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bi tp phn tch

bi tp phn tch

Phn 1: Bi tp v dng tin

Bi 1: Bn mun n khi v hu (15 nm na) ngoi tin lng hu bnh qun mi thng bn c thm 1 tr. ng tiu xi. T nay n lc v hu mi nm bn phi gi vo tit kim bao nhiu lc v hu khon tin dnh dm ca bn c mc sinh li tho mn mun ca bn. G/s trong 15 nm ti t nc trong giai on pht trin nn l/s bnh qun mc cao l 9% nm, cn t khi bn v hu kinh t pht trin n nh nn l/s ch mc 0,5% thng.

Bi gii: y l bi ton tnh gi tr hin ti ca dng thu nhp trong tng lai.

B1: Cn phi tnh c s tin cn phi c trong tng lai. Vi l/s 0,5% thng, nhn c 1 tr/thng th cn c ST l: 1/0,5% = 200tr.

B2: Cng thc GT hin ti ca mt ng trong tng lai l: PV1 = FVA1 (n,r)

GT hin ti ca C ng trong tng lai s l: PV(C) = C ( FVA1 (n, r)

200 = C ( FVA1 (15,9%) (xem ph lc C SGK)

200 = c ( 29,361 ( C = 200/29,631 = 6,811757 tr.

Bi 2: Gi tit kim 8.000 USD trong 15 nm vi l/s 15% sau 15 nm c bao nhiu tin?

Bi gii: FV1 (n, r) = PV1 (1 + r)n

= 8.000 ( (1 + r)15 = 8.000 ( 8.137 = 65.096 USD (xem ph lc A SGK)

Phn 2: Bi tp v tri phiu

Bi 1: (TP l/sut chit khu):

Cng tri gio dc c MG l 200.000, thi gian o hn l 4 nm, l/s gp 40%/4 nm, cn 3 nm na o hn ang bn gi 220.000 , l/s tit kim di hn hai nm ang l 8%/nm. Trn quan im gi tr TP, c nn mua TP trn khng? V sao?

Bi gii: xem xt c nn mua TP trn hay khng th phi ca GT hin ti ca khon thu nhp khi TP o hn vi gi bn hin ti.

i vi cc bi TP cn phi v dng tin ra.

1 ------ 2 ------ 3 ------ 4

Po P1 P2

P3 = 200 + 80

Phn thu nhp khi o hn = MT + tin li = 200.000 + 40% ( 200.000 = 280.000

Po = 280.000 ( PV1(3,8%) (xem ph lc bng B SGK)

Po = 280 ( 0.794 = 222,32 > 220.000 ( nn mua

Bi 2: (TP l/sut coupon): Tri phiu CP pht hnh vo ngy 25/11/05, F = 100, C = 8, M = 5, l/s = 9%.

Vit 3 cng thc nh gi TP vo ngy hm nay (10/5/07)

8888 + 100

15/11/0525/11/0625/11/0725/11/0825/11/0925/11/10

10/5/07

P-1P0P1P2P3P4

Tnh t ngy 10/5/07 n ngy 25/11/07 l: 198 ngy. t ( = 198/365.

Cch 1:

Cch 2:

Cch 3:

Bi 3: Mt khch hng ang mun u t vo TP A c cc thng s sau:

- Thi gian o hn n = 4 nm, f = 100

- Tri phiu zero coupon

- Li sut yu cu ca khch hng l r = 9%

Bn hy gip khch hng xc nh:

a) Gi TP m nh NT mua.

b) Thi gian o hn bnh qun (D)

c) Thi gian o hn bnh qun iu chnh (MD)

d) li K

e) Gi TP bin i bao nhiu % theo D v K nu li sut yu cu ca khch hng tng 1%.

Gii:

a) Tnh gi ca TP ls chit khu

Po = F/(1 + r)n = 100/1.094 = 100 ( 0.708 = 70.8

b) Thi gian o hn bnh qun ca TP l/s chit khu = tg o hn ca TP = 4 nm.

c) MD = -D/1 + r = -4/1.09 = -3.67.

d) li

y l TP l/s CK nn C = 0

c) Gi TP thay i theo D v K theo cng thc sau:

dP = dP (K) + dP (D)

Khi l/s tng 1% ta c cng thc:

dP = -0.0358

Khi L/s tng 1% gi TP gim 3.58%.

