Chapter 9, Problem 3BP

a. 1.

To determine

Calculate the depreciation expense of the machine’s useful life for the period 2015-2020 under the straight-line depreciation method.

Explanation of Solution

Depreciation expense:

Depreciation expense is a non-cash expense, which is recorded on the income statement reflecting the consumption of economic benefits of long-term asset on account of its wear and tear or obsolescence.

Straight-line depreciation method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset could be distributed equally throughout the useful life of the asset is referred to as straight-line method.

Compute the depreciation expense of machine per year using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\\ =\$32,550\end{array}$

The depreciation expense under the straight-line method is same for every year. Hence, $32,550 is the depreciation expense of the machine for all the four years 2015-2020.

a. 2.

To determine

Calculate the depreciation expense of the machine’s useful life for the period 2015-2020 under the double-declining balance method.

Explanation of Solution

Double-declining-balance method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset is high in the early years but gradually declines towards the end of its useful life is referred to as double-declining-balance method.

Compute the depreciation expense of machine as on January 2, 2016 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\text{Acquisition cost }\times \text{ Depreciation rate}\\ =\$218,700\times \frac{33.3}{100}\\ =\$72,827\end{array}$

Compute the depreciation expense of machine as on January 2, 2017 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\left(\begin{array}{l}\text{Acquisition cost}\\ -\text{ Depreciation charged as }\\ \text{on January 2, 2016 }\end{array}\right)\times \text{ Depreciation rate}\\ =\left(\$218,700-\$72,827\right)\times \frac{33.3}{100}\\ =\text{ \$48,576}\end{array}$

Compute the depreciation expense of machine as on January 2, 2018 using double-declining balance method.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning book value }\\ -\left(\begin{array}{l}\text{Depreciation charged as}\\ \text{ on January 2, 2016}\end{array}\right)\\ -\left(\begin{array}{l}\text{Depreciation charged as }\\ \text{on January 2, 2017}\end{array}\right)\end{array}\right)\times \left(\begin{array}{l}\text{Depreciation }\\ \text{rate}\end{array}\right)\\ \text{= }\left(\text{\$218,700 – \$72,827–\$48,576}\right)\text{ × }\frac{33.3}{\text{100}}\\ \text{= \$32,400}\end{array}$

Compute the depreciation expense of machine as on January 2, 2019 using double-declining balance method.

$\text{Depreciation}=\left(\begin{array}{l}\text{Acquisition cost }\\ -\left(\begin{array}{l}\text{Depreciation charged as}\\ \text{ on January 2, 2016}\end{array}\right)\\ -\left(\begin{array}{l}\text{Depreciation charged ias}\\ \text{ on January 2, 2017}\end{array}\right)\\ -\left(\begin{array}{l}\text{Depreciation charged as }\\ \text{on January 2, 2018}\end{array}\right)\end{array}\right)\times \left(\begin{array}{l}\text{Depreciation }\\ \text{rate}\end{array}\right)$

$\begin{array}{c}=\left(\$218,700-\$72,827-\$48,576-\$32,400\right)\times \frac{33.3}{100}\\ =\$21,611\end{array}$

Compute the depreciation expense of machine as on January 2, 2020 using double-declining balance method.

$\text{Depreciation}=\left(\begin{array}{l}\text{Acquisition }\\ \text{cost}\end{array}\right)-\left(\begin{array}{l}\text{Depreciation charged as on January 2, 2016}\\ -\text{Depreciation charged as on January 2, 2017}\\ -\text{Depreciation charged as on January 2, 2018}\\ -\text{Depreciation charged as on January 2, 2019}\\ -\text{Salvage value}\end{array}\right)$

$\begin{array}{c}=\$218,700-\left(\begin{array}{l}\$72,827-\$48,576-\$32,400\\ -\$21,611-\$23,400\end{array}\right)\\ =\$19,886\end{array}$

Working Note:

Compute the depreciation rate applied each year.

Useful life = 6 years

$\begin{array}{c}\text{Depreciation rate }=\frac{\text{100\%}}{\text{6 years}}\times \text{ 2}\\ =33.3\%\end{array}$

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

a. 3.

