Income, Depreciation &
Cash Flow
Chapter 11
Mechanical Engineering 431
Engineering Economics
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.
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MECH 431 — Engineering Economics
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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, or investment in, an asset spread
over its depreciable life.
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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
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Causes of depreciation
Reason
Example
Use-related physical loss—
car; light bulb
deterioration
Time-related loss— even if the asset machinery and
is not used
equipment
Functional loss— the asset is unable calculators and
to meet demand expectations
computers
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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
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Depreciation for tax purposes
Depreciable lifetime— the period over which an asset is
depreciated; the capital recovery period
Depreciation
 is a non-cash expense, i.e. no cash actually flows as capital is
recovered.
 is used to allocate an asset’s loss of value over time.
 is treated as an expense that is deducted from revenue and thus
reduces the taxable income of a business.
 does generate a cash flow— a reduction in taxes, known as a
tax shield.
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Depreciable property
Depreciable property
 is primarily hard assets that are used for business purposes in
the production of income;
 has a useful lifetime that can be determined, and the useful
lifetime is usually longer than one year;
 decays, is used up, wears out, becomes obsolete, or loses value
from natural causes.
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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
 Goodwill
 Brand loyalty, customer loyalty
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Depreciation models
A reliable model of depreciation
 establishes the value of owned assets accurately and
realistically for making decisions;
 supports planning, e.g. indicates 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.
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General depreciation guidelines
Depreciate an asset as rapidly as is legally possible to
derive the largest benefit from 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.
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General depreciation guidelines …
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(depreciation
expenses).
 This value declines as the asset ages.
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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
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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.
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Depreciation methods …
Sum-of-years-digits (SOYD) method:
 Declining annual depreciation expense, dt.
 dt = (B – S)(N – t + 1)/SOYD
 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.
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Depreciation methods …
Declining balance (DB) method:
 Constant annual depreciation rate, D.
 Declining annual depreciation expense, dn.
 BVn = B(1 – D)n.
 dn = BD(1 – D)n1
 The constant depreciation rate is applied to a declining
depreciation base.
 The DB method does not account for the full depreciation base
(B – S) unless the annual depreciation rate D is set or
calculated to force the final book value to S.
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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 required method for corporate business tax purposes
and
 it can provide the greatest present value of depreciation tax
shields.
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Depreciation methods …
Unit-of-production (UOP) method:
 Annual depreciation expenses, dt, 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.
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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 seven years
and a salvage value of $15,000. 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
28½% and a discount rate of 12% for straight-line,
SOYD and declining balance depreciation. For
declining balance, use a rate of 30%, then a custom rate
for full depreciation.
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Depreciation methods …
Acquisition cost:
Addl capital cost:
Salvage value:
Lifetime (years):
Discount rate:
Tax rate:
$150,000
$25,000
$15,000
7
12%
28.5%
SOYD:
28
2
$22,857
$129,286
$6,514
Year
3
$22,857
$106,429
$6,514
4
$22,857
$83,571
$6,514
5
6
7
$22,857 $22,857 $22,857
$60,714 $37,857 $15,000
$6,514 $6,514 $6,514
2
$34,286
$100,714
$9,771
Year
3
$28,571
$72,143
$8,143
4
$22,857
$49,286
$6,514
5
6
7
$17,143 $11,429 $5,714
$32,143 $20,714 $15,000
$4,886 $3,257 $1,629
2
$36,750
$85,750
$10,474
Year
3
$25,725
$60,025
$7,332
4
$18,008
$42,018
$5,132
5
6
7
$12,605 $8,824 $6,177
$29,412 $20,589 $14,412
$3,592 $2,515 $1,760
Straight-Line Depreciation
Annual depreciation=
$22,857
Depreciation amount=
Book value (end of year)=
Tax shield=
PV(depreciation tax shields)=
1
$22,857
$152,143
$6,514
$29,729.61
Sum-of-Years'-Digits Depreciation
Depreciation amount=
Book value (end of year)=
Tax shield=
PV(depreciation tax shields)=
1
$40,000
$135,000
$11,400
$33,063.30
Declining Balance Depreciation
Depreciation rate:
30%
Depreciation amount=
Book value (end of year)=
Tax shield=
PV(depreciation tax shields)=
2009-2010 Term 2
1
$52,500
$122,500
$14,963
$34,222.06
MECH 431 — Engineering Economics
11-20
Depreciation for tax purposes
Corporations in Canada are required to depreciate capital
assets by a declining balance 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).
