Depreciation and Income Taxes

Chapter 9

Advanced Engineering Economy

Depreciation• Definition: 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

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

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 part of business expenses that reduce taxable income.

Factors to Consider in Asset Depreciation

Depreciable life (how long?)

Salvage value (disposal value)

Cost basis (depreciation basis)

Method of depreciation (how?)

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.

Cost Basis

Without Trade-In Allowance With Trade-In Allowance

Cost of a new hole-punching machine (Invoice price) $62,500+ Freight 725

+ Installation labor 2,150

+ Site preparation 3,500

Cost basis to use in depreciation calculation

$68,875

Cost of a new hole-punching machine (Invoice price) $62,500+ Freight 725

+ Installation labor 2,150

+ Site preparation 3,500

Cost basis to use in depreciation calculation

$68,875

Old hole-punching machine (book value) $4,000

Less: Trade-in allowance 5,000

Unrecognized gains $1,000

Cost of a new hole-punching machine $62,500

Less: Unrecognized gains (1,000)

Freight 725

Installation labor 2,150

Site preparation 3,500

Cost of machine (cost basis) $67,875

Old hole-punching machine (book value) $4,000

Less: Trade-in allowance 5,000

Unrecognized gains $1,000

Cost of a new hole-punching machine $62,500

Less: Unrecognized gains (1,000)

Freight 725

Installation labor 2,150

Site preparation 3,500

Cost of machine (cost basis) $67,875

Useful Life and Salvage Value

Useful life – Adopt the Asset Depreciation Ranges (ADR) published by the IRS. Salvage value – Asset’s estimated value at the end of its useful life. Every effort should be made to estimate a reasonable residual value of the asset, but if not possible, a 10% rule (10% of the initial value) could be adopted for depreciation purpose.

Types of Depreciation• Book Depreciation

– In reporting net income to Investors/stockholders– 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 versus Tax Depreciation – An Overview

Component of Depreciation Book Depreciation Tax depreciation (MACRS)

Cost basis

Based on the actual cost of the asset, plus all incidental costs such as freight, site preparation, installation, etc.

Same as for book depreciation

Salvage value

Estimated at the outset of depreciation analysis. If the final book value does not equal the estimated salvage value, we may need to make adjustments in our depreciation calculations.

Salvage value is zero for all depreciable assets

Component of Depreciation

Book Depreciation Tax depreciation (MACRS)

Depreciable life

Firms may select their own estimated useful lives or follow government guidelines for asset depreciation ranges (ADRs)

Eight recovery periods– 3,5,7,10,15,20,27.5,or 39 years– have been established; all depreciable assets fall into one of these eight categories.

Method of depreciation

Firms may select from the following: Straight-lineAccelerated methods (declining balance, double declining balance, and sum-of- years’ digits)Units-of-proportion

Exact depreciation percentages are mandated by tax legislation but are based largely on DDB and straight-line methods. The SOYD method is rarely used in the U.S. except for some cost analysis in engineering valuation.

Book Depreciation Methods

• Purpose: Used to report net income to stockholders/investors

• Types of Depreciation Methods:– Straight-Line (SL) Method– Declining Balance Method– Unit Production Method

Straight – Line (SL) Method

• Principle A fixed asset as providing its service in a uniform fashion over its life

• Formula•Annual Depreciation

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

Bn = I – n (D)where I = cost basis

S = Salvage valuen = depreciable life

Example: 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

0 10,0001 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 Method• Principle: A fixed asset as providing its service in a decreasing fashion• Formula

• Annual Depreciation

• Book Value

1 nn BD 1)1( n

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

Note: if is chosen to be the upper bound, = 2(1/N),

we call it a 200% DDB or Double Declining Balance method.

Example: Declining Balance Method

D1

D2

D3D4

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 Depreciation

Book Value

n012345

Dn

$4,0002,4001,440

1600

Bn$10,00

06,0003,6002,16020002000

1

1

= $10,000

= 5 years

= $2000

=

= (1-

(1 )

n n

n

nn

I

N

S

D B

I

B I

n

ά =2(1/N) =2(1/5) =40%

Example: 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

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 entirecost of the asset and thus have not taken full advantage of depreciation’s tax deferring benefits.

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

5 0 2,000 – 0 = 2,000

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

Units-of-Production Method

• PrincipleService units will be consumed in a non

time-phased fashion

• Formula•Annual Depreciation

Dn = Service units consumed for yeartotal service units

(I - S)

Example

• 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

Tax Depreciation

Tax Depreciation• Purpose: Used to 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 Accelerated Cost Recovery System (ACRS) Table

•Assets placed in service after 1986

Use Modified Accelerated Cost Recovery System MACRS Table

Modified Accelerated Cost Recovery Systems (MACRS)

• Personal Property• Depreciation method based on DB method

switching to SL• Half-year convention• Zero salvage value

• Real Property• SL Method• Mid-month convention• Zero salvage value

MACRS Property Classifications

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

MACRS Depreciation Schedules for Personal Property with Half-Year Convention

Property Class 3, 5, 7, 10-Year with 200% DB 15 and 20-Year with 150% DB

Sample Calculation – 5-Year MACRS:

