Engineering Economic Analysis
Canadian Edition
Chapter 11:
Income, Depreciation & Cash Flow
Chapter 11 …
 Describes depreciation, deterioration, and
obsolescence.
 Distinguishes between types of depreciable
property and differentiates depreciation from
other expenses.
 Uses historical methods to calculate annual
depreciation expenses and book value.
 Uses capital cost allowance (CCA) to
calculate annual depreciation expenses and
book value for assets of various classes.
 Accounts for capital gains and losses, loss on
disposal of fixed assets, and recaptured CCA.
11-2
Basic Aspects of Depreciation
 Depreciation is an important component in
computing income taxes.
 For tax purposes, depreciation is the
systematic allocation of the cost of an asset
spread over its depreciable life.
11-3
Depreciation
 In an economic context:
• Definition: a decrease in value
 Market value
 Value to the owner
 In an accounting context:
• Definition: a systematic allocation of the cost of an
asset over its depreciable life.
 Deterioration
 Obsolescence
11-4
Causes of Depreciation
Reason
Example
Use-related physical
car; light bulb
loss (deterioration)
Time-related loss (even machinery and
if asset is not used)
equipment
Functional loss (asset
is unable to meet
demand expectations)
electronic calculators
and computers
11-5
Depreciation and Expenses
 Expenses are subtracted from business
revenues as they occur.
• labour, utilities, materials, insurance, etc.
 Depreciation is subtracted from business
revenues over time as the asset is used up.
• machinery, installation costs
11-6
Depreciation for Tax Purposes
 Depreciable life: the period over which an
asset is depreciated (recovery period).
 Depreciation is a non-cash cost: money does
not change hands during the recovery period.
 Depreciation is used to allocate an asset’s
loss of value over time.
 Depreciation is deducted from revenue and
reduces the taxable income of a business
over time.
 Depreciation therefore gives rise to a cash
flow known as a tax shield.
11-7
Depreciable Property
 Used for business purposes in the production
of income.
 Has a useful life that can be determined, and
the useful life is longer than one year.
 Decays, gets used up, wears out, becomes
obsolete or loses value from natural causes.
11-8
Classification of Property
 Tangible property can be seen, touched, and
felt.
• Real: land, buildings, and things growing on, or
attached to the land
• Personal: equipment, furnishings, vehicles, office
machinery, or not defined as real property
 Intangible property: has value but cannot be
seen or touched.
• Patents, copyrights, and trade marks.
• Brand loyalty, customer loyalty.
11-9
Depreciation Models
 A reliable model of depreciation:
• establishes the accurate value of owned assets to
make good managerial decisions;
• supports planning (e.g., when to keep or sell an
asset);
• determines the cost of current production as
accurately as possible; and
• reflects taxes payable and profits as accurately as
possible.
11-10
General Depreciation Guidelines
 Depreciate an asset as rapidly as is legally
possible to derive the largest benefit from
offsetting tax shields as early as possible in
an asset’s life.
 Depreciation has an indirect effect on cash
flows and a direct effect on net income.
 Initial Capital Cost: total cost of acquiring an
asset and putting it into service. This is the
cost basis for depreciation of the asset.
 Book Value = Initial Capital Cost – Σ(Deprec.
Expenses). This value declines with age.
11-11
Depreciation Methods
 Historical methods:
•
•
•
•
Straight line
Sum-of-years-digits
Declining balance
Unit-of-production
 Tax reporting depreciation methods:
• Canada: Capital Cost Allowance (CCA)
• United States: Modified accelerated cost recovery
system (MACRS)
11-12
Depreciation Methods …
 Straight Line (SL) Method:
• Constant annual depreciation expense (d).
• d = (B – S)/N; where B = initial capital cost (cost
basis), S = salvage value, N = depreciable life.
• Book value at the end of period t is BVt = B  td;
where t = 1, 2, … N.
• Accounts fully for the depreciation base (B  S)
during the depreciable lifetime.
11-13
Depreciation Methods …
 Sum-Of-Years-Digits (SOYD):
• Declining annual depreciation expenses (dt).
• dt = (B  S)(N  t + 1)/SOYD; where SOYD = N(N
+1)/2 = 1 + 2 + … + N.
• Variable annual rate applied to a constant
depreciation base.
• Accounts fully for the depreciation base (B  S)
during the depreciable lifetime.
• Depreciates an asset more rapidly than the SL
method, i.e. larger dt values occur earlier in the
asset’s life.
11-14
Depreciation Methods …
 Declining Balance (DB) Method:
• Constant annual depreciation rate (D).
• Declining annual depreciation expenses (dn).
• dn = DB(1  D)n1; where D = annual depreciation
rate.
• BVn = B(1  D)n.
• Constant depreciation rate applied to a declining
depreciation base
• DB does not account for the full depreciation base
(B  S) unless the annual depreciation rate D is
calculated to force the final book value to S.
11-15
Depreciation Methods …
 The DB method depreciates an asset more
rapidly than the SL method, similar to the
SOYD method, i.e. larger dn values occur
earlier in the asset’s life.
 The DB method may be preferred because it
is the “official” method used for tax purposes
and it can provide the greatest present value
of depreciation tax shields.