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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.
See the information on the CCA, along with descriptions
of CCA classes and rates, at:
http://www.parl.gc.ca/information/library/PRBpubs/prb0
606-e.htm#TOP.
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Depreciation for tax purposes …
Asset class accounting:
 Assets of a single class are grouped in a single account.
 Assets may be added to or subtracted from the account each
year.
For year t, CCAt = UCCbase  d
 d = CCA rate
 UCCbase is the Undepreciated Capital Cost of the asset class,
i.e. the book value or the amount that is eligible for
depreciation.
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Depreciation for tax purposes …
CCA allowed in year t = min(CCAt, amount of CCA that
would reduce taxable income to 0)
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.
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Depreciation for tax purposes …
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.
CCA1 = B(d/2)
CCAt = Bd(1 – d/2)(1 – d)t2
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Depreciation for tax purposes …
Example: an asset that cost $250,000 was added to
Class 8 (rate = 20%) in 2007, then in 2009, an asset
worth $300,000 was added and an asset was salvaged for
$80,000. Find the CCAs and UCCs of Class 8 through
2009 if its UCC was $630,000 at the end of 2006.
CCA Class:
8
CCA rate:
Year Net Acquisitions Base UCC CCA Tak en
2006
2007
$250,000
$755,000
$151,000
2008
$729,000
$145,800
2009
$220,000
$693,200
$138,640
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20%
End UCC
$630,000
$729,000
$583,200
$664,560
11-26
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 can 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.
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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
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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)
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Depreciation for tax purposes …
By convention,
 an asset is acquired at the beginning of a year;
 an asset is sold (salvaged) at the end of a year after we have
taken the CCA for the year;
 the asset’s salvage value is deducted from the UCC of the
corresponding asset class;
 the asset class has other assets and remains open when an asset
is sold; and
 the full CCA can be deducted every year for income tax.
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Depreciation for tax purposes …
The salvage value will no longer be included in the UCC
of the asset class.
Thus, the PV of the CCA tax shields that would have
been generated by the salvage value must be deducted
from the NPV of the project.
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.
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Depreciation for tax purposes …
Note: the pre-disposal UCC is the UCC of the asset
class after the CCA has been taken in the year of
disposal.
If the disposed 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.
 Terminal loss = pre-disposal UCC – salvage value
 The terminal loss produces a tax shield in the year of disposal.
 The asset class must be closed; i.e. its final UCC is set to zero.
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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.
 Recaptured depreciation = salvage value – pre-disposal UCC
 The firm must pay taxes on the recaptured depreciation 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.
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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.
 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.
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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 = 30% and MARR = 13% if: (a) other
assets remain in the asset classes, and (b) these assets
were the only ones in the asset classes.
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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:
Equipment 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
2009-2010 Term 2
$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
30%
13%
Open
Closed
-$750,000.00
-$750,000.00
$415,270.60
$415,270.60
-$36,336.18
-$36,336.18
-$545,000.00
-$545,000.00
$36,257.68
$36,257.68
$74,979.41
$74,979.41
-$5,292.66
-$5,551.33
$0.00
$1,099.33
-$625,000.00
-$625,000.00
$123,289.26
$123,289.26
$3,460.59
$3,460.59
-$724.31
-$507.24
$0.00
-$311.14
-$1,309,095.62 -$1,308,349.01
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Natural resources
Depletion: consumption of natural resources.
 Mineral properties, oil and gas wells, timber.
Federal and provincial governments collect income tax
on natural resources.
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.
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Suggested problems — Chapter 11
11-6, 11-9, 11-21, 11-24, 11-29, 11-35, 11-36.
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