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Depreciation -definitions
A decline in the value of a property due to
general wear and tear or obsolescence
Method of writing off wear and tear on assets
that are used to produce income.
Amount of value that a possession loses over
time.
Depreciation basis is that part of the asset’s
purchase price that is spread over the
depreciation period (service life).
Depreciation
The cost is spread out over its
estimated useful life in the form
of an expense given various
depreciation methods.
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Causes of Depreciation
Question: What are the causes of depreciation?
Answers:
Fixed assets are those assets bought by the company
for the intention to be used for a long period of time.
Fixed assets are said to depreciate over a period of
time due to the following factors:
Causes of Depreciation
1) Physical deterioration
i) Wear and tear – When a motor vehicle or machinery or
fixtures and fittings are used, they eventually wear out.
Some last many years, others last only a few year.
ii) Erosion, rust, rot and decay – Land may be eroded or
wasted away by the action of wind, rain, sun and other
elements of nature. Similarly, the metals in motor
vehicles or machinery will rust away.
Causes of Depreciation
2) Economic factors
i) Obsolescence
This is the process of becoming out of date.
For instance, replacing a computer with old operatingsystem with a new computer with XP system.
ii) Inadequacy
This arises when an asset is no longer used because of thegrowth and changes in the size of the firm. Forinstance, a small ferryboat that is operated by a firm ata coastal resort will become entirely inadequate whenthe resort becomes more popular, to be more efficientand economical, the firm may replace it with a largeferryboat.
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Causes of Depreciation
3) The time factor (the effluxion of time)
Some assets might have a legal life fixed in terms of
years. For example, the patents, and leasehold. You may
agree to rent some buildings for 10 years. This is
normally called a lease. When the years are finished, the
lease is worth nothing to you, as it has finished.
Whatever you paid for the lease is now of no value.
Causes of Depreciation
4) Depletion
Other assets are of wasting character, perhaps due to the
extraction of raw materials from them. These materials
are then either used by the firm to make something else, or
are sold in their raw state to other firms. Natural
resources such as mines, quarries and oil wells come
under this heading.
Factors that affect the calculation of Depreciation
Question: What are the factors that affect the calculation of depreciation?
Answers:
1) Cost of asset (include expenses and capital expenditure incurred eg. The installation fees, the legal fees)
2) Estimated useful life of asset
This is the number of years that the asset is expected to be used)
3) Residual or scrap value of the asset
This is the value of the asset at the end of its life.
4) Method of calculating depreciation
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4 factors required for depreciation
calculations
1. Cost Net purchase price.
All reasonable and necessary expenditures to get the asset in place and ready for use.
2. Residual Value (Salvage or Scrap Value)– Asset value at the end of its expected “useful life”.
3. Depreciable Cost Cost less residual value.
Depreciable cost is allocated over the useful life of an asset.
4. Life useful life period of the asset
Depreciation Methods
Straight-line Method
Accelerated Methods
– Declining balance method
– Sum-of-the-years digits
Production or Use Methods
Cost - Residual Value
Estimated Useful Life
Straight Line Method
This method spreads the depreciable costs
evenly over the asset’s estimated useful life.
Annual depreciation is computed as follows:
$10,000 - $1000
5 years= = $1800 / year
Check the help for SLN function in Excel for more details
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The straight line formula
N
SId
N
SIADA
N
SIAIS A
Where: -
N = life of the structure in years
I = the original cost
S = the values at the end of the life of structure
d = the annual cost of depreciation
DA = depreciation up to age A years
SA = the value of the end of A years
B C D E F
2 Depreciation Schedule3 Straight Line Method - SLN function
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5 Scrap Value - 1000
6 Years - 5
7
8
9perio d yrs C o st
A nnual
D epreciat io n
A ccumulated
D epreciat io nC arrying Value
10 DOP 0 10000 0 0 10000
11 End of Yr 1 1 10000 1800 1800 8200
12 End of Yr 2 2 10000 1800 3600 6400
13 End of Yr 3 3 10000 1800 5400 4600
14 End of Yr 4 4 10000 1800 7200 2800
15 End of Yr 5 5 10000 1800 9000 1000
Same Increases Decreases Stop at
each Uniformly Uniformly Residual Value
year
Carrying Value(CV) = Cost – Accumulated Depreciation
=D10-F10
=SLN(D11,$D$5,$D$6)
Book Value
The book value of a plant asset is
the net cost of the asset after
accumulated depreciation (the
contra account) has been
subtracted.
$50,000 Beg. Book Value
-12,000 Accum. Depre.