To determine

Calculate the depreciation expense of the machine’s useful life for the period 2015-2020 under the units-of-production balance method.

Explanation of Solution

Units-of-production method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset is based on the production capacity or output is referred to as units-of-production method.

Compute the depreciation expense of machine for the year 2015 using units-of-production method.

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ 2015\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per plating}\\ \times \text{ Number of platings in 2015}\end{array}\right\}\\ =\$0.25\times 140,000\text{ platings}\\ =\$35,000\end{array}$

Compute the depreciation expense of machine for the year 2016 using units-of-production method.

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ 2016\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per plating}\\ \times \text{ Number of platings in 2016}\end{array}\right\}\\ =\$0.25\times 180,000\text{ platings}\\ =\$45,000\end{array}$

Compute the depreciation expense of machine for the year 2017 using units-of-production method.

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ 2017\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per plating}\\ \times \text{ Number of platings in 2017}\end{array}\right\}\\ =\$0.25\times 150,000\text{ platings}\\ =\$37,500\end{array}$

Compute the depreciation expense of machine for the year 2018 using units-of-production method.

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ 2018\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per plating }\\ \times \text{ Number of platings in 2018}\end{array}\right\}\\ =\$0.25\times 125,000\text{ platings}\\ =\$31,250\end{array}$

Compute the depreciation expense of machine for the year 2019 using units-of-production method.

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ 2019\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per plating }\\ \times \text{ Number of platings in 2019}\end{array}\right\}\\ =\$0.25\times \text{ 105},000\text{ platings}\\ =\$26,250\end{array}$

Compute the depreciation expense of machine for the year 2020 using units-of-production method.

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ 2020\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Depreciation per plating × }\\ \text{Number of platings in 2020}\end{array}\right\}\\ \text{= \$0}\text{.25 × 81,200 platings}\\ \text{=\$20,300}\end{array}$

Working Note:

Compute the depreciation rate per plating.

$\begin{array}{c}\begin{array}{l}\text{Depreciation }\\ \text{per plating}\end{array}\}=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Total estimated cuttings}}\\ =\frac{\text{\$218,700 }-\text{ \$23,400}}{\text{781,200 cuttings}}\\ =\text{ \$0}\text{.25 per plating}\end{array}$

b. 1.

To determine

Calculate the depreciation expense of the machine’s useful life for the period 2015-2021 under the straight-line depreciation method.

Explanation of Solution

Depreciation expense:

Depreciation expense is a non-cash expense, which is recorded on the income statement reflecting the consumption of economic benefits of long-term asset on account of its wear and tear or obsolescence.

Straight-line depreciation method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset could be distributed equally throughout the useful life of the asset is referred to as straight-line method.

Compute the depreciation expense of machine for the year 2015 using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\times \text{Time period}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\times \frac{4}{12}\left(\text{September 1 to December 31}\right)\\ =\$10,850\end{array}$

Compute the depreciation expense of machine for the year 2016 using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\\ =\$32,550\end{array}$

Compute the depreciation expense of machine for the year 2017 using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\\ =\$32,550\end{array}$

Compute the depreciation expense of machine for the year 2018 using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\\ =\$32,550\end{array}$

Compute the depreciation expense of machine for the year 2019 using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\\ =\$32,550\end{array}$

Compute the depreciation expense of machine for the year 2020 using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\\ =\$32,550\end{array}$

Compute the depreciation expense of machine for the year 2021 using straight-line method.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost – Salvage value}}{\text{Useful life}}\times \text{Time period}\\ =\frac{\text{\$218,700}-\text{\$23,400}}{\text{6 years}}\times \frac{8}{12}\left(\text{January 1 to September1}\right)\\ =\$21,700\end{array}$

b. 2.

To determine

Calculate the depreciation expense of the machine’s useful life for the period 2015-2020 under the double-declining balance method.

Explanation of Solution

Double-declining-balance method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset is high in the early years but gradually declines towards the end of its useful life is referred to as double-declining-balance method.

