Depreciation

Lecture No.20Chapter 8Fundamentals of Engineering EconomicsCopyright © 2008

• Definition: Loss of value for a fixed asset between two periods• Example: Market values of a vehicle over 5 years

Dep

reciation

End of Year

Market

Value

Loss of

Value

2004

2005

2006

2007

2008

2009

$20,00014,00010,000

7,0005,0004,000

$6,0004,0003,0002,0001,000

What is Depreciation?

Depreciation Concept

Economic Depreciation

Purchase Price – Market Value(Economic losses due to both physical deterioration and technological obsolescence)

Accounting DepreciationA systematic allocation of the cost basis over a period of time.

Factors to Consider in Asset Depreciation

Depreciable life (how long?)

Salvage value (disposal value)

Cost basis (depreciation basis)

Method of depreciation (how?)

What Can Be Depreciated? Assets used in business or held for production of income

Assets having a definite useful life and a life longer than one year

Assets that must wear out, become obsolete or lose value

A qualifying asset for depreciation must satisfy all of the three conditions above.Note: You never depreciate “land.”

Cost of a new hole-punching machine (Invoice price) $62,500

+ Freight 725

+ Installation labor 2,150

+ Site preparation 3,500

Cost basis to use in depreciation calculation

$68,875

Cost BasisCost basis – the total cost that is claimed as an expense over an asset's life, which includes the actual cost of the asset and all incidental expensessuch as freight, insurance, and site preparation.

Old hole-punching machine (book value) $4,000

Less: Trade-in allowance 5,000

Unrecognized gains $1,000

Cost of a new hole-punching machine $62,500

Less: Unrecognized gains (1,000)

Freight 725

Installation labor 2,150

Site preparation 3,500

Cost of machine (cost basis) $67,875

Cost Basis with Trade-In Allowance

Asset Depreciation Ranges (ADRs)

Book Depreciation In reporting net income to investors/stockholders In pricing decision

Tax Depreciation In calculating income taxes for the IRS In engineering economics, we use depreciation

in the context of tax depreciation

Types of Depreciation

Types of Accounting Depreciation and Their Primary Purposes

Book Depreciation Methods Purpose: Used to report net income to

stockholders/investors Types of Book Depreciation Methods:

Straight-Line Method Declining Balance Method Unit Production Method

Straight – Line (SL) Method

Principle A fixed asset as providing its service in a uniform fashion over its life

Formula•Annual Depreciation

Dn = (I – S) / N, and constant for all n.•Book Value

Bn = I – n (D)where I = cost basis

S = Salvage value N = depreciable life

Example 8.2 – Straight-Line Method

D1

D2

D3

D4

D5

B1

B2B3

B4

B5

$10,000

$8,000

$6,000

$4,000

$2,000

0 1 2 3 4 5

Total depreciation at end of

lifen Dn Bn

1 1,600 8,4002 1,600 6,8003 1,600 5,2004 1,600 3,6005 1,600 2,000

I = $10,000N = 5 YearsS = $2,000D = (I - S)/N

Annual Depreciation

Book Value

n

Declining Balance Method• Principle:

A fixed asset as providing its service in a decreasing fashion• Formula

• Annual Depreciation

• Book Value

1 nn BD 1)1( n

nB )1( where 0 << 2(1/N)

Note: if is chosen to be the upper bound, = 2(1/N),

we call it a 200% DB or double declining balance method.

Example 8.3 – Declining Balance Method

D1

D2

D3

D4D5

B1

B2

B3

B4 B5

$10,000

$8,000

$6,000

$4,000

$2,000

0 1 2 3 4 5

Total depreciation at end of

life

$778

Annual Depreciation

Book Value

n012345

Dn

$4,0002,4001,440

864518

Bn$10,000

6,0003,6002,1601,296

778

I

N

S

D B

I

B I

n n

n

nn

= $10,

= years

= $778

=

= ( -

000

5

1

1

1

1

( )

n

• SL Dep. Rate = 1/5• (DDB rate) = (200%) (SL rate)

= 0.40

Asset: Invoice Price $9,000 Freight 500 Installation 500

Depreciation Base $10,000Salvage Value 0Depreciation 200% DBDepreciable life 5 years

Example 8.4 DB Switching to SL

n Depreciation

Book

Value

12345

10,000(0.4) = 4,000 6,000(0.4) = 2,400 3,600(0.4) = 1,440 2,160(0.4) = 864 1,296(0.4) = 518

$6,0003,6002,1601,296

778

n

Book

Depreciation Value

12345

4,000 $6,0006,000/4 = 1,500 < 2,400 3,6003,600/3 = 1,200 < 1,440 2,1602,160/2 = 1,080 > 864 1,0801,080/1 = 1,080 > 518 0

(a) Without switching (b) With switching to SL

Note: Without switching, we have not depreciated the entirecost of the asset and thus have not taken full advantage of depreciation’s tax deferring benefits.

