lecture # 7 depreciation i

Lecture # 7

Cost Estimation

Depreciation – part 1

16-1

Dr. A. Alim

What is Depreciation ?

Federal tax law permits the reduction of Gross

Income (GI) by a category of elements termed “deductions”.

Deductions are the costs incurred.

Costs are divided into two categories * expensed costs (E) * capitalized (depreciated) costs (D)

Expensed costs are those consumed over short periods of time. They do not lose value gradually over time. Examples are wages, utilities, materials, insurance,..etc

These expenses are written off (deducted) in the year they occur.

16-2 © 2005 by McGraw-Hill, New York, N.Y All Rights Reserved Slide Sets to accompany Blank & Tarquin, Engineering

Economy, 6th Edition, 2005

What is Depreciation ?

Capitalized costs are due to capital assets. They are

not written off when they occur. Capital assets lose value gradually and are depreciated over an extended period of time.

In general, a business asset can be depreciated if it meets three criteria: 1) The property must be used to produce income. 2) Must have a defined service life longer then one year. 3) The asset wears out, decays, becomes obsolete, or loses value over the useful life.

Depreciation thus is how the government allows businesses to recover the lost value of their capitalized assets over a period of time.



Depreciation is a tax Deduction

While expenses are real cash flows, depreciation amounts represent “non-cash flow” streams within an accounting period.

Federal and state tax laws recognize various forms

of depreciation amounts to be “tax deductible” – but are not real cash flows per se.



Important Terms First Cost or Unadjusted Basis - B

Initial purchase price + all costs incurred in placing the asset in service

Book Value - BV

Remaining undepreciated capital investment on the accounting books

Recovery Period – n

Depreciable life of the asset in question – often set by law

Market Value - MV

Amount realized by sale on the open market at any time

Salvage Value - S

Estimated trade-in value or market value at the end of the asset’s useful life

Depreciation Rate - dt

The fraction of the first cost removed by depreciation in year t

Depreciation Charge - Dt

Amount of annual depreciation in year t

Personal Property

All property except real estate used in the pursuit of profit or gain

Real Property

Real estate and improvements, buildings and certain structures

Land is Real Property, but by law is NOT depreciable for tax purposes



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.



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.

Examples of methods used: Straight Line,

Declining Balance;

Sum of the years digits;

Other.



Tax Depreciation

Tax Depreciation:

Must follow current state and federal law pertaining to acceptable methods for computing depreciation for income tax purposes.

US Federal Law (2001) MACRS Methods

By US Federal Tax Law, all assets placed in service and eligible for depreciation MUST use the current MACRS methods of calculation of depreciation amounts.

Tax Law permits states to have their own respective depreciation methods for state income tax purposes (complicating factor)

MACRS – Modified Accelerated Cost Recovery System



Straight Line (SL) Depreciation

The standard on which all other depreciation models are compared

t

t

Notation:

t = year (t = 1,2,...,n)

D = annual depreciation charge

B = first cost or unadjusted basis

S = Estimated salvage value

n = recovery period

d = depreciation rate

tD =(B-S)d

B-S =

n

1

t t

t

BV B tD

d dn

Excel Function: Dt = SLN(B,S,n)



Example:

B = $ 160,000, n = 10 years.

Tabulate the SL depreciation for each of the 10 years if S = $ 10,000

The Excel function is SLN(160000,10000,10)

Year D Acc D BV

1 $15,000.00 $15,000.00 $145,000.00

2 $15,000.00 $30,000.00 $130,000.00

3 $15,000.00 $45,000.00 $115,000.00

4 $15,000.00 $60,000.00 $100,000.00

5 $15,000.00 $75,000.00 $85,000.00

6 $15,000.00 $90,000.00 $70,000.00

7 $15,000.00 $105,000.00 $55,000.00

8 $15,000.00 $120,000.00 $40,000.00

9 $15,000.00 $135,000.00 $25,000.00

10 $15,000.00 $150,000.00 $10,000.00



Declining Balance (DB) and Double

Declining Balance (DDB) Depreciation

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 R x SL rate.

R is between 1 and 2. Often R = 2, this is called Double declining balance (DDB)

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 the straight

line rate



DDB illustration, B=1000, n=5 therefore: d=2/5=0.4

n Dt BV

0 0 1000

1 0.4 (1000) (1000) (1 – 0.4)

2 0.4 (1000) (1 – 0.4) (1000) (1 – 0.4) 2

3 0.4 (1000) (1 – 0.4) 2

(1000) (1 – 0.4) 3

4 0.4 (1000) (1 – 0.4) 3

(1000) (1 – 0.4) 4

5 0.4 (1000) (1 – 0.4) 4

(1000) (1 – 0.4) 5



DB Family of Depreciation

n Dt BV

0 0 B

1 dB B(1-d)

2 dB(1-d) B(1-d) 2

3 dB(1-d) 2 B(1-d) 3

….

t dB(1-d) t-1 B(1-d) t



Declining Balance Expressions

Annual depreciation determined in either of 2 ways

Using book value of previous year

Dt = d × (BV)t-1

Using first cost basis B

Dt = dB(1-d )t-1

Annual book value determined in either of 2 ways

Using first cost basis B

(BV)t = B(1-d )t

Using sum of accumulated depreciation for years i=1 to t

(BV)t = B – ΣDi

……………………………………………………………………………………………………

……




Annual depreciation rate for each year t, relative to

first cost B, is dt

Dt = dt B = dB (1-d)t-1

dt = d(1-d)t-1

Salvage value is not used in DB method formulas

Implied salvage is book value in year n

Implied S = (BV)n = B(1-d)n

If a salvage value is estimated, and estimated S > implied S,

stop depreciating whenever expected S value is reached



Implied S is the BV at n. We have three cases:

1) Implied S > Estimated S. This leads to an asset not fully depreciated. 2) Implied S = Estimated S. Asset is “just” fully depreciated. 3) Implied S < Estimated S. Asset is fully depreciated, but in less than n years.

