10. depreciation
TRANSCRIPT
10: Depreciation
Dr. Mohsin Siddique
Assistant Professor
Ext: 29431
Date:
Engineering Economics
University of SharjahDept. of Civil and Env. Engg.
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Part I
Outcome of Today’s Lecture
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� After completing this lecture…
� The students should be able to:.
� Describe depreciation
� Distinguish various types of depreciable property and differentiate between depreciation expenses and other business expenses. .
� Use depreciation methods to calculate the annual depreciation charge and book value over the asset's life.
Depreciation
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� Introduction
� Depreciation Calculation Fundamentals
� Depreciation Methods:
� Straight Line
� Sum of Year’s Digits
� Declining Balance
Depreciation
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� Depreciation is a decrease in value of an asset each year:� a decrease in market value
� a decrease in the value to the owner
� Important reasons for depreciation include� deterioration
� obsolescence
� 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 income taxes, which is most important because it affects the taxes that firms pay:� TAXES proportional to TAXABLE INCOME (PROFIT –COSTS)
� COSTS = Maintenance Cost + Depreciated Initial Cost
Depreciation
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� Depreciable life is the number of years over which a machine is depreciated. It is also called 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 noncash cost. No money changes hands.
� Usually you pay for the asset “up front”, but depreciate it over time (e.g., a new truck).
� Depreciation is a business expense the government allows to offset the loss in value of business assets.
� Depreciation deductions reduce the taxable income of businesses and thus reduce the amount of tax paid.
Depreciation Calculation Fundamentals
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� Example: A PC costs $1,800. Its annual depreciation charges are $800, $600, and $350 for three years.
� $1,800 is called the cost, initial cost, or cost basis.
� dt denotes the depreciation deduction in year t
� d1= $800, d2= $600, d3= $350
� BVt denotes the book value at the end of year t
Depreciation Calculation Fundamentals
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� Book value = Cost –Depreciation charges made to date
� BVt= Cost Basis –(d1+ d2+ … + dt) = BVt-1- dt
i.e.,BV2= BV2-1- d2= BV1- d2
� 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.
� 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, to a value of S = $50 at time 3.
� Numerous depreciation methods are possible.
Depreciation Methods
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� Depreciation Methods:
� Straight Line
� Sum of Year’s Digits
� Declining Balance
(1). Straight Line (SL) Depreciation
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� Straight line depreciation is the simplest and best known:
� Annual depreciation charge, dt= (B-S)/N
� Example: An asset has a cost of B = $900, a useful life of N = 5 years, and an EOL salvage value of S = $70.
� Using straight line, depreciation:
� Annual depreciation charge: dt= (B-S)/N = (900-70)/5 = 830/5 = $166each year
(1). Straight Line (SL) Depreciation
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(2). Sum-of-Years Digits (SOYD) Depreciation
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Sum-of-Years Digits (SOYD) Depreciation
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� 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
t
(2). Sum-of-Years Digits (SOYD) Depreciation
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(3). Declining Balance Depreciation
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� 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:
� Since Book value = Initial cost –total charges to date
(3). Declining Balance Depreciation
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� 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 Depreciation Sum of Depreciation
Book Value
t 2/N dt=(2/N)BVt-1 ∑dt BVt=B-∑dt
0 900
1 2/5 (2/5)900= 360 360 900-360=540
2 2/5 (2/5)540 =216 576 900-576=324
3 2/5 (2/5)324 = 130 706 900-706=194
4 2/5 (2/5)194= 78 784 900-784=116
5 2/5 (2/5)116= 46 830 900-830=70
(3). Declining Balance Depreciation
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(3). Declining Balance Depreciation
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� 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 150% Declining depreciation method, we would compute the following:
Year Multiplier Depreciation Sum of Depreciation
Book Value
t 1.5/N dt=(1.5/N)BVt-1 ∑dt BVt=B-∑dt
0 900
1
2
3
4
5
Double Declining Balance Depreciation
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� Summary
� DDB is an accelerated depreciation compared to straight line method
� Book value (not first cost) is reduced by same fraction (or %) each year (not same constant amount, as in straight line)
� Converges to an implied salvage value usually different than estimated salvage value
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Part II
Problem: 11-4, 11-5, 11-7
11-4
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� Some special handling devices can be obtained for $12,000. At the end of 4 years, they can be sold for $600. Compute the depreciation schedule for the devices using the following methods:
� (a) Straight-line depreciation.
� (b) Sum-of-years' -digits depreciation.
� (c) Double declining balance depreciation.
11-4
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Year Initial Book Value Depreciation Charge EOY Book Value
B dt=(B-S)/N B-dt
0 12000
1 12000 2125 9875
2 9875 2125 7750
3 7750 2125 5625
4 5625 2125 3500
� P=B=$12,000 S=$3,500 N=4
(a) Straight Line Depreciation
11-4
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Year Life Multiplier B-S Depreciation Charge EOY book Value
t (N-t+1)/SOYD (N-t+1)/SOYD*(B-S)
0 12000
1 4 0.4 8500 3400 8600
2 3 0.3 8500 2550 6050
3 2 0.2 8500 1700 4350
4 1 0.1 8500 850 3500
10 SOYD
� P=B=$12,000 S=$3,500 N=4
(b) Sum-of-Years Digits Depreciation
11-4
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Year Multiplier
Depreciation
Charge
Sum of
Depreciation
EOY Book
Value
t 2/N dt=(2/N)BVt-1∑dt BVt=B-∑dt
0 12000
1 0.50 6000 6000 6000
2 0.50 3000 9000 3000
3 0.50 1500 10500 1500
4 0.50 750 11250 750
P=B=$12,000 S=$3,500 N=4
(c) Double Declining Balance Depreciation
� DDB in any year = 2/N(Book Value)
11-5
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� The company treasurer is uncertain which of three depreciation methods the firm should use for office furniture that costs $50,000, and has a zero salvage value at the end of a 1O-year depreciable life. Compute the depreciation schedule for the office furniture using the methods listed:
� (a) Straight line.
� (b) Double declining balance.
� (c) Sum-of-years' -digits.
The computations for the first three methods (SL, DB, SOYD) are similar to Problem 11-4
11-7
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� The Acme Chemical Company purchased $45,000 of research equipment, which it believes will have zero salvage value at the end of its 5-year life. Compute the depreciation schedule for the equipment by each of the following methods:
� (a) Straight line.
� (b) Sum-of-years'-digits.
� (c) Double declining balance.
11-7
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(a) Straight Line
� SL depreciation in any year= ($45,000 - $0)/5= $9,000
(b) SOYD
� sum = (n/2) (n+1) = (5/2) (5) = 15
� Depreciation in Year 1 = (5/15) ($45,000 - $0) = $15,000
� Gradient = (1/15) ($45,000 - $0) = -$3,000
(c) DDB
� Year DDB
� 1 (2/5) ($45,000 - $0)= $18,000
� 2 (2/5) ($45,000 - $18,000)= $10,800
� 3 (2/5) ($45,000 - $28,800)= $6,480
� 4 (2/5) ($45,000 - $35,280)= $3,888
� 5 (2/5) ($45,000 - $39,168)= $2,333
