CHAPTER 6
DEPRECIATION AND INCOME
TAXES
DEPRECIATION
• Decrease in value of physical properties
with passage of time and use
• Accounting concept establishing annual
deduction against before-tax income
- to reflect effect of time and use on asset’s
value in firm’s financial statements
- to match yearly fraction of value used by asset
in production of income over asset’s economic
life
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
DEPRECIABLE PROPERTY
• TANGIBLE - can be seen or touched
personal property - includes assets such as
machinery, vehicles, equipment, furniture, etc...
real 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
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
DEPRECIATION METHODS
Time Implemented
Method
Before 1981
(SL) Straight-Line
(DB) Declining Balance
(SYD) Sum-of-the-years-digits
> 1980 > 1987
(ACRS) Accelerated Cost
Recovery System
Implemented by (ERTA)
Economic RecoveryTax Act of
1981
>1986
(MACRS) Modified Accelerated
Cost Recovery System
Brought about by (TRA 86)
TaxReform Act of 1986
DEPRECIATION CONCEPTS
• Adjusted cost basis -- allowable adjustment
(increase or decrease) to original cost
basis, used to calculate depreciation and
depletion deductions
• Basis, or cost basis -- also called
unadjusted cost -- initial cost of acquiring
an asset, plus sales tax, transportation, and
normal costs of making asset serviceable
DEPRECIATION CONCEPTS
• Book Value (BV) -- Worth of depreciable
property as shown on accounting records
-- Original cost basis of property, including
adjustments, less allowable depletion or
depreciation deductions
-- Represents amount of capital remaining
invested in property and must be recovered in
future through accounting
(Book Value)k=
adjusted cost basis - Skj=1 (depreciation deduction)j
DEPRECIATION CONCEPTS
• Market Value (MV) -- Amount paid by willing
buyer to willing seller for property where no
advantage and no compulsion to transact
-- apporximates present value of what will
be received through ownership of property,
including time-value of money (or profit)
DEPRECIATION CONCEPTS
• 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)
• Recovery Rate -- Percentage for each year of
MACRS recovery period used to calculate an
annual depreciation deduction.
DEPRECIATION CONCEPTS
• Salvage Value (SV) -- Estimated value of property
at the end of useful life.
-- expected selling price of property when asset
can no longer be used productively
-- net salvage value used when expenses incurred
in disposing of property; cash outflows must be
deducted from cash inflows for final net salvage
value
-- with classical methods of depreciation,
estimated salvage value is established and used
-- with MACRS, the salvage value of depreciable
property is defined to be zero
DEPRECIATION CONCEPTS
• Useful Life -- Expected (estimated)
period of time property will be
used in trade or business or to
produce income; sometimes
referred to as depreciable life.
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 (SL) METHOD
• Simplest depreciation method
• Assumes constant amount is depreciated
each year over depreciable (useful) life
d k = ( B - SVN ) / N
d k* = kdk for 1 < k < N
BVk = B - d k*
• This method requires an estimate of the
final SV ( also the final book value at the
end of year N )
DECLINING BALANCE (DB) METHOD
• Sometimes called constant percentage method or
Matheson formula
• Assumed annual cost of depreciation is fixed percentage
of BV at beginning of year
• R is constant
R = 2 / N when 200% declining balance used
R = 1.5 / N when 150% declining balance used
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
so asset’s SVN will be zero or other desired value
SUM-OF-THE-YEARS-DIGITS (SYD) METHOD
1. Number for each permissable year of life are listed in
reverse order
2. Sum the digits of this reverse order
3. The depreciation factor for any year is the corresponding
number from the reverse order listing divided by the sum
of those digits, or the following
2 (N - k + 1 )
df = ----------------N(N+1)
4. Depreciation for any year is the product of thst year’s SYD
depreciation factor and the difference between B and the
final estimated SV
d k = ( B - SV N ) • df
SUM-OF-THE-YEARS-DIGITS (SYD) METHOD
• Book value at the end of year k
2(B - SVN)
(B - SVN)
BVk = B - ----------------- k + ----------- k (k + 1 )
N
N (N + 1)
• The cumulative depreciation through the
kth year
d k* = B - BV k
UNITS-OF-PRODUCTION METHOD
• Not based on the idea that decrease in
value of property is a function of time
• Decrease in value is mostly a function of
use
• Method results in cost basis (minus final
SV) being allocated equally over the
estimated number of units produced during
useful life of asset.
Depreciation per unit of production =
( B - SVN ) / ( Estimated lifetime production in units )
ACCELERATED COST
RECOVERY SYSTEM (ACRS)
• Recognizes an asset as belonging to
one of four (tangible) property
classes
• IRS prescribes the specific series of
depreciation per property class
• Rates are based on 150% Declining
Balance depreciation, switching to
Straight-Line
MODIFIED ACCELERATED COST RECOVERY
SYSTEM (MACRS)
• The principal method for computing depreciation
deductions for property in engineering projects.
