91Ó°ÊÓ

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

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

Calculating depreciation for 2018

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

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

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

Calculating depreciation for 2018

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

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

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

Calculating depreciation for 2018

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

Computing sum of year digits

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

Computing depreciation for 2017

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

Computing depreciation for 2018 for five months

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

Computing depreciation for 2018 for seven months

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

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

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

Calculating depreciation for 2017

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

Calculating depreciation for 2018

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