Income, Depreciation & Cash Flow Chapter 11 Mechanical Engineering 431 Engineering Economics

Income, Depreciation & Cash Flow

Chapter 11

Mechanical Engineering 431

Engineering Economics

2009-2010 Term 2 MECH 431 — Engineering Economics 11-2

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 depreciationDepreciation 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.


DepreciationIn 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 expensesExpenses 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 purposesDepreciable lifetime— the period over which an asset is

depreciated; the capital recovery periodDepreciation

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.


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 propertyTangible 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 marksGoodwillBrand loyalty, customer loyalty


Depreciation modelsA 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 guidelinesDepreciate 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.


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.


Depreciation methodsHistorical methods:

Straight-lineSum-of-years-digitsDeclining balanceUnit-of-production

Tax reporting depreciation methods:Canada— Capital Cost Allowance, CCAUnited 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 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.


Depreciation methods …Acquisition cost: $150,000Addl capital cost: $25,000

Salvage value: $15,000Lifetime (years): 7 SOYD: 28

Discount rate: 12%Tax rate: 28.5%

Annual depreciation= $22,857

1 2 3 4 5 6 7Depreciation amount= $22,857 $22,857 $22,857 $22,857 $22,857 $22,857 $22,857

Book value (end of year)= $152,143 $129,286 $106,429 $83,571 $60,714 $37,857 $15,000Tax shield= $6,514 $6,514 $6,514 $6,514 $6,514 $6,514 $6,514

PV(depreciation tax shields)= $29,729.61




Depreciation rate: 30%




Declining Balance Depreciation

Year

Straight-Line Depreciation

Sum-of-Years'-Digits Depreciation

Year

Year


Depreciation for tax purposesCorporations 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).


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 dd = CCA rateUCCbase is the Undepreciated Capital Cost of the asset class,

i.e. the book value or the amount that is eligible for depreciation.


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.


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)t2


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: 20%Year Net Acquisitions Base UCC CCA Taken End UCC2006 $630,0002007 $250,000 $755,000 $151,000 $729,0002008 $729,000 $145,800 $583,2002009 $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:

ratediscount i

rate tax sfirm’ T

classasset specified for the rateCCA d

todayacquiredasset ofcost 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

valuesalvage 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; 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.


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.


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 valueThe 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.


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 UCCThe 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: $15,000Equipment UCC at end= $10,504.55 RD

Equipment CCA class: 43Equipment CCA rate: 30%

Planned lifetime (years): 12Marginal 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 resourcesDepletion: 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.


Suggested problems — Chapter 1111-6, 11-9, 11-21, 11-24, 11-29, 11-35, 11-36.

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Income, Depreciation & Cash Flow Chapter 11 Mechanical Engineering 431 Engineering Economics