Question

(Depreciation for Partial Periods—SL, Act., SYD, and DDB) On January 1, 2015, a machine was purchased for \(90,000. The machine has an estimated salvage value of \)6,000 and an estimated useful life of 5 years. The machine can operate for 100,000 hours before it needs to be replaced. The company closed its books on December 31 and operates the machine as follows: 2015, 20,000 hours; 2016, 25,000 hours; 2017, 15,000 hours; 2018, 30,000 hours; and 2019, 10,000 hours.

Instructions

(a) Compute the annual depreciation charges over the machine’s life assuming a December 31 year-end for each of the following depreciation methods.

1. Straight-line method.
2. Activity method.
3. Sum-of-the-years’-digits method.
4. Double-declining-balance method.

(b) Assume a fiscal year-end of September 30. Compute the annual depreciation charges over the asset’s life applying each of the following methods.

1. Straight-line method.
2. Sum-of-the-years’-digits method.
3. Double-declining-balance method

Short answer

The basic formula to calculate depreciation expense is:

$\text{Depreciation}\text{expense}=\frac{\text{Cost}\text{of}\text{asset}-\text{Salvage}\text{value}}{\text{Useful}\text{life}}$

Step-by-step solution

Step 1: Meaning of Depreciation

Depreciation is a branch of accounting that deals with systematically spreading or dividing the cost or other principal value of a fixed asset over its expected useful life by charging regular expenses or revenues.

(a 1) Computing depreciation under the straight-line method

Calculating depreciation expense

$\begin{array}{rcl}\text{Depreciation}\text{expense}& =& \frac{\text{Cost}\text{of}\text{asset}-\text{Salvage}\text{value}}{\text{Useful}\text{life}}\\ & =& \frac{\$90,000-\$6,000}{5}\\ & =& \$16,800\\ & & \end{array}$

(a2) Computing depreciation using the activity method

Calculating depreciation expense

$\begin{array}{rcl}\text{Depreciation}\text{expense}& =& \frac{\text{Cost}\text{of}\text{asset}-\text{Salvage}\text{value}}{\text{Total}\text{capacity}\text{of}\text{machine}}\\ & =& \frac{\$90,000-\$6,000}{100,000}\\ & =& \$0.84\text{per}\text{hour}\\ & & \end{array}$

Year	Calculation	Result
2015	$20,000\text{hrs}.\times \$0.84$	$16,800
2016	$25,000\text{hrs}.\times \$0.84$	21,000
2017	$15,000\text{hrs}.\times \$0.84$	12,600
2018	$30,000\text{hrs}.\times \$0.84$	25,200
2019	$10,000\text{hrs}.\times \$0.84$	8,400

(a 3) Computing depreciation using the Sum-of-years digits method

Calculating the sum of years’ digit

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

Year	Calculation	Result
2015	$\frac{5}{15}\times \left(\$90,000-\$6,000\right)$	$28,000
2016	$\frac{4}{15}\times \$84,0000$	22,400
2017	$\frac{3}{15}\times \$84,0000$	16,800
2018	$\frac{2}{15}\times \$84,0000$	11,200
2019	$\frac{1}{15}\times \$84,0000$	5,600

(a 4) Computing depreciation using the Double-declining-balance method

Double-Declining-Balance Method: Each year is 20% of its total life. Double the rate to 40%.

(b 1) Computing depreciation using the Straight-line method

Calculating depreciation expense for 2015

$\begin{array}{rcl}\text{Depreciation}\text{expense}& =& \frac{\text{Cost}\text{of}\text{asset}-\text{Salavge}\text{value}}{\text{Useful}\text{life}}\times \frac{\text{Number}\text{in}\text{month}}{\text{Number}\text{ofmonth}\text{in}\text{a}\text{year}}\\ & =& \frac{\$90,000-\$6,000}{5}\times \frac{9}{12}\\ & =& \$12,600\\ & & \end{array}$

Year	Calculation	Result
2015	For 9 months	$12,000
2016	Full year	16,800
2017	Full year	16,800
2018	Full year	16,800
2019	Full year	16,800
2020	$\text{Full}\text{yea}r\times \frac{3}{2}\text{year}$	4,200

 Step 7: (b 2) Computing depreciation using the Sum-of-the-years’-digits method.

Calculating depreciation expense

(b 3) Computing depreciation using the Double-declining-balance method