Chapter 9, Problem 3AP

a.

To determine

Calculate each year’s depreciation expense for the machine’s useful life under each of the depreciation methods.

Explanation of Solution

1.

Calculate the depreciation expense for each year of the machine’s useful life under the straight-line depreciation method.

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.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$90,000}-\text{\$5,000}}{\text{4 years}}\\ =\$21,250\end{array}$

The depreciation expense under the straight-line method is same for every year. Hence, $21,250 is the depreciation expense of the machine for all the four years.

2.

Calculate the depreciation expense for each year of the machine’s useful life under the double-declining balance method.

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 for the first year using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\text{ Beginning book value }\times \text{ Depreciation rate}\\ =\$90,000\times \frac{50}{100}\\ =\text{ \$45,000}\end{array}$

Compute the depreciation expense of machine for the second year using double-declining balance method.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning book value}\\ -\left(\begin{array}{l}\text{Depreciation charged }\\ \text{in first year}\end{array}\right)\end{array}\right)\text{× Depreciation rate}\\ =\left(\$90,000-\$45,000\right)\times \frac{50}{100}\\ =\text{ \$22,500}\end{array}$

Compute the depreciation expense of machine for the third year using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\left(\begin{array}{l}\text{Beginning book value }\\ -\text{ Depreciation charged in first year }\\ -\text{Depreciation charged in second year}\end{array}\right)\times \text{ Depreciation rate}\\ =\left(\$90,000-\$45,000-\$22,500\right)\times \frac{50}{100}\\ =\text{ \$11,250}\end{array}$

Compute the depreciation expense of machine for the fourth year using double-declining balance method.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning }\\ \text{book value}\end{array}\right)-\left(\begin{array}{l}\text{Depreciation charged in first year}\\ -\text{ Depreciation charged in the second year}\\ -\text{Depreciation charged in the third year}\\ -\text{ Salvage value}\end{array}\right)\\ =\$90,000-\left(\$45,000-\$22,500-\$11,250-\$5,000\right)\\ =\$6,250\end{array}$

Working Note:

Compute the depreciation rate applied each year.

Useful life = 4 years

$\begin{array}{c}\text{Depreciation rate }=\frac{\text{100\%}}{\text{4 years}}\times \text{ 2}\\ =50\%\end{array}$

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

Hence, the depreciation expenses for the machine under the double-declining balance method for the four years are $45,000, $22,500, $11,250, and $6,250 respectively.

3.

Calculate the depreciation expense for each year of the machine’s useful life under the units-of-production balance method.

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 first year using units-of-production method.

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ \text{first year}\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per cutting}\\ \times \text{ Number of cuttings in first year}\end{array}\right\}\\ =\$0.1\times 200,000\text{ cuttings}\\ =\$20,000\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ \text{second year}\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per cutting}\\ \times \text{ Number of cuttings in second year}\end{array}\right\}\\ =\$0.1\times 350,000\text{ cuttings}\\ =\$35,000\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ \text{third year}\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per cutting}\\ \times \text{ Number of cuttings in third year}\end{array}\right\}\\ =\$0.1\times 260,000\text{ cuttings}\\ =\$26,000\end{array}$

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

$\begin{array}{c}\begin{array}{l}\text{Depreciation in }\\ \text{fourth year}\end{array}\}=\left\{\begin{array}{l}\text{Depreciation per cutting }\\ \times \text{ Number of cuttings in fourth year}\end{array}\right\}\\ =\$0.1\times \text{ 4}0,000\text{ cuttings}\\ =\$4,000\end{array}$

Working Note:

Compute the depreciation rate per cutting.

$\begin{array}{c}\begin{array}{l}\text{Depreciation }\\ \text{per cutting}\end{array}\}=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Total estimated cuttings}}\\ =\frac{\text{\$90,000 }-\text{ \$5,000}}{\text{850,000 cuttings}}\\ =\text{ \$0}\text{.1 per cutting}\end{array}$

Hence, the depreciation expenses for the machine under the units-of-production method for the four years are $20,000, $35,000, $26,000, and $4,000 respectively.

b.

