Chapter Outline
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Chapter 16 – Depreciation
Methods
INEN 303
Sergiy Butenko
Industrial & Systems Engineering
Texas A&M University
Chapter 16 – Depreciation Methods
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Chapter 16 – Depreciation Methods
Depreciation Terminology
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Book Depreciation – used by businesses
for internal accounting purposes
Tax Depreciation – used in tax
calculations according to government
regulations.
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Chapter 16 – Depreciation Methods
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Amount realized by sale on the open marketdepending on the asset, can be drastically
different from BV
Classical methods for book depreciation
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Estimated trade-in value or market value at the
end the asset’s useful life
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Straight Line (SL) Model
Declining Balance (DB) Model
Modified Accelerated Cost Recovery System
(MACRS) Methods
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The fraction of the first cost removed by
depreciation each year
Chapter 16 – Depreciation Methods
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Depreciation Methods
Depreciation Rate - dt
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Depreciable life of the asset in question – often set
by law.
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Salvage Value - S
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Remaining undepreciated capital investment on
the books after total amount of depreciation
charges to date have been subtracted from the
basis.
Recovery Period – n
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Market Value - MV
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Initial purchase price + all costs incurred in placing
the asset in service
Book Value - BVt
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Important Terms
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First Cost or Unadjusted Basis - B
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Wear and tear, use;
Deterioration;
Obsolescence.
Chapter 16 – Depreciation Methods
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Important Terms
Depreciation is the reduction in value
over time of an asset.
Brought on by:
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Depreciation terms
Straight line
Declining Balance
MACRS
Depletion
Method for tax depreciation in the U.S.
Acceptable for book depreciation also.
Chapter 16 – Depreciation Methods
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General Book value Curves for Different
Depreciation Models
Straight Line (SL) Depreciation
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The standard on which all other depreciation
models are compared
Notation:
t = year (t = 1,2,...,n)
D t = annual depreciation charge
B = first cost or unadjusted basis
S = Estimated salvage value
n = recovery period
d t = depreciation rate
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Chapter 16 – Depreciation Methods
Declining Balance (DB) and Double Declining
Balance (DDB) Depreciation
Straight Line (SL) Depreciation
B−S
n
1
Dt
dt =
=
B−S n
BVt = B − tDt
Dt = D =
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BVt is the book value at the end of year t
Excel Function: =SLN(B,S,n)
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Declining Balance (DB)
d
DB is an accelerated depreciation method
Provides greater depreciation amounts in
the early time periods over straight line
Fixed percentage (OR) Uniform
percentage method
A fixed percentage is removed each
annually
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Chapter 16 – Depreciation Methods
Fixed percentage:
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Chapter 16 – Depreciation Methods
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Chapter 16 – Depreciation Methods
Declining Balance (DB)
Book value at EOY t:
BV t
Depreciation for year t, relative to B:
Then, Depreciation for year t:
−
Dt = dBVt −1 = Bd(1− d)t 1
Dt = (d )BVt −1
BVt = BVt −1 − Dt = (1− d )BVt −1
Book value for year t, relative to first cost B:
BVt = B (1 − d )
Chapter 16 – Depreciation Methods
Actual depreciation “rate” for year t,
relative to B:
dt =
t
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Dt Bd (1 − d ) t −1
=
= d (1 − d )t −1
B
B
Chapter 16 – Depreciation Methods
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Declining Balance (DB) and Double Declining
Balance (DDB)
Max allowable
depreciation rate:
d max =
Acceptable range for d is :
2
n
Salvage Value in DB method
How to handle when both S and d are given?
„ d gets priority over the given S in finding BVt
„ Call the given S, the estimated salvage value
(Se) and find the implied salvage value
Double DB Method used this
percentage.
0 < d < dmax
When 0<d<1, BV never goes to zero for finite t.
Si = B(1-d)n
1/ n
When given Salvage S >0, the implied d is =
When given d, the implied
Salvage Value is calculated as:
S
1−  
B
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S = BVn = B(1 − d ) n
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Excel Function: =DDB(B,S,n,t,d) *Read carefully before using !
Chapter 16 – Depreciation Methods
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Example 16.2
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Chapter 16 – Depreciation Methods
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A fiber optics testing device is to be DDB
depreciated. It has a first cost of $25,000 and
an estimated salvage value 0f $2500 after 12
years. (a) Calculate the depreciation and
book value for years 1 and 4. (b) Calculate
the implied salvage value after 12 years.
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Modified Accelerated Cost Recovery
System (MACRS)
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Chapter 16 – Depreciation Methods
Example 16.2
Chapter 16 – Depreciation Methods
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Usually, Se is in the range of 0 to Si – if so
ignore Se
If Se is more than Si , then it is correct to stop
charging depreciation from that point
onwards
Modified Accelerated Cost Recovery
System (MACRS) (Sec 16.4-5)
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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 and SL method.
MACRS assumes all assets depreciated by this
method will have a “0” salvage value at the end of the
recovery life.
dt is from tables.
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Dt = dtB
BVt = BV t-1 – Dt
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BVt = first cost – sum of accumulated depreciation
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B Vt = B −
Chapter 16 – Depreciation Methods
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t
∑
D
j =1
Chapter 16 – Depreciation Methods
j
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Depletion Methods (Section 16.6)
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Depreciation is applied to assets that can be
replaced.
Depletion applies only to natural resources like:
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Chapter 16 – Depreciation Methods
Timber,
Mineral deposits,
Oil and gas,
etc.
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Chapter 16 – Depreciation Methods
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Chapter 16 – Depreciation Methods
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Chapter 16 – Depreciation Methods
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Depletion Methods (Section 16.6)
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Cost Depletion (See Ex 16.5)
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Also called factor depletion
Based upon the level of activity or usage;
Time is not involved.
first cost
resource capacity
pt = cos t depletion factor for year t
pt =
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Percentage Depletion (See Ex 16.6)
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Applies a stated % of the resource's gross income
provided it does not exceed 50% of the firm’s current
taxable income.
Percentage depletion amount = percentage x gross
income from property
Chapter 16 – Depreciation Methods
Percentage Depletion
Chapter 16 – Depreciation Methods
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