Lecture # 7 depreciation i

Lecture # 7
Cost Estimation
Depreciation – part 1
16-1
Dr. A. Alim

What is Depreciation ?
 Federal tax law permits the reduction of Gross
Income (GI) by a category of elements termed
“deductions”.
 Deductions are the costs incurred.
 Costs are divided into two categories
* expensed costs (E)
* capitalized (depreciated) costs (D)
 Expensed costs are those consumed over short
periods of time. They do not lose value gradually over
time. Examples are wages, utilities, materials,
insurance,..etc
 These expenses are written off (deducted) in the year
they occur.
16-2 © 2005 by McGraw-Hill, New York, N.Y All Rights ReservedSlide Sets to accompany Blank & Tarquin, Engineering
Economy, 6th Edition, 2005

What is Depreciation ?
 Capitalized costs are due to capital assets. They are
not written off when they occur. Capital assets lose
value gradually and are depreciated over an extended
period of time.
 In general, a business asset can be depreciated if it
meets three criteria:
1) The property must be used to produce income.
2) Must have a defined service life longer then one
year.
3) The asset wears out, decays, becomes obsolete, or
loses value over the useful life.
 Depreciation thus is how the government allows
businesses to recover the lost value of their capitalized
assets over a period of time.

Depreciation is a tax Deduction
 While expenses are real cash flows, depreciation
amounts represent “non-cash flow” streams within
an accounting period.
 Federal and state tax laws recognize various forms
of depreciation amounts to be “tax deductible” –
but are not real cash flows per se.

Important Terms
 First Cost or Unadjusted Basis - B
 Initial purchase price + all
costs incurred in placing the
asset in service
 Book Value - BV
 Remaining undepreciated
capital investment on the
accounting books
 Recovery Period – n
 Depreciable life of the asset in
question – often set by law
 Market Value - MV
 Amount realized by sale on
the open market at any time
 Salvage Value - S
 Estimated trade-in value or
market value at the end of
the asset’s useful life
 Depreciation Rate - dt
 The fraction of the first cost
removed by depreciation in
year t
 Depreciation Charge - Dt
 Amount of annual
depreciation in year t
 Personal Property
 All property except real
estate used in the pursuit of
profit or gain
 Real Property
 Real estate and
improvements, buildings
and certain structuresLand is Real Property, but by law is
NOT depreciable for tax purposes

Types of Depreciation
 Book Depreciation
Used by a firm for internal financial and
managerial management.
 Tax Depreciation
Used by a firm for state and federal
income tax reporting.
Follows strict rules and regulations.

Book Depreciation
 Value of the asset on the firm’s
accounting records at any given point in
time.
 Used for internal managerial decision
making.
 Management is free to use any method
they so choose to compute book
depreciation amounts.
 Examples of methods used:
 Straight Line,
 Declining Balance;
 Sum of the years digits;
 Other.

Tax Depreciation
 Tax Depreciation:
 Must follow current state and federal law pertaining to
acceptable methods for computing depreciation for
income tax purposes.
 US Federal Law (2001)
 MACRS Methods
 By US Federal Tax Law, all assets placed in service and
eligible for depreciation MUST use the current MACRS
methods of calculation of depreciation amounts.
 Tax Law permits states to have their own respective
depreciation methods for state income tax purposes
(complicating factor)
MACRS – Modified Accelerated Cost Recovery System

Straight Line (SL) Depreciation
 The standard on
which all other
depreciation models
are compared
t
t
Notation:
t = year (t = 1,2,...,n)
D = annual depreciation charge
B = first cost or unadjusted basis
S = Estimated salvage value
n = recovery period
d = depreciation rate
tD =(B-S)d
B-S
=
n
1
t t
t
BV B tD
d d
n
 
 
Excel Function: Dt = SLN(B,S,n)

Example:
B = $ 160,000, n = 10 years.
Tabulate the SL depreciation for each of the 10 years if S = $ 10,000
The Excel function is SLN(160000,10000,10)
Year D Acc D BV
1 $15,000.00 $15,000.00 $145,000.00
2 $15,000.00 $30,000.00 $130,000.00
3 $15,000.00 $45,000.00 $115,000.00
4 $15,000.00 $60,000.00 $100,000.00
5 $15,000.00 $75,000.00 $85,000.00
6 $15,000.00 $90,000.00 $70,000.00
7 $15,000.00 $105,000.00 $55,000.00
8 $15,000.00 $120,000.00 $40,000.00
9 $15,000.00 $135,000.00 $25,000.00
10 $15,000.00 $150,000.00 $10,000.00

