Depreciation
Lecture No.20
Chapter 8
Fundamentals of Engineering Economics
Copyright © 2008
What is Depreciation?
• Definition: Loss of value for a fixed asset
between two periods
• Example: Market values of a vehicle over 5 years
End of
Year
$20,000
14,000
10,000
7,000
5,000
4,000
Loss of
Value
$6,000
4,000
3,000
2,000
1,000
Depreciation
2004
2005
2006
2007
2008
2009
Market
Value
Depreciation Concept
 Economic Depreciation
Purchase Price – Market Value
(Economic losses due to both physical
deterioration and technological obsolescence)
 Accounting Depreciation
A systematic allocation of the cost basis over a
period of time.
Factors to Consider in Asset
Depreciation
 Depreciable life (how long?)
 Salvage value (disposal value)
 Cost basis (depreciation basis)
 Method of depreciation (how?)
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.
Note: You never depreciate “land.”
Cost Basis
Cost basis – the total cost that is claimed as an expense over an asset's
life, which includes the actual cost of the asset and all incidental expenses
such as freight, insurance, and site preparation.
Cost of a 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
$68,875
Cost Basis with Trade-In Allowance
Old hole-punching machine (book value)
Less: Trade-in allowance
Unrecognized gains
Cost of a 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)
$67,875
Asset Depreciation Ranges (ADRs)
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
Types of Accounting Depreciation and
Their Primary Purposes
Book Depreciation Methods

Purpose: Used to report net income to
stockholders/investors

Types of Book Depreciation Methods:



Straight-Line Method
Declining Balance Method
Unit Production Method
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
Example 8.2 – Straight-Line Method
Annual Depreciation
$10,000
$8,000
D2
$6,000
$4,000
D3
B1
D4
B2
B3
D5
Total depreciation at end of life
D1
Book Value
I = $10,000
N = 5 Years
S = $2,000
D = (I - S)/N
n
B4
$2,000
B5
0
1
2
3
4
5
n
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
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.
Example 8.3 – Declining Balance Method
Annual Depreciation
$10,000
Book Value
Total depreciation at end of life
D1
$8,000
$6,000
D2
$4,000
B1
B2
D3
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
$2,000
B3
D4
D5
$778
0
1
2
3
B4
4
B5
5
n
Dn
$4,000
2,400
1,440
864
518
Bn
$10,000
6,000
3,600
2,160
1,296
778
Example 8.4 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
Case 1: S = 0
(a) Without switching
n
Depreciation
1
2
3
4
5
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.
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
2,60 – 160 = 2,000
5
0
2,000 – 0 = 2,000
Note: Tax law does not permit us to depreciate assets below
their salvage value.
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
Example 8.5 Units-of-Production
Depreciation


Given: I = $55,000, S = $5,000, Total service
units = 250,000 miles, usage for this year =
30,000 miles
Solution:
30, 000
Dep 
($55, 000  $5, 000)
250, 000
 3 

 ($50, 000)
 25 
 $6, 000
Tax Depreciation
 Purpose: Used to compute income taxes for the IRS
Assets placed in service prior to 1981
Use book depreciation methods (SL, DB, SOYD)
Assets placed in service from 1981 to 1986
Use ACRS (Accelerated Cost Recovery System) Table
Assets placed in service after 1986
Use MACRS (Modified ACRS) Table
Modified Accelerated Cost Recovery
Systems (MACRS)

Personal Property
 Depreciation method based on DB method
switching to SL
 Half-year convention
 Zero salvage value

Real Property
 SL Method
 Mid-month convention
 Zero salvage value
MACRS Property Classifications
Recover
y Period
Personal
Property
ADR Midpoint Class
ADR  4
3-year
4  ADR  10
5-year
10  ADR  16
7-year
10-year
15-year
Real
Property
Applicable Property
16  ADR  20
20  ADR  25
25  ADR
Special tools for manufacture of plastic
products, fabricated metal products, and
motor vehicles.
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.
20-year
Municipal sewers, electrical power plant.
27.5year
Residential rental property
39-year
Nonresidential real property including
elevators and escalators
ADR: Asset Depreciation Range
MACRS Depreciation Schedules for Personal
Property with Half-Year Convention
Example 8.6 MACRS Depreciation:
Personal Property
MACRS Percentage Calculation: 5-Year Property
Year (n)
1
2
Calculation in %
(0.5)(0.40)(100%)
(0.4)(100%-20%)
DDB
MACRS (%)
20%
32%
DDB
SL = (1/4.5)(80%)
17.78%
DDB
3
4
5
6
(0.4)(100%-52%)
19.20%
SL = (1/3.5)(48%)
13.71%
(0.4)(100%-71.20%)
SL = (1/2.5)(29.80%)
Switch to SL
SL = (1/1.5)(17.28%)
SL = (0.5)(11.52%)
SL
SL
11.52%
11.52%
11.52%
5.76%
MACRS for Real Property
Types of Real Property
• 27.5-year (Residential)
• 39-year (Commercial)
 Underlying assumptions
• SL Method
• Zero salvage value
• Mid-month convention
9.5 months
Jan
•Example: Placed a residential property in service in March.
Find the depreciation allowance in year 1.
D1 = (9.5/12)(100%/27.5)
= 2.879%
Dec
Depreciation Allowances for a 10-year
Ownership of the Property
Year (n)
Calculation
Allowed Depreciation (%)
1
(9.5/12)(100%/27.5)
2.8788%
2
100%/27.5
3.6364%
3
100%/27.5
3.6364%
4
100%/27.5
3.6364%
5
100%/27.5
3.6364%
6
100%/27.5
3.6364%
7
100%/27.5
3.6364%
8
100%/27.5
3.6364%
9
100%/27.5
3.6364%
10
(11.5/12)(100%/27.5)
3.4848%
Assume that the property will be sold in December of the10th year.
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.
Component of
Depreciation
Cost basis
Book Depreciation
Based on the actual cost
of the asset, plus all
incidental costs such as
freight, site preparation,
installation, etc.
Tax depreciation (MACRS)
Same as for book
depreciation
Salvage value Estimated at the outset of Salvage value is zero for
depreciation analysis.
all depreciable assets
Make sure that the book
value cannot be lower than
the salvage value at any
time.
Component
of
Depreciation
Book Depreciation
Tax depreciation (MACRS)
Depreciable
life
Firms may select their
own estimated useful
lives or follow the
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)
Units-of-proportion
Exact depreciation percentages
are mandated by tax legislation
but are based largely on DDB
and straight-line methods.