Download - Depreciation Lecture No.20 Chapter 8 Fundamentals of Engineering Economics Copyright © 2008
• Definition: Loss of value for a fixed asset between two periods• Example: Market values of a vehicle over 5 years
Dep
reciation
End of Year
Market
Value
Loss of
Value
2004
2005
2006
2007
2008
2009
$20,00014,00010,000
7,0005,0004,000
$6,0004,0003,0002,0001,000
What is Depreciation?
Depreciation Concept
Economic Depreciation
Purchase Price – Market Value(Economic losses due to both physical deterioration and technological obsolescence)
Accounting DepreciationA 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 of a 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
Cost BasisCost 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 expensessuch as freight, insurance, and site preparation.
Old hole-punching machine (book value) $4,000
Less: Trade-in allowance 5,000
Unrecognized gains $1,000
Cost of a 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
Cost Basis with Trade-In Allowance
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 Depreciation
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
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
Declining Balance Method• Principle:
A fixed asset as providing its service in a decreasing fashion• Formula
• Annual Depreciation
• Book Value
1 nn BD 1)1( n
nB )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.
Example 8.3 – 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
( )
n
• SL Dep. Rate = 1/5• (DDB rate) = (200%) (SL rate)
= 0.40
Asset: Invoice Price $9,000 Freight 500 Installation 500
Depreciation Base $10,000Salvage Value 0Depreciation 200% DBDepreciable life 5 years
Example 8.4 DB Switching to SL
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
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 belowtheir salvage value.
Case 2: S = $2,000
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)
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($55,000 $5,000)
250,000
3($50,000)
25
$6,000
Dep
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
Recovery Period
ADR Midpoint Class Applicable Property
Personal Property
3-year Special tools for manufacture of plastic products, fabricated metal products, and motor vehicles.
5-year Automobiles, light trucks, high-tech equipment, equipment used for R&D, computerized telephone switching systems
7-year Manufacturing equipment, office furniture, fixtures
10-year Vessels, barges, tugs, railroad cars
15-year Waste-water plants, telephone- distribution plants, or similar utility property.
20-year Municipal sewers, electrical power plant.
Real Property
27.5-year
Residential rental property
39-year Nonresidential real property including elevators and escalators
ADR 4
4 10 ADR
10 16 ADR
16 20 ADR
20 25 ADR
25 ADR
ADR: Asset Depreciation Range
MACRS Property Classifications
Year (n)12
3
4
56
Calculation in %(0.5)(0.40)(100%) 20%(0.4)(100%-20%) 32%
SL = (1/4.5)(80%) 17.78%
(0.4)(100%-52%) 19.20%
SL = (1/3.5)(48%) 13.71%
(0.4)(100%-71.20%) Switch to SL 11.52%SL = (1/2.5)(29.80%) 11.52%
SL = (1/1.5)(17.28%) 11.52%SL = (0.5)(11.52%) 5.76%
MACRS (%)DDB
DDB
DDB
SL
SL
MACRS Percentage Calculation: 5-Year Property
MACRS for Real Property
• 27.5-year (Residential)• 39-year (Commercial)
• SL Method• Zero salvage value• Mid-month convention
•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%
Types of Real Property
Underlying assumptions
9.5 months
Jan Dec
Depreciation Allowances for a 10-year Ownership of the PropertyYear (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.
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.
Summary
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. Make sure that the book value cannot be lower than the salvage value at any time.
Salvage value is zero for all depreciable assets
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-lineAccelerated 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.