1. (c) 2001 Contemporary Engineering Economics
Chapter 10 Depreciation
Asset Depreciation
Factors Inherent to Asset Depreciation
Book Depreciation
Tax Depreciation
Depletion
Repairs or Improvements to Depreciable Assets
(c) 2001 Contemporary Engineering Economics

2. (c) 2001 Contemporary Engineering Economics
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
Market
Value
Loss of 1 2 3 4 5
$15,000
10,000
8,000
6,000
5,000
4,000
$5,000
2,000
1,000
Depreciation
(c) 2001 Contemporary Engineering Economics

3. 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)
(c) 2001 Contemporary Engineering Economics

4. (c) 2001 Contemporary Engineering Economics
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.
(c) 2001 Contemporary Engineering Economics

5. Asset Depreciation Physical depreciation Economic depreciation
the gradual decrease in
utility in an asset with
use and time
Functional
depreciation
Depreciation
Book
depreciation
Accounting depreciation
The systematic allocation
of an asset’s value in
portions over its
depreciable life—often
used in engineering
economic analysis
Tax
depreciation
(c) 2001 Contemporary Engineering Economics

6. Factors to Consider in Asset Depreciation
Depreciable life (how long?)
Salvage value (disposal value)
Cost basis (depreciation basis)
Method of depreciation (how?)
(c) 2001 Contemporary Engineering Economics

7. 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?
(c) 2001 Contemporary Engineering Economics

8. (c) 2001 Contemporary Engineering Economics
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
(c) 2001 Contemporary Engineering Economics

9. 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
(c) 2001 Contemporary Engineering Economics

10. 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
Automobiles, taxis
2.5 3
3.5
Buses 9 11
Light trucks 4
Heavy trucks (concrete ready-mixer)
Railroad cars and locomotives 15 18
Tractor units
Vessels, barges, tugs, and water transportation system
14.5
21.5
Industrial steam and electrical generation and or distribution systems
17.5 22
26.5
Manufacturer of electrical and nonelectrical machinery
Manufacturer of electronic components, products, and systems
Manufacturer of motor vehicles
9.5
Telephone distribution plant 28 35 42
(c) 2001 Contemporary Engineering Economics

11. (c) 2001 Contemporary Engineering Economics
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
(c) 2001 Contemporary Engineering Economics

12. 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
(c) 2001 Contemporary Engineering Economics

13. 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
(c) 2001 Contemporary Engineering Economics

14. Example 10.3 – Straight-Line Method
Annual Depreciation
Book Value
$10,000 D1
Total depreciation at end of life
I = $10,000
N = 5 Years
S = $2,000
D = (I - S)/N
$8,000 D2
$6,000 D3 D4 B1
$4,000
n Dn Bn
1 1,600 8,400
2 1,600 6,800
3 1,600 5,200
4 1,600 3,600
5 1,600 2,000 B2 D5 B3
$2,000 B4 B5 n
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15. Declining Balance Method
Principle:
A fixed asset as providing its service in a
decreasing fashion
Formula
Annual Depreciation
Book Value
where 0 < a < 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.
(c) 2001 Contemporary Engineering Economics

16. Example 10.4 – Declining Balance Method
Annual Depreciation
Book Value
$10,000
Total depreciation at end of life D1
$8,000
$6,000 D2 B1 n 1 2 3 4 5 Dn
$4,000
2,400
1,440
864
518 Bn
$10,000
6,000
3,600
2,160
1,296
778
$4,000 D3 B2 D4
$2,000 B3 D5 B5 B4 n
(c) 2001 Contemporary Engineering Economics

17. Example 10.5 DB Switching to SL
Asset: Invoice Price $9,000
Freight
Installation
Depreciation Base $10,000
Salvage Value
Depreciation 200% DB
Depreciable life 5 years
SL Dep. Rate = 1/5
a (DDB rate) = (200%) (SL rate)
= 0.40
(c) 2001 Contemporary Engineering Economics

18. (c) 2001 Contemporary Engineering Economics
Case 1: S = 0
(a) Without switching
(b) With switching to SL n
Depreciation
Book
Value 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) =
1,296(0.4) =
$6,000
3,600
2,160
1,296
778 n
Book
Depreciation Value 1 2 3 4 5
4, $6,000
6,000/4 = 1,500 < 2,400 3,600
3,600/3 = 1,200 < 1,440 2,160
2,160/2 = 1,080 > ,080
1,080/1 = 1,080 >
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.
(c) 2001 Contemporary Engineering Economics

