(Depreciation Computations—Four Methods) Robert Parish Corporation purchased a new machine for its assembly process on August 1, 2017. The cost of this machine was \(117,900. The company estimated that the machine would have a salvage value of \)12,900 at the end of its service life. Its life is estimated at 5 years, and its working hours are estimated at 21,000 hours. Year-end is December 31.

Instructions

Compute the depreciation expense under the following methods. Each of the following should be considered unrelated.

1. Straight-line depreciation for 2017.
2. Activity method for 2017, assuming that machine usage was 800 hours.
3. Sum-of-the-years’-digits for 2018.
4. Double-declining balance for 2018.

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:

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

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

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

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

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

Sum of year depreciation for 2018 = $32,083

Working Notes:

Calculation depreciation for the first 7 months

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

Calculating Depreciation for 5 months

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

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

Calculating Double-declining-balance for 1^st year

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

Calculating Double-declining-balance for 2^nd year

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

Calculating depreciation for 2017

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

Calculating depreciation for 7 months in 2018

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

Calculating depreciation for 5 months in 2018

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

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