• Applies to most tangible depreciable property placed in
service after December 31, 1986
• SVN is defined to be 0 ; useful life estimates are not used
directly in calculating depreciation amounts
• Consists of two systems for computing depreciation
deductions:
1. The General Depreciation System (GDS)
2. The Alternative Depreciation System (ADS)
Provides longer recovery period and uses only
straight-line method of depreciation
Assets depreciated under ADS include property
placed in any tax-exempt use and property used
predominantly outside the U.S.
INFORMATION NEEDED TO CALCULATE
MACRS 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)
GENERAL DEPRECIATION SYSTEM
(GDS) BASIC INFORMATION
1. Tangible depreciable property assigned to one of
six personal property classes (3, 5, 7, 10, 15 and
20-year) - Corresponds to GDS recovery period;
personal depreciable property not corresponding
to these periods is considered 7-yr property class.
2. Real property assigned to two real property
classes -- nonresidential real property and
residential rental property.
3. GDS recovery period is 39 years for
nonresidential real property (31.5 years if in
service before May 13, 1993) and 27.5 years for
residential rental property.
ALTERNATIVE DEPRECIATION SYSTEM
(ADS) BASIC INFORMATION
1. ADS recovery period for tangible personal
property is normally the same as the class life of
the property, with some exceptions ( i.e., asset
class 00.12 and 00.22 )
2. Any tangible personal property that does not fit
into one of the asset classes is depreciated using
a 12-year ADS recovery period
3. ADS recovery period for nonresidential real
property is 40 years
CALCULATING DEPRECIATION DEDUCTIONS
UNDER MACRS
Depreciation
Method
GDS
GDS
GDS
ADS
Personal
Property
Class
3-, 5-, 710-year
Approach
200% DB method
with switch to SL
when deduction greater
15- & 20150% DB method
year
with switch to SL
when deduction greater
residential
SL over fixed GDS recovery
& real rental periods
personal &
SL method over fixed ADS
real
recovery periods
HALF-YEAR TIME CONVENTIONS FOR
MACRS DEPRECIATION
CALCULATIONS
• All assets placed in service during the year
are treated as if use began in the middle of
the year -- 1/2- year depreciation is allowed
• 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 (GDS) PROPERTY CLASSES AND CLASS LIFE
GDS Property Class and
Class Life
Depreciation Method
3-year, 200% DB with
4 years or less
switchover to SL
5-year, 200% DB with
More than 4 years
switchover to SL
to less than 10 years
7-year, 200% DB with
10 years to less than
switchover to SL
16
10-year, 200% DB with
16 years to less than
switchover to SL
20
15-year, 150% DB with
20 years to less than
switchover to SL
25
20-year, 150% DB with
25 years or more
switchover to SL
27.5 year, SL
N/A
39-year, SL
N/A
MACRS DEPRECIATION
GDS OR ADS ?
MACRS DEPRECIATION
GDS OR ADS ?
GDS
Ascertain property
class;
Same as recovery
period for personal
ADS
Ascertain recovery
period
MACRS DEPRECIATION
GDS OR ADS ?
GDS
Ascertain property
class;
Same as recovery
period for personal
Obtain recovery rates
ADS
Ascertain recovery
period
Compute depreciation
amount;
Asset’s cost basis
SL = -------------------------Recovery period
MACRS DEPRECIATION
GDS OR ADS ?
GDS
Ascertain property
class;
Same as recovery
period for personal
Obtain recovery rates
Compute depreciation
deduction in year k (dk)
by multiplying cost basis
by recovery period.
ADS
Ascertain recovery
period
Compute depreciation
amount;
Asset’s cost basis
SL = -------------------------Recovery period
Compute depreciation
deduction in year k (dk)
DEPLETION
• Used to indicate the decrease in the
value of the resource base when
natural resources are being consumed
in producing products or services.
• Term most commonly used in
connection with mining properties, oil
and gas wells, timberlands, etc...
