技術(shù)經(jīng)濟(jì)學(xué)第4章CASH FLOW ANALYSIS

LOGOChapter

4CASH

FLOWANALYSIS4.1

Basic

Tax

StructureDomestic

AgreementsInternational

ContractsSummarycontents·4.1.1

Depreciation·4.1.2

Income

Taxes4.1 Basic

Tax

Structure4.1.1

DepreciationDefinition·In

literal

sense,

it

means

a

decrease

invalue.·In

economic

analysis,

it

is

treated

as

areplacement

cost.A

property

can

be

depreciatedif

it

satisfie·It

must

be

used

in

business

or

production

oincome.·It

must

have

a

life

longer

than

one

year.·It

must

be

something

that

wears

out,

decaysbecomes

obsolete

or

loses

value

fromnaturalcauses.For

Example:

equipment,

buildings,

and

other

kind

of

fixedassets.These

characteristics

are

most

appropriate

for

equipment;

however,

they

can

also

be

applied

tobuilding,

patents

and

copyrights.costscostsInvestment

in

property

such

as

building

,patentsCapitalized

and

copyrights

is

called

Capitalized

costs

.In

production

operations,

this

cost

will

includecosts

of

casing,

piping,

tank

batteries,

pumps,compressors,

buildings,

etc.

(tangible/intangiThe

costs

incurred

for

regular

maintenance,

upkeOperating

and

utilities

for

running

the

equipment,

includithe

labor

costs

are

considered

operating

costs.And

it

can

be

deducted

from

the

operating

revenuein

the

same

year

for

tax

purposescapitalized

costs

and

operating

costsExampleAlthough

the

distinction

between

the

capitalized

costsand

the

operating

costs

is

clear

in

most

instances,

insome

instances

the

distinction

is

difficult

to

achieve.

Agood

example

would

be

the

costs

of

drilling

a

well.These

costs

include:Costs

related

to

agreements

with

drilling

contractors.Surveys

related

to

location

of

a

well.Road

costs

and

dirt

work

related

to

well

location.Rig

transportation

and

set

up

costs.Fuel,

water,

drilling

mud

costs.Labor

costs

including

supervisors,

well

sitegeologists

and

testing

of

well.Stimulation

costs.Cementing

costs

(does

not

include

casing).Surface

damage

costs.Since

the

drilling

costs

are

incurred

before

the

actualproduction

begins,

they

cannotbe

considered

operatingcosts.On

the

other

hand,

the

costs

for

labor,

utilities,

drillingmud,

and

rig

rental

cannot

be

considered

tangible

costs.How

to

treat

these

costs

is

indeed

a

legislative

decision.Different

countries

have

different

rules

with

respect

tocategorizing

the

costs

of

drilling.ExplanationCost

Basis-B0·Cost

basis

represents

thecost

of

acquiring(purchase)

a

property.·This

is

the

total

cost

which

will

be

capitalizedover

the

property.·This

cost

includes

the

cost

of

the

property

aswell

as

all

the

other

incidental

(auxiliary)expenses

such

as

installation,

freight

(shippingcharge),

and

site

preparation.some

basic

definitionsBook

Value

(Bk)Book

value

is

cumulative

depreciation

subtractedfrom

the

cost

basis

of

the

property.

In

year

k

,

thebook

value

can

be

defined

as,(4.1)where

Dj

is

the

depreciation

in

year

j.

The

amountdepreciated

in

each

year

will

depend

upon

themethod

used.Salvage

ValueSalvage

valueis

the

price

obtained

from

the

saleof

property

at

the

endof

its

useful

life.Repair

CostsRepair

costs

are

costs

related

to

keeping

theproperty

in

an

ordinary

efficient

operatingcondition.Capitalized

CostsCapitalized

costs

related

to

the

existing

property

arecosts

related

to

alterations,

additions

or

improvementsthat

increase

property’s

useful

life

or

value

or

make

itadaptable

for

a

different

use.The

distinction

between

repair

costs

and

capitalizedcosts

for

an

existing

property

is

useful

because

repaircosts

can

be

deducted

as

operating

costs,

whereas,capitalized

costs

will

have

to

be

depreciated.

