11

EGGC4214 EGGC4214 Systems Engineering & EconomySystems Engineering & Economy

Lecture 8Lecture 8DepreciationDepreciation

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IntroductionIntroduction

Depreciation is important because it affects the taxes that firms Depreciation is important because it affects the taxes that firms pay. pay.

TAXES proportional to TAXABLE PROFITS (INCOME – COSTS)TAXES proportional to TAXABLE PROFITS (INCOME – COSTS)COSTS = Maintenance Cost + Depreciated Initial CostCOSTS = Maintenance Cost + Depreciated Initial Cost

Roughly speaking, Roughly speaking, depreciation is a decrease in value of an asset each yeardepreciation is a decrease in value of an asset each year..

Depreciation is a deduction from taxable incomeDepreciation is a deduction from taxable income..

Thus the greater the depreciation, the less the taxable income – Thus the greater the depreciation, the less the taxable income – hence taxes.hence taxes.

Governments may allow some choice among depreciation methods. Governments may allow some choice among depreciation methods.

Obviously, Obviously, a well-run firm wants to choose the depreciation a well-run firm wants to choose the depreciation method that will minimize its taxable incomemethod that will minimize its taxable income. .

To do so, the firm representatives must understand how the To do so, the firm representatives must understand how the depreciation methods work.depreciation methods work.

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A firm has $1,000,000 of taxable income. A firm has $1,000,000 of taxable income.

If its tax rate is 25%, it would pay $250,000 in taxes ignoring If its tax rate is 25%, it would pay $250,000 in taxes ignoring depreciation.depreciation.

If it can deduct $50,000 in depreciation charges, its net taxable If it can deduct $50,000 in depreciation charges, its net taxable income is $950,000. income is $950,000.

Thus, it would pay taxes of 0.25 (950,000) = $237,500. Thus, it would pay taxes of 0.25 (950,000) = $237,500.

Depreciation saves 250,000 – 237,500 = $12,500 = 0.25(50,000). Depreciation saves 250,000 – 237,500 = $12,500 = 0.25(50,000).

If it could deduct more than $50,000 it would pay even less taxes.If it could deduct more than $50,000 it would pay even less taxes.

Individual investors encounter similar situations. Individual investors encounter similar situations.

If you invest $10,000 and get a 10% return, your taxable income is If you invest $10,000 and get a 10% return, your taxable income is $1,000. $1,000.

If you are in the 25% tax bracket, taxing takes $250, so your net If you are in the 25% tax bracket, taxing takes $250, so your net return is $750 return is $750 7.5%. 7.5%.

If you could have found an 8% investment for your $10,000 that If you could have found an 8% investment for your $10,000 that was not taxable, you would have made a better choice (800 > 750).was not taxable, you would have made a better choice (800 > 750).

Depreciation: ExampleDepreciation: Example

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DepreciationDepreciation

Depreciation can meanDepreciation can mean– a decrease in a decrease in market valuemarket value,,– a decrease in a decrease in the the value to the ownervalue to the owner..  

Important reasons for depreciation includeImportant reasons for depreciation include–       deteriorationdeterioration,,–       obsolescenceobsolescence..

Accountants define depreciation as follows: Accountants define depreciation as follows: the systematic allocation of the cost of an asset over its the systematic allocation of the cost of an asset over its usefuluseful, or , or

depreciable, lifedepreciable, life..

The latter definition is used for determining taxable income – hence, The latter definition is used for determining taxable income – hence, income taxes. income taxes.

Thus, this definition is most important to us.Thus, this definition is most important to us.

Market value is the value others would Market value is the value others would place on the property of interestplace on the property of interest

A machine can begin to wear out andA machine can begin to wear out andno longer perform its function as wellno longer perform its function as wellas when it was new.as when it was new.