• Amounts charged as depletion cannot
be used to replace sold resources
PAYMENTS TO RESOURCE
OWNERS
Annual payments to resource
owners consist of two parts:
1. Earned profit
2. Portion of owner’s capital
returned, marked as depletion
TWO WAYS TO COMPUTE
DEPLETION ALLOWANCE
1. Cost method
Applies to all types of property and is more
widely used method
Depletion unit is determined by dividing
adjusted cost basis by the number of units
to be mined or harvested
Depletion allowance for tax year is the
product of the number of units sold times
the depletion unit
TWO WAYS TO COMPUTE
DEPLETION ALLOWANCE
2. The Percentage Method
Based on percentage of year’s gross income,
provided amount charged does not exceed 50% of
net income (before deduction of depletion
allowance)
Can be used for most types of metal mines,
geothermal deposits and coal mines
Can not be used for timber and, in most cases, is
not applicable to oil and gas
When percentage method applies, depletion
allowance must be calculated by cost and
percentage method -- the larger of the two applies
TYPES OF TAXES
1. Income taxes - assessed as a function of gross revenues
minus allowable deductions
- levied at federal, most state, and some municipal
governments
2. Property taxes - assessed as a function of owned
property value;
- independent of income or profit of firm
- levied at municipal, county, and / or state level
3. Sales taxes - assessed on purchases of goods and
services
- independent of gross income or profits
- relevent to engineering studies as added cost
4. Excise taxes - assessed on sale of certain nonessential
goods and services
- independent of business income and profit
BEFORE-TAX MARR
( Before Tax MARR ) [ ( 1- effective income tax rate ) ] ~
~ After Tax
MARR
BEFORE-TAX MARR
( Before Tax MARR ) [ ( 1- effective income tax rate ) ] ~
~ After Tax
MARR
After-tax MARR
Before-tax MARR ~ -------------------------------~
( 1 - effective tax rate )
BEFORE-TAX MARR
( Before Tax MARR ) [ ( 1- effective income tax rate ) ]
~
~ After Tax MARR
-
After-tax MARR
Before-tax MARR ~-------------------------------~( 1 - effective tax rate )
• If the asset is nondepreciable and there are no
gains or losses on disposal, tax credits, or other
types of deductions involved this approximation
in the equation above is exact
BEFORE-TAX MARR
( Before Tax MARR ) [ ( 1- effective income tax rate ) ] ~
~ After Tax
MARR
After-tax MARR
Before-tax MARR ~ -------------------------------~
( 1 - effective tax rate )
• If the asset is nondepreciable and there are no
gains or losses on disposal, tax credits, or other
types of deductions involved this approximation
in the equation above is exact
• Otherwise, some degree of error is introduced,
since the factors cited affect amount and timing
of income tax payments
CALCULATING TAXABLE INCOME
- NET INCOME BEFORE TAXES ( NIBT ) • Calculate Gross Income
Gross Profits ( revenues from sales - cost of
goods sold )
+ income from dividends, interest, rent, royalties,
and gains (losses) from sale or exchange of
capital assets
• Deduct all ordinary and necessary
operating expenses to conduct business
Include interest but exclude capital investments
• Deduct depreciation
taxable income = gross income - all expenses - depreciation
NET INCOME AFTER TAXES
(NIAT)
• The income after taxes have
been deducted from the
taxable income or Net Income
Before Taxes
Net Income After Taxes = NIBT - income taxes
EFFECTIVE (MARGINAL) CORPORATE
INCOME TAX RATE
• As personal income tax rates are based on
income brackets, so, too, is corporate
income tax
• Depending on the bracket a firm’s income
falls within, the marginal federal rate can
vary from 15% to a maximum of 39% (for
incomes between $100,000 and $335,000)
• Incomes above $18,333,333 are taxed at a
flat rate of 35%
– TRA 86 responsible for lowering maximum rate from
46% to 35%
– Also created alternative minimum tax (AMT)
GAIN (LOSS) ON DISPOSAL OF A
DEPRECIABLE TANGIBLE ASSET
[ GAIN (LOSS) ON DISPOSAL ] N = MVN - BVN
• If gain, referred to as depreciation recapture
• Tax for gain (loss) is usually the same as
ordinary income gain (loss) -- effective
income tax rate, t
• For capital asset sold or exchanged, gain
(loss) referred to as capital gain (loss)
• capital assets are stocks, bonds, gold,
silver, other metals, and real property
BEFORE-TAX ECONOMIC ANALYSIS
NIBT = ( Rk – Ek- dk )
Tk = - t ( Rk – Ek – dk )
Rk = revenues (and savings from the project: cash inflow from
project during period ‘k’
Ek = cash outflows during year k for deductible expenses and
interest
dk = sum of all noncash, or book costs during year ‘k’, such
as depreciation and depletion
t = effective income tax rate on ordinary income (federal,
state and other); assumed to remain constant during the
study period
Tk= income taxes paid during year ‘k’
ECONOMIC VALUE ADDED
(EVA)
An economic measure for estimating
wealth creation potential of capital
investments:
EVA = (Net Operating Profit After Taxes )k – Cost of
Capital Used to Produce Profit)k
EVA = NOPATk – i . BVk-1
Where k = index for year in question (1 < k < N)
i = after-tax MARR based on firm’s cost of capital
BVk-1= Beginning of year book value
N = the study (analysis) period in years
ECONOMIC VALUE ADDED
(EVA)
• NOPATK = ( 1 –t ) ( Rk – Ek –dk)
• EVAk = ( 1 –t ) ( Rk – Ek –dk) – i . BVk-1
When k > 0, ATCFk = ( 1 –t ) ( Rk – Ek –dk) + dk
When k = 0, ATCF0 = BV0
• ATCFk = EVAk + i . BVk + dk
dk is the sum of all noncash, or book costs during
the year k, such as depreciation or depletion