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)

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+ wK w# C k

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<,P

F=? n= + i= M'( F= ?

i= M'(

(

)

A= ,((

P= '(((

F P "e@ #- # C ” F1 = P + Pi = P (1 + i )

K- # C F2 = F1 + F1i

F2 = F1 (1 + i ) = P(1 + i )(1 + i ) = P(1 + i ) 2 F2 = P(1 + i ) 2

“

“ K n# C

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F = P (1 + i ) n

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1 (1 + I ) n

n (

)

n ")

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E3P L0

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i ) (1 + i ) n − 1

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(A/P,•2†I , 67) =? (A/P, •2 , 67) = 7†6 ;I@ = 7†6 ; (A/P, •@ , 67) = 7†6 47I =7†6 47

N'+)+ (

N* M8

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c d

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= 7†77(( ! -

- f

F P A P F A

(P/F , i% , n) (F/P , i% , n) (P/A , i% , n) (A/P , i% , n) (A/F , i% , n) (F/A , i% , n)

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= I†I27

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) …;X(

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0 8 >P

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ˆ At

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# ˆt

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i≠ j

i= j

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‚

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+ J 1 J 8 >P •67

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/ N, = r

•(

, '0- : w

! ,VW N, T - I7777 - 0-,

! N, 1 0- : / ,e # 67

) J

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M $ 8J , $, 1 M " B k 1

Effective Interest Rate Nominal Interested Rate Number Of Compounding Periods

T - 6 777 S

F= ?

7 '

)

'((( (

',(( ( *((( (

9 +

'( ,

ie = (6 + 7†7( /;) ; - 6 = 7†7(74 = • (†74

,VW N,

F = 67777(F/P, • (†74 ,67) + I7777(F/P, • (†74 , ( ) + 6 777(F/P, • (†74 , ) = 24†@I2

D 0 .! T : -

5 ! &M $ - , C

5 # &M 0 8 1 '

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5 b 3P

5 b 3P 0 % ,

' \G

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k J

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n ?# -

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ie = 1 +

r t

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U , 0 8 / ,VW N, .! T :

,VW N,

&$ B Q h!

C JU ,

3" ,G

1 1# k J

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−1

S ', 9 1 8 >P

k.J

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3" $ G, C J

F = P (6… r/t)tn ! #

/ N, ˆ r

C JU , k J1

3" ˆ t 3" ˆ n

F= P lim (6… r/t)tn =Per.n t F = Per.n

e = ;†26@;@

F = P(F/P, r, n) C J U , 1 .S ,

M $ < L0

P = Fe –rn P = F(P/F, r, n) C JU , 1$ M ie=er - 6

J1#

•6; $, 1 N, k.J

E3P L0

k ,G

‚ %1

1 + O1 0

T - 67777

+ w # 6 0 ‚ ) ,G .S ,

U , ,VW N,

FJ ,G - . b

1 $, 1 +R

•6; / 6; = •6

$, 1 N,

6 “ 6; = 6@7 $

F = A(F/A, •6 ,6@7) = 67777(F/A, •6 , 6@7) = ? 1R Ie = (6…r/t)t –6 = (6 + •6;/6;)6; –6= •6;†(@

F = A(F/A, ie, 6 ) = 67k777“6;†(@ ' \G

U ,

O1 #

Z / Y •6; N, 1 ! Z?,P - B Y k 1

F= P(F/P, •6; , ) F= ;77777(6†@;;6) = I( ;7

T - ;77777 ‡E ,G h- . +w

, #

0‚) J

@ !

0 9& \ I

E3P L0 L-

! .S M L-

, .9G0 1 N, L-

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\Q N,

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> PW

$f-, J 1 . „ ,G - '

•67 MARR $

. ," '

\Q N,

Present Worth Method Equivalent Uniform Annual Cost (Benefit) Benefit to Cost Method

$f-, ' $f-, k

k J1

E3P L0 Œ ,G •

@ @ / & +

J 1 J $f-, :j $ 7* -

w ,G (

B- A:J - - .

; 77

I 77

477

277

;77

I 7

" E/

y + L0 ,/

PWA = ; 77 + 477 (P/A, •67 , ) – ;77 (P/F, •67 , ) = 2@@ PWB = I 77 + 277 (P/A,•67 , ) l I 7 (P/F, •67 , ) = 4I( k J

F ,/

E3P L0 : J .E31 A : J

@ @ ,H

$f-, ' ,1

.! T

, 9 ,/ . 1

Ex& .

1 !k J

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L- :

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, 0 : J - h- . Tk J1

,1 ,1 : J

66777

6@777

I 77

I677

" E/

6777

;777

A + L0

(

k J1

( - 4 `, 9

,r : , Mw

'((( SV='(((

'(((

A=*,((

''((

PWA= 66777 + 66777(P/F, •6 , () – 6777(P/F, •6 , () + 66777(P/F,•6 , 6;) – 6777(P/F, •6 , 6;) – 6777(P/F, •6 , 6@) + I 77 (P/A, •6 , 6@) = I@ 4 h

B : J ' ,1 SV=)(((

A=*'((

'E(((

PWB= 6@777 + 6@777(P/F, •6 , 4) – ;777(P/F, •6 , 4) l ;777(P/F,•6 , 6@) + I677(P/A, •6 , 6@) = 6I@

k. , /

> C w

PWA<PWB

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n→∞ i (1 + i ) n (1 + i ) n − 1

A=P

lim A = P lim

i (1 + i ) n = Pi (1 + i ) n − 1

n→∞ A = Pi → P = A i

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9 b %

> ,G k J

]

] j,A <

eu ’ T 0 ‚ b :

, .9G0 1 N,

T k.

- % T - ;7777

? > 1

! b ’ T0‚

J },P - J 1 ! $f-, : K ]

,1< ' ,1 h- .

< k

T - I 7777 b K0[ '

k J1 PWB P=

A 20000 = = 400000 350000 i 0.05

k. '

j,A : K ]

EUAC , EUAB " K M V .S M ', % 1 T $ , $f-, 1 = ", '

> -

\#L -

E L- :

k J N, - j,A ! C ,Q b aA

Z L- ,

R •

" [ # 3

Y L- : 0 $

.Q •

k J 1 :J- a o L- ,

0 ," C < - , 3 , . ,1 ,1

$f-, ,/

! T ' ,1 L- : k J1

k J1

j,A

> - <

$, 1

E ' ,1 [ L0

•

T ' e1 Q

5 BaS O1 • - R k ,G

j,A !-

j,A

SV =

y + L0

},P

> ,/

. 1 kkk - j,A y + L-,P 0 B T < - E3P >

! L0

EUAC= P(A/P, i%, n)-SV(A/F, i%, n) + … k. J1 !

T - 777 C< y + L0 - ! T - 4777 [ : J k

" E/

:J :

T - @7777 : J % > ,G k J 1 ! .S M

,S > - .

# @:J :

> ) J },P •( $, 1 N, -

EUAC= @7777(A/P, •(,@) + 4777 – 777 (A/F, •(,@ )= ;6I@7 c

] ‚ƒ - $ /

" E3P L0

1 j,A ' k

> 1

,rEB T .

> , -$ /

,S k

> "

- A + L0

P * C< 1 - $ -< . 1 $, 1 N,

. 1

< 0 %,

k 1

S $f-, : ," '

E L- :

! .S M

> 1

,* (A/P,i%,n)

" &( )

< -

1 L- : P

< -

> ,

- A+

\# " #C k# T 3 :j $

W "/# <

> J1 [

1 )$f-,

w & + ' ,1

> :,/ '

/ & + •6 $, 1 N, y,J 1 EUAC L- | ,A 0 k A

B T - : 3"

' $f-,

,0$e /

- -.

B " %

B ;(777

I(777

@77

,S > I77

[ b , /3" >

66777

4(77

[

E ,

;777

I777

A + L0

(

> > ,/

EUACA = ;(777(A/P, •6 ,() – ;777(A/F,•6 ,() + 66777 + @77 = 6@ ; EEUACB = I(777(A/P,•67,67) – I777(A/F,•6 ,67) + 4(77 + I77 = 6(4; k.

,0 J

EUACB < EUACA

B "B$e

(i) "#

JY3 @ b R

ROR= Rate Of Return MARR= Minimum Attractive Rate of Return A 1, ' .

1 Q " 1 j,A %

k J 1 , 9 1 E T % 0 ' \G

' \G

, : 0

, .Q J

,J C 0 , /

" B h \!

,G ROR >

= MARR

,G ROR < MARR / " C< 0 ‚ -

P, \ j,A

J / P, \ j,A

, .9G0 1 N,

1 j,A %

' \G

, ' ,1 ‚

k < E3P L0 L- 0 $ . 1

E3P L0

E3P L0 C

1 ROR , '- &" 0

/31 ', G 5 +R

, .9G0 1 N, k <

NPW=7 PWB=PWC

PWB – PWC = 7

i = ROR

h] -P +A(P/A, i%,n) + SV(P/F,i%,n) +…=7

,e #

T - 77 .P k

-C

T - 6777 ' \G

, .9G0 1 N, ),e # •

+-.

, !

T - 6 77 -

l 6777 + 77(P/F,i%, I) +6 77 (P/F,i%, )=7

,+"

O1 U ,*

k J1

- # 67 b k

1 ! 5

T - 677 .P

-C

, .9G0 1 N, # 67 C

G R

T l6

OS - 3

1 C-

i =•6(†4 # „ :

k , e1 ,H , C

,0 ! !

