Chapter 7, Problem 7.5AP

Determine depreciation under three methods (LO7–4)

University Car Wash built a deluxe car wash across the street from campus. The new machines cost $270,000 including installation. The company estimates that the equipment will have a residual value of $24,000. University Car Wash also estimate’s it will use the machine for six sears or about 12,000 total hours.

Required:

Prepare a depreciation schedule for six wars using the following methods:

1.    Straight-line.

2.    Double-declining-balance.

3.    Activity-based.

Actual use per war was as follows:

Year	Hours Used
1	3,100
2	1,100
3	1,200
4	2,800
5	2,600
6	1,200

To determine

To prepare: A depreciation schedule for six years using straight line depreciation method.

Explanation of Solution

Depreciation: Depreciation refers to the reduction in the monetary value of a fixed asset due to its wear and tear or obsolescence. It is a method of distributing the cost of the fixed assets over its estimated useful life. The following is the formula to calculate the depreciation.

$\text{Depreciation cost = }\frac{\text{Cost of the asset-Salvage value}}{\text{Estimated useful life of the asset}}$

Straight-line method:

Under the straight-line method of depreciation, the same amount of depreciation is allocated every year over the estimated useful life of an asset.

• A depreciation schedule for six years using straight line depreciation method. is detremined as follows:

UC Wash
Year	Depreciable cost (1)	Depreciation rate	Depreciation expense	Accumulated depreciation	Book Value
1	246,000	$\frac{1}{6}$	41,000	41,000	239,000
2	246,000	$\frac{1}{6}$	41,000	82,000	188,000
3	246,000	$\frac{1}{6}$	41,000	123,000	147,000
4	246,000	$\frac{1}{6}$	41,000	164,000	106,000
5	246,000	$\frac{1}{6}$	41,000	205,000	65,000
6	246,000	$\frac{1}{6}$	41,000	246,000	24,000
	Total		246,000

Note:

$\text{Depreciation expense }=\text{ Depreciable cost }\times \text{ Depreciation rate}$

$\text{Book value = \$270,000}-\text{Accumulated depreciation}$

Determine the depreciable cost:

$\begin{array}{c}\text{Depreciable cost }=\text{Orginal cost}-\text{Residual value}\\ =\$270,000-\$24,000\\ =\$246,000\end{array}$ (1)

To determine

To prepare: A depreciation schedule for six years using double declining balance depreciation method.

Explanation of Solution

Double-declining-balance method:

It is an accelerated method of depreciation under which the depreciation declines in each successive year until the value of asset becomes zero. Under this method, the book value (original cost less accumulated depreciation) of the long-term asset is decreased by a fixed rate. It is double the rate of the straight-line depreciation.

• A depreciation schedule for six years using double declining balance depreciation method is detremined as follows:

UC Wash
Year	Beginning book value	Depreciation rate (2)	Depreciation expense	Accumulated depreciation	Book Value
1	270,000	$\frac{1}{3}$	90,000	90,000	180,000
2	180,000	$\frac{1}{3}$	60,000	150,000	120,000
3	120,000	$\frac{1}{3}$	40,000	190,000	80,000
4	80,000	$\frac{1}{3}$	26,667	216,667	53,333
5	53,333	$\frac{1}{3}$	17,778	234,445	35,555
6	35,555	$\frac{1}{3}$	11,555	246,000	24,000
	Total		246,000

Note:

$\begin{array}{c}\text{Depreciable rate }=\frac{2}{6}\text{years}\\ =\frac{1}{3}\text{years}\end{array}$ (2)

Last year’s amount must reduce the book value to residual value.

To determine

To prepare: A depreciation schedule for six years using activity based depreciation method.

Explanation of Solution

Unit-of-activity Method: Under this method of depreciation, the depreciation expense is calculated on the basis of units produced in a year. This method is suitable when a company has fluctuating productive rate. The formula to calculate the depreciation expense under this method is as follows:

$\text{Depreciation per unit = }\frac{\text{Cost}-\text{Residual value}}{\text{Estimated units of useful life}}$

• A depreciation schedule for six years using activity based depreciation method is detremined as follows:

UC Wash
Year	Hours used	Depreciation rate (3)	Depreciation expense	Accumulated depreciation	Book Value
1	3,100	$20.50	63,550	63,550	206,450
2	1,100	$20.50	22,550	86,100	183,900
3	1,200	$20.50	24,600	110,700	159,300
4	2,800	$20.50	57,400	168,100	101,900
5	2,600	$20.50	53,300	221,440	48,600
6	1,200	$20.50	24,600	246,000	24,000
	Total		246,000

Working note:

$\begin{array}{c}\text{Depreciation per unit}=\frac{\text{Depreciable}\text{cost}}{\text{Total units expected to be produced}}\\ =\frac{\$246,000}{\$12,000\text{hours}}\\ =\$20.5\text{0/hour}\end{array}$ (3)