Matakuliah
Tahun
: D0762 – Ekonomi Teknik
: 2009
Depreciation and Taxes
Course Outline 12
Outline
•
•
•
•
•
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Introduction next
next
Depreciation Example
Straight Line Methodnext
SOYD next
DBD next
Switching DBD to SLnext
References :
- Engineering Economy – Leland T. Blank, Anthoy J.
Tarquin p.387-423
- Engineering Economic Analysis, Donald G. Newman,
p.261-286
2
Introduction
Depreciation is important because it affects the taxes that firms pay.
TAXES proportional to TAXABLE INCOME (PROFIT – COSTS)
COSTS = Maintenance Cost + Depreciated Initial Cost
Roughly speaking,
depreciation is a decrease in value of an asset each year.
Depreciation is a deduction from taxable income.
Thus the greater the depreciation, the less the taxable income – hence taxes.
The U. S. Government allows some choice among depreciation methods.
Obviously,
a well-run firm wants to choose the depreciation method that will minimize its
taxable income.
To do so, the firm owner/employees must understand how the depreciation
methods work.
3
Depreciation: Example
A firm has $1,000,000 of taxable income.
If its tax rate is 25%, it would pay $250,000
depreciation.
in taxes ignoring
If it can deduct $50,000 in depreciation charges, its net taxable income is
$950,000.
Thus, it would pay taxes of 0.25 (950,000) = $237,500.
Depreciation saves 250,000 – 237,500 = 12,500 = 0.25(50,000).
If it could deduct more than $50,000 it would pay even less taxes.
Individual investors encounter similar situations.
If you invest $10,000 and get a 10% return, your taxable income is $1,000.
If you are in the 25% tax bracket, U.S. takes $250, so your net return is $750
 7.5%.
4
If you could have found an 8% investment for your $10,000 that was not
Depreciation
Depreciation can mean
– a decrease in market value,
– a decrease in the value to the owner.
Important reasons for depreciation include
–
deterioration,
–
obsolescence.
Market value is the value others would
place on the property of interest
A machine can begin to wear out and
no longer perform its function as well a
when it was new.
Accountants define depreciation as follows:
the systematic allocation of the cost of an asset over its useful, or depreciable, life.
The latter definition is used for determining taxable income – hence, income taxes.
Thus, this definition is most important to us.
5
Depreciation: Requirements
In general business assets can only be depreciated if they meet the
following basic requirements:
 The property must be used for business purposes to produce
income
 The property must have a useful life that can be determined, and
this life must be longer than one year
 The property must be an asset that decays, gets used up, wears
out, becomes obsolete, or loses value to the owner from natural
causes
6
Depreciation Example: Joe’s Pizza
Joe runs a pizza parlor. He classifies some of his cost items as follows.
Cost Item
Type of Cost
Reason
Pizza dough, toppings
Expensed
Life < 1 yr, loses value immediately
Delivery van
Depreciated
Meets 3 depreciation requirements*
Employee wages
Expensed
Life < 1 yr, loses value immediately
Furnishings for dining room
Depreciated
Meets 3 depreciation requirements
New baking oven
Depreciated
Meets 3 depreciation requirements
Utilities for refrigerator
Expensed
Life < 1 yr, loses value immediately
Expensed Items: Labor, Utilities, Materials, Insurance
Expensed items are (often recurring) expenses in regular business operations.
They are consumed over short periods (e.g., monthly or biweekly salaries).
Expenses are subtracted from business revenues for tax purposes.
Expenses reduce income taxes at the time period when they occur.
Req. for Depreciation:
1.
The property must be
used for business
purposes to produce
income
2.
The property must
have a useful life that
can be determined,
and this life must be
longer than one year
3.
The property must be
an asset that decays,
gets used up, wears
out, becomes
obsolete, or loses
value to the owner
from natural causes
Depreciated Items: van, furniture, baking oven, cash register, computer.
Usually you pay for the asset “up front”, but depreciate it over time.
7
Depreciation: Overview
Definition. The number of years over which a machine is depreciated is
called its depreciable life or recovery period.
This period may differ from the useful life - The depreciation method
determines the depreciable life.
At least six different depreciation methods are available.
 Depreciation is a non-cash cost. No money changes hands.
 Depreciation is a business expense the government allows to offset the
loss in value of business assets.
 Usually you pay for the asset “up front”, but depreciate it over time
(e.g., a new truck).
 Depreciation deductions reduce the taxable income of businesses and
thus reduce the amount of tax paid.
8
Classes of Business Property
Classes of Business Property
Almost all tangible properties
can be depreciated as
business assets
•
Tangible property can be seen, touched, and felt. (It is “tangible.”)
