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1 ROI
ROI AB C

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2PBP

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Pay back Period (PBP)
0
-40 K

1
10 K

2
12 K

3
15 K

4
10 K

5
7K

PBP .



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Pay back Solution (#1)
0
-40 K (-b)

1
10 K 10 K

2
12 K 22 K

3 (a)
15 K 37 K(c)

4
10 K (d) 47 K

5
7K 54 K



PBP =a+(b-c)/d = 3 + (40 - 37) / 10 = 3 + (3) / 10 = 3.3 Years

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Pay back Solution (#2)
0
-40 K
-40 K

1
10 K
-30 K

2
12 K
-18 K

3
15 K
-3 K

4
10 K
7K

5
7K
14 K

PBP


= 3 + ( 3K ) / 10K = 3.3 Years
: .



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PBP
BW PBP 3.5 ?

! 3.5 . [3.3 Years < 3.5 Year Max.]



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PBP
:
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Net Present Value (NPV)

? ? 1 ?

NPV څ

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?

NPV=NCFt (P/F, i , n )
t = 0 n

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Net Present Value (NPV)

? ? 1 ? NPV

.

NCF1 NPV = (1+i)1

NCF2 + (1+i)2

+..

NCFn + (1+i)n

- ICO
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2s



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3 0 0
4

13

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5


?

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NPV

Example

Julie Miller BW 15 10,000,$12,000,$15,000, 10,000, and $7,000 40,000. BW (k) 13%NPV

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NPV
10000
0 1

12000 15000 10000 7000
2 3 4 5

40000 NPV $10,000 + $12,000 +$15,000 + (1.13)1 (1.13)2 (1.13)3

$10,000
(1.13)4

+

$7,000
(1.13)5

- $40,000
16



NPV
NPV = + + NPV = $10,000(P/F,13%,1) + $12,000(P/F,13%,2) $15,000(P/F,13%,3) + $10,000(P/F,13%,4) $ 7,000(P/F,13%,5) - $40,000 $10,000(.885) + $12,000(.783) + $15,000(.693) + $10,000(.613) + $ 7,000(.543) - $40,000 NPV = $8,850 + $9,396 + $10,395 + $6,130 + $3,801 - $40,000 = - $1,428
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Net Present Value
$000s 15 Net Present Value Sum of CFs Plot NPV for each discount rate.

10
5 0 -4 IRR

NPV@13%

0

3

6 9 12 15 Discount Rate (%)()


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NPVR
? ?

1
NPVR

?



100%



? NPVR

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NPVR
?

2

0 ? 0
?





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NPVR
:
? ?
?

:

?



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(PI)
()
1
PI .

NCF1 NCF2 NCFn PI = + +...+ 1 2 (1+k) (1+k) (1+k)n
<< OR >>

ICO

PI = 1 + [ NPV / ICO ]

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(PI)
2 ? PI: ? PI1, ? PI1
?
?

PI PI



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PI
PI = $38,572 / $40,000 = .9643 ?

! PI 1.00. . [PI < 1.00 ]



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PI
:
NPV ?
? ?

:
?
?

NPV



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(IRR)
IRR 1
IRR ( NPV)

CF1 CF2 + ICO = (1+IRR)1 (1+IRR)2


+...+

CFn (1+IRR)n
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(IRR)
? 2

IRR ? IRR
?

3



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IRR
:
? ?

:
IRR ?IRR
?

?

TVM



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IRR
$10,000 $12,000 $40,000 = + + (1+IRR)1 (1+IRR)2 $15,000 $10,000 $7,000 + + (1+IRR)3 (1+IRR)4 (1+IRR)5
IRR.



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IRR (Try 10%)
$40,000 = $10,000(P/F,10%,1) + $12,000(P/F,10%,2) + $15,000(P/F,10,3) + $10,000(P/F,10%,4) + $ 7,000(P/F,10%,5) $40,000 = $10,000(.909) + $12,000(.826) + $15,000(.751) + $10,000(.683) + $ 7,000(.621) $40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347 = $41,444 [Rate is too low!!]

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IRR (Try 15%)
$40,000 = + + $40,000 = $10,000(P/F,15%,1) + $12,000(P/F,15%,2) $15,000(P/F,15%,3) + $10,000(P/F,15%,4) $ 7,000(P/F,15%,5) $10,000(.870) + $12,000(.756) + $15,000(.658) + $10,000(.572) + $ 7,000(.497) $40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479 = $36,841 [Rate is too high!!]

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IRR ()
.05

X

.10 IRR .15

$41,444 $40,000 $36,841

$1,444 $4,603

X=

($1,444)(0.05) $4,603

X = .0157

IRR = .10 + .0157 = .1157 or 11.57%

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IRR
BW13%. ?

! 11.57% 13%. [ IRR < ]



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IRR Example
?

100 10 10 10%
?

?
?





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?
? ? ? ?

: 100 1010
NCF101020 NPV10020P/A,10%,10 22.8914

? ? ?

P/A, IRR,10100/205 10 P/A,14%,105.216125 P/A,16%,104.833235

35


?


?5.21612-5

? IRR14%

(16%-14%)

?5.21612-4.83323

15.13%



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B W

PBP IRR NPV PI

3.3 11.57% -$1,428 .96

3.5 13% $0 1.00


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?
NPV0NPVR 0PI 1IRR ic; NPV= 0NPVR =0 PI =1 IRR =ic; NPV0NPVR 0PI 1IRR ic



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]
1. 2.P249. 3.

NPV 0NPVR 0PI 1,IRR ic, PPN/2,ROIi.

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NPV 0NPVR 0PI 1,IRR ic, PP N/2, ROI i.
NPV 0NPVR

0PI 1,IRR ic,

PP N/2, ROI i.

40



NPV 0NPVR 0PI 1, IRR ic,

PP N/2, ROI i.



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1. 2.P252. 3. NPV NPVR IRR



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AI3 17 5111 3 1.28 1551 6 2.4A12%30% NCF IRR

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NA ¦



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A 33003 900415 200 51505 750 8%



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n=3+15=18( NCF0-2 =-300 NCF3 =0 NCF4-18 =200 NPV200x(P/A,8%,15)x(P/F,8%,3)[300x(P/A,8%,2)+300]=523.92 NA523.92x(A/P,8%,18)=55.99 n=5+15=20( NCF0-4 =-150 NCF5 =0 NCF6-20 =200 NPV200x(P/A,8%,15)x(P/F,8%,5)[150x(P/A,8%,4)+150]=518.65 NA518.65x(A/P,8%,20)=52.85 NA=55.99 NA=52.85

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P262



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