Question

A machine costing \(257,500 with a four-year life and an estimated \)20,000 salvage value is installed in Luther Company’s factory on January 1. The factory manager estimates the machine will produce 475,000 units of product during its life. It actually produces the following units: 220,000 in 1st year, 124,600 in 2nd year, 121,800 in 3rd year, 15,200 in 4th year. The total number of units produced by the end of year 4 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 total depreciation after four years is $237,500

Step-by-step solution

Computation of depreciation by the straight method

$\begin{array}{rcl}\mathit{D}\mathit{e}\mathit{p}\mathit{r}\mathit{e}\mathit{c}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}& \mathbf{=}& \frac{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{t}\mathbf{-}\mathbf{s}\mathbf{a}\mathbf{l}\mathbf{v}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{v}\mathbf{a}\mathbf{l}\mathbf{u}\mathbf{e}}{\mathbf{u}\mathbf{s}\mathbf{e}\mathbf{f}\mathbf{u}\mathbf{l}\mathbf{}\mathbf{l}\mathbf{i}\mathbf{f}\mathbf{e}}\\ deprecition& =& \frac{\$257,500-\$20,000}{4years}\\ deprecition& =& \frac{\$237,500}{4year}\\ deprecition& =& \$59375\end{array}$

The depreciation of the machine by the straight-line method is $59,375.

Computation of depreciation by units of production method

$\begin{array}{rcl}depreciationperunit& =& \frac{\cos t-salvagevalue}{totalunitsofproduction}\\ depeciationexpense& =& depreciationperunit\times unitspoducedinperiod\\ depreciationperunit& =& \frac{\$257,500-\$20,000}{475,000}\\ depreciationperunit& =& 0.5\\ depreciationexpense(1styear)& =& 0.5\times 220,000=\$110,000\\ depreciationexpense(2ndyear)& =& 0.5\times 124,600=\$62,300\\ depreciationexpense(3rdyear)& =& 0.5\times 121,800=\$60,900\\ depreciationexpense(4thyear)& =& 0.5\times 8,600=\$4,300\\ Note:8,600& =& balanceofproductionunitof{4}^{th}year.\\ 475,000-\left(220,000+124,000+121,800\right)& =& 8,600\end{array}$

Computation of depreciation by double declining method

$\begin{array}{rcl}Straightlinerate& =& 100\%÷Usefullife\\ Doubledecliningbalancerate& =& 2\times Straightlinerate\\ Depreciationexpense& =& Doubledecliningbalancerate\times Beginningperiodbookvalue\\ straightlinerate& =& 100\%÷4years\\ & =& 25\%\\ doubledecliningbalancerate& =& 2\times 25\%\\ & =& 50\%\\ depreciationexpense(1styear)& =& 50\%\times \$257,500=\$128,750\\ depreciationexpense(2ndyear)& =& 50\%\times \$128,750=\$64,375\\ depreciationexpense(3rdyear)& =& 50\%\times \$64,375=\$32,187.5\\ depreciationexpense(4thyear)& =& \$32,187.7-\$20,000\\ & =& \$12,187.5or\$12,188\end{array}$

Note: If the last year’s book value is depreciated by 50%, then the result will be less than salvage value. Therefore, we need to deduct the salvage value from the book value of the last year.

Tabular representation of depreciation

Year	Straight line	Units of production	Double declining balance
1	$59,375	$110,000	$128,750
2	$59,375	$62,300	$64,375
3	$59,375	$60,900	$32,187.5
4	$59,375	$4,300	$12,187.5
Total	$237,500	$237,000	$237,500