Straight-Line (SL)
Annual SL
Depreciation
= Acquisition cost - Residual value
Estimated useful life in years
SL
Straight-Line
Example
On January 1, we purchase equipment for
$50,000 cash. The equipment has an estimated
useful life of 5 years and residual value of
$5,000.
What is the annual straight-line depreciation?
SL
Straight-Line
Example
Annual SL
Depreciation
=
Acquisition cost - Residual value
Estimated useful life in years
Annual SL
Depreciation
=
Annual SL
Depreciation
= $9,000
$50,000 - $5,000
5 years
SL
Straight-Line
Example
Year
1
2
3
4
5
Depreciation
Expense
(debit)
Accumulated
Depreciation
(credit)
Accumulated
Depreciation
Balance
$
$
$
$
9,000
9,000
9,000
9,000
9,000
45,000
$
9,000
9,000
9,000
9,000
9,000
45,000
9,000
18,000
27,000
36,000
45,000
Undepreciated
Balance
(book value)
$
50,000
41,000
32,000
23,000
14,000
5,000
Residual Value
SL
Activity Method
• Depreciation may be based on measures of
input or output like. . .
Service hours
Productive output (units-of-production)
• No depreciation is taken if the asset is idle.
Service Hours (SH)
Depreciation
Per SH
=
Acquisition cost - Residual value
Estimated service life in hours
Depreciation
Expense
Depreciation × Number of hours
=
Per SH
running time
Productive Output (PO)
Depreciation rate
per unit of output
Depreciation
Expense
=
Acquisition Cost - Residual Value
Estimated Productive Output in Units
Depreciation
=
rate per unit
×
Number of units
produced
Productive Output (PO)
Example
On January 1, we purchased equipment for $50,000
cash. The equipment is expected to produce 100,000
units during its life and has an estimated residual
value of $5,000.
If 22,000 were produced this year, what is the amount
of depreciation expense?
Productive Output (PO)
Example
Depreciation rate
per unit of output
=
$50,000 - $5,000
100,000 Units
Depreciation
expense
=
$.45 per unit
Depreciation
expense
=
$9,900
= $.45 per unit
× 22,000 units
Productive Output (PO)
Example
In addition to the 22,000 units produced the first
year, we produced 28,000 units in year 2, zero
units in year 3, 32,000 units in year 4, and 18,000
units in the fifth and final year of the asset’s life.
Let’s look at a schedule of depreciation for the
five-year period.
Productive Output (PO)
Example
Units
22,000
28,000
32,000
18,000
100,000
Depreciation
Expense
(debit)
Accumulated
Depreciation
Balance
$
$
$
9,900
12,600
14,400
8,100
45,000
9,900
22,500
22,500
36,900
45,000
Undepreciated
Balance
(book value)
$
50,000
40,100
27,500
27,500
13,100
5,000
Residual Value
No depreciation expense if the equipment is idle.
Accelerated Depreciation
Accelerated depreciation methods result in more
depreciation expense in the early years of an
asset’s useful life and less depreciation expense
in later years of an asset’s useful life.
Accelerated Depreciation
Accelerated depreciation methods . . .
– Match higher depreciation expense with higher revenues in the
early years of an asset’s useful life when the asset is more efficient.
– Maintain a more uniform total use expense for an asset:
Depreciation
Expense
Early Years
High
Later Years
Low
Repair
Expense
Low
High
Accelerated Depreciation Methods
• Sum-of-the-Years Digits
• Double-Declining Balance
Sum-of-Years’ Digits (SYD)
Annual depreciation is calculated with
the following formula:
(Cost - Residual Value) ×
Remaining Years
of Useful Life
Sum-of-the-Years’ Digits
Sum-of-Years’ Digits (SYD)
The sum-of-the-years’ digits may be computed as follows
for an asset with a five-year life:
1 + 2 + 3 + 4 + 5 = 15
However, the following convenient formula is often more
useful:
SYD = n
[
n+ 1
2
]
5+ 1
= 5
2
[
Where n = Total useful life in years.