Bi 4 (danh mc 2 TP)

Mt nh T c khon tin 10 tr. ng v d nh u t trong thi hn 2.5 nm vo danh mc c cc TP nh sau:

- TP A: TP CK, thi hn o hn 3 nm, F = 100 ng ng

- TP P: TP c C = 6%, thi hn o hn 2 nm, F = 100 ng ng

L/s thi trng r = 10%. Bn hy xc nh gip NT mt danh mc 2 TP nu trn t mc tiu ra v phng tranh c ri ro.

Bi gii:

Gi WA, WB l t trng u t TP A, TP B.

DA, DB l thi gian o hn bnh qun ca A, B.

Ta c h pt:

WA + WB = 1

DA WA + DB WB = 2,5

B1: Tnh thi gian o hn bnh qun (D)

DA = 3 (TP chit khu)

/v TP coupon: CT:

tnh c D, cn phi tnh P ti thi im hin ti

B2: Gii h pt:

Thay s vo ta c:

WA + WB = 1

3 WA + 1.94 WB = 2.5

WB = 0.47

GT u t vo A l: 0.53 ( 10TR = 5.3TR ( SL = 5.3/75.131 = 754

GT u t vo B l: 0.47 ( 10TR = 4.7TR ( SL = 4.7/93.057 = 505

Bi 5: (im v ngn hng): Mt ngn hng c tng s vn l 200 t ng, trong 30 t ng vn t c. Vn i vay c thi hn o hn bnh qun l 6 thng. G NH l ngi kinh doanh mo him nn ly ton b s vn vay mua t hp TP c thi gian o hn bnh qun l 15 nm. L/s chit khu ca th trng l 7%. Hy xc nh im v ca Ngn hng.

Bi gii: y l bi ton xc nh l/s thay i bao nhiu th NH mt k/n thanh ton, c ngha khi vn t c ca Ngn hng = 0 (hay TS n = Tng ti sn)

Ta c cc d kin nh sau:

PA = vn T danh mc (vn t c + vn vay) = 200 t.

PL : vn vay = 170 t, r = 7%; DL: thi hn vay = 6 thng = 0.5 nm

DA thi hn u t = 15 nm

p dng cng thc:

$ vi MD l thi gian o hn bnh qun iu chnh l/s, P l gi TP.

- Khi l/s thay i 1% th

Ti sn n thay i:

$ t

Tng ti sn thay i:

$ t

- Khi l/s thay i (r:

Ti sn n: 170 - 79.439 (r

Tng ti sn: 200 - 79.439 (r

NH mt kh nng thanh ton khi GT TS n = GT TTS

170 - 79.439 (r = 200 - 79.439 (r ( (r = 1.1%

Nh vy khi l/s tng 1.1% hay l/s n 7% + 1.1% = 8.1% th NH mt kh nng thanh ton.

Phn 3: Bi tp v c tc v c phiu

Bi 1: Cng ty A c li sut yu cu l 16% v c tc l 3.00. Nu GT hin ti l 55.000 /CP, t l tng trng c tc l bao nhiu?

Ta c cc d liu: r = 16%, Do = 3.000, Po = 55.000. Tnh g.

Xut pht t cng thc M hnh Gordon:

(

hay g = 10%.

Bi 2: T l tng trng c tc ca 1 cng ty 10% v duy tr trong tng lai. T l chit khu dng thu nhp l 15%. P/E l 5,5%. D bo kh nng tr c tc:

Ta c cc d liu: P/E = 5.5 g = 105 = 0.1 r = 15%. Tnh D/E = 1 - b (thu nhp li).

Khi cng ty c g tng trng u, p dng M hnh Gordon:

(

hay kh nng tr c tc ca cng ty l 25%.

Bi 3: Mt cng ty c t l n so vi tng TS l 0,4, tng n l 200 tr, li rng sau thu l 30 tr. Tnh ROE.

Ta c cc d liu: Tng n / TTS = 0.4, Tng n = 200, LN rng = 30

Cng thc tnh:

hay 10%.