<,P

k J1 1-.

T - 777 ' \G !

T - 2777 .P

, -# h T

P= k777 N=67 A= 677

[

F= 277

< F=8((( A='((

)

# '

[

P = ,(((

l k777…677 ZP/A , i• ,67Y …2777 ZP/F , i• ,67Yˆ7 Z#

0 L0 : P,G ,H

C- 1Y

< : /F" ' ,1

Fˆ67“677…2777ˆ@777 777ˆ@777 ZP/F , i• n,Y ZP/F , i• n,Y ˆ 777†@777 ˆ 7†(; #- Q 1 3Q ,

• –i–• k / 1 C- C "

• a c

‚k J

(4† ( b

7 d

BTb

•(

l I †64

a c = b d 6% − 5% a → a = 0.16 = 69.46 − 355.19 − 69.46 ROR = i = 5 + 0.16 = 5.16%

! .S M L- 0 $

, .9G0 1 N,

5 l; L-

NEUA=7 NUAB=EUAC

EUAB-EUAC=7 h]

-P(A/P,i%,n)+A+SV(A/F,i%,n) +7777=7

0 N # N, )$, 1 N, ˆ i ' \G

, j,A %

,* T \G

, %

T ˆ MARR k /

k J k /

B T ' \G

, %0

N, ˆ ROR

' \G

, j,A

, k J 1 ROR MARR ,G

k / / ' \G

, j,A

, k J 1 MARR–ROR ,G ROR L- 1 $f-,

d! S L0 Y NEUA - Zd! S E3P L0 Y NPW ' J- 1

w & +

b- " L- : k

Z ! .S M

#- $f-, o >! J 1 (B) ,e $f-, 0 , 9 1 (A) $f-, % ROR ,G L- : 0

L- : 1

$f-, '

& + ' ,1 k J 1 / ," '

k /$

P * ' \G 5m

h , 9 1 !-

PWX

> 1 $f-, + $f-, - : 1 !-

k.J

)&HG > 1 G0

"#Cf $f-, -

> b- "

> 1 ' $f-, )$f-, - : 1 0 ,G E

9G0 1 N,

S ,< 0 , 9 1

.5" L-

NPW

C 31 , 9 1 !-

MARR 0 , —9 1 — ,—1 ,1

PWY

—F $f-,— : ,—" ' —

. K]

E5" - >]" C

; 0 lY "#

$ / k , e1 ,H

> 1 $f-, = , /

(B) K- $f-, 0 (A)

" 1

S $f-,

MARR ,1 ,1

O1 l6

C "

9G0 1 N, > $f-, - : 1 b- " ME1

k J

F , 9 1 !-

, 1 j,A

7 ˆ – NPW

k J

F ,/

, 1 j,A

7 ˜ NPW

k J

F , 9 1 !-

, 1 j,A

7 ˆ – NEUA

k J

F ,/

, 1 j,A

7 ˜ NEUA

5 - / ," b B - 1 P * ' \G

E5" - >]" L- t ,9" k 7&

$f-,

< -

- ' ,1 > 1 y 1, y +

E3P L0 3 $ /

b- " =S ,e M 1 y + : # " 0 k

> <

E3P L0

1 L- :

‚ƒ k

dF9 b

F 5 B '-

$f-, ,

k ,G ,G

PWBX X

, 0 j,A l; # „

PWBZ

PWBY

Y PW CX Extra Inuestment Analysis PWCY

PWBW W

PWCZ

PWCW

k i / : 3" $f-, : ," '

PWB

/ ," L- 1 h T NPW=(

PWBZ

PWBY

MARR=a%

PWBW

W X

PWBX

PWCX PWCY

PWCZ

PWCW

PWC

MARR=a% ,G ROR

MARR

=S '[ 1

ROR

MARR

=S : k '

Z-Y-X

k J1 / ' > 1 Q " 1 Yj,A .

0 81UJ'

XY =S C w h X,Y & + k. ," '

> 1 Q " 1 Y j,A .

0 ,/ UJ'

,"[ 1 !-

YZ =S C w h Z,Y & + k. ," '

'- & ). b- " !-

, .9G0 1 N, .+ +T

> 1 $f-, b

- , 9 1 !-

k Q@ ] C 1'

$f-, C<

b- " =S - 0 U ,* ,G

> 1 $f-, J 1 $

, .9G0 1 N,

/ & +

', 9 1 .9G0 1 N,

Q ' $f-, : 1 0

P * ' \G

. ," '

' $f-, J 1 ,1 ,1

\Q N,

& +

', 9 1 !," '

1- 1>

. ', /

T & + 1 ,<

$f-,

' $f-, b

1 < : ,"

M" B

, .9G0 1 N, : ,"[ 1 !-

1 MARR 0 8 1 b- "

> '

w - $ G, l;

E5" - >]" % M" 1

$f-, ) J ,1 ,1

' $f-,

,1 l6

' $f-, C< )$f-, : ," '

k J1 ,G k

F ,/

" 1 $f-, ,

k '

k J

JY3 @ b R

5 -

, .9G0 1 N, L- 1 Q " 1

ME1 ) J 1 / J 1 J

T0 81

\ "#

k / : 3" MARR $ o >!

\Q N,

> M" B

, .9G0 1 N,

. ," ' k J1

, 0 j,A - 0

P * ' \G k J1

X j,A

E5" - >]" / ," L- 0 $

•67 $

\Q N,

1 h+ - .

/ dF9

< : ,"

Y j,A ;77

277

6;7 7

6 7 (

> <

A + L0 6;

k j,A X

,/ b- " 1 Q " 1 $ - -

PWC= ;77 – 7(P/F,•67,()+;77 (P/F,•67,() –

7(P/F,•67,6;)

= ;(4 PWB= 4 (P/A,•67,6;)= ( 2 j,A Y

PWC= 277 l 6 7(P/F,•67,6;)= ( ; PWB= 6;7(P/A, •67, 6;)= @6@

PWB E(( 8(( 7(( ,(( +(( *(( )(( '(( (

E'E

NPW=( '(M . +, S @ T#-

7+8 X

7,)

)79

,((

B " ‚ k. $ 1 J 1

7((

,1 ,1

8(( '((

E(( )((

PWC +((

*((

MARR=67• U J 0 , / k JK] ,/

XY =S U J > 1 j,A

< A + L0 - #

;7 e/

,/ k , G k.

,H •( $

, 0 j,A

h; # „

\Q N,

Tk J1

k. ," '

j,A K

PWB= 27I Xj,A PWC=;777 PWB=2I;4 Yj,A PWC= 777 PWB=@7;4 Zj,A PWC= 777

NPW=( 7M= MARR

PWB E(( ( 7(( ( +(( ( )(( (

C’ B’

A’

7((( )(((

PWC +(((

, ‚ k

0 8 1 < U JY • ( 0 8 1

, .9G0 1 j,A k J1

k. ," ' . ,/

> '

' $f-,

Y ‚ k.

3 Y $f-, ‚ k.

Q Q

, l6 <

0 8 1 XY =S U J l; 0 , / YZ =S U J lI k J

< : ," '

- & +

/ ," L- -

, .9G0 1 N, L- 0

, 0 ' $f-, hI # „ k

/ dF9

n= ;7 , MARR= • ( k

U",

, ' 3B U "," 1

$f-,

PWC

D 6777

B ;777

A 777

C (777

E 4777

PWB

6627

677

(I47

2(67

2@ 7

PWB

9((( E((( 8((( 7((( ,((( +((( *((( )((( '((( (

NPW=( MARR=7M

8E, C

887' (E,(

7*9 +'(

,(((

7(((

8((( E((( 9((( '((( '((( )(((

'(((( *(((

PWC +(((

k J1 k ,G

, =S C< '- MARR - . k J1

k J

P,G ,H

5 '- Q

, { C< :

=S ) NPW=7 =S h6 M

-' <

Z NPW=7 =SY k , G

A j,A )j,A : ," '

s P =S '[ 1 ' $f-, h; M E3P L0 -

E3P L0 hI M

, =S : '- PWC=PWB

$f-, h

G R h, 0 U "," 1

, .9G0 1 N, L- 0

J U", ' 3B U "," 1 !k J

C< ) 1 (MARR) $

$f-, '

\Q N,

> U&T,1 $f-, l6

5 $f-, ,

T 0 , / ' $f-,

, .9G0 1 N, l; , .9G0 1 N, ,G lI

k ,G 1-

1 - ) P * ' \G

\T & + 0 $f-,

E5" - >]" L- 0 $

1 U ", 1

$f-, l

& +

, 0 ' $f-, h- .

k J S J $f-, : ," ' .9G0 1 N, L- 0 - P * ' \G MARR=(• - # ;7

$f-,

E5" - >]" 0 $

E ,/ k

/ dF9

& + 0

< : ," '

- & +

, k.

A B C 777 ;777 (777 (I4

67 2(6 k

B 6777 662

D E 6777 4777 662

U", ' 3B U "," 1

$f-,

A ;777 777

E 4777

C (777

(I4

2(6 !

2@ !-

> < 1h T

;777l6777ˆ6777

B-D:1 & +

6777

> b- "

;4I

< b- "

•( 0 8 1 b- "

, .9G0 1 N,

ROR=•;4

F , 9 1 !-

> 1 B $f-, \! k.

