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1. . :
(NPV) - ( , , );
(PI) - ;
(IRR) - ( . );
(MIRR) -
(DPP) - ;
2. :
(PP) - ;
(ARR) - .
, . .
, .
: 18. ., - 20 . . :
: - 1.5 ., 3.6 ..
: 1.5 . ., 4 .. 0.45 .
, 10% 20%.
.
ˠ 2. (NPV) " "
- . (NPV) :
1. :
= nåt=1 FVt/(1+rt)n - Ic, :
FVt - () ;
rt - - - ;
n - ;
Ic - .
FVt = PVt (1+rt)n, :
PVt - () ()
2. :
= nåt=1 FVt/(1+rt)n - nåt =1 Ict /(1+rt)n
(NPV) . .
Ic1 = | 18 | .. | ||||||
Ic2 = | 20 | .. | ||||||
PV1.2 |
1/(1+r1.2 ) |
FV1.2 |
||||||
1 | 2 | r1.2=10% | r1.2 =20% | r1 =10% | r1 =20% | r2 =10% | r2 =20% | |
1 | 1.5 | 1.5 | 0.91 | 0.83 | 1.36 | 1.25 | 1.36 | 1.25 |
2 | 3.6 | 4.0 | 0.83 | 0.69 | 2.98 | 2.50 | 3.31 | 2.78 |
3 | 3.6 | 4.0 | 0.75 | 0.58 | 2.70 | 2.08 | 3.01 | 2.31 |
4 | 3.6 | 4.0 | 0.68 | 0.48 | 2.46 | 1.74 | 2.73 | 1.93 |
5 | 3.6 | 4.0 | 0.62 | 0.40 | 2.24 | 1.45 | 2.48 | 1.61 |
6 | 3.6 | 4.0 | 0.56 | 0.33 | 2.03 | 1.21 | 2.26 | 1.34 |
7 | 3.6 | 4.0 | 0.51 | 0.28 | 1.85 | 1.00 | 2.05 | 1.12 |
8 | 3.6 | 4.0 | 0.47 | 0.23 | 1.68 | 0.84 | 1.87 | 0.93 |
9 | 3.6 | 4.0 | 0.42 | 0.19 | 1.53 | 0.70 | 1.70 | 0.78 |
: | 30.3 | 33.5 | 18.82 | 12.76 | 20.76 | 14.04 | ||
|
(NPV) |
0.82 | -5.24 | 0.76 | -5.96 |
, , :
(NPV) >0 , .
(NPV) =0 , .
(NPV) < 0, , .. .
:
20% - , .. (NPV) < 0
10% - , .. (NPV) >0
10%, .. (NPV), , (NPV) 10%, .
3. (PI) " "
- :
1. :
(PI)= (nåt=1 FVt/(1+rt)n )/ Ic, :
FVt - () ;
rt - - - ;
n - ;
Ic - .
2. :
(PI) = nåt=1 (FVt/(1+rt)n) / ( nåt =0 Ict /(1+rt)n)
(PI) :
;
;
, ;
(PI).
(PI) . .
Ic1 = | 18 | .. | |||||||
Ic2 = | 20 | .. | |||||||
PVt |
1/(1+r1.2 ) | FV1.2 | |||||||
1 | 2 | r1.2=10% | r1.2 =20% | r1 =10% | r1 =20% | r2 =10% | r2 =20% | ||
1 | 1.5 | 1.5 | 0.91 | 0.83 | 1.36 | 1.25 | 1.36 | 1.25 | |
2 | 3.6 | 4.0 | 0.83 | 0.69 | 2.98 | 2.50 | 3.31 | 2.78 | |
3 | 3.6 | 4.0 | 0.75 | 0.58 | 2.70 | 2.08 | 3.01 | 2.31 | |
4 | 3.6 | 4.0 | 0.68 | 0.48 | 2.46 | 1.74 | 2.73 | 1.93 | |
5 | 3.6 | 4.0 | 0.62 | 0.40 | 2.24 | 1.45 | 2.48 | 1.61 | |
6 | 3.6 | 4.0 | 0.56 | 0.33 | 2.03 | 1.21 | 2.26 | 1.34 | |
7 | 3.6 | 4.0 | 0.51 | 0.28 | 1.85 | 1.00 | 2.05 | 1.12 | |
8 | 3.6 | 4.0 | 0.47 | 0.23 | 1.68 | 0.84 | 1.87 | 0.93 | |
9 | 3.6 | 4.0 | 0.42 | 0.19 | 1.53 | 0.70 | 1.70 | 0.78 | |
: | 30.3 | 33.5 | 18.82 | 12.76 | 20.76 | 14.04 | |||
(PI) |
1.05 | 0.71 | 1.04 | 0.70 | |||||
|
|||||||||
(PI) > 1, .
