Depreciation Methods

12/20/2022 1
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 Basic Idea

 The capital investments of a corporation in tangible

assets (equipment, computers, vehicles, buildings and
machinery) are commonly recovered on the books of
the corporation through depreciation.
 Although the depreciation amount is not an actual cash
flow, the process of depreciating an asset, also referred
to as capital recovery, accounts for the decrease in an
asset’s value because of age, wear and obsolescence.
 Even though an asset may be in excellent working
condition, the fact that it is worth less (has less value), is
taken into account.

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 Depreciation

 An income tax system generally does not allow

a deduction for the cost of an asset in the year
that it is purchased. Instead, it spreads out the
deduction over a period roughly consistent
with the asset's useful economic life.
 The amount allowed as an annual deduction
roughly reflects the reduction in the value of
the capital asset as it ages, and is called
depreciation.

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 Why Do Capital Assets Depreciate?

 A capital asset might depreciate -- fall in value as it ages over

its useful life -- for several reasons.
 One reason is that as it ages it gets closer to the end of its
useful life. The value of an asset is the present discounted
value of the net cash flow it can produce.
 Older assets have fewer years left to produce income, and
therefore are worth less than otherwise similar, yet newer,
assets that will produce an income flow over a longer life
span.
 Another reason is that capital assets wear out as they age,
and so are less productive, or require more maintenance,
than do newer capital assets.
 Certain types of quality improvements in similar new assets
will also reduce the value of older assets due to obsolescence.

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 Significance of Depreciation

 Economic depreciation measures the expected

decline in the real market value of the asset in
each period.
 Depreciation lowers income taxes via the
relation:
 Taxes = (income - deductions)(tax rate)

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 Depreciation Amounts
 Federal tax law states that: Any productive asset with a finite
life (greater than one year) must be depreciated for tax
purposes rather than “expensed” in the year of purchase.
 Depreciation amounts represent a prorated amount per year
that can be treated as an “expense” (deduction) but is not a
real cash flow.
 Depreciation amounts represent a form of tax savings to the
profitable firm.
 Assume a tax rate of 30% of taxable income.
 For every $1 of eligible deductions the resultant tax savings
is:
 (0.30)($1.00) = $0.30.
 $1 of additional deductions saves the firm $0.30.
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 Depreciation

 Depreciation is the reduction in value of an asset.

 The method used to depreciate an asset is a way to
account for the decreasing value of the asset to the
owner and to represent the diminishing value of the
capital funds invested in it.
 The annual depreciation amount Dt does not
represent an actual cash flow, nor does it necessarily
reflect the actual usage pattern of the asset during
ownership.

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 Terminology

 Book value represents the remaining, capital

investment (not yet depreciated) on the books after
the total amount of depreciation charges (to date)
have been subtracted from the basis. The book value
(BV) is usually determined at the end of each year.
 Market Value (MV) is the amount realized from sale
on the open market.
 Salvage Value (S) is the estimated trade-in value or
market value at the end the asset’s useful life.

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 Important Terms
 First Cost or Unadjusted Basis (B)
 Initial purchase price + all costs incurred in placing the asset in
service
 Recovery Period (n)
 Depreciable life of the asset in question – often set by law
 Depreciation Rate (dt)
 The fraction of the first cost removed by depreciation each year
 Personal Property
 All property except real estate used in the pursuit of profit or
gain
 Real Property
 Real estate and improvements, buildings and certain structures

Land is Real Property, but by law is NOT depreciable for tax purposes 10
 Notation
I = Cost Basis; Initial Price plus
installation expenses.
S = Salvage Value
Dn = Depreciation in Year n
Bn = Book Value in Year n
N = estimated years of useful life
n = the year currently under
consideration

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 Book vs Tax Depreciation
 Depreciation may be performed for two reasons:
 1. Use by a corporation or business for internal financial accounting (book
depreciation).
 2. Use in tax calculations per government regulations (tax depreciation).
 The methods applied for these two purposes may or may not utilize the same formulas.
 Book depreciation indicates the reduced investment in an asset based upon the usage
pattern and expected useful life of the asset. There are classical, internationally accepted
depreciation methods used to determine book depreciation: straight line, declining
balance, and the infrequently used sum-of-year digits method.
 Tax depreciation is important because it is tax deductible; it can be subtracted from
income when calculating the amount of taxes due each year. However, the tax
depreciation amount must be calculated using a government approved method.
 Tax depreciation must be calculated using MACRS; book depreciation may be calculated
using any classical method or MACRS.
 MACRS has the DB and SL methods, in slightly different forms, embedded in it, but these
two methods cannot be used directly if the annual depreciation is to be tax deductible.
 Many U.S. companies still apply the classical methods for keeping their own books,
because these methods are more representative of how the usage patterns of the asset
reflect the remaining capital invested in it. Additionally, most other countries still
recognize the classical methods of straight line and declining balance.