$38,000 End. Book Value
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Example
An equal amount of depreciation
is recorded each fiscal year.
Straight-Line Depreciation Schedule
Straight-line method (Examples)
Example 1:
ABC Ltd. Bought a machine at a cost of £80,000. Themachine has an expected useful life of 5 years and at the endof the 5th year, it can be sold for £10,000. calculatedepreciation per annum?
Cost Annual
Depreciation
Provision for
Depreciation
NBV
Date of
purchase
80,000 80,000
End of 1st year 80,000 14,000 14,000 66,000
End of 2cd year 80,000 14,000 28,000 52,000
End of 3rd year 80,000 14,000 42,000 38,000
End of 4th year 80,000 14,000 56,000 24,000
End of 5th year 80,000 14,000 70,000 10,000
Depreciation for 5 years would be:
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Example 2:
ABC Ltd. Bought a machine at a cost of £80,000. The
depreciation is to be charged at a 20% per annum on cost.
Solution:-
Depreciation per annum = £80,000 x 20%
= £16,000 per year
Straight-line method (Examples)
Decling-Balance (DB) Method -Type
1. Fixed DB method
– computes depreciation at a fixed rate.
2. Double DB method
– computes depreciation at an accelerated rate.
3. Variable DB method
– Also computes depreciation at an accelerated rate.
– switches to straight-line depreciation when depreciation is greater than the declining balance calculation
Check the help for DB, DDB and VDB functions in Excel for more details
Accelerated Depreciation
Declining balance method
Depreciation is calculated on a fixed percentage on the
Diminishing Balance of the Asset (the NBV). This
results in a higher depreciation charge in the earlier years
of the asset’s estimated useful life.
Example 3: A machine costs £50,000 is to be
depreciated at 15% on Reducing Balance Method.
Accelerated Depreciation
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Declining balance method
Cost Annual Depreciation Provision for
Depreciation
NBV
Date of purchase 50,000 0 - 50,000
End of 1st year 50,000 50,000 x 15% = 7,500 7,500 42,500
End of 2cd year 50,000 42,500 x 15% = 6,375 13,875 36,125
End of 3rd year 50,000 36,125 x 15% = 5,419 19,294 30,706
End of 4th year 50,000 30,706 x 15% = 4,606 23,900 26,100
End of 5th year 50,000 26,100 x 15% = 3,915 27,815 22,185
Accelerated Depreciation
The ratio of the depreciation in any one year to the
salvage value at the beginning of that year is constant
throughout the life of the structure and is designated
by X.
X = the annual fixed ratio of depreciation
Deprecation during the first year (d1) = I X
Depreciation value (Book value) at the end of the
1st year = I – I X = I (1 – X)
Depreciation value (Book Value) at the end of n
years (S) = I (1 – X)n
S/I = (1 – X)n
X = 1 – (S/I)(1/n)
The Matheson formula or declining balance method
Accelerated Depreciation
Double-declining-balance method, it would
Multiply the straight-line rate by two, e.g. 2/1 x
¼ = 2/4
$25,000 = $50,000 x2
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Double-declining-balance
depreciation expense= Book Value x
2 x straight-line
Expected useful
life
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A B C D E
(A xB) ($50k - D)
Year
2004 2/4 $50,000 $25,000 $25,000 $25,000
2005 2/4 25,000 12,500 37,500 12,500
2006 2/4 12,500 6,250 43,750 6,250
2007 2/4 6,250 4,250 48,000 2,000
Ending
Book
Value
Double-
Declining-
Balance
Rate
Beginning
Book
Value
Debit
Depreciation
Expense
Credit
Accumulated
Depreciation
Double-Declining Balance
Depreciation Schedule
Accelerated Depreciation
$6,250 – $2,000
(residual value)
Reasons for Using Accelerated Depreciation
1. An asset is more useful earlier in its life than
later, and the useful life may be difficult to
estimate.
2. Depreciation expense is deductible in computing
taxable income and income taxes.
The second reason is the most
common reason for using
accelerated depreciation.
