Chapter 11, Problem 11.3BE

Depreciation methods; partial periods

• LO11–2

Refer to the situation described in BE 11–2. Assume the machine was purchased on March 31, 2018, instead of January 1. Calculate depreciation expense for 2018 and 2019 using each of the following depreciation methods: (a) straight line, (b) sum-of-the-years’-digits, and (c) double-declining balance.

To determine

Partial period depreciation:

Partial period depreciation is calculated when acquisition and disposal occur at different times in a fiscal year, a company must determine the depreciation, depletion, and amortization to record for the part of the year that each asset actually is used.

To Calculate: Depreciation expense for 2018 and 2019 using straight line depreciation method.

Explanation of Solution

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.

$\text{Dpreciationexp}\text{expenses}\text{=}\frac{\left(\text{cost}\text{of}\text{the}\text{asset}\text{-}\text{salvage}\text{value}\right)}{\text{Estimated}\text{useful}\text{life}\text{of}\text{the}\text{asset}}$

Cost of the equipment is $30,000. Residual value at the end of an estimated four-year service life is expected to be $2,000.  The annual depreciation is calculated as follows.

$\begin{array}{c}\text{Dpreciationexp}\text{expenses}\text{=}\frac{\left(\text{cost}\text{of}\text{the}\text{asset}\text{-}\text{salvage}\text{value}\right)}{\text{Estimated}\text{useful}\text{life}\text{of}\text{the}\text{asset}}\\ =\frac{\left(\$30,000-\$2000\right)}{4\text{years}}\\ =\frac{\$28,000}{4}\\ =\$7,000\end{array}$

Therefore the annual depreciation is $7,000.

Calculate depreciation for 2018.

The equipment was purchased on March 31, 2018, that is in the year 2018 the equipment used only for 9 months (April - December).

Therefore the depreciation for 2018 is as follows:

$\begin{array}{c}\text{ Depreciation expense}\text{= Annual depreciation }\times \frac{\text{Number}\text{of}\text{months}\text{used}}{\text{12}\text{months}}\\ =\$7,000\times \frac{9}{12}\\ =\$5250\end{array}$

Therefore depreciation expense for 2018 under straight line method is $5250.

Calculate depreciation for 2019:

In 2019, the equipment used for total 12 months that is January – December.

Therefore the depreciation for 2018 is as follows:

$\begin{array}{c}\text{ Depreciation expense}\text{= Annual depreciation }\times \frac{\text{Number}\text{of}\text{months}\text{used}}{\text{12}\text{months}}\\ =\$7,000\times \frac{12}{12}\\ =\$7,000\end{array}$

Therefore depreciation expense for 2019 under straight line method is $7,000.

To determine

To calculate: Depreciation expense for 2018 and 2019 using sum-of-the-years’-digits depreciation method.

Explanation of Solution

Sum-of- the-years’ digits (SYD) method:

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

$\begin{array}{c}\text{Depreciation}\text{expense}\text{=}\{\begin{array}{l}\text{Cost of the asset }\times \left(\begin{array}{l}\text{Number of years of}\\ \text{estimated life remaining }\\ \text{at the beginning of the year}\end{array}\right)\begin{array}{l}\text{÷}\text{SYD}\hfill \end{array}\\ \times \frac{\text{number of months used}}{\text{12months}}\end{array}\\ \text{SYD}\text{=}\frac{\text{n}\left(\text{n+1}\right)}{\text{2}}\end{array}$

Where n is estimated life time of the asset.

Calculate depreciation for 2018.

The equipment was purchased on March 31, 2018, that is in the year 2018 the equipment used only for 9 months (April - December).

Therefore the depreciation for 2018 is as follows:

$\begin{array}{l}\text{Depreciation}\text{expense}=\left(\$30,000-\$2,000\right)\times \frac{4}{10}\times \frac{9}{12}\\ =\$28,000\times \frac{36}{120}\\ =\$8,400\end{array}$

Therefore depreciation expense for the year 2018 is $8,400.

Calculate depreciation for 2019:

In 2019, the equipment used for total 12 months that is January – December.