A !-

67l662ˆ;4I

6777= ;4I(P/A, i%, ;7) k ,G

> b- "

B "/# <

;777 ROR=•67

< b- "

;;4 k ,G

F A $f-, \! . •( 0 8 1 b- "

, .9G0 1 N, C

> b- "

A"/# <

;777 ROR=•;

< b- "

F A

3 ,/

6;4 !-

> 1 $f-, \! k J 1

MARR=•( 0 , /

, .9G0 1 N, k ,G E

> b- "

\T C A "/# <

777 ROR~ •7 c

< b- "

k ,G

F - J1

6 ( ,1

$f-,

: 1 $f-, : ," '

C 31 A $f-, ‚

o Z "@ n k <

. 1

> 1

B / C = (_P – k J

. & 0 $f-, % C 1 '

,* ) / Z^ F Y

3 L- :

_P 0 ME1 J / P *

> 1

,* J

9 M

E3P L0 l#- L(B/C)= (_P PW / ^ F PW) = (PWB / PWC) ! .S M L0 lK- LB/C= _P EUA / ^ F EUA = EUAB / EUAC s P ' L- 0 % , ,G B/C > = 6 ,G B/C < 6

B-C > = 7

9 ,0

6777777

6 7777

7777

I7777

; ! k. '

$f-,

k J1 / '

j,A

B-C <7

k. $ !-

k. '

! !

Z >Y Z_P Y

T-

Z >Y

T-

Z ,*Y

T-

$f-, : K ] < k J 1 •67 $

Z_P Y \Q N,

100000 + 150000 − 30000 B EUAB = 1.3135 1 = = C EUAC 1000000( A P,10%,20) + 50000

k J

\ j,A ' k J

3 B j,A % K ] ' ,1 h# „

T-

677777

F9 1 $f-,

T - # ;7 j,A : ,/ ,G k. '

e - ] ' ,1 o/ + & B T j,A ] ,V

j,A

" #C

/ y 1, o/ + & j,A

S 1[ o /3 - -

: 1 0 j,A ] ,V

;

' Q _P

k J1 P * ' \G

E5" - >]" 0

< & + ' ,1 J 1 J j,A w

- ,G

h 3 k /$ B / C = PWB / PWC B / C = EUAB / EUAC k J k J :3

j,A : ," '

F . , 9 1 !F . ,/

> ' !-

T,A J 1 ( B / C) ˜ = 6 ,G

> '

T,A J 1 ( B / C)–6 ,G -

^ F 1 _P L- 0 $

1 , 0 G0

' j,A C 0 h# „ k

A B C 6777 ;777 777 6I 7 6 †I

D E (777 4777

277 2II7 @2I7 ;†I

6†@I

k $ J U", Z !A- B

& + -

PWC

4777

6† ( >

PWB

6 Y

B/C , ' 3B U ", 1 j,A

PWC= 6777 PWB= II(7 B-C

B / C = I†I( ˜ 6 & + -

F B

F C

PWC= ;777 PWB= ;(I7 D- C

B / C = 6†I; ˜ 6 & + -

PWC= ;777 PWB=6 77

B / C = 7†27 – 6

E- C

& + -

PWC= 777 B / C = 7†II – 6

PWB=6(27

.& :,91'

j,A :

J . k ,G k J1

F $f-, : ," ' j,A : ," '

F C

C 31 C j,A

!- J 1 / ^ F 1 _1

"- J

$f-, '

& + ' ,1 k J1

,1 hD ,3"

, 1 DE F C 0 -

% L0 k

% L0 8

J 1 P,G b B L0 8

pa Z M",w X Z i

&T : J X ," ƒ Y 'f ! M" .P,9 l6 8

)b , /3" )'

Z: J Z

)#K

>Y G

,P - ^-0 `a Y b ,+ b , ~" lI

&1Y K->!

‚ -, ? -

Z -,M s Q Y

, ~" l

Q - ! b &S ] l 5q

C< !-

L0 0 .&"

,P l;

C 0,

% ', P L0 hD ,3"

kC 0 C< " `a

‡! ? /] ,&

0‚

" G 0 Q

%&< / OV R 5 , 0 O1 | A -

P,G ,H

.1 V

! `a

+ L- : k ,G

D = (P-SV) / n ! `a - !-

+ =D > =P

A + L0 = SV

Depreciation Book Value

Z k ,G A + L0 - # 67 Z /

5 , 0 O1 0 #

,/ = n

m 0 ‚ ', P L0

m= 6 , ; , I , … , n

BVm = P-m.D k

,/ Y

,/ 1 !

0 ‚ ', P L0 -

T - @7k777 : J % ! `a

+ k.

> h- . T - 67777

P − SV 80000 − 10000 → → 7000 n 10 BV5 = P − 5D = 80000 − (5 × 7000) = 45000 D=

! m= 7

BV7 = P =

m= n

BVn = P- nD = SV

T-

!- L0 A + L0 $ - ', P L0

BVm= BVml6 – D

1 Q " 1 ', P L0

. & % U&T,1 -

+ : , 9 1 #- # k

: , / ,S< #

n7 R

+ L- : MiQ " 1

dF9

n − m +1 ( P − SV ) SYD M = 1,2,..., n Dm =

m# Zkkkk - : J )$ e j,A Z !-

+ = Dm

Y $f-,

,/ = n

# =m

> Y !- L0 = P

j,A y + L0 = SV

Sum of the years Digits Method (SOYD)

SYD =

m= m =1

n(n + 1) 2

_/Q

0 BVm =

P − m ( n − ( m 2) + 0.5) ( P − SV ) SYD

T - 67777 y + L0 - # 67 K

R3 ,4

_/Q L- 0 Y

,/ 1 !

K- #

T - @7777 : J %

' ,1 ', P L0 - `a

> h- .

+ k.

! Zb

(SOYD) P = 80000 n = 10 SV = 10000 n( n + 1) 10 × 11 = = 55 SYD = 2 2 n − m +1 ( P − SV ) Dm = SYD 10 − 2 + 1 (80000 − 10000) = 11.455 D2 = 55 m( n − ( m 2) + 0.5) ( P − SV ) BVm = SYD 80000 − 2(10 − (2 2) + 0.5) (80000 − 10000) = 55.818 BV2 = 55 6?

# ', P L0

.1 V N, %

,rEB T 0 # , `a

( C 0

+ L- : k <

Œ 1-

!-> ' Q k ,G

L- Œ

L- :

, #- ' !

Declining Balance Method (DB)

J P,G ,H

;/n .1 V N, : ,G

+ : , 9 1 L- :

. t* - k

. 1

Dm = BVml6(d) BVm= P(6-d)m Dm = d.P(6-d)ml6 .1 V N, ˆ d k J1 ,1 ,1 ' ,1 E ! \! -

, +

' J- ' ,

) ,

A + L0 L- :

Q- A + L0 1 ,S< #

k J 1 ,S< #

', P L0 C J

', P L0 ,1 ,1 A + L0

F1 ,G

SV= BVn = P(6-d)n SV/P = (6-d)n d = 6- (SV/P)6/n L-

1 J 1 7†6@@ .1 V U ,* M " B

# „ ' ,1 k

- ', P L0 h- .

5 K w # ' ,1 !-> ' Q

P = @7777 n = 67 Dm = d.P(6-d)ml6 D = 7†6@@ “ @7k777(6 –7†6@@ ) l6 = @†474 BVm = P(6-d)m BV = @7777(6 –7†6@@) = I †224 6+

•

1 31 ' !

L0 - `a

+ k.J

+ : , / #- # S

`a J

Dm = (P-SV) (A/F, i%, n) (F/P, i%, ml6) BVm = P-(P-SV) (A/F, i%, n) (F/A,i%,m)

+ L- :

+ : , 9 1 ,S< # k

Sinking Fund Method

- 1

5 , 0 =1 - 0 L- :

8 >P ', P

! ,

T - A ‡E !

! C "

# n

T - (P-SV) ‡E $ - C

,/ 0 ‚ "

/ 0

>e Q ' ,1

‚ (i%) $

\Q N,

k J1 J

T ". Q

A = (P-SV) (A/F, i%, n) !

T - 67777 C<

A+

$ Q- L- 0 ) J 1 #

L0 -

•67 $ k

T-

\Q N,

@7777 : J % T - # 67

5 K w#

,/ ,G k J 1

', P L0 - `a

D = ( @7777 –67777 ) (A/F, •67 , 67 ) (F/P, •67 , I) = @ († ; BV = @7777 – ( @7777 –67777 ) (A/F, •67 , 67) (F/A, •67 , ) = 4(6 7

&( + k J $f-,

P,G ,H ,/

! "

.1 V

+ %

1 # C< ! "

! " T - , ' ,1 L- : 3" . & 1 ,1 ,1 # , `a

ky + L0 - !-

> b- "

1,*

Dm= (P-SV)Um / U m# H

! " = Um ! "

&H7* k J

P,G ,H

" E/ .

0- , ' ,1 `a

+ L- :

Dm = (P-SV) (Qm / Q) m# ,/ # A

b E/ b = Qm b E/ b

pa M" B

" !

Q P,B

h, 0 =1 - 0 $

8+ U 1 J1 J

L-

/ ' 0< `a

F 5 L-

n PWD =

Dm (P/F, i%, m) m=6 h -

EUAD = PWD(A/P, i%, n) k

5 DE F ' J- 0

k. L- : ," ' P,BŒ ,H 0

C9 ,91

, + .S M L0 J1 J

PWD : ,"[ 1

EUAD

!- ' !

