Chapter 6
Depreciation And Income Taxes
Preliminary Statement
• The material presented in this chapter does not apply to
the current (2001) U.S. Federal Corporate Income Tax
Code relating to depreciation
• As such, parts of this chapter could be modified by
legislation enacted after publication of this text
• You may use the current depreciation rules as they may
pertain to the material in this chapter
• Access the IRS web site {www,irs.gov} for IRS
Publication 946 for the current rules and regulations
Learning Objectives
• Depreciation Terminology
• Depreciation Methods
– Straight-Line Depreciation
– Double Declining Balance Depreciation
– Modified Accelerated Cost Recovery System
(MACRS)
– Determining the MACRS Recovery Period
Depreciation – Definition
• Depreciation is the reduction of an asset’s value over time.
• Brought on by:
– Wear and tear, Use, Deterioration, Obsolescence
• Deprecation represents a proper charge against future
income produced by the asset in question.
• TANGIBLE - can be seen or touched
– Personal property - includes assets such as machinery, vehicles,
equipment, furniture, etc…
– Peal property - anything erected on, growing on, or attached to
land (Since land does not have a determinable life itself, it is not
depreciable)
• INTANGIBLE - personal property, such as copyright,
patent or franchise
Personal Property
• Personal property is the income-producing, tangible
possessions of a corporation used to conduct business.
– Not to be confused with an individual’s personal property like
clothes, furniture, etc.
• Included are:
– most manufacturing and service industry property vehicles,
– manufacturing equipment, materials handling devices,
computers, and networking equipment, telephone equipment
office furniture, refining process equipment, and much more.
Real Property
• Real property includes real estate and all improvements
– office buildings manufacturing structures, warehouses,
apartments, and other structures.
• Land itself is considered real property, but it is not
depreciable because it has an infinite life – land can
never be depreciated for tax purposes.
Importance of Depreciation
• Federal tax law defines the concept of taxable income as:
– Gross Income – Real Cash Expenses – interest – Depreciation
amounts
• Tax Due ={Taxable Income}(Tax Rate)
• Federal Tax law permits the reduction of Gross Income by
a category of elements termed “deductions”
–
–
–
–
–
Wages and salaries;
Cost of materials;
Utilities;
Interest Paid on debt;
State and local taxes paid;
Depreciable?
• Property is depreciable if it must:
– be used in business or held to produce income
– have a determinable useful life which is longer than
one year
– wear out, decay, get used up, become obsolete, or lose
value from natural causes
– not be inventory, stock in trade, or investment
property
When Depreciation Starts And Stops
• Depreciation starts when property is placed in service
for use in business or for production of income
• Property is considered in service when ready and
available for specific use, even if not actually used yet
• Depreciation stops when cost of placing it in service is
removed or it is retired from service
Tax Equation
• General Federal Tax Equation
• Taxable Income = Gross Income – {Real Expenses +
Interest Paid + Depreciation+Depletion}
• All of the above amounts EXCEPT depreciation amounts
and depletion amounts are real cash flow to the firm
• Depreciation and depletions amounts will lower the
taxable income amount and hence the tax liability if
claimed
– For every $1 of eligible deductions the resultant tax savings is
$0.30
– $1 of additional deductions saves the firm $0.30
Types of Depreciation
• 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
• Tax Depreciation
– Used by a firm for state and federal income tax reporting
– Follows strict rules and regulations.
Depreciation Terms
• The Basis (B) of an asset is:
– Purchase cost plus,
– Delivery costs plus,
– Installation costs and,
– Any other costs associated with installing and preparing the
asset for use.
• Book Value of an Asset (BVt)
– The remaining, undepreciated capital investment on the firm’s
books after the accumulated amounts of depreciation have been
subtracted from the original cost basis.
– BV’s are usually updated at the end of the firm’s accounting
year.
Market Value
• Market Value (MVt)
– Market value is the estimated amount realizable if the
asset were sold on the open market.
– Because of the structure of depreciation laws, the book
value and market value may substantially differ.
