Engineering Economy Chapter 16x

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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Authored by Don Smith, Texas A&M University 2004

CHAPTER 16

DEPRECIATION METHODS

Mc

GrawHill

ENGINEERING ECONOMY Sixth Edition Blank and

Tarquin

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Chapter 16 Preliminary Statement

The material presented in this chapter applies to the current (2001) U.S. Federal Corporate Income Tax Code relating to depreciation. As such, which changing legislation, parts of this chapter could be modified by legislation enacted after publication of this text.

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Chapter 16 Preliminary Statement cont.

Students are encouraged to research the current depreciation rules as they may pertain to the material in this chapter. The IRS web site { www.irs.gov } should be accessed for IRS Publication 946 for the current rules and regualtions.

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Chapter 16 Learning Objectives

1. Depreciation Terminology

2. Straight Line Depreciation

3. Double Declining Balance

Depreciation

4. Modified Accelerated Cost

Recovery System (MACRS)

5. Determining the MACRS Recovery

Period

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Section 16.1 Depreciation - Definition

Depreciation is the reduction in value over time of an asset. Brought on by: Wear and tear, use; Deterioration; Obsolescence.

Other definitions follow:

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16.1 Depreciation - Definition

Depreciation – Original Reason: Purely economic!

Economic View: Depreciation represents a “ratable”

using up of devaluation of a productive asset.

The asset must have a finite life span that can be reasonably estimated.

Deprecation represent a proper charge against future income produced by the asset in question.

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16.1 Depreciation and Depletion

Depreciation provides for the retirement of a productive asset; Depletion provides for the use of a natural resource; Amortization recognizes a prepaid expense for tax purposes.

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16.1 Importance of Depreciation

Federal tax law defines the concept of “taxable income” as: Gross Income – Real Cash Expenses –

interest – Depreciation amounts.

Tax Due = {Taxable Income}(Tax Rate).

Taxes and after-tax cash flows are presented in Chapter 17.

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16.1 Tax Deductions

Federal Tax law permits the reduction of Gross Income by a category of elements termed “deductions”. Most “deductions” are real cash flows: Wages and salaries; Cost of materials; Utilities; Interest Paid on debt; State and local taxes paid; Etc

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16.1 Tax Equation

The General Federal Tax Equation is:

Tax. Income = Gross Income – {Real Expenses + Interest Paid + Depreciation + Depletion}

All of the above amounts EXCEPT depreciation amounts and depletion amounts

are real cash flow to the firm.

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16.1 Non-cash flow amounts

Depreciation and depletion amounts represent “non-cash flow” amounts within an accounting period. Federal and state tax laws recognize various forms of depreciation amounts and depletions amounts to be “tax deductible amounts” – but are not real cash flows per se.

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16.1 After-Tax Cash Flows

All “for profit” firms seek to minimize legally their respective income tax liabilities. Depreciation and depletions amounts will lower the taxable income amount and hence the tax liability if claimed. This chapter focuses on the various forms of depreciation and depletion calculations.

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16.1 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.

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16.1 Tax Savings from Depreciation

Depreciation amounts represent a form of tax savings to the profitable firm. Assume a tax rate of say 30%. 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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16.1 Simple Example

Consider a basic sewing machine that is used to sew shoes; Assume this sewing machine sews 300,000 pairs of shoes, pair by pair. The sewing machine is loosing value over time due to the use of the machine. An Economic Concept is at play….

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16.1 Simple Example

If the sewing machine costs $2500 to begin with then; The initial cost of the sewing machine should be prorated over the 300,000 pairs of shoes. The initial cost of the sewing machine is termed the BASIS of the asset. One can allocate the original basis over the number of pairs of shoes the machine produces.

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16.1 Types of Depreciation

Book Depreciation Used by a firm for internal financial

and managerial management.

Tax Depreciation Used by a firm for state and federal

income tax reporting. Follows strict rules and regulations.

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16.1 Book Depreciation

Value of the asset on the firm’s accounting records at any given point in time. Used for internal managerial decision making. Management is free to use any method they so choose to compute book depreciation amounts.

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16.1 Book Depreciation

Used internally by the firm; Be any method: Straight Line, Declining Balance; Sum of the years digits; Other.

