Depreciation and Income Taxes
Chapter 9
Advanced Engineering
Economy
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
Loss of
Value
$15,000
10,000 $5,000
8,000 2,000
6,000 2,000
5,000 1,000
4,000 1,000
Depreciation
0
1
2
3
4
5
Market
Value
Why Do We 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)
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.
Cost Basis
Without Trade-In Allowance
Cost of a new hole-punching
machine (Invoice price)
+ Freight
Old hole-punching machine (book value)
$62,500
725
+ Installation labor
2,150
+ Site preparation
3,500
Cost basis to use in depreciation
calculation
With Trade-In Allowance
$68,875
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
Useful Life and Salvage Value
 Useful life – Adopt the
Asset Depreciation
Ranges (ADR) published
by the IRS.
 Salvage value –
Asset’s estimated value
at the end of its useful
life. Every effort should
be made to estimate a
reasonable residual value
of the asset, but if not
possible, a 10% rule
(10% of the initial value)
could be adopted for
depreciation purpose.
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
Book versus Tax Depreciation – An
Overview
Component of
Depreciation
Cost basis
Salvage
value
Book Depreciation
Tax depreciation (MACRS)
Based on the actual cost of
the asset, plus all
incidental costs such as
freight, site preparation,
installation, etc.
Same as for book
depreciation
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
Component of
Depreciation
Depreciable
life
Method of
depreciation
Book Depreciation
Tax depreciation (MACRS)
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.
Firms may select from
the following:
Straight-line
Accelerated methods
(declining balance,
double declining
balance, and sum-ofyears’ 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.
Book Depreciation Methods
• Purpose: Used to report net income to
stockholders/investors
• Types of Depreciation Methods:
– Straight-Line (SL) 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: 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
B4
$2,000
B5
0
1
2
3
4
5
n
n
0
1
2
3
4
5
Dn
1,600
1,600
1,600
1,600
1,600
Bn
10,000
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  I (1   ) n where 0 <  < 2(1/N)
Note: if  is chosen to be the upper bound,  = 2(1/N),
we call it a 200% DDB or Double Declining Balance method.
Example: Declining Balance Method
Annual Depreciation
$10,000
ά =2(1/N)
=2(1/5) =40%
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 = $2000
Dn =  Bn 1
=  I (1-   n 1
Bn  I (1   ) n
D4
$2,000
B3
$778
0
1
2
3
B4
4
B5
5
n
n
0
1
2
3
4
5
Dn
$4,000
2,400
1,440
160
0
Bn
$10,000
6,000
3,600
2,160
2000
2000
Example: 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
2,160 – 160 = 2,000
5
0
2,000 – 0 = 2,000
Note: Tax law does not permit us to depreciate assets below
their salvage values.
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
• 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
Tax Depreciation
• Purpose: Used to 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 Accelerated Cost Recovery System (ACRS) Table
•Assets placed in service after 1986
Use Modified Accelerated Cost Recovery System MACRS 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
Recovery Period
3-year
ADR Midpoint
Class
Applicable Property
ADR  4 Special tools for manufacture of plastic
products, fabricated metal products, and
motor vehicles.
5-year
4  ADR  10
7-year
10  ADR  16
10-year
15-year
20-year
16  ADR  20
20  ADR  25
25  ADR
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.
Municipal sewers, electrical power plant.
27.5-year
Residential rental property
39-year
Nonresidential real property including
elevators and escalators
MACRS Depreciation Schedules for Personal
Property with Half-Year Convention
 Property Class
 3, 5, 7, 10-Year with
200% DB
 15 and 20-Year with 150%
DB
 Sample Calculation – 5Year MACRS:
MACRS Rate Calculation
Asset cost = $10,000
Property class = 5-year
DB method = Half-year convention, zero salvage value,
200% DB switching to SL
20% 32%
19.20% 11.52% 11.52% 5.76%
$2000 $3200 $1920 $1152 $1152
Full Full
Full
1
2
3
4
Half-year Convention
$576
Full
5
6
Year (n)
Calculation in %
1
2
(0.5)(0.40)(100%)
(0.4)(100%-20%)
MACRS (%)
DDB
DDB
SL = (1/4.5)(80%)
3
(0.4)(100%-52%)
20%
32%
17.78%
DDB
SL = (1/3.5)(48%)
19.20%
13.71%
4
(0.4)(100%-71.20%) Switch to SL 11.52%
SL = (1/2.5)(29.80%)
11.52%
5
6
SL = (1/1.5)(17.28%)
SL = (0.5)(11.52%)
SL
SL
11.52%
5.76%
Comparison between DDB with Switching to
SL and MACRS Method
 Conventional
DDB
Method:
 Cost basis:
$10,000
 Salvage value: $0
 Depreciable life: 5
years
 DB rate: 200%
 MACRS Method:
 Property class: 5year
 Salvage value: $0
 Half-year
convention
• Depreciation Rates
MACRS for Real Property
 Types:
 27.5-Year
 Depreciation Allowances for a 10-year Ownership of the Property
(Residential)
 39-Year
Year (n)
Calculation
Allowed Depreciation (%)
(Commercial)
1
(9.5/12)(100%/27.5)
2.8788%
 SL Method
2
100%/27.5
3.6364%
 Mid-month convention
3
100%/27.5
3.6364%
 Zero salvage value
 Example:
Placed a residential
property in service in
March. Find the
depreciation allowance in
year 1.