]
= 15
Sum-of-Years’ Digits
Example
On January 1, we purchase equipment for
$50,000 cash. The equipment has a useful life
of 5 years and an estimated residual value of
$5,000.
What is depreciation expense for the first two
years?
Sum-of-Years’ Digits
Example
SYD = n
[
n+ 1
2
]
= 5
[
5+ 1
2
]
= 15
Sum-of-Years’ Digits
Example
SYD = n
[
n+ 1
2
]
= 5
[
5+ 1
2
]
= 15
1st year depreciation:
($50,000 - $5,000) ×5/15 = $15,000
Sum-of-Years’ Digits
Example
SYD = n
[
n+ 1
2
]
= 5
[
5+ 1
2
]
= 15
1st year depreciation:
($50,000 - $5,000) ×5/15 = $15,000
2nd year depreciation:
($50,000 - $5,000) × 4/15 = $12,000
Sum-of-Years’ Digits
Example
Fraction
5/15
4/15
3/15
2/15
1/15
Depreciation
Expense
(debit)
Accumulated
Depreciation
Balance
$
$
$
15,000
12,000
9,000
6,000
3,000
45,000
15,000
27,000
36,000
42,000
45,000
Undepreciated
Balance
(book value)
$
50,000
35,000
23,000
14,000
8,000
5,000
Residual Value
Declining-Balance Methods
• Declining-balance depreciation is based on the
straight-line rate multiplied by an acceleration
factor.
For example, when the acceleration factor is 200
percent, the method is referred to as doubledeclining-balance (DDB) depreciation.
• Declining-balance depreciation computations
initially ignore residual value.
Double-Declining-Balance Method
Annual Depreciation is calculated with
the following formula:
Book Value ×(2 × Straight-Line Rate)
100%
Book Value × 2 × Useful Life in Years
(
)
Double-Declining-Balance
Example
On January 1, we purchase equipment for
$50,000 cash. The equipment has a useful
life of 5 years and an estimated residual
value of $5,000.
What is depreciation expense for the first
two years using double-declining-balance?
Double-Declining-Balance
Example
(
Book Value × 2 ×
100%
Useful Life in Years
)
Double-Declining-Balance
Example
100%
Book Value × 2 × Useful Life in Years
(
1st year depreciation:
100%
$50,000 × 2 × 5 years
(
)
= $20,000
)
Double-Declining-Balance
Example
100%
Book Value × 2 × Useful Life in Years
(
)
1st year depreciation:
100%
$50,000 × 2 × 5 years
(
)
= $20,000
2nd year depreciation:
100%
($50,000 - $20,000) × 2 × 5 years
(
)
= $12,000
Double-Declining-Balance
Example
100%
Book Value × 2 × Useful Life in Years
(
)
1st year depreciation:
100%
$50,000 × 2 × 5 years
(
)
= $20,000
2nd year depreciation:
100%
($50,000 - $20,000) × 2 × 5 years
(
)
= $12,000
Double-Declining-Balance
Example
Let’s calculate
depreciation expense
for the life of the asset
using DDB.
Double-Declining-Balance
Example
Year
1
2
3
4
5
Depreciation
Expense
(debit)
Accumulated
Depreciation
Balance
$
$
$
20,000
12,000
7,200
4,320
1,480
45,000
20,000
32,000
39,200
43,520
45,000
Undepreciated
Balance
(book value)
$
50,000
30,000
18,000
10,800
6,480
5,000
We usually have to force depreciation expense in the
latter years to an amount that brings BV to residual value.
Comparison of Methods
• The total amount of depreciation recorded over the useful
life of an asset is the same regardless of the method used.
• Depreciation expense recorded in any one period will vary
according to method used.
• The straight-line method is
used by about 95 percent of
companies because it is easy
to use and to explain.
