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4.1-Mt thit b gi 1 triu , hng nm c th gim bt c chi ph snxut l 400 ngn . Thit b c tui th l 5 nm nhng sau 3 nm vn hnhphi i tu vi chi ph c tnh l 500 ngn . Nu x nghip s dngMARR = 10% v phn tch theo tiu chun IRR th c hi u t ny c nggi khng ?
1 1
2 2
2
5
5 3
2
2 1
1 2
1.000.000 400.000 500.000 0
15% 12.
(1 IR ) 1 1W
(1
103,92
17% 32.446,81
15,5% 1
(1
0%
) )
R
IRR IRR IP
IRR PW
IRR PW
IRR
RR
PW
PIRR IRR IRR MARR
W PW
Vy c hi ny ng gi.
0 1 2 3 4 5
1.000.000 500.000
A= 400.000
4.2-Mt ngi u t bt ng sn mua li mt ti sn gi 60 triu v 17nm sau bn gi 210 triu . Tin thu l 800 ngn trong nm u, 900ngn trong nm th 2 v tng thm 10% hng nm k t sau cho n khibn ti sn ? Tnh gi tr IRR ca hot ng u t ny.
26
2 3 4
15 6
17 17
16
6
2
800.000 900.000 900.000 1,1 900.000 1,160 10 ...
1 (1 ) (1 ) (1 )
900.000 1,1 210 10
(1 ) (1 )
1,11
800.000 900.000 160 10 *
1,11 (1 )1
1
IRR IRR IRR IRRP
IRR IRR
IRR
IRR IRR
IR
W
PW
R
6
17
210 10
(1 )IRR
IRR1=6% => PW1=64012 IRR2=7% => PW2= -9869181IRR= IRR2 + (IRR1- IRR2)[ PW2/( PW2- PW1)]=6%
4.3-Tnh gi tr PW trong phm vi i = 10% n 80% ca chui dng tin tsau y, xc nh cc gi tr IRR.
Nm 0 1 2 3-6
CF1 (triu ) 500 -1.000 50 200
I(%) 10 20 30 40 50 60 70 80
PW
(triu
)
156,2 60,9 16,7 -0,08 -1,78 4,87 16,1 29.68
Ni suy ta c:
=> Ta c kt quIRR1 = 39,95%IRR2 = 52,68%
11 2 1
1 2
WIR ( ).
W W
PR i i i
P P
4.4-Mt nh my ru c d kin xy dng mt phn xng lm v chai.c lng s chai cn thit hng nm l 600.000 chai. u t ban u s l50 triu , thi gian lm vic d tnh l 20 nm, chi ph vn hnh hng nmkhong 7,5 triu , thu bo him 2,5 triu /nm. Hi nh my nn xydng phn xng hay nn mua chai t 1 Cng ty khc vi gi 30 /vchai? Dng phng php so snh PA theo IRR bit rng MARR = 12%.
Phng n A: u t phn xng lm v chai.- u t ban u: 50 triu .- Chi ph vn hnh + thu v bo him (hng nm): 10 triu .- Thi gian lm vic d tnh: 20 nm.- S chai cn thit: 600.000 chai/nm.
Phng n B: Mua chai t mt Cng ty khc.- u t ban u: 0 triu .
- Chi ph mua v chai (hng nm): = 18 triu .- Thi gian mua v chai: 20 nm.Do 2 phng n c thu nhp ging nhau nn ta gi s phng n c u t ban u nh hn l ng gi (phng n B).
Gii cu 4.4:
50 0 10 18 / , %,20 0 / , %,20 6,25 : PWC A B P A i P A iTa c
Vi i% = 15%
Vi i% = 16%
1 0,07465 PWC
2 2,5692 PWC
Ni suy: 0,07465
% 15% 16% 15% 15,03%0,07465 2,5692
i IRR
IRR MARR Vi th ta kt lun, phng n c u t ban u cao hn s l ng gi. Tc l ta chn phng n A: xy dng phn xng sn xut v chai.
4.5- Mt nh my sn xut chi tr em d kin mua mt thit b sn xutmi. C hai PA thit b cng nng sut X v Y c xem xt. Chi ph c tnh(tnh bng n v ngn ) nh sau:
Phng n X Y
Gi mua ban u
Chi ph vn hnh nm
Gi tr cn li
Tui th (nm)
12.000
3.000
0
12
21.000
1.200
1.500
12
Ngoi ra PA thit b X cn yu cu i tu mi 4 nm mt ln vi chi ph mi ln l 2.5 triu .a) Lp bng dng tin t rng.b) La chn PA thit b nu MARR = 12% theo phng n phn tch sut thua li.
