Basics_3e_Chapter_12_Depreciation.pptx

Because learning changes everything.®
Slides to accompany
Basics of Engineering Economy
Third edition
by
Leland Blank and Anthony Tarquin
Chapter 12
Depreciation Methods
© 2021 McGraw Hill. All rights reserved. Authorized only for instructor use in the classroom.
No reproduction or further distribution permitted without the prior written consent of McGraw Hill.

© McGraw Hill 2
Chapter 12 – Depreciation Methods
PURPOSE
Use a specific method to
reduce the book value of
capital invested in an asset
(by depreciation) or natural
resource (by depletion)
TOPICS
• Depreciation terms.
• Straight line.
• Declining balance.
• MACRS in USA.
• Two more methods.
• Switching methods.
• Spreadsheet usage.
• Depletion methods.

© McGraw Hill 3
Section 12.1 – Depreciation - Overview
Definition: Depreciation reflects 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 represents the diminishing amount of capital invested in
the asset.
Deprecation amount is NOT actual cash flow and may not reflect actual
usage patterns of the asset.

© McGraw Hill 4
Section 12.1 – Terminology 1
In most countries, depreciation is a tax deductible expense. It
reduces income tax liability for a corporation, even though it is
not an actual cash flow. General relation is:
Taxes = (income − expenses − depreciation)(tax rate)
Two types of depreciation used by corporations:
• Book depreciation - Used internal to the corporation for
financial and accounting purposes.
• Tax depreciation - Per government regulations, specified
methods are used in calculating taxes.
In economic analyses, tax depreciation is usually the type
applied.

© McGraw Hill 5
First cost, B – Total
cost of asset including
purchase, installation
fees, training, etc.
Book Value, BV Remaining,
undepreciated investment after all
depreciation to date is removed.
Recovery period, n – Depreciable life in years. Tax
and book depreciation lives are often different.
Salvage, S
Estimated market
value (MV) at end
of recovery period.

© McGraw Hill 6
Some additional terms
Depreciation rate, d –
Fraction of first cost removed
each year.
(Rate is dt when it varies each
year.)
Half-year convention –Assumes
asset is placed into initial service
or disposed of in midyear,
regardless of when it actually
occurs.
(Applies to US-required MACRS
method.)
Types of depreciable property
Tangible – Income-producing,
tangible property of a
corporation, for example,
vehicles, equipment, etc. (Also
called personal property.)
Real – Real estate and its
improvements, such as,
buildings, factories, other
construction.
Note: Land itself is not
depreciable.

© McGraw Hill 7
Section 12.1 – Different Depreciation Methods
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, with few exceptions.

© McGraw Hill 8
Section 12.1 – Section 179 Deduction
• Exception to regular depreciation methods provided by
government as an economic incentive to make new capital
investments.
• Good for new, small and medium-sized businesses.
• Allows full depreciation of initial cost of newly-installed
asset in first year of ownership.
• Limits vary considerably over the years ($500,000 in 2015;
$1 M in 2018; currently indexed for inflation annually).
• Any amount above allowed 179 deduction limit is
depreciated over the asset’s recovery period.

© McGraw Hill 9
Section 12.1 – Summary of Notation
B = First cost or basis for depreciation
n = Recovery period in years
S = Estimated salvage value at end of recovery period
t = year, t = 1, 2, …, n
Dt = Depreciation charge for year t
dt = Depreciation rate for year t (simply d if rate is the
same each year)
BVt = Book value after t years of depreciation

© McGraw Hill 10
Section 12.2 – Straight Line & Example 12.1 1
( )
t d
B S
D
n
B S


 

dt = d = 1/n (constant each
year)
BVt = B − (t × Dt) = BVt-1 − Dt
t = 1, 2, …, n
Dt based on time, not usage
Spreadsheet function to display
Dt
= SLN(B,S,n)
Example 12.1
• First cost is $50,000 with life
of 5 years and estimated
salvage of $10,000.
• Plot SL book value.
B = $50,000
S = $10,000
n = 5 years