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 Depreciation Methods
We will cover five methods:
• Straight Line
• Declining Balance
• Sum of Years Digits
• Units of Production
• MACRS – Modified
Accelerated Cost Recovery
System

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 Depreciation Models

 There are several models for depreciating assets. The

straight line (SL) model is used historically.
 Accelerated models, such as the declining balance
(DB) model, decrease the book value to zero (or to
the salvage value) more rapidly than the straight line
method.
 For the classical methods, straight line, declining
balance, and sum-of-year digits (SYD), there are Excel
functions available to determine annual
depreciation.

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 Depreciation Models (2)
Straight Line (SL)
 It writes off capital investment linearly over n years.
 The estimated salvage value is always considered.
 This is the classical, nonaccelerated depreciation model.
Declining Balance (DB)
(also known as fixed percentage or uniform percentage method)
 The model accelerates depreciation compared to straight line.
 The book value is reduced each year by a fixed percentage.
 The most used rate is twice the SL rate; called double declining balance (DDB).
 It has an implied salvage that may be lower than the estimated salvage.
 It is not an approved tax depreciation method in the United States. It is frequently used for book
depreciation purposes.
Modified Accelerated Cost Recovery System (MACRS)
 It is the only approved tax depreciation system in the United States.
 It automatically switches from DDB or DB to SL depreciation.
 It always depreciates to zero; that is, it assumes S = 0.
 Recovery periods are specified by property classes.
 Depreciation rates are tabulated.
 The actual recovery period is 1 year longer due to the imposed half-year convention.
 MACRS straight line depreciation is an option, but recovery periods are longer than for regular
MACRS.
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 Straight Line Method
Dn = ( I – S )
N

Bn = I – Dn (n)
Where:
I = Cost Basis; Initial Price plus installation
expenses.
S = Salvage Value
Dn = Depreciation in Year n
Bn = Book Value remaining in Year n
N = estimated years of useful life
n = the year currently under consideration

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 Straight Line

 If an asset has a first cost of $50,000 with a $10,000

estimated salvage value after 5 years,
 Calculate the annual depreciation.

Solution

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Declining Balance Method
= 1
(Multiplier)
N

= % reduction each year

Dn =  I (1–)n–1

Bn = I (1–)n

Typical multipliers are 150% and 200%.

200% is also called Double Declining Balance (DDB).

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 Double Declining Balance (DDB)
 A fiber optics testing device is to be DDB depreciated. It has a first cost of
$25,000 and an estimated salvage of $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.

Solution
 The DDB fixed depreciation rate is d = 2/n = 2/12 = 0.1667 per year.
 Year 1: D1 = (0.1667)(25,000)(1 - 0.1667)1-1 = $4167
 BV1 = 25,000(1 - 0.1667)1 = $20,833
 Year 4: D4 = (0.1667)(25,000)(1 - 0.1667)4-1 = $2411
 BV4 = 25,000(1 - 0.1667)4 = $12,054

 Implied S = 25,000(1 - 0.1667)12 = $2803

 Since the estimated S = $2500 is less than $2803, the asset is not fully depreciated when it reaches
its 12-year expected life.
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 DB compared with DDB
 Freeport-McMoRan Mining Company has purchased a
computer-controlled gold ore grading unit for $80,000. The
unit has an anticipated life of 10 years and a salvage value of
$10,000.
 Use the DB and DDB methods to compare the schedule of
depreciation and book values for each year.