55

Depreciation: RequirementsDepreciation: Requirements

In general, business assets can only be In general, business assets can only be depreciated if they meet the following depreciated if they meet the following basic requirements:basic requirements: The property must be used for business purposes to The property must be used for business purposes to

produce incomeproduce income

The property must have a useful life that can be The property must have a useful life that can be determined, and this life must be longer than one yeardetermined, and this life must be longer than one year

The property must be an asset that decays, gets used up, The property must be an asset that decays, gets used up, wears out, becomes obsolete, or loses value to the owner wears out, becomes obsolete, or loses value to the owner from natural causesfrom natural causes

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Depreciation Example: Joe’s Depreciation Example: Joe’s PizzaPizza

Joe runs a pizza parlor. He classifies some of his cost items as follows.Joe runs a pizza parlor. He classifies some of his cost items as follows.

Cost ItemCost Item Type of Type of CostCost

ReasonReason

Pizza dough, toppingsPizza dough, toppings ExpensedExpensed Life < 1 yr, loses value Life < 1 yr, loses value immediatelyimmediately

Delivery vanDelivery van DepreciateDepreciatedd

Meets 3 depreciation Meets 3 depreciation requirementsrequirements**

Employee wagesEmployee wages ExpensedExpensed Life < 1 yr, loses value Life < 1 yr, loses value immediatelyimmediately

Furnishings for dining Furnishings for dining roomroom

DepreciateDepreciatedd

Meets 3 depreciation Meets 3 depreciation requirementsrequirements

New baking ovenNew baking oven DepreciateDepreciatedd

Meets 3 depreciation Meets 3 depreciation requirementsrequirements

Utilities for Utilities for refrigeratorrefrigerator

ExpensedExpensed Life < 1 yr, loses value Life < 1 yr, loses value immediatelyimmediately

Req. for Depreciation:

1. The property must be used for business purposes to produce income

2. The property must have a useful life that can be determined, and this life must be longer than one year

3. The property must be an asset that decays, gets used up, wears out, becomes obsolete, or loses value to the owner from natural causes

Expensed Items: Labor, Utilities, Materials, InsuranceExpensed items are (often recurring) expenses in regular business operations. They are consumed over short periods (e.g., monthly or biweekly salaries).Expenses are subtracted from business revenues for tax purposes.Expenses reduce income taxes at the time period when they occur.Depreciated Items: van, furniture, baking oven, cash register, computer.

Usually you pay for the asset “up front”, but depreciate it over time. 

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Depreciation: OverviewDepreciation: Overview

Definition.Definition. The number of years over which a machine is The number of years over which a machine is depreciated is called its depreciated is called its depreciable lifedepreciable life or or recovery periodrecovery period..

This period may differ from the useful life - The depreciation This period may differ from the useful life - The depreciation method determines the depreciable life. method determines the depreciable life.

At least six different depreciation methods are available.At least six different depreciation methods are available.

Depreciation is a Depreciation is a non-cash costnon-cash cost. No money changes . No money changes hands. hands. 

Depreciation is Depreciation is a business expense the government a business expense the government allows to offset the loss in value of business assetsallows to offset the loss in value of business assets..  

Usually you pay for the asset “up front”, but Usually you pay for the asset “up front”, but depreciate it over time (e.g., a new truck). depreciate it over time (e.g., a new truck). 

Depreciation deductions reduce the taxable income Depreciation deductions reduce the taxable income of businesses and thus reduce the amount of tax of businesses and thus reduce the amount of tax paid.paid.

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Classes of Business PropertyClasses of Business PropertyClasses of Business PropertyClasses of Business Property

Tangible propertyTangible property can be seen, touched, and felt. can be seen, touched, and felt.– Real propertyReal property (think “real estate”) includes land, buildings, and all things growing (think “real estate”) includes land, buildings, and all things growing

on, built on, constructed on, or attached to the land.on, built on, constructed on, or attached to the land.– Personal propertyPersonal property includes equipment, furnishing, vehicles, office machinery, and includes equipment, furnishing, vehicles, office machinery, and

anything that is tangible excluding those assets defined as real property. (Note anything that is tangible excluding those assets defined as real property. (Note “personal” does not refer to being owned by a person or being private).“personal” does not refer to being owned by a person or being private).