© McGraw Hill 11
Section 12.2 – Straight Line & Example 12.1 2
SL depreciation: Dt = (50,000 − 10,000)/5 = $8000
SL book value: BVt = BVt-1 − Dt
Year, t Dt, $ BVt, $
0 8000 50,000
1 8000 42,000
2 8000 34,000
3 8000 26,000
4 8000 18,000
5 8000 10,000
Spreadsheet function: = SLN(50000,10000,5) displays
Dt of $8000.

© McGraw Hill 12
Section 12.3 – Declining Balance (DB) - Intro
• DB write-off of asset value is accelerated compared to
SL.
• Larger annual depreciation amounts in the early years
of recovery period.
• Also called fixed percentage or uniform percentage
method.
• Annual depreciation Dt equals book value at
beginning of year BVt-1 (which is same as end of
previous year) times fixed rate d.
Dt = d × BVt-1

© McGraw Hill 13
Section 12.3 – DB and DDB Models
Values of d are related to SL depreciation rate
2 times SL rate: d = 2/n.
• This is dmax and is largest allowed.
• Model now called double declining balance (DDB).
Example: If n = 5, dmax = 2/n = 0.4; that is, 40% of BV is removed
each year.
• 150% of SL rate: d = 1.5/n.
• If d is 100% of SL rate, d = 1/n, which is SL depreciation.
Notation reminder for DB and DDB
• d = fixed percentage of BV removed each year.
• dt = depreciation rate for each year t.

© McGraw Hill 14
Section 12.3 – DB Depreciation and Book Value
Annual depreciation determined in either of 2 ways
• Using book value of previous year.
t t
D d BV 
  1
• Using first cost basis B.
1
(1 ) 
   t
t
D d B d
Annual book value determined in either of 2 ways
• Using first cost basis B.
t
t
BV B(1 d)
 
• Using accumulated depreciation for years j = 1 to t.
t j
j
BV B D
  

© McGraw Hill 15
Section 12.3 – BV Graphs for Comparison
Characteristic BV plots of SL, DB and DDB
Access the text alternative for slide images.

© McGraw Hill 16
Section 12.3 – DB - Formulas and Functions
Annual depreciation rate for each year t, relative to first cost B,
is:
 
t
t
d d d

 
1
1
Salvage value is not used in DB method formulas.
• If a salvage value is estimated, and estimated S > implied S,
stop depreciating when estimated S value is reached.
• Implied salvage is book value in year n:
 
n
n
Implied S BV B 1 d
  
Spreadsheet function for DDB: = DDB(B,S,n,t,d)
for DB: = DB(B,S,n,t)
where d is between 1 and 2

© McGraw Hill 17
Section 12.3 – Declining Balance - Example 12.2 1
B = $80,000 S = $10,000 n = 5 years
Develop BV graphs for two methods:
DB at 150% SL rate and DDB
DB rate: d = 1.5/5 = 0.3 DDB rate: dmax = 2/5 = 0.4
Year, t Declining
Balance, d =
0.30 at Dt
Declining
Balance, d =
0.30 at BVt
Double Declining
Balance, d = 0.40
at Dt
Double Declining
Balance, d = 0.40
at BVt
0 $80,000 $80,000
1 $24,000 56,000 $32,000 48,000
2 16,800 39,200 19,200 28,800
3 11,760 27,440 11,520 17,280
4 8,232 19,208 6,912 10,368
5 5,762 13,446 368 10,000