Bi 4: Mt ngn hng c tng TS l 200 t, trong vn vay 150 t, li thun 15 t. T l c tc d kin l 3 t. Hy d bo tng trng c tc trong tng lai.

g = ROE ( b

b l t l thu nhp li

Cng th tnh:

g = 0.3 ( 0.8 = 0.24 hay 24%.

Bi 5: T l tng trng c tch ca 1 cng ty g = 11,25%, h s hon vn CSH ROE = 15%. D bo kh nng tr c tc.

Kh nng tr c tc = 1 - b

T cng thc g = ROE ( b ( b = g/ROE = 11.25/15 = 0.75

( 1-b = 0.25 hay 25%.

Bi 6: Cng ty A d on chia c tc 3 USD trong vng 4 nm ti, sau tc tng trng c tc l 7,5% hng nm. G/s l/s chit khu l 12%. Hy nh gi CP ny.

Tnh theo phng php chit khu lung c tc kt hp M hnh Gordon.

M hnh Gordon:

Po = Pv(Dt) + PV(Pn)

Po = Pv(D4) + PV(P4)

Bi 7: Cng ty XYZ c mc tng trng 3 nm u l g1 = g2 = g3 = 2,5%; nhng nm tip theo c tc tng trng c tc n nh mc 7%. C tc ln tr gn nht l 1.2 USD. L/s yu cu ca NT l 12,4%. Hy xc nh gi CP m NT chp nhn.

Tnh theo phng php chit khu lung c tc kt hp M hnh Gordon.

Po = Pv(D3) + PV(P3)

( Cn phi tnh DiVt cho 2 giai on c tc tng trng khc nhau 3 nm u tng trng 2,5%

DiV1 = DiV0 (1 + g1)1 = 1.12 ( 1.0251

DiV2 = DiV0 (1 + g2)2 = 1.12 ( 1.0252

DiV3 = DiV0 (1 + g3)3 = 1.12 ( 1.0253

Bt u nm th 4 tc tng trng 7%

DiV4 = DiV3 (1 + g4) = 1.12 ( 1.0253 ( 1.07

(

Phn 4: Bi tp v ri ro v danh mc u t

Bi 1: (Ri ro ca 1CP): Gi CP REE hin ti l 28$, d on CP trong 1 nm sau, bng phng php iu tra mt s chuyn gia phn tch chng khon ngi ta c t liu nh sau: Hy d bo mc ri ro u t vo REE vi t liu .......................... kt qu.

Nhc li l thuyt

*> y l d on ri ro theo s liu thng k, nn vic tnh ton phi theo nguyn l thng k.

( So snh theo 1 k gc.

Nu l s liu trong qu kh: xc nh mc sinh li bnh qun (dng phng php bnh qun s hc) v s dng n xc nh mc chnh lch ca tng nm so vi mc bnh qun.

Nu l s liu d bo: xc nh mc sinh li k vng bng phng php bnh qun gia quyn v s dng n xc nh mc chnh lch ca tng nm so vi mc k vng.

**> Theo nh ngha v ri ro trong u t CK: l s dao ng c hai chiu trong mc sinh li nn ngi ta bnh phng cc chnh lch trit tiu s m v loi b vic tng cc chnh lch bng khng.

Nu s liu qu kh:

Nu s liu tng lai :

Trong : Ri: Ri ro so vi gi hin ti

Wi l xc sut;

C 2 cch tnh Ri:

C1:Tnh theo s tuyt i Ri = Pi - Po

C2:Tnh theo s tng i Ri = (Pi - Po)/Po

C1

Gi PiS ngWiRiRiWi

2150.1-7-0.7

28100.200

30200.420.8

32100.240.8

3650.180.8

Cng501.7

Kt qu ny cho thy, mc ri ro bnh qun d on l 1.7 $

C2:

Gi PiS ngWiRi %RiWi

2150.1-0.25-0.0250

28100.20.00-

30200.40.070.0286

32100.20.140.0286

3650.10.290.0286

Cng500.0607

Kt qu ny cho thy, mc ri ro bnh qun d on l 6.07%

Thay s vo ta c:

(2 = 0.1(-7-1.7)2 + 0.2(0-1.7)2 +0.4(2-1.7)2 +0.1(8-1.7)2

Bi 2: (Danh mc 2 CP) C phiu A v B c xc sut mc sinh li nh sau cho cc nm ti

Tnh trng kinh t Xc xut WiKh nng sinh li ca A % EAKh nng sinh li ca B % EB

Tng trng mc 10.21420

Tng trng mc 20.4-5-2

Tng trng mc 30.4109

a) Tnh mc sinh li mong i ca A v B.

b) nh gi ri ro u t cho mi CP

c) Tnh tch sai mong i ca li nhun A v B

d) A v B c th kt hp gim thiu ri ro trong danh mc u t khng? V sao?

a)

Er(A) = 0.2 ( 14 + 0.4 ( (-5) + 0.4 ( 10 = 4.8

Er(B) = 0.2 ( 20 + 0.4 ( (-2) + 0.4 ( 9 = 6.8

b)

c)

= 0,2((14-4,8)(20-6,8) + 0,4(-5-4.8)(-2-6.8) + 0.4(-5-4.8)(-2-6.8) +

+ 0.4(10-4.8)(9-6.8) = 63.36

d) c th kt hp gim thiu ri ro nhng hiu qu khng cao v gn bng 1.

Bi 3: Bn ang xem xt u t vo mt CP c li sut mong i l 14%, l/s TP kho bc l 7%, h s ri ro ( ca c phiu ang xem xt l 2, mc b ri ro ca CP l 4%. Bn c th u t vo CP ny khng? V sao?

Rf = 7% ; RM - Rf = 4 ; ( = 2

RA = Fr + ((RM - Rf) = 7 + 2 ( 4 = 15% > li sut mong i 14% ( khng nn T.

Bi 4: (danh mc ri ro + phi ri ro)

Qu u t VF1 d kin c danh mc u t nh sau:

- Chng khon nim yt: 20% vn (a)

- Chng khon cha nim yt: 15% vn (b)

- Tri phiu chnh ph: 55% (c)

- S vn cn li u t khc (d)

Gi s ta c thng tin v ri ro nh sau: (a = 8% ; (b = 12%; (d = 15% v cc thng tin v tch sai nh sau: Cov(a,b) = 96, cov(a,c) = 0,

cov(a,d) = -110; cov(b,c) = -140; cov(c,d) = 0

Hy d bo ri ro ca VF1 theo cc t liu gi nh trn.

Wi(i

a0.20.08

b0.150.12

c0.550

d0.10.15

Cov(i,j) = ( (i(j

Cov(a,b) = 96, cov(a,c) = 0, cov(a,d) = -110

Cov(b,c) = 0. cov(b,d) = -140

cov(c,d) = 0

p dng cng thc:

Thay s v ta c:

Bi 5: Ngn hng ca bn c ngha v tr n theo thi hn v gi tr theo bng sau:

SauLng tin cn tr n

1 nm 10,000,000

2 nm 40,000,000

3 nm 38,000,000

4 nm 60,000,000

tn dng ngun vn ngn hng nh dng chin lc u t vo danh mc TP vi cc loi TP hin c nh sau:

TP coupon 1 nm c C = 9%, F = 100.000

TP chit khu 2 nm c C = 0, F = 100.000

TP coupon 3 nm c C = 8%, F = 100.000

TP zero coupon 4 nm c F = 100.000

Bn hy gip lnh o xc nh mt danh mc u t sao cho tng tin ch ra cho danh mc ny l b nht (ch yu cu lp bi ton), bit r = 7%.

Cn phi v lung tin cho tng nm

x1 109

x2 100

x3 8 8 108

x4 100

Tnh gi ca mi loi TP

P1 = 109/1.07 = 101.87

P2 = 100/1.072 = 87.34

P3 = 8/1.07 + 8/1.073 = 102.62

P4 = 100/1.074 = 76.29

Ta c h pt: tm x1, x2, x3, x4 tho mn: 109x1 + 8x3 = 20.000

102x2 + 8x3 = 40.000 108x3 = 38.000 100x4 = 60.000 v

101.87x1 + 102.62x3 + 76.29x4 min.

