Download - 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.
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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.
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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.
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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 structures
Land is Real Property, but by law is NOT depreciable for tax purposes
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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.
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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.
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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
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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 dn
Excel Function: Dt = SLN(B,S,n)
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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
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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
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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
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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
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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
……………………………………………………………………………………………………
……
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Declining Balance Expressions
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
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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
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Declining Balance Expressions
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
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Example 16.2,
Page 420
Blank, 7th ed.
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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
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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.
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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.
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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
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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!
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MACRS Recovery Periods
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
Farm buildings,
Telephone switching equipment,
Power production equipment,
Water utilities equipment.
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MACRS Recovery Periods
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.
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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
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MACRS vs. DDB : Example
Example from Blank, 7th ed. Example 16.4, p. 424 DDB, MACRS
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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
Bo
ok
Va
lue
YEARS
YEARS
MACRS
DDB
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