Chapter 8, Problem 8E

Computing Depreciation under Alternative Methods

LO8-3 Strong Metals Inc. purchased a new stamping machine at the beginning of the year at a cost of $950,000. The estimated residual value was $50,000. Assume that the estimated useful life was five years and the estimated productive life of the machine was 300,000 units. Actual annual production was as follows:

Year	Units
1	70,000
2	67,000
3	50,000
4	73,000
5	40,000

Required:

1. 1. Complete a separate depreciation schedule for each of the alternative methods. Round your answers to the nearest dollar.
   1. a. Straight-line.
   2. b. Units-of-production.
   3. c. Double-declining-balance.

Method:__________
Year	Computation	Depreciation Expense	Accumulated Depreciation	Net Book Value
At acquisition
1
2
etc.

  2.    Assuming that the machine was used directly in the production of one of the products that the company manufactures and sells, what factors might management consider in selecting a preferable depreciation method in conformity with the expense principle?

To determine

Prepare the depreciation expense schedule under straight-line method.

Explanation of Solution

Straight-line method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset could be distributed equally throughout the useful life of the asset is referred to as straight-line method.

Formula for straight-line depreciation method:

$\begin{array}{c}\begin{array}{l}\text{Depreciation }\\ \text{expense}\end{array}\}=\text{Depreciable cost }\text{×Depreciation rate}\\ \text{= }\left(\text{Cost–Residual value}\right)\text{×}\frac{1}{\text{Useful life}}\end{array}$

Depreciation expense:

Depreciation expense is a non-cash expense, which is recorded on the income statement reflecting the consumption of economic benefits of long-term asset.

Accumulated depreciation:

The total amount of depreciation expense deducted, from the time asset acquired till date, as reported in the account as on a particular date, is referred to as accumulated depreciation.

Formula for accumulated depreciation:

$\text{Accumulated depreciation = }\left\{\begin{array}{l}\text{Depreciation expense in the previous years+}\\ \text{Depreciation in current year}\end{array}\right\}$

Book value:

The amount of acquisition cost of less accumulated depreciation as on a particular date is referred to as book value.

Formula for book value:

$\text{Book value = }\left\{\begin{array}{l}\text{Acquisition cost–}\\ \text{Accumulated depreciation}\end{array}\right\}$

Depreciation schedule under straight-line method:

Year	Computation	Depreciation Expense	Accumulated Depreciation	Net Book Value
At Acquisition				$950,000
1	$\left(\$950,000-\$50,000\right)\times \frac{1}{5}$	$180,000	$180,000	770,000
2	$\left(\$950,000-\$50,000\right)\times \frac{1}{5}$	180,000	360,000	590,000
3	$\left(\$950,000-\$50,000\right)\times \frac{1}{5}$	180,000	540,000	410,000
4	$\left(\$950,000-\$50,000\right)\times \frac{1}{5}$	180,000	720,000	230,000
5	$\left(\$950,000-\$50,000\right)\times \frac{1}{5}$	180,000	900,000	50,000

Table (1)

To determine

Prepare the depreciation expense schedule under units-of-production method.

Explanation of Solution

Units-of-production method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset is based on the production capacity or output is referred to as units-of-production method.

Formula for units-of-production depreciation method:

$\begin{array}{c}\begin{array}{l}\text{Depreciation }\\ \text{expense}\end{array}\}=\text{Depreciable cost }\text{× Depreciation rate}\\ \text{= }\left(\text{Cost–Residual value}\right)\text{×}\frac{\text{Actual production}}{\text{Estimated total production}}\end{array}$

Depreciation schedule under units-of-production method:

Year	Computation	Depreciation Expense	Accumulated Depreciation	Net Book Value
At Acquisition				$950,000
1	$\left(\$950,000-\$50,000\right)\times \frac{70,000\text{ units}}{300,000\text{ units}}$	$210,000	$210,000	740,000
2	$\left(\$950,000-\$50,000\right)\times \frac{67,000\text{ units}}{300,000\text{ units}}$	201,000	411,000	539,000
3	$\left(\$950,000-\$50,000\right)\times \frac{50,000\text{ units}}{300,000\text{ units}}$	150,000	561,000	389,000
4	$\left(\$950,000-\$50,000\right)\times \frac{73,000\text{ units}}{300,000\text{ units}}$	219,000	780,000	170,000
5	$\left(\$950,000-\$50,000\right)\times \frac{40,000\text{ units}}{300,000\text{ units}}$	120,000	900,000	50,000

Table (2)

To determine

Prepare the depreciation expense schedule under double-declining-balance method.

Explanation of Solution

Double-declining-balance method:

The depreciation method which assumes that the consumption of economic benefits of long-term asset is high in the early years but gradually declines towards the end of its useful life is referred to as double-declining-balance method.

Formula for double-declining-balance depreciation method:

$\begin{array}{c}\begin{array}{l}\text{Depreciation }\\ \text{expense}\end{array}\}=\left(\begin{array}{l}\text{Book value at the }\\ \text{beginning of the period }\end{array}\right)\text{× Depreciation rate}\\ \text{= }\left(\text{Cost–Accumulated depreciation}\right)\text{×}\frac{\text{2}}{\text{Useful life}}\end{array}$

Depreciation schedule under double-declining-balance method:

Year	Computation	Depreciation Expense	Accumulated Depreciation	Net Book Value
At Acquisition				$950,000
1	$\left(\$950,000-\$0\right)\times \frac{2}{5}$	$380,000	$380,000	570,000
2	$\left(\$950,000-\$380,000\right)\times \frac{2}{5}$	228,000	608,000	342,000
3	$\left(\$950,000-\$608,000\right)\times \frac{2}{5}$	136,800	744,800	205,200
4	$\left(\$950,000-\$744,800\right)\times \frac{2}{5}$	82,080	826,880	123,120
5	$\left(\$950,000-\$826,880\right)\times \frac{2}{5}$	73,120	900,000	50,000

Table (3)

Note: In Year 5, the net book value of the asset cannot be less than the residual value of such asset. Hence, calculate the depreciation expense as given in the working note below.

Working Note:

Compute depreciation expense in Year 5.

$\begin{array}{c}\text{Depreciation in Year 5 }=\left(\begin{array}{l}\text{Cost–}\\ \text{Accumulated depreciation in Year 4–}\\ \text{Residual value}\end{array}\right)\\ =\text{\$950,000–\$826,880–\$300,000}\\ =\$73,120\end{array}$

To determine

Identify the factors which the management might consider in selecting a preferable depreciation method in conformity with the expense principle.

Explanation of Solution

• If there is an equal consumption of asset during the useful life of the asset and if there is a steady decline in its efficiency every year over its useful life, then the management can prefer straight-line depreciation method.
• If there is high consumption of asset in the early years of useful life and decline in usage towards the end of its useful life and if it perform efficiently in their earlier useful life and earn more revenue than in their later years, then the management can prefer double-declining-balance depreciation method.
• If the asset is not used at a uniform rate from period to period and if its efficiency varies from year to year in accordance with the rate of the output, then the management can prefer units-of-production depreciation method, as the depreciation expense would be better matched with the revenue earned under this method.