MACRS Rate Calculation

Asset cost = $10,000Property class = 5-yearDB 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

Year (n)

12

3

4

56

Calculation in %

(0.5)(0.40)(100%) 20%(0.4)(100%-20%) 32%

SL = (1/4.5)(80%) 17.78%

(0.4)(100%-52%) 19.20%

SL = (1/3.5)(48%) 13.71%

(0.4)(100%-71.20%) Switch to SL 11.52%SL = (1/2.5)(29.80%) 11.52%

SL = (1/1.5)(17.28%) 11.52%SL = (0.5)(11.52%) 5.76%

MACRS (%)

DDBDDB

DDB

SL

SL

Comparison between DDB with Switching to SL and MACRS Method

Conventional DDB Method:

Cost basis: $10,000 Salvage value: $0 Depreciable life: 5 years DB rate: 200%

MACRS Method: Property class: 5-year Salvage value: $0 Half-year convention

• Depreciation Rates

MACRS for Real Property

Types: 27.5-Year (Residential) 39-Year (Commercial)

SL Method Mid-month convention Zero salvage value

Example: Placed a residential property in service in March. Find the depreciation allowance in year 1. D1 = (9.5/12)(100%/27.5) = 2.8788%

Year (n) Calculation Allowed Depreciation (%)

1 (9.5/12)(100%/27.5) 2.8788%

2 100%/27.5 3.6364%

3 100%/27.5 3.6364%

4 100%/27.5 3.6364%

5 100%/27.5 3.6364%

6 100%/27.5 3.6364%

7 100%/27.5 3.6364%

8 100%/27.5 3.6364%

9 100%/27.5 3.6364%

10 (11.5/12)(100%/27.5) 3.4848%

Year (n) Calculation Allowed Depreciation (%)

1 (9.5/12)(100%/27.5) 2.8788%

2 100%/27.5 3.6364%

3 100%/27.5 3.6364%

4 100%/27.5 3.6364%

5 100%/27.5 3.6364%

6 100%/27.5 3.6364%

7 100%/27.5 3.6364%

8 100%/27.5 3.6364%

9 100%/27.5 3.6364%

10 (11.5/12)(100%/27.5) 3.4848%

Depreciation Allowances for a 10-year Ownership of the Property

Net Income Versus Cash Flow

Taxable Income and Income Taxes

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

Net income

Item

Example:- 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

01 2 3 4 5 6 7 8

0 87673 41 2

$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)

Cash Flow vs. Net Income

Net income: Net income is an accounting means of measuring a firm’s profitability based on the matching concept. Costs become expenses as they are matched against revenue. The actual timing of cash inflows and outflows are ignored.

Cash flow: Given the time value of money, it is better to receive cash now than later, because cash can be invested to earn more money. So, it is desirable why cash flows are relevant data to use in project evaluation.

Why Do We Use Cash Flow in Project Evaluation?

Company A Company B

Year 1 Net income

Cash flow

$1,000,000

1,000,000

$1,000,000

0

Year 2 Net income

Cash flow

1,000,000

1,000,000

1,000,000

2,000,000

Example: Both companies (A & B) have the same amount ofnet income and cash sum over 2 years, but Company A returns $1 million cash yearly, while Company B returns $2 millionat the end of 2nd year. Company A can invest $1 million in year1, while Company B has nothing to invest during the same period.

Example:– 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)

Corporate Taxes

Taxable Income and Income Taxes

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

Net income

Item

U.S. Corporate Tax Rate (2010)

Taxable income0-$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 $16,000,000

Taxable income Marginal Tax Rate

Amount of Taxes

Cumulative 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: Corporate Income Taxes

Facts:Capital expenditure $100,000(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.

Disposal of a MACRS Property and Its Effect on Depreciation Allowances

Case 1: Salvage Value < Cost Basis

• Gains (losses) = Salvage value – book value

• These gains, commonly known as either ordinary gains or depreciation recapture, are taxed as ordinary income.

• Most gains experienced in manufacturing environment refer to these ordinary gains.

• Any losses (ordinary) can be deducted from the ordinary gains from other assets first and any remaining balance can be deducted from the ordinary taxable income.

Cost basis Book value Salvage value

Ordinary gains

Cost basis Book value Salvage value

Ordinary gains

Case 2: Salvage Value > Cost Basis

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

Capital gains

+ (Cost basis – book value)

Ordinary gains

Capital gain is taxed as ordinary income under current tax law.

Cost basis Book value Salvage value

Capital gains

Ordinary gainsor

depreciation recapture

Total gains

Cost basis Book value Salvage value

Capital gains

Ordinary gainsor

depreciation recapture

Total gains

Gains or Losses on Depreciable Asset

Example: 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

Calculation of Gains or Losses on MACRS Property