Question

Silverman Company purchased machinery for \(162,000 on January 1, 2017. It is estimated that the machinery will have a useful life of 20 years, salvage value of \)15,000, production of 84,000 units, and working hours of 42,000. During 2017, the company uses the machinery for 14,300 hours, and the machinery produces 20,000 units. Compute depreciation under the straight-line, units-of-output, working hours, sum-of-the-years’-digits, and double-declining-balance methods.

Short answer

Answer

1. Straight line method = $7,350
2. Units of output method = $35,000
3. Working hours method = $50,050
4. Sum of years digit method = $14,000
5. Double declining method = $16,200

Step-by-step solution

Meaning of Depreciation

Depreciation is an expense incurred on an asset that has become obsolete due to erosion and abrasion. An asset can be depreciated in various ways, which help in bringing the exact value of the asset at the time of sale.

Computing of depreciation under different methods 

Computing depreciation under the straight-line method

$\begin{array}{rcl}\text{Depreciation}\text{base}& =& \text{Cost}-\text{Salvage}\text{value}\\ & =& \$162,000-\$15,000\\ & =& \$147,000\\ & & \end{array}$

$\begin{array}{rcl}\text{Depreciation}& =& \frac{\text{Original}\text{cost}-\text{Salvage}\text{value}}{\text{Useful}\text{life}}\\ & =& \frac{\$147,000-\$0}{20}\\ & =& \$7,350\end{array}$

Computing depreciation under the units-of-output method

$\begin{array}{rcl}\text{Depreciation}& =& \frac{\text{Cost}\times \text{Output}\text{in}\text{year}2017}{\text{Total} \text{production}}\\ & =& \frac{\$147,000\times 20,000}{84,000}\\ & =& \$35,000\end{array}$

Computing depreciation under the working hour method

$\begin{array}{rcl}\text{Depreciation}& =& \frac{\text{Cost}\times \text{Working}\text{hours}\text{in}2017}{\text{Total}\text{working}\text{hours}}\\ & =& \frac{\$147,000\times 14,300}{42,000}\\ & =& \frac{\$2,102,100,000}{42,000}\\ & =& \$50,050\end{array}$

Computing depreciation under the sum of years digit method

$\begin{array}{rcl}\text{Depreciation}& =& \frac{\text{Cost}\times \text{Estimated}\text{life}}{\frac{\text{Estimated}\text{life}\left(\text{Estimated}\text{life}+1\right)}{2}}\\ & =& \frac{\$147,000\times 20}{\frac{20\left(20+1\right)}{2}}\\ & =& \frac{\$2,940,000}{210}\\ & =& \$14,000\end{array}$

Computing depreciation under the double-declining balance method

$\begin{array}{rcl}\text{Depreciation}& =& \text{Original}\text{cost}\times \text{Double}\text{declining}\text{depreciation}\text{rate}\\ & =& \$162,000\times 10\%\\ & =& \$16,200\end{array}$