, .
, , . , , .
. , , , .
, . , , , .
:
ð ;
ð , () ;
ð , , .. , .
, : .
NPV (net present value) . .
:
(4‑1)
CFk n , k = 1, 2, , n;
Z ;
r .
, (m), :
(4‑2)
NPV [40], , :
Ø NPV > 0 ;
Ø NPV < 0 ,
Ø NPV = 0 ,
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4‑1
, 150 . ., 4-1, 10% .
. 4‑1
Excel , .4-2.
. 4‑2 MS Excel c (4-1)
. 4‑3 MS Excel c (6-1)
:
Ø " " () ;
Ø " " ;
Ø " " . , " 4 " : =C3+B4;
Ø " D " . , " D3 " : =(B3/(1+0)^A3)/B3; " D4 " : =((B4/(1+0.1)^A4))/B4 ..;
Ø " E " . , " E4 " : =B4*D4
Ø " F " . , " F3 " ( ): =D3; " F4 " : =F3+E4 ..
Ø G . , G3 : =(C3>0;" ";" "), G4:G11 .
, :
= 32,01
= -(-150)+32,01 = 182,01
182,01 =NPV(10%;C4:C11), _("") ("1".,..) , .
MS Excel NPV .
. 4‑4 ()
, , , NPV (, ) , , Present Value (PV) ( /).
.
() () , , ( ) ( ).
: (;1;2;...)
.
1, 2,... 1 29 , .
1, 2,... , .
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1, 2,... ( , ( ) )
=NPV(10%;C4:C11) , 3
=(10%;B4:B11)+B3
? . .
NPV , ,
4‑2
, .4-5, 15%
. 4‑5 4-2
4‑3 () 1
Ø B8 (), 8
Ø 9 9 1 2.
2, , .
, (payback period method) , . , [41]:
(4‑3)
:
(4‑4)
4‑4
, 1 . ., 5 : 250; 400; 800; 900; 900 . . . 15%.
.
Excel , .4-7
. 4‑6 Excel 4-3
. 4‑7 Excel 6-3
:
Ø C1:G1 ;
Ø C2:G2 ( CFk);
Ø C3:G3 . , 3 =C2/((1+15%)^C1), 6-3;
Ø C4:G4 . , 4 =B4+C3 ( (1) ), D4 =C4+D3 ( (2) ) ..
, 2 3 . 7-4 :
=D1+(-D4/E3) =2+480,15/526,01 =2,91
, , , 2,91 2 332 .
, 5 : =(C4>0;C1-(B4+C3)/C3;0) [42] .
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(benefit-cost ratio, profitability index - PI) , . :
(4‑5)
PI > 1, , NPV. .
PI = 1 NPV= 0 .
, PI < 1,
PI , , .
4‑5
, .1. 250000,00.
. 4‑8
( " "), (NPV) , (PI) 1. , 250000,00, . - () , 250000,00.
" ".
" 8 " : =(B2:B7;E2:E7);
: " " : "1" ; "0" .
" 9 " :
=(B2:B7;C2:C7);
" " :
. 4‑9 " "
" " :" ", " ", " D " " ", NPV 121000.
: NPV, PI.
4.3.1. . () [43]
[44] (internal rate of return - IRR) .
, .
:
(4‑6)
, NPV = 0, ( PV ) I0, . , IRR, . IRR r. IRR > r, NPV, , IRR r. IRR < r, .
IRR :
Ø () " " ( , NPV=0;
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Ø () [45]
. 4‑10 ()
4‑6
1 2005. 200 . . , 5 40, 60, 80, 90 100 . .
, 1
, 10%
F 1. " " IRR
ð " 3" "3" =(10%;B2:G2;B1:G1) =(C4;B2:G2;B1:G1),
ð " 3 " ѭ_ ...;
. 4‑11
:
ð" " - $C$3;
"" - 0;
ð" " $C$5.
" " 5 IRR =20.94%
F 2. ()
ð " 6 " =(B2:G2;B1:G1), IRR=20,94%
? , 24% .