, , , .
: , , , , . , , "" . , , :
(14).
PV - , PMT - , n - , , i - . (14), :
(15).
,
(16)
.
(15) , . , , (15) , .
6. 1000 . 5 . , 12%
:
(20), (21) , . PMT m ( ),
(17).
n n * m .
(17)
(18).
i - , , .
7. 6, . 1000 , , 250 . . 5 . 12%. .
: : PMT = 250, i = 0.12, n = 5, m = 4.
, , 6, 1000 . . , , , .
j c m , (23) :
(19)
( n * m ),
(20).
8. 7 j = 12% (m = 4).
: : PMT = 250, j = 0.12, n = 5, m = 4.
5:
1. 35 . . .,
18 . . . ( ).
:
a) NPV; ) IRR; ) PI; ) PP.
|
|
2. 250 . . . 30 .
. :, 9,5 . . . - 5 , = 10 %.
:
a) NPV; ) IRR; ) PI; ) PP.
3. ,
.
1 2 | -23616 -23616 | 10000 0 | 10000 5000 | 10000 10000 | 10000 32675 | ||
4. : | |||||||
-1600 | - 10000 | ||||||
IRR .
5. .
I | P1 | P2 | PV | NPV | IR | |
-100 | ||||||
-1000 |
10%
6.
I | |||||||
5%.
7. 250 . . . 30 . . ., 9,5 . . ., - 5 , = 10 %.
: a) NPV; ) IRR; ) PI
8. 35 . . .,
18 . . . : a) NPV;)IRR; ) PI
9. 3 . - 10000 ., 5000, 4000 3000 . , 10%.
10. 150 . .
- 5 .
- 10 . . 25
. . . ?
?
11. , 160000 .,
30 000 . 15 .
,
- 15%.
12. , 150000 .,
30 000 . 15 .
, 16-
10 000 . NPV,
, - 8%.
13. , 15 , 150000 .
5 , 10
50 000 . ,
15%?
|
|
, , , Net Present Value, NPV. ( ) , . ,
t= Ft
NPV = å (1+r)t , (1)
t=0
ft - t, - .
, ( ), , ) 0, (Cft) t, , :
_
t= Ft t= (C0)t
NPV = å (1+r)t - å (1+r)t, (2)
t=0 t=0
NPV .
NPV , :
NPV > 0 ;
NPV < 0 .
() (); , IRR (internal rate of return) - , , .
IRR , , , - .
: , . , .
:
NPV = 0
t= (CF)t t= (C0)t
å * (1+r)t +å * (1+r)t = 0 (3)
t=0 t=0
. NPV = f(r)
f(r1) ___
IRR = r1 + f(r1) - f(r2) * (r1 - r2) (4)
r1 - , f(r1) > 0;
r2 - , f(r2) < 0.
, r1 r2 - ( ).
6:
1 :
1- | 2- | 3- | 4- | 5- | |
, ... | 6 000 | - | - | - | - |
, ... | - | 5 000 | 6 000 | 7 000 | 8 000 |
, % | - | ||||
, , ... | - | 1 000 | 1 100 | 1 200 | 2 400 |
.
2 :
1- | 2- | 3- | 4- | 5- | |
, ... | 7 000 | - | - | - | - |
, ... | - | 5 000 | 6 000 | 8 000 | 10 000 |
, % | - | ||||
, , ... | - | 1 000 | 1 100 | 1 500 | 1 800 |
.
3 :
1- | 2- | 3- | 4- | 5- | |
, ... | 8 000 | - | - | - | - |
, ... | - | 6 000 | 7 000 | 8 000 | 9 000 |
, % | - | ||||
, , ... | - | 1 000 | 1 100 | 1 300 | 1 500 |
.
|
|
4 . , .
1 | 2 | |
, . . | ||
, . . | ||
, . . | 2 280 | 2 300 |
, . . | ||
, . . | 2 070 | |
, . . |
. , , 20%.
, .
5 . .
1 | 2 | |
, . . | 1 840 | 2 000 |
, . . . | ||
, . . | 1 750 3 870 | 3 870 |
, . . | ||
, . . | 1 520 3 430 | 1 520 3 330 |
, . . |
, : , 11%.
.
( , (payback period)).
=