Compute the depreciation expense of machine as on December 31, 2015 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\left(\begin{array}{l}\text{Acquisition cost }\times \text{ Depreciation rate}\\ \times \text{Time period}\end{array}\right)\\ =\$218,700\times \frac{33.3}{100}\times \frac{4}{12}\left(\text{September 1 to December 31}\right)\\ =\$24,276\end{array}$

Compute the depreciation expense of machine as on December 31, 2016 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\left(\begin{array}{l}\text{Acquisition cost}\\ -\left(\begin{array}{l}\text{Depreciation charged }\\ \text{for 2015 }\end{array}\right)\end{array}\right)\times \text{ Depreciation rate}\\ =\left(\$218,700-\$24,276\right)\times \frac{33.3}{100}\\ =\text{ \$64,743}\end{array}$

Compute the depreciation expense of machine as on December 31, 2017 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\left(\begin{array}{l}\text{Acquisition cost }-\\ \text{Depreciation charged for 2015}\\ -\text{Depreciation charged for 2016 }\end{array}\right)\times \left(\begin{array}{l}\text{Depreciation }\\ \text{rate}\end{array}\right)\\ =\left(\$218,700-\$24,276-\$64,743\right)\times \frac{33.3}{100}\\ =\text{ \$43,184}\end{array}$

Compute the depreciation expense of machine as on December 31, 2018 using double-declining balance method.

$\text{Depreciation }=\left(\begin{array}{l}\text{Acquisition cost}\\ -\text{ Depreciation charged for 2015}\\ -\text{Depreciation charged for 2016}\\ -\text{Depreciation charged for 2017 }\end{array}\right)\times \left(\begin{array}{l}\text{Depreciation }\\ \text{rate}\end{array}\right)$

$\begin{array}{c}=\left(\$218,700-\$24,276-\$64,743-\$43,184\right)\times \frac{33.3}{100}\\ =\$28,804\end{array}$

Compute the depreciation expense of machine as on December 31, 2019 using double-declining balance method.

$\text{Depreciation }=\left(\begin{array}{l}\text{Acquisition cost}\\ -\text{ Depreciation charged for 2015}\\ -\text{Depreciation charged for 2016}\\ -\text{Depreciation charged for 2017}\\ -\text{Depreciation charged for 2018 }\end{array}\right)\times \left(\begin{array}{l}\text{Depreciation }\\ \text{rate}\end{array}\right)$

$\begin{array}{c}=\left(\begin{array}{l}\$218,700-\$24,276-\$64,743\\ -\$43,184-\$28,804\end{array}\right)\times \frac{33.3}{100}\\ =\$19,212\end{array}$

Compute the depreciation expense of machine as on December 31, 2020 using double-declining balance method.

$\text{Depreciation}=\left(\begin{array}{l}\text{Acquisition cost }\\ -\text{ Depreciation charged for 2015}\\ -\text{Depreciation charged for 2016}\\ -\text{Depreciation charged for 2017}\\ -\text{Depreciation charged for 2018}\\ -\text{Depreciation charged for 2019 }\end{array}\right)\times \left(\begin{array}{l}\text{Depreciation }\\ \text{rate}\end{array}\right)$

$\begin{array}{c}=\left(\begin{array}{l}\$218,700-\$24,276-\$64,743\\ -\$43,184-\$28,804-\$19,212\end{array}\right)\times \frac{33.3}{100}\\ =\text{ \$12,814}\end{array}$

Compute the depreciation expense of machine as on September 1, 2021 using double-declining balance method.

$\text{Depreciation }=\left(\begin{array}{l}\text{Acquisition cost }-\text{ Depreciation charged for 2015}\\ -\text{Depreciation charged for 2016}\\ -\text{Depreciation charged for 2017}\\ -\text{Depreciation charged for 2018 }\\ -\text{Depreciation charged for 2019}\\ -\text{Depreciation charged for 2020}\\ -\text{Salvage value}\end{array}\right)$

$\begin{array}{c}=\left(\begin{array}{l}\$218,700-\$24,276-\$64,743-\$43,184\\ -\$28,804-\$19,212-\$12,814-\$23,400\end{array}\right)\\ =\text{ \$2,267}\end{array}$

Working Note:

Compute the depreciation rate applied each year.

Useful life = 6 years

$\begin{array}{c}\text{Depreciation rate }=\frac{\text{100\%}}{\text{6 years}}\times \text{ 2}\\ =33.3\%\end{array}$

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