Intangible propertyIntangible property is all property that has value to the owner but cannot be directly is all property that has value to the owner but cannot be directly seen or touched. Examples include patents, trademarks, trade names, and franchises. seen or touched. Examples include patents, trademarks, trade names, and franchises.

Examples of depreciable business assetsExamples of depreciable business assets::– Copy machines, Helicopters, Buildings, Interior furnishing, Production equipment, Copy machines, Helicopters, Buildings, Interior furnishing, Production equipment,

Computer networksComputer networksMany different types of properties that wear out, decay, or lose value can be depreciated Many different types of properties that wear out, decay, or lose value can be depreciated as business assets.as business assets.

Examples of nondepreciable business assetsExamples of nondepreciable business assets:: Land: it does not wear out, lose value, or have a determinable useful life. Indeed, often Land: it does not wear out, lose value, or have a determinable useful life. Indeed, often

it increases in value.it increases in value. Leased property: only the owner of property may claim depreciation expenses.Leased property: only the owner of property may claim depreciation expenses.

Sometimes tangible property is used for both business and personal activities, such as a Sometimes tangible property is used for both business and personal activities, such as a home office. The depreciation deduction can be taken only home office. The depreciation deduction can be taken only in proportionin proportion to the use for to the use for business expenses.business expenses.

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Depreciation Calculation Depreciation Calculation FundamentalsFundamentals

Example.Example.

A PC costs $1,800. Its annual A PC costs $1,800. Its annual depreciation charges are depreciation charges are $800, $600, and $350 for $800, $600, and $350 for three years.three years.

$1,800 is called the cost, initial cost, or cost basis.dt denotes the depreciation deduction in year t.

Thus d1 = $800, d2 = $600, and d3 = $350.

BVt denotes the book value at the end of year t.

BV0 = cost basis (e.g., $1,800)

BV1 = BV0 – d1 = cost basis – d1 (e.g., $1,000)

BV2 = BV1 – d2 = cost basis – (d1 + d2) (e.g., $400)

BV3 = BV2 – d3 = cost basis – (d1 + d2 + d3) (e.g., $50)

YearYear DepreciatioDepreciationn

Book Book ValueValue

00 $1,800$1,800

11 $800$800 $1,000$1,000

22 $600$600 $400$400

33 $350$350 $50$50

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Depreciation Calculation Depreciation Calculation FundamentalsFundamentals

BVBVtt = cost basis – (d = cost basis – (d11 + d + d22 + … + d + … + dtt))This equation is used to compute the book value of an asset at the end This equation is used to compute the book value of an asset at the end of any time t.of any time t.

Book value can be viewed as the remaining unallocated cost of an asset:Book value can be viewed as the remaining unallocated cost of an asset:

Book value = Cost – Depreciation charges made to dateBook value = Cost – Depreciation charges made to date  

Note:Note: If the item has a salvage value then the final book value will be the If the item has a salvage value then the final book value will be the salvage value.salvage value.

Example: Example: The book value of the PC declines during the useful life from a value of The book value of the PC declines during the useful life from a value of B = $1,800 at time 0 in the recovery period, to a value of S = $50 at B = $1,800 at time 0 in the recovery period, to a value of S = $50 at time 3.time 3.

Numerous depreciation methods are possible.Numerous depreciation methods are possible.

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Straight Line (SL) DepreciationStraight Line (SL) Depreciation

ExampleExample

An asset has a cost of B = An asset has a cost of B = $900, a useful life of N = 5 $900, a useful life of N = 5 years, and an EOL salvage years, and an EOL salvage value of S = $70. value of S = $70.