Defines the reduced investment in an asset based upon usage pattern and an assumed life.

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16.1 Tax Depreciation

Tax Depreciation: Must follow current state and federal

law pertaining to acceptable methods for computing depreciation for income tax purposes.

Federal Lever (2001) MACRS Methods

General Depreciation System (GDS).Alternate Depreciation System

(ADS).

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16.1 Book Value of an Asset

Book value: Accounting Term, Reflects the undepreciated (value) on

the firms books at a given point in time.

May or may not reflect the true market value of the asset at a point in time.

Market value of an asset is what a willing buyer and willing seller agree to consummate a sale or exchange.

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CHAPTER 16

Section 16.1 DEPRECIATION TERMINOLOGY

Important Terms and their meanings

Mc

GrawHill

ENGINEERING ECONOMY Fifth Edition

Blank and Tarquin

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16.1 Terminology

The following slides state and define depreciation terminology;

Terminology is very important to the understanding of this chapter;

Please focus on the terms and their respective meanings.

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16.1 BASIS of an Asset (B)

The Basis of an asset is: Purchase cost plus, Delivery Costs plus, Installation costs and, Any other costs associated with

installing and preparing the asset for use.

To be eligible for depreciation the asset MUST be placed in-service and ready for use.

Symbol: B for “Basis” – A dollar amount.

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16.1 Book Value of an Asset (BVt)

The remaining, undepreciated capital investment on the firm’s books after the accumulated amounts of depreciation have been subtracted from the original cost basis.

BV’s are usually updated at the end of the firm’s accounting year.

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16.1 Recovery period - n

Recovery Period (in years) is the depreciable life n of the asset in years.

Often there are different n values for book and tax depreciation.

Both of these values may be different from the asset's estimated productive life.

Also know as the Depreciable life.

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16.1 Market Value (MVt)

Market value, a term also used in replacement analysis, is the estimate amount realizable if the asset were sold on the open market.

Because of the structure of depreciation laws, the book value and market value may substantially different.

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16.1 Market Value (MVt)

For example, a commercial building tends to increase in market value, but the book value will decrease as depreciation charges are taken.

A Computer workstation may have a market value much lower than its book value due to rapidly changing technology.

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16.1 Salvage Value - S

Salvage value is the estimated trade-in or market value at the end of the asset's useful life.

The salvage value, S expressed as an estimated dollar amount or as a percentage of the first cost, may be positive, zero, or negative due to dismantling and carry-away costs.

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16.1 Salvage Value - S

Salvage values are estimated “up-front” – at the time of the original purchase.

As an estimated value, the actual salvage value out at time t = n may or may not reflect the original estimate.

Generally speaking, one cannot depreciate an asset below it’s estimated salvage value.

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16.1 Depreciation rate - dt

Depreciation rate or recovery rate is the fraction of the first cost removed by depreciation each year.

This rate, denoted by dt may be

the same each year, which is called the straight-line rate, or different for each year of the recovery period.

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16.1 Personal property

Personal property, one of the two types of property for which depreciation is allowed, is the income-producing, tangible possessions of a corporation used to conduct business.

Not to be confused with an individual’s personal property like clothes, furniture, etc.

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16.1 Personal property - continued

Included are most manufacturing and service

industry property-vehicles, manufacturing equipment, materials

handling devices, computers and networking equipment,

telephone equipment office furniture, refining process equipment, and much more.

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16.1 Real property

Real property includes: real estate and all improvements office buildings, manufacturing structures, test facilities, warehouses, apartments, and other structures.

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16.1 Real property

Real property includes real estate and all improvements-office buildings manufacturing structures, test facilities, warehouses, apartments, and other structures.

Land itself is considered real property, but it is not depreciable because it has an infinite life – land can never be depreciated for tax purposes.

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16.1 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.

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16.1 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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16.1 Property Eligible for Depreciation

Real or Personal; Productive Assets; Buildings and structures but not land.

Used in the pursuit of income generation;

Have a finite, estimatable life

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16.1 Section “38” Property

Often the term “Section 38” or, Section 1238” is used:

Section 1238 (from the IRS Code, Section 1238) is defined as: Tangible personal property (but not

buildings or their structural components) that is eligible for depreciation under the Federal tax code.

