Question

(Depreciation for Partial Period—SL, SYD, and DDB) Alladin Company purchased Machine #201 on May 1, 2017. The following information relating to Machine #201 was gathered at the end of May.

Price	\(85,000
Credit terms	2/10, n/30
Freight-in	\) 800
Preparation and installation costs	\( 3,800
Labor costs during regular production operations	\)10,500

It is expected that the machine could be used for 10 years, after which the salvage value would be zero. Alladin intends to use the machine for only 8 years, however, after which it expects to be able to sell it for $1,500. The invoice for Machine #201 was paid May 5, 2017. Alladin uses the calendar year as the basis for the preparation of financial statements.

Instructions

1. Compute the depreciation expense for the years indicated using the following methods. (Round to the nearest dollar.)
   1. Straight-line method for 2017.
   2. Sum-of-the-years’-digits method for 2018.
   3. Double-declining-balance method for 2017.
2. Suppose Kate Crow, the president of Alladin, tells you that because the company is a new organization, she expects it will be several years before production and sales reach optimum levels. She asks you to recommend a depreciation method that will allocate less of the company’s depreciation expense to the early years and more to later years of the assets’ lives. What method would you recommend?

Short answer

Answer

a) Depreciation

1. Straight-line method = $7,342
2. Sum of years digits method = $17,131
3. Double-declining–balance method = $14,683

b) Double declining method.

Step-by-step solution

Meaning of Depreciation

Depreciation is an accounting term used as an expense in the books of accounts for the assets whose value declines over time. It is computed at the end of the year or whenever an asset is sold.

(a 1) Calculation of depreciation using the straight-line method.

Computing cost of the machine

Purchase price	$85,000
Add: Freight-in	$800
Preparation and installation Cost	$3,800
Total Capital Cost of Machine	$89,600

Calculating depreciation as per the straight-line method annually

$\begin{array}{rcl}\mathrm{Depreciation}& =& \frac{\mathrm{Cost}\mathrm{of}\mathrm{asset}-\mathrm{Salvage}\mathrm{value}}{\mathrm{Useful}\mathrm{life}}\\ & =& \frac{\$89,600-\$1,500}{8}\\ & =& \frac{\$88,100}{8}\\ & =& \$11,013\end{array}$

Calculating depreciation for 2017 for eight months (from May to December)

$\begin{array}{rcl}\mathrm{Depreciation}& =& \mathrm{Annual}\mathrm{depreciation}\times \frac{\mathrm{Number}\mathrm{of}\mathrm{months}}{\mathrm{Months}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& \$11,013\times \frac{8}{12}\\ & =& \$7,342\end{array}$

(a 2) Calculation of depreciation using the Sum-of-the-years’-digits method.

Calculating the sum of years’ digit

$\begin{array}{rcl}\mathrm{Sum}\mathrm{of}\mathrm{year}\mathrm{digit}& =& \frac{\mathrm{n}\left(\mathrm{n}-1\right)}{2}\\ & =& \frac{8\left(8-1\right)}{2}\\ & =& 36\end{array}$

Calculating depreciation for 2018

$\begin{array}{rcl}\mathrm{Depreciation}& =& (\mathrm{Cost}\mathrm{of}\mathrm{asset}-\mathrm{Salvage}\mathrm{value})\times \frac{\mathrm{Number}\mathrm{of}\mathrm{years}\mathrm{of}\mathrm{remaining}\mathrm{life}\mathrm{of}\mathrm{asset}}{\mathrm{Total}\mathrm{of}\mathrm{all}\mathrm{digits}\mathrm{of}\mathrm{the}\mathrm{life}\mathrm{of}\mathrm{asset}}\\ & =& (\$89,600-\$1,500)\times \frac{7}{36}\\ & =& \$88,100\times \frac{7}{36}\\ & =& \$17,131\end{array}$

(a 3) Calculation of depreciation using the Double-declining-balance method.

Calculating straight-line depreciation rate

$\begin{array}{rcl}\mathrm{Straight}\mathrm{line}\mathrm{depreciation}\mathrm{rate}& =& \frac{\mathrm{Annual}\mathrm{depreciation}}{\mathrm{Cost}\mathrm{of}\mathrm{asset}-\mathrm{Salvage}\mathrm{value}}\times 100\\ & =& \frac{\$11,013}{88,100}\times 100\\ & =& 12.5\%\end{array}$

Calculating depreciation for 2017

$\begin{array}{rcl}\mathrm{Depreciation}& =& 2\times \mathrm{SLDP}\times \mathrm{BV}\times \frac{\mathrm{Number}\mathrm{of}\mathrm{months}}{\mathrm{Months}\mathrm{in}\mathrm{a}\mathrm{year}}\\ & =& 2\times 12.5\%\times \$88,100\times \frac{8}{12}\\ & =& \$14,683\end{array}$

Note: SLDP = Straight line depreciation percent

BV = Book value at the beginning of the period

(b) Explaining the methods that should be recommended for the company.

Early in the asset life, the double-declining balance approach results in a higher depreciation cost while the depreciation cost decreases later.

When dealing with assets that depreciate rapidly, this strategy makes sense.