With SL depreciation, the With SL depreciation, the following is found:following is found:

Annual depreciation charge:Annual depreciation charge:

ddii = (B-S)/N = 830/5 = $166.  = (B-S)/N = 830/5 = $166. 

The book value of the asset The book value of the asset

decreases by $166 each yeardecreases by $166 each year

YearYear Initial Book Initial Book ValueValue

DeprDepr.. ChargeCharge

EOY Book EOY Book ValueValue

00 $900$900

11 Cost = $900Cost = $900 $166$166 734734

22 $734$734 $166$166 568568

33 568568 $166$166 402402

44 402402 $166$166 236236

55 236236 $166$166 Salvage Value Salvage Value 7070

Total Total DDeprepr.:.: $830$830

Initial Initial CostCost

Salvage Salvage ValueValue

900

70

Book Value

Useful LifeUseful Life

1 2 3 4 5 N

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Straight Line (SL) DepreciationStraight Line (SL) Depreciation

ExampleExample.. Depreciation to Intangible Property Depreciation to Intangible Property

Veronica’s firm bought a patent in April, 1Veronica’s firm bought a patent in April, 1stst. It was not acquired . It was not acquired as part of acquiring a business. as part of acquiring a business.

The firm paid $6,800 for the patent. The firm paid $6,800 for the patent. They must depreciate it using SL depreciation over 17 years, with They must depreciate it using SL depreciation over 17 years, with

no salvage value. no salvage value.

Annual depreciation is $400 = $6,800/17.Annual depreciation is $400 = $6,800/17.The firm bought the patent in April, 1The firm bought the patent in April, 1stst. . This means the This means the depreciation for the first year must be prorateddepreciation for the first year must be prorated over the 9 months of ownership. over the 9 months of ownership. Therefore the first year depreciation is (9/12) Therefore the first year depreciation is (9/12) 400 = $300. 400 = $300. In later years the depreciation can be $400.In later years the depreciation can be $400.For the last 3 months of depreciation life = (3/12) For the last 3 months of depreciation life = (3/12) 400 = $100. 400 = $100.

Straight line depreciation is the simplest and best known:Straight line depreciation is the simplest and best known:C = Annual depreciation charge = (B-S)/N.C = Annual depreciation charge = (B-S)/N.

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Sum-Of-Years Digits (SOYD) Sum-Of-Years Digits (SOYD) DepreciationDepreciation

ExampleExample An asset has a cost of B = $900, a useful life of N = 5 years, An asset has a cost of B = $900, a useful life of N = 5 years, and an EOL salvage value of S = $70. With SOYD depreciation, we and an EOL salvage value of S = $70. With SOYD depreciation, we would compute the following:would compute the following:

The product of the multiplier and B-S for the year is the depreciationcharge for the year. Note the multipliers add to 1.

Year Life, FOY Multiplier B - S Depreciation Charge EOY Book Value 0 $900 1 5 5/15 $830 $277 623 2 4 4/15 830 221 402 3 3 3/15 830 166 236 4 2 2/15 830 111 125 5 1 1/15 830 55 70

15 1 $830

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Sum-Of-Years Digits (SOYD) Sum-Of-Years Digits (SOYD) DepreciationDepreciation

  

ddtt=(N+1-t)/SOYD(B-S)= 2(N+1-t)/[N(N+1)](B-S)=(N+1-t)/SOYD(B-S)= 2(N+1-t)/[N(N+1)](B-S)

SOYD depreciation causes larger decreases in book value in earlier years than in later years.

Question. If you were a firm, would you prefer SOYD or SL depreciation?