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16.1 Code Section 1250 Property

Under the IRS code, Section 1250 property is “real” property: Buildings and structures eligible for

depreciation.

Summary: Section 1238 – Personal Property, Section 1250 – Real Property.

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16.1 Depreciation Models

Basic (traditional) models are: Straight Line Method (SL), Sum-of-the years Digits (SYD), Declining Balance Method (DB). Today, the MACRS Method (a form of

declining balance-modified).

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16.1 Classical Methods

Classical Methods (supporting Excel functions) are: Straight-line, SYD; DB.

See Appendix at the end of chapter 16.

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16.1 Section 179 Deduction

Section 179 Deduction: Special provision of the tax code: Benefits the small business: Provides an economic incentive for

small businesses to invest in assets required to produce a profit:

Permits the “expensing” of up to a certain amount of investment in depreciable assets in a given tax year. (one-year write-off).

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16.1 Section 179 Allowance

The 179 allowance can reduce the current year’s income tax liability. Has a statutory maximum: For 2001 – Max. Amount = $24,000 For 2003 – increases to $25,000.

If more than $200,000 is invested in a given year the 179 amount is reduced dollar for dollar.

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16.1 History

Before 1981 – US code recognized the classical methods. 1981 and after: Classical methods were disallowed for

Federal Tax purposes and replaced with a system termed “ACRS”.

ACRS – Accelerated Capital Recovery System.

1986 ACRS was replaced with MACRS – Modified Accelerated Capital Recovery System.

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16.1 Today….

US Federal Corporate Income Taxes must be computed using the MACRS system! States who have corporate income tax laws generally permit all or part of the classical methods to be used for state corporate tax analysis.

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16.1 Comparison of Methods

It is beneficial to compare: Straight-line, SYD, and DB methods.

The best way is to plot the book values of each method vs. the recovery period (time). See Figure 16.1 on page 510.

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16.1 Book value vs. Time: General Case

In general, a book value plot will look like:

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16.1 Book Value Plot for Classical Methods

For SL, DB, and MACRS we have:

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16.1 Accelerate Depreciation

From Figure 16-1 on page 510: SL book values decline in a linear

fashion down to a specified salvage value.

The DB methods allows the book value to accelerate faster since the DB plot of book value is below the SL book values.

MACRS also permits accelerated book values but not as good as the pure DB method permits.

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16.1 Accelerating Depreciation

The SL methods writes off the asset in equal amounts over the recovery period. The DB methods permits greater depreciation amounts in the early years and hence, reduces the book value faster than the SL method. Likewise for the MACRS method!

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16.1 Accelerating Depreciation

More depreciation in the early years means more tax savings sooner. Assumes a profitable firm. Tax savings early in the life of an asset has a greater present value that tax savings out in time. Larger depreciation amounts early on result is increased PW of future tax savings to the firm.

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16.1 What Does it Mean?

If the firm is profitable then more depreciation amounts in the early years means: Lower tax liability; Pay less taxes – more $$ available for

reinvestment! The firm can retain more after-tax

funds if the depreciation is accelerated in the early years of an assets’ life.

Thus, more depreciation $$ early on are better!

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16.1 Keeping Up

All engineers engaged in the analysis of industrial projects need to be reasonably informed regarding the current Federal Tax law regarding depreciation. The law does change! Must keep up with the changes! IRS Web site: www.irs.gov Check it out for downloadable

publications

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CHAPTER 16

Section 16.2STRAIGHT-LINE (SL)

DEPRECIATION

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16.2 Straight-Line: The Standard (SL)

SL depreciation is the standard from which all other plans are compared.

Assumes the book value declines in a uniform manner down to a specified salvage value – S over n time periods.

Assume n years for an asset’s life: The depreciation rate –dt is then:

Dt = 1/n

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16.2 SL Example

Notation (to be followed herein) t = the year (t = 1,2, …, n) Dt = Annual depreciation charge,

B = the first cost or unadjusted Basis,

S = Estimated Salvage Value at t = n,

n = The Recovery Period, d = The Depreciation Rate = 1/n

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16.2 Straight Line Method

Compute the Basis minus the estimated salvage value and divide by n

( )t

t

D B S d

B SD

n

[16.1]

[16.2]

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16.2 SL Excel Function

In Excel the built-in function is:

SLN(B,S,n)

Displays the annual depreciation Dt as a single cell operation.

