Engineering Economics Ch 4

7/23/2019 Engineering Economics Ch 4

1/42

Engineering Economics

Dr. KarimDr. Karim


2/42

Chapter 4:Chapter 4:

Infation and Its Impact on ProjectInfation and Its Impact on Project


3/42

3

Inflation and Economic Analysis

What is inflation?

How do we measure inflation?

How do we incorporate the effect of inflationin economic analysis?


4/42

4

What is Inflation?

Value of Money

Earning ower

urchasing ower

Earning ower

urchasing power

In!estment "pportunity

#ecrease in purchasing power $inflation%Increase in purchasing ower $deflation%


5/42

&

Purchasing Power

'(()

*'))

'(() +))'

*'))

,ou could -uy &) .ig Macsin year '(()/

,ou can only -uy 4) .igMacs in year +))'/

*+/))0 unit *+/&)0 unit+&1

Price change

due toinflation

2he *')) in year +))' has only *)

!alue purchasing power of '(()


6/42

5+ 5' ) '

*'))

5+ 5' ) '

*'))

,ou could purchase3/( liters of unleaded

gasoline a year ago/

,ou can now purchase) liters of unleaded gas/

*'/&60 gallon *'/+&0 gallon

rice change due to

deflation

+)/31


7/42

6

Measuring Inflation

7onsumer rice Inde8 $7I%9the 7Icompares the cost of a sample :mar;et -as;et< of

goods and ser!ices in a specific period relati!e to

the cost of the same :mar;et -as;et< in an earlier

reference period/ 2his reference period is designatedas the base period or base year.

Mar;et -as;et

.ase eriod $'(6% +))'*')) *&'+/(

7I for +))' = &'+/(


8/42

rice Increase #ue to Inflation$2he annual percentage change in a 7I is used to measure inflation%

Item '(6 rice

$.ase ,ear%

+))) rice 1 Increase

7onsumer price inde8 $7I% ')) &'+/( >$&'+/( 5'))% 0 ')) @ ')) = 4'3 1

Monthly housing e8pense *''4/3' *(43/(6 6+ 1

Monthly automo-ile e8pense +/( 46'/3 46) 1

oaf of -read /++ '/4 63 1

ound of ham-urger /3( +/( &4 1

ound of coffee /&( 4/') &(& 1

7andy -ar /') )/() >$)/( B )/'% 0)/' @ ')) = )) 1

MenCs dress shirt &/)) 3(/)) ) 1

ostage $first5class% )/)& )/33 ) 1

Annual pu-lic college tuition +(4/)) 3D()/)) 'D+46 1


9/42


10/42

A!erage Inflation ate $f%

FpecificD indi!idual commodities do not always reflect

the general inflation rate in their price changes/ We

can calculate an average inflation rate (f ) for a

specific commodity $G% if we ha!e an inde8 $that isD a

record of historical costs% for that commodity/


11/42

''

A!erage Inflation ate $f%Fact:

.ase rice = *')) $year )%Inflation rate $year '% = 41

Inflation rate $year +% = 1

A!erage inflationrate o!er + years?

Step 1:ind the actual inflated price at the end of year +/ *')) $ ' )/)4% $ ' )/)% = *''+/3+

Step 2:ind the a!erage inflation rate -y sol!ing the following eJui!alence eJuation/

*')) $ 'f% = *''+/3+

f= &/(1

+

*'))

*''+/3+

) '

+


12/42

'+

A!erage Inflation ate $f%

Item '(6 rice +))) rice A!erage Inflationate

7onsumer price inde8 $7I% ')) &'+/( &/)61

Monthly housing e8pense *''4/3' *(43/(6 /'

Monthly automo-ile e8pense +/( 46'/3 &/4+

oaf of -read )/++ '/4 /4

ound of ham-urger )/3( +/( /3

ound of coffee )/&( 4/') /)&

7andy -ar )/') )/() /MenCs dress shirt &/)) 3(/)) /4+

ostage $first5class% )/)& )/33 &/(

Annual pu-lic college tuition +(4/)) 3D()/)) /'(


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'3

E8ample 9 ,early and A!erage Inflation ates

,ear 7ost

) *&)4D)))

' &3D)))+ &66D)))

3 +(D&))

What are the annual inflation rates $f'Kf+Kf3%

and the a!erage inflation rate $f% o!er 3 years?