SOYD Depreciation SOYD Depreciation looks like thislooks like this

$S

Book Value

N

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Declining Balance DepreciationDeclining Balance Depreciation

For straight line depreciation with N years, the rate of decrease each year is For straight line depreciation with N years, the rate of decrease each year is 1/N. 1/N. Declining balance depreciation uses a rate of either 150% or 200% of the Declining balance depreciation uses a rate of either 150% or 200% of the straight-line rate. straight-line rate. Since 200% is twice the straight-line rate, it is called Since 200% is twice the straight-line rate, it is called doubledouble declining declining balance (DDB). balance (DDB). The DDB equation for any year isThe DDB equation for any year is

DDB depreciation dDDB depreciation dtt = (2/N) ( Book value)  = (2/N) ( Book value) Book value = Initial cost – total charges to dateBook value = Initial cost – total charges to date , , 

So,So,DDB deprec. dDDB deprec. dtt = (2/N) (Initial cost – total charges to date) = (2/N) (Initial cost – total charges to date)

It can be shown for DDB, that the depreciation schedule in year t is given by:It can be shown for DDB, that the depreciation schedule in year t is given by:

DDB depreciation in year t = (2B/N)(1 – 2/N)DDB depreciation in year t = (2B/N)(1 – 2/N) t-1t-1

For 150% declining balance depreciation, the depreciation in year t is given by:For 150% declining balance depreciation, the depreciation in year t is given by:

DDB depreciation in year t =(1.5 B/N)(1 – 1.5/N)DDB depreciation in year t =(1.5 B/N)(1 – 1.5/N) t-1t-1..

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Declining Balance Depreciation: Declining Balance Depreciation: ExampleExample

ExampleExample An asset has a cost of B = $900, a useful life of N = 5 years, and an EOL An asset has a cost of B = $900, a useful life of N = 5 years, and an EOL salvage value of S = $70. With DDB depreciation, we would compute the following:salvage value of S = $70. With DDB depreciation, we would compute the following:

YearYear MultiplierMultiplier Cost – Cost – depreciation depreciation

charges to datecharges to date

Depreciation Depreciation ChargeCharge

EOY EOY Book Book ValueValue

00 $900$900

11 2/52/5 900900 360360 540540

22 2/52/5 540540 216216 324324

33 2/52/5 324324 130130 194194

44 2/52/5 194194 7878 116116

55 2/52/5 116116 4646 7070

$830$830

If the salvage value of this example had not been $70, a modification of DDB would be necessary.

Several possibilities exist:• stop further depreciation when the book value equals the salvage value;• “switch over” from DB depreciation to straight line.

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Modified Accelerated Cost Recovery Modified Accelerated Cost Recovery SystemSystem

((MACRSMACRS) Depreciation) Depreciation This is the newest depreciation method that can be used for This is the newest depreciation method that can be used for

income taxing purposes.income taxing purposes.

The computations are made using “property class lives” that are The computations are made using “property class lives” that are lessless than the “actual useful lives.” than the “actual useful lives.”

In 1971, the U. S. Treasury Department published guidelines for In 1971, the U. S. Treasury Department published guidelines for about 100 broad classifications of depreciable assets. For each about 100 broad classifications of depreciable assets. For each classification, there were classification, there were lower limit, midpoint, and upper limit lower limit, midpoint, and upper limit of useful life. of useful life.

This life is called the Asset Depreciation Range (ADR). The ADR This life is called the Asset Depreciation Range (ADR). The ADR midpoint lives were midpoint lives were somewhat shortersomewhat shorter than the actual average than the actual average useful lives.useful lives.

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MACRS DepreciationMACRS Depreciation

Example Class Lives and MACRS Property ClassesExample Class Lives and MACRS Property Classes

ADR: Asset Depreciation Range; GDS: general depreciation systemADS: alternative depreciation system

GDS is based on declining balance with a switch to straight line depreciation.ADS uses SL depreciation and provides for a longer period of recovery. It is less economically attractive than GDS.

