- The document discusses depreciation and its treatment for accounting (book depreciation) and tax purposes (tax depreciation). - It defines depreciation as the reduction in value of an asset due to usage, age, and obsolescence. For accounting, depreciation is allocated systematically over the useful life of the asset, while for tax purposes, depreciation methods allow for faster write-offs. - Common depreciation methods discussed include straight-line, declining balance, and units-of-production, as well as the Modified Accelerated Cost Recovery System (MACRS) used for tax depreciation since 1986.

1. DEPRECIATION AND INCOME TAXES
CHAPTER 9

2.  Asset Depreciation
 Book Depreciation
 Tax Depreciation
 Corporate Taxes

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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.
Depreciation
End of
Year
Market
Value
Loss of
Value
0
1
2
3
4
5
$15,000
10,000
8,000
6,000
5,000
4,000
$5,000
2,000
2,000
1,000
1,000p

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Why Do We Consider Depreciation?
Gross Income -Expenses:
(Cost of goods sold)
(Depreciation)
(operating expenses)
Taxable Income
- Income taxes
Net income (profit)
Business
Expense:
Depreciation is
viewed as a part
of business
expenses that
reduce taxable
income.

5. Depreciation Concept
is a term used in accounting, economics, and finance to spread the cost of an asset
over the period of several years.
is the reduction in the value of an asset due to usage, passage of time, and
technological outdating or other factors.
Economic Depreciation
Purchase Price – Market Value
Economic losses due to both physical deterioration and technological
obsolescence.
Accounting Depreciation
Systematic allocation (distribution) of the initial cost of an asset in parts
over a time or decline in value over time and sometimes referred to more generally as
asset depreciation.

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

7. Factors to Consider in the process of an Asset Depreciation
 What is the cost of the asset?
 What is asset’s value at the end of its useful life?
 What is the depreciable life of the asset?
 What method of depreciation do we choose?

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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.

9. What Can Be Depreciated?
Depreciable property has the following characteristics
1. Assets must be used in business or held for production of income.
2. Assets must have a definite service (useful) life which must be longer than one
year.
3. Assets must be wear out, become obsolete or loses value from natural causes.
A qualifying asset for depreciation must satisfy all of the three conditions above.

10. Example 9.1 on Cost Basis
Cost Basis of an asset represents the total cost that is claimed as an expense
over an asset's life and generally includes the actual cost of an asset and all
accompanying expenses, such as freight, site preparation, and installation.
Cost of a new stamping machine
(Invoice price) $22,700
Freight 525
Installation labor 1,350
Site preparation 2,125
Cost of Machine (Cost basis) $26,700

11. Useful Life and Salvage Value:
The following questions must be answered when determining an asset's
depreciable life. i.e., the number of years over
which the asset is to be depreciated.
Q1) How long will an asset be useful to the company?
Q2) What do statutes (law) and accounting rules mandate in determining an
asset's depreciable life?
Determining the service life of an asset is often very difficult.
The uncertainty of these estimates often led to disputes between taxpayers
and the Internal Revenue Service (IRS= Agency for collecting tax at US)
The IRS publishes guidelines on lives for categories of assets known as
Asset Depreciation Ranges or ADRs.
These guidelines specify a range of lives for classes of assets, based on
historical data allowing taxpayers to choose a depreciable life within the
specified range for a given asset.

12. Asset Depreciation Range ADR (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
Automobiles, taxis 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 17.5 22 26.5
Manufacturer of electrical and non-electrical
machinery
8 10 12
Manufacturer of electronic components, products, 5 6 7
Manufacturer of motor vehicles 9.5 12 14.5
Telephone distribution plant 28 35 42

13. Types of Depreciation
 Book Depreciation [financial report]
 Firms report depreciation and net income to investors / stockholders (such as in
balance sheet or income statement)
 Tax Depreciation [Internal Revenue Service]
 In calculating income taxes for the IRS
 In engineering economics, we use depreciation in the context of tax depreciation
 Tax depreciation method allows firms to benefit from the tax advantages of
depreciating assets, (will not pay high income tax).
 Tax depreciation methods generally permit a higher depreciation in earlier years
than do book depreciation methods,.
 Firms generally pay lower taxes in the initial years of an investment project.

