Engineering Economics, Chapter 8
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Transcript of Engineering Economics, Chapter 8
Chapter 8
Depreciation
Definition:
Depreciation is the reduction in value of an asset over
time.
Depreciation represents the loss in value due to:
– Use, and wear and tear on the asset
– Deterioration over time
– Obsolescence
– Technological replacement
Depreciation terms
Depreciation is important because it affects the tax that firms pay.
TAX = (PROFIT – COSTS) (TAX RATE)
COSTS = EXPENSES + DEPRECIATION
Depreciation is a deduction from taxable income.
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.
Depreciation terms
Depreciation terms
Depreciation: Example A firm has $1,000,000 of taxable income. If its tax rate is 25%, it would pay $250,000 in taxes ignoring
depreciation.
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 = 0.25(50,000) = 12,500. If it could deduct more than $50,000 it would pay even less taxes.
Unlike other real expenses, depreciation is not an actual cash flow amount.
Two types of depreciation used by corporations Book depreciation -- Use by a corporation for internal financial accounting
Tax depreciation -- Use in tax calculations for government regulations.
Depreciation terms
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
Depreciation terms
Cost Item Type of Cost Reason
Pizza dough, toppings
Delivery van
Employee wages
Furnishings for dining room
New baking oven
Utilities for refrigerator
Example: Joe runs a pizza restaurant. He classifies some of his costs as follows.
Expense
Depreciation
Expense
Depreciation
Depreciation
Expense
Life < 1 yr, loses value immediately
Meets 3 depreciation requirements
Life < 1 yr, loses value immediately
Meets 3 depreciation requirements
Meets 3 depreciation requirements
Life < 1 yr, loses value immediately
1. Must be used for business purposes to produce income
2. Must have a useful life that can be determined, and this life must be longer than one year
3. Must be an asset that decays, gets used up, wears out, becomes obsolete, or loses value to the owner from natural causes
Depreciation terms
Classes of Business Property Tangible property can be seen, touched, and felt.
– Real property includes real estate and its improvements, such as, buildings, factories, other construction
– Personal property Income-producing, tangible property of a corporation, e.g., vehicles, equipment, etc.
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.
Depreciation terms
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.
Depreciation terms
Time, years
BV, $
S
Basis (First cost), B – Total cost of asset including purchase, installation fees, etc.
Recovery period, n – Depreciable life in years. Tax and book depreciation lives often vary
Salvage, S – Estimated value at end of recovery periodBook Value, BV –
Remaining, undepreciated investment after all depreciation to date is removed
Depreciation terms
.
..
Some additional terms to know Depreciation rate, d – rate for reducing the
value of assets using depreciation. (Rate is dt when it varies each year t)
Market Value - the value others would place on the property of interest.
Half-year convention – assumes asset is placed into initial service or disposed of in midyear, regardless of when it actually occurs. (Used in US-approved tax depreciation method)
Depreciation terms
Some methods used in the US and other countries
Straight Line (SL) Standard against which
other methods are compared
Book value decreases linearly over time
Declining Balance (DB) Accelerated write-off
compared to SL method Defers part of tax liability to
later in recovery period Modified Accelerated Cost
Recovery System (MACRS) Required tax depreciation
method in US since 1986
Depreciation terms
n – Recovery period in years
t – year, t = 1, 2, …, n
B – First cost or basis for
depreciation
S – Estimated salvage value at
end of recovery period
Dt – Depreciation charge for
year t
dt – Depreciation rate for year t
(d, if same each year)
BVt – Book value after t years
of depreciation
Straight Line (SL) Depreciation
Notation
1 2 … n t
S
BVt
B D1D2
Excel function to display Dt:
= SLN(B,S,n)
Straight Line (SL) Depreciation
B – S n
Dt = = (B - S) d
BVt = BVt-1 - Dt = B - t×Dt
dt = d = 1/n
Depreciation charge for year t
Book value after t years of depreciation
Depreciation rate for year t
Example 8.1: An asset has a first cost of B = $900, a useful life of n = 5 years, and a salvage value of S = $70.
Year,t Dt BVt
0 - $900
1 166 734
2 166 568
3 166 402
4 166 236
5 166 70
Initial Cost
Salvage Value
Useful Life
900
70
Book Value
1 2 3 4 5 N
Straight Line (SL) Depreciation
Dt = (B-S)/n = (900-70) / 5 = 830/5 = $166. BVt = B - t×Dt = 900 – 166 × t
Accelerated depreciation: higher depreciation charges in the early years, and gradually decreasing charges in subsequent years. More realistic reflection of an asset's actual expected benefit from the use of the asset.
Declining Balance (DB) is also called fixed percentage or uniform percentage method.
Annual depreciation Dt equals book value BVt-1 at beginning of year t (which is same as end of year t-1) times fixed rate d
Dt = BVt-1 × d
Declining Balance (DB)
Values of d are related to Straight Line depreciation rate
Straight Line (SL) Rate:d = 1 / n
Maximum Rate of DB Depreciation:
dmax = 2 / n• Known as double declining balance (DDB)• If recovery period n = 5 years, dmax = 2 / n = 0.4• 40% of book value is removed each year
150% of SL rate: d = 1.5 / n
Declining Balance (DB)
Declining Balance (DB)
Annual depreciation BVt = BVt-1 - Dt
BV0 = B
BV1 = BV0 – D1 = BV0 – BV0d= BV0 (1-d)
D1 = BV0d BV2 = BV1 – D2 = BV1 – BV1d= BV0 (1-d)2
D2 = BV1d = BV0 (1-d) d ….
BVt = BVt-1 – Dt = BVt-1 – BVt-1d= BV0 (1-d)t
Dt = BV0 d (1 - d )t-1
Annual depreciation rate for each year t, relative to first cost B, is
dt = d ×(1 - d )t-1
then, Dt = dt × B
Implied Salvage value
Implied S = BVn = B ×(1 – d)n >0
Declining Balance (DB)
Estimated S
Implied S
n
BV
Implied S
Estimated S
n
BV
kk-1
Book value plots of SL, DB and DDB
SL depreciation
DB depreciation at 150% SL rate
DDB depreciation
Declining Balance (DB)
Example 8.2: First cost, B = $80,000
Salvage value, S = $10,000
depreciable life, n = 5 years
Compare the book values for two methods:
(1) DB at 150% SL rate
(2) DDB
Declining Balance (DB)
DB rate at 150% SL rate is: d=1.5/5 = 0.3 DDB rate is: dmax = 2/5 = 0.4
BVt = B × (1 - d )t
Dt = d × BVt-1
Declining Balance (DB)
Example 8.2 (cont): B = $80,000, S = $10,000, n = 5 years DB rate at 150% SL rate is: d = 0.3
BVt = B×(1 - d )t
Dt = d × BVt-1
Example 8.2 (cont): B = $80,000, S = $10,000, n = 5 years DDB rate is: dmax = 0.4
BVt = B×(1 - d )t
Dt = d × BVt-1
Declining Balance (DB)
BV5 = B(1-d)5
= 80,000 (1-0.4)5
= 6,220.8 < 10,000
So, BV5 = 10,000
and D5 = 368.