© McGraw Hill 18
Spreadsheet function: = DDB(80000,10000,5,t,factor)
where: t = 1, 2, 3, 4, 5 for each year
Factor = 1.5 for 150% of SL rate
= 2 for DDB
How was the salvage of $10,000 used?
• Neither method used the estimated S to calculate Dt or
BVt, except …
• For DDB, depreciation in year 5 is limited, since BV5
would go below S = $10,000.
• Only a $368 write-off is allowed in year 5, which is
much less than the calculated amount of
D5 = d(BV4) = 0.4(10,368) = $4,147
Double
Declining
Balance, d =
0.40 at Dt
Double
Declining
Balance, d =
0.40 at BVt
$80,000
$32,000 48,000
19,200 28,800
11,520 17,280
6,912 10,368
368 10,000

© McGraw Hill 20
Section 12.4 – MACRS Overview
• MACRS became the only allowed tax depreciation method in
the US in 1986.
• Statutory depreciation rates dt are tabulated (Table 12.2).
• Rates are derived using the DDB or DB method initially with a
switch to SL at the optimal time.
• Recovery period n is prescribed and tabulated by asset types
(Table 12.4).
• MACRS incorporates the half-year convention into the rates
and recovery period.
• MACRS does not utilize the estimated S, since the entire basis
B is always depreciated to zero.

© McGraw Hill 21
Section 12.4 – MACRS - Tangible Property Rates
Table 12.2

© McGraw Hill 22
Section 12.4 – MACRS Formulas – Dt and BVt
• MACRS is required for tax depreciation purposes.
• Any method can be applied for book depreciation within the
corporation.
• Depreciation formula is ultra simple:
Dt = dt × B
• Book value after t years is based on BVt − 1 or B:

 
1
BV BV D
t t t
for 1,2,...,
j
j
B D j t
  


© McGraw Hill 23
Section 12.4 – MACRS Recovery Periods
• Tangible Property Recovery Periods – n set at 3, 5, 7, 10, 15
and 20 years.
• For n = 3, 5, 7, and 10 – Depreciation rates start with DDB
method, and switch to SL rates to ensure faster write-off of B.
• For n = 15 and 20 – Depreciation rates start with150% DB
method, and switch to SL rates to ensure faster write-off of B.
• Half-year (Mid-year) convention – Built in to allow only 50%
of first year depreciation; leftover amount is removed in year
n+1. (This removes some of the advantage of accelerated
depreciation. Check it out on next slide.)

© McGraw Hill 24
Section 12.4 – MACRS Rates – Real Property
• Real property includes buildings and permanent improvements
(not land).
• MACRS rates utilize SL method for n = 39 years with half-year
convention built in.
• Depreciation rates in % are:
Year 1 d1= 1.391%
Years t = 2-39 dt = 2.564%
Year 40 d40 = 1.177%
Total is 100%

© McGraw Hill 25
Section 12.4 – MACRS - Example 12.3 1
Use MACRS to depreciate asset with
B = $400,000 n = 3 years S = $20,000

© McGraw Hill 26
Compare MACRS tax depreciation with DDB book
depreciation after 2 and 3 years.
Year Rate
MACRS Tax
Depreciation
MACRS
Book Value
DDBs Book
Depreciation
DDBs Book
Value
0 $400,000 $400,000
1 0.3333 $133,320 266,680 $266,667 133,333
2 0.4445 177,800 88,880 88,889 44,444
3 0.1481 59,240 29,640 24,444 20,000
4 0.0741 29,640 0
• Depreciation amounts and book values vary significantly.
• MACRS BV after 2 years is ~2 times DDB BV.
• DDB stops at S = $20,000, resulting in reduced D3 value.