– For example, a commercial building tends to increase in
market value, but the book value will decrease as
depreciation charges are taken
Salvage Value
• Salvage Value (SV) is the estimated trade-in or
market value at the end of the asset's useful life
– Expressed as an estimated dollar amount or as a
percentage of the first cost
– Salvage values are estimated “up-front” – at the time
of the original purchase.
– Generally speaking, one cannot depreciate an asset
below its estimated salvage value.
Depreciation Models
• Basic (traditional) models are:
– Straight-Line Method (SL),
– Sum-of-the-Years Digits Method (SYD),
– Declining Balance Method (DB).
• Today, the MACRS Method (a form of
declining balance-modified).
History
• Before 1981 – U.S. code recognized the classical
methods.
• 1981 and after:
– Classical methods were disallowed for federal tax purposes
and replaced with a system termed ACRS – Accelerated
Capital Recovery System
– In 1986 ACRS was replaced with MACRS – Modified
Accelerated Capital Recovery System.
• Today--U.S. Federal Corporate Income Taxes must be
computed using the MACRS system!
• States generally permit all or part of the classical
methods to be used for state corporate tax analysis
Recover Period
• Recovery Period -- Number of years over which basis
of property is recovered through accounting process.
– Normally the useful life for classical methods
– Property class for General Depreciation System (GDS)
under MACRS
– Class Life for Alternative Depreciation System (ADS)
• If useful life not given
– Use class life (Table 6-2) for SL and DB
• Use Property Class (Table 6-2 or 6-4)
– MACRS (General Depreciation System)
Depreciation Concepts
• The following terms are used in the classical (historical)
depreciation method equations:
–
–
–
–
–
–
–
–
N = depreciable life of the asset in years
B = cost basis, including allowable adjustments
d k = annual depreciation deduction in year k (1< k <N)
d k* = cummulative depreciation through year k
BV k = book value at the end of year k
BV N = book value at the end of the depreciable (useful) life
SV N = salvage value at the end of year N
R = the ratio of depreciation in any one year to the BV at the
beginning of the year
Straight-Line: The Standard (SL)
• Assumes the book value declines in a uniform manner
down to a specified salvage value – S over n time periods
• Compute the Basis minus the estimated salvage value and
divide by n
d k = ( B - SVN ) / N
d k* = kdk for 1 < k < N
BVk = B - d k*
Declining Balance Method (DB)
• DB is an accelerated depreciation method;
• Provides greater depreciation amounts in the early time
periods over the SL method
• Requires assuming a DB rate (R)
• dk for year k is found by multiplying the beginning of
time period book value by the rate (R)
• The maximum DB rate set by law is:
– By law, the maximum rate for DB is specified to
RMAX=2(1/N), or twice what the straight rate would be
– If R = 1.5 (SL rate), it is termed the 150% DB rate
Declining Balance (DB) Method
• Assumed depreciation is fixed percentage of BV at
beginning of year
d1=B(R)
d k = B ( 1 - R ) k-1( R )
d k* = B [ 1 - (1 - R ) k ]
BV k = B ( 1 - R ) k
BV N = B ( 1 - R ) N
• Because declining balance method never reaches BV = 0,
it’s permissible to switch from this to straight-line method
Example
• A computer was purchased for $20,000 and $2,000 was
spent installing it. The computer has an estimated
salvage value of $4,000 at the end of its class life.
Compute the depreciation deduction in year 3 and the
book value at the end of year 6 using:
• a) straight-line method
• b) 200% declining balance method
Solution
• Compute the Cost Basis (B); B =...
• Determine the Class Life
From Table 6-2, N = ...
• Straight Line Method
– d 3 = [( B - SVN ) / N ] = [(22,000-4000)/6)]=$3,000
– BVk = B - d k* = BV6=
• 200% Declining Balance
R = 2/6 = 1/3 = 0.33; d k = B ( 1 - R ) k - 1 ( R )
d3 = B (1-R)k-1 (R) = 22,000(0.67)2 (0.33) =
d k* = B [ 1 - (1 - R ) k ]= d 6* = 22000 [ 1 - (1 - 0.33 ) 6 ]=...
