Chapter 8 Depreciation and Income

Taxes Asset Depreciation

Book Depreciation

Tax Depreciation

How to Determine “Accounting Profit”

Corporate Taxes

DepreciationDefinition: Loss of value for a fixed asset

Example: You purchased a car worth $15,000 at the beginning of year 2000.

Dep

reciation

End of Year

Market

Value

Loss of

Value

0

1

2

3

4

5

$15,00010,000

8,0006,0005,0004,000

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

Depreciation Concept

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

Economic Depreciation (Purchase Price – Market Value) Economic losses due to both physical deterioration and technological obsolescence)

Accounting DepreciationSystematic allocation of the initial cost of an

asset in parts over time or decline in value over time

known as its depreciable life.

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 Asset Depreciation

What is the depreciable life of the asset?

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

What is the cost 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 service (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. Depreciable property includes buildings, machinery, equipment, vehicles, and some intangible properties. If an asset has no definite service life, the asset can not be depreciated such as land.

Example 8.1 Cost Basis of an asset represents the total cost that is claimed as an expense over an asset's life and generally includes the followings

Cost of a new hole-punching machine (Invoice price) $62,500

+ Freight 725

+ Installation labor 2,150

+ Site preparation 3,500

Cost of Machine (Cost basis) to use in depreciation calculation

$68,875

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 7

Airplanes 5 6 7

Automobiles, taxis 2.5 3 3.5

Buses 7 9 11

Light trucks 3 4 5

Heavy trucks (concrete ready-mixer) 5 6 7

Railroad cars and locomotives 12 15 18

Tractor units 5 6 7

Vessels, barges, tugs, and water transportation system 14.5 18 21.5

Industrial steam and electrical generation and or distribution systems

17.5 22 26.5

Manufacturer of electrical and non-electrical machinery 8 10 12

Manufacturer of electronic components, products, and systems

5 6 7

Manufacturer of motor vehicles 9.5 12 14.5

Telephone distribution plant 28 35 42

Types of Depreciation Book Depreciation

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

In pricing decision

Tax Depreciation In calculating income taxes for the IRS In engineering economics, we use depreciation in the

context of tax depreciation

Book Depreciation Methods

Three different methods can be used to calculate the periodic depreciation allowances for financial reporting.

Types of Depreciation Methods:

Straight-Line Method Declining Balance Method Unit Production Method

Straight – Line (SL) MethodPrinciple A fixed asset as an asset that provides its services in a uniform fashion. That is, the asset provides equal amount of service in each year of its useful life.

Formula• Annual Depreciation

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

• Book ValueBn = I – n (D)

where I = cost basisS = Salvage valueN = depreciable life

Example 8.2 – Straight-Line Method

D1

D2

D3

D4

D5

B1

B2B3

B4

B5

$10,000

$8,000

$6,000

$4,000

$2,000

0 1 2 3 4 5

Total depreciation

at end of

lifen Dn Bn

1 1,600 8,4002 1,600 6,8003 1,600 5,2004 1,600 3,6005 1,600 2,000

I = $10,000N = 5 YearsS = $2,000D = (I - S)/N

Annual Depreciation

Book Value

n

Declining Balance MethodPrinciple: A fixed asset as providing its service in a decreasing fashion.Formula The fraction, = (1/N) (multiplier)

• Annual Depreciation

• Book Value1 nn BD 1)1( n

nB )1( where 0 << 2(1/N)

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

Example 8.3 – Declining Balance Method

D1

D2

D3

D4

D5

B1

B2

B3

B4 B5

$10,000

$8,000

$6,000

$4,000

$2,000

0 1 2 3 4 5

Total depreciation

at end of

life

$778

Annual DepreciationBook Value

n012345

Dn

$4,0002,4001,440

864518

Bn$10,00

06,0003,6002,1601,296

778

I

N

S

D B

I

B I

n n

n

nn

= $10,

= years

= $778

=

= ( -

000

5

1

1

1

1

( )

n

Example 8.4 Declining Balance (DB) Switching to SL

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

= 0.40

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

Depreciation Base $10,000Salvage Value 0Depreciation 200% DBDepreciable life 5 years

n Depreciation

Book

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 = 4,000 $6,0006,000/4 = 1,500 < 2,400 3,6003,600/3 = 1,200 < 1,440 2,1602,160/2 = 1,080 > 864 1,0801,080/1 = 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 tax deferring 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.

Case 1: S = 0

Case 2: S = $2,000

End of Year

Depreciation Book Value

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 = 2,000

Adjusting to salvage value

5 0 2,000 – 0 = 2,000

Note: Tax law does not permit us to depreciate assets below their salvage values.

