() , 1 . , : , , 1 . , , , .. . ? 3 .
1. . 1 . - 20% 1,2 . . , - 1 . , 833,3 . .
2. . 1 . , 500 . , 1 . 500 . .
3. . , 1 . , . , . - : , , . () . () -FV, r n- () :
FV = PV
PV () , .
n (, )
: 1 . ., r 10% 1 + 0,1 = 1,1 . ., 1,1 + 0,1 =1 1,1 = 1,21 . . . (1+ ) , () .
, , , 1 . 330 . ., 10% . 1,33 . . , . (PV) (FV) (1 + ) , () :
: 5 1 . . , 10%.
PV = = = 0,62 . .
.. ( ).
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. , , , : - , , .
. : , , , , , . - , .
, , , , , , . - ,
, , :
) ?
) () ?
) , .. ?
, -. . . .
, , , , , . : - , , , ? , . , , . , , ?
, , , -, Computer Model of Feasibility Analysis and Reporting (COMFAR), Project Profite Screening and Preappraisal Information System (PROPSIN), Project Expert, -.
. .
.1. .
(, ), , , . : ) ; ) () . :
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- (Net Present Value, NPV);
- (Profitability Index, PI);
- (Internal Rate of Return, IRR);
- (Modified Internal Rate of Return, MIRR);
- (Discounted Payback Period, DPP).
:
- (Payback Period, PP);
- (Accounting Rate of Return, ARR).
. (I) , . , q. . , ( ), , .
, , (I) n 1, 2,..., Pn. (Present Value, PV) (Net Present Value, NPV) :
.
, NPV > 0, ; NPV < 0, ; NPV = 0 , .
NPV . NPV < 0, , .. . NPV = 0, , .. . NPV > 0, , , .
, , . , , .
, , NPV :
.
IC 0 = IC.
, NPV . - , .. NPV . , .
, , . . a(0), a(1), a(2), a(3),..., a(t),.... a(k) , , - . - a(0) = (-IC)
a (1) = 1, a(2) = 2,..., a (n) = Pn.
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, , , , ( , ), .. , :
NPV = a(0) + a(1)(1) + a(2)(2) + a(3)(3) +... + a(t)(t) +... (4),
(t) - -. , - = 1/(1+q), q - ( ), :
NPV = NPV (q) = a (0) + a (1)/(1 +q) + a (2)/(1 +q) 2 +
+ a (3)/(1 +q) 3 +... + a (t)/ (1 + q) t +....(5)
1. a (0) = - 10, a (1) = 3, a (2) = 4, a (3) = 5. q = 0,12, , , (2) - : (1) = 0,89, (2) = 0.80, (3) = 0,71. (4)
NPV (0,12) = - 10 + 3 × 0,89 + 4 × 0.80 + 5 × 0,71 =
= - 10 + 2,67 + 3,20 + 3,55 = - 0,58.
, , NPV (0,12) , (.. = 1, q = 0) : NPV (0) = - 10 + 3 + 4 + 5 = 2 > 0, . , -. . , . , , . , .
() - , . , :
;
;
;
;
.
, . , , , 6%. 12%, - 15%. , , 20%, - 25%. . 16%, - 20%, , , - 24%. , () , , . , - . , .
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. . (I) :
.
, I > 1, ; I < 1, ; I = 1 , .
: , .. , , . I , NPV. , NPV, , , , .
- . . - (). , , = - , = / - 1. , - , , 1 . . .
( IRR Internal Rate of Return, :, ) q, NPV :
IRR = q, NPV(q) = 0.
, I = CF0 CFk , k - , IRR :
.
, , : IRR , , , . , , IRR , . , , . , , .., , . , , (WACC Weight Average Cost of Capital). , , .
, IRR : , " " . WACC, , , . IRR, , .
IRR < , ; IRR > , ; IRR = , .
. , - , . () . , , . . , , . :
= min n, .
, .. ; , .
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. , q = WACC, , DPP, :
DPP = min n, .
, , .. DPP > . , , , DPP. , , q=0.
, - , . , ( ) . , . " " , .
. : -, ; -, PN ( ). , . , (ARR), PN ( ). , , . (RV), . , ARR. :
.
, , ( -). , , , , . , , , , , , ..
(, ) , . (, ) , . - : , , , ..