© McGraw Hill 27
0
100,000
200,000
300,000
400,000
0 1 2 3 4
Year
Book value,
$
DDB MACRS
• MACRS always depreciates to
$0; estimated S > 0 ignored.
• DDB method depreciates to an
implied S or estimated S at end of
the recovery period.
• MACRS depreciation in year 1 is
½ the DDB or DB amount due to
implicit half-year convention.
• MACRS takes one additional year
for write-off (half-year convention)

© McGraw Hill 28
Section 12.4 – MACRS - Recovery Period Systems
GDS and ADS (GDS is used in this text)
GDS (General Depreciation System)
• Used for most assets.
• Tabulates MACRS-allowed years for different types of assets.
• Recovery ranges from 3 to 39 years; 7 years is default recovery period.
ADS (Alternative Depreciation System)
• Uses SL depreciation instead of MACRS rates.
• Recovery period is longer than for GDS.
• Removes early-life tax advantage of MACRS rates.
• Good for start-up businesses with lower revenues.
Note: See Table 12.4 for values of GDS and ADS

© McGraw Hill 29
Section 12.5 – Unit-of-Production Depreciation
• SL, DB, DDB, and MACRS models all reduce asset value
based on time.
• UOP model is based on usage over time.
• Usage is commonly volume, hours, units, etc.
• Depreciation charge for each year t is:
 
Actual usuage for year
basis salvage
Total lifetime usuage
t
t
D   

© McGraw Hill 30
Section 12.5 – Unit-of-Production - Example 12.4
B = $200,000 n = 5 year Total usage estimate = 3 M 3
m
Actual usage in 1000
3
m is shown. Determine Dt and BVt using UOP.
In the following table, read ‘m3’ as m cubed.
Year, t
Actual Usage,
1000 m3
Annual Depreciation,
Dt, $
Cumulative
Depreciation, $ Book Value, $
1 420 28,000 28,000 172,000
2 630 42,000 70,000 130,000
3 630 42,000 112,000 88,000
4 660 44,000 156,000 44,000
5 660 44,000 200,000 0
Total 3,000 200,000
For example: D2 = (630/3000) × (200,000) = $42,000
Note: If more than 3000
3
m used, no more depreciation.

© McGraw Hill 31
Section 12.5 – Sum-of-Years-Digits Depreciation
• One of earlier accelerated write-off models when compared to SL
depreciation.
• Larger depreciation amounts in early years.
• First determine the sum of digits from 1 to n, or SUM.
SUM = n(n + 1)/2
• Depreciation charge for each year t is:
 
Depreciable years remaining
basis salvage
Sum of years digits
  
t
D
 
1
SUM
 
  
n t
B S
Spreadsheet function for Dt: = SYD(B,S,n,t)

© McGraw Hill 32
Section 12.5 – SYD Depreciation - Example
• Let B = $100,000, n = 10 and S = 0
SUM = 10(11)/2 = 55
D1 = [(10-1+1)/55] × 100,000 = $18,182 Largest, year 1
D5 = [(10-5+1)/55] × 100,000 = $10,909 Smaller amount
D10 = [(10-10+1)/55] × 100,000 = $1818 Lowest, year n
Function: = SYD(100000,0,10,t) for t = 1, 2,…, 10

© McGraw Hill 33
Section 12.6 – Switching Between Methods
• Objective of switching methods is to
maximize PW of total depreciation.
The relation to maximize is:
( , , )
1
PW


 
t n
D t
t
D P F i t
• Maximizing PWD will minimize PW of taxes paid over entire
recovery period.
• As mentioned earlier, MACRS includes embedded switching
from DDB (n = 3, 5, 7, and 10) or 150% DB (n = 15 and 20) to
SL rates to improve the tax deduction.

© McGraw Hill 34
Section 12.6 – Rules for Switching
General rules for switching between two methods
Usually, DB method to SL method works best
1. Switch to new method in year that its Dt exceeds the current
method’s Dt.
2. Can switch only one time during recovery period.
3. Never depreciate below estimated S, if there is one
(Not a problem for MACRS, since all of B is removed.)
4. When no switch is made, the BVt is used as the basis for next
year’s depreciation calculation and switching decision in year
t+1.
Note: MACRS uses these rules to determine the annual rates, with
the half-year convention imposed in years 1 and n+1.