Solution

Inflation rate during year ' $f'%9

>$*&3D4)) 5 *&)4D)))% 0 *&)4D)))@ ')) = /31/

Inflation rate during year + $f+%9

>$*&66D))) 5 *&3D4))% 0 *&3D4)) @ ')) = 6/'6 1/

Inflation rate during year 3 $f3%9

>$*+(D&)) 5 *&66D)))% 0 *&66D))) @ ')) = (/')1/

2he a!erage inflation rate o!er 3 years is

*&)4D))) $ 'f%3 = *+(D&))

f= 6/( 1


14/42


15/42

Inflation 2erminology 5 II

With inflation all dollars are not the same/

When inflation is considered in an economic analysisD money

is e8pressed -y two measures9 real and actual dollars/

We will see that either measure can -e used for an analysisD

-ut it is important to understand the distinction -etween the

two/


16/42

eal and Actual #ollars

'5 Actual 0 7urrent #ollars $An %9 Estimates of future cash

flows for year n that ta;e into account any anticipated

changes in amount caused -y inflationary or deflationary

effects/

+5 7onstant 0 eal #ollars $ACn %9 Estimates of future cash

flows for year n in constant purchasing powerD independent

of the passage of time $-ase year dollars%/


17/42

Conversion Fro !eal " Constant to #ctual $ollars

If we ha!e a cash flow e8pressed in real dollars $-aseyear dollars%D it is e8pressed in actual dollars -y

inflating the amounts indi!idually for each period/

we use the general inflation rate $f% as an inflation

factor/


18/42

Conversion Fro !eal " Constant to #ctual $ollars

A A f A F P f nn n n n= + L $ % L $ 0 D D %M M

'

*'D))) $' )/)%

= *'D+)

3

7onstant

#ollars

n

f

=

=

3

1M

*'D)))

3Actual

#ollars

*'D+)

3


19/42

'(

7on!ersion from 7onstant to Actual #ollars

eriod Net 7ash low in7onstant *

7on!ersionactor

7ash low inActual *

) 5*+&)D))) $')/)&%) 5*+&)D)))

' '))D))) $')/)&%' ')&D)))

+ '')D))) $')/)&%+ '+'D+6&

3 '+)D))) $')/)&%3 '3D('&

4 '3)D))) $')/)&%4 '&D)'

& '+)D))) $')/)&%& '&3D'&4


20/42

+)

)

' + 3 4 &

)

' + 3 4 &

*+&)D)))

*')&D)))*'+'D+6&

*'3D('& *'&D)'

*'&3D'&4

,ears

$-% Actual dollars

*+&)D))

)

*'))D)))*'')D)))

*'+)D))) *'3)D)))

*'+)D)))

,ears

$a% 7onstant dollars

*+&)D)

))$'I)/)&%)

*'))D)))$'I)/)

&%

*'')D)

))$'I)/)

&%+

*'+)D)

))$'I)/)

&%3

*'3)D)

))$'I)/)

&%4

*'+)

D)))$'I)/)

&%&

A li d E l


21/42

Applied E8ampleA +& year old college graduate has Gust -een hired for her first Go-/ Fhe -rags that she

will sa!e enough money to retire at && with one million dollars/ .ut wait/ etCs

assume a 31 annual inflation rate o!er her 3) year career/ If she wants her

retirement fund to ha!e the !alue of one million of todayCs dollarsD how much must

she sa!e?

When the college student is planning for her retirementD she is pro-a-ly thin;ing of the

' million dollars in terms of todayCs dollars/ If she could retire todayD she thin;s she

can li!e happily with ' million dollars/ .ut after 3) yearsD that amount will not -uy

what it can today %ow big ust her retireent be in actual

dollars to have the spending power of 1 illion of

today&s real dollars'

F l ti


22/42

Folution

2he *' million is in real dollars/ 7hanging it to actual dollars

we find that she will ha!e to sa!e almost *+/& million/ Fhe

will start spending her retirement money in 3) years/ Money

spent is always measured in actual dollars/ 2he actual dollar

eJui!alent assuming 31 inflation is almost *+/& million

dollars = ')))))) $')/)3%3)= +4+6++/46*

WouldnCt she -e disappointed if she only sa!ed ' million??

C i f # t l t C t t $ ll


23/42

Conversion fro #ctual to Constant $ollars

"ur illustration is the same as the one used earlier e8cept now

we start with the actual dollars/ 2he amounts in each year

are deflated -y the general inflation rate We use the

general inflation rate $f% as measured -y the 7I in the

discount factor/

"f courseD we o-tain the uniform series that we started with/

We should note from our e8amples that the amount at time )

did not change/ Amounts at time ) are the same in real or

actual dollars -ecause there is no passage of time/

C i f # t l t C t t $ ll


24/42

Conversion fro #ctual to Constant $ollars

A A f A P F f nn nn

nL $ % $ 0 D D %M M

= +

'

7onstant

#ollars *'D+) $' )/)%= *'D)))

53

n

f

=

=

3

1M

*'D)))

3Actual

#ollars

*'D+)