–
Real property (think “real estate”) includes land, buildings, and all things growing on, built on, constructed on, or attached to
the land.
–
Personal property includes equipment, furnishing, vehicles, office machinery, and anything that is tangible excluding those
assets defined as real property. (Note “personal” does not refer to being owned by a person or being private.)
•
Intangible property is all property that has value to the owner but cannot be directly seen or touched. Examples include patents,
trademarks, trade names, and franchises.
Examples of depreciable business assets:
–
Copy machines, Helicopters, Buildings, Interior furnishing, Production equipment, Computer networks
Many different types of properties that wear out, decay, or lose value can be depreciated as business assets.
Examples of nondepreciable business assets:


Land: it does not wear out, lose value, or have a determinable useful life. Indeed, often it increases in value.
Leased property: only the owner of property may claim depreciation expenses.
Sometimes tangible property is used for both business and personal activities, such as a home office.
The depreciation deduction can be taken only in proportion to the use for business expenses.
9
Depreciation Calculation Fundamentals
Example.
A PC costs $1,800.
Its annual depreciation charges are
$800, $600, and $350 for three years.
Year
Depreciation
0
Book Value
$1,800
1
$800
$1,000
2
$600
$400
3
$350
$50
$1,800 is called the cost, initial cost, or cost basis.
dt denotes the depreciation deduction in year t.
Thus d1 = $800, d2 = $600, d3 = $350.
BVt denotes the book value at the end of year t.
BV0 = cost basis
(e.g., $1,800)
BV1 = BV0 – d1 = cost basis – d1
BV2 = BV1 – d2 = cost basis – (d1 + d2)
BV3 = BV2 – d3 = cost basis – (d1 + d2 + d3)
(e.g., $1,000)
(e.g., $400)
(e.g., $50)
10
Depreciation Calculation Fundamentals
BVt = cost basis – (d1 + d2 + … + dt)
This equation is used to compute the book value of an asset at the end
of any time t.
Book value can be viewed as the remaining unallocated cost of an asset:
Book value = Cost – Depreciation charges made to date
Note: If the item has a salvage value then the final book value will be the
salvage value.
Example:
The book value of the PC declines during the useful life
from a value of B = $1,800 at time 0 in the recovery period, to a value of S
= $50 at time 3.
Numerous depreciation methods are possible.
11
Straight Line (SL) Depreciation
Year
Initial Book Value
Depr. Charge
EOY Book Value
0
Example
An asset has a cost of B = $900,
a useful life of N = 5 years,
and an EOL salvage value of S = $70.
1
Cost = $900
$166
734
2
$734
$166
568
3
568
$166
402
4
402
$166
236
5
236
$166
Total Depr.:
With straight line depreciation,
we would compute the following:
Annual depreciation charge:
di = (B-S)/N = 830/5 = $166.
$900
Salvage Value 70
$830
Book Value
Initial
Cost
900
The book value of the asset
decreases by $166 each year
Salvage
Value
70
1
N
2
Useful Life
3
4
5
12
Straight Line (SL) Depreciation
Example. Depreciation to Intangible Property
Veronica’s firm bought a patent in April. It was not acquired as part of acquiring a
business.
The firm paid $6,800 for the patent.
They must depreciate it using SL depreciation over 17 years, with no salvage
value.
Annual depreciation is $400 = $6,800/17.
The firm bought the patent in April.
This means the depreciation for the first year must be prorated over the 9 months
of ownership.
Therefore the first year depreciation is (9/12)  400 = $300.
In later years the depreciation can be $400.
Straight line depreciation is the simplest and best known:
C = Annual depreciation charge = (B-S)/N.
13
Sum-Of-Years Digits (SOYD) Depreciation
Example An asset has a cost of B = $900, a useful life of N = 5 years, and an EOL
salvage value of S = $70. With SOYD depreciation, we would compute the following
Year
0
1
2
3
4
5
15
Life, FOY Multiplier
5
4
3
2
1
5/15
4/15
3/15
2/15
1/15
1
B-S
$830
830
830
830
830
Depreciation Charge
$277
221
166
111
55
EOY Book Value
$900
623
402
236
125
70
$830
The product of the multiplier and B-S for the year is the depreciation charge
for the year.
Note the multipliers add to 1.
14
Sum-Of-Years Digits (SOYD) Depreciation
dt=(N+1-t)/SOYD(B-S)= 2(N+1-t)/[N(N+1)](B-S)
Book Value
SOYD depreciation causes larger decreases in
book value in earlier years than in later years.
SOYD Depreciation
looks like this.
Question.
If you were a firm, would you prefer SOYD or SL depreciation?
$S
N
15
Declining Depreciation Balance
For straight line depreciation with N years, the rate of decrease each year is 1/N.