Units-of-Production Method

PrincipleThe number of service units will be consumed in that period.

FormulaAnnual Depreciation

Service units consumed for year

Dn =

total service units

(I - S)

Example 8.5

Given: I = $55,000, S = $5,000, Total service units = 250,000 miles, usage for this year = 30,000 miles

Solution: 30,000

($55,000 $5,000)250,000

3($50,000)

25

$6,000

Dep

Modified Accelerated Cost Recovery Systems (MACRS)

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

Depreciation method based on DB method switching to SL Half-year convention Zero salvage value

Real Property [Real properties 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 (IRS Publication 534)Recovery Period ADR Midpoint Class Applicable 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.

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

ADR: Asset Depreciation Range

MACRS Table The percentages shown in the table use the half year convention, all the assets are placed in service at mid-year and will have zero salvage value.

Example 8.6 MACRS Depreciation

Asset cost = $10,000Property class = 5-year recovery periodDB 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

Taxable Income and Income Taxes

Gross IncomeExpenses Cost of goods sold (revenues) Depreciation Operating expensesTaxable incomeIncome taxes

Net income

Item

Example 8.8 - Net Income Calculation

Item Amount

Gross income (revenue) $50,000

Expenses

Cost of goods sold

Depreciation

Operating expenses

20,000

4,000

6,000

Taxable income 20,000

Taxes (40%) 8,000

Net income $12,000

Capital Expenditure versus Depreciation Expenses

0

1 2 3 4 5 6 7 8

0 8 (5.76)7 (8.93)6 (8.92)7 (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

$28,000

Capital expenditure(actual cash flow)

Allowed depreciation expenses (not cash flow)

(7-year MACRS property)

Example 8.9 – Cash Flow versus Net Income

Item Income Cash Flow

Gross income (revenue $50,000 $50,000

Expenses

Cost of goods sold

Depreciation

Operating expenses

20,000

4,000

6,000

-20,000

-6,000

Taxable income 20,000

Taxes (40%) 8,000 -8,000

Net income $12,000

Net cash flow $16,000

Net income versus net cash flow

$0

$50,000

$40,000

$30,000

$20,000

$10,000

$8,000

$6,000

$20,000

Net income

Depreciation

Income taxes

Operating expenses

Cost of goods sold

Netcash flow

Grossrevenue

$4,000

$12,000

Net cash flows = Net income + non-cash expense (depreciation)

U.S. Corporate Tax Rate (2005)

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

(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

$16,000,000Taxable income Marginal

Tax RateAmount of

TaxesCumulative

Taxes

First $50,000 15% $7,500 $7,500

Next $25,000 25% 6,250 13,750

Next $25,000 34% 8,500 22,250

Next $235,000 39% 91,650 113,900

Next $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 $5,530,000

Average tax rate =$5,530,000

$16, ,.

000 00034 56%

Example 8.10 - 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:First $50,000 @ 15% $7,500

$25,000 @ 25% $6,250$25,000 @ 34% $8,500$232,000 @ 39% $90,480

Total taxes $112,730

Average tax rate:

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

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

39%

Average tax rate =$112,730

$332,000

33 95%.

Disposal of Depreciable Asset

If a MACRS asset is disposed of during the recovery period,

Personal property: the half-year convention is applied to depreciation amount for the

year of disposal.

Real property: the mid-month convention is applied to the month of disposal.

Depreciation recapture

Gains = Salvage value – book value = (Salvage value - cost basis)

Capital gains

+ (Cost basis – book value)

Ordinary gains

Depreciation recapture is taxed as ordinary income.

Capital Gains and Ordinary Gains

Cost basis Book value Salvage value

Capital gains

Ordinary gainsor

depreciation recapture

Total gains

Gains or Losses on Depreciable Asset

Example 8.11: A Drill press: $230,000Project year: 3 yearsMACRS: 7-year property classSalvage value: $150,000 at the end of Year 3

14.29 24.49 17.49 12.49 8.92 8.92 8.92

Full Full Half

Total Dep. = 230,000(0.1429 + 0.2449 + 0.1749/2) = $109,308Book Value = 230,000 -109,308 = $120,693Gains = Salvage Value - Book Value = $150,000 - $120,693

= $29,308Gains Tax (34%) = 0.34 ($29,308) = $9,965Net Proceeds from sale = $150,000 - $9,965 = $140,035

Disposal of a MACRS Property and Its Effect on Depreciation

Allowances

Calculation of Gains or Losses on MACRS Property