Thisdifference

can

have

significant

tax

consequences.Useful

LifeThe

time

over

which

property

is

kept

in

productive

use

ina

business.Tax

LifeThe

period

of

time

over

which

depreciation

is

calculatedto

offset

taxable

income.

This

period

is

usually

shorterthan

the

useful

life

of

the

property.

It

is

determined

by

thetax

code

of

a

particular

country

depending

on

the

type

ofproperty.Example

4.1

An

oil

company

ordered

a

new

submersiblepump

for

improving

production

from

an

old

well.

The

costof

the

pump

is

$20,000.

The

company

will

have

to

pay

7%sales

tax

on

the

pump.

In

addition,

shipping

costs

are$300,

and

the

installation

costs

are

$l,000.

What

is

thecost

basis

for

the

pump?SolutionIn

calculating

the

cost

basis,

any

cost

associated

withpurchase,

shipping,

installation

and

site

preparation

willhave

to

be

included.

Therefore,

the

cost

basis

for

thepump

is,Cost

of

Pump$20,000Sales

Tax

(7%)1,400Shipping

Cost

(freight)300Installation

cost1,000Cost

Basis$22,700AttentionIn

calculating

cost

basis,

it

is

critical

thatthe

costs

including

some

non-monetarytransactions

are

included.

One

such

exampleof

non-monetary

transaction

would

be

trade-in

benefit.·(1)Straight

Line

Depreciation-SLD·(2)Declining

Balance

Depreciation-DBD·(3)Sum

of

Years

Digits

Depreciation--SYDD·(4)Unit

of

ProductionDepreciation·(5)Declining

Balance

and

Straight

lineDepreciation·(6)Declining

Class

Account

DepreciationDifferent

Methods

of

Depreciation（1）Straight

Line

Depreciation-SLDStraight

line

depreciation

is

one

of

the

easiest

methods

ofestimating

the

depreciation.Mathematically,

the

depreciation

is

calculated

as.(4.2)where

Dk

is

the

depreciation

in

year

k

,

B0

is

the

cost

basis,S

is

the

salvage

value

at

the

end

of

tax

life

and

n

is

thenumber

of

years

of

tax

life.Alternately,

depreciation

can

also

be

calculated

as,(4.3)where

Bk-1

is

the

book

value

at

the

end

of

period

k-l.

Bothequations

would

give

the

same

result.

The

book

value

iscalculated

usingA

common

term,

S,

in

both

Eq.

4.2

and

Eq.

4.3

is

difficultto

estimate

at

the

beginning

of

taxable

life

for

manyproperties.

Many

tax

codes

simplify

the

calculations

byassuming

that

the

salvage

value

is

zero

at

the

end

of

taxlife.Example

4.2Consider

a

piece

of

equipment

purchasedfor

$5,000.

If

the

tax

life

is

five

years,

and

the

salvagevalue

is

zero,

calculate

the

depreciation

schedule

over

thefive

year

period.YearDepreciationDkBook

ValueBk5,00011,0004,00021,0003,00031,0002,00041,0001,00051,0000（2）Declining

Balance

Depreciation-DBDThe

amount

of

depreciation

in

each

year

is

a

certain

percentage

of

the

book

value

at

the

end

of

previousyear.*This

percentage

is

constant

throughout

the

tax

lifethe

property.*This

percentage

is

usually

defined

as

the

ratio

ofdeclining

balance

rate

to

the

tax

life.If

we

denote

this

percentage

change

in

fraction

as

R

,

wecan

calculate

the

depreciation

in

year

k

as,(4.4)where

the

book

value

at

the

end

of

year

k

can

becalculated

as.(4.5)Substituting

Eq.

4.5

in

Eq.

4.4,

we

can

calculate

thedepreciation

in

year

k

as,(4.6)where

B0

is

the

cost

basis.Thedeclining

balance

rate

canvary

between100%to

200%

(double

declining

balance=DDB)

;

the

most

common

value

being

200%.Example

4.3Using

the

same

information

as

in

Example4.2

and

using

the

double

declining

balance

methodestimate

the

depreciation

schedule.SolutionFor

year

one,

depreciation

is

calculated

as

(using

Eq.

4.6)D1

=

RB0where

R

is

200%/5

=

40%,

and

B0

=

$5,000.Substituting,D1=0.4×5,000=$2,000The

book

value

at

the

end

of

year

1

can

be

calculatedusing

Eq.