Declining Balance (DB) and Double
Declining Balance (DDB) Depreciation
 DB is an accelerated
depreciation method;
 Provides greater
depreciation amounts
in the early time
periods over straight
line.
 The method is more
complex that the SL
method.
 Requires assuming a
DB rate – normally
taken to equal R x SL
rate.
 R is between 1 and 2.
Often R = 2, this is
called Double
declining balance
(DDB)
 Given the DB rate,
 Dt for year t is
found by
multiplying the
beginning of time
period book value
by the rate.
 The maximum DB
rate set by law is:
 dMAX = 2(1/n) or
twice the straight
line rate

DDB illustration, B=1000, n=5
therefore: d=2/5=0.4
n Dt BV
0 0 1000
1 0.4 (1000) (1000) (1 – 0.4)
2 0.4 (1000) (1 – 0.4) (1000) (1 – 0.4) 2
3 0.4 (1000) (1 – 0.4) 2 (1000) (1 – 0.4) 3
4 0.4 (1000) (1 – 0.4) 3 (1000) (1 – 0.4) 4
5 0.4 (1000) (1 – 0.4) 4 (1000) (1 – 0.4) 5

DB Family of Depreciation
n Dt BV
0 0 B
1 dB B(1-d)
2 dB(1-d) B(1-d) 2
3 dB(1-d) 2 B(1-d) 3
….
t dB(1-d) t-1 B(1-d) t

Declining Balance Expressions
Annual depreciation determined in either of 2 ways
 Using book value of previous year
Dt = d × (BV)t-1
 Using first cost basis B
Dt = dB(1-d )t-1
Annual book value determined in either of 2 ways
 Using first cost basis B
(BV)t = B(1-d)t
 Using sum of accumulated depreciation for years i=1 to t
(BV)t = B – ΣDi
……………………………………………………………………………………………………
……

 Annual depreciation rate for each year t, relative to
first cost B, is dt
Dt = dt B = dB (1-d)t-1
dt = d(1-d)t-1
 Salvage value is not used in DB method formulas
 Implied salvage is book value in year n
Implied S = (BV)n = B(1-d)n
 If a salvage value is estimated, and estimated S > implied S,
stop depreciating whenever expected S value is reached

Implied S is the BV at n. We have three cases:
1) Implied S > Estimated S. This leads to an asset not fully depreciated.
2) Implied S = Estimated S. Asset is “just” fully depreciated.
3) Implied S < Estimated S. Asset is fully depreciated, but in less than n years.
In this case, Excel stops depreciating the asset at time “t” years, forcing BV
to remain constant at S, with no further depreciation for the remainder of n.
The concept of Implied S
Estimated
Salvage value

Excel function for DDB depreciation:
Dt = DDB(B,S,n,t,R)
S is estimated salvage value
R is between 1 and 2. If omitted, a value of 2 is
assumed, i.e. DDB

Example 16.2,
Page 420
Blank, 7th ed.

Slide Sets to accompany Blank & Tarquin, Engineering
© 2005 by McGraw-Hill, New York, N.Y All Rights Reserved
16-19
S = 2500 B = 25000
t D Acc D BV
1 $4,167 $4,167 $20,833
2 $3,472 $7,639 $17,361
3 $2,894 $10,532 $14,468
4 $2,411 $12,944 $12,056
5 $2,009 $14,953 $10,047
6 $1,674 $16,628 $8,372
7 $1,395 $18,023 $6,977
8 $1,163 $19,186 $5,814
9 $969 $20,155 $4,845
10 $808 $20,962 $4,038
11 $673 $21,635 $3,365
12 $561 $22,196 $2,804

Modified Accelerated Cost
Recovery System (MACRS)
 MACRS was derived
from the 1981 ACRS
system and went into
effect in 1986.
 Defines statutory
recovery (depreciation)
percentages.
 Percentages were
derived from the DDB
method with a switch
to SL at the optimal
time and,
 Incorporates the half-
year convention.
 By current law – MACRS
assumes all assets
depreciated by this method
will have a “0” salvage value
at the end of the recovery
life.
 Dt = dtB
 dt is provided in tabulated
form.
 BVt = BV t-1 – Dt
 BVt = first cost – sum of
accumulated depreciation
1
t
t j
j
BV B D

  

The Half-year convention
 During a tax year, assets
are purchased and installed
throughout the first year.
 Under past laws, the first
year of depreciation had to
be prorated by the number
of months remaining in the
tax year.
 Under current federal tax
law the first and last years
are handled using the half-
year convention.
 Half-year
convention assumes
that assets are
placed in service and
disposed of in
midyear, regardless
of when these
events actually occur
during the year.
 Half-year convention
therefore adds one
year to the recovery
period.

