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Depreciation and Depletion
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Accounting for Depreciation and Income Taxes
Asset DepreciationBook DepreciationTax DepreciationHow to Determine
“Accounting Profit”Corporate Taxes
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Depreciation• Definition: Loss of value for a fixed asset• Example: You purchased a car worth $15,000 at the beginning of year 2000.
Dep
reciation
End of Year
Market
Value
Loss of
Value
0
1
2
3
4
5
$15,00010,000
8,0006,0005,0004,000
$5,0002,0002,0001,0001,000p
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Why Do We Consider Depreciation?
Gross Income -Expenses:(Cost of goods sold)(Depreciation)(operating expenses)
Taxable Income
- Income taxes
Net income (profit)
Business Expense: Depreciation is viewed as part of business expenses that reduce taxable income.
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Depreciation Concept
Economic Depreciation
Purchase Price – Market Value(Economic loss due to both physical deterioration and technological obsolescence)
Accounting DepreciationA systematic allocation of cost basis over a period of time.
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Asset Depreciation
Depreciation
Economic depreciationthe gradual decrease inutility in an asset with
use and time
Accounting depreciationThe systematic allocation
of an asset’s value inportions over its
depreciable life—oftenused in engineeringeconomic analysis
Physicaldepreciation
Functionaldepreciation
Book depreciation
Taxdepreciation
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What Can Be Depreciated?
Assets used in business or held for production of income
Assets having a definite useful life and a life longer than one year
Assets that must wear out, become obsolete or lose value
A qualifying asset for depreciation must satisfy all of the three conditions above
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Factors to Consider in Asset Depreciation
Depreciable life (how long?)
Salvage value (disposal value)
Cost basis (depreciation basis)
Method of depreciation (how?)
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Asset Depreciation Range (years)
Assets Used Lower Limit Midpoint Life Upper Limit
Office furniture, fixtures, and equipment 8 10 12
Information systems (computers) 5 6 7
Airplanes 5 6 7
Automobiles, taxis 2.5 3 3.5
Buses 7 9 11
Light trucks 3 4 5
Heavy trucks (concrete ready-mixer) 5 6 7
Railroad cars and locomotives 12 15 18
Tractor units 5 6 7
Vessels, barges, tugs, and water transportation system
14.5 18 21.5
Industrial steam and electrical generation and or distribution systems
17.5 22 26.5
Manufacturer of electrical and nonelectrical machinery 8 10 12
Manufacturer of electronic components, products, and systems
5 6 7
Manufacturer of motor vehicles 9.5 12 14.5
Telephone distribution plant 28 35 429
Cost Basis
Cost of new hole-punching machine (Invoice price) $62,500
+ Freight 725
+ Installation labor 2,150
+ Site preparation 3,500
Cost basis to use in depreciation calculation
$68,875
10
Cost Basis with Trade-In Allowance
Old hole-punching machine (book value) $4,000
Less: Trade-in allowance 5,000
Unrecognized gains $1,000
Cost of new hole-punching machine $62,500
Less: Unrecognized gains (1,000)
Freight 725
Installation labor 2,150
Site preparation 3,500
Cost of machine (cost basis) $67,875
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Types of Depreciation
• Book Depreciation– In reporting net income to investors and
stockholders– In pricing decision
• Tax Depreciation– In calculating income taxes for the IRS– In engineering economics, we use
depreciation in the context of tax depreciation
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Book Depreciation Methods
• Purpose: Used to report net income to stockholders/investors
• Types of Depreciation Methods:– Straight-Line Method– Declining Balance Method– Unit Production Method– Sum-of-the-Year’s-Digits (SOYD)
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Straight – Line (SL) Method
• Principle A fixed asset is providing its service in a uniform fashion over its life
• Formula•Annual Depreciation
Dn = (I – S) / N, and constant for all n.•Book Value
Bn = I – n (D)where I = cost basis
S = Salvage valueN = depreciable life
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Example – Straight-Line Method
D1
D2
D3
D4
D5
B1
B2B3
B4
B5
$10,000
$8,000
$6,000
$4,000
$2,000
0 1 2 3 4 5
Total depreciation at end of
lifen Dn Bn
1 1,600 8,4002 1,600 6,8003 1,600 5,2004 1,600 3,6005 1,600 2,000
I = $10,000N = 5 YearsS = $2,000D = (I - S)/N
Annual Depreciation
Book Value
n
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Declining Balance Method• Principle: A fixed asset is providing its service in a decreasing fashion• Formula
• Annual Depreciation
• Book Value
1 nn BD 1)1( nI
nn IB )1( where 0 << 2(1/N)
Note: if is chosen to be the upper bound, = 2(1/N),
we call it a 200% DB or double declining balance method. 16
Example – Declining Balance Method
D1
D2
D3
D4D5
B1
B2
B3
B4 B5
$10,000
$8,000
$6,000
$4,000
$2,000
0 1 2 3 4 5
Total depreciation at end of
life
$778
Annual Depreciation
Book Value
n012345
Dn
$4,0002,4001,440
864518
Bn$10,000
6,0003,6002,1601,296
778
I
N
S
D B
I
B I
n n
n
nn
= $10,
= years
= $778
=
= ( -
000
5
1
1
1
1
( )
n17
Example- DB Switching to SL
• SL Dep. Rate = 1/5• (DDB rate) = (200%) (SL rate)
= 0.40
Asset: Invoice Price $9,000Freight 500Installation 500
Depreciation Base $10,000Salvage Value 0Depreciation 200% DBDepreciable life 5 years
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n Depreciation
Book
Value
12345
10,000(0.4) = 4,000 6,000(0.4) = 2,400 3,600(0.4) = 1,440 2,160(0.4) = 864 1,296(0.4) = 518
$6,0003,6002,1601,296
778
n
Book
Depreciation Value
12345
4,000 $6,0006,000/4 = 1,500 < 2,400 3,6003,600/3 = 1,200 < 1,440 2,1602,160/2 = 1,080 > 864 1,0801,080/1 = 1,080 > 518 0
(a) Without switching (b) With switching to SL
Note: Without switching, we have not depreciated the entirecost of the asset and thus have not taken full advantage of depreciation’s tax deferring benefits.