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16.2 SL Example

B = $50,000;“n” = 5 years; S = $10,000 at t = 5; Dt for each year is: ($50,000 - $10,000)/5 = $8,000/year

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16.2 SL Example: Tabulation

t Dt BVt

1 $8,000 $42,000

2 8,000 34,000

3 8,000 26,000

4 8,000 18,000

5 8,000 10,000

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16.2 Plot of the Straight-line Book Value

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16.2 SL Observations

The SL method starts at B and directly targets “S” n time periods from the present. The Depreciation amounts are all equal ($8,000 in this case). The book values decline at the same rate down to $10,000.

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CHAPTER 16

Section 16.3DECLINING BALANCE AND

DOUBLE DECLINING BALANCE DEPRECIATION

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16.3 Declining Balance Method (DB)

DB is an accelerated depreciation method; Provides greater depreciation amounts in the early time periods over straight-line. The method is more complex that the SL method. Requires assuming a DB rate – normally taken to equal 2 x SL rate.

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16.3 DB Rate

Given the DB rate, Dt for year t is found by multiplying the

beginning of time period book value by the rate.

The maximum DB rate set by law is: dMAX = 2(1/n) or, twice what the straight rate

would be.

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16.3 DB Equations

[16.5]

[16.6]

Depr. For year “t”

Depr. Rate

1

1

( )

( ) (1 )

t t

tt

D d BV

d d B d

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16.3 DB if BVt-1 Not Known

If BV at the end of the preceding year is not known apply:

1( ) (1 )ttD d B d [16.7]

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16.3 DB: Book Value Determination

BVt can be determined in two ways: 1. Using the rate d and the basis, B or, 2. Subtracting the current year’s

depreciation from the previous year’s book value.

BVt from d and B: Apply:

1

(1 )tt

t t

BV B d

BV BV D

[16.8]

[16.9]

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16.3 DB: Implied Salvage Value

Note, from equations 16.4 – 16.9 there is no mention of the salvage value –S! DB does not directly use the estimated salvage value. DB has its own implied salvage value. The pure DB method will never depreciate an asset down to a “0” salvage value unless you solve for a “d” rate ( Eq. 16.11).

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16.3 DB: Implied Salvage Value

The implied salvage value built into the DB method is:

(1 )nnS BV B d [16.9]

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16.3 Implied SV for DB Depreciation

Permissible range for d is:

0 < d < (2/n) To force a prescribed salvage value – S apply: Implied d = 1 – (S/B)1/n

[16.11]

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16.3 DB rate - d

By law, the maximum rate for DB is specified to =: Twice the SL rate for a given n. This is called “The Double Declining

Balance Rate”. If d = 1.5(SL rate) it is termed the

150% DB rate. d can never exceed 2(1/n) but can be

less!

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16.3 Excel DB Functions

Excel supports the DB approach as a single cell function:Use: DDB(B,S,n,t,d) as a cell function. “d” argument can be omitted: If so, a

“d” of 2 is assumed by Excel.

Excel also supports a “DB” function. Suggest one avoid using this one as

special care must be taken! DB(B,S,n,t)

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16.3 Example 16.3

B = $80,000; n = 10 years; S = $10,000; Apply the DB and DDB methods to compute the depreciation amounts and associated BV’s.

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16.3 Example 16.3 DB approach

The DB methods first computes the implied salvage value from: d = 1 – (10,000/80,000)1/10 = 0.1877 d = 18.77% will target the $10,000 SV

at t = 10.

See Table 16-1 on page 515.

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16.3 Spreadsheet Model for Ex. 16.3

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CHAPTER 16

Section 16.4MODIFIED ACCELERATED COST

RECOVERY SYSTEMMACRS

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16.4 MACRS Method

MACRS was derived from the 1981 ACRS system and went into effect in 1986. Defines statutory recovery (depreciation) percentages. Percentages were derived from the DB method with a switch to SL at the optimal time and, Incorporates the half-year convention.

