ise 307- chapter 9

DEPRECIATION AND INCOME TAXES

CHAPTER 9

Asset Depreciation

Book Depreciation

Tax Depreciation

Corporate Taxes

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Depreciation• Definition: Loss of value for a fixed asset• Example: You purchased a car worth $15,000 at the beginning of year 2000.

Depreciatio

nEnd of Year

Market Value

Loss of Value

012345

$15,00010,000

8,0006,0005,0004,000

$5,0002,0002,0001,0001,000p


Why Do We Consider Depreciation?

Gross Income -Expenses:(Cost of goods sold)(Depreciation)(operating expenses)

Taxable Income

- Income taxes

Net income (profit)

Business Expense: Depreciation is viewed as a part of business expenses that reduce taxable income.

Depreciation Concept

is a term used in accounting, economics, and finance to spread the cost of an asset over the period of several years.

is the reduction in the value of an asset due to usage, passage of time, and technological outdating or other factors.

Economic Depreciation Purchase Price – Market Value

Economic losses due to both physical deterioration and technological obsolescence.

Accounting Depreciation Systematic allocation (distribution) of the initial cost

of an asset in parts over a time or decline in value over time and sometimes referred to more generally as asset depreciation.


Asset Depreciation

Depreciation

Economic depreciationthe gradual decrease inutility in an asset with

use and time

Accounting depreciationThe systematic allocation

of an asset’s value inportions over its

depreciable life—oftenused in engineeringeconomic analysis

Physicaldepreciation

Functionaldepreciation

Book depreciation

Taxdepreciation

Factors to Consider in the process of an Asset Depreciation

What is the cost of the asset?

What is asset’s value at the end of its useful life?

What is the depreciable life of the asset?

What method of depreciation do we choose?


What Can Be Depreciated?

Assets used in business or held for production of income

Assets having a definite useful life and a life longer than one year

Assets that must wear out, become obsolete or lose value

A qualifying asset for depreciation must satisfy all of the three conditions above.

What Can Be Depreciated?Depreciable property has the following characteristics

1. Assets must be used in business or held for production of income.

2. Assets must have a definite service (useful) life which must be longer than one year.

3. Assets must be wear out, become obsolete or loses value from natural causes.

A qualifying asset for depreciation must satisfy all of the three conditions above.

Example 9.1 on Cost Basis

Cost Basis of an asset represents the total cost that is claimed as an expense over an asset's life and generally includes the actual cost of an asset and all accompanying expenses, such as freight, site preparation, and installation.

Cost of a new stamping machine (Invoice price) $22,70

0Freight 525Installation labor 1,350Site preparation 2,125Cost of Machine (Cost basis)

$26,700

Useful Life and Salvage Value:

The following questions must be answered when determining an asset's depreciable life. i.e., the number of years overwhich the asset is to be depreciated.

Q1) How long will an asset be useful to the company?

Q2) What do statutes (law) and accounting rules mandate in determining an asset's depreciable life?

Determining the service life of an asset is often very difficult. The uncertainty of these estimates often led to disputes between taxpayers and the Internal Revenue Service (IRS= Agency for collecting tax at US) The IRS publishes guidelines on lives for categories of assets known as

Asset Depreciation Ranges or ADRs. These guidelines specify a range of lives for classes of assets, based on historical data allowing taxpayers to choose a depreciable life within the specified range for a given asset.

Asset Depreciation Range ADR (years)

Assets Used Lower Limit

Midpoint Life

Upper Limit

Office furniture, fixtures, and equipment

8 10 12

Information systems (computers) 5 6 7Airplanes 5 6 7Automobiles, taxis 2.5 3 3.5Buses 7 9 11Light trucks 3 4 5Heavy trucks (concrete ready-mixer) 5 6 7Railroad cars and locomotives 12 15 18Tractor units 5 6 7Vessels, barges, tugs, and water transportation system

14.5 18 21.5

Industrial steam and electrical generation

17.5 22 26.5

Manufacturer of electrical and non-electrical machinery

8 10 12

Manufacturer of electronic components, products,

5 6 7

Manufacturer of motor vehicles 9.5 12 14.5Telephone distribution plant 28 35 42

Types of Depreciation Book Depreciation [financial report]

Firms report depreciation and net income to investors / stockholders (such as in balance sheet or income statement)

Tax Depreciation [Internal Revenue Service] In calculating income taxes for the IRS In engineering economics, we use depreciation in the context of

tax depreciation Tax depreciation method allows firms to benefit from the tax

advantages of depreciating assets, (will not pay high income tax). Tax depreciation methods generally permit a higher depreciation

in earlier years than do book depreciation methods,. Firms generally pay lower taxes in the initial years of an

investment project.