14. Book Depreciation Methods
Purpose: Used to report net income to stockholders/investors
Types of Depreciation Methods:
 Straight-Line Method
 Declining Balance Method
 Unit Production Method

15. Straight – Line (SL) Method
Principle of this method
A fixed asset as providing its service in a uniform fashion over its life.
That is, the asset provides equal amount of service in each year of its useful
life.
Formula
Annual Depreciation
Dn = (I – S) / N and constant for all n (years).
Book Value after Depreciation charge
Bn = I – n (Dn) where I = cost basis
S = Salvage value
N = depreciable life

16. Example 9.2 Straight – Line Method
Consider the following data on an automobile, compute
the annual depreciation allowances and resulting book values
using the straight-line method.
n Dn Bn
0 $10,000
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
I = $10,000
N = 5 Years
S = $2,000
D = (I – S)/N
Bn = I – n (Dn)
Find: Dn and Bn
n

17. Declining Balance Method ( D B M )
Principle:
-A fixed asset as providing its service in a decreasing fashion over time.
-DBM calculating depreciation allocates a fixed fraction α
-α is obtained from S L depreciation rate (1/N) as a basis:
α = (1/N) x (multiplier). N and multiplier are given.
Most commonly used multipliers in the USA are 1.5 DB or 2.0 DDB
Annual Depreciation
Book Value
Note: if α is chosen to be the upper bound, α = 2(1/N), we call it a 200% DB or double
declining balance method.
1−= nn BD α 1
)1( −
−= n
αα
* (1 )n
nB I α= − where 0 < α < 2(1/N)

18. Example 9.3
Declining Balance (DB) Depreciation
SL Dep. Rate = 1/5=0.2
a (DDB rate) = (200%) (SL rate) = 0.40
Asset: Invoice Price ………………...... $9,000
Freight …………………….... 500
Installation …………………...... 500
Depreciation Base …………………........ $10,000
Salvage Value ......................................... 2,000
Depreciation 200% DDB (Double) multiplier=2
Depreciable life 5 years

19. S = $2,000
End of Year Depreciation Book Value
Bn
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
Adjusting to salvage value
5
0
Total = $8,000
2,000 – 0 = 2,000
Note: Tax law does not permit to depreciate assets below their salvage values.
1−= nn BD α

20. Example 9.4
Declining Balance (DB) Depreciation
SL Dep. Rate = 1/5
a (DDB rate) = (200%) (SL rate) = 0.40
Asset: Invoice Price ………………...... $9,000
Freight ………………………... 500
Installation …………………...... 500
Depreciation Base …………………........ .$10,000
Salvage Value .............................................. 0
Depreciation 200% DDB
Depreciable life 5 years

21. 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) = 864
1,296(0.4) = 518
$6,000
3,600
2,160
1,296
778
n
Book
Depreciation Value
1
2
3
4
5
10,000/5 = 2,000 < 4,000 $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 > 864 1,080
1,080/1 = 1,080 > 518 0
(a) Without switching (b) With switching to SL
Note: Without switching, we have not depreciated the entire cost of the asset and thus have not
taken full advantage of depreciation’s benefits. The rule is; if DB depreciation in any year is less
than (or equal to) the depreciation amount calculated by SL, switch to and remain with the SL
method for the duration of the asset’s depreciable life. The Switch can be in any of the n years.
Example 9.4 Declining Balance (DB) with conversion to
Straight Line Depreciation (Bn > S)
Suppose the asset given in example 9.3 has a zero salvage value instead of $2,000

22. Units – of – Production Method
No. of units or operating hours are different from year to year
Principle
The number of service units will be consumed in that period.
Formula
Annual Depreciation
Service units consumed for year
Dn =
total service units
x ( I – S )

23. Example 9.5 Units – of – Production Depreciation
 A truck for hauling coal has an estimated net cost of $55,000( i.e. I) and is expected to
give service for 250,000 miles(i.e: total service unit) , resulting in $5,000 a salvage
value. Compute the allowed depreciation amount for the truck this year usage of
30,000 miles
Find: Depreciation amount this year
Solution:
30, 000
($55, 000 $5, 000)
250, 000
3
($50, 000)
25
$6, 000
Dep = −
 
