Chapter 10
Depreciation
• Asset Depreciation
• Factors Inherent to
Asset Depreciation
• Book Depreciation
• Tax Depreciation
• Depletion
• Repairs or
Improvements to
Depreciable Assets
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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.
End of
Year
Loss of
Value
$15,000
10,000
8,000
6,000
5,000
4,000
$5,000
2,000
2,000
1,000
1,000
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p
Depreciation
0
1
2
3
4
5
Market
Value
2
Why Do We Need to Consider
Depreciation?
Business
Expense:
Depreciation is
viewed as part
of business
expenses that
reduce taxable
income.
Gross Income -Expenses:
(Cost of goods sold)
(Depreciation)
(operating expenses)
Taxable Income
- Income taxes
Net income (profit)
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Depreciation Concept
• Economic Depreciation
Purchase Price – Market Value
(Economic loss due to both physical
deterioration and technological obsolescence)
• Accounting Depreciation
A systematic allocation of cost basis over a
period of time.
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Asset Depreciation
Economic depreciation
the gradual decrease in
utility in an asset with
use and time
Physical
depreciation
Functional
depreciation
Depreciation
Accounting depreciation
The systematic allocation
of an asset’s value in
portions over its
depreciable life—often
used in engineering
economic analysis
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Economics
Book
depreciation
Tax
depreciation
5
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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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. Can you depreciate land?
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Cost Basis
Cost of new hole-punching
machine (Invoice price)
+ Freight
$62,500
725
+ Installation labor
2,150
+ Site preparation
3,500
Cost basis to use in
depreciation calculation
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$68,875
8
Cost Basis with Trade-In Allowance
Old hole-punching machine (book value)
Less: Trade-in allowance
Unrecognized gains
Cost of new hole-punching machine
Less: Unrecognized gains
Freight
$4,000
5,000
$1,000
$62,500
(1,000)
725
Installation labor
2,150
Site preparation
3,500
Cost of machine (cost basis)
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Economics
$67,875
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Asset Depreciation Range ADRs (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
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
9.5
12
14.5
35
42
Automobiles, taxis
Manufacturer of motor vehicles
Telephone distribution plant
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Economics 28
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Types of Depreciation
• Book Depreciation
– In reporting net income to investors/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
Sum of the Years’ Digits Method
Unit Production Method
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Straight – Line (SL) Method
• Principle
A fixed asset as 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 value
N = depreciable life
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Example 10.3 – Straight-Line Method
Annual Depreciation
$10,000
Book Value
$8,000
D2
$6,000
$4,000
D3
D4
B1
B2
B3
D5
Total depreciation at end of life
D1
I = $10,000
N = 5 Years
S = $2,000
D = (I - S)/N
n
$2,000
B4
B5
0
0 1
2
3
4
5
n
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1
2
3
4
5
Dn
1,600
1,600
1,600
1,600
1,600
Bn
8,400
6,800
5,200
3,600
2,000
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Declining Balance Method
• Principle:
A fixed asset as providing its service in a
decreasing fashion
• Formula
• Annual Depreciation
Dn  Bn1   (1   ) n 1
• Book Value
B  (1   ) n
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.
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Example 10.4 – Declining Balance Method
Annual Depreciation
Book Value
$10,000
Total depreciation at end of life
D1
$8,000
$6,000
B1
D2
$4,000
B2
$2,000
00
D3
B3
1
2
3
I = $10,000
N = 5 years
S = $778
Dn =  Bn 1
=  I (1 -   n 1
Bn  I (1   ) n
n
0
1
2
3
4
5
D4
B4
4
D5
B5
5
Dn
$4,000
2,400
1,440
864
518
Bn
$10,000
6,000
3,600
2,160
1,296
778
n
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Example 10.5
DB Switching to SL
Asset: Invoice Price
Freight
Installation
Depreciation Base
Salvage Value
Depreciation
Depreciable life
$9,000
500
500
$10,000
0
200% DB
5 years
• SL Dep. Rate = 1/5
•  (DDB rate) = (200%) (SL rate)
= 0.40
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Case 1: S = 0
(a) Without switching
n
1
2
3
4
5
Depreciation
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
(b) With switching to SL
Book
Value
$6,000
3,600
2,160
1,296
778
n
1
2
3
4
5
Depreciation
4,000
6,000/4 = 1,500 < 2,400
3,600/3 = 1,200 < 1,440
2,160/2 = 1,080 > 864
1,080/1 = 1,080 > 518
Book
Value
$6,000
3,600
2,160
1,080
0
Note: Without switching, we have not depreciated the entire
cost of the asset and thus have not taken full advantage of
depreciation’s tax deferring benefits.