BI TP TNG HP

Cu 1: Sau 15 nm na bn v hu, ngoi tin lng hu bn mun c thm bnh qun mi thng 3 tr t tin gi tit kim tiu xi. Hin ti bn cha c ng no d tr. Trong 15 nm ti nn kinh t trong thi k pht trin nhanh vi li sut tin gi t mc 9% nm v k t khi bn v hu li sut tin gi ny ch t 6% nm. Nu bn mun t mc tiu trn th t nay, hng nm bn phi b ra 1 khon tit kim l bao nhiu tin?

TL: Gi khon tin l C.

Hng nm cho n khi v hu, bn s b C vo TK dng gi. Trong thi gian ny, li sut tin gi t 9%/nm. Nh vy, n khi v hu, bn s c 1 khon tin l C. FVA1 (15,9%).

Khi v hu, hng thng bn tiu 3tr. Nh vy 1 nm bn tiu 36tr.

Bn khng th d on bn sng c bao lu khi v hu ( coi n ( (.

Vo thi im ny, li sut t 6%/nm

Gi tr ca khon tin ti thi im v hu l 36 tr/6%

Nh vy: C ( 29.361 = 600 tr ( C = 20.435.272 .

Cu 2: Mt ngn hng c phn c tng ti sn l 200 t ng, trong vn vay l 150 t ng. Li thun ca NH nm nay c th l 20 t ng. C tc d kin chi l 3 t ng. Bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin .

TL: g = ROE ( (1 - DIV/EPS)

ROE = LN/ (Tng vn - vn vay) = 0.4

g = 0.4 ( (1 - 3/20) = 0.34 ( g = 34%.

Cu 3: Gi s ngn hng bn ang s hu 1 lng tri phiu chnh ph, k hiu CP1 - 0102 pht hnh ngy 18/1/2002. Gim c ca bn ang c bn chng vo ngy hm bn lm bi thi (nm nay khng phi nm nhun 23/3/2007). Bit rng F = 100.000; C = 7.4%; Mc = 10 nm; li sut di hn chit khu l 8.4%. Bn hy gip G ca mnh nh gi Tp trn (ch cn vit 3 cng thc nh gi)

(v hnh)

T 18/1/07 - 23/3/07 c 65 ngy.

Gi

1. CK trc tip

2. V P1 trc

Trong :

3. V P1 trc

P0 = P-1 ( 1.084(

Trong :

Cu 4: Cng tri gio dc c mnh gi l 500.000. Thi gian o hn l 5 nm, c li sut gp l 40%/5 nm cn 2 nm na o hn ang bn gi 350.000, li sut tit kim di hn 2 nm ang l 8%/nm. Trn quan im li sut Tp bng li sut tit kim 2 nm th c mua TP trn c khng? V sao?

TL: Mua, v:

C = 6,96% ( 500.000 = 34.800

Gi TP ti thi im hin ti l:

Nh vy TT ang bn r hn gi tr thc ca TP ( Nn mua.

Cu 5: Gi s ch s VN index hin l 1100 im, d on tr gi ca ch s ny vo thng sau, bng PP iu tra mt s chuyn gia phn tch chng khon, ngi ta c t liu nh sau:

VN - Index sau 1 nm S ngi d on

16005

150010

140010

130010

120025

110020

100010

90010

a. Hy d bo mc sinh li k vng khi u t vo Vn-Index

b. Hy d bo mc ri ro u t vo VN - Index

VnindexS ngi d onPiRiPiRiRi -

(Ri - )Pi(Ri - )2

160050.050.4550.02275

1500100.10.3640.0364

1400100.10.2730.0273

1300100.10.18220.0182

1200250.250.0910.02275

1100200.200

1000100.1-0.091-0.0091

900100.1-0.182-0.0182

(10010.1001

Cu 6: Ngn hng ca bn c ngha v tr n theo thi hn v gi tr theo bng sau:

SauLng tin cn tr n

1 nm 12.000.000

2 nm 20.000.000

3 nm 18.000.000

4 nm 40.000.000

tn dng ngun vn, NH nh dng chin lc u t vo DM tri phiu vi cc loi tri phiu hin c nh sau:

TP coupon 1 nm c C = 9%, F = 100.000

TP chit khu 2 nm F = 100.000

TP coupon 3 nm c C = 10%, F = 100.000

TP zero coupon 4 nm c F = 100.000

T l CK l 9%.