Gii cu 4.5:
a) Bng dng tin t:
Nm X Y Y-X
0 -12.000 -21.000 -9.000
1-3 -3.000
-1.200
1.800
4-3.000
-2.500
1.800
2.500
5-7 -3.000 1.800
8-3.000
-2.500
1.800
2.500
9-11 -3.000 1.800
12 -3.000-1.200
+1.500
1.800
1.500
Gii cu 4.5:
b) Gi s PA X l ng gi.
- Xt (Y-X):
12
12 4 8 12
W 9000 1800.( / , %,12) 2500.( / , %,4)
2500.( / , %,8) 1500.( / , %,12)
(1 ) 1 1 1 10 9000 1800 2500 1500
(1 ) (1 ) (1 ) (1 )
25.5%
P P A i P F i
P F i P F i
i
i i i i i
i
Vy chn Y
4.6- Mt k s Cng ty thuc l mun phn tch RR ca hai PA my nggi theo gi tr hng nm. Chi ph theo n v ngn cho bng sau. Ngik s ang n o khng bit nn s dng gi tr MARR no, 8% hay 10%nm. Xt xem theo anh ta c phi thay i quyt nh la chn PA hay khngkhi MARR thay i, dng phng php phn tch theo gia s u t.
S liu c bn My A My B
u t ban u
Chi ph lao ng hng nm
Chi ph bo hnh hng nm
Gi tr cn li
Tui th (nm)
10.000
5.000
500
1.000
6
9.000
5.000
300
1.000
4
Gii:Phng n A: chn my APhng n B: chn my BDo 2 phng n c thu nhp ging nhau nn ta gi s phng n c u t ban u nh hn l ng gi (phng n B).
Gii cu 4.6:
Ta xt:
10 / , %,6 5,5 1 / , %,6
9 / , %,4 5,3 1 / , %,4 0
AWC A B A P i A F i
A P i A F i
10 / , %,6 9 / , %,4 / , %,6
/ , %,4 0,2
A P i A P i A F i
A F i
Vi i% = 30%
Vi i% = 40%
1 0,2872AWC
2 0,1747AWC
Ni suy:
0,2 0,2872
% 30% 40% 30% 37,75%0,1747 0,2872
i IRR
Vy vi c hai gi tr MARR = 8% v MARR = 10% th ngi k s ny khng cn phi thay i quyt nh. V phng n c chn l phng n A: chn my A.
4.7- Mt cng on trong dy chuyn lm tht hp yu cu dng nhng thitb ring r vi cc chc nng nh sau: nn, ct lt, cn v ng hp. Gi nhtt c cc thit b u c tui th l 6 nm v gi tr cn li SV = 0. Michc nng c 2 PA thit b nh sau (chi ph tnh bng triu )
Thit b
chc nng
Phng n I Phng n II
Chi ph
ban u
Chi ph
hng nm
Chi ph
ban u
Chi ph
hng nm
Chc nng nn
Chc nng ct lt
Chc nng cn
Chc nng ng hp
5
4
12
3
13
10
15
9
10
17
15
11
14
4
13
7
a) Nu MARR = 20% nm; la chn thit b cho mi chc nng theo IRR;b) Vi cc thit b chn phn (a), tnh u t ban u v chi ph vn hnhnm ca cng on sn xut.
Gii cu 4.7:
a) Nu MARR th chn PA2
Nu < MARR th chn PA1Thit b Loi chi
phPA1 PA2 PA2-PA1 Phng php ni
suy(%) La chn
PANn Ban u 5 10 10 5 = 5 -5-(-2)*
(1+)61
(1+)6= 0 32,68 PA2
Hng nm 13 11 11 13 = -2
Ct lt Ban u 4 17 17 4 = 11 -11-(-6)*(1+)61
(1+)6=0 49,71 PA2
Hng nm 10 4 4 10 = -6
Cn Ban u 12 15 15 12 = 3 -3-(-2)*(1+)61
(1+)6=0 63,20 PA2
Hng nm 15 13 13 15 = -2
ng hp Ban u 3 11 11 3 = 8 -8-(-2)*(1+)61
(1+)6=0 13,11 PA1
Hng nm 9 7 7 9 = -2
b) Da vo cu a, ta c:u t ban u ca d n l: PWC= 10 + 17 + 15 +3 =45 triuChi ph vn hnh hng nm: AWC = 11 + 4 +13 + 9 = 37 triu
4.8- PA u t A c chi ph ban u 20 triu v IRR(A) = 35% nm. PA u t B c cc thng s tng ng 30 triu v IRR(B) = 25% nm. Pht biu no trong cc pht biu sau y v RR() (tc gia u t 10 triu ) ng ?a) S ln hn 35% nm. b) Chnh xc bng 35% nm.c) Nm gia 25% v 35% nm. d) Chnh xc bng 25% nm.e) Nh hn 25% nm. f) Bng v cng.