Therefore the depreciation for 2018 is as follows:

Depreciation expenses for 2019 1^st January to 31^st March (first 3 months)

$\begin{array}{c}\text{ Depreciation expense}\text{= }\left[\text{\$28,000}\times \frac{4}{10}\times \frac{3}{12}\right]\\ =\$2,800\end{array}$

Depreciation expenses for 2019 1^st April to 31^st December (remaining 9 months)

$\begin{array}{c}\text{ Depreciation expense}\text{= }\left[\text{\$28,000}\times \frac{3}{10}\times \frac{9}{12}\right]\\ =\$6,300\end{array}$

Depreciation for the year 2019 is as follows

$\begin{array}{c}\text{Depreciation expense = }\left(\text{first}\text{3}\text{months}\right)\text{ + }\left(\text{remaining}\text{9}\text{months}\right)\\ =\$2,800+\$6,300\\ =\$9,100\end{array}$

Therefore depreciation expense for 2019 under sum-of-the years’ digits method is $9,100.

Note:

Equipment is purchased on 31^st March, 2018 useful life of the equipment is 4 years, that is till March 31st, 2022. Due to that for every year depreciation is calculated based on the useful life of the equipment, which is equipments 4 years life cycle.

To determine

To calculate: Depreciation expense for 2018 and 2019 using double-declining-balance (DDB) depreciation method.

Explanation of Solution

Double declining balance (DDB) method:

In this method of depreciation, the depreciation is calculated by multiply beginning of year book value, not depreciable base, by an annual rate that is a multiple of the straight line rate.

$\text{Depreciation expense}\text{=}\left[\begin{array}{l}\left(\begin{array}{l}\text{Begining}\text{value}\\ \text{of}\text{the}\text{asset}\end{array}\right)\text{×}\left(\begin{array}{l}\text{Straight}\text{line}\text{rete}\\ \text{of}\text{depreciation }\times \text{ 2}\end{array}\right)\\ \text{×}\left(\frac{\text{Number}\text{of}\text{months}\text{used}}{\text{12}\text{months}}\right)\end{array}\right]$

Calculate depreciation for 2018.

The equipment was purchased on March 31, 2018, that is in the year 2018 the equipment used only for 9 months (April - December).

Therefore the depreciation for 2018 is as follows:

$\begin{array}{c}\text{Depreciation expense}\text{=}\left[\begin{array}{l}\left(\begin{array}{l}\text{Begining}\text{value}\\ \text{of}\text{the}\text{asset}\end{array}\right)\text{×}\left(\begin{array}{l}\text{Straight}\text{line}\text{rete}\\ \text{of}\text{depreciation }\times \text{ 2}\end{array}\right)\\ \text{×}\left(\frac{\text{Number}\text{of}\text{months}\text{used}}{\text{12}\text{months}}\right)\end{array}\right]\\ \text{= \$30,000}\times \left(\frac{1}{4\text{years}}\right)2\times \left(\frac{9}{12}\right)\\ =\$11,250\end{array}$

Therefore depreciation expense for 2018 is $11,250.

Calculate depreciation for 2019.

Depreciation expenses for 2019 1^st January to 31^st March (first 3 months)

$\begin{array}{c}\text{Depreciation = }\left[\text{\$30,000}\times \left(\frac{1}{4\text{years}}\right)2\times \left(\frac{3}{12}\right)\right]\\ =\$ 3,750\end{array}$

Depreciation expenses for 2019 1^st April to 31^st December (remaining 9 months)

$\begin{array}{c}\text{Depreciation = }\left[\text{\$30,000}-\text{\$15,000}\times \left(\frac{1}{4\text{years}}\right)2\times \left(\frac{9}{12}\right)\right]\\ =\$ 5,625\end{array}$

Depreciation for the year 2019 is as follows

$\begin{array}{c}\text{depreciation expense = }\left(\text{first}\text{3}\text{months}\right)\text{ + }\left(\text{remaining}\text{9}\text{months}\right)\\ =\$3,750+\$5,625\\ =\$9,375\end{array}$

Therefore depreciation expense in the year 2019 is $9,375.

Note:

Equipment is purchased on 31^st March, 2018 useful life of the equipment is 4 years, that is till March 31st, 2022. Due to that for every year depreciation is calculated based on the useful life of the equipment, which is equipment’s 4 years life cycle.