1. Engineering Economic Analysis
Chapter 11
Depreciation
Donald G. Newnan
San Jose State University
Ted G. Eschenbach
University of Alaska Anchorage
Jerome P. Lavelle
North Carolina State University
Neal A. Lewis
University of New Haven
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2. Chapter Outline Income, Depreciation, & Cash Flow
Basic Aspects of Depreciation
Time-Based Depreciation Methods
Modified Accelerated Cost Recovery System (MACRS)
Depreciation & Asset Disposal
Unit-of-Production Depreciation
Depletion
Spreadsheets & Depreciation
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3. Learning Objectives
Understand depreciation, deterioration, & obsolescence
Understand types of depreciable property
Use classic methods to calculate annual depreciation charge & book value
Use MACRS to calculate annual depreciation & book value
Account for capital gains/losses, ordinary losses, & depreciation recapture due to asset disposal
Use unit-of-production & depletion methods
Use spreadsheets to calculate depreciation
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4. Vignette: Depreciation & Intangible Property
Firms depreciate tangible
property—forklifts, computers,
buildings—as expenses that
reduce taxable income
Purchased intangible assets can be amortized over time
Patents, copyrights, licenses, non-compete agreements
Goodwill ≡ firm’s value over value of its assets
Intangible property ~80% of total market value of “typical” U.S. firm
Nike, Coke, … brands
Patent lawsuits between tech firms such as Apple & Samsung
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5. Vignette: Depreciation & Intangible Property
Other examples of legal battles over intangible assets are _______?
If you had to develop a method to amortize a patent, how would you do this? What parameters must you consider?
Does % of U.S. firm market value tied to intangible assets surprise you? Why or why not? Is % likely to differ in other countries? Why or why not?
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6. Depreciation & Expenses
Expenses: subtract from revenues as occur
Labor
Utilities
Materials, etc.
Capital:
Cannot be expensed all at once
Must be expensed over its lifetime
Method = depreciation
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7. Income Statement
Revenue Sales of products & services Total Revenue $184 Costs Cost of Goods Sold Wages, materials, Utilities 110 Depreciation 35 Selling, Admin., Financing 19 Total Costs $164 Net Income Before Taxes 20 Taxes 7 Profit 13
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8. Basic Aspects of Depreciation Definitions
Decline in asset’s market value due to deterioration or obsolescence
Decline in asset’s value to owner
Systematic allocation of asset’s cost over its useful or depreciable life (accountant’s & tax agency’s definition)
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9. Depreciation & Expenses
Part of regular business operations
“Consumed” over short period of time
Sometimes recurring
Do not lose value gradually over time
Subtracted from business revenues as they occur
 Reduce taxable income & taxes
Examples: labor, utilities, materials, insurance, …
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10. Depreciation & Expenses
Capital asset costs depreciated over time not expensed as occur
Capital assets lose value gradually over time
Over depreciable life or recovery period
Each year’s depreciation charge reduces taxable income & taxes that year
Non-cash accounting entry
Examples: buildings, vehicles, machines, …
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11. Basic Requirements for Depreciation
Property depreciable if:
Used for business purposes to produce income
Useful life is longer than one year
Asset decays, gets used up, wears out, becomes obsolete, or loses value from natural causes
Only property owner may claim depreciation expenses
Not if:
Land, inventory, containers as inventory
Leased rather than owned
Only business % if business & personal use
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12. Types of Property Tangible property: can be seen, touched, & felt
Real property: land, buildings, & things growing on, built upon, constructed on, or attached to land
Personal property: equipment, furnishings, vehicles, office machinery, tangible items excluding real property
Intangible property: cannot be directly seen or touched; examples include patents, copyrights, trademarks—see vignette
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13. Depreciation Calculation Fundamentals
Book value = Cost basis − Depreciation charges made to date
(11-1)
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14. Time-based Depreciation Methods
Pre-1981 classic methods:
Straight-line (SL)
Sum-of-the-years’-digits (SOYD)
Declining balance (DB)
: Accelerated Cost Recovery System (ACRS)
Property class lives were created
Salvage value was ignored
Shorter recovery periods were used
1986-present: Modified ACRS (MACRS)
More property classes
Half-year convention for first & final years
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15. Classic Depreciation Methods
Straight-line (SL)
𝑑 𝑡 = 𝐵−𝑆 𝑁
(11-2)
Where
Dt = depreciation charge in
year t
B = cost of asset made
ready to use
S = Salvage value after
depreciable life
N = Number of years of
SOYD = sum of years’ digits
= N(N+1)/2
Sum-of-the-years’-digits (SOYD)
𝑑 𝑡 = 𝑁−𝑡+1 𝑆𝑂𝑌𝐷
(11-3)
Double declining balance (DDB)
𝑑 𝑡 = 2 𝑁 𝐵𝑉 𝑡−1
= 2 𝑁 (𝐵− 𝑗=1 𝑡−1 𝑑 𝑗 )
(11-4)
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16. Depreciation: which is not true?
