engineering economic analysis canadian edition chapter 11: income, depreciation & cash flow

Engineering Economic AnalysisCanadian Edition

Chapter 11:

Income, Depreciation & Cash Flow

11-2EECE 450 — 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.


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.


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


Causes of Depreciation

Reason Example

Use-related physical loss— deterioration

car; light bulb

Time-related loss— even if the asset is not used

machinery and equipment

Functional loss— the asset is unable to meet demand expectations

calculators and computers


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


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.

Depreciation is used to allocate an asset’s loss of value over time.

Depreciation is treated as an expense that is deducted from revenue and thus reduces the taxable income of a business.

Depreciation does generate a cash flow— a reduction in taxes, known as a tax shield.


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.


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


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.


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.

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(Deprecation Expenses).• This value declines as the asset ages.


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


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 – td; where t = 1, 2, … N.

• Accounts fully for the depreciation base (B – S) during the depreciable lifetime.


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.


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)n1

• 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.


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.


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.


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 30% 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).


Depreciation Methods …Acquisition cost: $150,000

Addl capital cost: $25,000Salvage value: $35,000

Lifetime (years): 5 SOYD: 15Discount rate: 12%

Tax rate: 30%

Annual depreciation= $28,000

1 2 3 4 5Depreciation amount= $28,000 $28,000 $28,000 $28,000 $28,000

Book value (end of year)= $147,000 $119,000 $91,000 $63,000 $35,000Tax shield= $8,400 $8,400 $8,400 $8,400 $8,400

PV(depreciation tax shields)= $30,280




Depreciation rate: 30%




Declining Balance Depreciation

Year

Straight-Line Depreciation

Sum-of-Years'-Digits Depreciation

Year

Year


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).


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/prb0606-e.htm#TOP.


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.

CCA allowed in year t = Min(CCAt, amount of CCA that would reduce taxable income to 0)


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.

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.


Depreciation for Tax Purposes … CCA1 = B(d/2)

CCAt = Bd(1 – d/2)(1 – d)t2

Example: an asset that cost $250,000 was added to Class 8 (rate = 20%) in 2006, then in 2008, an asset worth $300,000 was added and an asset was salvaged for $80,000. Find the CCAs and UCCs of Class 8 through 2008 if its UCC was $630,000 at the end of 2005.

CCA Class: 8 CCA rate: 20%Year Net Acquisitions Base UCC CCA Taken End UCC2005 $630,0002006 $250,000 $755,000 $151,000 $729,0002007 $729,000 $145,800 $583,2002008 $220,000 $693,200 $138,640 $664,560


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.


Depreciation for Tax Purposes … Present value of the perpetual CCA tax

shields gained on acquiring an asset:

rate discount i

ratetax sfirm’ T

class asset specified the for rateCCA d

today acquired asset of cost capital B

1

21

C

i

i

di

BdTC


Depreciation for Tax Purposes … Present value (today) of the perpetual CCA

tax shields lost on disposing of an asset:

disposal) of (year lifetime N

earlier defined as i ,T ,d

value salvage S

1

1

C

N

C

idi

SdT


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; and• the asset class has other assets and remains

open when an asset is sold.

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.


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.


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.

• 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 zero.


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.


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.


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.


Depreciation for Tax Purposes …Land acquisition cost: $750,000

Land salvage value: $1,800,000Building acquisition cost: $545,000

Building salvage value: $325,000Building UCC at end= $340,883.63 TL

Building CCA class: 1Building CCA rate: 4%

Equipment acquisition cost: $625,000Equipment salvage value: $15,000

Building UCC at end= $10,504.55 RDEquipment CCA class: 43

Equipment CCA rate: 30%Planned lifetime (years): 12

Marginal tax rate: 30%MARR: 13%

Open Closed- Land acquisition -$750,000.00 -$750,000.00+ PV(Land salvage) $415,270.60 $415,270.60- PV(Capital gain tax on land) -$36,336.18 -$36,336.18- Building acquisition -$545,000.00 -$545,000.00+ PV(CCA TS gained on building) $36,257.68 $36,257.68+ PV(Building salvage) $74,979.41 $74,979.41- PV(CCA TS lost on building) -$5,292.66 -$5,551.33+ PV(TS on terminal loss on building) $0.00 $1,099.33- Equipment acquisition -$625,000.00 -$625,000.00+ PV(CCA TS gained on equipment) $123,289.26 $123,289.26+ PV(Equipment salvage) $3,460.59 $3,460.59- PV(CCA TS lost on equipment) -$724.31 -$507.24- PV(Tax on recap deprec on equipment) $0.00 -$311.14= Present value of acquisition/disposal -$1,309,095.62 -$1,308,349.01


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 discon-tinued in 1990; existing mines grandfathered.

Percentage depletion: allowance = percent of property’s gross income.

Cost depletion: like unit-of-production depreciation.


Suggested Problems 11-6, 9, 15, 21, 26, 27, 31, 33.

engineering economic analysis canadian edition chapter 11: income, depreciation & cash flow

Documents

annual depreciation

depreciation cash flow

engineering economics

reliable model of depreciation

value market value value

assets loss of value

book value

expenses expenses