Comparison of Methods:
Straight-Line Method
10000
Depreciation
8000
6000
4000
2000
0
1
2
3
Life in Years
4
5
Comparison of Methods:
Productive Output Method
Depreciation
16000
14000
12000
10000
8000
6000
4000
2000
0
1
2
3
Life in Years
4
5
Comparison of Methods:
Sum-of-the-Years’ Digits Method
Depreciation
16000
14000
12000
10000
8000
6000
4000
2000
0
1
2
3
Life in Years
4
5
Comparison of Methods:
Double-Declining-Balance Method
20000
Depreciation
15000
10000
5000
0
1
2
3
Life in Years
4
5
Conceptual Evaluation of Depreciation Methods
$
Depreciation
Expense
Sum-of-the-Years-Digits
Straight-Line
Double-Declining-Balance
2006 2007 2008 2009 2010
During Year
Conceptual Evaluation of Depreciation Methods
$
Sum-of-the-Years-Digits
Book Value
Straight-Line
Double-Declining-Balance
2006 2007 2008 2009 2010
At End of Year
Tax Depreciation
• For an asset purchased in 1987 and later, the Modified
Accelerated Cost Recovery System (MACRS) is required for tax
purposes.
• A mandated tax life, which is usually shorter than the
economic life.
• MACRS provides for rapid write-off of an asset’s cost in order
to stimulate investment in modern facilities.
• MACRS ignores residual value.
• Depreciation is based upon percentages related to the “class
life”of the asset.
Tax Depreciation
Percentages are based on the DDB method using the
“half-year” convention--one-half year depreciation in
the first and last years of the asset’s class life.
Year
1
2
3
4
5
6
Recovery Percentages
Three-Year
Five-Year
33.33%
20.00%
44.45%
32.00%
14.81%
19.20%
7.41%
11.52%
11.52%
5.76%
100.00%
100.00%
Tax Depreciation
• Three-year property includes special tools, horses and R&D
activities.
• Five-year property includes machinery and equipment,
automobiles and light trucks.
Year
1
2
3
4
5
6
Recovery Percentages
Three-Year
Five-Year
33.33%
20.00%
44.45%
32.00%
14.81%
19.20%
7.41%
11.52%
11.52%
5.76%
100.00%
100.00%
Tax Depreciation
Example
On January 1, we purchase equipment for $50,000 cash. The
equipment has a useful life of 4 years and an estimated
residual value of $5,000. For tax purposes, the asset is
classified as five-year property.
Determine proper depreciation expense for each year of the
asset’s life.
Tax Depreciation
Example
Rate
20.00%
32.00%
19.20%
11.52%
11.52%
5.76%
Depreciation
Expense
(debit)
Accumulated
Depreciation
Balance
$
$
$
10,000
16,000
9,600
5,760
5,760
2,880
50,000
10,000
26,000
35,600
41,360
47,120
50,000
Undepreciated
Balance
(book value)
$
50,000
40,000
24,000
14,400
8,640
2,880
-
MACRS ignores residual value
Depreciation Disclosures
• Depreciation expense.
• Balances of major classes of depreciable assets.
• Accumulated depreciation by asset or in total.
• General description of
depreciation methods used.
Conceptual Evaluation of Depreciation Methods
If a company expects that repairs and
maintenance costs and the total
economic benefits of the asset will
remain similar each period, a similar
total cost each period can be achieved
through straight-line depreciation and
the similar repair and maintenance
costs.
Conceptual Evaluation of Depreciation Methods
If the company expects that benefits of
having the asset will decline each year
for the life of the asset, and repairs and
maintenance costs are constant each
period, a declining total cost will be
achieved by using accelerated
depreciation.
Selection of Depreciation Method
Depreciation Policy
• Depreciation expense, unlike
most other expenses, does
not require a cash outflow.
• Because depreciation is tax
deductible, it reduces the
cash outflow related to taxes.
Fractional-Year Depreciation
I bought an asset on May 19
this year. Do I get a full year
depreciation or a half-year
depreciation?
May
19
Fractional-Year Depreciation
You have several choices.
Consider the following
policies used by many
companies.
May
19
Fractional-Year Depreciation
Example
On June 30, 19X1 we purchased equipment for
$100,000 cash. The equipment has a useful life of
5 years and estimated residual value of $20,000.