• note: BV6 = B - d6* =
SL and DB Comparison
Straight Line 200%
Declining Balance
--------------------------------------------------------------------EOY
0
1
2
3
4
5
6
dk
0
3,000
3,000
3,000
3,000
3,000
3,000
BVk
22,000
19,000
16,000
13,000
10,000
7,000
4,000
dk
0
7,333
4,889
3,259
2,173
1,448
966
BVk
22,000
14,667
9,778
6518
4,345
2,897
1,931
MACRS Method
• MACRS was derived from the 1981 ACRS system and
went into effect in 1986.
• Defines statutory recovery (depreciation) percentages
• Percentages were derived from the DB method with a
switch to SL at the optimal time and incorporates the
half-year convention.
• The MACRS approach assumes a salvage value of “0”
even though that might not be the case!
• By current law – MACRS assumes all assets
depreciated by this method will have a “0” salvage
value at the end of the recovery life
The Half-Year Convention
• During a tax year, assets are purchased and installed
throughout the first year.
• The half-year convention assumes that assets are placed in
service or disposed of in midyear, regardless of when these
events actually occur during the 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 year is handled using
the half-year convention.
• If asset is disposed of before the full recovery period is
used, only half of the normal depreciation deduction can be
taken for that year
MACRS Recovery Periods
• For Personal Property the following MACRS recovery
periods apply:
– 3- years,5-years,7-years,10-years,15-years and, 20-years.
• Property Classes
– 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 Personal Property Recovery Rates
Year-t
3-Year
5-Year
7-Year
10-Year
15-Year
20-Year
1
0.3333
0.4445
0.1481
0.0741
0.2000
0.3200
0.1920
0.1152
0.1152
0.0576
0.1429
0.2449
0.1749
0.1249
0.0893
0.0892
0.0893
0.0446
0.1000
0.1800
0.1440
0.1152
0.0922
0.0737
0.0655
0.0655
0.0656
0.0655
0.0328
0.0500
0.0950
0.0855
0.0770
0.0693
0.0623
0.0590
0.0590
0.0591
0.0590
0.0591
0.0590
0.0591
0.0590
0.0591
0.0295
0.0375
0.0722
0.0668
0.0618
0.0571
0.0529
0.0489
0.0452
0.0446
0.0446
0.0446
0.0446
0.0446
0.0446
0.0446
0.0446
0.0446
0.0446
0.0446
0.0446
0.0223
1.0000
1.0000
1.0000
1.0000
1.0000
1.0000
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Note, for each life
category there are N+1
percentage values where
N is the class life.
N+1 Rule
• Note, for each life category there are N+1 percentage
values where N is the class life
• Why is this the case?
• The actual recovery of a given class life assumes a halfyear convention.
• That is, it is assumed by law that an asset is placed inservice 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.
Property Classes – Examples
• 3-Year Property:
– Special manufacturing and handling devices, tractors and
racehorses.
• 5-Year Property:
– Computers and peripherals, Duplicating equipment,
Automobiles, trucks, buses, Cargo containers, Some
manufacturing equipment.
• 7-Year Property Class:
– 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!
Property Classes – continued
• 10-Year Class:
– Water transportation equipment, Petroleum refining,
Agricultural processing equipment, Durable goods
manufacturing equipment, Ship building
• 15-Year Class:
– Land improvements, Landscaping, Pipelines,
– Nuclear power production equipment, Telephone distribution
and switching equipment.
• 20-Year Class:
– Municipal sewers, (developers), Farm buildings, Telephone
switching equipment, Power production equipment, Water
utilities equipment.
The Alternate Depreciation System
• The IRS offers what is termed the Alternate
Depreciation System – ADS.
• It is a modified form of the MACRS system.
• Applies a straight-line approach with the half-year
convention.