Case 1: S = 0
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Case 2: S = $2,000
End of Year
Depreciation Book Value
1 0.4($10,000) = $4,000 $10,000 - $4,000 = $6,000
2 0.4(6,000) = 2,400 6,000 – 2,400 = 3,600
3 0.4(3,600) = 1,440 3,600 –1,440 = 2,160
4 0.4(2,160) = 864 > 160 2,160 – 160 = 2,000
5 0 2,000 – 0 = 2,000
Note: Tax law does not permit us to depreciate assets belowtheir salvage values.
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Units-of-Production Method
• PrincipleService units will be consumed in a non
time-phased fashion
• Formula•Annual Depreciation
Dn = Service units consumed for yeartotal service units
(I - S)
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Example
• Given: I = $55,000, S = $5,000, Total service units = 250,000 miles, usage for this year = 30,000 miles
• Solution:
30,000($55,000 $5,000)
250,000
3($50,000)
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$6,000
Dep
22
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Sum-of-the-Year’s Digits (SOYD)
Annual depreciation =
(Cost - Salvage value) X RL
SOYD• RL = remaining years of useful life as of
the beginning of the year.• SOYD = sum of all the numbers from 1
through the estimated useful life= n(n+1)/2
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Sum-of-the-Year’s Digits (an example)
Asset cost = $50,000Asset life = 5 yearsSalvage value = $10,000Annual Depreciation:
Year 1 = (40,000) X (5/15) = $13,333.32Year 2 = (40,000) X (4/15) = $10,666.68Year 3 = (40,000) X (3/15) = $ 8,000.00Year 4 = (40,000) X (2/15) = $ 5,333.33
Year 5 = (40,000) X (1/15) = $ 2,666.67
Depletion• Depletion, though similar to
depreciation, is applicable only to natural resources (mines, wells, quarries, forests, etc.)
• When the resources are removed, they cannot be replaced or repurchased in the same manner as can a machine, computer, or structure
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Depletion
There are two methods of depletion
①Cost depletion
②Percentage depletion
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DepletionCost Depletion
• Cost depletion is based on the level of activity or usage, not time, as in depreciation
• The cost depletion factor for year t, denoted by Pt, is the ratio of the first cost of the resource to the estimated number of units recoverable
• The annual depletion charge is Pt times the year's usage or volume
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DepletionCost Depletion – Example
A company has negotiated the rights to cut timber on privately held forest area for $700,000
An estimated 350 million board feet of lumber are harvestable
•Determine the depletion amount for the first 2 years if 15 million and 22 million board feet are removed•After 2 years the total recoverable board feet was re-estimated to be 450 million from the time the rights were purchased. Compute the new cost depletion factor for years 3 and later
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DepletionCost Depletion – Example
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Multiply Pt by the annual harvest to obtain depletion of $30,000 in year 1 and $44,000 in year 2
Continue using Pt until we reach $700,000
DepletionCost Depletion – Example
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After 2 years, a total of $74,000 has been depleted
A new pt value must be calculated based on the remaining $700,000 – 74.000 = $626,000 investment
Additionally, with the new estimate of 450 million board feet, a total of 450 – 15 – 22 = 413 million board feet remain
For years t = 3, 4, …., the cost depletion factor is
DepletionPercentage Depletion
In this method, the cost depletion amount is given by the following equation:
cost depletion percentage
×
gross income from property
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DepletionPercentage Depletion
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DepletionPercentage Depletion – Example
A gold mine was purchased for 10 million. It has an anticipated gross income of $5 million per year for years 1 to 5 and $3 million per year after year 5
Compute:•Annual depletion amounts for the mine•How long will it take to recover the initial investment at i = 0%?
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DepletionPercentage Depletion – Example
A 15% depletion applies to gold. Depletion amounts are:
Years 1 to 5: 0.15×5 million = $750,000
Years thereafter: 0.15×3 million = $450,000
A total of $3.75 million is written off in 5 years
The remaining $6.25 million is written off at $450,000 per year. The total number of years is:
In 19 years, the initial investment could be fully depleted 34