, , , , , . - . - . () :
1) (NPV);
2) () ;
3) ;
4) ().
, . NPV . NPV >0 , NPV . NPV , , .
, .
(). , ( ) (. . 8):
= (-100; -150; 50; 150; 200; 200),
= (-200; -50; 50; 100; 100; 200).
. 8
, .. i = 10% :
NPV = 162,2; NPV = 57,7.
- (n ). , . . n , .
. n . :
50 + 150 + 200 x = 250, x = 0,25 .
, n = 2 + 0,25 = 2,25 .
: 50 + 100 + 100 = 250, , n = 3 .
, . . . [1]. .
1. , ;
2. m , ,
m - , nt. ( - m)/ Rm +1 Vm +1.
3.
nt = m + (- m)/ Rm +1 Vm +1.
nt . t = 2 - , i = 10 %.
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: ,
= 100(1+0,1) +150 = 260.
, 2 = 169,4; 3 = 319,7 .. 2 < < 3.
, m = 2 ,
: = 200(1+0,1) +50 = 270,
3 = 203,2; 4 = 339,8 .. 3 < < 4, m = 3 :
, . , . , .
. i B, . , .. , . RS (RS < 0 - , RS > 0 - ), i B
(30)
NPV (i)=0 i B, (internal rate of return = irr) . , , , , .
, i = i B ( ).
i < i B, . i > i B , i B.
, NPV (i)=0.
(1). [2] , , (R (1), R (2),, R (n)), R (k)= R 1+ R 2++ Rk - t k, , R 0 ¹0 R (n) ¹ 0, , (30) .
, , (30).
. , f(a) f(b) , , f(a) > 0, f(b) < 0,
. :
Rk = (-5, 1, -3, 8, 4) tk = (0, 1, 2, 3, 4).
i B.
. . Rk = (-5, -4, -7, 1, 5), .. { Rk } . ,
f (i) = -5 + (1+ i)-1 3(1+ i)-2 + 8 (1+ i)-3 + 4(1+ i)-4 = 0
i B. f(i) 0,20 0,25 0,01, , f (0,22) > 0, f (0,23) < 0 .. i BÎ(0,22; 0,23). 0,01, :
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, i B = 22.11 %.
() r :
Pk - tk, Rk - , S = 1,2,3, n 1; j = 1,2, n 2, n 1 , n 2 . r < 1, . , r > 1, . , r NPV.
. ( i = 10 %). :
. , , , . , . , , . , 20 %, r A= 1,105, r B = 0,763. , , . , , . - i B- NPV NPV - i B. , , (. [ 6 ]).
, , , .
8.1. 10 (..) t = 0, 4 .. 2 20 .. 5 . NPV, i B , i = 10%.
8.2. : R = (-80, 10, 10, 20, 40, 30, 50), t = (0, 1, 2, 3, 4, 5, 6). PV , n ( ), i = 10%.
8.3. R = (-90, 10, 20, 30, 30, 40, 50), t = (0, 1, 2, 3, 4, 5, 6) NPV, (i = 10%).
8.4. 1000$ 500, 1000 200$ , , . 5 % . NPV, i = 10%? : NPV = 556$.
8.5. , 500 .. 800 .. . 715 .., 1100 .. 10%. : R A = 1,3; R B = 1,25.
8.6. NPV A NPV B .
8.7. i B., i = 10%
: A: f(0,31) > 0, f(0,33) < 0, i B = 31,2 %;
: f(0,16) > 0, f(0,18) < 0, i B = 17,1 %.
: 1: | 1.3; 1.5 |
2: | 2.1; 2.4 |
3: | 3.2; 3.4; 3.6; |
4: | 4.3; |
5: | 5.1; 5.3; 5.5; 5.8, 5.9 |
6: | 6.1; 6.4; |
7: 8: | 7.3; 7.6. 8.3; 8.6; 8.7 |
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1. .. . .: , 1995. 320.
2. .. . .: -, 1999. 247.
3. .., .. . .: - , 1994.
4. .., .. . .: , -, 1997. 176.
5. .. . .: " ", 1998. 144.
6. . . .: -, 1996. 432.
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