Book Depreciation Methods

Purpose: Used to report net income to stockholders/investors

Types of Depreciation Methods:

Straight-Line Method Declining Balance Method Unit Production Method

Straight – Line (SL) Method

Principle of this methodA fixed asset as providing its service in a uniform fashion over its life.

That is, the asset provides equal amount of service in each year of its useful life.

FormulaAnnual Depreciation

Dn = (I – S) / N and constant for all n (years).

Book Value after Depreciation chargeBn = I – n (Dn) where I = cost basisS = Salvage valueN = depreciable life

Example 9.2 Straight – Line MethodConsider the following data on an automobile, compute the annual depreciation allowances and resulting book values using the straight-line method.

n Dn Bn

0 $10,000 1 1,600 8,400 2 1,600 6,800 3 1,600 5,200 4 1,600 3,600 5 1,600 2,000

I = $10,000N = 5 YearsS = $2,000D = (I – S)/N Bn = I – n (Dn)Find: Dn and Bn

n

Declining Balance Method ( D B M )

Principle:

-A fixed asset as providing its service in a decreasing fashion over time. -DBM calculating depreciation allocates a fixed fraction - is obtained from S L depreciation rate (1/N) as a basis: = (1/N) x (multiplier). N and multiplier are given.Most commonly used multipliers in the USA are 1.5 DB or 2.0 DDB

Annual Depreciation

Book Value

Note: if is chosen to be the upper bound, = 2(1/N), we call it a 200% DB or double declining balance method.

1 nn BD 1)1( n

*(1 )nnB I where 0 < < 2(1/N)

Example 9.3

Declining Balance (DB) Depreciation

SL Dep. Rate = 1/5=0.2 a (DDB rate) = (200%) (SL rate) = 0.40

Asset: Invoice Price ………………...... $9,000Freight …………………….... 500Installation …………………...... 500

Depreciation Base …………………........ $10,000Salvage Value ......................................... 2,000Depreciation 200% DDB (Double) multiplier=2Depreciable life 5 years

S = $2,000

End of Year Depreciation Book ValueBn

1 0.4($10,000) = $4,000 $10,000 - $4,000 = $6,000

2 0.4(6,000) = 2,400 6,000 – 2,400 = 3,600

3 0.4(3,600) = 1,440 3,600 –1,440 = 2,160

4 0.4(2,160) = 864 $160

2,160 – 160 = 2,000Adjusting to salvage

value

5 0Total = $8,000

2,000 – 0 = 2,000 Note: Tax law does not permit to depreciate assets below their salvage values.

1 nn BD

Example 9.4

Declining Balance (DB) Depreciation

SL Dep. Rate = 1/5 a (DDB rate) = (200%) (SL rate) = 0.40

Asset: Invoice Price ………………...... $9,000

Freight ………………………... 500

Installation …………………...... 500

Depreciation Base …………………........ .$10,000Salvage Value .............................................. 0Depreciation 200% DDBDepreciable life 5 years

n DepreciationBook Value

12345

10,000(0.4) = 4,000 6,000(0.4) = 2,400 3,600(0.4) = 1,440 2,160(0.4) = 864 1,296(0.4) = 518

$6,0003,6002,1601,296

778

n

Book Depreciation

Value 12345

10,000/5 = 2,000 < 4,000 $6,000 6,000/4 = 1,500 < 2,400

3,600 3,600/3 = 1,200 < 1,440

2,160 2,160/2 = 1,080 > 864

1,080 1,080/1 = 1,080 > 518

0

(a) Without switching (b) With switching to SL

Note: Without switching, we have not depreciated the entire cost of the asset and thus have not taken full advantage of depreciation’s benefits. The rule is; if DB depreciation in any year is less than (or equal to) the depreciation amount calculated by SL, switch to and remain with the SL method for the duration of the asset’s depreciable life. The Switch can be in any of the n years.

Example 9.4 Declining Balance (DB) with conversion to Straight Line Depreciation (Bn > S)

Suppose the asset given in example 9.3 has a zero salvage value instead of $2,000

Units – of – Production MethodNo. of units or operating hours are different from year to year

Principle The number of service units will be consumed in that

period.

