# ISE211 Chapter 11

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ISE 211
Engineering Economy
Depreciation
Chapter 11
Introduction
 While considering the different analysis techniques, we have avoided
income taxes, which are an important element of most economical
analyses.
 For capital equipment, depreciation is required to compute income
taxes.
 Depreciation is defined as a “decrease in value” – depreciation of assets
is an important component of many after-tax economic analyses, since
depreciation may be deducted from taxable income.
 The cost of the asset, less the total depreciation charges made, is know
as the book value – which can also be defined as the remaining
unallocated cost of an asset.
Introduction (cont’d)
 Types of Property: the rules for depreciation are linked to the classification
of business property as either tangible or intangible.
 Tangible property: can be seen, touched, and felt -- real property (land,
buildings, etc) and personal property (equipment, vehicles, office machinery,
etc).
 Intangible property: all property that has value to the owned but cannot
be directly seen or touched (patents, copyright, trademarks, etc)
 Many of the properties that wear out, decay, or lose value can be depreciated
 Almost all tangible properties (exception: land) can be depreciated.
Depreciation Calculation Fundamentals
 Book Value (BV) = Cost – Depreciation charges made to date
General Depreciation
Depreciation Calculation Fundamentals
t
BVt = Cost Basis -
d
i 1
i
 Where BVt = Book Value of the depreciated asset at the end of time t
 Cost Basis = B = the dollar amount that is being depreciated - - this
includes the asset’s purchase price as well as any other costs necessary to
make the asset ready for use.
t

d
i 1
i
= the sum of depreciation deduction taken from time 0 to time
t, where di is the depreciation deduction in year i.
 The above equation shows that year-to-year depreciation charges reduce
an asset’s book value over its life.
Depreciation Calculation Methods

