(Depreciation for Partial Periods—SL, Act., SYD, and Declining-Balance) The cost of equipment purchased by Charleston, Inc., on June 1, 2017, is \(89,000. It is estimated that the machine will have a \)5,000 salvage value at the end of its service life. Its service life is estimated at 7 years, its total working hours are estimated at 42,000, and its total production is estimated at 525,000 units. During 2017, the machine was operated 6,000 hours and produced 55,000 units. During 2018, the machine was operated 5,500 hours and produced 48,000 units.

Instructions Compute depreciation expense on the machine for the year ending December 31, 2017, and the year ending December 31, 2018, using the following methods.

1. Straight-line.
2. Units-of-output.
3. Working hours.
4. Sum-of-the-years’-digits.
5. Declining-balance (twice the straight-line rate).

In accounting, depreciation is charged on tangible assets due to the abrasion or corrosion of assets. It is taken as an expense in the books of accounts assessed by different accounting firms through different methods.

Calculating annual depreciation

$\begin{array}{rcl}\mathrm{Depreciation}& =& \frac{\mathrm{Original}\mathrm{cost}-\mathrm{Salvage}\mathrm{value}}{\mathrm{Useful}\mathrm{life}}\\ & =& \frac{\$89,000-\$5,000}{7}\\ & =& \$12,000\mathrm{annually}\end{array}$

Calculating depreciation for 2017

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Annual}\mathrm{depreciation}\times \frac{\mathrm{Number}\mathrm{in}\mathrm{a}\mathrm{month}}{\mathrm{Month}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \$12,000\times \frac{7}{12}\\ & =& \$7,000\end{array}$

Calculating depreciation for 2018

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Annual}\mathrm{depreciation}\times \frac{\mathrm{Number}\mathrm{in}\mathrm{a}\mathrm{month}}{\mathrm{Months}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \$12,000\times \frac{12}{12}\\ & =& \$12,000\end{array}$

Calculating per unit value

$\begin{array}{rcl}\mathrm{Depreciation}& =& \frac{\mathrm{Cost}-\mathrm{Salvage}\mathrm{value}}{\mathrm{Total}\mathrm{production}}\\ & =& \frac{\$89,000-\$5,000}{525,000}\\ & =& \$0.16\mathrm{per}\mathrm{unit}\end{array}$

Calculating depreciation for 2017

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Total}\mathrm{production}\times \mathrm{Per}\mathrm{unit}\mathrm{value}\\ & =& 55,000\times 0.16\\ & =& \$8,800\end{array}$

Calculating depreciation for 2018

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Total}\mathrm{production}\times \mathrm{Per}\mathrm{unit}\mathrm{value}\\ & =& 48,000\times 0.16\\ & =& \$7,680\end{array}$

Calculating per unit value

$\begin{array}{rcl}\mathrm{Depreciation}& =& \frac{\mathrm{Cost}-\mathrm{Salvage}\mathrm{value}}{\mathrm{Total}\mathrm{working}\mathrm{hours}}\\ & =& \frac{\$89,000-\$5,000}{42,000}\\ & =& \$2.00\mathrm{per}\mathrm{hour}\end{array}$

Calculating depreciation for 2017

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Total}\mathrm{hour}\mathrm{operated}\times \mathrm{Per}\mathrm{unit}\mathrm{value}\\ & =& 6,000\times \$2.00\\ & =& \$12,000\end{array}$

Calculating depreciation for 2018

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Total}\mathrm{hour}\mathrm{operated}\times \mathrm{Per}\mathrm{unit}\mathrm{value}\\ & =& 5,500\times \$2.00\\ & =& \$11,000\end{array}$

Computing sum of year digits

$\begin{array}{rcl}\mathrm{Sum}\mathrm{of}\mathrm{year}\mathrm{digit}& =& \frac{\mathrm{n}\left(\mathrm{n}+1\right)}{2}\\ & =& \frac{7\left(7+1\right)}{2}\\ & =& \frac{7\times 8}{2}\\ & =& 28\end{array}$

Computing depreciation for 2017

$\begin{array}{rcl}\mathrm{Depreciation}& =& \left(\mathrm{Cost}-\mathrm{Salvage}\mathrm{value}\right)\times \frac{\mathrm{Number}\mathrm{of}\mathrm{year}}{\mathrm{Sum}\mathrm{of}\mathrm{year}\text{'}\mathrm{s}\mathrm{digit}}\times \frac{\mathrm{Number}\mathrm{of}\mathrm{month}}{\mathrm{Number}\mathrm{of}\mathrm{month}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \left(\$89,000-\$5,000\right)\times \frac{7}{28}\times \frac{7}{12}\\ & =& \$84,000\times \frac{7}{28}\times \frac{7}{12}\\ & =& \$12,250\end{array}$

Computing depreciation for 2018 for five months

$\begin{array}{rcl}\mathrm{Depreciation}& =& \left(\mathrm{Cost}-\mathrm{Salvage}\mathrm{value}\right)\times \frac{\mathrm{Number}\mathrm{of}\mathrm{year}}{\mathrm{Sum}\mathrm{of}\mathrm{year}\mathrm{digit}}\times \frac{\mathrm{Number}\mathrm{of}\mathrm{month}}{\mathrm{Number}\mathrm{of}\mathrm{month}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \left(\$89,000-\$5,000\right)\times \frac{7}{28}\times \frac{5}{12}\\ & =& \$84,000\times \frac{7}{28}\times \frac{7}{12}\\ & =& \$8,750\end{array}$

Computing depreciation for 2018 for seven months

$\begin{array}{rcl}\mathrm{Depreciation}& =& \left(\mathrm{Cost}-\mathrm{Salvage}\mathrm{value}\right)\times \frac{\mathrm{Number}\mathrm{of}\mathrm{year}}{\mathrm{Sum}\mathrm{of}\mathrm{year}\mathrm{digit}}\times \frac{\mathrm{Number}\mathrm{of}\mathrm{month}}{\mathrm{Number}\mathrm{of}\mathrm{month}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \left(\$89,000-\$5,000\right)\times \frac{6}{28}\times \frac{7}{12}\\ & =& \$84,000\times \frac{6}{28}\times \frac{7}{12}\\ & =& \$10,500\end{array}$

Therefore, the total depreciation for 2018 is $19,250 ($8,750+$10,000)

Declining balance rate =$\frac{2}{7}$

Calculating depreciation for 2017

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Cost}\times \mathrm{Declining}\mathrm{rate}\times \frac{\mathrm{Number}\mathrm{in}\mathrm{a}\mathrm{month}}{\mathrm{Month}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \$89,000\times \frac{2}{7}\times \frac{7}{12}\\ & =& \$14,833\end{array}$

Calculating depreciation for 2018

$\begin{array}{rcl}\mathrm{Depreciation}& =& \left(\mathrm{Cost}-\mathrm{Depreciation}\mathrm{of}2017\right)\times \mathrm{Declining}\mathrm{rate}\\ & =& \left(\$89,000-\$14,833\right)\times \frac{2}{7}\\ & =& \$74,167\times \frac{2}{7}\\ & =& \$21,191\end{array}$