4.5,B1=B0(1-R)1=5,000(1-0.4)=$3,000Similarly,

for

year

2,D2=RB1=RB0(1-R)2-1=0.4*5,000(1-0.4)=$l,200D2=RBk-1=0.4(3,000)=$1,200Or,

using

Eq.

4.4,

.The

book

value

is,B2=

(5,000)(1

-

0.4)2

=

$l,800Calculations

can

be

repeated

for

other

years

as

well,

asshown

in

the

table

below:After

five

years,

the

total

amount

of

depreciation

allowedis

$4,61l

which

is

not

equal

to

the

cost

of

the

equipment.This

is

one

of

the

major

disadvantage

declining

balancemethod.

That

is,

the

cost

of

the

equipment

cannot

berecovered

fully

over

the

tax

life.

Only

at

very

large

timescan

the

total

cost

be

fully

recovered.YearBook

ValueDepreciation5,00013,0002,00021,8001,20031,08072046484325389259Total$4,611（3）Sum

of

Years

Digits

DepreciationSYDDThis

method

also

results

in

a

larger

depreciation

at

thebeginning

of

a

useful

life

than

the

straight

linedepreciation

method.

It

is

not

a

very

common

methodused

for

depreciation.

To

calculate

the

depreciation

usingthis

method,

we

first

need

to

know

the

sum

of

years

digits.This

sum

represents

the

sum

of

all

the

years

in

a

tax

life.For

example,

if

n

is

the

tax

life

of

a

property,

sum

iscalculated

as,sum

=

l+2

+3+...+n

(4.7)Alternately,

we

can

also

calculate

the

sum

as,(4.8)Depreciation

in

year

k

can

be

calculated

as,(4.9)We

can

write

Eq.

4.9

as,(4.10)Book

value

can

be

calculated

using

Eq.

4.

1.Example

4.4

Using

the

same

information

as

in

Example

4.2,

calculate

the

depreciation

schedule

using

the

sum

ofyears

digits

depletion.SolutionUsing

Eq.

4.10,

depreciation

in

year

1

can

be

calculated

as,For

year

two,kThe

book

value

after

year

two

is.Similar

calculations

can

be

done

for

other

years.Unlike

declining

balance

method,

sum

of

years

digitsmethod

allows

the

depreciation

of

the

entire

cost

of

anasset.YearDkBook

Value500011,6673,33321,3332,00031,0001,000466733353330Total

Depreciation$5,000（4）Unit

of

Production

DepreciationThis

method

of

estimating

the

depreciation

is

based

onthe

number

of

units

produced

by

an

equipment

ratherthan

the

life

of

the

equipment.

It

is

assumed

that

the

totalnumber

of

units

that

can

be

produced

from

the

equipmentis

known.

The

amount

of

depreciation

using

this

methodcan

be

calculated

as,(4.1l)where

(u)

is

the

number

of

units

produced

in

a

given

year,(U)

is

the

total

number

of

units

that

can

be

produced

fromthe

unit,

(C)

is

the

cost

of

the

equipment,

and

(S)

is

thesalvage

value.(5)

Declining

Balance

and

Straight

line

DepreciationTo

remove

the

major

disadvantage

of

the

declining

balancemethod,

i.e.,

not

being

able

to

recover

the

entire

cost

of

anasset;

at

the

same

time,

to

allow

for

the

rapid

depreciation

ascalculated

by

the

declining

balance

method,

a

combination

ofdeclining

balance

and

a

straight

line

method

is

used.This

method

allows

the

calculation

of

depreciation

using

boththe

declining

balance

and

the

straight

line

methods

andswitching

from

one

method

to

another

when

method

predictsa

higher

depreciation

than

the

other

method.Recall

that

straight

line

depreciation

can

be

calculated

as(4.3)and

the

declining

balance

depreciation

is

calculated

as,(4.4)For

each

year,

we

compute

the

depreciation

using

bothmethods

and

choose

the

value

which

is

higher.If (4.12),

we

select

the

declining

balanceMethod;Ifmethod.(4.13),

we

select

the

straight

lineIf

we

assume

that

the

salvage

value

is

zero,

we

cansimplify

Eq.

