number of months in 2018 }}{\text{Number of months in a year}}\end{array}\right)\\ =\$11,000\times \frac{3}{12}\\ =\$2,750\text{per}\text{year}\end{array}$

Calculate the depreciation expense for the year 2019.

$\begin{array}{c}\text{Depreciation expense for 2019 = }\left(\begin{array}{l}\text{Depreciation expense for the year }\\ \times \frac{\text{Number of months in 2019 }}{\text{Number of months in a year}}\end{array}\right)\\ =\$11,000\times \frac{12}{12}\\ =\$11,000\text{per}\text{year}\end{array}$

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 2018, and 2019 as per straight line method is $2,750, and $11,000 respectively.

To determine

To Calculate: The depreciation amount for the year 2018, and 2019 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 2018.

Year	Depreciable Base(2)  ($)		Depreciation rate per year		Number of months the asset is in service		Depreciation ($)
2018	110,000	$\times$	$\frac{10}{55}$	$\times$	$\frac{3}{12}$	=	5,000

Table (1)

Calculate the depreciation expense for the year 2019.

Year	Depreciable Base(2)  ($)		Depreciation rate per year		Number of months the asset is in service		Depreciation ($)
2019	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 2018 and 2019 is $5,000, and $19,500 respectively.

To determine

To Calculate: The depreciation amount for the year 2018, and 2019 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 2018.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning book value }\\ \text{× Depreciation rate}\\ \times \frac{\text{Number of months}}{\text{12}}\end{array}\right)\\ =\$115,000\times \frac{20}{100}\times \frac{3}{12}\\ =\$5,750\end{array}$ (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 2019.

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

Conclusion

Thus, the depreciation expense as per double declining balance method for the year 2018 and 2019 is $5,750, and $21,850 respectively.

To determine

To Calculate: The depreciation amount for the year 2018, and 2019 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 2018.

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

Calculate the depreciation expense for the year 2019.

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

Conclusion

Thus, the depreciation expense as per one hundred fifty percent declining balance method for the year 2018 and 2019 is $4,313, and $16, 603 respectively.

To determine

To Calculate: The depreciation amount for the year 2018, and 2019 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 2018.

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

Determine the depreciation expense for the year 2019.

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

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 2018 and 2019 is $5,000, and $12,500 respectively.