Calculate the straight-line depreciation for the
year ended December 31, 19X1.
June
30
Fractional-Year Depreciation
Example
Depr. = ($100,000 - $20,000) ÷5 = $16,000
Depr. = $16,000 ÷2 = $8,000
June
30
Fractional-Year Depreciation
Example
On June 30, 19X1 we purchased equipment for
$100,000 cash. The equipment has a useful life of 5
years and estimated residual value of $20,000.
Calculate DDB depreciation for the year ended
December 31, 19X1.
June
30
Fractional-Year Depreciation
Example
Depr. = ($100,000 - $0) ×(2 /5) = $40,000
Depr. = $40,000 ÷2 = $20,000
June
30
Fractional-Year Depreciation
1. A full month of depreciation for assets
acquired before mid-month, none for assets
acquired after mid-month.
1st of
month
Asset acquired
Asset acquired
Full month of
Depreciation
No
Depreciation
Midmonth
End of
month
Fractional-Year Depreciation
2. A full year of depreciation for assets acquired
before mid-year, and none for assets acquired
after mid-year.
1st of
year
Asset acquired
Asset acquired
Full year of
Depreciation
No
Depreciation
Midyear
End of
year
Fractional-Year Depreciation
3. One-half year of depreciation in the year of
acquisition and retirement, without regard to
the month of acquisition or retirement.
First
year
Intervening
years
Asset
acquired
One-half year
of depreciation
Last
year
Asset
retired
Full year of
depreciation
One-half year
of depreciation
Depreciation Systems
• Depreciation systems reduce accounting cost
because fewer calculations are required.
• Accumulated depreciation records are not
maintained for individual assets.
Additional Depreciation Methods
Inventory Appraisal Depreciation
Depreciation expense is the result of appraisal of
numerous low-cost assets.
Group Depreciation
Homogeneous assets are treated as a group.
Composite Depreciation
Heterogeneous assets are treated as a group.
Inventory Appraisal Depreciation
• Plant assets are appraised at the end of each
period.
• The decline in appraised value is recorded as
depreciation expense with a corresponding
credit to the plant asset account.
• Proceeds from disposal of tools reduces
depreciation expense.
Inventory Appraisal Depreciation
Example
Assume this information on the hand tools
plant asset account of Miller Company, which
began operation in 2005:
Purchase of hand tools in 2005: $1,900
Appraisal value of tools at the end of 2005: $1,080
Proceeds from disposal of tools in 2005: $70
Inventory Appraisal Depreciation
Example
During 2005:
Hand tools
1,900
Cash
Cash
1,900
70
Depreciation expense
70
December 31, 2005:
Depreciation expense
Hand tools ($1,900-$1,080)
820
820
Group and Composite Depreciation
• Assets are grouped by common
characteristics.
• A “composite rate” is calculated.
• Annual depreciation is determined by
multiplying the composite rate times the total
group acquisition cost.
Group and Composite Depreciation
Composite =
rate
Group
A
B
C
D
Annual group SL depreciation
Total group acquisition cost
Acquisition
Cost
Re sidua l
Va lue
$
$
250,000
500,000
1,000,000
750,000
$ 2,500,000
25,000
35,000
75,000
50,000
$ 185,000
Use ful
Life
5
10
15
20
Annua l SL
De pre cia tion
$
$
45,000
46,500
61,667
35,000
188,167
Composite rate = ($188,167 ÷ $2,500,000) = 7.527%
Group and Composite Depreciation
• The composite rate (7.527%) is applied to the total cost of
the assets.
• If assets in the group are sold or new assets added, the
composite rate remains the same.
• When an asset in the group is sold or retired, the debit to
Accumulated Depreciation is the difference between the
asset’s cost and the proceeds from the sale or retirement.
Plant Asset Impairment
(SFAS 144)
• Impairment is the loss of a significant portion
of the utility of an asset through . . .
Casualty.
Obsolescence.
Lack of demand for the asset’s services.
• When plant assets suffer a permanent
impairment in value, a loss should be recorded.
