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1.
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t+1 t
-- ---------------------------------------------------------
,
,
().
PV A1 A2 A3
PV1
PV2
" r "
PV3
+-----------+------------+-------------+-------------------
0 1 2 3
1 = 0 + 0*r 1
1 = 0(1+r) ----> 0 = --------
(1+r)
PV1(0) = 1 * -----
(1+r)
2
2 = 1 +1*r2 ----> 1 = --------
(1+r2)
1=0(1+r1), 0(1+r)=A2/(1+r2)
0= 2/(1+r1)(1+r2) r1=r2
0= 2(1+r)^2
PV2(0) = 2/(1+r)^2
PV= PV1+PV2= A1/(1+r1)+A2/(1+r2)^2
.......................................
------------------------
PV= n/(1+rn)^n
L------------------------
= -
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: PV= C/(1+r) + C/(1+r)^2 +C/(1+r)^3 +...
,
a=C/(1+r); x=1/(1+r)
PV= a(1 + x + x^2 + x^3 +...)
x
PV*x=a(x +x^2 + x^3 +...)
,
PV(1-x)=a, PV=a/(1-x)
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------------
r = C/PV PV= C/r..........(1)
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DIV1 + P1 - P0
= r = ---------------
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DIV1 DIV1
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"r" :
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( PV ,.,)
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2.3.
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EPS -
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P0
, -
,..:
C1 C2 C3 Ct
NPV =C0 + -------- + --------- + --------- +...+--------- =0
|
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1 + IRR (1+IRR)^2 (1+IRR)^3 (1+IRR)^t
:
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4,000 ; C1=2,000
C2=4000. (IRR):
2000 4000
NPV = 0 = -4000+------ +---------
1+IRR (1+IRR)^2
. IRR=0,NPV=2000;
IRR=0.5,NPV=-889; :
NPV
.
2000+
.
1000+
L-+--+--+--+--+-----------+----
10 20 30.40 50 100 %
.
.
,
1. ?
2. .
3. .
4. .
2.4.
PV
= ----.
-C0
,
1
:
IRR NPV
C0 C1 C2 C3 4 (%) r=10%
--------------------------------------------------------------
1 -1000 +1500 - - +50 +364
+1000 -1500 - - +50 -364
+1000 -3600 +4320 -1738 +20 -0.75
-------------------------------------------------------------
2 -4000 +25000 -25000 25 400 -1934
+1000 -3000 +2500 +339
-------------------------------------------------------------
3 -10000 +20000 100 8182
-20000 +35000 75 11818
- -10000 +15000 50 3636
------------------------------------------------------
-9000 +6000 +5000 +4000 - 33 3592
-9000 +1800 +1800 =3=4=5 20 9000
0(!) -6000 +1200 =3=4=5 20 6000
- 0 -4200 -3200 -2200 1800 15.6 5.408
--------------------------------------------------------------
NPV
C0 C1 .
r=10% r=10%
-------------------------------------------------------
-100 +200 182 1.82 82
-10000 +15000 13636 1.82 3636
- -9900 +14800 13454 1.36 3554
------------------------------------------------------------
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