© McGraw Hill 35
Section 12.6 – Switching - Relations for
Steps 1 and 2
Procedure to switch from DDB to SL
1. For each year t, compute the two depreciation charges.
For DBB: DDB 1
(BV )
t
D d 

For SL: 1
SL
BV
1
t
D
n t


 
2. The depreciation for each year is
DDB SL
max[ , ]
t
D D D

VDB function displays annual Dt for DB-to-SL switch.
(Illustrated in next section.)

© McGraw Hill 36
Section 12.6 – Switching DDB-to-SL - Example 12.5 1
B = $100,000 n = 5 years i = 15% per year
Apply DDB-to-SL switching and determine PWD

© McGraw Hill 37
Section 12.6 – Switching Methods – Example 12.5 2
Year t
DDB
Model at
DDDB
DDB
Model at
BVt
SL Model
DSL Larger Dt
(P/F,15%
,t) Factor
Present
Worth of
Dt
0 — $100,000
1 $40,000 60,000 $20,000 $ 40,000 0.8696 $34,784
2 24,000 36,000 15,000 24,000 0.7561 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 10,800 0.4972 5,370
Totals $92,224 10,800 $73,943
* Year of switch to SL
• PW of depreciation with switching at i = 15% is $73,943
• PW for SL: PWD = 20,000(P/A,15%,5) = $67,044

© McGraw Hill 38
Section 12.7 – Spreadsheet Functions 1
Functions for depreciation calculations
• Straight Line: = SLN(B,S,n)
Same Dt value each year.
Double Declining Balance: = DDB(B,S,n,t,d)
• Different value for each year t = 1, 2, …, n.
• Fixed rate d is an entry between 1 (SL) and 2 (DDB).
• Entry of d is optional; assumed 2 for DDB, if omitted.
• Entry of d = 1.5 applies the 150% DB method.

© McGraw Hill 39
Section 12.7 – Spreadsheet Functions 2
More functions for depreciation calculations
MACRS: = VDB(B,0,n,MAX(0,t-1.5),MIN(n,t-0.5),d)
• There is no function to calculate MACRS directly; use VDB.
• Salvage value S is entered as zero.
• MAX and MIN functions replace start and end periods.
• Rate d is entered as 2 (DDB) for MACRS recovery periods of n = 3, 5, 7, and 10
years.
• Rate d is entered as 1.5 (150% DB) for MACRS recovery periods of n = 15 and 20
years.
Switching: = VDB(B,S,n,start_pd,end_pd,d)
• VDB automatically switches from DB or DDB to SL to max PWD.
• Optional rate d is between 1 and 2; DDB assumed, if omitted.
• start_pd and end_pd are always one year apart.

© McGraw Hill 40
Section 12.7 – Spreadsheet - SL - Example 12.6 1
B = $500,000 S = $5,000 n = 5 years
(a) Straight Line function: = SLN(500000,5000,5)

© McGraw Hill 41
Section 12.7 – Spreadsheet - DDB/DB - Example 12.6 2
B = $500,000 S = $5,000 n = 5 years
(b) DDB function:= DDB(500000,5000,5,t,2) Optional
(c) 150% DB function: = DDB(500000,5000,5,t,1.5)
Not optional

© McGraw Hill 42
Section 12.7 – Spreadsheet - MACRS - Example 12.6 3
B = $500,000 S = $5,000 n = 5 years
(d) MACRS function (for t = 1, 2, 3, 4, 5, 6)
= VDB(500000,0,5,MAX(0,t-1.5),MIN(5,t-0.5),2)
Salvage, S = 0 is required
in VDB function
Factor
Insert 2 for n = 3, 5, 7, 10
Insert 1.5 for n = 15, 20
MACRS using VDB function, year 6
= VDB (500000,0,5,MAX(O,Al2-1.5),MIN(5,A12-0.5),2)

© McGraw Hill 43
B = $500,000 S = $5,000 n = 5 years
(e) DDB-to-SL switch function: = VDB(500000,5000,5,t,t+1)
Salvage, S = 5000 is required as an entry now in VDB function
Switch from DDB to SL
occurs in year 4
VDB function for switching, years 3 to 4
= VBD(500000,5000,5,A 9,A 10)

© McGraw Hill 44
(f) Graph of BV versus years for all 5 models
Conclusions: DDB-to-SL switch is most accelerated.
MACRS ignores S completely; may cause recaptured
depreciation (RD) when sold.

