Chapter 11, Problem 11.3BE

(a)

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 2016 and 2017 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.

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

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.

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

Therefore the annual depreciation is $7,000

Calculate depreciation for 2016.

The equipment was purchased on March 31, 2016, that is in the year 2016 the equipment used only for 9 months (April - December).

Therefore the depreciation for 2016 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 2016 under straight line method is $5250.

Calculate depreciation for 2017:

In 2017, the equipment used for total 12 months that is January – December.

Therefore the depreciation for 2016 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 2017 under straight line method is $7,000.

(b)

To determine

To calculate: Depreciation expense for 2016 and 2017 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 2016.

The equipment was purchased on March 31, 2016, that is in the year 2016 the equipment used only for 9 months (April - December).

Therefore the depreciation for 2016 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 2016 is $8,400.

Calculate depreciation for 2017:

In 2017, the equipment used for total 12 months that is January – December.

Therefore the depreciation for 2016 is as follows:

Depreciation expenses for 2017 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 2017 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 2017 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 2017 under sum-of-the years’ digits method is $9,100.

Equipment is purchased on 31^st March, 2016 useful life of the equipment is 4 years, that is till March 31st, 2020. Due to that for every year depreciation is calculated based on the useful life of the equipment, which is equipments 4 years life cycle.

(c)

To determine

To calculate: Depreciation expense for 2016 and 2017 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.

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

Calculate depreciation for 2016.

The equipment was purchased on March 31, 2016, that is in the year 2016 the equipment used only for 9 months (April - December).

Therefore the depreciation for 2016 is as follows:

$\begin{array}{c}\text{Depreciation = \$30,000}\times \left(\frac{1}{4\text{years}}\right)2\times \left(\frac{9}{12}\right)\\ =\$11,250\end{array}$

Therefore depreciation expense for 2016 is $11,250.

Calculate depreciation for 2017.

Depreciation expenses for 2017 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 2017 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 2017 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 2017 is $9,375.

Equipment is purchased on 31^st March, 2016 useful life of the equipment is 4 years, that is till March 31st, 2020. Due to that for every year depreciation is calculated based on the useful life of the equipment, which is equipments 4 years life cycle.