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16.4 MACRS Salvage Value

The MACRS approach assumes a salvage value of “0” even though that might not be the case! By current law – MACRS assumes all assets depreciated by this method will have a “0” salvage value at the end of the recovery life.

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16.4 MACRS Actual Depreciation

Depreciation for year “t” is:

Dt = dt(B)

[16.12]

dt = a depreciation rate (per cent)

applicable for the t-th year.

The dt’s are published percentage

rates and cannot be changed.

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16.4 MACRS Book Values

MACRS book values are determined from: BVt = BVt-1 – Dt [16.13] Or, BVt = Basis – sum of accumulated

depreciation.

1

j t

t jj

BV B D

[16.14]

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16.4 Observations

Under MACRS: The entire Basis (B) is fully depreciated

(recovered) over a specified number of years (recovery periods).

A “0” salvage value is a functional part of the MACRS system – by law.

In reality, there may be a positive, “0”, or negative salvage value at some point in time.

Adjustments will have to be made at that time. (Disposal analysis)

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16.4 MACRS Recovery Periods

For Personal Property the following MACRS recovery periods apply: 3- years, 5-years, 7-years, 10-years, 15-years and, 20-years.

Six Property Classes for Personal Property – mid-year convention applies.

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16.4 MACRS Personal Property Recovery Rates

Year-t 3-Year 5-Year 7-Year 10-Year 15-Year 20-Year

1 0.3333 0.2000 0.1429 0.1000 0.0500 0.03752 0.4445 0.3200 0.2449 0.1800 0.0950 0.07223 0.1481 0.1920 0.1749 0.1440 0.0855 0.06684 0.0741 0.1152 0.1249 0.1152 0.0770 0.06185 0.1152 0.0893 0.0922 0.0693 0.05716 0.0576 0.0892 0.0737 0.0623 0.05297 0.0893 0.0655 0.0590 0.04898 0.0446 0.0655 0.0590 0.04529 0.0656 0.0591 0.0446

10 0.0655 0.0590 0.044611 0.0328 0.0591 0.044612 0.0590 0.044613 0.0591 0.044614 0.0590 0.044615 0.0591 0.044616 0.0295 0.044617 0.044618 0.044619 0.044620 0.044621 0.0223

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

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16.4 Real Property Classes

Real Property – buildings, structures, residential rental and non-residential office-factory types: 27.5-years for residential rental

property; 39 years for all other properties. Published percentages prorated by

months of the year the property is placed in service.

Assumes a mid-month convention.

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16.4 39-Year Depreciation Rates

Straight Line Method for n = 39. d = 1/39 = 0.02564 or 2.564% per year; Except in year 1 and in year 40 where technical adjustments are made in the percentages.

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16.4 Recovery Lives

Examine Table 16-2 on page 518. You will see the 6 Recovery Classes and their associated percentages. Note, for each life category there are n+1 percentage values where n is the class life. Example: Three-year Recovery period there are 4

recovery percentages!

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16.4 Nominal Recovery Periods

3- year property is really recovered over 4 years; 5-year property is really recovered over 6 years; And so forth for each of the other classes. Why is this the case?

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16.4 n+1 Rule

The actual recovery of a given class life assumes a half-year convention. That is, it is assumed by law that an asset is placed in-service at the middle of the first year. It does not matter when it is actually placed in-service; So, only a ½ year of recovery is permitted in the first year.

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16.4 n+1 Explained

By law, ½ year of recovery is permitted in the first year and, The remaining recovery is spread out over n additional years. See Appendix 16A.3 for more details.

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16.4 Derivation of the 3-year MACRS rates

For recovery periods of 3,5,7, and 10 years, the 200% DB with a switch to straight line is imposed. For n = 3, the Straight-line rate is 1/3. Twice the straight-line rate is 2(1/3) or 2/3. (0.6667) Assume a basis of $1.00 for simplicity; Let the original basis at time t = 0 = 1.000.