E3P L0

J-

k. L- : , 1 Œ " ! L0 k. $ J ' ) 9J #

,S !

T - 7777

> 1# @

: J : ', P L0 - `a

,/ 1 L ," : J % h- .

+ k J1

Z$,/ Y b 1-

T - 67777 C< y + K

_/Q L- 1 ZD!

!-> ' Q L- 1 Z k

v ,w v. ," '

L- K

&( - `a

b ,V : P,G ,H

E5" - >]" -

C- 1

,1 1

B 7 r G( @ 0

$f-, '

& + -

C / c 5! 1

)&HG

"#Cf

E5" - >]" C

k 0 ,

,1 b !

' $f-, 61

(TX) 1U

+T - + +T R FJ

,1 k

Q- 0 .&"

\S A 1, :

- `a

S-[

) " E/ '

b !

- b ,+ | A - < C > 64

U( V

(GI) kZkkk - b

! L-,P 0 B T < 0 .&"

d! S

(GFAT)

d! S

> ,& 0 ‚ d! S

U( V

0 .&"

< kb !

(OC) > ,

- 'f, )

& '-, )

1 y 1, '

> 0 .&"

&H7* 0 " #C ,

" E/ '

> k ! '

(TR) k ,G

: 3"

/! 3

U&T,1 b ! ' ,1 .!- = "

@ (

# U( V

&( b , .

" G R

Cash Flow After Tax (CFAT) b ! ,& 0 (TX) TAX Gross Income Cash Flow After Tax Operating Costs Tax Rate

<,P

5 Z6

Cash Flow Before Tax b ! 0 ' <,P = d! S

< – " E/ '

CFBT = GI – OC `a 2

b ! # /9

(TI) b ! # /9

< =b ! 0

5 Z; <

5 ZI

<,P – `a

TI = CFBT – D TI = GI – OC – D

b ! = b ! # /9

(Tax) b !

5 Z

d! S <

5 Z

“ b ! N,

TX = TI .TR (CFAT) d! S < = b ! ,& 0

<,P l b !

CFAT = CFBT – TX CFAT = CFBT – (CFBT – D) TR CFAT = CFBT (6-TR) + D.TR $

, 0 ' J- 0

M C "

$f-, '

E5" ' ,1 s P

,1 1 Q " 1 k

(NPW) d! S E3P L0 L- Z6 n NPW = - P + CFATj (P/F, i%, j) j=6 k J1

,{b

-. '

$f-, J 1 NPW 7 ,G

(NEUA) d! S NEUA = NPW (A/P, i%, n) k. ' , { $f-, b

Taxable Income

,{ -'

! .S M L- Z;

$f-, J 1 NEUA 7 ,G

Zd! S E3P L0 Y

, .9G0 1 N, L- ZI

NPW = 7 n -P+

CFATj (P/F, i%, j)=7

i=?

j=6 i MARR

i<MARR

Zd! S

! .S M L- Y

, .9G0 1 N, L- Z

NEUA = 7 NPW(A/P, i%, n) = 7

i=?

P * ' \G

i MARR

i<MARR

E5" - >]" 0 . K0[ J 1 J $f-, h.

j,A w ,G

Q , 0 j,91 ' $f-, h- .

P= 7777 SV= 7 N= K= 6, ;, I, , !

(GI) (OC)

< = ;@777 –6777 K !

! d! S

> = 4 77 + 77K < [ o- k J

v. '

$f-, :

> `a

5 k

},P • 7 b ! N, - + & =S `a

< J P,G ,H C9

•2 $

CFAT d! S

\Q N, <

L-

T ,G o V k 5

/ : 3"

T , , 0 #- Q h T

k. $ J $

C 9 #- Q

#- Q j,J Za #- Q ,S< C

GI-OC Z6Y

Z;Y

GI #

ZIY

OC ! >

CFBT ZIYˆZ6YlZ;Y

Z Y D `a

1 Q "1

5 Zb

CFBT-D

TI.TR

CFBT-TX

Z Y

Z(Y

Z2Y

IT Z YˆZIYlZ Y

TX Z(Yˆ7† Z Y

CFAT Z2YˆZIYlZ(Y

777

l 777

l 7777

;2777

67777

62777

67777

2777

;@77

6 ;77

;

;(777

67 77

6 77

67777

;;77

6II77

; 777

66777

6 777

67777

777

6(77

6; 77

; 777

66 77

6; 77

67777

; 77

6777

66 77

;I777

6;777

66777

67777

6777

67(77

n NPW = - P +

CFATj (P/F, i%, j) j=6

NEUA=NPW(A/P, i%, n) h.J

S J$

, 0 O1 0 u w

NPW= - 777 + 6 ;77 (P/F, •2 , 6) + 6II77(P/F, •2 , ;) + 6; 77 (P/F, •2, I) + 66 77 (P/F, •2, ) + 67(77 (P/F, •2, ) h , 0 O1 NPW= 6I 7†@6

. '

NEUA= 6I 7†@6 (A/P, •2, ) NEUA= I;2

. ' k. '

,G k J 1

T - 67777 C< A + L0 - !

b ! N, - J 1 # =S L- 0 `a

•2 $

\Q N,

T 1

\ $f-,

T - 677777 ' $f-, !-

> h- .

T - ;7777 ,1 ,1 b ! 0

' ,1 v, S . ' k

$f-, :

/ },P •67 $

<,P - # 4 $f-, /

\Q N,

,1 , e1 ,H

,/ • 7

T-$ / $

h) k

M9" b ! 0 31 #- Q

CFBT

CFAT

l677777

6l 4

;7777

67777

777

6 777

67777

d! S E3P L0

O1 0 $

l677777 + 6 777(P/A, i%, 4) + 67777(P/F, i%, 4)=7 ROR= •2†2 k.& '

$f-, ) J 1

ROR<MARR hC w

0 k. ," ' " !

j,A - , 9 1 j,A

Q P,B : , 9 1

J 1 , / b ! N, w,

1 J- )`a

L-

I< E

O1 l

1y "

k / ] j,A '-

DE F ' J- ,V

k / d F" K>E & `a k /

L-

L- : ," '

DE F ' J- 1 j,A % '

H : ' ,1 '," $

F ' ,1

- , 8 0<

]

k J1

P,A 0 l

' 0 > ]

(TS) 6q " ! N,

,rEB T 0 .&"

! :/ 1l

" !

-C 0

" X

Q P,B k.

CFAT=(GI-OC)-(GI-OC-D).TR =(GI-OC)-(GI-OC)TR+D.TR =(CFBT)(6-TR)+D(TR) TS=D(TR) k‚M3! 1 - 1 P * d! S

8 >P d! S <

1-$ J

1 8 >P D ,G

Q P,B b ! .S ,

.& < ,e 1 , S O1 . '

+ D(TR) .+ +T k. $

- `a

' J- & + - $f-, % ,/ # A

. 1 J- : k J1

" ! " !

Q P,B E3P L0

Q P,B E3P L0 h0 .&"

n PWTS =

Dm (P/F, i%, m) (TR) m=6

Tax Saving

" ! 1

5 ' ,1

L- : ," '

+ :,91 " !

Q P,B >G,1

F .

J- .

Q P,B E3P L0

- -< 5

0 .P

!- ' \G

, ' ,1 (i) $, 1 N, 1 K - C 31 ~E $f-, % K ] ' ,1 ,G

k 0 ,

k ,G

,1 1

.S , # , '

S' J

E5"

" ,V k J

M9" 8F1 - 0

! =&

PR ˆ 4 B Z6 I ˆ (7$, 1 Z; k J

5 , 0 | ,A 1 .! T :

d! S <

CFBT=GI-OC TI=CFBT-D-I TX=TI.TR CFAT=CFBT-TX-I-PR 0

S , $, 1 k

+ ,0k J b !

k J1 J 8

Q P,B 8+ `a d! S E3P L0

5 % 1 = ,J . k.

, 9 1 E3P L0 -

P,B 1 C-,+ K - .P

0 31

\! - J

. :M/ J 1

d! S E3P L0 C 9 8 >P K -

b ! # /9

1 j,A ,

,1 # T

BaS

O1 )

T-7

,/ ZI

T - 2777 !

! d! S

T - 6777 + & =S `a

TR =• 7

Principle Interest

> Z6

y + L0 Z;

# !

, 0 b F9 1 T,A h- .

T - 6 777 !

0 K - $, 1 N, ,G L- :

& T 1 L0 : M " B

k. !

, .9G0 1 N, .! T :

" E/

< Z > Z

5 L- Z( b ! N, Z2

MARR =•6

$ k

- PR=6 77 )Z$

O1Y •67

\Q N,

, .9G0 1 N, ZD!

! $, 1 N, = ,J .5" % 1 = " !k

> • 7 ,G Z

, .9G0 1 N, .! T :

v ,w v. '

T Z@

k J 1 I=2 7

$f-, : K ] ' ,1 K - .P

< Z^ ,A(

15000 − 0 = 3000 5

Any year = GI-OC = 2777l6777ˆ(777

CFBT

CFAT

l6 777

(777

I777

6 77

2777l6777ˆ(777 l6 77 …

77(P/A, i%, )=7

ROR= •6 †;

NPW= @ †4 MARR= •6 M 6 777 “ • 7 ˆ 2 77 ˆ K - C > I= 2 77 (•67)=2 7 PR= (2 77) / = 6 77

CFBT

CFAT

l2 77

(777

I777

2 7

6† 77

; †; 7

6†6;

;†(;

CFAT = (777lZ66; …2 7…6 77Yˆ;(;

NPW= 7

l2 77 + ;†(; (P/A, i%, )= 7 i= ROR=•;;†;; Mo

, 9 1 D! .! T 1 . &

, .9G0 1 N, - d! S E3P L0 k J k. '

$f-, :

9 M

\ = ,J 1 K - .P

‚ k. $ J

' ]1

% ', G M1 ' k J1

Z. $ J y + - $

>e Q

1 C<

#C[#

C< e &9 0 1 k J

,/ 0

% C , ^ S$ saA (I_P

Y Q [ /J 3 @

0 - : J \G

j,A J J \G

, m5

>e Q

(

,„

T ", B0

U j,A

,/ 0 $ / 1 ' ! $ / 1 ,/ Y n

T 1 j,A '

T 1 y 1, # k

: 1k

7* 2&&

). 8

8 >P /

H 5

,/ EUAC k 1

Replacement Analysis

Retirement Defender Replacement Challenger

p5 :

U "," : 1 k J 1

- $ / 1 ,/ Y n , + 0 % , ' ,1 ,/ EUAC

"@ " 3"

#C[#

% ', G M1 - $

" #C ) > MiQ ")

C&( N

E5" - >]"

: 1k

:J : k J1 L0 M

/F" , + 1 Q " 1 k.S-,P ! 1 Q " 1-. $ J$

s P :J 0

1 ,e #

! '

5 ) J1 +w _P /

T - 7777 ' 0 1 ./

, 0 #- Q v.

2&Q

: J % h- .

1C "

,* T # T

>e Q ' ,1 ). $ , ,/ #

M- "@L

> - A+

•67 #

$ / 1'

:J '

! !

e - b , /3" '

> - A + L0 &7 " #C " &( 0

7777

(

7777

;

I 777

6777

I7777

;777

; 777

I777

;7777

777

(

;7777

777

;7777

(777

;7777

2777

;7777

@777

;7777

4777

;7777

67777

7k777 ZA/A ,•67 ,6Y X 7k777 ZF/A ,•67 ,6Y k777l 7k777ˆ6 k777 6777ZA/G ,•67 ,;Yˆ @7

,/ ,e b 31 k J $

e - b , /3" ' T < R3 (SV)

[

k. , 0 j,91 EUAC # 7& " &( "( MR (n)#

5 )

1# b

" #C " &( -

L0 3@

(A/P,67•,n) 777

[

(A/G, 67•,n)6777

EUAC

–SVt(A/F,67•,n) 7

6 777

;

6;6 7

6;(;7

667 7

4 7

664@7

67I47

6I@7

66227

4467

6@67

662;7

(

@@47

;;;7

66667

@6(7

;(;7

672@7

2(;7

I777

67(;7

2;67

II27

67 @7

(@@7

I2;7

67(77

((;7

7(7

67(@7

-8 :J

# M

" /

:J : 0 $

1 Q " 1-. # 4:J : $ / 1' k

C 9 b aA : ,/

3 k 1

# 6 1 C< . S ,/ ). $ , ,/ # _P

EDRV= _P EDRV>7

‘ 3" L0 = EUACD - EUACC EUACD>EUACC

8 >P ‚ƒ

. '

‘ 3"

>e Q L0

A + L0 - ! '

$ J

" E/

T - 4 77 " E/

F U

k J1

> -$ 1 !

' !

. $,

. # 20 81

\Q N,

+w ,S

Q$e

J h- .

# I ,/ C

T - I777 A + L0 - # 6 ,/ - !

T ) J 1 •6 $ v.

> '

T ,G k.

- .P, \ $ ,

T - I 77

T - ;@777 !!

T-

77 C<

# I : J ' ,1 C "

EUACD = P(A/P, •6 , 2) – I 77 (A/F, •6 , 2) + 4 77 = 7†; 7I( P + 4†6@ ˆ4k6@ EUACC = ;@777(A/P,•6 ,6 )l I777(A/F,•6 ,6 )+ 77 = 67†I ; ˆ67kI ; 7†; 7I( P + 4k6@ – 67kI ; =7 P= †6@ mm

, ~" 1 $ J K ] '

1 0

1 ',e 0 1 0 .&"

& / C&( N

j,A % . &T > ! < • kj,A !- ' ,

•

j,A !- ' ,

b , ~" , Vz" C >

,1 1 ,G

E5" ). &T > ! < k0 ,

S j,A K ] . Q \G

1 ', 9 1 C /A -

•

)j,A

J 1 , / b ,V :

+w,

•

k '-

•

K ] j,A ' , k

, ~" 1 !

<,P %

J1 , b

%" %" ' ,1 C " 0

,M" Œ 0 .&"

G k J1

] • &T ,

', e/9w , ~" , % ,

•67 * +" tO ,G k J 1

|1 O j,A E3P L0

C< !

1 1 8 >P •67 •

. &T ,

, ~" ,G •

C< 1 . & j,A E3P L0 h- .

> ,G : u/ ) J 1 J 8 >P •67 k /

Sensivity Analysis

O1 •

& + - EB ' ,

T - I77777 ‚ -, % i E ,

. &T > ! < BaS

kŒ !- b aA 0 $ < . 1 • J

. &T > ! < •

, ~" , 0 #- Q

k. $ J . V , 0 #- Q

5 DE F ' ! T ' ,1 E3P L0

; < se t+? I# C

*aT

t+? I !

$ " #C

PW= ;7777

PW= I77777

PW= ; 7777

EB b aA

7777

PW= I67777

PW= ; 777

• 8 >P

PW= ( 777

PW= I; 777

PW= ;( 7777

•67 8 >P

PW=

' 0 . &T E , k.

> 1 . & PW

&1 * +" , ~" 1 . & PW m_

< $0

† j,A

,/ b

F 5B

)y + 0 ' ) J1

"- " 1

, B E3P d! S L0 '

1Y F W X

U % > !V W X = F U % W X -# Z#% W X ? Isoquant Curve

5 ) !

5 : :

/] - j,A L, \

"- " 1

5 '[ 1 y + k

j,A C 1

-. k. . P= 627k777

MARR= •6I

= I777

N= 67 #

SV= ;7k777

y + L0

= I k777

< k

dF9

, 0 b F9 1 T ,A

j,A #

< -

/ > ' ,

j,A d! S E3P L0 lD! 1 "- " 1

1l k

< -

> 1.&

j,A . &T l^ ZD!

NEUAˆ627k777ZA/P ,•6I ,67YlIk777 … ;7k777ZA/F ,•6I ,67Y…I 777ˆ4 I7 Z NEUAˆ627k777ZA/P ,•6I ,67YlIk777Z6…YY … ;7k777ZA/F ,•6I ,67Y …I 777Z6…XY ˆ4 I7 NEUA= 62 2+I 77X-I77Y '

$f-, NEUA>7 "- " 1 =S NEUA=7

' k I 777X- I777Y+ 62 2= 7 X= 7

Y= 62 2/ I777= 7† @

Y= 7

X= 62 2/ I 777= 7†7

Z "- " 1 =S

, { $f-, NEUA<7 3 Y NEUA=7 =S

Y ![ &?

(O,

NEUA>( \\\\\ U % W X 06

(O+ NEUA<( -# \\ U % W X

(O* (O) (O'

-(O, -(O+ -(O* -(O) (O'

\\\

X Z#-

]\\\ F

NEUA= (

k. k J1

&T :

&1 Z < Y X b , ~" 1 . & j,A

. &T '

Y b , ~" 1 . & j,A

C—0 Œ —B

— < $0

S )$ — < —1 y — "

,——H

—— ,+"

: —/F" —1

——O1

_—O —— ,

—] $ — <

1 UE{ '

—O1 C —" / $ eu C w k , ——+ \——! k

—,

k.P,G ,H %— 0 — " ,—G - —J 1 — k. $ < = ,J Š

.! T

,V ! $ <,P ,1

, ~"

/ 5 : /F" l6 J$

R1_ R`% = a% !#. R1_=

D ,3" , 0 j,91 : /F" ‚

--:e

: /F" J S : /F" l;

h (P) 26

1 1 : /F" lI

u #

Œ 1 ' < _ 0 "Œ

2&7Z k J

: /F" ' ,1 k J 1

1 1 1 0 0b

-$ <

" 31 - , G

J S 1 0 h (O) 27

$ <0

[ ——A $f-,—— $ - ——M 0 — $ —/

C "

E5" b

! — — <,P : ," " / T h (M) (4= k 1

,——H .——

:— 0 —S,1 —1 y — "

2&7Z

2&[ &

O^+M+P 7 ) O-P 7

—+ s —P —O1 |— A k J 1

/F" %

1 0 0 ,"

[ o /3 k

/F"

,M -

C0- : , 9 1 =

: /F" h# „

$f-,— C 1 '

) B 6 $

\Q N,

T - P, O, M : /F"

1 Q "1 k

Estimate Most likely Optimistic Pessimistic Mean Variance Beta Distribution

67 ;7

67777

6477

64@7

;777

6777

" &(

67 ;7= 6477 (P/A, i%, 4)

T < R3

RORO = 62•

RORP= 66• 1 1

, .9G0 1 N, C w

k J1 > =

: /F" : e

T = (67777… (67777)+ 67 ;7) / ( = 677@(

< =

T = (;777… (64@7)+ 6477) / ( = 6427

A + L0 = ,/ =

T = (6777… (7)+ 7) / ( = 6((k2 T = (6;… (6;)+ 4) / ( = 66k

677@(= 6427(P/A, i , 66k ) + 6((k2(P/F, i%, 66k )

ROR= 6(• k J1 _6

—+

RORM= 6(k2•

.—9G0 1 N,— — 5 1 0 \! . , / MARR 0

O) 67777= ;777 (P/A, i%, 6;) + 6777(P/F, i%, 6;) M) 67777= 64@7 (P/A, i%, 6;)

"&( " #C

,9 ,

3O , { , Point to point

: k J1 J

j,A : - J 1

,1 .