D1 =
(9.5/12)(100%/27.5)
= 2.8788%
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%
Net Income Versus Cash Flow
Taxable Income and Income Taxes
Item
Gross Income
Expenses
Cost of goods sold (revenues)
Depreciation
Operating expenses
Taxable income
Income taxes
Net income
Example:- Net Income Calculation
Item
Gross income (revenue)
Expenses
Cost of goods sold
Depreciation
Operating expenses
Taxable income
Taxes (40%)
Net income
Amount
$50,000
20,000
4,000
6,000
20,000
8,000
$12,000
Capital Expenditure versus Depreciation
Expenses
0
$28,000
0
1
2
3
4
5
6
7
8
4
7
6
7
8
Capital expenditure
(actual cash flow)
1
2
3
$1,250
$4,000
$4,900
$6,850
$3,500 $2,500
$2,500 $2,500
Allowed depreciation expenses (not cash flow)
Cash Flow vs. Net Income
Net income: Net income is an accounting means of
measuring a firm’s profitability based
on the matching concept. Costs become
expenses as they are matched against
revenue. The actual timing of cash inflows
and outflows are ignored.
Cash flow: Given the time value of money, it is better
to receive cash now than later, because cash
can be invested to earn more money. So,
it is desirable why cash flows are relevant
data to use in project evaluation.
Why Do We Use Cash Flow in Project
Evaluation?
Example: Both companies (A & B) have the same amount of
net income and cash sum over 2 years, but Company A returns
$1 million cash yearly, while Company B returns $2 million
at the end of 2nd year. Company A can invest $1 million in year
1, while Company B has nothing to invest during the same period.
Company A
Company B
Year 1
Net income
Cash flow
$1,000,000
1,000,000
$1,000,000
0
Year 2
Net income
Cash flow
1,000,000
1,000,000
1,000,000
2,000,000
Example:– Cash Flow versus Net Income
Item
Income
Gross income (revenue
Expenses
Cost of goods sold
Depreciation
Operating expenses
Taxable income
Taxes (40%)
Net income
$50,000
$50,000
20,000
4,000
6,000
20,000
8,000
$12,000
-20,000
Net cash flow
Cash Flow
-6,000
-8,000
$16,000
Net income versus net cash flow
Net cash flows = Net income + non-cash expense (depreciation)
$50,000
$40,000
$30,000
$20,000
$10,000
$0
Net
cash flow
Net income
$12,000
Depreciation
$4,000
Income taxes
$8,000
Operating expenses
Cost of goods sold
$6,000
$20,000
Gross
revenue
Corporate Taxes
Taxable Income and Income Taxes
Item
Gross Income
Expenses
Cost of goods sold (revenues)
Depreciation
Operating expenses
Taxable income
Income taxes
Net income
U.S. Corporate Tax Rate (2010)
Taxable income
Tax rate
0-$50,000
15%
$50,001-$75,000
25%
$75,001-$100,000
34%
$100,001-$335,000
39%
$335,001-$10,000,000
34%
$10,000,001-$15,000,000 35%
$15,000,001-$18,333,333 38%
$18,333,334 and Up
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
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
 34.56%
$16,000,000
Example: Corporate Income Taxes
Facts:
Capital expenditure
(allowed depreciation)
Gross Sales revenue
Expenses:
Cost of goods sold
Depreciation
Leasing warehouse
Question: Taxable income?
$100,000
$58,000
$1,250,000
$840,000
$58,000
$20,000
Taxable income:
Gross income
- Expenses:
(cost of goods sold)
(depreciation)
(leasing expense)
Taxable income
• Income taxes:
First $50,000 @ 15%
$25,000 @ 25%
$25,000 @ 34%
$232,000 @ 39%
Total taxes
$1,250,000
$840,000
$58,000
$20,000
$332,000
$7,500
$6,250
$8,500
$90,480
$112,730
• Average tax rate:
Total taxes =
$112,730
Taxable income = $332,000
$112,730
Average tax rate =
$332,000
 33.95%
• Marginal tax rate:
Tax rate that is applied to the last dollar
earned
39%
Disposal of Depreciable Asset
• If
a MACRS asset is disposed of during the
recovery period,
• Personal property: the half-year convention
is applied to depreciation amount for the year
of disposal.
• Real property: the mid-month convention is
applied to the month of disposal.
Disposal of a MACRS Property and
Its Effect on Depreciation Allowances
Case 1: Salvage Value < Cost
Basis
• Gains (losses) = Salvage
value – book value
• These gains, commonly
known as either ordinary
gains or depreciation
recapture, are taxed as
ordinary income.
• Most gains experienced in
manufacturing
environment refer to
these ordinary gains.
• Any losses (ordinary) can
be deducted from the
ordinary gains from other
assets first and any
remaining balance can be
deducted from the
ordinary taxable income.
Ordinary
gains
Cost basis
Book value
Salvage value
Case 2: Salvage Value > Cost
Basis
Gains = Salvage value – book value
= (Salvage value - cost basis)
Capital gains
Capital gains
Total gains
Ordinary gains
or
depreciation recapture
+ (Cost basis – book value)
Ordinary gains
Capital gain is taxed as ordinary
income under current tax law.
Cost basis
Book value
Salvage value
Gains or Losses on Depreciable
Asset
Example: A Drill press:
$230,000
Project year: 3 years
MACRS:
7-year property class
Salvage value: $150,000 at the end of Year 3
Full
Full
Half
8.92
8.92
14.29 24.49 17.49 12.49
8.92
Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308
Book Value = 230,000 -109,308 = $120,693
Gains = Salvage Value - Book Value = $150,000 - $120,693
= $29,308
Gains Tax (34%) = 0.34 ($29,308) = $9,965
Net Proceeds from sale = $150,000 - $9,965 = $140,035
Calculation of Gains or Losses on
MACRS Property