Income before depreciation
and taxes $100,000 $100,000
Depreciation expense 12,000 25,000
Pretax income 88,000 75,000
Income taxes (35%) 30,800 26,250
Net income $ 57,200 $ 48,750
Straight-Line Accelerated
Comparison of Straight-Line and
Accelerated Depreciation Methods in 2004
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B C D E F
2 Depreciation Schedule3 Fixed Decling Method - DB function
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5 Scrap Value - 1000
6 Years - 5
7
8
9perio d yrs C o st
A nnual
D epreciat io n
A ccumulated
D epreciat io nC arrying Value
10 DOP 0 10000 0 0 10000
11 End of Yr 1 1 10000 3690 3690 6310
12 End of Yr 2 2 10000 2328 6018 3982
13 End of Yr 3 3 10000 1469 7488 2512
14 End of Yr 4 4 10000 927 8415 1585
15 End of Yr 5 5 10000 585 9000 1000
Increases Decreases Can't go
Quickly Quickly below scrap
Value
Carrying Value(CV) = Cost – Accumulated Depreciation
=D10-F10
=DB(D11,$D$5,$D$6,C11)
B C D E F
2 Depreciation Schedule3 Accelerated Double Decling Method - DDB function
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5 Scrap Value - 1000
6 Years - 5
7
8
9perio d yrs C o st
A nnual
D epreciat io n
A ccumulated
D epreciat io nC arrying Value
10 DOP 0 10000 0 0 10000
11 End of Yr 1 1 10000 4000 4000 6000
12 End of Yr 2 2 10000 2400 6400 3600
13 End of Yr 3 3 10000 1440 7840 2160
14 End of Yr 4 4 10000 864 8704 1296
15 End of Yr 5 5 10000 296 9000 1000
Increases Decreases Can't go
Quickly Quickly below scrap
Value
Carrying Value(CV) = Cost – Accumulated Depreciation
=D10-F10
=DDB(D11,$D$5,$D$6,C11)
Summary - depreciation
VDB Variable-decling balance
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B C D E F
2 Depreciation Schedule3 Formulae
4 Asset - Equipment C12 =SLN($D$5,$D$6,$D$7)
5 Cost 100,000 D12=DB($D$5,$D$6,$D$7,B12)
6 Scrap Value - 2000 E12=DDB($D$5,$D$6,$D$7,B12)
7 Years - 5 F12=VDB($D$5,$D$6,$D$7,B11,B12)
8 D20=D19-C11
9 Depreciation Amt.
10 Years SLN DB DDB VDB
11 1 19,600 54,300 40,000 40,000
12 2 19,600 24,815 24,000 24,000
13 3 19,600 11,341 14,400 14,400
14 4 19,600 5,183 8,640 9,800
15 5 19,600 2,368 5,184 9,8001617 Value of Asset
18 period yrs SLN D B D D B VD B
19 DOP 0 100,000 100,000 100,000 100,000
20 End of Yr 1 1 80,400 45,700 60,000 60,000
21 End of Yr 2 2 60,800 20,885 36,000 36,000
22 End of Yr 3 3 41,200 9,544 21,600 21,600
23 End of Yr 4 4 21,600 4,362 12,960 11,800
24 End of Yr 5 5 2,000 1,993 7,776 2,000
Asset value vs Life time
0
20,000
40,000
60,000
80,000
100,000
120,000
0 1 2 3 4 5 6
Period (years)
Asset V
alu
e
SLN
DB
DDB
VDB
Depreciation Vs Period
-
10,000
20,000
30,000
40,000
50,000
60,000
0 1 2 3 4 5 6
Period (years)
De
pre
cia
tio
n A
mt
SLN
DB
DDB
VDB
Comparison of Depreciation Methods
To obtain the depreciation charge in any year of
life by the sum-of-the year digits method
(commonly designated by SYD), the digits
corresponding to the number of each year of life
are listed in reverse order.
The sum of the digits is then determined.
The depreciation factor for any year is the reverse
digit for that year divided by the sum of the digits.
For example, for a property having a life of five
years,
Sum of digits plan
12
year Number of the year in
reverse order (digits)
Depreciation
1 5 5/15
2 4 4/15
3 3 3/15
4 2 2/15
5 1 1/15
Sum of the digits 15
Sum of digits plan
The depreciation for any year is the product of the SYD
depreciation factor for that year and the depreciable
value, I – S.
The general expression for the annual cost of
depreciation for any year, A, when the total life is N, is
)()1(
)1(2SI
NN
AN
DA =
Sum of digits plan
Units-of-Production Depreciation
At the beginning of 2005, Mom’s Cookie Company
purchased a truck for $30,000. Management
expects the useful life of the truck to be 100,000
miles, at which time it will be sold for $10,000.
Cost – Residual Value
Expected Units
$30,000 – $10,000
100,000 miles
Activity Depreciation
$0.20 per mile
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If the truck were driven
12,000 miles in 2005,
Hydro would record
depreciation expense of
$2,400 (12,000 x $0.20).
Activity Depreciation
Units-of-Production Depreciation