11-16
Depreciation Methods …
 Unit-of-Production (UOP) Method:
• Annual depreciation expenses (dt) that vary from
year to year.
• dt is more closely related to use of the asset than
to time.
• dt = (Annual production/Lifetime production)(BS).
• UOP is appropriate for depreciating assets used in
processing natural resources that are exhausted;
it is not considered appropriate for depreciating
general industrial assets.
11-17
Depreciation Methods …
 Example: An asset is acquired for $150,000
and it requires $25,000 of capital expenses to
put it into service. It is estimated to have a
lifetime of five years and a salvage value of
$35,000. Find the depreciation expense,
book value, and tax shield for each year, then
find the present value of the tax shields for a
tax rate of 38% and a discount rate of 12% for
these methods: straight-line, SOYD and
declining balance (use a rate of 30%, then a
custom rate for full depreciation).
11-18
Depreciation Methods …
Acquisition cost:
Addl capital cost:
Salvage value:
Lifetime (years):
Discount rate:
Tax rate:
$150,000
$25,000
$35,000
5
12%
38%
SOYD:
15
Straight-Line Depreciation
Annual depreciation=
$28,000
Depreciation amount=
Book value (end of year)=
Tax shield=
PV(depreciation tax shields)=
Year
3
$28,000
$91,000
$10,640
4
$28,000
$63,000
$10,640
5
$28,000
$35,000
$10,640
2
$37,333
$91,000
$14,187
Year
3
$28,000
$63,000
$10,640
4
$18,667
$44,333
$7,093
5
$9,333
$35,000
$3,547
2
$36,750
$85,750
$13,965
Year
3
$25,725
$60,025
$9,776
4
$18,008
$42,018
$6,843
5
$12,605
$29,412
$4,790
1
2
$28,000 $28,000
$147,000 $119,000
$10,640 $10,640
$38,355
Sum-of-Years'-Digits Depreciation
Depreciation amount=
Book value (end of year)=
Tax shield=
PV(depreciation tax shields)=
1
$46,667
$128,333
$17,733
$41,237
Declining Balance Depreciation
Depreciation rate:
30%
Depreciation amount=
Book value (end of year)=
Tax shield=
PV(depreciation tax shields)=
1
$52,500
$122,500
$19,950
$42,970
11-19
Depreciation for Tax Purposes
 Corporations in Canada are required to
depreciate capital assets by a DB method
known as Capital Cost Allowance (CCA).
 Companies seek rapid depreciation to
maximize tax savings from depreciation.
 Governments want companies to depreciate
assets as slowly as possible to keep tax
savings at a minimum.
 The CCA is a compromise, i.e. it forms part of
government’s economic policy (give & take).
11-20
Depreciation for Tax Purposes …
 For calculating CCA, assets are assigned to
asset classes that have specified CCA rates.
 Most asset classes use the declining balance
method for computing CCA.
 Common CCA classes and their rates are
listed along with some recent regulatory
changes at:
http://www.parl.gc.ca/information/library/PRBp
ubs/prb0606-e.htm#appendixa.
11-21
Depreciation for Tax Purposes …
 Asset class accounting:
• Assets of a single class are grouped in a single
ledger account.
• Assets may be added to or subtracted from the
account each year.
 For year t, CCAt = UCCbase  d; where d =
CCA rate, and UCCbase is the Undepreciated
Capital Cost of the asset class that is eligible
for depreciation.
 Maximum CCA for a year = CCA that reduces
taxable income to zero.
11-22
Depreciation for Tax Purposes …
 A maximum of 50% of the initial cost of an
asset acquired during a year can be used as
the basis for calculating the depreciation in
the year of purchase. This is known as the
“50% rule”, or sometimes the “half-year rule”.
 For most asset classes, the value of assets
disposed of during the year is netted against
acquisitions made in the same year.
• This netting of values mitigates the effect of the
50% rule since it applies to net acquisitions.
11-23
Depreciation for Tax Purposes …
 CCA1 = B(d/2)
CCAt = Bd(1 – d/2)(1  d)t2
 Example: an asset that cost $250,000 was
added to Class 8 (rate = 20%) in 2004, then
in 2006, an asset worth $300,000 was added
and an asset was salvaged for $80,000. Find
the CCAs and UCCs of Class 8 if its UCC
was $630,000 at the end of 2003.
CCA rate:
20%
Year Net Acquisitions Base UCC CCA Tak en
2003
2004
$250,000
$755,000
$151,000
2005
$729,000
$145,800
2006
$220,000
$693,200
$138,640
End UCC
$630,000
$729,000
$583,200
$664,560
11-24
Depreciation for Tax Purposes …
 The tax shields generated by the CCA
generally have an infinite life. But, projects
typically have a finite life.
 When computing NPV, we normally calculate
the present value of the operating cash flows
separately from the present value of the CCA
tax shields.
 We assume that the acquired asset will be
held forever, so we add the present value of
the asset’s perpetual CCA tax shields to the
NPV of the project.