Plant Asset Impairment
(SFAS 144)
An asset is impaired if . . .
Recoverable cost < Carrying value
Expected future total undiscounted net
cash inflows generated by use of the asset.
Plant Asset Impairment
(SFAS 144)
Impairment
loss
Reported as
part of
income from
continuing
operations.
Carrying _
=
value
Fair
value
•Market value, price of
similar assets, or present
value of future net cash
inflows.
•Fair value is less than
recoverable value due to
the time value of money.
Plant Asset Impairment
(SFAS 144)
$0
Fair
Value
$125
Case 1:
$50 Carrying value
No loss recognized
Recoverable
Cost
$250
Case 3:
$275 Carrying value
Loss = $275 - $125
Case 2:
$150 Carrying value
No loss recognized
Impairment of a Noncurrent Asset
On January 1, 2004, the Hall Company
purchased a factory for $1 million (20-year life)
and machinery for $3 million (10-year life).
Late in 2007, the company believes that its
asset(s) may be impaired and the remaining
useful life is 5 years. The company estimates
that the asset will produce cash inflows of
$700,000 and incur cash outflow of $300,000
each year for the next 5 years.
Impairment of a Noncurrent Asset
Impairment Test
December 31, 2007
Factory cost
$1,000,000
Less: Accumulated depreciation
(4 x $50,000)
(200,000)
Book value
$ 800,000
Machinery cost
$3,000,000
Less: Accumulated depreciation
(4 x $300,000)
(1,200,000)
Book value
1,800,000
Total Book Value
$2,600,000
Impairment of a Noncurrent Asset
Impairment Test
Undiscounted expected
net cash flows
= 5 x ($700,000 - $300,000)
Years Cash
= 5 x $400,000
Inflows
= $2,000,000
Because $2,000,000 is less than
$2,600,000 (the book value), an
impairment loss must be recognized.
Cash
Outflows
Impairment of a Noncurrent Asset
Measurement of the Loss
Undiscounted annual cash flows
Present value of the expected
cash flows (fair value)
Book value
Fair value
Impairment loss
= $400,000 x 3.274294
= $1,309,718 (rounded)
$2,600,000
(1,309,718)
$1,290,282
n= 5, i = 0.16
from Table
4 in
Appendix
Impairment of a Noncurrent Asset
FASB Statement No. 121 does not specify
how to record the write-down. It does
indicate that the reduced book value is to be
accounted for as the new cost.
Although FASB Statement No. 121 has
been replaced by FASB Statement No.
144, the principles it established have
only changed slightly.
Plant Asset Impairment
(SFAS 144)
Loss on Impairment
150
Accumulated Depreciation
150
Impairment of a Noncurrent Asset
Loss from Impairment
Accumulated Depreciation:
Factory
Accumulated Depreciation:
Machinery
Factory (new cost)
Machinery (new cost)
Factory (old cost)
Machinery (old cost)
1,290,282
200,000
1,200,000
327,429
982,289
1,000,000
3,000,000
$1,309,718 x [$1,000,000 ÷ ($3,000,000 + $1,000,000)]
$1,309,718 x [$3,000,000 ÷ ($3,000,000 + $1,000,000)]
Is this boat impaired
or fully depreciated?
Natural Resources
• Sometimes referred to as wasting assets.
• Supplied by nature and extracted from
natural environment.
Gold, oil, timber, coal, and other minerals.
• Presented on the balance sheet as
noncurrent assets.
Natural Resources
• SFAS No. 19 identifies total costs as including
acquisition costs
exploration costs
development costs
production costs
support equipment and facilities cost.
• Total cost is allocated over periods benefited by
means of depletion.
Depletion
Depletion is calculated using the
units-of-production method.
Unit depletion rate is calculated as follows:
Capitalized Cost of
Natural Resource
-
Residual
Value
Estimated Recoverable Units
The numerator, cost -residual value,
is called the depletion base.
Depletion
Total depletion cost for a period is:
UNIT DEPLETION
RATE
x
NUMBER OF UNITS
EXTRACTED IN PERIOD
The unit depletion rate . . .