19. (c) 2001 Contemporary Engineering Economics
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
2,000 – 0 = 2,000
Note: Tax law does not permit us to depreciate assets below
their salvage values.
(c) 2001 Contemporary Engineering Economics

20. 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
Book Value
where SOYD=N(N+1)/2
(c) 2001 Contemporary Engineering Economics

21. Example 10.7 – Sum-of-years’ digits method
Annual Depreciation
Book Value
$10,000
Total depreciation at end of life D1
I = $10,000
N = 5 years
S = $2,000
SOYD = 15
$8,000
$6,000 D2 B1 D3
$4,000 n 1 2 3 4 5 Dn
(5/15)(8,000)=$2,667
(4/15)(8,000)=$2,133
(3/15)(8,000)=$1,600
(2/15)(8,000)=$1,067
(1/15)(8,000)=$533 Bn
$7,333
5,200
3,600
2,533
2,000 B2 D4 D5
$2,000 B3 B5 B4 n
(c) 2001 Contemporary Engineering Economics

22. 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
total service units
(I - S)
(c) 2001 Contemporary Engineering Economics

23. (c) 2001 Contemporary Engineering Economics
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
(c) 2001 Contemporary Engineering Economics

24. 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
(c) 2001 Contemporary Engineering Economics

25. MACRS Property Classifications
Recovery Period
ADR Midpoint Class
Applicable Property
3-year
Special tools for manufacture of plastic products, fabricated metal products, and motor vehicles. (ADR =Asset Depreciation Range)
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.
27.5-year
Residential rental property
39-year
Nonresidential real property including elevators and escalators
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26. (c) 2001 Contemporary Engineering Economics
MACRS Table
(c) 2001 Contemporary Engineering Economics

27. 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%
$2000
32%
$3200
Full
19.20%
$1920
11.52%
$1152
5.76%
$576
Half-year Convention
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28. (c) 2001 Contemporary Engineering Economics
Year (n) 1 2 3 4 5 6
Calculation in %
(0.5)(0.40)(100%) 20%
(0.4)(100%-20%) 32%
SL = (1/4.5)(80%) %
(0.4)(100%-52%) %
SL = (1/3.5)(48%) %
(0.4)(100%-71.20%) Switch to SL 11.52%
SL = (1/2.5)(29.80%) %
SL = (1/1.5)(17.28%) %
SL = (0.5)(11.52%) %
MACRS (%)
DDB
DDB
DDB SL SL
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29. 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,
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30. 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%
(c) 2001 Contemporary Engineering Economics

31. Percentage Depletion vs. Cost Depletion
(Example 10.12)
Percentage Depletion
Gross income from sale of 45,000 ounces
$16,425,000
Depletion percentage
Computed percentage depletion
$2,463,750
Cost depletion
= ($30,000,000/300,000)(45,000)
= $4,500,000
Gross income from sale of 45,000 ounces
$16,425,000
Less mining expenses
12,250,000
Taxable income from mine
4,175,000
Deduction limitation
Maximum depletion deduction
$2,088,000
Allowable deduction
= $2,088,000
Select cost depletion
with $4,500,000
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32. Calculating the Allowable Depletion Deduction
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33. 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
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
(c) 2001 Contemporary Engineering Economics

34. 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.
(c) 2001 Contemporary Engineering Economics

35. (c) 2001 Contemporary Engineering Economics
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.
(c) 2001 Contemporary Engineering Economics

36. (c) 2001 Contemporary Engineering Economics
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.
(c) 2001 Contemporary Engineering Economics

37. (c) 2001 Contemporary Engineering Economics
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.
(c) 2001 Contemporary Engineering Economics

38. (c) 2001 Contemporary Engineering Economics
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.
(c) 2001 Contemporary Engineering Economics

39. 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
(c) 2001 Contemporary Engineering Economics

40. 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 straight-line methods. The SOYD method is rarely used in the U.S. except for some cost analysis in engineering valuation.
(c) 2001 Contemporary Engineering Economics