Straight line depreciation used around world
Accelerated methods used around world
Straight line depreciation used to report annual financial results
Most countries allow accelerated methods for determining taxes
All of above are true
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17. Depreciation: which is not true?
Straight line depreciation used around world
Accelerated methods used around world
Straight line depreciation used to report annual financial results
Most countries allow accelerated methods for determining taxes
All of above are true
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18. Example 11-2 SL Depreciation
Cost of the asset, B
$900
Depreciable life, in years, N 5
Salvage value, S
$70
Year
900 1
166
734 2
332
568 3
498
402 4
664
236 5
830 70
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19. Example 11-3 SOYD Depreciation
Cost of the asset, B
$900
Depreciable life, in years, N 5
Salvage value, S
$70
Year
$900 1
$277
623 2
221
498
402 3
166
664
236 4
111
775
125 5 55
830 70
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20. Example 11-4 DDB Depreciation
Cost of the asset, B
$900
Depreciable life, in years, N 5
Salvage value, S
$70
Year
900 1
360
540 2
216
576
324 3
130
706
194 4 78
784
116 5 46
830 70
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21. Advantages of Modified Accelerated Cost Recovery System
“Property class lives” < “actual useful lives”
MACRS classes based on asset depreciation range (ADR)
With ADR, each property class’s life has lower limit, midpoint, & upper limit
ADR midpoint lives somewhat < actual average useful lives
MACRS property class lives < ADR midpoint lives
Salvage value assumed = 0
Tables of annual % simplify computations
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22. Modified Accelerated Cost Recovery System (MACRS)
General Depreciation System (GDS)
Base is declining balance with switch to straight-line
Faster depreciation than ADS; tax savings sooner
Alternative Depreciation System (ADS)
ADS provides a longer recovery period & uses straight-line
ADS must be used for
Tangible property used primarily outside U.S.
Property that is tax exempt or financed by tax-exempt bonds
Farming property placed in service when uniform capitalization rules are not applied
ADS may be elected for an asset; can’t switch back to GDS
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23. Procedures in Applying MACRS Depreciation
Determine asset’s cost basis (B)
Cost to obtain & place asset in service
May include fees & charges
Determine property class & recovery period
Property class given in problem
Asset named in Table 11-1 or -2 or IRS tables
Recovery period for that class
7-year for all other property not assigned to class
Determine asset’s placed-in-service date
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24. Table 11-1 Example Class Lives & MACRS Property Classes
IRS Asset Class
Asset Description
Class Life (Years)
ADR
MACRS Property Class (years)
GDS
ADS
00.11
Office furniture, fixtures, & equipment 10 7
00.12
Information Systems: computer/peripheral 6 5
00.22
Automobiles, taxis 3
00.241
Light general-purpose trucks 4
00.25
Railroad cars & locomotives 15
00.40
Industrial steam & electric distribution 22
01.11
Cotton gin assets 12
01.21
Cattle, breeding or dairy
13.00
Offshore drilling assets
7.5
13.30
Petroleum refining assets 16
15.00
Construction assets
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25. Table 11-1 Example Class Lives & MACRS Property Classes
IRS Asset Class
Asset Description
Class Life (Years)
ADR
MACRS Property Class (years)
GDS
ADS
21.10
Manufacture of grain & grain mill products 17 10
22.2
Manufacture of yarn, thread, & woven fabric 11 7
24.10
Cutting of timber 6 5
32.20
Manufacture of cement 20 15
37.11
Manufacture of motor vehicles 12
48.11
Telephone Communications assets & buildings 24
48.2
Radio & television broadcasting equipment
49.12
Electric utility nuclear production plant
49.13
Electric utility steam production plant 28
49.23
Natural gas production plant 14
50.00
Municipal wastewater treatment plant
80.00
Theme & amusement park assets
12.5
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26. Table 11-2 MACRS GDS Property Classes
Personal Property (all property except real estate)
3-Year Property
Special handling devices for food & beverage manufacture
Special tools for the manufacture of finished plastic products, fabricated metal products, & motor vehicles
Property with ADR class life of 4 years or less
5-Year Property
Automobiles & trucks (The depreciation for automobiles is limited to $3560 the first tax year, $5700 the second year, $3560 the third year, & 2075 per year in subsequent years.)