3


25/42

+&

7on!ersion from Actual to 7onstant #ollars

End ofperiod

7ash lowin Actual *

7on!ersionatf = &1

7ash low in7onstant *

oss inurchasing

ower

) 5*+)D))) $')/)&%) 5*+)D))) )1

' +)D))) $')/)&%5' 5'(D)4 4/6

+ +)D))) $')/)&%5+ 5'D'4' (/3)

3 +)D))) $')/)&%53 5'6D+66 '3/+

4 +)D))) $')/)&%54 5'D4&4 '6/63


26/42

+

EJui!alence 7alculation Onder Inflation

1. ypes of nterest !ate

2. ypes of Cash Flow

*. ypes of #nalysis +ethod

Mar;et Interest ate $i%

eal Interest ate $iC%

In 7onstant 0 eal #ollarsIn Actual 0 7urrent #ollars

7onstant #ollar AnalysisActual #ollar Analysis

#eflation Method

AdGusted5discount method

I fl i 2 i l III


27/42

Inflation 2erminology 5 IIIInterest rates for proGect e!aluation may -e stated in one of two forms9

Mar;et 0 Nominal Interest ate $i%9 A rate which com-ines the effects

of interest and inflation/

eal Interest ate (i): A rate from which the effects of inflation ha!e

-een remo!ed/

!eal nterest !ate (i&) , -oinal nterest !ate (i) /eneral nflation !ate (f )!eal nterest !ate (i&) , -oinal nterest !ate (i) /eneral nflation !ate (f )

-oinal nterest !ate(i) , !eal nterest !ate (i&) 0 /eneral nflation !ate (f )-oinal nterest !ate(i) , !eal nterest !ate (i&) 0 /eneral nflation !ate (f )

, +aret nterest !ate nder Continuous, +aret nterest !ate nder Continuous

CopoundingCopounding t reflects botht reflects both 3arning Power3arning Power

44 Purchasing PowerPurchasing Power

# 4 C


28/42

#ctual 4 Constant $ollars

Pro5ect cash flows ay be stated in one of two fors:

16 #ctual " Current $ollars (#n): #ollars that reflect

the inflation or deflation rate/

+5 Constant " !eal $ollars (#&n): ,ear ) dollars

fl i 4 C h Fl # l i


29/42

nflation 4 Cash Flow #nalysis

I 5 Actual 0 7urrent #ollar Analysis

5If the cash flow is estimated in terms of the dollars that will -e used in

n yearsD we say the amounts are in actual $or year5nD or current% dollars/

II 5 7onstant 0 eal #ollar Analysis

5If the cash flow is estimated in terms of constant5!alue dollarsD we say

the amounts are in real $or year5)D or constant% dollars/

# t l " C t $ ll # l i


30/42

6#ctual " Current $ollars #nalysiso calculate the present value of actual dollars7 we can use a two6

step or a one6step ethod:

$eflation +ethod8wo Steps:

'/7on!ert any cash flow elements in actual dollars into

constant dollars -y deflating with the general inflation rate $f %/

+/ 7alculate the present !alue of constant dollars -y discounting

at the real interest rate (i)/

#d5usted6discount +ethod89ne Step:

'/ 7ompute the nominal 0 mar;et interest rate $i%/

+/ Ose the mar;et interest rate $i% directly to find the present

!alue/


31/42

3'

Ftep '9

7on!ert actual dollars to 7onstant dollars

n 7ash lows in Actual #ollars Multiplied -y#eflation actor

7ash lows in 7onstant$or year B )% #ollars

) 5*6&D))) ' 5*6&/)))

' 3+D))) $')/)&%5' 3)D46

+ 3&D6)) $')/)&%5+ 3+D3'

3 3+D)) $')/)&%53

+D334

4 +(D))) $')/)&%54 +3D&

& &D))) $')/)&%5& 4&D44&


32/42

3+

Ftep +97on!ert 7onstant dollars to EJui!alent resent !alue

n 7ash lows in 7onstant $oryear B )% #ollars

Multiplied -y#iscounting actor

EJui!alent resent!alue

) 5*6&D))) ' 5*6&D)))

' 3)D46 $')/')%5' +6D6)

+ 3+D3' $')/')%5+ +D6'

3 +D334 $')/')%53 +'D+

4 +3D& $')/')%54

'D+(&& 4&D44& $')/')%5& +D+'

;

$eflation +ethod:


33/42

33

$eflation +ethod:Converting actual dollars to constant dollars and then to e?uivalent

present value

5*6&D))) *3)D46 *3+D3' *+D334 *+3D& *4&D4&&

5*6&D))) *3+D))) *3&D6)) *3+D)) *+(D))) *&D)))

5*6&D)))