4.13

to

write,Eq.4.14

provides

a

condition

for

switching

to

a

straightline

method.

For

example,

if

n=

5,

and

R

=

0.4,

k

>

3.5

toswitch

to

a

straight

line

method.

That

is,

we

will

switch

inyear

4

to

a

straight

line

method.

The

following

exampleillustrates

the

technique.(4.14)Example

4.6Using

the

same

information

as

in

Example4.2,

calculate

the

depreciation

schedule

using

thecombination

(double

declining

and

straight

line)

method.Assume

double

declining

balance

(DDB).YearDepreciation(Declining

balance)Depreciation(Straight

Line)Book

ValueAt

The

EndSelectedDepreciation5,00012,0001,0003,0002,00021,2007501,8001,20037206001,080720443254054054052165400540(6)

Declining

Class

Account

DepreciationFor

equipment

which

is

assembled

from

variouscomponents,

it

is

difficult

to

depreciate

individualcomponents

separately.

An

example

would

be

a

pipelinenetwork

or

a

gas

processing

plant.

It

is

difficult

to

keeptrack

of

a

valve

or

a

flange

or

a

tee

in

a

pipeline

network;and

depreciate

it

individually.

To

minimize

this,accounting

complexity

another

method

commonly

usedfor

depreciation

is

the

declining

class

account

(DCA)depreciation.This

method

is

based

on

whole

investment

perpetualdeclining

class

account

(DCA)

schedule.

The

method

isrelatively

easy

to

use.

Assuming

that

the

average

tax

lifeof

the

equipment

is

known,

the

depreciable

amount

in

agiven

year

is

calculated

as,(4.15)where

Bk-l

is

the

book

value

at

the

end

of

previous

yearand

Ak

is

the

sum

of

capital

expenditures

during

year

k.Depreciation

in

year

k

is

then

calculated

as,(4.16)where

R

is

the

declining

balance

ratio.

This

equation

is

continued

to

be

used

so

long

as

the

equipment

is

used

fora

given

purpose.If

any

part

of

the

capital

equipment

is

disposed,

theincome

received

is

treated

as

a

taxable

income.4.l

.2

Income

TaxesTaxing

the

income

can

take

several

forms;

the

mostcommon

being

income

tax

which

is

levied

on

thedifference

between

the

gross

revenue

and

alloweddeductions

for

tax

purposes.It

is

based

on

the

value

of

real

estatePropertytaxsalestaxLuxurytaxEntertainmenttaxvalue

addedtaxOther

taxesIt

is

based

on

the

price

of

goodsIt

is

based

on

items

which

arenot

considered

necessitiesIt

is

based

on

entertainment

expensesIt

is

based

on

the

difference

in

a

valueof

a

good

as

it

passes

from

one

party

toanotherBasic

Principles

of

Tax

Laws·The

first

principle

about

the

income

taxis

thatit

is

assessed

based

on

thetaxable

income.·The

second

principle

common

to

mostof

the

income

tax

laws

is

that

the

ratesat

which

the

tax

applied

tends

to

beprogressive.In

most

economic

evaluations,

one

needstousemarginal

rate

for

calculations.

Marginal

tax

raterepresentsthe

tax

rate

applied

to

thelast

dollar

earin

the

taxable

income.Marginal

tax

rateFor

example,In

U.S.

the

tax

rate

is

15%

for

a

corporation

with

ataxable

income

less

than

$50,000;

the

rate

increase

to39%

for

taxable

income

exceeding

$200,000.If

the

corporation

has

earned

$30,000

last

year

andexpects

to

add

another

$10,000

in

taxable

income

witha

new

project,

it

is

reasonable

to

assume

a

marginaltax

rate

of

15%;

however,

if

the

corporation

earned$l,000,000

last

year

and

is

considering

a

new

projectwith

a

potential

additional

taxable

income

of

$500,000,it

is

better

to

use

39%

as

a

marginal

tax

rate

ineconomic

analysis.

Because,

that

is

the

income

taxrate

that

will

be

applied

to

any

additional

taxableincome.Tax

ComputationsTaxable

income

is

calculated

by

subtracting

the

allowabledeductions

from

gross

revenue.

In

mathematical

terms,taxable

income

=

gross

revenue

–

tax

deduction

(4.1Most

common

deductions

include

operating

costs,

depreciatioverhead

costs

and

other

related

expenses.