The six major depreciation methods that will be presented herein are:
1) Straight Line Depreciation (SL)
2) Sum-of-Years Digits Depreciation (SOYD)
3) Declining Balance Depreciation (DB)
4) Composite Declining Balance Depreciation (CDB)
5) Unit of Production Depreciation (UOP)
6) Modified Accelerated Cost Recovery System Depreciation
(MACRS)
 Depreciation methods generally result in the same total depreciation
deductions, so it is the timing of the deductions that characterize the
different methods.
Depreciation Calculation Methods (cont’d)
 Immediate tax savings are more valuable than tax savings
some years in the future due to the time value of money.
 For this reason, a profitable firm prefers to depreciate its
assets as rapidly as possible.
 On the other hand, firms which are not profitable would
have a little or no incentive to depreciate their assets rapidly.
1) Straight Line (SL) Depreciation
 The most straightforward and best-known of the various depreciation methods is
the straight line approach.
 In this method, a constant depreciation charge is made based on the cost of the
asset (B), the salvage value (S), and the useful life in years (N) as follows:
Annual Depreciation Charge = dt = (B-S)/N
 where (B-S) represent the total amount to be depreciated.
 The depreciation charges (dj) for a specific year j, j=1,2,…, n, may also be
computed based on the book value at the end of the jth year as follows:
 The book value at the end of the jth year is:
j
BVj  B   di  B  j
i 1
(B  S )
N
Example 1
A special type of equipment has a
first cost of \$900, a 5 year useful
life, and a \$70 salvage value.
Compute the SL depreciation
schedule.
Example 1 Solution (cont’d)
2) Sum-of-Years Digits (SOYD) Depreciation
 The Sum-of-Years Digits method results in depreciation charges that
are larger than those of straight line depreciation during the early years
of the useful life of an asset, and necessarily, smaller during the later
years.
 The SOYD depreciation charge (dt) for year t is expressed as:
dt 
N  t 1
(B  S )
SOYD
Where : dt = depreciation charge in any year t
N = number of years in depreciable life
SOYD = sum-of-year digits, calculated as: SOYD 
B = cost of the asset made ready for use
S = estimated salvage value after depreciable life
N ( N  1)
2
Example 1
A special type of equipment has a
first cost of \$900, a 5-year useful
life, and a \$70 salvage value.
Compute the SOYD depreciation
schedule.
Example 1 Solution (cont’d)
3) Declining Balance (DB) Depreciation
 DB depreciation charge is computed by applying a constant depreciation
rate to the property’s declining book value.
 The DB depreciation charge for year t can be found as follows:
dt 
r
BV t 1
N
 Since the book value equals the cost minus depreciation charge to date, the
above equation can be rewritten as follows:
t 1
r
r
rB
r
dt  BVt 1  ( B   di ) 
(1  )t 1
N
N
N
N
i 1
 The two rates specified in the Tax Reform Act of 1986 are 150% and 200%
of the SL rate.
 Hence r = 2 or 1.5
3) Declining Balance (DB) Depreciation
 Therefore, the Double Declining Balance (DDB) is obtained, when r = 2, as
follows:
DDB  d t 
2B
2
(1  ) t 1
N
N
 The Book Value, BVt, can be found by using the following general form:
BVt  B (1 
r t
)
N
Example 1: A special type of equipment has a first cost of \$900, a 5 year useful
life, and a \$70 salvage value.
a)
Determine the DDB BV at the end of the third year.
b) Determine the total DDB depreciation charges at the end of the third year.
c)
Compute the DDB depreciation schedule.
d) Compute the 150% DB depreciation schedule.
Example 1 Solution (cont’d)
4) Composite Declining Balance (CDB) Depreciation
 Since a DB depreciation schedule is independent of the estimated salvage
value, any of the three situations illustrated below might occur:
 First: in Figure (a), the book value of the asset is seen to decline below the
salvage value.
 Since the depreciation charges are not permitted to reduce the book value
below the salvage value, the schedule must be modified in accordance with
the IRS regulations.
4) Composite Declining Balance (CDB) Depreciation
Second: the schedule in Figure (b) presents no problem, since the DB depreciation
schedule results in a book value which (coincidentally) corresponds exactly to the
salvage value at the end of the asset’s useful life.
Lastly: Figure (c ) illustrates the situation where the asset is not fully depreciated by
the end of its useful life. This problem may be resolved in either of two approaches:
1)
If the asset is retained in service beyond its estimated useful life, then DB
depreciation will continue to be charged in subsequent years until either the
current estimated salvage value is reached, or until the asset is disposed of.
2)
The second alternative is to use a composite method. With this approach, a
“switch” to another depreciation method (e.g., SL) is made at some point during
the life of the asset. The point (in time) of the switch is selected such that the
book value of the asset is reduced to its salvage value as quickly as possible.
Example 1
Equipment (a special handling device for food
and beverage manufacture) has a first cost of
\$14500, a 5-year useful life, and a \$1000
salvage value. Determine the Double
Declining Balance depreciation schedule
with conversion to SL at the most desirable
time.
6) Unit of Production (UOP) Depreciation
 In rare situations, the recovery of depreciation on a particular asset is
more closely related to use than to time.
 Example: if the natural resources will be exhausted before the
machinery wears out.
 In these instances, UOP depreciation may be employed and is defined as:
UOP depreciation in any year =
Pr oduction for  year
(B  S )
Total  lifetim e production
 This is not considered an acceptable method for general use in
depreciating industrial equipment.
Example 1
A truck for hauling coal has an estimate net
cost of \$55,000 and is expected to give service
for 250,000 miles, resulting in a zero salvage
value. Compute the allowed depreciation
amount for the truck usage of 30,000 miles.
Example 2
A piece of equipment that costs \$900 has been purchased for use
in a san and gravel pit. The pit will operate for five years, while a
nearby airport is being reconstructed and paved. Then the pit will
be shut down, and the equipment removed and sold for \$70.
Compute the UOP depreciation schedule, if the airport
reconstruction schedule calls for 40,000 cubic meters of sand and
gravel as follows:
Year
1
2
3
4
5
Required sand and gravel (m3)
4,000
8,000
16,000
8,000
4,000
5) Modified Accelerated Cost Recovery System (MACRS)
 The MACRS was created as part of the TAX Reform Act of 1986.
 It is now the principal means for computing depreciation expenses.
 Three major advantages of MACRS depreciation are:
1) The computations are made using “property class lives” that are
less than the “actual useful lives”
2) Salvage values are assumed to be zero
3) Tables of the annual percentage simplify computations
5) Modified Accelerated Cost Recovery System (MACRS)
Steps in MACRS depreciation:
1) Determine the property type and class (within a type) of the asset being
depreciated.
 There are two types of property: personal and real (estate) property. All
personal property falls into one of the six classes displayed in Table 10-2
(page 378)
 Real estate, on the other hand, is categorized as either residential rental or
nonresidential property.
2) After the property class is determined, determine depreciation charges from the
schedules listed in Tables 10-4* and 10-5*., for personal or real property,
respectively.
Example 4
On July 1st, Nancy Silva (Silvia’s mother) paid
\$600,000 for a commercial building and an
additional \$150,000 for the land on which it
stands. Four years later, she sold the property for
\$850,000. Compute the MACRS depreciation
for each of the five calendar years during which
she had the property.
Depreciation Technique
Excel Function
Straight Line
SLN(cost, salvage, life)
Declining Balance
DDB(cost, salvage, life, period, factor)
Sum of Years’ Digits
SYD(cost, salvage, life, period)
MACRS
VDB(cost, salvage, life, start-period, endperiod, factor, no-switch)
Spreadsheets and Depreciation (Use of VDB)
1- Salvage = 0, since MACRS assumes no salvage value.
2- Life = recovery period of 3, 5, 7, 10, 15, or 20 years.
3- 1st period runs from 0 to 0.5, 2nd period from 0.5 to 1.5, tth period from t-0.5 to
t-0.5, and last period from life-0.5 to life.
4- factor = 2 for recover periods of 3, 5, 7, or 10 years and =1.5 for recovery
periods of 15 or 20 years.
5- Since MACRS includes a switch to straight line, no-switch can be omitted.
Example I
Consider a 7-year MACRS property asset,
which has \$150,000 of office equipment. Use
VDB to compute the depreciation amounts.
Homework # 11 (Chapter # 11)
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