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The term depreciation refers tothe loss of value in assets due to abrasion and erosion over time. Companies use different methods to value their assets, but straight-line depreciation is the easiest one to apply.

$\begin{array}{rcl}\mathrm{Depreciation}& =& \frac{\mathrm{Cost}\mathrm{of}\mathrm{the}\mathrm{asset}-\mathrm{Salvage}\mathrm{value}}{\mathrm{Estimated}\mathrm{life}\mathrm{of}\mathrm{the}\mathrm{asset}}\\ & =& \frac{\$117,900-\$12,900}{5}\\ & =& \$21,000\end{array}$

The depreciation expense for 5 months is calculated as follows:

$\begin{array}{rcl}Depreciationexpensefor5month& =& Depreciationamountperyear×\frac{Numberofmonths}{Monthsinayear}\\ & =& \$21,000×\frac{5}{12}\\ & =& \$8,750\end{array}$

$\begin{array}{rcl}\mathrm{Rate}\mathrm{per}\mathrm{hour}& =& \frac{\mathrm{Cost}\mathrm{of}\mathrm{asset}-\mathrm{Salvage}\mathrm{value}}{\mathrm{Estimated}\mathrm{working}\mathrm{hours}}\\ & =& \frac{\$117,900-\$12,900}{21,000}\\ & =& \$5.00\mathrm{per}\mathrm{hour}\end{array}$

$\begin{array}{rcl}\mathrm{Machine}\mathrm{usage}& =& \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{hours}×\mathrm{Rate}\mathrm{per}\mathrm{hours}\\ & =& 800×\$5.00\\ & =& \$4,000\end{array}$

$\begin{array}{rcl}\mathrm{Sum}\mathrm{of}\mathrm{year}\mathrm{digit}& =& \mathrm{Total}\mathrm{sum}\mathrm{of}\mathrm{year}\\ & =& 5+4+3+2+1\\ & =& 15\end{array}$

$\begin{array}{rcl}\mathrm{Depreciation}\mathrm{amount}& =& \mathrm{Cost}\mathrm{of}\mathrm{the}\mathrm{asset}-\mathrm{Salvage}\mathrm{value}\\ & =& \$117,900-\$12,900\\ & =& \$105,900\end{array}$

Sum of year depreciation for 2018 = $32,083

Working Notes:

Calculation depreciation for the first 7 months

$\begin{array}{rcl}Depreciation& =& \left(Depreciable×\frac{Year}{Sumofyeardigit}×\frac{Numberofmonth}{Numberofmonthinayear}\right)\\ & =& \$105,000×\frac{5}{12}×\frac{7}{12}\\ & =& \$20,417\end{array}$

Calculating Depreciation for 5 months

$\begin{array}{rcl}Depreciation& =& \left(Depreciableamount×\frac{Year}{Sumofyeardigit}×\frac{Numberofmonth}{Numberofmonthinayear}\right)\\ & =& \$105,000×\frac{4}{15}×\frac{5}{12}\\ & =& \$11,667\end{array}$

$\begin{array}{rcl}Totaldepreciationin2018& =& Depreciationof7month+Depreciationof5month\\ & =& \$20,417+\$11,667\\ & =& \$32,084\end{array}$

Calculating Double-declining-balance for 1^st year

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Cost}\mathrm{of}\mathrm{machine}×\mathrm{Double}\mathrm{depreciation}\mathrm{rate}\\ & =& \$117,900×\frac{40}{100}\\ & =& \$47,160\end{array}$

Calculating Double-declining-balance for 2^nd year

$\begin{array}{rcl}\mathrm{Depreciation}& =& \left(\mathrm{Cost}\mathrm{of}\mathrm{machine}-1\mathrm{st}\mathrm{year}\mathrm{depreciation}\right)×\mathrm{Double}\mathrm{depreciation}\mathrm{rate}\\ & =& \left(\$117,900-\$47,160\right)×\frac{40}{100}\\ & =& \$28,296\end{array}$

Calculating depreciation for 2017

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Depreciation}\mathrm{for}1\mathrm{st}\mathrm{year}×\frac{\mathrm{Number}\mathrm{in}\mathrm{month}}{\mathrm{Number}\mathrm{of}\mathrm{months}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \$47,160×\frac{5}{12}\\ & =& \$19,650\end{array}$

Calculating depreciation for 7 months in 2018

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Depreciation}\mathrm{for}1\mathrm{st}\mathrm{year}×\frac{\mathrm{Number}\mathrm{in}\mathrm{a}\mathrm{month}}{\mathrm{Number}\mathrm{of}\mathrm{months}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \$47,160×\frac{7}{12}\\ & =& \$27,510\end{array}$

Calculating depreciation for 5 months in 2018

$\begin{array}{rcl}Depreciation& =& Depreciationfor2ndyear×\frac{Numberinamonth}{Numberofmonthsinayear}\\ & =& \$28,296×\frac{5}{12}\\ & =& \$11,790\end{array}$

Total depreciation for 2018 is $27,510 + $11,790 = $39,300