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16.4 3-Year analysis: First Year

B = 1.000

DDB rate = 0.6667;

But only ½ year in year 1 is permitted by law so,

d1 = 0.6667/2 = 0.3333;

D1 = (0.3333)(1) = 33.33%

BV1 = 1 – 0.3333 = 0.6667

remaining at the end of year 1.

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16.4 Year 2.

BV at the end of year 1: 0.6667B;

To be recovered over 3 years.

Rate for year 2 is (from DDB) 0.6667(0.6667) = 0.4445 or 44.45%

So, d2 = 44.45% and,

D2 = 44.45% of B.

BV2 = BV1 – D2 = 0.6667B – 0.4445B;

BV2 = 0.2222B ( 2 years remaining to

recover).

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16.4 Year 3: Should one switch to SL? BV2 = 0.2222B;

SL amount over 2 years would be: 0.2222/2 = 0.1111 for each year;

What is the MACRS deduction for year 3 if DDB is applied? d3 = 0.6667(0.2222B) = 0.1481 or 14.81%

Which is greater for year 3?11.11% by switching or,14.81% by staying with DDB?Ans: Go with the 14.81% …greater than

11.11%

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16.4 Year 4

Take the 14.81% of the Basis for year 3;

Book value at the end of year 3 will be

BV2 – D3 = 0.2222B - .1481B = 0.0741B.

If BV3 = 0.0741B and there is only one

more year remaining then to achieve a “0” salvage value at the end of year 4

we take d4 = 0.0741 – we are done!

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16.4 Completed MACRS 3-year Rates

t dt BVt

1 0.3333 0.6667B

2 0.4445 0.2222B

3 0.1481 0.0741B

4 0.0741 0

1.0000

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CHAPTER 16

Section 16.5DETERMINING THE MACRS

RECOVERY PERIOD

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16.5 MACRS Recovery Periods

For book depreciation one should use a life the best reflects the anticipated or expected useful life. For tax depreciation one generally wants as short as possible recovery period to generate more immediate tax savings. For book depreciation use whatever life best defines the usage rate of the asset.

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16.5 MACRS Recovery Lives

For Federal tax purposes, the proper recovery life is found from IRS publications (Pub 946). Table 16-4 illustrated general asset descriptions and their respective MACRS recovery periods permitted by law. These breakdowns are termed Property Classes.

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16.5 Property Classes - Examples

3- Year Property: Special manufacturing and handling

devices, tractors and racehorses.

5- Year Property: Computers and peripherals, Duplicating equipment. Automobiles, trucks, buses, Cargo containers, Some manufacturing equipment.

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16.5 Property Class Examples

7 –Year Property Class: Office furniture, Some manufacturing equipment, Railroad cars, engines and tracks, Agricultural machinery, Petroleum equipment and natural gas

equipment, All property not in another class!

The 7-year class is the ‘default’ class!

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16.5 MACRS Recovery Lives

10-Year Class: Water transportation equipment, Petroleum refining, Agricultural processing equipment, Durable goods manufacturing

equipment, Ship building.

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16.5 Property Classes - continued

15-Year Class: Land improvements, Landscaping, Pipelines, Nuclear power production equipment, Telephone distribution and switching

equipment.

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20-Year Class: Municipal sewers, (developers) Farm buildings, Telephone switching equipment, Power production equipment, Water utilities equipment.

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27.5-Year Property: (Real Property) Residential rental property (homes and

mobile homes).

39-Year Property (Real Property) Nonresidential real property attached to

the land, but NOT the land itself.

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16.5 Recovery Classifications

Engineers should have access to the current IRS publications regarding property classes. If, in doubt, an inquiry can be made (in writing, to the regional office of the IRS for a ruling as to what class questionable property will be accepted.

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16.5 The Alternate Depreciation System

The IRS offers what is termed the Alternate Depreciation System – ADS. It is a modified form of the MACRS system. Applies a straight-line approach with the half-year convention. Generally used by small or growing firms that do not have sufficient taxable income now and in the immediate future.

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16.5 ADS: Overview: 5-Year Example

ADS applies a form of the straight-line method with the half-year convention. Assume 5-Year Property Class; “n” = 5; 1/n = 0.20 per year except in the first

year and in the last year (n=6) Year 1: d1 = ½(0.20) = 0.10 or 10% of B Years 2-5 = 0.20 or 20% of B; Remaining amount – 10% flows over to

the last year, t = 6.