= ÷
 
=

24. 9.3 History of Tax Depreciation Methods
Purpose: compute income taxes for the IRS
Assets placed in service prior to 1981
Use book depreciation methods (SL, DB)
 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

25. Modified Accelerated Cost Recovery Systems (MACRS)
Personal Property: (movable property, includes assets such as machinery,
vehicles, equipment, furniture, and similar items)
 Depreciation method based on DB method switching to SL
 Half-year convention (assumed all assets are placed I service at
midyear)
 Half year is allowed for the first year.
 Half year is taken in the year following the end
 Zero salvage value
Real Property: (includes houses and land) are classified into two categories:
1. residential rental property and
2. commercial building or properties
 SL Method
 Mid-month convention

26. MACRS Property Classifications (ADR = Asset Depreciation Rate)
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

27. M A C R S Depreciation TABLE for Personal Property with Half-Year Conversion from
Internal Revenue Service (IRS)

28. Example MACRS Depreciation (Also read EXAMPLE 9.6)
Asset cost = $10,000
Property class = 5 year MACRS
Depreciation method = Half – year convention, zero salvage value, 200% DB switching
to SL
20%
$2000
32%
$3200
Full
19.20%
$1920
Full
11.52%
$1152
Full
11.52%
$1152
Full
5.76%
$576
1 2 3 4 5 6
Half-year Convention

29. Gross Income
Expenses
Cost of goods sold (revenues)
Depreciation
Operating expenses
Taxable income
Income taxes
Net income (Accounting Profit)
Item
How to Determine “Accounting Profit”

30. Example Net Income within a year
A company buys a numerically control (NC) machines for $28,000 (year Zero) and uses it
for five years, after which time it is scrapped. The allowed depreciation deduction
during the first year is $4,000, as the equipment falls into the seven year MACRS
property category. (The first year depreciation rate is 14.29%) The cost of goods
produced by this NC machine should include a charge for the depreciation of the
machine. Suppose the company estimates the following revenues and expenses,
including the depreciation for the first operating year.
Gross income = $50,000
Cost of goods sold = $20,000
Depreciation on NC machine = $4,000
Operating expenses = $6,000
If the company pays taxes at the rate of 40% on its taxable income, what is the net
income from the project during the first year?

31. Example of Net Income within a year
Item Amount
Gross income (revenue) $50,000
Expenses
Cost of goods sold
Depreciation
Operating expenses
20,000
4,000
6,000
Taxable income 20,000
Taxes (40%) 8,000
Net income $12,000

32. Capital Expenditure versus Depreciation Expenses
0
1 2 3 4 5 6 7 8
0 8 (4.46)7 (8.93)6 (8.92)5 (8.93)3 (17.49) 4 (12.49)1(14.29) 2 (24.49)
$4,000
$6,850
$4,900
$3,500 $2,500 $2,500 $2,500
$1,250
$28,000
Capital expenditure
(actual cash flow)
Allowed depreciation expenses (not cash flow)
( 7 - year MACRS property )

33. Example
Cash Flow from Operation versus Net Income
Item Income Cash Flow
Gross income (revenue) $50,000 $50,000
Expenses
Cost of goods sold
Depreciation
Operating expenses
20,000
4,000
6,000
-20,000
-6,000
Taxable income 20,000
Taxes (40%) 8,000 -8,000
Net income $12,000
Net cash flow from operation $16,000

34. Net income versus net cash flow

35. U.S. Corporate Tax Schedule
Marginal tax rate is defined as the rate applied to the last dollar of income.
Taxable income
0-$50,000
$50,001-$75,000
$75,001-$100,000
$100,001-$335,000
$335,001-$10,000,000
$10,000,001-$15,000,000
$15,000,001-$18,333,333
$18,333,334 and Up
Tax rate
15%
25%
34%
39%
34%
35%
38%
35%
Tax computation
$0 + 0.15(D)
$7,500 + 0.25 (D)
$13,750 + 0.34 (D)
$22,250 + 0.39 (D)
$113,900 + 0.34 (D)
$3,400,000 + 0.35 (D)
$5,150,000 + 0.38 (D)
$6,416,666 + 0.35 (D)
(D) denotes the taxable income in excess of the lower bound of each tax bracket