Aircraft (of non-air-transport companies)
Equipment used in research & experimentation
Computers
Petroleum drilling equipment
Property with ADR class life of more than 4 years & less than 10 years
7-Year Property
All other property not assigned to another class
Office furniture, fixtures, & equipment
Property with ADR class life of 10 years or more & less than 16 years
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27. Table 11-2 MACRS GDS Property Classes
Personal Property (all property except real estate)
10-Year Property
Assets used in petroleum refining & certain food products
Vessels & water transportation equipment
Property with ADR class life of 16 years or more & less than 20 years
15-Year Property
Telephone distribution plants
Municipal sewage treatment plants
Property with ADR class life of 20 years or more & less than 25 years
20-Year Property
Municipal sewers
Property with ADR class life of 25 years or more
Real Property (real estate)
27.5 Year
Residential rental property (does not include hotels & motels)
39 Years
Nonresidential real property
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28. Computer depreciation
What is cost recovery period for a computer?
3 years
4 years
5 years
Depends on expected life
I don’t know
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29. Computer depreciation
What is cost recovery period for a computer?
3 years
4 years
5 years
Depends on expected life
I don’t know
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30. Procedures in Applying MACRS Depreciation
where = depreciation deduction in year t
= cost basis being depreciated
= appropriate MACRS percentage rate
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31. Table 11-3 MACRS GDS Percentage Rate
Recovery Year
3-year
class
5-year
7-year
10-year class
15-year class
20-year class 1
33.33
20.00
14.29
10.00
5.00
3.750 2
44.45
32.00
24.49
18.00
9.50
7.219 3
*14.81
19.20
17.49
14.40
8.55
6.677 4
7.41
*11.52
12.49
11.52
7.70
6.177 5
*8.93
9.22
6.93
5.713 6
5.76
8.92
7.37
6.23
5.285 7
8.93
*6.55
*5.90
4.888 8
4.46
6.55
5.90
4.522 9
6.56
5.91
*4.462 10
4.461 11
3.28
4.462
12-15
In 15-year alternate 5.90 & 5.91
5.9x 16
2.95
17-20
In 20-year alternate & 4.462
4.46x 21
2.231
* Convert to straight-line
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32. Calculation of MACRS GDS Percentages
Declining balance start
3-, 5-, 7-, & 10-year classes use 200%;
15- & 20-year classes use 150% declining balance depreciation
Convert to straight-line depreciation in optimal year (* in table)
Half-year depreciation for first & last years
Salvage value assumed = 0
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33. Example 11-5 Calculation of MACRS Percentages
Develop 5-year class MACRS % rates. B=100%, S=0, half-year for 1st & last year
Year
DDB Calculation
SL Calculation
MACRS Rates
Cum. Dep. 1
(½)(2/5)(100%)=20.00%
(½)(100%/5)=10.00%
20.00% 2
(2/5)(80.00%) = 32.00%
(80.00%/4.5)=17.78%
32.00%
52.00% 3
(2/5)(48.00%) = 19.20%
(48.00%/3.5)=13.71%
19.20%
71.20% 4
(2/5)(28.80%) = 11.52%
(28.80%/2.5)=11.52%
11.52%
82.72% 5
94.24% 6
(½)11.52%= 5.76%
5.76%
100.00%
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34. Example 11-6 Calculation of MACRS Depreciation
7-year property class; B=$150,000; S=$30,000
Year
MACRS Calculation
Book Value
$150,000 1
14.29%
($150,000)(14.29%)
$21,435
128,565 2
24.49%
(150,000)(24.49%)
36,735
91,830 3
17.49%
(150,000)(17.49%)
26,235
65,595 4
12.49%
(150,000)(12.49%)
18,735
46,860 5
8.93%
(150,000)(8.93%)
13,395
33,465 6
8.92%
(150,000)(8.92%)
13,380
20,085 7
6,690 8
4.46%
(150,000)(4.46%)
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35. Example 11-7 Calculation of MACRS Depreciation (ADS Table 11-4)
39-year property class, B=$20,000,000, purchased in April, disposed 5 years later in August.