Declining balance depreciation uses a rate of either 150% or 200% of the straight-line rate.
Since 200% is twice the straight-line rate, it is called double declining balance (DDB).
The DDB equation for any year is
DDB depreciation dt = (2/N) ( Book value)
Book value = Initial cost – total charges to date,
So,
DDB deprec. dt = (2/N) (Initial cost – total charges to date)
It can be shown for DDB, that the depreciation schedule in year t is given by:
DDB depreciation in year t = (2B/N)(1 – 2/N)t-1
For 150% declining balance depreciation, the depreciation in year t is given by:
DDB depreciation in year t =(1.5 B/N)(1 – 1.5/N)t-1.
we just replace each “2” in the DDB formula by “1.5”.
16
Declining Balance Depreciation: Example
Example An asset has a cost of B = $900, a useful life of N = 5 years,
and an EOL salvage value of S = $70. With DDB depreciation, we would compute the following
Year
Multiplier
Cost – depreciation
Depreciation Charge
EOY Book
0
$900
1
2/5
900
360
540
2
2/5
540
216
324
3
2/5
324
130
194
4
2/5
194
78
116
5
2/5
116
46
70
$830
If the salvage value of this example had not been $70, a modification of DDB
would be necessary.
Several possibilities exist:
• stop further depreciation when the book value equals the salvage value;
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• “switch over” from DB depreciation to straight line.
We can skip these modifications because MACRS is now the legally appropriate system, and it incorporates the switch from DB to SL.
Switching DBD to SL
• General rules
– Switching recommended when the depreciation for year t by the
currently used model is less than that for a new model. The
selected depreciation Dt is the larger amount
– BV can never go below estimated SV
– We assume the estimated SV = 0 in all cases
– The underappreciated amount BV is used as new adjusted basis
to select the larger Dt, for the next switching decision
– Switching from a DB model, SV (not the DB-implied SV) used to
compute the depreciation for the new method
– Only one switch can take place during the recovery period
18
Procedure of Switching
•
For each year t, compute the two depreciation charges
For DDB : DDDB
= (d)BVt-1
For SL
•
•
: DSL=
BVt-1
n-t+1
Select the larger deprecation value so that te depreciatiaon for each year t =
1,2,3,…n, is
Dt = Dmax [DDDB, DSL}
Compute the present worth of total depreciation, PWD, using equation :
t n
PWD   Dt P / F , i, t 
t 1
19
Example 13.5
•
M-E cyberspace, Inc., has purchased a $100,000 computer-controlled on
line document imaging system with estimated imaging system with and
estimated useful life of 8 years. Compute the annual capital recovery and
compare the present worth for a)SL method, b) DDB method, c) DDB to
SL switching. i= 15%
Use recovery period = 5years
Solution
a) Compute Depreciation charges
Straight line
Dt = 1000,000-0 = $20,000
Since Dt is the same for all years t = 1,2,3…., t the P/A factor P/F in equation to
compute PWD
PWD = 20,0005(P/A,15%,5) = 20,000(3,3522) = $67,044
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•
DDB
d= 2/5 =0,40
Year t
Example 13.5
Dt
0
BVt
(P/F,15%,t)
PW of Dt
100,000
1
40,000
60,000
0,8696
34,784
2
24,000
36,000
0,76561
18,146
3
14,400
21,600
0,6575
9,468
4
8,640
12,960
0,5718
4,940
5
5,184
7,776
0,4972
2,577
$92,224
21
Switching SL-DDB
Year
DDB Model
SL Depr,
Selected Dt
P/F Factor
PW of Dt
DDDS
BVt
1
40,000
60,000
20,000
40,000
0,8696
34,784
2
24,000
36,000
15,000
24,000
0,76561
18,146
3
14,400
21,600
12,000
14,400
0,6575
9,468
4
8,640
12,960
10,800
10,800*
0,5718
6,175
5
5,184
7,776
12,960
10,800
0,4972
5,370
* Indicate switch from DDB to SL Depreciation
Note :
DSL values change each year since the adjusted BVt-1 is different. Only
I year t=1 is DSL = 20,000
Example for t =4, BV3 = $21,600 by the DDB method, and
DSL = 21,600-0 = $10,800
5-4+1
22
Calculating Income Taxes
•
Equation
Taxable income = Gross income – Expenses – Depreciation deduction
Example
Suppose that a firm for a tax has a gross income of $5,270,000 expenses (excluding
capital) of $2,927,500 and depreciation deduction of $1,874,300. What would be its
taxable income? If tax =15% what would be income tax ?
Solution
Taxable income
Income tax
= $5,270,000 - $2,927,500 – $1,874,300
= $468,200
= $468,200 x 15%
= 7,0230
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