36. Marginal and Effective (Average) Tax Rate for a Taxable Income of $16,000,000
Taxable income Marginal Tax
Rate
Amount of Taxes Cumulative Taxes
First $50,000 15% $7,500 $7,500
Next $25,000 25% 6,250 13,750
Next $25,000 34% 8,500 22,250
Next $235,000 39% 91,650 113,900
Next $9,665,000 34% 3,286,100 3,400,000
Next $5,000,000 35% 1,750,000 5,150,000
Remaining
$1,000,000
38% 380,000 $5,530,000
Average tax rate =
$5,530,000
$16, ,
.
000 000
34 56%=

37. Example Corporate Income Taxes
Facts:
Capital expenditure $290,000
(allowed depreciation) $58,000
Gross Sales revenue $1,250,000
Expenses:
Cost of goods sold $840,000
Depreciation $58,000
Leasing warehouse $20,000
Question: Taxable income?

38. Taxable income:
Gross income $1,250,000
- Expenses:
(cost of goods sold) $840,000
(depreciation) $58,000
(leasing expense) $20,000
Taxable income $332,000
Income taxes:
Taxable income Marginal
Tax Rate
Amount of
Taxes
Cumulative
Taxes
First $50,000 15% $7,500 $7,500
$25,000 25% 6,250 13,750
$25,000 34% 8,500 22,250
$232,000 39% 90,480 112,730

39. 39%
Average tax rate:
Total taxes = $112,730
Taxable income = $332,000
Marginal tax rate: Tax rate that is applied to the last dollar earned
Average tax rate =
$112,730
$332,000
=33 95%.

40. Taxable Gains (or Losses) are defined as the differences between
the salvage value and the book value.
Case 1: Salvage value < Cost basis:
gains (losses) = salvage value – book value
Case 2: Salvage value > Cost basis:
gains = salvage value – book value
= (salvage value – cost basis)
capital gains
+ (cost basis – book value)
ordinary gains
ordinary gains (depreciation recapture)
When you sell an asset above its purchase price, you pay a tax
on your gains. That's called a capital gains tax.

41. Capital Gains and Ordinary Gains
Cost basis Book value Salvage value
Capital gains
Ordinary gains
or
depreciation recapture
Total gains

42. Disposal of a MACRS Property and Its Effect on Depreciation Allowances

43. Example 9.9
Gains or Losses
on
Depreciable Asset
A Drill press: $230,000
Project year: 3 years
MACRS: 7-year property class
Salvage value: $150,000 at the end of Year 3
Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308
Book Value = 230,000 -109,308 = $120,692
Ordinary Gains = Salvage Value - Book Value = $150,000 - $120,692 = $29,308
Gains Tax (34%) = 0.34 ($29,308) = $9,965
Net Proceeds from sale = $150,000 - $9,965 = $140,035

44. Calculation of Gains or Losses on – Cases 2 - 4

45. Case 2: S = $120,692
Case 3: S = $100,000
Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308
Book Value = 230,000 – 109,308 = $120,692
Ordinary Gains = Salvage Value – Book Value = $100,000 - $120,692 = -$20,692
Gains Tax or Tax credit (34%) = 0.34 (-$20,692) = - $7,035
Net Proceeds from sale = $100,000 – (-$7,035) = $107,035.28

46.
Case 4: S = $250,000
Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308
Book Value = 230,000 -109,308 = $120,692
Ordinary Gains = Salvage Value – Book Value = $250,000 - $120,692 = $129,308
Gains Tax (34%) = 0.34 ($129,308) = $43,965
Net Proceeds from sale = $250,000 – $43,965 = $206,035

47. PRACTICE PROBLEMS
9; 12; 17; 39; 40

48. Cost of the asset, I $120,000
Useful life, N 7 years
Salvage value, S $0
9.9) Consider the following data on an asset:
Compute the annual depreciation allowances and resulting
book values, using the following methods.
a)Double Declining balance
b)Straight-line depreciation method with zero salvage value