To determine

Calculate each year’s depreciation expense for the machine’s useful life under each of the depreciation methods, assuming that the machine was purchased on July 1, 2015.

Explanation of Solution

1.

Calculate the depreciation expense for each year of the machine’s useful life under the straight-line depreciation method.

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 the machine for the year 2015.

$\begin{array}{c}\text{Depreciation=Depreciation per year}\times \text{Time period}\left(\text{July to December}\right)\\ =\$21,250\times \frac{6}{12}\\ =\$10,625\end{array}$

Compute the depreciation expense of the machine for the year 2016.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$90,000}-\text{\$5,000}}{\text{4 years}}\\ =\$21,250\end{array}$

Compute the depreciation expense of the machine for the year 2017.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$90,000}-\text{\$5,000}}{\text{4 years}}\\ =\$21,250\end{array}$

Compute the depreciation expense of the machine for the year 2018.

$\begin{array}{c}\text{Depreciation }=\frac{\text{Acquisition cost }-\text{ Salvage value}}{\text{Useful life}}\\ =\frac{\text{\$90,000}-\text{\$5,000}}{\text{4 years}}\\ =\$21,250\end{array}$

Compute the depreciation expense of the machine for the year 2019.

$\begin{array}{c}\text{Depreciation=Depreciation per year}\times \text{Time period}\left(\text{January 1 to July 1}\right)\\ =\$21,250\times \frac{6}{12}\\ =\$10,625\end{array}$

2.

Calculate the depreciation expense for each year of the machine’s useful life under the double-declining balance method.

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 for the year 2015 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\text{ Beginning book value }\times \text{ Depreciation rate}\times \text{Time period}\\ =\$90,000\times \frac{50}{100}\times \frac{6}{12}\text{months}\\ =\text{ \$22,500}\end{array}$

Compute the depreciation expense of machine for the year 2016 using double-declining balance method.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning book value}\\ -\left(\begin{array}{l}\text{Depreciation charged }\\ \text{in first year}\end{array}\right)\end{array}\right)\text{× Depreciation rate}\\ =\left(\$90,000-\$22,500\right)\times \frac{50}{100}\\ =\text{ \$33,750}\end{array}$

Compute the depreciation expense of machine for the year 2017 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\left(\begin{array}{l}\text{Beginning book value }\\ -\text{ Depreciation charged in first year }\\ -\text{Depreciation charged in second year}\end{array}\right)\times \text{ Depreciation rate}\\ =\left(\$90,000-\$22,500-\$33,750\right)\times \frac{50}{100}\\ =\text{ \$16,875}\end{array}$

Compute the depreciation expense of machine for the year 2018 using double-declining balance method.

$\begin{array}{c}\text{Depreciation }=\left(\begin{array}{l}\text{Beginning book value }\\ -\text{ Depreciation charged in first year }\\ -\text{Depreciation charged in second year}\\ -\text{Depreciation charged in third year}\end{array}\right)\times \text{ Depreciation rate}\\ =\left(\$90,000-\$22,500-\$33,750-\$16,875\right)\times \frac{50}{100}\\ =\text{ \$8,438}\end{array}$

Compute the depreciation expense of machine for the year 2019 using double-declining balance method.

$\begin{array}{c}\text{Depreciation}=\left(\begin{array}{l}\text{Beginning }\\ \text{book value}\end{array}\right)-\left(\begin{array}{l}\text{Depreciation charged in first year}\\ -\text{ Depreciation charged in the second year}\\ -\text{Depreciation charged in the third year}\\ -\text{Depreciation charged in the fourth year}\\ -\text{ Salvage value}\end{array}\right)\\ =\$90,000-\left(\$22,500-\$33,750-\$16,875-\$8,438-\$5,000\right)\\ =\$3,437\end{array}$

Working Note:

Compute the depreciation rate applied each year.

Useful life = 4 years

$\begin{array}{c}\text{Depreciation rate }=\frac{\text{100\%}}{\text{4 years}}\times \text{ 2}\\ =50\%\end{array}$

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