Therefore,

we

cawrite,taxable

income

=

gross

revenue

-

operating

costs-

related

expenses

-

depreciation

(4.1Once

the

taxable

income

is

calculated,

the

income

tax

iscalculated

by

using

the

applicable

marginal

tax

rate.

That

iincome

tax

=

taxable

income

×

tax

rate

（4.19）To

calculate

net

revenue,

we

need

to

subtract

the

actuexpenses

from

the

gross

revenue.

These

expenses

do

noinclude

depreciation

or

other

deductions

which

areonly

deducted

for

tax

purposes.Net

revenue

is

calculated

as,net

revenue

=

gross

revenue-operating

costs-

related

expenses-tax

(4.20)jIf

we

use

the

following

notation:

A

=

gross

revenue

in

yearO

=

operating

costs

in

year

jjD

=

depreciation

in

year

jjT

=

marginal

tax

rateE

=

other

related

expenses

yeajwe

can

write

taxable

income

as,

=

A

-O

-E

-Dj

j

j

jwe

can

write

the

income

tax

as,

=

T(A

-

O

-E

-D

)j

j

j

jand

we

can

write

the

equation

for

net

revenue

as,(4.2(4.2=

A

-O

-E

-

T(A

-

O

-E

-D

)j

j

j

j

j

j

jnet

revenue

=(l-

T)(

A

-O

-E

)+

TDj

j

j

j(4.23)Eq.

4.23

can

be

repeated

for

all

the

years

in

which

a

projectoperation.Example

4.8

A

company

wishes

to

buy

a

workstation

computerfor

$15,000.

With

the

use

of

this

machine,

the

company

can

sa$5,000

in

outside

computing

costs.

The

maintenance

agreemencalls

for

a

payment

of

$800

per

year

for

the

machine.

Assumethat

the

useful

life

of

the

machine

is

five

years.

Assume

furthat

a

straight

line

depreciation

is

allowed

over

a

five

yearIf

the

income

tax

rate

is

28%,

calculate

the

NPV

of

thisinvestment

for

the

MROR

of

15%.SolutionSample

calculation

for

year

1,

gross

revenue

(savings)

=

5,Using

Eq.

4.18,taxable

income

=

gross

revenue

-

operating

costs

-depreciation=

5,000

-

800-

3,000

=

$l,200Using

Eq.

4.19tax

=

taxable

income

×

tax

rate

=

l,200×0.28

=

$336Using

Eq.

4.20,net

revenue

=

gross

revenue

-

operating

costs

-

taxes=

5,000

-

800-

336

=

$3,864In

these

calculations,

we

assumed

a

straight

line

depreciatTherefore,The

following

table

lists

the

calculations

for

other

years.YearGrossIncomeTaxableIncomeTaxNetRevenue0-15,000-15,00015,0001,2003363,86425,0001,2003363,86435,0001,2003363,86445,0001,2003363,86455,0001,2003363,864We

are

assuming

that

all

the

income

is

collected

at

the

end

ofyear,Since

the

NPV

is

negative,

the

project

is

not

feasible.Alternately,

if

we

use

Eq.

4.23,

we

can

write

the

net

revenueequation

as,net

revenue

=(l-

T)(

Aj-Oj-Ej

)+

TDjSubstituting,

.=

(l

-

0.28)(5,000-

800)

+

0.28×3,000

=

$3,864Since

the

revenue

is

constant

each

year,

we

can

write,We

will

get

the

same

answer

as

before.Example

4.9A

gas

well

is

expected

to

produce

at

exponentialdecline

rate

based

on

the

adjacent

producing

wells.

Based

oninitial

testing,

the

following

production

profile

is

predicthe

next

five

years.

The

total

capitalized

cost

for

this

well$2,000,000.

The

operating

costs

per

year

are

$600,000

and

ar

expected

to

increase

at

a

rate

of

5%

per

year.

Assume

that

gas

sold

at

a

rate

of

$l.75/MSCF,

and

all

the

money

is

collected

aend

of

each

year.

Assume

that

the

local

tax

is

7%

of

the

gross

revenue.Assume

that

the

capitalized

cost

is

depreciated

over

a

five-yperiod

using

a

combination

method(double

declining

balance

and

straightline).