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16.5 ADS: 5-Year Rates Tabulated

“t” dt BVt

1 0.10 0.90B

2 0.20 0.70B

3 0.20 0.50B

4 0.20 0.30B

5 0.20 0.10B

6 0.10 0

1.00

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16.5 ADS: Reason For.

The ADS is available to smaller firms or firms that are just starting up. Some firms may not be generating sufficient profits to take advantage of the more accelerated depreciation rates that the MACRS-GDS provides. Thus, if GDS is elected, the firm may be loosing deductions in the early years. ADS provides some relief for firms in this situation.

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16.5 ADS: Election

For both the ADS and the GDS: For a given tax year the firm elects

either the:ADS system for all assets placed in

service for the current tax year or,The GDS (accelerated method) for all

assets placed in service for the current tax year.

The firm cannot mix ADS with GDS within the tax year! (one or the other.)

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16.5 ADS - GDS:

In engineering economy analysis of industrial projects: Most analysis will be accomplished

using the GDS – accelerated depreciation rates.

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Section 16.6 DEPLETION METHODS

Depreciation or cost recovery is applied to assets that can be replaced. Depletion applies to resources that are not easily replaced like: Timber, Mineral deposits, Oil and gas, Etc.

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16.6 DEPLETION: Two Types

Cost Depletion Called “factor depletion”; Based upon the level of activity or

usage; Time is not involved.

Percentage Depletion Applies a constant, stated percentage

of the resource's gross income provided it does not exceed 50% of the firm’s current taxable income.

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16.6 DEPLETION: Cost Depletion

First, the cost basis of the resource is determined – first cost or investment cost. Second – one must estimate the amount of the resource that is available for extraction. Termed: Resource Capacity. It is an estimated value since it is impossible

to predict exactly the true resource capacity!

Then, cost depletion factor pt for year t

is calculated …next slide…

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16.6 DEPLETION: Cost Depletion Factor

Let t denote the year;

pt denotes the depletion factor for

year t.

Then, pt is defined as:

first cost

resource capacitytp [16.15]

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16.6 DEPLETION: Cost Method Example

Example 16.5 page 523 Company buys timber rights to land for $700,000 at time t = 0. Estimated 350 million board feet that can be harvested. This is important: A realistic estimate

of the resource must be accomplished up front!

Re-estimates can be made in the future and adjustments made.

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16.6 DEPLETION: Important Issue

Major Point for Depletion: There must be a reasonable estimate

of the amount of the resource that is being extracted.

For firms engaged in extraction activities the process of resource estimation is an important activity and requires expert analysis.

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16.6 DEPLETION: Example 16.5

Determine the cost depletion amount for the first two years of harvesting if: Year 1: Harvest 15 million bdft and, Year 2: Harvest 22 million bdft.

Compute pt as: pt = ($700,000)/350 m-bdft = $2,000/m-

bdft. Deplt=1 = 15M-bdft($2,000) = $30,000. Deplt=2 = 22M-bdft($2,000) = $44,000.

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Year 1 depletion allowance = $30,000 Year 2 depletion allowance = $44,000 For year 1 the $30,000 can be treated as a deduction from gross income so long as the depletion amount does not exceed the first cost of the resource.Likewise, $44,000 can be deducted from year 2’s Gross Income.

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16.6 DEPLETION Example

For the first 2 years the recovery is: Year 1: $700,000 - $30,000 = $670,000 left to

recover: Year 2:

$670,000 - $44,000 = $626,000 left to recover.

This process continues so long as the original estimate applies.

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16.6 DEPLETION - Example

Original Estimate – 350 m-bdft After years 1 and 2, 37 m-bdft have been extracted leaving and estimated: 350 – 37 = 313 m-bdft of the resource

left.

This process continues on until the original $700,000 investment is written off or…. A revised estimate of the resource is made.

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16.6 DEPLETION: Revision of the Resource

Assume at the end of year 2 the resource capacity is re-estimated. Assume the re-estimate reveals that there is 450 m-bdft remaining to start year 3. Revision of the factor is now necessary. Remember, $626,000 remains from the initial investment of $700,000.