Freeport-McMoRan Copper & Gold Inc. (FCX) is a leading international mining company with headquarters in
Phoenix, Arizona. FCX operates large, long-lived, geographically diverse assets with significant proven and
probable reserves of copper, gold and molybdenum. FCX has a dynamic portfolio of operating, expansion and
growth projects in the copper industry and is the world’s largest producer of molybdenum. The company’s
portfolio of assets includes the Grasberg mining complex, the world's largest copper and gold mine in terms of
recoverable reserves; significant mining operations in the Americas, including the large scale Morenci/Safford
minerals district in North America and the Cerro Verde and El Abra operations in South America; and the potential
world-class Tenke Fungurume development project in the Democratic Republic of Congo. 20
 Solution
 An implied DB depreciation rate is determined using

 d = 1 – (10,000/80,000) 1/10 = 0.1877

 0.1877 < 2/n = 0.2, so this DB model does not exceed twice the straight
line rate.
 Table 16–1 presents the Dt values using Equation [16.5] and the BVt values
from Equation [16.9] rounded to the nearest dollar. For example, in year t =
2, the DB results are:
 D2 = d(BV1) = 0.1877(64,984 next slide) = $12,197
 BV2 = 64,984 - 12,197 = $52,787
 Because we round off to even dollars, $2312 is calculated for depreciation in
year 10, but $2318 is deducted to make BV10 = S = $10,000 exactly.
Similar calculations for DDB with d = 0.2 result in the depreciation and
book value series in Table 16–1. 21
DB compared with DDB

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 Tax Depreciation
 The depreciation method that you use for any particular asset
is fixed at the time you first place that asset into service.
Whatever rules or tables are in effect for that year must be
followed as long as you own the property.
 Since Congress has changed the depreciation rules many times
over the years, you may have to use a number of different
depreciation methods if you've owned business property for a
long time.
 Corporations may apply any of the classical methods for book
depreciation.
 For most business property placed in service after 1986, if you
don't claim the equipment expensing deduction for the full
cost of the item, the IRS requires you to depreciate the asset
using MACRS.

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 Modified Accelerated Cost Recovery System (MACRS)
 MACRS was derived from the 1981 ACRS system and went
into effect in 1986.
 Defines statutory recovery (depreciation) percentages.
 Through MACRS, the 1986 Tax Reform Act defined statutory
depreciation rates that take advantage of the accelerated DB
and DDB methods.
 Incorporates the half-year convention.
 By current law – MACRS assumes all assets depreciated by
this method will have a “0” salvage value at the end of the
recovery life.
 Dt = dtB [16.12]
 BVt = BVt-1 – Dt [16.13]
 BVt = first cost – sum of accumulated depreciation [16.14]
t
BVt  B   D j
j 1 24
 The Half-year convention
 During a tax year, assets are purchased and installed throughout the first
year.
 Under past laws, the first year of depreciation had to be prorated by the
number of months remaining in the tax year.
 Under current federal tax law the first year is handled using the half-year
convention.
 Half-year convention assumes that assets are placed in service or
disposed of in midyear, regardless of when these events actually occur
during the year.
 This convention is utilized in this text and in most U.S.- approved tax
depreciation methods.
 There are also mid-quarter and mid-month conventions.

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 Omniture, a leading provider of online business optimization
software, has acquired new workstations and 3D modeling
software for its 100 affiliate sites at a cost of $4000 per site.
 The estimated salvage for each system after 3 years is
expected to be 5% of the first cost.
 The Utah office wants to compare the depreciation for a 3-
year MACRS model (tax depreciation) with that for a 3-year
DDB model (book depreciation), most curious about the
depreciation over the next 2 years.
 (a) Determine which model offers the larger total
depreciation after 2 years.
 (b) Determine the book value for each model after 2 years
and at the end of the recovery period.

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 Solution
The basis is B = $400,000 and the estimated S = 0.05(400,000) = $20,000.
The MACRS rates for n = 3 are taken from Table 16–2 (next slide) and the
depreciation rate for DDB is dmax = 2/3 = 0.6667.
Dt = dtB [16.12]
BVt = BVt-1 – Dt [16.13]
Table 16–3 presents the depreciation and book values. Year 3 depreciation for
DDB would be (0.6667)$44,444 = $29,629, except that this would make BV3 <
$20,000 (44,444 - 29,629 = 14815). BV – tax depr = BV3

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Depreciation rates

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 Solution
 Only the remaining amount of $24,444 is removed (44,444 - 20,000).
 (a) The 2-year accumulated depreciation values from Table 16–3 are
 MACRS: D1 + D2 = $133,320 + 177,800 = $311,120
 DDB: D1 + D2 = $266,667 + 88,889 = $355,556
 The DDB depreciation is larger. (Remember that for tax purposes, Omniture
does not have the choice in the United States of the DDB model.)