• is inventoried with each extracted unit.
• is expensed as a part of cost of goods sold for
each unit sold.
• remains in inventory with each unsold unit.
Depletion - Example
Reggio Company purchases land for $3,000,000
from which it expects to extract 1,000,000 tons
of coal, the estimated residual value is $200,000,
and it mines 80,000 tons of coal in the first year.
Depletion - Example
Cost - Residual Value
Unit Depletion Rate =
Units
$3,000,000 - $200,000
Unit Depletion Rate =
1,000,000 tons
Unit Depletion Rate = $2.80 per ton
Depletion for Year = $2.80 x 80,000 = $224,000
Natural Resources
Restoration Costs
• In some cases, the extractor is required to
restore the land to its original state subsequent
to the resources being extracted.
• The estimated cost of restoration increases the
depletion base.
Natural Resources
Change in Estimate
• The unit depletion rate is based on estimated
recoverable units.
• Those estimates may change over time.
• The revised unit depletion rate is computed for
the remaining costs.
• Prior depletion costs are not revised.
Natural Resources
Income Tax Reporting
• The cost-based depletion method is for
financial reporting purposes.
• The Internal Revenue Code allows the use of
statutory depletion (also called percentage
depletion) for tax purposes.
• Use of different methods for tax and financial
reporting purposes leads to different incomes.
Exploration Costs
Oil and Gas Industry
• The costs of exploration for the oil and gas industry are very
large.
• An accounting question arises as to how much of the
exploration costs can be capitalized.
• Two basic methods are allowed when accounting for those
costs:
Full-cost method
Successful-efforts method
Exploration Costs
Full-Cost Method
• All exploration costs are capitalized as part of
the cost of the natural resource.
• This method tends to be used by smaller firms
primarily in the exploration business.
Exploration Costs
Successful-Efforts Method
• Only the exploration costs associated with
successful wells are capitalized in the cost of
the natural resource.
• The costs associated with unsuccessful wells
are expensed as incurred.
Exploration Costs
Example
World-Wide Oil Company (WOWOCO) spent
$25,000,000 in 19X8 exploring for oil. Of all the
wells drilled, 90% were dry. As a result of the
remaining 10%, 20 million barrels of oil worth
$10 per barrel were discovered.
Exploration Costs
Example
Record the exploration costs for WOWOCO
assuming they use the successful-efforts
method.
Exploration Costs
Example
Record the exploration costs for WOWOCO
assuming they use the successful-efforts
method.
GENERAL JOURNAL
(All amounts shown are in thousands.)
Page:
Date
Description
Cost of Oil Reserves
Exploration Expense
Cash, payables, etc.
to record exploration costs
for the period
PR
Debit
15
Credit
2,500
22,500
25,000
Exploration Costs
Example
What is WOWOCO’s unit depletion cost if they
use the successful-efforts method?
Exploration Costs
Example
What is WOWOCO’s unit depletion cost if they
use the successful-efforts method?
Unit
Depletion =
Cost
Cost
of Oil
Reserves
Estimated
÷ Removable
Units
= $ 2,500,000 ÷
= $
0.125
20,000,000
per barrel
Exploration Costs
Example
Record the exploration costs for WOWOCO
assuming they use the full-cost method.
Exploration Costs
Example
Record the exploration costs for WOWOCO
assuming they use the full-cost method.
GENERAL JOURNAL
(All amounts shown are in thousands.)
Page:
Date
Description
Cost of Oil Reserves
Cash, payables, etc.
to record capitalization of
exploration costs for the period
PR
Debit
15
Credit
25,000
25,000
Exploration Costs
Example
What is WOWOCO’s unit depletion cost if they
use the full-cost method?
Exploration Costs
Example
What is WOWOCO’s unit depletion cost if they
use the full-cost method?
Unit
Depletion =
Cost
Cost
of Oil
Reserves
Estimated
÷ Removable
Units
= $ 25,000,000 ÷
= $
1.250
20,000,000
per barrel
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