Year
MACRS Calculation
Book Value
$20,000,000 1
1.819%
($20,000,000)(1.819%)
$363,800
19,636,200 2
2.564%
(20,000,000)(2.564%)
512,800
19,123,400 3
(20,000,000)(2.564 %)
18,610,600 4
18,097,800 5
17,585,000 6
(20,000,000)(1.605%)
321,000
17,264,000
2,736,000
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36. Example 11-8 Comparison of Depreciation MethodsSL
SOYD
MACRS
MACRS
DDB
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37. Depreciation & Asset Disposal
At disposal if asset’s market value differs from book value, the difference is:
Depreciation recapture (ordinary gains): asset sold for more than book value, but less than original basis
Losses: asset sold for less than book value
Capital gains: asset sold for more than original cost basis
Rare for depreciated assets
Common for stocks, bonds, real estate, art, …
Gains may be taxed at lower rate
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38. Depreciation & Asset Disposal
$4000
Capital
Gain
$2000
Depreciation
Recapture
$5000
Depreciation
Recapture
$3000
Loss
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39. Example 11-9 Depreciation & Asset Disposal
3-year property class; B=$10,000; disposed of at 5 years
If market value = $7000, the recaptured depreciation = $7000
b) If market value = $0, no recaptured depreciation or loss
c) If market value = −$2000, there is a loss of $2000
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40. Example 11-10 Depreciation & Asset Disposal
B = $10,000; depreciated using MACRS, 3-yr; Sold during Year 2 for $5000
MV2 = $5000; BV1 = 10,000 – 10,000 x = $6667
50% depreciation claimed in year 2 (IRS rule)
D2 = 10,000(r2/2) = 10,000(0.4445/2) = $
BV2 = BV1 – D2 = 6667 – = $
Recaptured depreciation = 5000 – = $555.50
Total deduction = – = $1667
0% depreciation claimed in year 2
D2 = 0 (easier math hand calc.; same result)
Market value – book value = 5000 – 6667 = – 1667
Total deduction = $1667
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41. Example 11-10 Depreciation & Asset Disposal
100% depreciation claimed in year 2
(easier spreadsheet; same result)
D2 = 10,000(r2) = 10,000(0.4445) = $4450
BV2 = BV1 – D2 = 6667 – 4450 = $2217 < MV2
Recaptured depreciation = 5000 – 2217 = $2783
Total deduction = 4450 – 2783 = $1667
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42. Unit-of-Production Depreciation
When depreciation related to use more than time
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43. Example 11-11 Unit-of-Production Depreciation
5-year depreciable life, B=$900K, S=$70K
Year
Annual Production
UOP Depreciation
Calculation
Book Value
$900 1
4,000
(4,000/40,000)(830)
$83
817 2
8,000
(8,000/40,000)(830)
166
651 3
16,000
(16,000/40,000)(830)
332
319 4
153 5 83 70
40,000
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44. Depletion Exhaustion of natural resources by removal
Depletion allowance is larger of two methods (some exceptions)
Cost depletion
Similar to unit-of-production depreciation
Permissible for standing timber & most oil & gas wells
Cost of land must be excluded
Percentage Depletion:
% of property’s gross income during year
Cannot exceed 50% of property’s taxable income without depletion deduction
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45. Example 11-12 Cost Depletion
Cost of property (timber) = $35,000
Cost of land = $5000 (included in the cost of property)
Estimated timber production = 1.5 million board-feet
First year’s production = 100,000 board-feet
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46. Table 11-6 Percentage Depletion Allowance
Type of Deposits
Rate
Sulfur, uranium, and, if from deposits in U.S., asbestos, lead ore, zinc ore, nickel ore, & mica
22%
Gold, silver, copper, iron ore, & certain oil shale, if from U.S. deposits
15%
Borax, granite, limestone, marble, mollusk shells, potash, slate, soapstone, & carbon dioxide produced from a well
14%
Coal, lignite, & sodium chloride
10%
Clay & shale used or sold for use in making sewer pipe or bricks or used or sold for use as sintered or burned lightweight aggregates
7½%
Clay used or sold for making drainage & roofing tile, flower pots, & kindred products, & gravel, sand, & stone (other than stone used or sold for use by a mine owner or operator as dimension or ornamental stone) 5%
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47. Example 11-13 Percentage Depletion
Gross income = $250,000
Mining expenses = $210,000
Coal has a 10% depletion allowance
Percentage depletion = (10%)($250,000) = $25,000
Taxable income = 250,000 – 210,000 = $40,000
Taxable Income limitation = $40,000(50%) = $20,000
Limitation < percentage depletion; deduction = $20,000
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48. Spreadsheet & Depreciation
Technique
Excel Function
Straight-line
SLN(cost, salvage, life)
Double-declining balance
DDB(cost, salvage, life, period, [factor])
Sum-of-years' digits
SYD(cost, salvage, life, period)
MACRS
VDB(cost, salvage, life, start_period, end_period, [factor], [no_switch])
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49. Using VDB for MACRS
=VDB(cost, salvage, life, start_period, end_period, [factor], [no switch])
Excel’s VDB returns depreciation for any period using declining balance with or without straight-line switch
Cost is initial basis
Salvage is salvage value; use 0 for MACRS
Life is recovery period; use 3, 5, 7, 10, 15, or 20 years
First period is 0-0.5, second is , etc.
Factor is declining balance rate; default is 2 = double declining balance
No_switch; if TRUE, Excel does not switch to straight-line
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50. Using VDB for MACRS
Determine 7-year class MACRS depreciation values. B=$150,000, S=$0, half-year for the 1st & last period.
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