IRS IRS asset asset classclass

Asset descriptionAsset description Class life Class life (years)(years)

MACRS property MACRS property class (years)class (years)

ADRADR GDSGDS ADSADS

00.1100.11 Office furniture, fixtures & equipmentOffice furniture, fixtures & equipment 1010 77 1010

00.1200.12 Information systems: Information systems: ccomputers/peripheralomputers/peripheral 66 55 66

00.2200.22 Automobiles, taxisAutomobiles, taxis 33 55 66

00.2400.24 Light general purpose trucksLight general purpose trucks 44 55 66

00.2500.25 Railroad cars & locomotivesRailroad cars & locomotives 1515 77 1515

a) Any tangible property used primarily outside of the U.S.b) Any property that is tax-exempt or financed by tax-exempt bondsc) Farming property placed in service when uniform capitalization rules are not applied

1919

MACRS DepreciationMACRS DepreciationMACRS has major advantagesMACRS has major advantages::

1. The computations are made using “property class lives” that are 1. The computations are made using “property class lives” that are lessless than the “actual useful lives”.  than the “actual useful lives”. 2. Salvage values are assumed to be zero.2. Salvage values are assumed to be zero.3. Tables of annual percentages simplify computations. 3. Tables of annual percentages simplify computations.

Steps in DepreciationSteps in Depreciationa) Determine that the property is eligible for depreciation.a) Determine that the property is eligible for depreciation.b) Calculate its depreciation deductions over its life, usingb) Calculate its depreciation deductions over its life, using1.1. the cost basis of the property;the cost basis of the property;2.2. the property class and recovery period of the asset;the property class and recovery period of the asset;3.3. the asset’s placed-in-life service date the asset’s placed-in-life service date

(1) Cost Basis.(1) Cost Basis.The cost basis B is the cost to obtain and place the asset in service fit The cost basis B is the cost to obtain and place the asset in service fit for use. For for use. For real propertyreal property the basis may also include certain fees and the basis may also include certain fees and charges the buyer pays as part of the purchase, e.g., legal and charges the buyer pays as part of the purchase, e.g., legal and recording fees, abstract fees, survey charges, transfer taxes, title recording fees, abstract fees, survey charges, transfer taxes, title insurance, and amounts the seller owes that you pay (such as back insurance, and amounts the seller owes that you pay (such as back taxes).taxes).

(3) Placement In Service.(3) Placement In Service.If the asset is a business asset, depreciation begins when the asset is If the asset is a business asset, depreciation begins when the asset is placed in service.placed in service.

2020

Property classProperty class Personal propertyPersonal property

3-Year 3-Year PropertyProperty

Special handling devices for food and beverage mfg.Special handling devices for food and beverage mfg.Special tools …Special tools …Property with ADR midpoint life of 4 years or lessProperty with ADR midpoint life of 4 years or less

5-Year 5-Year PropertyProperty

Automobiles and trucksAutomobiles and trucksAircraftAircraftComputersComputers……

7-Year 7-Year PropertyProperty

All other property not assigned to another classAll other property not assigned to another classOffice furniture, fixtures & equipmentOffice furniture, fixtures & equipmentProperty with ADR midpoint life of 10 years or more and Property with ADR midpoint life of 10 years or more and less than 16 years.less than 16 years.

10-Year 10-Year PropertyProperty

Assets used in petroleum refining & certain food Assets used in petroleum refining & certain food products.products.……Property with ADR midpoint life of 16 years or more and Property with ADR midpoint life of 16 years or more and less than 20 years.less than 20 years.

15-Year 15-Year PropertyProperty

Telephone distribution plants;Telephone distribution plants;Municipal sewage treatment plants;Municipal sewage treatment plants;Property with ADR midpoint life of 20 years or more and Property with ADR midpoint life of 20 years or more and less than 25 years.less than 25 years.

20-Year 20-Year PropertyProperty

Municipal sewers;Municipal sewers;Property with ADR midpoint life of 25 years and more.Property with ADR midpoint life of 25 years and more.