Nominal Recovery Periods
 3- year property is really
recovered over 4 years;
 5-year property is really
recovered over 6 years;
 And so forth for each of
the other classes.
 Why is this the case?
 The actual recovery of a given
class life assumes a half-year
convention.
 That is, it is assumed by law that
an asset is placed in-service at
the middle of the first year.
 It does not matter when it is
actually placed in-service;
 So, only a ½ year of recovery is
permitted in the first year.
 Another ½ year of recovery is
added at year n+1
 MACRS depreciation rate for year
n+1 is therefore one half the rate
for year n.

MACRS Details
 Under MACRS:
 The entire basis (B) is
fully depreciated
(recovered) over a
specified number of years
(recovery periods).
 A “0” salvage value is a
functional part of the
MACRS system – by law.
 In reality, there may be a
positive, “0”, or negative
salvage value at some
point in time.
 Adjustments will have to
be made at that time.
(Disposal analysis)
 There are 8 major
classes and their
corresponding recovery
periods:
 3- years
 5-years
 7-years
 10-years
 15-years, and
 20-years
 27.5-years
 39-years
 Half-year convention
applies

MACRS Recovery Periods
 3- Year Property:
 Special
manufacturing and
handling devices,
tractors
 5- Year Property:
 Computers and
peripherals,
 Duplicating
equipment.
 Automobiles,
trucks, buses,
 Cargo containers,
 Some
manufacturing
equipment.
 7 –Year Property:
 Office furniture,
 Some
manufacturing
equipment,
 Railroad cars,
engines and
tracks,
 Agricultural
machinery,
 Petroleum
equipment and
natural gas
equipment,
 All property not in
another class!
 The 7-year class is
the ‘default’ class!

 10-Year Class:
 Water
transportation
equipment,
 Petroleum
refining,
 Agricultural
processing
equipment,
 Durable goods
manufacturin
g equipment,
 Ship building.
 15-Year Class:
 Land
improvements,
 Landscaping,
 Pipelines,
 Nuclear power
production
equipment,
 Telephone
distribution
and switching
equipment.
 20-Year Class:
 Municipal
sewers
 Farm
buildings,
 Telephone
switching
equipment,
 Power
production
equipment,
 Water
utilities
equipment.

 27.5-Year Property: (Real Property)
Residential rental property (homes and mobile
homes).
 39-Year Property (Real Property)
Nonresidential real property attached to the land, but
NOT the land itself.

MACRS Recovery Rates
Year-t 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year
1 0.3333 0.2000 0.1429 0.1000 0.0500 0.0375
2 0.4445 0.3200 0.2449 0.1800 0.0950 0.0722
3 0.1481 0.1920 0.1749 0.1440 0.0855 0.0668
4 0.0741 0.1152 0.1249 0.1152 0.0770 0.0618
5 0.1152 0.0893 0.0922 0.0693 0.0571
6 0.0576 0.0892 0.0737 0.0623 0.0529
7 0.0893 0.0655 0.0590 0.0489
8 0.0446 0.0655 0.0590 0.0452
9 0.0656 0.0591 0.0446
10 0.0655 0.0590 0.0446
11 0.0328 0.0591 0.0446
12 0.0590 0.0446
13 0.0591 0.0446
14 0.0590 0.0446
15 0.0591 0.0446
16 0.0295 0.0446
17 0.0446
18 0.0446
19 0.0446
20 0.0446
21 0.0223
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
 Current MACRS recovery
percentages for the
property classes
 Assumes a 0 salvage
value over the class life
 Has the ½ year
convention built into the
tables
 There is NO Excel
function for MACRS
 Simplifies depreciation
computations but is less
flexible than classic
methods

MACRS vs. DDB : Example
Example from Blank, 7th ed.
Example 16.4, p. 424 DDB, MACRS

Example 16.4, page 424, Blank 7th ed.

B = $400,000
S = $20,000 0 400,000 400,000
n = 3 1 266,680 133,320
2 88,880 44,444
MACRS ( Tax depreciation): 3 29,640 20,000
4 0 20,000
Year dt Dt = 400,000 X dt Cummulative D BVt
0 $400,000
1 0.3333 $133,320 $133,320 $266,680
2 0.4445 $177,800 $311,120 $88,880
3 0.1481 $59,240 $370,360 $29,640
4 0.0741 $29,640 $400,000 0
Total 1.0000 $400,000
DDB ( Book depreciation)
d = 2/3 = 0.667
Year d Dt Cummulative D BVt
0 $400,000
1 0.6667 $266,667 $266,667 $133,320
2 0.6667 $88,889 $355,556 $44,444
3 0.6667 $24,444 $380,000 $20,000
Total $380,000
Note = D3 is not 0.6667 X 44,444 =29,644, since this leads to BV less than 20,000
0
50000
100000
150000
200000
250000
300000
350000
400000
450000
BookValue
YEARS
YEARS
MACRS
DDB

Lecture # 7 depreciation i

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