© McGraw Hill 45
Section 12.8 – Depletion - Overview
Depreciation is applied to assets that can be replaced – computers, machines,
etc.
Depletion applies to natural resources not easily replaced, such as:
• Forests (timber).
• Geothermal deposits.
• Mineral deposits and quarries (gold and other
ores, gravel, copper, zinc, etc.).
• Oil and gas wells.
Two methods of depletion:
• Percentage depletion.
• Cost depletion.

© McGraw Hill 46
Section 12.8 – Percentage Depletion
• This method is a special consideration for natural resources.
• Constant percentage of resource’s gross income (GI) is depleted each
year, provided it does not exceed 50% of the firm’s taxable income.
Deposit Percentage
Sulfur, uranium, lead, nickel. Zinc, and some other ores and minerals 22%
Gold, silver. copper. iron ore, and some oil shale 15
Oil and natural gas wells 15
Coal, lignite, sodium chloride 10
Gravel, sand, some stones 5
Most other minerals, metallic ores 14
• Annual depletion allowance is:
Percentage depletion = allowed percentage × GI
• Total depletion may exceed first cost of resource.

© McGraw Hill 47
Section 12.8 – Percentage Depletion - Example 12.7
Gold mine costs $10 M. Gross income per year was:
GI = $8 M for years 1 to 5
GI = $5 M thereafter Determine annual depletion
Assume annual depletion will not exceed 50% of TI.
Percentage depletion for gold is 15% of GI.
Years 1 to 5: Depletion = 0.15(8 M) = $1.2 M
Years 6+: Depletion = 0.15(5 M) = $750,000
Years to recover initial cost of $10 M:
• Years 1 to 5 recovers 1.2 M × 5 = $6 M
• $4 M left at $750,000 per year
• Total recovery in 5 + (4 M/0.75 M) = 10.3 years

© McGraw Hill 48
Section 12.8 – Cost Depletion
• Annual depletion based on level of activity or usage of natural
resource.
• Initially, calculate the cost depletion factor pt using:
First cost
Resource capacity
t
p 
• Annual cost depletion charge is:
pt × annual activity level
• Total cost depletion can not exceed first cost of resource.
• If resource capacity changes (re-estimated), new pt is
determined.

© McGraw Hill 49
Section 12.8 – Cost Depletion - Example 12.8
• $700,000 paid for timber cutting rights.
• Estimated 350 M board-feet will be harvested.
• 15 M and 22 M board-feet are harvested in years 1 and 2,
respectively. Determine cost depletion amounts.
pt = 700,000/350 = $2,000/M board-feet
Year 1: Depletion = 2,000(15) = $30,000
Year 2: Depletion = 2,000(22) = $44,000
After 2 years, re-estimate due to pine bark beetle damage indicates
remaining timber at only 250 M board-feet. Find new pt.
New pt = (700,000 − 74,000)/250 = $2,504/M board-feet

Because learning changes everything.®
www.mheducation.com
© 2021 McGraw Hill. All rights reserved. Authorized only for instructor use in the classroom.
No reproduction or further distribution permitted without the prior written consent of McGraw Hill.

Basics_3e_Chapter_12_Depreciation.pptx

Recommended

Recommended

More Related Content

Similar to Basics_3e_Chapter_12_Depreciation.pptx

Similar to Basics_3e_Chapter_12_Depreciation.pptx (20)

Recently uploaded

Recently uploaded (20)

Basics_3e_Chapter_12_Depreciation.pptx