Property ClassProperty Class Real property (real estate)Real property (real estate)

27.5 years27.5 years Residential rental property (excludes hotels and motels)Residential rental property (excludes hotels and motels)

39 years39 years Nonresidential real propertyNonresidential real property

MACRS DepreciationMACRS Depreciation

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How to compute the year-to-year depreciation deductions How to compute the year-to-year depreciation deductions for GDS assets, given the MACRS property class, the for GDS assets, given the MACRS property class, the placed-in-service date, and cost basis?placed-in-service date, and cost basis?Use, for each year t, Use, for each year t,

ddtt = B = B r rtt

where where 

ddtt = depreciation deduction in year t = depreciation deduction in year tB = cost basis being depreciatedB = cost basis being depreciated

rrtt = appropriate MACRS percentage rate = appropriate MACRS percentage rate

MACRS DepreciationMACRS Depreciation

MACRS Depreciation for Personal Property – Half-year MACRS Depreciation for Personal Property – Half-year ConventionConvention

Recovery Recovery yearyear

3-yr. class3-yr. class 5-yr.5-yr. 7-yr.7-yr. 10-yr.10-yr. 15-yr.15-yr. 20-yr.20-yr.

The applicable percentage for the class of property isThe applicable percentage for the class of property is

11 33.3333.33 20.0020.00 14.2914.29 10.0010.00 5.005.00 3.7503.750

22 44.4544.45 32.0032.00 24.4924.49 18.0018.00 9.509.50 7.2197.219

33 14.8114.81** 19.2019.20 17.4917.49 14.4014.40 8.558.55 6.6776.677

44 7.417.41 11.52*11.52* 12.4912.49 11.5211.52 7.707.70 6.1776.177

55 11.5211.52 8.93*8.93* 9.229.22 6.936.93 5.7135.713

66…… 5.765.76 8.928.92 7.377.37 6.236.23 5.2855.285

……2020 4.4614.461

2121 2.2312.231

2222

timetime

Book valueBook value

SLSL

DBDB

timetime

Book valueBook value

SLSL

DBDB

MACRS DepreciationMACRS Depreciation

2323

How are MACRS Percentage Rates developed?How are MACRS Percentage Rates developed?MACRS is basically a combination of DB and SL methods. MACRS is basically a combination of DB and SL methods. It starts out as a DB method and then switches over at some point to SL. It starts out as a DB method and then switches over at some point to SL.

Three assumptions are important:Three assumptions are important:1. Salvage values are zero for all assets.1. Salvage values are zero for all assets.2. The first and last years of the recovery period are each ½ years.2. The first and last years of the recovery period are each ½ years.3. The DB rate is 200% for 3,5, 7 and 10 year property; 3. The DB rate is 200% for 3,5, 7 and 10 year property;

it is 150% for 15 and 20 year property.it is 150% for 15 and 20 year property.

A 5-year MACRS property asset has an installed and “made ready for A 5-year MACRS property asset has an installed and “made ready for use” cost basis of $100use” cost basis of $100..

MACRS DepreciationMACRS Depreciation

Year DDB Calculation SL Calculation MACRS (rt) % Rates

Cumul. Deprec.

1 ½ (2/5)(100-0) = 20 ½ (100-0)/5 = 10.00 20.00 (DDB) 20.00 2 (2/5)(100-20) = 32.00 (100-20)/4.5 = 17.78 32.00 (DDB) 52.00 3 (2/5)(100-52) = 19.20 (100-52)/3.5 = 13.71 19.20 (DDB) 71.20 4 (2/5)(100-71.20) =

11.52 (100-71.20)/2.5 = 11.52 11.52 (either) 82.72

5 11.52 11.52 (SL) 94.24 6 ½ (11.52) = 5.76 5.76 (SL) 100.00

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MACRS Depreciation: ExampleMACRS Depreciation: Example

Use the MACRS GD method. Calculate the yearly depreciation allowances and book Use the MACRS GD method. Calculate the yearly depreciation allowances and book values for a firm that has purchased $150,000 worth of office equipment. The values for a firm that has purchased $150,000 worth of office equipment. The equipment qualifies as depreciable property. Estimated salvage value is $30,000. equipment qualifies as depreciable property. Estimated salvage value is $30,000. 