– Generally used by small or growing firms that do not have
sufficient taxable income now and in the immediate future.
– Some firms may not be generating sufficient profits to take
advantage of the more accelerated depreciation rates that the
MACRS-GDS provides.
– Thus, if GDS is elected, the firm may be losing deductions in
the early years.
– ADS provides some relief for firms in this situation.
ADS or GDS
• For both the ADS and the GDS:
– For a given tax year the firm elects either the:
• ADS system for all assets placed in service for the current
tax year or,
• The GDS (accelerated method) for all assets placed in
service for the current tax year.
• The firm cannot mix ADS with GDS within the tax
year! (It must be one or the other.)
• In engineering economy analysis of industrial projects:
– Most analysis will be accomplished using the GDS –
accelerated depreciation rates.
ADS: Overview: 5-Year Example
• ADS applies a form of the straight-line method with the
half-year convention.
• Assume 5-Year Property Class;
– N = 5, R = 0.20 per year except in the first year and in the last
year (N=6)
– Year 1: R1 = ½(0.20) = 0.10 or 10% of B
– Years 2-5 = 0.20 or 20% of B;
– Remaining amount – 10% flows over to the last year, k= 6.
Information Needed To Calculate
MARCS Depreciation
1. The cost basis
2. The date the property was placed in service
3. The property class and recovery period
4. The MACRS depreciation used (GDS or ADS)
5. The time convention that applies (half year)
Book Value Plot for Classical Methods
• For SL, DB, and MACRS we have:
•SL book values decline in
a linear fashion down to a
specified salvage value.
•The DB method allows the
book value to accelerate
faster since the DB plot of
book value is below the SL
book values
•MACRS also permits
accelerated book values,
but is not as good as the
pure DB method permits.
Accelerating Depreciation
• The SL methods writes off the asset in equal amounts
over the recovery period.
• The DB method permits greater depreciation amounts in
the early years, and hence reduces the book value faster
than the SL method.
• Likewise for the MACRS method!
• More depreciation in the early years means more tax
savings sooner.
• Larger depreciation amounts early on result in increased
PW of future tax savings to the firm.
Example
• The La Salle Bus Company has decided to purchase a
new bus for $85,000, with a trade-in of their old bus. The
old bus has a trade-in value of $10,000. The new bus will
be kept for 10 years before being sold. Its estimated
salvage value at that time is expected to be $5,000.
• Compute the following quantities using (a) the straightline method, (b) the 200% declining balance method, and
(c) the MACRS method.
1. depreciation deduction in the first year and the fourth year
2. cumulative depreciation through year four
3. book value at the end of the fourth year
Solution
• First, we must calculate the cost basis.
B = $10,000 + $85,000 = $95,000
• Next, we must determine the depreciable life.
From Table 6-2, the class life = 9 years and the GDS recovery
period = 5 years for buses.
• SL
dk =(95000-5000)/9 = $10,000;
1. d1 = d 4 = $… ;
2. d4* = 4 ($10,000) = $40,000;
3. BV4 = B - d4* = $95,000 - $40,000 = $55,000
200% Declining Balance Method
• R=2/9; d 1 = B ( R )= 95000(2/9)=...
1. d k =B(1 - R) k - 1 ( R )= d 4 = 95000(1 - (2/9) )3 (2/9)=...
2. d k* = B [ 1 - (1 - R ) k ]= ...
3. BV k = B ( 1 - R ) k
• MACRS Method (Note: A class life = 9 years
corresponds to an MACRS recovery period = 5 years
1. d1 = (0.2) ($95,000) = $19,000
d4 = (0.1152) ($95,000) = $10,944
2. d4* = $95,000 (0.2 + 0.32 + 0.192 + 0.1152) = $
3. BV4 = $95,000 - $78,584 = $
• What happens if the asset is sold before the end of the recovery
period?-- can only take half of the normal MACRS deduction
• For example, if the bus is sold in year 4, d4 = $95,000 (0.1152)
(0.5) = $5,472