Gi s gi tr cn li ca mi phng n bng vi u t ban u. Khi ta c bng sau:
Chi ph v thu nhp(triu ng)
Phng n A Phng n B B-A
u t ban u 20 30 10IRR 35% 25% ???Thu nhp nm rng 7 7.5 0.5
Khi : IRR()= 0.5/10 = 5%Vy : IRR() nh hn 25% nm. (A: e)
4.9- C 6 PA v tr p to h cha cp nc cho thnh ph c xemxt. Chi ph u t v thu nhp ch bng sau. Xem rng cng trnh c thphc v vnh vin, la chn v tr p trn quan im n thun kinh t nuMARR = 6% nm.
u t ban u ( triu )
Thu nhp nm ( triu )
Phng n v tr p
A B C D E F
6.000
350
8.000
420
3.000
125
10.000
400
5.000
350
11.000
700
Ta c bng sau:
Phng n v tr pC E EA EB ED EF
u t ban u (triu ) 3.000 5.000 1.000 3.000 5.000 6.000Thu nhp nm (triu ) 125 350 0 70 50 350
IRR() 4,17% 7% 0% 2,33% 1% 5,83%Gia s l ng gi? Khng C Khng Khng Khng Khng
Vy ta chn v tr p E
4.10- C 4 PA u t sau ang c xem xt nh gi.a) Nu cc PA l c lp, PA no s c la chn nu MARR = 15% ?b) Nu cc PA l loi tr nhau, PA no s c la chn nu MARR = 13% ?c) Nu cc PA l loi tr nhau, PA no s c la chn nu MARR = 30% ?
Phng n u t
ban u
(triu )
IRR ca
mi PA
(%)
IRR() khi so snh vi PA
A B C
A
B
C
D
40
75
100
200
29%
15%
16%
14%
1%
7%
10%
20%
30% 12%
Gii cu 4.10:
a) Nu cc phng n l c lp, vi MARR = 15%, ta s chn phng n A, B v C v c IRR > 15%.
b) Nu cc phng n l loi tr nhau, vi MARR = 13%.
- Phng n A c vn u t ban u nh nht. Ta li thy IRR(A-0) = 29% > MARR = 13%, tc l gia s ca phng n A so vi phng n 0 l ng gi, nn phng n A ng gi. Cc gia s ca B, C v D so vi A ln lt to ra IRR()
4.13- Dng c 4 loi ch s sut thu li phn tch cc c hi u t sauy, nu k = MARR = 10%, tui th ca cc d n u l 5 nm.
Chi ph v thu nhp
(triu )
Cc c h u t
A B C D E F
u t ban u
Thu nhp rng
hng nm
Gi tr cn li
8.0
2.0
-1.0
10.0
3.0
2.0
12.0
3.2
1.0
15.0
3.5
1.0
15.0
3.5
2
16.0
4.0
0
Gii cu 4.13:5
5 5
(1 ) 1 1* ( ): 8 2. 1. 0
.(1 ) (1 )
0.75540.01 0.004. 4.4%
0.7554 0.1246
iPA A
i i i
i
Chi ph v thu
nhp (triu )
B C-B D-B E-B F-B
u t ban u
Thu nhp nm
Gi tr cn li
IRR
Gia s l ng gi
10
3
2
19,1%
C
2
0,2
-1
-185%
Khng
5
0,5
-1
-171%
Khng
5
0,5
0
-19,22%
Khng
6
1
-2
-45,2%
Khng
PW
A B C D E F
-1,04 2,61 0,75 -1,11 -0,49 -0,83
Vy PA(B) l PA c chn