11-25
Depreciation for Tax Purposes …
 Present value of the perpetual CCA tax
shields gained on acquiring an asset:
 BdTC  1  i 2 
 i  d  1 i 



B  capital cost of asset acquired today
d  CCA rate for the specified asset class
TC  firm’ s tax rate
i  discount rate
11-26
Depreciation for Tax Purposes …
 Present value (today) of the perpetual CCA
tax shields lost on disposing of an asset:
 SdTC   1 

 i  d 
N

  1  i  
S  salvage value
d, TC , i  as defined earlier
N  lifetime (year of disposal)
11-27
Depreciation for Tax Purposes …
 By convention,
• an asset is sold (salvaged) at the end of a year
and we have taken the CCA for the year;
• its salvage value is deducted from the UCC of the
corresponding asset class; and
• the asset class remains open.
 Since the salvage value will no longer be
included in the UCC of the asset class, the
present value of the perpetual CCA tax
shields from the salvage value must be
deducted from the NPV of the project.
11-28
Depreciation for Tax Purposes …
 Special cases occur when:
• the salvaged asset is the last one in the class;
• the salvage value > UCC of the asset class;
• the salvage value > original cost of the asset.
 Note: for the following, “pre-disposal UCC”
means the UCC of the asset class after the
CCA has been taken in the year of disposal.
11-29
Depreciation for Tax Purposes …
 If the asset is the last remaining in the CCA
class and salvage value < pre-disposal UCC:
• deduct the present value of the perpetual CCA tax
shields on the pre-disposal UCC from the project
NPV.
• There is a terminal loss (= pre-disposal UCC 
salvage value); deducting this loss from income
produces a tax shield in the year of disposal.
• The asset class must be closed and its final UCC
must be set to zero.
11-30
Depreciation for Tax Purposes …
 When the salvage value > pre-disposal UCC
(even if the asset class is not closed):
• deduct the present value of the perpetual CCA tax
shields on the pre-disposal UCC from the NPV of
the project.
• There is recaptured depreciation (= salvage
value  pre-disposal UCC) on which the firm must
pay taxes in the year of disposal.
• The UCC of the asset class is set to zero.
• The asset class is closed if this was the last
remaining asset; otherwise it stays open.
11-31
Depreciation for Tax Purposes …
 When the salvage value > original cost of the
asset:
• deduct the present value of the perpetual CCA tax
shields on the original cost from the NPV of the
project.
• There is a capital gain (= salvage value  original
cost).
• The firm must pay taxes on ½ of the capital gain in
the year of disposal.
• Subtract the original cost from the UCC of the
asset class.
11-32
Depreciation for Tax Purposes …
 Example: FMI Corporation has purchased:
land = $750,000, a building = $545,000 (CCA
asset class 1), and manufacturing equipment
= $625,000 (CCA asset class 43). Planned
lifetime = 12 years. Expected salvage values:
land—$1.8 million, building—$325,000, and
equipment—$15,000. Find the present value
of acquiring and disposing of the assets if
FMI’s marginal tax rate = 38% and MARR =
13% if: (a) other assets remain in the asset
classes, and (b) these assets were the only
ones in the asset classes.
11-33
Depreciation for Tax Purposes …
Land acquisition cost:
Land salvage value:
Building acquisition cost:
Building salvage value:
Building UCC at end=
Building CCA class:
Building CCA rate:
Equipment acquisition cost:
Equipment salvage value:
Building UCC at end=
Equipment CCA class:
Equipment CCA rate:
Planned lifetime (years):
Marginal tax rate:
MARR:
- Land acquisition
+ PV(Land salvage)
- PV(Capital gain tax on land)
- Building acquisition
+ PV(CCA TS gained on building)
+ PV(Building salvage)
- PV(CCA TS lost on building)
+ PV(TS on terminal loss on building)
- Equipment acquisition
+ PV(CCA TS gained on equipment)
+ PV(Equipment salvage)
- PV(CCA TS lost on equipment)
- PV(Tax on recap deprec on equipment)
= Present value of acquisition/disposal
$750,000
$1,800,000
$545,000
$325,000
$340,883.63 TL
1
4%
$625,000
$15,000
$10,504.55 RD
43
30%
12
38%
13%
Open
-$750,000.00
$415,270.60
-$46,025.82
-$545,000.00
$45,926.39
$74,979.41
-$6,704.04
$0.00
-$625,000.00
$156,166.39
$3,460.59
-$917.46
$0.00
Closed
-$750,000.00
$415,270.60
-$46,025.82
-$545,000.00
$45,926.39
$74,979.41
-$7,031.69
$1,392.49
-$625,000.00
$156,166.39
$3,460.59
-$642.50
-$394.11
-$1,277,843.94 -$1,276,898.24
11-34
Natural Resources
 Depletion: consumption of natural resources.
• Mineral properties, oil and gas wells, timber.
 Federal and provincial governments collect
income tax on natural resources.
• Royalties and tax rates vary across the country.
 Depletion calculation methods were discontinued in 1990; existing mines grandfathered.
 Percentage depletion: allowance = percent of
property’s gross income.
 Cost depletion: like unit-of-production
depreciation.
11-35
Suggested Problems
 11-6, 9, 15, 21, 26, 27, 31, 33.
11-36