*+6D6)*+D6' *+'D+

*'D+(&

*+D+'

*4&D+

#ctual

$ollars

Constant

$ollars

Present

value

n= ) n= ' n= + n= 3 n= 4 n= &


34/42

34

Method +9 AdGusted5#iscount Method

P A

i

A

i

A

f i

i i i

i f i f

nn

n

n

n

n

n n

=

+

+

=

+ +

+ = + +

= + + +

$ %

$ % $ % $ L %

$ % $ %$ L %

L L

'

' ' '

' ' '

'

P

A

f

in

nn

n=

+

+

$ %

$ L %

'

'

=

+ +

A

f i

n

n n$ % $ L %' '

=+ +

A

f i

n

n n$ % $ L %' ' i i f i f = + +L L

Ftep '

Ftep +


35/42

AdGusted5#iscounted Method

n 7ash lows in Actual #ollars Multiplied

-y

EJui!alent

resent !alue

) 5*6&D))) ' 5*6&D)))

' 3+D))) $')/'&&%5' +6D6)

+ 3&D6)) $')/'&&%5+ +D6'

3 3+D)) $')/'&&%53 +'D+

4 +(D))) $')/'&&%54 'D+(

& &D))) $')/'&&%5& +D+'6

;

i i f i f = + +

= + +

=

L L

/ / $ / %$ / %

/

) ') ) )& ) ') ) )&

'& &1

P n = An / (1+i)n

= An (1+i)- n


36/42

3

AdGusted5discount method

)

' + 3 4 &

5 *6&D)))

*+6D6)

*+D6'

*+'D+

*'D+(&

*+D+'

*4&D+

=*3+D)

))$

0HD

'&/&

1D

'%

= *

3 &

D 6 ) ) $

0 H

D

' &

/ & 1

D +

%

=*3+D

))$0HD

'&/&

1D

3%

=*+(D)))

$0HD'&

/&1 D

4%

=*

&3D)

))

$0 H

D'&

/&1 D& %

*3+D)))*3&D6))

*3+D))*+(D)))

*&D)))

#d5usted $iscount +ethod


37/42

36

#d5usted $iscount +ethodConverting actual dollars to present value dollars by applying the

aret interest rate

n= ) n = ' n = + n = 3 n = 4 n = &

5*6&D))) *3+D))) *3&D6)) *3+D)) *+(D))) *&D)))

#ctual

$ollars

5*6&D)))

*+6D6)*+D6' *+'D+

*'D+(&

*+D+'

*4&D+

Present

value

1&/'&=++= fifii


38/42

6 Constant " !eal $ollar #nalysis

2wo Fteps Approach9

Ftep '5 7on!ert any cash flow elements in constant dollars

into actual dollars -y using the general inflation rate $f %/

Ftep +5 Ose the mar;et interest rate $i% to find the eJui!alent

present !alue/

3

E8ample5 EJui!alence 7alculation with 7omposite 7ash low Elements9


39/42

E8ample EJui!alence 7alculation with 7omposite 7ash low Elements9

Fa!ing for 7ollegeAge 7ollege e8penses

$in todayCs dollars%

7ollege e8penses

$in actual dollars%

' $reshman% *3)D))) *3)D)))$F0PD1D'3% = *3D(

'( $Fophomore% 3)D))) 3)D)))$F0PD1D'4% = 6D+6

+) $Punior% 3)D))) 3)D)))$F0PD1D'&% = 6'D(6

+' $senior% 3)D))) 3)D)))$F0PD1D'% = 6D+''

Note: saving begins when child is age 5, 13 years before entering college


40/42

4)

V'= C$F0AD +1D 4%

V+= *++(D+''

et V'= V+and sol!e

for C9

C= *+D/4

eJuired Quarterly 7ontri-utions to 7ollege unds


41/42

4'

Item Effects of Inflation

ate of eturn

and NW

Onless re!enues are

sufficiently increased to ;eeppace with inflationD ta8 effectsand0or a wor;ing capital drainresult in lower rate of return or

lower NW/


42/42

ate of eturn Analysis under Inflation

rinciple92rue $real% rate of

return should -e -ased on

constant dollars/

If the rate of return is

computed -ased on actual

dollarsD the real rate of

return can -e calculated as9

n

Net cashflows inactualdollars

Net cashflows inconstantdollars

)'

+

3

4

5*3)D)))'3D&6)

'&D)

'3D3&

'3D+

5*3)D)))'+D33

'3D')

')D)3

(D3)6

IRR 31.34% 19.40%i

i

fL

/

/

/4)1

M=

+

+

=+

+

=

'

' '

' ) 3'34

' ) ')'

'(Not correct I

fM

= ')1

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Engineering Economics Ch 4