49. Cost of the asset, I $120,000
Useful life, N 7 years
Salvage value, S $0
SOLUTION 9.9)
DDB method With switching
n Dn =2/N = 0.2857 SL method Dn =1/N Bn
0 $120,000
1 $34,284 7 / $17,143 $ 85,716
2 $24,489.10 6 / $14,286 $ 61,227
3 $17,492.6 5 / $12,245.4 $ 43,735
4 $12,495.1 4/ $10,933.8 $ 31,240
5 $8,925.3 shift }}}}}} 3 /$10,413 $ 20,827
6 2 /$10,413.5 $10,413.5
7 1 /$10,413.5 $0

50. Cost of the asset, I $38,000
Useful life, N 6 years
Salvage value, S $0
9.12) Consider the following data on an asset:
Compute the annual depreciation allowances and resulting book values,
by using DDB method and then switching to the SL method to reach with zero
salvage value

51. Cost of the asset, I $38,000
Useful life, N 6 years
Salvage value, S $0
SOLUTION 9.12)
With switching
n DDB method Dn = .33333 SL method Dn = 1 / 6 Bn
0 $38,000
1 $12,667 6 / $6,333.33 $25,333
2 $8,444.40 5 / $5,066.6 $16,889.60
3 $5,629.47 4 / $4,222.15 $11,260.13
4 $3,753.34 3 / $3,753.4 shift to SL $7,506.73
5 2 / $3,753.4 $3,753.40
6 1 / $3,763.4 $0

52. 9.17)
New York Limousine Service owns 10 limos and uses the units of production method in
computing depreciations on its limos. Each limo costing $32,000 is expected to be driven
200,000 miles and is expected to have a salvage value of $3,000. Limo # 1 was driven
24,000 miles in year 1 and 28,000 miles in year 2. Determine the depreciation for each
year and the book value at the end of year 2.
SOLUTION
1
24, 000
($32,000 $3,000) $3, 480
200,000
D = − =
2
28,000
($32,000 $3,000) $4,060
200,000
D = − =
The book value of Limo # 1 at the end of year 2:
2 32, 000 3, 480 4, 060 $24, 460B = − − =

53. 9.39
Consider a five year MACRS asset that was purchased for $76,000. Compute the
gain and loss amounts if the asset were disposed of in
a) year 3 with a salvage value of $20,000;
b) year 5 with a salvage value of $10,000;
c) year 6 with salvage value of $5,000.

54. allowed depreciation $76,000(0.20 0.32 0.192 / 2)
$46,816
book value $76,000 $46,816
$29,184
loss $20,000 $29,184 ($9,184)
= + +
=
= −
=
= − =
allowed depreciation $76, 000(0.20 0.32 0.192
0.1152 0.1152 / 2)
$67, 244.8
book value $76, 000 $67, 244.8
$8, 755.2
Taxable gains $10, 000 $8, 755.2 $1, 224.8
= + +
+ +
=
= −
=
= − =
allowed depreciation $76,000
book value $0
Taxable gains $5,000
=
=
=
Disposed of in year 3:
Disposed of in year 5:
Disposed of in year 6:

55. 9.40)
An electrical appliance company purchased an industrial robot costing $320,000 in year
0. The industrial robot, to be used for welding operations, is classified as a seven year
MACRS recovery property. If the robot is to be sold after five years, compute the
amounts of gains (losses) for the following three salvage values, assuming that both
capital gains and ordinary incomes are taxed at 35%;
a) $15,000 b) $125,000 c) $200,000

56. allowed depreciation $320,000(0.1429 0.2449 0.1749
0.1249 0.0893 / 2)
$234,320
book value $320,000 $234,320
$85,680
= + +
+ +
=
= −
=
losses $15,000 $85,680 ($70,680)
loss credit $70,680(0.35) $24,738
net loss ($70,680) $24,738 ($45,942)
= − =
= =
= + =
gains $125,460 $85,680 $39,780
gains tax $39,780(0.35) $13,923
net gain $39,780 $13,923 $25,857
= − =
= =
= − =
gains $200,000 $85,680 $114,320
gains tax $114,320(0.35) $40,012
net gain $114,320 $40,012 $74,308
= − =
= =
= − =
9.40) SOLUTION
If sold at $15,000:
If sold at $125,460:
If sold at $200,000: