: , .
, CF 0, CF 1, , CFn. (cash flow CF). CFt () () . , CFt , .
:
1. FV (future value) (FV = CFn).
2. PV (present value) () (PV = CF 0).
3. CFt (cash flow) t.
4. r (interest rate) .
5. n ( ) ( , . . 1 , n ).
, , .
() , n (, ).
, , . , :
{- PV; FV } ; ( - PV), ( + FV);
{ PV; - FV } ; ( + PV), ( - FV).
¨ . . , . . , .
MS Excel . , 5 (. ).
|
|
FV, PV, r, n (CFt = 0). . .
¨ . (n ³1), (n <1), n .
1
10000 . . 3 . 10% . . ?
: PV = 10000, r = 10% n = 3 .
:
FV = PV (1+ r) n. (2.12)
, :
FV = 10000 ´ (1+10%)3 = 10000 ´ 1,13 = 13310 (. .)
(2.12) .
¨ . (2.12) n, .
(2.12) PV, r n. () :
. (2.13)
(2.13) .
r n (2.12) , ( n) n - ( r).
FV, PV, r n MS Excel , :
FV;
PV;
r;
n.
, - :
FV;
PV;
r;
n;
{0; 1} : 1 ( ) 0 ( ). , 0;
CFt ( 0).
¨ :
) , 0;
) PV FV :
{- PV; FV } , (, );
{ PV; - FV } , (, );
|
|
) , (, ). - , .
. 2.3.15 1 .
A | B | C | D | E | |
1 | |||||
PV | r | n | FV | ? | |
-10000,00 | 10% | 13 310,00 | FV | ||
-10000,00 | 10% | 13310,00 | PV | ||
-10000,00 | 10% | 13310,00 | r | ||
-10000,00 | 10% | 13310,00 | n |
. 2.3.15
D3 :
=(B3;C3;0;A3;0),
A4:
=(B4;C4;;D4),
B5:
=(C5;;A5;D5;0),
C6:
=(B6;;A6;D6;0).
( , , ). (2.12)? 2.
2
, 1, 2 ( ).
(3 ), 2 ´ 3 = 6. ( 5%). 2 :
FV = PV (1+ r /2)2´3 = 10000 ´ (1+5%)6 =
10000 ´ 1,056 = 13400,96 (. .).
2, :
, (2.14)
m .
m = 1 (2.14) (2.12).
¨ . (3) m ´ n, .
. 2.3.16 2.
A | B | C | D | E | F | |
2 | ||||||
PV | r | n | m | FV | ||
-10000,00 | 10% | 13 310,00 | ||||
-10000,00 | 10% | 13 400,96 | 2 ( ) | |||
-10000,00 | 10% | 13 448,89 | 4 () | |||
-10000,00 | 10% | 13 481,82 | 12 () |
. 2.3.16
E11 :
=(B11/D11;C11*D11;;A11;0),
(E12:E14) .
, , . .
MS Excel, , (, , , ).
, , , .