8013 lecture depreciation

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Depreciation and Depletion

Accounting for Depreciation and Income Taxes

Asset DepreciationBook DepreciationTax DepreciationHow to Determine

“Accounting Profit”Corporate Taxes

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

reciation

End of Year

Market

Loss of

$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 part of business expenses that reduce taxable income.

Depreciation Concept

Economic Depreciation

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

Accounting DepreciationA systematic allocation of cost basis over a period of time.

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

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

Factors to Consider in Asset Depreciation

Depreciable life (how long?)

Salvage value (disposal value)

Cost basis (depreciation basis)

Method of depreciation (how?)

Asset Depreciation Range (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 nonelectrical machinery 8 10 12

Manufacturer of electronic components, products, and systems

Manufacturer of motor vehicles 9.5 12 14.5

Telephone distribution plant 28 35 429

Cost Basis

Cost of 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 Basis with Trade-In Allowance

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

Less: Trade-in allowance 5,000

Unrecognized gains $1,000

Cost of 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

Types of Depreciation

• Book Depreciation– In reporting net income to investors and

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 Depreciation Methods

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

• Types of Depreciation Methods:– Straight-Line Method– Declining Balance Method– Unit Production Method– Sum-of-the-Year’s-Digits (SOYD)

Straight – Line (SL) Method

• Principle A fixed asset is 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

$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

Declining Balance Method• Principle: A fixed asset is providing its service in a decreasing fashion• Formula

• Annual Depreciation

• Book Value

1 nn BD 1)1( nI

nn IB )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. 16

Example – Declining Balance Method

$10,000

$8,000

$6,000

$4,000

$2,000

0 1 2 3 4 5

Total depreciation at end of

Annual Depreciation

Book Value

n012345

$4,0002,4001,440

864518

Bn$10,000

6,0003,6002,1601,296

= $10,

= years

= $778

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

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

Depreciation Value

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)

$6,000

Sum-of-the-Year’s Digits (SOYD)

Annual depreciation =

(Cost - Salvage value) X RL

SOYD• RL = remaining years of useful life as of

the beginning of the year.• SOYD = sum of all the numbers from 1

through the estimated useful life= n(n+1)/2

Sum-of-the-Year’s Digits (an example)

Asset cost = $50,000Asset life = 5 yearsSalvage value = $10,000Annual Depreciation:

Year 1 = (40,000) X (5/15) = $13,333.32Year 2 = (40,000) X (4/15) = $10,666.68Year 3 = (40,000) X (3/15) = $ 8,000.00Year 4 = (40,000) X (2/15) = $ 5,333.33

Year 5 = (40,000) X (1/15) = $ 2,666.67

Depletion• Depletion, though similar to

depreciation, is applicable only to natural resources (mines, wells, quarries, forests, etc.)

• When the resources are removed, they cannot be replaced or repurchased in the same manner as can a machine, computer, or structure

Depletion

There are two methods of depletion

①Cost depletion

②Percentage depletion

DepletionCost Depletion

• Cost depletion is based on the level of activity or usage, not time, as in depreciation

• The cost depletion factor for year t, denoted by Pt, is the ratio of the first cost of the resource to the estimated number of units recoverable

• The annual depletion charge is Pt times the year's usage or volume

DepletionCost Depletion – Example

A company has negotiated the rights to cut timber on privately held forest area for $700,000

An estimated 350 million board feet of lumber are harvestable

•Determine the depletion amount for the first 2 years if 15 million and 22 million board feet are removed•After 2 years the total recoverable board feet was re-estimated to be 450 million from the time the rights were purchased. Compute the new cost depletion factor for years 3 and later

Multiply Pt by the annual harvest to obtain depletion of $30,000 in year 1 and $44,000 in year 2

Continue using Pt until we reach $700,000

After 2 years, a total of $74,000 has been depleted

A new pt value must be calculated based on the remaining $700,000 – 74.000 = $626,000 investment

Additionally, with the new estimate of 450 million board feet, a total of 450 – 15 – 22 = 413 million board feet remain

For years t = 3, 4, …., the cost depletion factor is

DepletionPercentage Depletion

In this method, the cost depletion amount is given by the following equation:

cost depletion percentage

gross income from property

DepletionPercentage Depletion

DepletionPercentage Depletion – Example

A gold mine was purchased for 10 million. It has an anticipated gross income of $5 million per year for years 1 to 5 and $3 million per year after year 5

Compute:•Annual depletion amounts for the mine•How long will it take to recover the initial investment at i = 0%?

DepletionPercentage Depletion – Example

A 15% depletion applies to gold. Depletion amounts are:

Years 1 to 5: 0.15×5 million = $750,000

Years thereafter: 0.15×3 million = $450,000

A total of $3.75 million is written off in 5 years

The remaining $6.25 million is written off at $450,000 per year. The total number of years is:

In 19 years, the initial investment could be fully depleted 34

8013 lecture depreciation

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