In this case, Excel stops depreciating the asset at time “t” years, forcing BV to remain constant at S, with no further depreciation for the remainder of n.

The concept of Implied S

Estimated

Salvage value




Excel function for DDB depreciation:

Dt = DDB(B,S,n,t,R)

S is estimated salvage value

R is between 1 and 2. If omitted, a value of 2 is assumed, i.e. DDB





Example 16.2,

Page 420

Blank, 7th ed.

Slide Sets to accompany Blank & Tarquin, Engineering


© 2005 by McGraw-Hill, New York, N.Y All Rights Reserved 16-19

S = 2500 B = 25000

t D Acc D BV

1 $4,167 $4,167 $20,833

2 $3,472 $7,639 $17,361

3 $2,894 $10,532 $14,468

4 $2,411 $12,944 $12,056

5 $2,009 $14,953 $10,047

6 $1,674 $16,628 $8,372

7 $1,395 $18,023 $6,977

8 $1,163 $19,186 $5,814

9 $969 $20,155 $4,845

10 $808 $20,962 $4,038

11 $673 $21,635 $3,365

12 $561 $22,196 $2,804

Modified Accelerated Cost Recovery System (MACRS)

MACRS was derived from the 1981 ACRS system and went into effect in 1986.

Defines statutory recovery (depreciation) percentages.

Percentages were derived from the DDB method with a switch to SL at the optimal time and,

Incorporates the half-year convention.

By current law – MACRS assumes all assets depreciated by this method will have a “0” salvage value at the end of the recovery life.

Dt = dtB

dt is provided in tabulated form.

BVt = BV t-1 – Dt

BVt = first cost – sum of

accumulated depreciation

1

t

t j

j

BV B D



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 and last years

are handled using the half-

year convention.

Half-year

convention assumes

that assets are

placed in service and

disposed of in

midyear, regardless

of when these

events actually occur

during the year.

Half-year convention

therefore adds one

year to the recovery

period.



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?

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.

Another ½ year of recovery is added at year n+1

MACRS depreciation rate for year n+1 is therefore one half the rate for year n.



MACRS Details

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)

There are 8 major

classes and their corresponding recovery periods:

3- years

5-years

7-years

10-years

15-years, and

20-years

27.5-years

39-years

Half-year convention applies



MACRS Recovery Periods 3- Year Property:

Special manufacturing and handling devices, tractors

5- Year Property: Computers and

peripherals, Duplicating

equipment. Automobiles,

trucks, buses, Cargo containers, Some

manufacturing equipment.

7 –Year Property: 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!



MACRS Recovery Periods

10-Year Class: Water

transportation equipment,

Petroleum refining,

Agricultural processing equipment,

Durable goods manufacturing equipment,

Ship building.

15-Year Class:

Land improvements,

Landscaping,

Pipelines,

Nuclear power production equipment,

Telephone distribution and switching equipment.

20-Year Class:

Municipal sewers

Farm buildings,

Telephone switching equipment,

Power production equipment,

Water utilities equipment.



MACRS Recovery Periods

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.



MACRS 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 0.0375

2 0.4445 0.3200 0.2449 0.1800 0.0950 0.0722

3 0.1481 0.1920 0.1749 0.1440 0.0855 0.0668

4 0.0741 0.1152 0.1249 0.1152 0.0770 0.0618

5 0.1152 0.0893 0.0922 0.0693 0.0571

6 0.0576 0.0892 0.0737 0.0623 0.0529

7 0.0893 0.0655 0.0590 0.0489

8 0.0446 0.0655 0.0590 0.0452

9 0.0656 0.0591 0.0446

10 0.0655 0.0590 0.0446

11 0.0328 0.0591 0.0446

12 0.0590 0.0446

13 0.0591 0.0446

14 0.0590 0.0446

15 0.0591 0.0446

16 0.0295 0.0446

17 0.0446

18 0.0446

19 0.0446

20 0.0446

21 0.0223

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Current MACRS recovery

percentages for the property classes

Assumes a 0 salvage value over the class life

Has the ½ year convention built into the tables

There is NO Excel function for MACRS

Simplifies depreciation computations but is less flexible than classic methods



MACRS vs. DDB : Example

Example from Blank, 7th ed. Example 16.4, p. 424 DDB, MACRS





Example 16.4, page 424, Blank 7th ed.

B = $400,000

S = $20,000 0 400,000 400,000

n = 3 1 266,680 133,320

2 88,880 44,444

MACRS ( Tax depreciation): 3 29,640 20,000

4 0 20,000

Year dt Dt = 400,000 X dt Cummulative D BVt

0 $400,000

1 0.3333 $133,320 $133,320 $266,680

2 0.4445 $177,800 $311,120 $88,880

3 0.1481 $59,240 $370,360 $29,640

4 0.0741 $29,640 $400,000 0

Total 1.0000 $400,000

DDB ( Book depreciation)

d = 2/3 = 0.667

Year d Dt Cummulative D BVt

0 $400,000

1 0.6667 $266,667 $266,667 $133,320

2 0.6667 $88,889 $355,556 $44,444

3 0.6667 $24,444 $380,000 $20,000

Total $380,000

Note = D3 is not 0.6667 X 44,444 =29,644, since this leads to BV less than 20,000

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

Bo

ok

Va

lue

YEARS

YEARS

MACRS

DDB



lecture # 7 depreciation i

Business

book depreciation value

computing depreciation

depreciation models

book depreciation amounts

cost estimation depreciation

depreciation rate td

various forms of depreciation

annual depreciation