Formula Annual Depreciation

Service units consumed for year Dn =

total service units

x ( I – S )

Example 9.5 Units – of – Production Depreciation

A truck for hauling coal has an estimated net cost of $55,000( i.e. I) and is expected to give service for 250,000 miles(i.e: total service unit) , resulting in $5,000 a salvage value. Compute the allowed depreciation amount for the truck this year usage of 30,000 miles

Find: Depreciation amount this year

Solution: 30,000 ($55,000 $5,000)250,000

3 ($50,000)25

$6,000

Dep

9.3 History of Tax Depreciation Methods

Purpose: compute income taxes for the IRS

Assets placed in service prior to 1981

Use book depreciation methods (SL, DB)

Assets placed in service from 1981 to 1986

Use ACRS (Accelerated Cost Recovery System) Table

Assets placed in service after 1986

Use MACRS (Modified ACRS) Table

Modified Accelerated Cost Recovery Systems (MACRS)

Personal Property: (movable property, includes assets such as machinery, vehicles, equipment, furniture, and similar items)

Depreciation method based on DB method switching to SL Half-year convention (assumed all assets are placed I service

at midyear) Half year is allowed for the first year. Half year is taken in the year following the end

Zero salvage value

Real Property: (includes houses and land) are classified into two categories:

1. residential rental property and 2. commercial building or properties

SL Method Mid-month convention Zero salvage value

MACRS Property Classifications (ADR = Asset Depreciation Rate)

Recovery Period

ADR Midpoint Class Applicable Property

Personal

Property

3-year Special tools for manufacture of plastic products, fabricated metal products, and motor vehicles.

5-year Automobiles, light trucks, high-tech equipment, equipment used for R&D, computerized telephone switching systems

7-year Manufacturing equipment, office furniture, fixtures

10-year Vessels, barges, tugs, railroad cars

15-year Waste-water plants, telephone- distribution plants, or similar utility property.

20-year Municipal sewers, electrical power plant.

Real Property

27.5-year Residential rental property

39-year Nonresidential real property including elevators and escalators

ADR 4

4 10 ADR

10 16 ADR

16 20 ADR

20 25 ADR

25 ADR

M A C R S Depreciation TABLE for Personal Property with Half-Year Conversion from Internal Revenue Service (IRS)

Example MACRS Depreciation (Also read EXAMPLE 9.6)

Asset cost = $10,000 Property class = 5 year MACRS Depreciation method = Half – year convention, zero salvage value, 200% DB switching to SL

20%

$2000

32%

$3200

Full

19.20%

$1920

Full

11.52%

$1152

Full

11.52%

$1152

Full

5.76%

$576

1 2 3 4 5 6

Half-year Convention

Gross IncomeExpenses Cost of goods sold (revenues) Depreciation Operating expenses

Taxable income Income taxes

Net income (Accounting Profit)

Item

How to Determine “Accounting Profit”

Example Net Income within a year

A company buys a numerically control (NC) machines for $28,000 (year Zero) and uses it for five years, after which time it is scrapped. The allowed depreciation deduction during the first year is $4,000, as the equipment falls into the seven year MACRS property category. (The first year depreciation rate is 14.29%) The cost of goods produced by this NC machine should include a charge for the depreciation of the machine. Suppose the company estimates the following revenues and expenses, including the depreciation for the first operating year.

Gross income = $50,000Cost of goods sold = $20,000Depreciation on NC machine = $4,000Operating expenses = $6,000

If the company pays taxes at the rate of 40% on its taxable income, what is the net income from the project during the first year?

Example of Net Income within a year

Item AmountGross income (revenue) $50,000Expenses Cost of goods sold Depreciation Operating expenses

20,0004,0006,000

Taxable income 20,000Taxes (40%) 8,000Net income $12,000

Capital Expenditure versus Depreciation Expenses

0 1 2 3 4 5 6 7 8

0 8 (4.46)7 (8.93)6 (8.92)5 (8.93)3 (17.49) 4 (12.49)1(14.29) 2 (24.49)

$4,000$6,850

$4,900$3,500 $2,500 $2,500 $2,500

$1,250

$28,000Capital expenditure

(actual cash flow)

Allowed depreciation expenses (not cash flow)

( 7 - year MACRS property )