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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 below
their salvage values.
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Sum-of-Years’ Digits (SOYD) Method
• Principle
Depreciation concept similar to DB but with
decreasing depreciation rate.
Charges a larger fraction of the cost as an expense
of the early years than of the later years.
• Formula
•Annual Depreciation
Dn  ( I  S )( N  n  1) / SOYD
•Book Value
Bn  I   j 1 D j
n
where SOYD=N(N+1)/2
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Example 10.7 – Sum-of-years’ digits method
Annual Depreciation
$10,000
D1
$6,000
$4,000
Total depreciation at end of life
$8,000
Book Value
D2
D3
B1
B2
D4
I = $10,000
N = 5 years
S = $2,000
SOYD = 15
n
1
2
3
4
5
D5
$2,000
B3
0
0 1
2
3
B4
4
B5
5
Dn
Bn
(5/15)(8,000)=$2,667 $7,333
(4/15)(8,000)=$2,133 5,200
(3/15)(8,000)=$1,600 3,600
(2/15)(8,000)=$1,067 2,533
(1/15)(8,000)=$533 2,000
n
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Units-of-Production Method
• Principle
Service units will be consumed in a non
time-phased fashion
• Formula
•Annual Depreciation
Dn = Service units consumed for year (I - S)
total service units
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Tax Depreciation
• Purpose: Used to compute income taxes for the IRS
•Assets placed in service prior to 1981
Use book depreciation methods (SL, BD, SOYD)
•Assets placed in service from 1981 to 1986
Use ACRS Table
•Assets placed in service after 1986
Use MACRS Table
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Modified Accelerated Cost Recovery Systems
(MACRS)
• Personal Property
• Depreciation method based on DB method
switching to SL (see page 468)
• Half-year convention
• Zero salvage value
• Real Property
• SL Method
• Mid-month convention
• Zero salvage value
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MACRS Property Classifications
Recovery Period
3-year
ADR Midpoint Class
Applicable Property
Special tools for manufacture of plastic
ADR  4 products, fabricated metal products, and motor
vehicles. (ADR =Asset Depreciation Range)
5-year
7-year
10-year
15-year
20-year
4  ADR  10
10  ADR  16
16  ADR  20
20  ADR  25
25  ADR
Automobiles, light trucks, high-tech equipment,
equipment used for R&D, computerized
telephone switching systems
Manufacturing equipment, office furniture,
fixtures
Vessels, barges, tugs, railroad cars
Waste-water plants, telephone- distribution
plants, or similar utility property.
Municipal sewers, electrical power plant.
27.5-year
Residential rental property
39-year
Nonresidential real property including elevators
and escalators
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MACRS Table
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MACRS Rate Calculation
Example 10.9
Asset cost = $10,000
Property class = 5-year
DB method = Half-year convention, zero salvage value,
200% DB switching to SL
20% 32%
19.20% 11.52% 11.52% 5.76%
$2000 $3200 $1920 $1152 $1152
Full Full
Full
1
2
3
4
Half-year Convention
$576
Full
5
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Year (n)
Calculation in %
1
2
(0.5)(0.40)(100%)
(0.4)(100%-20%)
MACRS (%)
DDB
DDB
SL = (1/4.5)(80%)
3
(0.4)(100%-52%)
20%
32%
17.78%
DDB
SL = (1/3.5)(48%)
19.20%
13.71%
4
(0.4)(100%-71.20%) Switch to SL 11.52%
SL = (1/2.5)(29.80%)
11.52%
5
6
SL = (1/1.5)(17.28%)
SL = (0.5)(11.52%)
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SL
SL
11.52%
5.76%
28
Conventional DB Switching to SL
4,000 2,400 1,440 1,080 1,080
MACRS with half-year convention
2,000 3,200 1,920 1,152 1,152 576
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MACRS for Real Property
• 27.5-year (Residential)
• 39-year (Commercial)
• SL Method
• Zero salvage value
• Mid-month convention
•Example: placed an asset (residential property) in March
D1 = (9.5/12)(100%/27.5)
= 2.879%
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Percentage Depletion vs. Cost Depletion
(Example 10.12)
Percentage Depletion
Gross income from sale of
45,000 ounces
$16,425,000
Depletion percentage
15%
Computed percentage
depletion
$2,463,750
Gross income from sale of
45,000 ounces
$16,425,000
Less mining expenses
12,250,000
Taxable income from mine
Cost depletion
= ($30,000,000/300,000)(45,000)
= $4,500,000
Allowable deduction
= $2,088,000
4,175,000
50%
Deduction limitation
Maximum depletion deduction
Select cost depletion
with $4,500,000
$2,088,000
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Calculating the Allowable Depletion