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 Solution
 (b) After 2 years the book value for DDB at $44,444 is 50% of the MACRS
book value of $88,880. At the end of recovery (4 years for MACRS due to
the built-in half-year convention, and 3 years for DDB), the MACRS book
value is BV4 = 0 and
 for DDB, BV3 = $20,000.
 This occurs because MACRS always removes the entire first cost,
regardless of the estimated salvage value.
 This is a tax depreciation advantage of the MACRS method.

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 Recovery Period
The expected useful life of property is estimated in years and
used as the n value in alternative evaluation and in depreciation
computations. For book depreciation, the n value should be the
expected useful life. However, when the depreciation will be
claimed as tax deductible, the n value should be lower.
The advantage of a recovery period shorter than the
anticipated useful life is leveraged by the accelerated
depreciation models that write off more of the basis B in the
initial years.
The U.S. government requires that all depreciable property be
classified into a property class that identifies its MACRS-allowed
recovery period.
Table 16–4, a summary of material from IRS Publication 946,
gives examples of assets and the MACRS n values.
Virtually any property considered in an economic analysis has a
MACRS n value of 3, 5, 7, 10, 15, or 20 years.
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MACRS categorizes all business assets into classes and specifies the time period over which you can
write off assets in each class. The most commonly used items are classified in the chart.
http://taxguide.completetax.com/text/Q14_2960.asp (similar to Table 16-4)

Class of Property Items Included

Tractor units, racehorses over two years old, and horses over 12
3-year property
years old when placed in service
Automobiles, taxis, buses, trucks, computers and peripheral
equipment, office machinery (faxes, copiers, calculators etc.),
5-year property
and any property used in research and experimentation. Also
includes breeding and dairy cattle.
Office furniture and fixtures, and any property that has not been
7-year property
designated as belonging to another class.
Vessels, barges, tugs, similar water transportation equipment,
10-year property single-purpose agricultural or horticultural structures, and trees
or vines bearing fruit or nuts.
Depreciable improvements to land such as shrubbery, fences,
15-year property
roads, and bridges.
20-year property Farm buildings that are not agricultural or horticultural structures.
27.5-year property Residential rental property.
Nonresidential real estate, including home offices. (Note that the
39-year property
value of land may not be depreciated.)
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 MACRS Recovery Periods
 Table 16–4 provides two MACRS n values for each property.
 The first is the general depreciation system (GDS) value that the text (MSE 304) uses
in examples and problems.
 The depreciation rates in Table 16–2 (slide 24) correspond to the n values for the GDS
column and provide the fastest write-off allowed.
 The rates utilize the DDB method or the 150% DB method with a switch to SL
depreciation. Note that any asset not in a stated class is automatically assigned a 7-
year recovery period under GDS.
 The far right column of Table 16–4 lists the alternative depreciation system (ADS)
recovery period range. This alternative method allows the use of SL depreciation over
a longer recovery period than the GDS. The half-year convention applies, and any
salvage value is neglected, as it is in regular MACRS.
 The use of ADS is generally a choice left to a company, but it is required for some
special asset situations. Since it takes longer to depreciate the asset, and since the SL
model is required (removing the advantage of accelerated depreciation), ADS is
usually not considered an option for the economic analysis.
 This SL option is sometimes chosen by businesses that are young and do not need
the tax benefit of accelerated depreciation during the first years of operation and
asset ownership.

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Table 16–4: Example MACRS Recovery Periods for Various Asset Descriptions

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http://www.pine-grove.com/depreciation/MACRS.htm 35
 Depletion

 Up to this point, we have discussed depreciation for

assets that can be replaced.
 Depletion, though similar to depreciation, is
applicable only to natural resources.
 When the resources are removed, they cannot be
replaced or repurchased in the same manner as can
a machine, computer, or structure.
 Depletion is applicable to natural deposits removed
from mines, wells, quarries, geothermal deposits,
forests, and the like.
 There are two methods of depletion - cost depletion
and percentage depletion.

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 Cost Depletion
 Cost depletion, sometimes referred to as factor depletion, is
based on the level of activity or usage, not time, as in
depreciation.
 It may be applied to most types of natural resources. The cost
depletion factor for year t, denoted by pt, is the ratio of the first
cost of the resource to the estimated number of units
recoverable.
 The annual depletion charge is pt times the year’s usage or
volume.
 The total cost depletion cannot exceed the first cost of the
resource.
 If the capacity of the property is re-estimated some year in the
future, a new cost depletion factor is determined based upon
the undepleted amount and the new capacity estimate.