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16.6 DEPLETION – Revision for Year 3 on

Cost basis for year 3 is $626,000

New pt is calculated as:

pt = $626,000/413 = $1,516/M-bdft.

For years 3 on the $1,516/m-bdft is applied to calculate the depletion allowance.

Use this factor until the $700,000 investment is fully written off or another re-estimation is conducted.

The process stops when the $700,000 is “0”.

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16.6 DEPLETION: Percentage Depletion

Percentage depletion uses IRS mandated percentages for classes of resources. The depletion allowance for this method cannot exceed 50% of the firm’s taxable income before the depletion allowance is claimed. Percent Depletion = Percentage(gross income from activity)

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16.6 DEPLETION: Percent MethodDeposit Percentage

Sulfur, uranium, lead, nickel ,zinc,

22%gold, silver ,copper, iron ore and geothermal deposits

15%

Oil and gas wells 15%Coal, lignite, sodium chloride

10%

Gravel, sand, peat, stone

5%

Most other minerals

14%

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16.6 DEPLETION: Percent Method

Warning: These percents change over time due

to changes in the tax law. If you are involved in extraction

industry analysis you must keep up with the current regulations and percents for this method!

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16.6 DEPLETION

See Example 16.6 on page 524 Gold mine purchased for $10 million. Estimated gross income for years 1-5 of $5.0 million and $3.0 million after year 5. Depletion charges cannot exceed 50% of taxable income in any given year (by current tax law). For gold the rate is 15%/year.

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Years 1- 5: (0.15)(5.0 million) = $750,000/year

Years 5 on… (0.15)(3.0 million) = $450,000/year

First 5 years: Write-off = (5)($750,000) = $3.75 million There is $10 million - $3.75 m = $6.25 m left.

Years 6 on… 5 + 6.25 m/$450,000 = 5 + 13.9 = 19 years The $10 m is fully recovered after 19 years.

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16.6 Depletion Law Requirement

The depletion allowance can be determined using either the cost or the percentage method. The current law requires: Cost depletion be used IF the percentage

depletion is smaller in any year. This means that one should apply both

methods in the beginning.

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16.6 Depletion Law Requirement

Calculate both amounts: Cost Depletion ($-Depl) And percentage Depletion (%-Depl). Then apply the following rule each year:

%Depl if %Depl $Depl

Annual Depletion =$Depl if %Depl $Depl

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Chapter 16 Summary

Depreciation may be determined for internal company records (book depreciation) or for income tax purposes (tax depreciation). In the U.S., the MACRS method is the only one allowed for tax depreciation. Depreciation does not result in actual cash flows directly – rather, tax savings are the result of depreciation.

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Chapter 16 Summary cont.

It is a book method by which the capital investment in tangible property is recovered. The annual depreciation amount is tax deductible, which can result in actual cash flow changes.

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Chapter 16 Summary cont.: Straight-Line Depreciation

It writes off capital investment linearly over n years. The estimated salvage value is always considered.This is the classical, nonaccelerated depreciation model. Simple to apply and is a popular method for computing book depreciation.

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Chapter 16 Summary cont.: Declining Balance

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, which is called double declining balance (DDB).

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Chapter 16 Summary cont.:Declining Balance

It has an implied salvage that may be lower than the estimated salvage.It is not an approved tax depreciation method in the U.S. It is frequently use for book depreciation purposes. May not target a specified salvage value.MACRS applies a modification of this method to determine MACRS recovery percents.

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Chapter 16 Summary cont.: 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.

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Chapter 16 Summary cont.: MACRS

The actual recovery period is 1 year longer due to the imposed half-year convention.MACRS alternate straight line depreciation is an option, and is generally used by firms that are growing and would be wasting MACRS accelerated depreciation amounts.

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Chapter 16 Summary cont.: Depletion

Depletion methods are used to recover investment in the extraction or harvesting of natural resources. Two Methods: Cost Depletion, Percentage Depletion.

Specific rules apply to both methods. Normally, one would calculate depletion

allowances by both methods then apply the IRS mandated permission rules.

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