Deduction
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Percentage Depletion Allowances for Mineral
Properties
Deposits
Percentage
Oil and gas wells (only for certain domestic and gas production)
15
Sulfur and uranium, and, if from deposits in the United States,
asbestos, lead, zinc, nickel, mica, and certain other ores and
minerals
22
Gold, silver, copper, iron ore, and oil shale, if from deposits in the
United States
15
Coal, lignite, and sodium chloride
10
Clay and shale to be used in making sewer pipe or bricks
7.5
Clay (used for roofing tile), gravel, sand, and stone
5
Most other minerals; includes carbon dioxide produced from a well
and metallic ores.
14
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Repairs and Improvements
Principle: Any repairs
or improvements extends
the life of the asset, the
depreciation amount also
needs to be adjusted.
Book Depreciation: Change
the current book value and
spread the value over the
extended life.
Tax Depreciation: Treat the
repairs or improvements as
separate MACRS properties.
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Summary
• The entire cost of replacing a machine cannot be
properly charged to any one year’s production;
rather, the cost should be spread (or capitalized)
over the years in which the machine is in service.
• The cost charged to operations during a particular
year is called depreciation.
• From an engineering economics point of view, our
primary concern is with accounting depreciation;
The systematic allocation of an asset’s value over
its depreciable life.
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• Accounting depreciation can be broken into two
categories:
1. Book depreciation—the method of depreciation
used for financial reports and pricing products;
2. Tax depreciation—the method of depreciation
used for calculating taxable income and income
taxes; it is governed by tax legislation.
• The four components of information required to
calculate depreciation are:
1. The cost basis of the asset,
2. The salvage value of the asset,
3. The depreciable life of the asset, and
4. The method of its depreciation.
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•Because it employs accelerated methods of
depreciation and shorter-than-actual depreciable
lives, the MACRS (Modified Accelerated Cost
Recovery System) gives taxpayers a break: It
allows them to take earlier and faster advantage
of the tax-deferring benefits of depreciation.
•Many firms select straight-line depreciation for
book depreciation because of its relative ease of
calculation.
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• Depletion is a cost allocation method used
particularly for natural resources. Cost depletion
is based on the units-of-production method of
depreciation. Percentage depletion is based on a
prescribed percentage of the gross income of a
property during a tax year.
• Given the frequently changing nature of
depreciation and tax law, we must use whatever
percentages, depreciable lives, and salvage values
mandated at the time an asset is acquired.
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Component
of
Depreciation
Book Depreciation
Tax depreciation (MACRS)
Cost basis
Based on the actual cost
of the asset, plus all
incidental costs such as
freight, site preparation,
installation, etc.
Same as for book depreciation
Salvage
value
Estimated at the outset of
depreciation analysis. If
the final book value does
not equal the estimated
salvage value, we may
need to make adjustments
in our depreciation
calculations.
Salvage value is zero for all
depreciable assets
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Component
of
Depreciation
Book Depreciation
Tax depreciation (MACRS)
Depreciable
life
Firms may select their
own estimated useful lives
or follow government
guidelines for asset
depreciation ranges
(ADRs)
Eight recovery periods–
3,5,7,10,15,20,27.5,or 39 years–
have been established; all
depreciable assets fall into one of
these eight categories.
Method of
depreciation
Firms may select from the
following:
•Straight-line
•Accelerated methods
(declining balance, double
declining balance, and
sum-of- years’ digits)
•Units-of-proportion
Exact depreciation percentages are
mandated by tax legislation but are
based largely on DDB and straightline methods. The SOYD method is
rarely used in the U.S. except for
some cost analysis in engineering
valuation.
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