Input DataInput Data 1. The assets qualify as depreciable property1. The assets qualify as depreciable property 2 B = $150,0002 B = $150,000 3. The assets placed in service in year 13. The assets placed in service in year 1 4. MACRS GD applies4. MACRS GD applies 5. Ignore the salvage value (0 with MACRS) 5. Ignore the salvage value (0 with MACRS) 

Look up office equipment in Table in page 20Look up office equipment in Table in page 20as 7-year property. as 7-year property.

Then obtain the MACRS percentages fromThen obtain the MACRS percentages fromTable in page 21.Table in page 21.

Then use the following equation Then use the following equation to compute depreciation amounts: to compute depreciation amounts: 

BVBVtt = cost basis – (d = cost basis – (d11 + d + d22 + … + d + … + dtt))

Year Year tt rrtt ((%%)) B B (($$)) ddt t (($$))

Cum. dCum. dt t

(($$)) BVBVt t (($$))

11 14.2914.29 150,000150,000 21,43521,435 21,43521,435 128,565128,565

22 24.4924.49 150,000150,000 36,73536,735 58,17058,170 91,83091,830

33 17.4917.49 150,000150,000 26,23526,235 84,40584,405 65,59565,595

44 12.4912.49 150,000150,000 18,73518,735 103,140103,140 46,86046,860

55 8.938.93 150,000150,000 13,39513,395 116,535116,535 33,46533,465

66 8.928.92 150,000150,000 13,38013,380 129,915129,915 20,08520,085

77 8.938.93 150,000150,000 13,39513,395 143,310143,310 6,6906,690

88 4.464.46 150,000150,000 6,6906,690 150,000150,000 00

SUMSUM 100.00100.00 150,000150,000

2525

Unit of Production DepreciationUnit of Production DepreciationOccasionally the recovery of depreciation on an asset is more closely related to use Occasionally the recovery of depreciation on an asset is more closely related to use than time. In such a case we can use Unit of Production (UOP) depreciation:than time. In such a case we can use Unit of Production (UOP) depreciation:

For any year, do the following:For any year, do the following:1. 1. Compute the ratio of the yearly production of the asset to its total lifetime Compute the ratio of the yearly production of the asset to its total lifetime

production.production.2.2. Multiply the ratio and (B-S) to get UOP.Multiply the ratio and (B-S) to get UOP.

This method is This method is not acceptable for general use in depreciating industrial equipmentnot acceptable for general use in depreciating industrial equipment. . It might be useful for machinery that processes natural resources when the It might be useful for machinery that processes natural resources when the resources are exhausted before the machinery wears out.resources are exhausted before the machinery wears out.

Example: Example: Asset cost Asset cost B = $900B = $900. Salvage value . Salvage value S = 70S = 70..The equipment will be used in a sand and gravel pit. The equipment will be used in a sand and gravel pit. The pit will be in operation during a five-year period The pit will be in operation during a five-year period while a nearby airport is built. while a nearby airport is built. After that time, the pit will be shut down, and After that time, the pit will be shut down, and the equipment removed and sold. the equipment removed and sold. The airport will need The airport will need 40,00040,000 cubic meters of sand cubic meters of sand and gravel. and gravel. B-S = $830B-S = $830..

YeaYearr

mm33 neededneeded

ratioratio UOP UOP deprec.deprec.

11 4,0004,000 0.10.1 $83$83

22 8,0008,000 0.20.2 166166

33 16,00016,000 0.40.4 332332

44 8,0008,000 0.20.2 166166

55 4,0004,000 0.10.1 8383

The actual UOP depreciation charge in any year is based on the actual production for the year, and not the scheduled production.