Q- ' 0 o & $ - 5 %

j,A

C&( N

j,A w - $ G, , ~" # / T - $

——— , $

:——— ,——— ~" $, ———&G - ——— j,———A ——— ,1 ———1 - $ ———/ C ——— 1 ,——— ~ _1 ———" b ——— 1

. —& ,

— : 1

— ,— ~ 0 ' ,—

—1 ,

—+ k J 1

O+

+ 1 Q " 1k ," '

91 '- & '

1, >! <

,1 : k 0 ,

kkkk - K- )#- j,A DE F ' $ - 5 L0 % '

) J

' j,A " J

UQ k

h# „ h J1

,0:J -

h6j,A % " " : J ;I7k777 ˆ !-

7k777 ˆ A + L0 # 67 ˆ: J ,/ .

T - 6;7 ˆ " ,

, 6ˆ ", !

T - I k777 ˆ ! .

" E/

3" >

:" @ ˆ ! " C > h; j,A @7k777 ˆ !-

ˆ A + L0 # . !

T - @7 ˆ " ,

, Iˆ ",

T - 6 k777 ˆ ! .

—" —J 1 :J K

—+ —w # ,S J 1 #

! "C> )

:" ;777 ! "

ˆ: J ,/

" E/

:" ( ˆ ! " C > E5" ,

1, > ! < L- 1 j,A - :

,1 ,G ) J 1 P,B 1 C-,+ % " " : J k. ," '

h T K

c ' 5Y cQ E % -[1G -

& ' W X

KX & . c 5Y

O+

# &M

')( E xQ',X ![ Q ')( &

:" U&T,1 ! "

+ ˆX

EUACO ˆ;I7k777 ZA/P ,•67 ,67Y l 7k7777ZF/A ,•67 ,67Y…I 777…6 X ' 7

ˆ (4†4;7…6 X ; j,A ' ,1 :" ,

> ˆ @7“I “

“Xˆ 7X

EUACD ˆ@7k777 ZA/P ,•67 , Y … 6 77… X ˆ I(†677… 7X EUACO ˆ EUACD

(4†4;7 … 6 x ˆ I(†677 … 7X

xˆ 6I ;†@ # †:"

\! . ," ' k J'

%" " :J ,S % " " : J

,S J 1 # J

:" 6I ;†@

B " J1 J

![ I ?

+ 0 8 1 ! " C > ,G

! "#

:" ;777 J 1 , ,G

![ ' W X I\

![ ) W X

B \\\\\ ![ W \X 5 b

\\\\\ ![ W \X 5 b

-. \\\\\: U.

K " C 0 .J\G 1 Z ,S b

# C< K " N,

F1 # %

, ~"Y b

S - [ ' 1 , ~" "

S [ % ./ , ~" N, " k # K

C k 1 $, 1 N,

dF9

= "

0 _O+ -

c > 8 >P 0 J K " • 3 A , S‹ E+" • 3 A ' a1 - t 2@

Inflation Price Inflation Cost Inflation

•

./ 8 >P 0 J K " • #

G "

M % 1 L0 d F" " ‡E - : 1 . & u < C

0 L0

•

" "

B N

@ )H*

,— 0 O1 1 K " N, ) J 1 P; 31 #

- P6 # %

A '[ =

b " G ./ ,G k J

D ,3"

if = ((p; – P6) / P6 ) 677 if = Z B Y [ K " N, h ,G P(t) = t C 0

[ ./ =

P(t+ t)= t C 0 .J\G 0 ‚ [ ./ = h1 J

,1 ,1

K "=

P(t+ t)= P(t)(6…if)

/3" C "

s P O1

J 1 .1 V K " ,G

P(t+n t)= P(t)(6…if)n t

0# A 1

K# k K# '

./ = K k # ' 1

6… ifk = ( K . # ' ifk = ( K . # '

J1 K#

K " N,

K " N, ifk ,G

./ “ (6…ifk)

./ ) / (K . # ' 1 ./ ) / (K . # ' 1

./ ) ./ ) l6 K n#

Inflation Rate

3" ˆ n

#—

./ - kkk - ifI - if; U "," 1 31 ' !

- J 1 if6

K " N, ,G

h 1 . ,1 ,1 K n #

J 1 P6

Pn= P6(6…if6) (6…if;) (6…ifI) …. (6…ifn) k

) J 1 P(t) ./ 1 [ % 0 T - V ,S > Y(t) ,G

V= (Y(t)) / (P(t)) k

/3"

O1 : C "

DE F

0 _A +

V= (Y(t6)) / (P(t6)) = (Y(t;)) / (P(t;)) = (Y(tI)) / (P(tI))

Z' Q [ Y k J 1

0 _O+ ,

.S ,

‡E

T-0 b q+

—

T - ,S b

U&T,1 $ <

T - ,S b

ZK " C- 1 [ l0-, k

@ D R3

@ K

[ l, B C 0 [ Y k J 1

) J 1 .1 V [ ' + C ,Q Y'(t) - k J 1 & + C 0 •

t7 ,G

Y'(t)= (Y(t)) . (P(t7)) / P(t)

P(t7) / P(t) = 6 / (6…if)n = Z.1 VY Dc / Z' QY Da , n= t - t7 / t

D(t) = P(t7) / P(t) = Dc / Da k ,G

, $

,e L0 1 [ 1 L0 % 1 [

D(t)= 6 / (6…if)n = P(t7) / P(t) = Rc /Ra

Actual Dollar Constant Dollar

3" U ,* " ' ,1 U ,* :

J 1 .1 V K " N, ,G

Y'(t)= D(t) Y(t) q1

[ — % ./ . & ——B T 677

——

,rEB T 0 D——E F

C 1

—— 0 _——O+ -

% = "[ o /3 ./ dS J

b k

6;777 L

+ 6I@; #

7& UV Q

——S - —— [ 0 —— -,G —— ‚ -,—— —— G

I777 ) 6I2 #

," -0

0 _O+ k J

• ,1 K,G E % ./ ,G h# „

h 1 . ,1 ,1 6I2 # ' ,1 ./ dS J k J 1 (6;777 / I777 ) 677 = 77 k 1 k J

S 677 ,1 ,1

D ,3" , 0 j,J 1 b

# ' ,1 dS J : ,1 1

S - [ 0 $-,G M ' ,1 6n dS J

In = ((Pn6 / PK6) + (Pn; / PK;) + …. + (Pnm / PKm)) / M # ˆK ,1 n# #

(K) — w — [ % . / ,G k. $ J P,G ,H k J

m? 0 [ m? 0 [

'- &

jaB , 0 b

# ˆn

3" ˆ M

T - % ./ ˆ Pnm T - % ./ ˆ PKm

E C0- s P O1 1 s P O1

J 1 +1 0 , 9 1 [

In = ((Pn6W6 / PK6) + (Pn;W; / PK;) + …. + (PnmWm / PKm)) / (W6+ W; + … + Wm) Ka 0 % ,

Price Index

0- U ,* ˆ Wi

UV Q q4

—S - — [ • >—1 $-,—G $ > — .—/ > ! — <

- — ,w b[ — 5 l Q & b[ - b >—EP l &1 - b[ —

—+ - /T

wl M [

- l'>EP , { b[

: 7*

7& UV Q ,+

— ,1 —J-,P $ / ./ dS J

5 l$ J ‚ -,

5 - \{ l

WPI

> b[

5 ) E/]

lC< , H

5 l#> K0 ! - C /E lb[ : J l'>EP b[

5 k J1

— U— "," : —1 k J 1 -

—J —

:—

< '

' $

— 5 - ',— G $0 — $ - ,—

CPI :

! > ) 3 L- :

S : = " P,

j,—O ' — -,G k ,—G — ^ ,F — K —" N, - & + k J1

S- [

k J

+ ‚ƒ

WPI J-,P $ / ./ dS J 0 ," E dS J

/ ' 0 1 L0 ? /] E d! S

' [ ./ : e

E ' $ - 1 C<

7& UV Q

" 31

E d! S

IPI kHe

! "

! " ' ,1 K " - ./ b , ~" L- :

7& UV Q

3 L- : k J1

UV Q k# T 3 c

3 Q tO b "

If(t…6)= ((CPI(t…6) – CPI(t)) / CPI(t)) 677 - $ # V k. dS J C / ',1 k. ,S b

1.&

,S b

= (6†;2;k ) 677 = 7kI2(

Wholesale Price Index Consumer Price Index Implicit Price Index

$- 5

./ dS J ‚M #

k J 1 ;2;k; ,1 ,1 CPI

+ 6I( #

,S b ,G h# „

$ —

,—

.—/ dS —J

— ,1Y 64@@ - 64 7 ' ! — : 1

[

,S b

, 0 #- Q Z CPI

CPI

64 7

;kI@6™

64(7

6k6;2™

642

7k(2@™

6k@ ™

64(6

6k66(™

642

7k(;6™

64 @

6kI@2™

64(;

