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