(PI) = !, .
(PI) < 1, .
:
20% - , .. (PI) < 1
10% - , .. (PI) >1
10%, .. (PI) (PI) 10%, .
ˠ 4. (IRR) " "
= .
:
1. = 0, rt/;
2. :
(IRR) = r1*( [1+ +(r2 -r1)] / [1+] + [2-] ), :
1+ - ( ) r1
2- - ( ) r2
r1 - ( ) 0
r2 - ( ) 0
(IRR) :
;
;
;
;
( ).
(IRR) . . .
(IRR) :
1 = 0.1104+([0.0112*(0.1106-0.1104)]/(0.0112+[-0.0039]) 11.05%
2 = 0,107+([0,1505*(0,109-0,107)]/(0,1505+[-0,0197]) 10.8%
ˠ 5. (PP) " "
. :
1. :
(PP) =Ic/PV
2. :
(PP) = Ic/PVå , :
Ic -
PV - () ()
PVå S Ic, .
(PP):
;
;
.
:
;
, .. ;
, .
(PP) . .
Ic1 = | 18 | .. | |||||||||||||||||
Ic2 = | 20 | .. | |||||||||||||||||
PVt |
1/(1+r1.2 ) | FV1.2 | |||||||||||||||||
1 | 2 | r1.2=10% | r1.2 =20% | r1 =10% | r1 =20% | r2 =10% | r2 =20% | ||||||||||||
1 | 1.5 | 1.5 | 0.91 | 0.83 | 1.36 | 1.25 | 1.36 | 1.25 | |||||||||||
2 | 3.6 | 4.0 | 0.83 | 0.69 | 2.98 | 2.50 | 3.31 | 2.78 | |||||||||||
3 | 3.6 | 4.0 | 0.75 | 0.58 | 2.70 | 2.08 | 3.01 | 2.31 | |||||||||||
4 | 3.6 | 4.0 | 0.68 | 0.48 | 2.46 | 1.74 | 2.73 | 1.93 | |||||||||||
5 | 3.6 | 4.0 | 0.62 | 0.40 | 2.24 | 1.45 | 2.48 | 1.61 | |||||||||||
6 | 3.6 | 4.0 | 0.56 | 0.33 | 2.03 | 1.21 | 2.26 | 1.34 | |||||||||||
7 | 3.6 | 4.0 | 0.51 | 0.28 | 1.85 | 1.00 | 2.05 | 1.12 | |||||||||||
8 | 3.6 | 4.0 | 0.47 | 0.23 | 1.68 | 0.84 | 1.87 | 0.93 | |||||||||||
9 | 3.6 | 4.0 | 0.42 | 0.19 | 1.53 | 0.70 | 1.70 | 0.78 | |||||||||||
: | 30.3 | 33.5 | 18.82 | 12.76 | 20.76 | 14.04 | |||||||||||||
(PP) |
6 | 6 | |||||||||||||||||
|
|||||||||||||||||||
(PP) .
6 , 5 5 . , , .. .
ˠ 6. Ƞ (DPP) " "
:
(DPP)= Ic/(å PV/(1+r)n)
, .. (DPP) >(PP).
(DPP) :
;
;
.
:
;
, .. ;
, .
(DPP) . .
Ic1 = | 18 | .. | |||||||||||||||||
Ic2 = | 20 | .. | |||||||||||||||||
PVt |
1/(1+r1.2 ) | FV1.2 | |||||||||||||||||
1 |
2 |
r1.2 =10% |
r1.2 =20% |
r1 =10% | r1 =20% | r2 =10% | r2 =20% | ||||||||||||
1 | 1.5 | 1.5 | 0.91 | 0.83 | 1.36 | 1.25 | 1.36 | 1.25 | |||||||||||
2 | 3.6 | 4.0 | 0.83 | 0.69 | 2.98 | 2.50 | 3.31 | 2.78 | |||||||||||
3 | 3.6 | 4.0 | 0.75 | 0.58 | 2.70 | 2.08 | 3.01 | 2.31 | |||||||||||
4 | 3.6 | 4.0 | 0.68 | 0.48 | 2.46 | 1.74 | 2.73 | 1.93 | |||||||||||
5 | 3.6 | 4.0 | 0.62 | 0.40 | 2.24 | 1.45 | 2.48 | 1.61 | |||||||||||
6 | 3.6 | 4.0 | 0.56 | 0.33 | 2.03 | 1.21 | 2.26 | 1.34 | |||||||||||
7 | 3.6 | 4.0 | 0.51 | 0.28 | 1.85 | 1.00 | 2.05 | 1.12 | |||||||||||
8 | 3.6 | 4.0 | 0.47 | 0.23 | 1.68 | 0.84 | 1.87 | 0.93 | |||||||||||
9 | 3.6 | 4.0 | 0.42 | 0.19 | 1.53 | 0.70 | 1.70 | 0.78 | |||||||||||
: | 30.3 | 33.5 | 18.82 | 12.76 | 20.76 | 14.04 | |||||||||||||
(DPP) |
9 | 9 | |||||||||||||||||
(DPP) .