ExampleCash Flow from Operation versus Net Income

Item Income Cash FlowGross income (revenue) $50,000 $50,000Expenses Cost of goods sold Depreciation Operating expenses

20,0004,0006,000

-20,000

-6,000

Taxable income 20,000Taxes (40%) 8,000 -8,000

Net income $12,000Net cash flow from operation

$16,000

Net income versus net cash flow

U.S. Corporate Tax Schedule

Marginal tax rate is defined as the rate applied to the last dollar of income.Taxable income

0-$50,000$50,001-$75,000$75,001-$100,000$100,001-$335,000$335,001-$10,000,000$10,000,001-$15,000,000$15,000,001-$18,333,333$18,333,334 and Up

Tax rate15%25%34%39%34%35%38%35%

Tax computation$0 + 0.15(D) $7,500 + 0.25 (D)$13,750 + 0.34 (D)$22,250 + 0.39 (D)$113,900 + 0.34 (D)$3,400,000 + 0.35 (D)$5,150,000 + 0.38 (D)$6,416,666 + 0.35 (D)

(D) denotes the taxable income in excess of the lower bound of each tax bracket

Marginal and Effective (Average) Tax Rate for a Taxable Income of $16,000,000

Taxable income Marginal Tax Rate

Amount of Taxes

Cumulative Taxes

First $50,000 15% $7,500 $7,500Next $25,000 25% 6,250 13,750Next $25,000 34% 8,500 22,250Next $235,000 39% 91,650 113,900Next $9,665,000

34% 3,286,100 3,400,000

Next $5,000,000

35% 1,750,000 5,150,000

Remaining $1,000,000

38% 380,000 $5,530,000Average tax rate = $5,530,000

$16, ,.

000 00034 56%

Example Corporate Income Taxes

Facts:Capital expenditure $290,000(allowed depreciation) $58,000

Gross Sales revenue $1,250,000

Expenses:Cost of goods sold $840,000Depreciation $58,000Leasing warehouse $20,000

Question: Taxable income?

Taxable income:Gross income $1,250,000 - Expenses:

(cost of goods sold) $840,000(depreciation) $58,000(leasing expense) $20,000

Taxable income $332,000

Income taxes: Taxable income

Marginal Tax Rate

Amount of Taxes

Cumulative

TaxesFirst

$50,00015% $7,500 $7,500

$25,000 25% 6,250 13,750$25,000 34% 8,500 22,250

$232,000 39% 90,480 112,730

39%

Average tax rate:

Total taxes = $112,730Taxable income = $332,000

Marginal tax rate: Tax rate that is applied to the last dollar earned

Average tax rate = $112,730$332,000

33 95%.

Taxable Gains (or Losses) are defined as the differences between

the salvage value and the book value.

Case 1: Salvage value < Cost basis: gains (losses) = salvage value – book value

Case 2: Salvage value > Cost basis: gains = salvage value – book value = (salvage value – cost basis)

capital gains

+ (cost basis – book value)

ordinary gains

ordinary gains (depreciation recapture)

When you sell an asset above its purchase price, you pay a tax on your gains. That's called a capital gains tax.

Capital Gains and Ordinary Gains

Cost basis Book value Salvage value

Capital gains

Ordinary gainsor

depreciation recapture

Total gains

Disposal of a MACRS Property and Its Effect on Depreciation Allowances

Example 9.9 Gains or Losses on Depreciable Asset

A Drill press: $230,000Project year: 3 yearsMACRS:7-year property classSalvage value: $150,000 at the end

of Year 3

Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308Book Value = 230,000 -109,308 = $120,692Ordinary Gains = Salvage Value - Book Value = $150,000 - $120,692 = $29,308Gains Tax (34%) = 0.34 ($29,308) = $9,965Net Proceeds from sale = $150,000 - $9,965 = $140,035

Calculation of Gains or Losses on – Cases 2 - 4

Case 2: S = $120,692

Case 3: S = $100,000

Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308Book Value = 230,000 – 109,308 = $120,692Ordinary Gains = Salvage Value – Book Value = $100,000 -

$120,692 = -$20,692Gains Tax or Tax credit (34%) = 0.34 (-$20,692) = - $7,035Net Proceeds from sale = $100,000 – (-$7,035) = $107,035.28

Case 4: S = $250,000

Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308

Book Value = 230,000 -109,308 = $120,692Ordinary Gains = Salvage Value – Book Value = $250,000 -