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  Brookfield Asset Management Inc. (BAM), a global asset manager focused
on property, power and other infrastructure assets with approximately $95
billion of assets under management, has negotiated the rights to cut timber
on privately held forest acreage for $700,000. An estimated 350 million
board feet of lumber are harvestable.
 (a) Determine the depletion amount for the first 2 years if 15 million and 22
million board feet are removed.
 (b) After 2 years the total recoverable board feet was re-estimated to be 450
million from the time the rights were purchased. Compute the new cost
depletion factor for years 3 and later.

 Brookfield has a 30-year track record of owning and operating timberlands in North
and South America that generate strong, sustainable cash flows.
 Today they have 2.5 million acres of high quality timberlands under management
which include: Island Timberlands, a private equity investment, Longview Timberlands
that encompasses 588,000 acres of high quality fee simple timberlands on the west
coast of Washington and Oregon, and Acadian Timber.

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 Solution
 (a) Determine the depletion amount for the first 2 years if 15 million and 22 million
board feet are removed.
 For $700,000 BAM may cut timber on privately held forest acreage.
 An estimated 350 million board feet of lumber are harvestable.
 Use Equation [16.15] for pt in dollars per million board feet.

 Multiply pt by the annual harvest to obtain depletion of $30,000 (15 * 2000) in year 1 and
$44,000 (22 * 2000) in year 2.
 Continue using pt until a total of $700,000 is written off.
 (b) After 2 years the total recoverable board feet was re-estimated (450 million from the
time the rights were purchased). Compute the new cost depletion factor for years 3 and
later.
 After 2 years, a total of $74,000 (30000 + 44000) has been depleted.
 A new pt value must be calculated based on the remaining $700,000 - 74,000 =
$626,000 investment.
 Additionally, with the new estimate of 450 million board feet, a total of:
 450 -15 - 22 = 413 million board feet remain.
 For years t = 3, 4, . . . , the cost depletion factor is
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 = $1516 per million board feet
 Percentage Depletion
 Percentage depletion is a special consideration given for natural resources.
 A constant, stated percentage of the resource’s gross income may be depleted each
year provided it does not exceed 50% of the company’s taxable income.
 For oil and gas property, the limit is 100% of taxable income.
 The annual depletion amount is calculated as using percentage depletion, total
depletion charges may exceed first cost with no limitation.
 The U.S. government does not generally allow percentage depletion to be applied to
oil and gas wells (except small independent producers) or timber.
 The depletion amount each year may be determined using either the cost method
or the percentage method, as allowed by law.
 Usually, the percentage depletion amount is chosen because of the possibility of
writing off more than the original cost.
 However, the law also requires that the cost depletion amount be chosen if the
percentage depletion is smaller in any year.

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 A gold mine was purchased for $10 million. It has an
anticipated gross income of $5.0 million per year for years 1
to 5 and $3.0 million per year after year 5.
 Assume that depletion charges do not exceed 50% of taxable
income. Compute annual depletion amounts for the mine.
How long will it take to recover the initial investment at i =
0%?

 Agnico-Eagle Mines Limited is an international growth company focused

on gold, with operations in Canada and advanced-stage projects and
opportunities in Canada, Mexico, Finland, and the USA. Agnico-Eagle's
LaRonde Mine in Quebec is Canada's largest gold deposit and is a strong
foundation for international expansion.
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 Solution

 A 15% depletion applies to gold. Depletion amounts are Years 1 to 5:

 0.15(5.0 million) = $750,000
 Years thereafter: 0.15(3.0 million) = $450,000
 A total of $3.75 million is written off in 5 years, and the remaining $6.25
million is written off at $450,000 per year.
 The total number of years is:

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Equations

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 DB Depreciation

Max. depr. rate by law: Book Value amounts (two methods)

2 BVt  B(1  d )t
d max 
n BVt  BVt 1  Dt
Depreciation for year t: Implied Salvage Value
Dt  (d ) BVt 1 impS  BVn  B(1  d ) n

Actual depreciation rate for year t: Implied d for S >0

dt  d (1  d )t 1 1/ n
S
If BVt-1 not known, apply:
1  
B
Dt  dB (1  d )t 1 Excel Function: =DDB(B,S,n,t,d)
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