Case 1: S = 0

End of Year

Depreciation Book Value

1 0.4($10,000) = $4,000 $10,000 - $4,000 = $6,000

2 0.4(6,000) = 2,400 6,000 – 2,400 = 3,600

3 0.4(3,600) = 1,440 3,600 –1,440 = 2,160

4 0.4(2,160) = 864 > 160 2,60 – 160 = 2,000

5 0 2,000 – 0 = 2,000

Note: Tax law does not permit us to depreciate assets belowtheir salvage value.

Case 2: S = $2,000

Units-of-Production Method

PrincipleService units will be consumed in a non

time-phased fashion

Formula•Annual Depreciation

Dn = Service units consumed for yeartotal service units

(I - S)

Example 8.5 Units-of-Production Depreciation

Given: I = $55,000, S = $5,000, Total service units = 250,000 miles, usage for this year = 30,000 miles

Solution:

30,000($55,000 $5,000)

250,000

3($50,000)

25

$6,000

Dep

Tax Depreciation Purpose: Used to compute income taxes for the IRS

Assets placed in service prior to 1981

Use book depreciation methods (SL, DB, SOYD)

Assets placed in service from 1981 to 1986

Use ACRS (Accelerated Cost Recovery System) Table

Assets placed in service after 1986

Use MACRS (Modified ACRS) Table

Modified Accelerated Cost Recovery Systems (MACRS)

Personal Property Depreciation method based on DB method

switching to SL Half-year convention Zero salvage value

Real Property SL Method Mid-month convention Zero salvage value

Recovery Period

ADR Midpoint Class Applicable Property

Personal Property

3-year Special tools for manufacture of plastic products, fabricated metal products, and motor vehicles.

5-year Automobiles, light trucks, high-tech equipment, equipment used for R&D, computerized telephone switching systems

7-year Manufacturing equipment, office furniture, fixtures

10-year Vessels, barges, tugs, railroad cars

15-year Waste-water plants, telephone- distribution plants, or similar utility property.

20-year Municipal sewers, electrical power plant.

Real Property

27.5-year

Residential rental property

39-year Nonresidential real property including elevators and escalators

ADR 4

4 10 ADR

10 16 ADR

16 20 ADR

20 25 ADR

25 ADR

ADR: Asset Depreciation Range

MACRS Property Classifications

MACRS Depreciation Schedules for Personal Property with Half-Year Convention

Example 8.6 MACRS Depreciation: Personal Property

Year (n)12

3

4

56

Calculation in %(0.5)(0.40)(100%) 20%(0.4)(100%-20%) 32%

SL = (1/4.5)(80%) 17.78%

(0.4)(100%-52%) 19.20%

SL = (1/3.5)(48%) 13.71%

(0.4)(100%-71.20%) Switch to SL 11.52%SL = (1/2.5)(29.80%) 11.52%

SL = (1/1.5)(17.28%) 11.52%SL = (0.5)(11.52%) 5.76%

MACRS (%)DDB

DDB

DDB

SL

SL

MACRS Percentage Calculation: 5-Year Property

MACRS for Real Property

• 27.5-year (Residential)• 39-year (Commercial)

• SL Method• Zero salvage value• Mid-month convention

•Example: Placed a residential property in service in March. Find the depreciation allowance in year 1. D1 = (9.5/12)(100%/27.5)

= 2.879%

Types of Real Property

Underlying assumptions

9.5 months

Jan Dec

Depreciation Allowances for a 10-year Ownership of the PropertyYear (n) Calculation Allowed Depreciation (%)

1 (9.5/12)(100%/27.5) 2.8788%

2 100%/27.5 3.6364%

3 100%/27.5 3.6364%

4 100%/27.5 3.6364%

5 100%/27.5 3.6364%

6 100%/27.5 3.6364%

7 100%/27.5 3.6364%

8 100%/27.5 3.6364%

9 100%/27.5 3.6364%

10 (11.5/12)(100%/27.5) 3.4848%Assume that the property will be sold in December of the10th year.

The entire cost of replacing a machine cannot be properly charged to any one year’s production; rather, the cost should be spread (or capitalized) over the years in which the machine is in service.

The cost charged to operations during a particular year is called depreciation.

From an engineering economics point of view, our primary concern is with accounting depreciation; The systematic allocation of an asset’s value over its depreciable life.

Summary

Component of Depreciation

Book Depreciation Tax depreciation (MACRS)

Cost basis Based on the actual cost of the asset, plus all incidental costs such as freight, site preparation, installation, etc.

Same as for book depreciation

Salvage value Estimated at the outset of depreciation analysis. Make sure that the book value cannot be lower than the salvage value at any time.

Salvage value is zero for all depreciable assets

Component of

Depreciation

Book Depreciation Tax depreciation (MACRS)

Depreciable life

Firms may select their own estimated useful lives or follow the government guidelines for asset depreciation ranges (ADRs)

Eight recovery periods– 3,5,7,10,15,20,27.5,or 39 years– have been established; all depreciable assets fall into one of these eight categories.

Method of depreciation

Firms may select from the following: Straight-lineAccelerated methods (declining balance, double declining balance)Units-of-proportion

Exact depreciation percentages are mandated by tax legislation but are based largely on DDB and straight-line methods.