6k67 ™

642(

7k @2™

64 4

6k 76™

64(I

6k746™

6422

7k 6™

64 7

6kI@2™

64(

6k72(™

642@

7k 6;™

64 6

6k;@ ™

64(

6k7@ ™

6424

7k (6™

64 ;

6k;@ ™

64((

6k7;4™

64@7

7k 7 ™

64 I

6k; @™

64(2

6k777™

64@6

7k (2™

6k; ;™

64(@

7k4(7™

64@;

7kI (™

6k; 2™

64(4

7k466™

64@I

7kII ™

64 (

6k;;4™

6427

7k@(7™

64@

7kI;6™

64 2

6k6@(™

6426

7k@; ™

64@

7.I67™

64 @

6k6 ™

642;

7k244™

64@(

7kI7 ™

64 4

6k6 ™

642I

7k2 ;™

64@2

7k;46™

64@@

7k;2@™

/ ' \G

, •6

01 1 #

—] . Q : 0 _1, , 6 7 —31, ,— ,—

,— 0 ,—H

dF—J :— ) J 1 •6@ $ < # k

— : — 0 — ,S ' ,—1

+ —

;77k777 ‡E BT

—5

—+w ,—* T # T

v.J

6(k777(6 7)= ;k 77k777 ;k 77k777- ;k777k777= 77k777 ,* T # T ,

#„

O1 : 0 ./ 8 >P N, ,G k. # k.J

F= P(F/P, 6 %, ) 31 #

},P h'

, _/Q 1 ] # '

: 0 ./ ,* T # T =

',&

M& T 6(k777

S EM9 w ] # C S

+w ] # C

F= ;k777k777(f/p, 6 %, )= ;k777k777(6+k†6 ) = Ik@ 7k@;4 # —1 —

—/ .—S , # — 6 7Z6(k777Y ˆ;k 777 h J

: 0 , 6 7 ,S ' ,1 ,* T # T

: w C< # 3 $ < ‡E ) •6@K " N, : P,G ,H

F= ;k 77k777 (F/P, •6@, ) = k 46k;77

31 #

: 0 ./

;k 77k777(6+if =7†6@) = k 46k;77 # k 46k;77- Ik@ 7k@;4= 6k( 7kI26 # ',—& —1 #

' 1

M" B

0 31 ',&

)

',& #

6k( 7kI26 ‡E dFJ : k.

— < — 5 — ) & 19 K

,H 0 #

,—G C —w ).—& C —&M # — h,1 ,1 # 6- (6/ 6k6 )= 7k6I

,S b

,S b k 1

—i - — 5 CPI K — b

- ./ 8 >P

77k777 ‡E w,

•6 1 ./ 8 >P •6 a o „ k. DE F

B ) (if= 6 •) ) 1 8 >P •6 C >

S ./ 8 >P •6 ' 0

,S b

— ,1 - —B U—&T,1 [ b —

—

5 B #- Q

'- —& 64(2 # — ' — ,—1 [ — 1 — # — :—

,S b

— ,S b — 64@I #

—S [ ? C /

,S ' ,1

1 ./

/ ' ,1 k. $

.& C< K

k / .S , # ,1 ,1

,G 7kII

3 6†7kII = ;k44 h'

/ : 3" 64(2

#„

[ 1 64@7 # ' Q [ : 1 O1 h T

64@7 # .1 V [ = (677†; (k@) (6 ) = (6†;k (@) (6™) = 7k 7 ™ # —— 6I b ——

K ——" ' —— S, —— h 3 )

Q-

=——

if C<

—— ;k (@= (6…if)6I # ——„ :——

" N, # , ' ,1 . 3 -

k (64@7- 64(2) J 1

(6…if(@)(6…if(4) … (6…if24)(6…if@7)= (6…if)6I h'

#„

— $ —/ .—P

6 77777 ‡E

- .—1 V K —" N,— ,—G k.— $ J P,G ,H

& W 0 ? 0, %

},P

@• K - $, 1 k / .S , 0 1 #

.— 1 .—1 V # — U—&T,1 C< .—S , 0 1 - K - $ —Q- C — ,Q

—S

67 b

) J 1 • ! K /" k

-< h T

A= 6 77777(A/P, @•, 67) = 6;7777 .—1 V # — # —3

. #

6;7777 '- & @• N,

,1 K - [ .S , =&

k < 6;7777/(6…7k7 )k = 6;7777(6k7 )-k

. 1 , 0 O1 0 K # ,

.1 V # h

) ] # ' ,1 a o„

6;7777(6…7k7 ) = 6;7777(7k2@I )= 447;7 # ‚M3 — —31 5 —B #- —Q —

—

‚T '

‡—E $ — < # — 67

a o „— k —

7k(6I4 L0 #

— '

— .—P

k. C G , G K - _ tO—

—

— K]

.1 V #

5 y& ,

& W )$ Q- C ,Q # 3 .1 V #

— ,S b — — " — — #

• — —

K-

—&T

U&T,1

) ——J —— P,G ——M1 D——E F ' ! —— [ — ' — — > \! ) J

,e b 31 k

-# L:

. ," $

w o + +T

6(;7777

E3P C 0 #

44 6@

) /1 .1 V C 0 # A ——3" ' ,——1 .——

:{- - .S

1 $ Q- C ,Q 1 ' Q # )#

U&T,1 $ Q- C ,Q # „ :

3 k

.1 V #

b & W ,* 1 K " Ex& . Q : 1 k.

'- ——& b —— #

k. $

&" .1 1 ,S< # '

' ,1 k. K E3 C /A 1 ' Q #

" % a o „ k ] .1 V #

' ,1

5 0‚ C

a o —/ 0-,— # — U—&T,1

, $ < # 67

1- M 1-'

h# ;

M @D

,—— s,——1 —— ! "

/ },P C "

/ , ~" .1 V # 1 $ Q- C ,Q

-# L:

. ! 3P

U&T,1

" , 0 #- Q (

66 ;@@

(6k7 )l6= 7k4 ;

6;7777

67@@ 7

(6k7 )l;= 7k4727

6;7777

;

67I( (

(6k7 )lI= 7k@(I@

6;7777

4@2;

(6k7 )l = 7k@;;2

6;7777

4 7;7

(6k7 )l = 7k2@I

6;7777

(6k7 )l(= 7k2 (;

6;7777

(

@ ;@

(6k7 )l2= 7k2672

6;7777

@6;6(

(6k7 )l@= 7k(2(@

6;7777

22I ;

(6k7 )l4= 7k( (

6;7777

44 6@

(6k7 )l67= 7k(6I4

6(;7777

:j $ : ,—— ——1 = ",—— —— > —— —— < ' —— # —

!- ) J 1

' Q# ——

+ ,1 ) J

—

-<,1

U&T,1 C 0 _O+ ,

t * " , 0 j,J 1 N, ?

— '

— 8 >—P K —" N,

y " :

J\G #

' \G ~E 0

, - ,VW

k ,G :J-

. $, 1 N, C /

`, 0 C \G

,—H — a o —/ — ' $,— 1 \! )

N,— ) —1

&Dv

——" ——u < ——1

$ 0 : /F"

—r31 — .—P,G , $

b — 0) —

— — E F ' —— S, : ——1 > ——/" ——" .——— ' -,———* K ——" , Vz———" C ——/

k J C< —1 _—

,1 —— .—— :——J- ).——J\G C

—H .— Q k —J — $ ] — .1 V # .———! S Ex———&

, k

0 1 $, 1 N,

G< K " b ,r 0 : u/ - _P U& ' ,1 # 3

k J1

,S b

k 1

8 >P > i $, 1 i' >q_: @ b

, —H - M —1 ba —3 —J 1 —J

— .&

—Q- K —" '

= ,J % k

—

1 - K " N, : J . k‚M ,1 - /

# — P

—M

,G k J

> .1 V # 1)

"' Q#

MJY

,G D ,3"

Market Interest Rate Inflation- Free Rate

1 ).1 V #

b5 B C

]

N, : !

> - <

—J — K ] i $, 1 N, 1 C 0 /

\T K " , Vz" N, : - J 1 • C<

$, 1 N, ) 3 - $, 1 N, : k.

O / ) —J 1 ' —Q # — U&T,1

kZ,— 0 D—! M—JY kZ, 0

S, i' N, k. $ J

i' $, 1 N, 0 )

(if) c

,1 , C "

i=i' b kkk O1

$ Q- C ,Q ' ,1

5 '- ‡E , ~" .1 V

,G t ,9" J\G F1 M " B

F \\\!# :6. ('^i)n '/ ('^i)n

n-'

)

'/ ('^if)n ('^if)n

!# b ('^i')n '/ ('^i')n

n-'

)

if ) i' ) i : 1 O1 C —&M — ,S b

- , .1 V #

-' Q#

# — - ' —Q # — C —1 '- —& —1 Q " 1 k - $ —/ — 5

kkk M—J

Z,* T # TY , B C 0 _O+

Q- ',1 1 ,e

0 _O+ š

- D—! ./—& C — 0 # —3 )Z, B # Y k

k <

. 1 kkk O1 0

& K n# '

) & _O+

.1 V

, , B '- & - ,

fC - f

" -.