$120,692 = $129,308Gains Tax (34%) = 0.34 ($129,308) = $43,965Net Proceeds from sale = $250,000 – $43,965 = $206,035

PRACTICE PROBLEMS

9; 12; 17; 39; 40

Cost of the asset, I $120,000

Useful life, N 7 years

Salvage value, S $0

9.9) Consider the following data on an asset:

Compute the annual depreciation allowances and resulting book values, using the following methods.

a)Double Declining balanceb)Straight-line depreciation method with zero salvage value

Cost of the asset, I $120,000

Useful life, N 7 years

Salvage value, S $0SOLUTION 9.9)

DDB method With switchingn Dn =2/N = 0.2857 SL method Dn =1/N Bn

0 　 $120,000 1 $34,284 7 / $17,143 $ 85,7162 $24,489.10 6 / $14,286 $ 61,2273 $17,492.6 5 / $12,245.4 $ 43,7354 $12,495.1 4/ $10,933.8 $ 31,2405 $8,925.3 shift }}}}}} 3 /$10,413 $ 20,8276 2 /$10,413.5 $10,413.57 1 /$10,413.5 $0

Cost of the asset, I $38,000Useful life, N 6 yearsSalvage value, S $0

9.12) Consider the following data on an asset:Compute the annual depreciation allowances and

resulting book values, by using DDB method and then switching to the SL method to reach with zero salvage value

Cost of the asset, I $38,000Useful life, N 6 yearsSalvage value, S $0

SOLUTION 9.12)

With switchingn DDB method Dn = .33333 SL method Dn = 1 / 6 Bn

0 　 $38,000 1 $12,667 6 / $6,333.33 $25,3332 $8,444.40 5 / $5,066.6 $16,889.603 $5,629.47 4 / $4,222.15 $11,260.134 $3,753.34 3 / $3,753.4 shift to SL $7,506.735 2 / $3,753.4 $3,753.406 1 / $3,763.4 $0

9.17)

New York Limousine Service owns 10 limos and uses the units of production method in computing depreciations on its limos. Each limo costing $32,000 is expected to be driven 200,000 miles and is expected to have a salvage value of $3,000. Limo # 1 was driven 24,000 miles in year 1 and 28,000 miles in year 2. Determine the depreciation for each year and the book value at the end of year 2.

SOLUTION

124,000 ($32,000 $3,000) $3,480200,000

D

228,000 ($32,000 $3,000) $4,060

200,000D

The book value of Limo # 1 at the end of year 2:

2 32,000 3,480 4,060 $24,460B

9.39

Consider a five year MACRS asset that was purchased for $76,000. Compute the gain and loss amounts if the asset were disposed of in

a) year 3 with a salvage value of $20,000; b) year 5 with a salvage value of $10,000; c) year 6 with salvage value of $5,000.

allowed depreciation $76,000(0.20 0.32 0.192 / 2)$46,816

book value $76,000 $46,816$29,184

loss $20,000 $29,184 ($9,184)

allowed depreciation $76,000(0.20 0.32 0.1920.1152 0.1152 / 2)$67,244.8

book value $76,000 $67,244.8$8,755.2

Taxable gains $10,000 $8,755.2 $1,224.8

allowed depreciation $76,000book value $0

Taxable gains $5,000

Disposed of in year 3:



9.40)

An electrical appliance company purchased an industrial robot costing $320,000 in year 0. The industrial robot, to be used for welding operations, is classified as a seven year MACRS recovery property. If the robot is to be sold after five years, compute the amounts of gains (losses) for the following three salvage values, assuming that both capital gains and ordinary incomes are taxed at 35%;

a) $15,000 b) $125,000 c) $200,000

allowed depreciation $320,000(0.1429 0.2449 0.17490.1249 0.0893 / 2)$234,320

book value $320,000 $234,320$85,680

losses $15,000 $85,680 ($70,680)loss credit $70,680(0.35) $24,738

net loss ($70,680) $24,738 ($45,942)

gains $125,460 $85,680 $39,780gains tax $39,780(0.35) $13,923net gain $39,780 $13,923 $25,857

gains $200,000 $85,680 $114,320gains tax $114,320(0.35) $40,012net gain $114,320 $40,012 $74,308

9.40) SOLUTION

If sold at $15,000:

If sold at $125,460:

If sold at $200,000:

ise 307- chapter 9

Economy & Finance