9 , : 8 3 , 8 2 , , . ( ) .
ˠ 7. (ARR) " "
. : , .
, , .. . .
(ARR) = / (Ic/2) = 2 /I c, :
- ;
Ic - .
, , , : ; ; .
:
- : Ic/2 = (Ic + Ic )/2;
: Ic/2 = (Ic + )/2;
: Ic = ;
: Ic = ;
(ARR): ; (ARR) (IRR); (ARR) c , (ARR) >1/, .
(ARR): ; , .
, , (ARR) :
, .. 45% . ` = å PV /n, : n- . `1 = (1,5+3,6*8)/9 = 3,367.. `2 = (1,5+4*8)/9 = 3,722 .. 1 = 1*0,45 = 3,367*0,45 = 1,515 .. 2 = 2*0,45 = 3,722*0,45 =1,675 .. 1(ARR1)=21/Ic1=2*1,515/18 = 0.1683 2 (ARR2)=22/Ic2 =2*1,675/20 = 0.1675 |
PVt |
|||
1 |
2 | ||
1 | 1.5 | 1.5 | |
2 | 3.6 | 4.0 | |
3 | 3.6 | 4.0 | |
4 | 3.6 | 4.0 | |
5 | 3.6 | 4.0 | |
6 | 3.6 | 4.0 | |
7 | 3.6 | 4.0 | |
8 | 3.6 | 4.0 | |
9 | 3.6 | 4.0 | |
: | 30.3 | 33.5 | |
(ARR) |
0.1683 | 0.1675 | |
(ARR) , . . , . |
1= 1/() =1/6=0,1666
2= 1/() =1/6=0,1666
1(ARR1) >1/
2(ARR2) >1/
ˠ 9. .
, :
;
;
;
.
():
(NPV) >0, (IRR)>(r) ( PI)>1;
(NPV) =0, (IRR)=(r) ( PI)=1;
(NPV) <0, (IRR) <(r) ( PI) <1;
(PP) ( ARR), .
, , "" "".
Ic1 = | 18 | .. | ||||||||||||||
Ic2 = | 20 | .. | ||||||||||||||
1/(1+r1.2 ) | FV1.2 | |||||||||||||||
1 | 2 | r1.2=10% | r1.2 =20% | r1 =10% | r1 =20% | r2 =10% | r2 =20% | |||||||||
1 | 1.5 | 1.5 | 0.91 | 0.83 | 1.36 | 1.25 | 1.36 | 1.25 | ||||||||
2 | 3.6 | 4.0 | 0.83 | 0.69 | 2.98 | 2.50 | 3.31 | 2.78 | ||||||||
3 | 3.6 | 4.0 | 0.75 | 0.58 | 2.70 | 2.08 | 3.01 | 2.31 | ||||||||
4 | 3.6 | 4.0 | 0.68 | 0.48 | 2.46 | 1.74 | 2.73 | 1.93 | ||||||||
5 | 3.6 | 4.0 | 0.62 | 0.40 | 2.24 | 1.45 | 2.48 | 1.61 | ||||||||
6 | 3.6 | 4.0 | 0.56 | 0.33 | 2.03 | 1.21 | 2.26 | 1.34 | ||||||||
7 | 3.6 | 4.0 | 0.51 | 0.28 | 1.85 | 1.00 | 2.05 | 1.12 | ||||||||
8 | 3.6 | 4.0 | 0.47 | 0.23 | 1.68 | 0.84 | 1.87 | 0.93 | ||||||||
9 | 3.6 | 4.0 | 0.42 | 0.19 | 1.53 | 0.70 | 1.70 | 0.78 | ||||||||
: | 30.3 | 33.5 | 18.82 | 12.76 | 20.76 | 14.04 | ||||||||||
(NPV) |
0.82 | -5.24 | 0.76 | -5.96 | ||||||||||||
(IRR)(%) |
11.05 | 10.08 | ||||||||||||||
(PI) |
1.05 | 0.71 | 1.04 | 0.70 | ||||||||||||
(PP) |
6 | 6 | ||||||||||||||
(DPP) |
9 | 9 | ||||||||||||||
(ARR) |
0.1683 | 0.1675 | ||||||||||||||
. . 10% , .
- . , ,
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