Assume

that

depletion

costsare

negligible.

If

the

income

taxIf

the

MROR

is

20%,is

this

investment

feasible?Production

ProfileYear1Production,MSCF1,561,51521,134,922rate

is

28%.Using

this

information,3calculate

the

ROR

for

this

investment.823,5314597,6885434,578SolutionThe

following

table

illustrates

the

results

over

a

five-yearSample

calculations

are

shown

below.*

Local

tax

can

be

treated

as

other

expenses

since

these

taxeassessed

based

on

the

gross

revenue,

and

not

taxable

income.YearProduction,GrossOperatingLocal*1MSCF1,561,515Revenue

($)2,732,651Costs

($)600,000Tax

($)191,28621,134,9221,986,114630,000139,0283823,5311,441,179661,500100,8834597,6881,045,954694,57573,2175434,578760,512729,30453,236Foryearone,gross

revenue

=

production

×

price

=

l,561,515×$l.75

=

$2,732,

651local

tax

=

gross

revenue×.07

=

2,732,651×.07

=

$191,286For

year

one,

Using

Eq.

4.4, depreciation

=

2/5

×

2,000,000=$800,00Using

Eq.

4.18,taxable

income

=

gross

revenue

-

operating

costs

-

local

tax

-

depreciatio=

2,732,651

-

600,000-

191.286

-

800,000

=

$l,141,365Using

Eq.

4.19,tax

=

taxable

income

x

tax

rate

=

1,141,365×0.28

=

$319,582Using

Eq.

4.20,net

revenue

=

revenue

-

operating

costs

-

local

tax

-

income

tax=

2,732,651

-

600,000

-

191,286

-319,582

=

$1,621,783YearDepreciationTaxable

IncomeTaxNet

Revenue($)($)($)($)1800,0001,141,365319,5821,621,7832480,000737,086206,3841,010,7023288,000390,796109,423569,3734216,00062,16217,405260,7575216,000-238,028-66,64844,620Note

that

for

the

last

year,

the

taxable

income

is

negative.result,

the

tax

is

also

negative.

Therefore,net

revenue

=

760,

512

-

729,304

-

53,236

-(-66,648)

=

$44,The

reason

we

use

negative

tax

is

because

of

the

assumption

tthis

is

one

of

several

projects

the

company

is

involved

in,

aa

result,

the

loss

in

this

project

will

result

in

a

reduction

in

other

ventures

and

thus

result

in

an

overall

lower

tax

pay

by

the

negative

amounts.

To

calculate

the

ROR,0

=

PV

–

PVcosts

benefitsBy

trial

and

error,

i

=

ROR

=

38.3%.

Since

ROR>MROR,

theproject

is

feasible.Effect

of

Depreciation

ScheduleAs

seen

in

the

previous

section,

depreciation

playsmajor

role

in

net

revenue

calculations.

In

this

sect

we

will

investigate

the

impact

of

depreciation

sche

on

the

after

tax

analysis

of

a

project.

Recall

Eq.

4.

which

states

that

the

net

revenue

is,=(l-

T)(

A

-O

-E

)+

TDj

j

jj(4.23

)That

is,

we

receive

an

"additional"

net

revenue

of

TDjas

a

reof

depreciation

deduction.

This

additional

revenue

is

colleover

the

life

of

the

project.

If

we

assume

that

the

tax

life

oasset

is

n

,

then

we

can

calculate

the

present

value

of

theadditional

future

revenues

as,(4.24)where

i

is

the

effective

interest

rate.

This

is

the

benefit

wreceive

as

a

result

of

the

capital

expenditure

B0Therefore,

after

tax

consideration,

the

net

cost

associatedthat

asset

is,(4.25)Obviously,smaller

the

net

cost,better

off(經(jīng)濟(jì)狀況好）

will

becorporation.This

net

cost

will

depend

on

the

depreciationschedule.Example

4.10A

new

water

injection

pump

will

bepurchased

for

$90,000.

It

can

be

depreciated

over

aseven

yearperiod.

If

the

marginal

tax

rate

is

34%,calculatethenet

cost

of

thepump

if

it

is

depreciateusing:

a)

straight

line

method,

b)

double

decliningbalance

method.

Assume

the

interest

rate

to

be

1