0 — ,—* T # —T

# — ;7777777 ' \—G

) J 1 .1 V $f-, #

,—

$f-, % d! S <

@ b ' ,1 - i= 6 • $, 1 N, ,G k. , 0

/ |1 O

k :— $ —Q- C — ,Q

5 ' Q#

—/ —J 1 2• —31 # —

U&T,1 $f-, : # T C 0 # 3 lD!

- (• #- # k

+,((

K "=

-< . 1 .1 V #

N, ,G l U&T,1 $f-,

+,((

)

S U

i=M',

)(O(( (

L 6#. !# #.[

P = A(P/A, 6 •, @) P= ' !— '

77(P/A, 6 •, @) .1 V #

U&T,1 # 3 K

]

k < aC6=

77 / (6… 7k7()6 = ; k;@I #

aC;=

77 / (6… 7k7(); = 77 k4@

aCI=

77 / (6… 7k7()I = I22@k;@2 #

' ,—1 (• K —" N,— , V —" .5" 9 " K w ' ! ' h

\! k

, b

' ,1 h)

(• K " .&F #

. 1 , 0 j,J 1 K

0 d! S < '

+1 ' ,1 2• K " N, - $f-, #- #

aC =

77 / (6… 7k7()I (6…7k72)6 = I I6k674 #

aC =

77 / (6… 7k7()I (6…7k72); = II77k67; #

" #-

aC(=

77 / (6… 7k7()I (6…7k72)I = I7@ k;72 #

aC2=

77 / (6… 7k7()I (6…7k72) = ;@@;k I2 #

aC@=

77 / (6… 7k7()I (6…7k72) = ;(4Ik@(( #

' —Q # — - .— .—1 V # — k J

— + ' ,1 ' \G

S , 0 MJ |1 O .1 V #

, #

;7777 ‡E .

" 0 ‚ $f-, $ Q- C ,Q k 1

S C &M

*(E+O)( *,*'O'( )79*OE7 +((+O9E 8 7 + +)+,O)E *88EO)E **((O'( )EE)O+* * 8 ) 8

)

)((((

S U

L 6#. !# #.[

(f) c k k

f =

C 9 f 1 , < - ./ 8 >P N, 0 .&"

K " N, k J 1

;6( 31 #

- ;77

K " N, [ dS J h- .

(b − a ) a

(216 − 200) = 0.08 200

dS J a

31 #

dS J b

K " N, k. $

;6( 1 62( 0 # I

SJ -.

216 176

176(1 + f ) 3 = 216 → 1 + f = 3 f = 71% → f = 7.1%

M0 -'

k ,G

0 :j $

,< [ o /3 Z B $

0 ,/ a o „Y J1 E5" ' ,1

<,P 1 K

$ JK

! '

@L c

<,P

k J1# tb

1 K " 0 31

\Q N,

/ /

H : ' ,1 EB # " 1 K " b ,V

<,P 1 $f-,

T 0 .&"

\T l6

E5" - >]" l;

if 0 kK " C / c 5E 0 31 $

C&( N

K " N, ,G

! 0b h0

3- !

wb " G

if ', g N,

L0 Ft - ,* T # T

L0 P ,G

P= Ft / (6…f)t (6…i)t P= Ft / (6…if)t

(6…i)t (6…f)t = (6…if)t if = i + f + if

', g N, J 1 • K " N, - •67 $

\Q N,

T ,G h# „

@ D h# ;

If = •67 + • + 7†7 7 = •6 †7

—F1 - —J 1 J bj,—91

— " .—1 V U ,—* 0

# - ' ,1 $ /

" ,e #

, ./

./ '

+ $ G,

1 K " 1 Q " 1 # &M k J

./ ,0

CPI =

1 + (214.1 − 195.4) = 1.098 195.4

Z6I2( # Y K

./ = I22777 “ 6†74@ = I@4777 c

[—

— > ) — .—/ dS J k , ', G $0 h 3 k e

R: d @ Q d# T 51 6 !

./ dS J %/

[

0 ;! ![ #0 B ![ #-

0 &Y :3

1C "

K "C>

[

% ' Q

> 1.&

'( K(

(Types of Inflation) c (Demand-Pull Inflation) * +" 89 0 J K " k6 (Cost Push Inflation) >

9P 0 J K " k;

; < IJ! 3 , 9 1 ,S 1 ,]

' V T , k ,1

K "p 1) J E '

,S 0 8 1 b

S- [

/ tO * +" 0 b&

[ $ J K /" ./ 8 >P ]

J 3

Q c

./ tO : P [ 1 k

k. $ 1 B

; 77 ' ! 1

M , < . % ,1 ,1 `

) B

@77

C E ," ; , ' 1

* +" 89 0 J

" #C J K "Œ ).

8 >P

!- )C G

k J 0

Q c

Œ >

[ K " N, 64@ #

J L0

C u < C /!< # 64;I , k J

(Effects of Inflation) c 0 , 3 , Z >/

N, Y

./ 8 >P 0 ,"

,G k

8 >P ,G - -

[1>

G 0 tO ) ./ 8 >P G 0 tO ) J $ ->P k <

k J 3 Q% 'r C k J'

] _ 0 " 1 ,] i

1 ,]

G 0 tO ) J 1 "

K " k6

K " k;

k J#~J

, ~" -

! " , ~" UQ

K " kI x !c *

(Inefficiency) 1

/ - L0 1 _1 ,G

r31

' . ! 3P 1 ,] K " k 18

J i<

01.& 0 ,91 K "

)

/ Q ,H 0

i . ! 3P

i < k. $ P 1 3 Q ' ,1 .

V< ,S - aA ) Q S # ) + +T i

' ! " , { 1 ' ! " ' 8F1 0

UQ ? * : `

! _1

'- '0 1

S La"

,5 UQ K " E k

O1 k '

+ . P,g - J

(Stagflation) 0 ! c = ,J E/Q 0 k J 1 K " 1 $ ,/ )[ 1 ' M 1 N, 8 >P )

& -,1- $0 " ' $ Œ'

K "Œ

1 ,* T C,

k. ./ 8

& 1 C, K- / $

: k

K "? :

-' M1) 3 Q 1>

' M 1 ) ./ tO S t * " C< o 31

(Economic growth) 0 ' 9

$ J ! "b

S - [ ,G k.

9 %

S-[ : [ o / T k. $ , J L

! " 1 &1 - )' G k ,1

Q J

) J1

# 0 81

S[1

G 0 tO

(Business Cycles) y f ' ]" + +T . ! 3P tO

) 9

l 9 >P ' . ,T ' e! )' ]" Z M Y - % k. 46

|- l

1 lI @4C ,51 l; @@' &

k6 ' &

! " N, 8

•

' M 1 8 >P • C ,51 ! " ' M 1 ,„ Recession Slump Expansion Boom

T• T•

1 ! " N, 8 >P • ' M18

• |-

! " ,„

T•

' M1 k. #

T•

o ,+" ' ]" - %

Gross National product (GNP) H U( V - S

[ ,H

! "

E - 1' ! " i b

J) E "

S - kkkk

5 L0 . 3/Q ,1

S - [ L0 ? /] ) E

! " )D ,3" : 1 Q " 1 k. : 3 $ - %

S ,H

- )kkk EM! , { b 1-,9 ) i \{

1 )[ 1

0 % ,

E d! S

! " ,G k <

! "

+ k J

) S>ƒJ< K0 ! , H

kkkk )',e9 < ) E3" )b- r ! " C 9 /] 0 -

BT ,

! ")

E d! S

&+"

Gross Domestic Product (GDP) HV U( V - Z. E 0 ,H P,BY k J M9"

k. $

9 % .P

E d! S . 1C,

$ J ! "b

^ S 0 E d! S ! "0

9F1

&5 C , (GDP) ES d! S E d! S GNP=GDP+NA

! "0

/& k. Z# % Y : 3 , ,G

< : , 0 k.& ! " ->Q )C ,

! " ˆ ES d! S

9 &(

S - [ L0 ) ES d! S .

k < /

! "

9 0 ^ S

. 1 E d! S

k J

ES d! S + '

&T 1 C , ! "…^ S0

! "

" ' ,1

% h# „ ' ,1

! " ->Q

A :/

E d! S

! " ->Q

k J

! "

' .P

d! S

/&H[ n 6. G. J. Thuesen, W. J. Fabrychy, Engineering Economy, (Prentice-Hall international Series in Industrial and Systems Engineering), PrenticeHall College Div; ISBN: 76I7;@6;X; 4 edition, ;777. ;. James L. Riggs, David D. Bedworch, Sabah U. Randhawa, Engineering Economic, McGraw-Hill, Higher Education, ISBN; 77246;; @ ,

edition, 644(.

I. Gerald W. Smit, Engineering Economy: Analysis of Capital Expenditures, Iowa state university press, ISBN: 7@6I@7 I@;

edition, 64@2. . Eugene Lodewick Grant, William B. Areson, William G. Ireson, Principle of Engineering Economy, @th edition, John Wiley & Sons; ISBN: 7 26(I ;(X; 6447. . Leland T. Blank, Anothony J. Tarquin, Engineering Economy, McGraw-Hill, Series in Industrial Engineering and Management science, McGraw-Hill Collage Div; ISBN; 772; I;I 4,

edition,

;776. (. J. C. Sprague, J. D. Whittaker, Economic Analysis for Engineers and Managers, Prentice-Hall, ISBN; 76I;; 7( , 64@ .