Question

On January 2, Manning Co. purchases and installs a new machine costing \(324,000 with a five-year life and an estimated \)30,000 salvage value. Management estimates the machine will produce 1,470,000 units of product during its life. Actua production of units is as follows: 355,600 in 1st year, 320,400 in 2nd year, 317,000 in 3rd year, 343,600 in 4th year, 138,500 in 5th year. The total number of units produced by the end of year 5 exceeds the original estimate—this difference was not predicted. (The machine must not be depreciated below its estimated salvage value.)

Required

Prepare a table with the following column headings and compute depreciation for each year (and total depreciation of all years combined) for the machine under each depreciation method

Year

Straight line

Units of production

Double declining balance

Short answer

The depreciation balance is $16,796.16

Step-by-step solution

Computation of depreciation by the straight method

$\begin{array}{rcl}\mathit{d}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}& \mathbf{=}& \frac{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{-}\mathbf{s}\mathbf{a}\mathbf{l}\mathbf{v}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{u}\mathbf{s}\mathbf{e}\mathbf{f}\mathbf{u}\mathbf{l}\mathbf{}\mathbf{l}\mathbf{i}\mathbf{f}\mathbf{e}}\\ depreciation& =& \frac{\$324,000}{5years}\\ depreciation& =& \frac{\$294,000}{5years}\\ \mathit{d}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}& \mathbf{=}& \mathbf{\$}\mathbf{55}\mathbf{,}\mathbf{800}\end{array}$

Computation of depreciation by units of production method

$\begin{array}{rcl}\mathit{d}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}& \mathbf{=}& \frac{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{-}\mathbf{s}\mathbf{a}\mathbf{l}\mathbf{v}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{u}\mathbf{n}\mathbf{i}\mathbf{t}\mathbf{s}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{p}\mathbf{r}\mathbf{o}\mathbf{d}\mathbf{u}\mathbf{c}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}}\\ \mathit{d}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{e}\mathit{x}\mathit{p}\mathit{e}\mathit{n}\mathit{s}\mathit{e}& \mathbf{=}& \mathit{d}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathbf{\times }\mathit{u}\mathit{n}\mathit{i}\mathit{t}\mathit{s}\mathbf{}\mathit{p}\mathit{o}\mathit{d}\mathit{u}\mathit{c}\mathit{e}\mathit{d}\mathbf{}\mathit{i}\mathit{n}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathit{i}\mathit{o}\mathit{d}\\ depreciationperunit& =& \frac{\$324,000-\$30,000}{1,470,000}\\ depreciationperunit& =& \frac{\$294,000}{1,470,000}\\ \mathit{d}\mathit{e}\mathit{p}\mathit{e}\mathit{r}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathbf{}\mathit{u}\mathit{n}\mathit{i}\mathit{t}& \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{2}\\ depreciationexpense\left(1styear\right)& =& 0.2\times 355,600=\$71,120\\ depreciationexpense\left(2ndyear\right)& =& 0.2\times 320,400=\$64,080\\ depreciationexpense\left(3rdyear\right)& =& 0.2\times 317,000=\$63,400\\ depreciationexpense\left(4thyear\right)& =& 0.2\times 343,600=\$68,720\\ depreciationexpense\left(5thyear\right)& =& 0.2\times 138,500=\$27,700\end{array}$

Computation of depreciation by double declining method

$$\begin{gathered} \mathit{S}\mathit{t}\mathit{r}\mathit{a}\mathit{i}\mathit{g}\mathit{h}\mathit{t}\mathbf{}\mathit{l}\mathit{i}\mathit{n}\mathit{e}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}\mathbf{=}\mathbf{100}\mathbf{\%}\mathbf{÷}\mathit{U}\mathit{s}\mathit{e}\mathit{f}\mathit{u}\mathit{l}\mathbf{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e} \\ \mathit{d}\mathit{o}\mathit{u}\mathit{b}\mathit{l}\mathit{e}\mathbf{}\mathit{d}\mathit{e}\mathit{c}\mathit{l}\mathit{i}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{b}\mathit{a}\mathit{l}\mathit{a}\mathit{n}\mathit{c}\mathit{e}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}\mathbf{=}\mathbf{2}\mathbf{\times }\mathit{S}\mathit{t}\mathit{r}\mathit{a}\mathit{i}\mathit{g}\mathit{h}\mathit{t}\mathbf{}\mathit{l}\mathit{i}\mathit{n}\mathit{e}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e} \\ \mathit{D}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{}\mathit{e}\mathit{x}\mathit{p}\mathit{e}\mathit{n}\mathit{s}\mathit{e}\mathbf{=}\mathit{D}\mathit{o}\mathit{u}\mathit{l}\mathit{b}\mathit{e}\mathbf{}\mathit{d}\mathit{e}\mathit{c}\mathit{l}\mathit{i}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{b}\mathit{a}\mathit{l}\mathit{a}\mathit{n}\mathit{c}\mathit{e}\mathbf{}\mathit{r}\mathit{a}\mathit{t}\mathit{e}\mathbf{\times }\mathit{B}\mathit{e}\mathit{g}\mathit{i}\mathit{n}\mathit{n}\mathit{i}\mathit{n}\mathit{g}\mathbf{}\mathit{p}\mathit{e}\mathit{r}\mathit{i}\mathit{o}\mathit{d}\mathbf{}\mathit{b}\mathit{o}\mathit{o}\mathit{k}\mathbf{}\mathit{v}\mathit{a}\mathit{l}\mathit{u}\mathit{e} \\ straightlinerate=100\%÷5years \\ =20\% \\ doubledecliningbalancerate=2\times 20\% \\ \mathbf{=}\mathbf{40}\mathbf{\%} \\ Depreciationexpense\left(1styear\right)=40\%\times \$324,000=\$129,600 \\ Depreciationexpense\left(2ndyear\right)=40\%\times \$194,400=\$77,760 \\ Depreciationexpense\left(3edyear\right)=40\%\times \$116,640=\$46,656 \\ Depreciationexpense\left(4thyear\right)=40\%\times \$69,984=\$27,993.6 \\ Depreciationexpense\left(5thyear\right)=40\%\times \$41,990.4=\$16,796.16 \end{gathered}$$

Tabular representation of depreciation

Year	Straight line	Units of production	Double declining balance
1	$55,800	$71,120	$129,600
2	$55,800	$64,080	$77,760
3	$55,800	$63,400	$46,656
4	$55,800	$68,720	$27,993.6
5	$55,800	$27,700	$16,796.16