Bn hy gip lnh o xc nh 1 DM u t sao cho tng s tin chi ra cho DM ny l b nht (ch yu cu lp bi ton)

TL: Gi vic u t vo mi TP ln lt l z1, x2, x3, x4

TPLN 1 nm LN 2 nm LN 3 nm LN 4 nm Gi TP

1107.00098.165

20100.00084.168

310.00010.000110.000102.532

4000100.00070.843

98.165 x1 + 84.168 x2 + 105.532 x3 + 70.843 x4 ( min

107 x1+

10.000 x3

= 12.000.000

100.000 x2 + 10.000 x3

= 20.000.000

110 x3

= 18.000.000

100.000 x4 = 40.000.000

Cu 7: Cng ty CP XYZ s c mc tng trng c tc trong 4 nm tip theo l 20%/nm. Nhng nm sau c tc tng trng c tc n nh mc 7%. C tc va tr l 35. Li sut yu cu ca NT vi CP ny l 15%. Hy xc nh gi CP ny 4 nm sau.

TL:g = 20%

g5 = 7%

DIV0 = 3$

r = 15%

Cu 8: Khi vo trang web http://www.investinginbonds.com v thay cc thng s ca TP quc t do VN va pht hnh th nhn c cc thng tin sau (gi TP ny l 98.228$)

- YTM: 7.13 (li sut o hn bnh qun)

- Duration: 7.525 (thi gian o hn bnh qun)

- Convexity: 64.953 ( li)

1. Hy tnh thi gian o hn bnh qun iu chnh ca TP ny

2. Nu li sut TT tng 1% th gi TP gim bao nhiu $?

TL:P = 98.228

r = 7,13%

D = 7,525

K = 64,953

a) Thi gian o hn bnh qun iu chnh MD = -D/(1 + r) = 7.024

b) dP/P(MD) = -MD ( dr

dP/P (K) = 1/2 K (dr)2

% thay i gi = -MD ( dr + 1/2 K (dr)2 = -0.06699 ( -6.699%

Nh vy, nu LSTT tng 1% th gi TP gim 6580$

Cu 9: Trn TT c 2 loi CK vi thng s nh sau:

Xc xut60%40%

Li sut CK A20%4%

Li sut CK B2%24%

Bn hy xc nh li sut k vng v ri ro u t vo 2 CK trn theo cc phng n nh sau:

a. 100% vo CK A

b. 100% vo CK B

c. 50% vo A v 50% vo B

Bn c nhn xt g khng v kt qu trn?

PA1:100% vo A:

E(r) = 0,6 ( 20 + 04 ( 4 = 13.6%

(2 = 0,6 ( (20 - 13.6)2 + 0.4 ( (4 - 13.6)2 = 61.44

( = = 7.84%

PA2: 100% vo B:

E(r) = 0,6 ( 2 + 04 ( 24 = 10.8%

(2 = 0,6 ( (2 - 10.8)2 + 0.4 ( (24 - 10.8)2 = 116.16

( = = 10.78%

PA3: 50% vo A, 50% vo B:

EAB = EA WA + EB WB = 12.2%

COVAB = 0.6 (20 - 13.6) (2 - 10.8) + 0.4 (4 - 13.6) (24 - 10.8) = -84.48

KL: PA3, 1 na u t vo A, 1 na u t vo B l c li nht v li sut gim khng nhiu nhng ri ro li gim ng k.

Cu 10: Gi s bn mua c phiu BT6 vo ngy 26/7/2006 vi gi 42,8 ngn ng v sau n ngy 31/7 l ngy giao dch khng hng quyn mua trong t pht hnh mi vi t l 5 : 1 (5 c phiu c mua 1 c phiu mi vi gi 33,6 ngn ng). Gi CP ngy vo phin trc 13/7 l 45 ngn ng. Gi CP ny vo ngy 4/10 l 55 ngn ng. Bn hy tnh t sut sinh li ca bn trong thi gian trn (26/7 ( 4/10) khi u t vo BT6. Bit rng s liu trn l s liu thc v trong thi gian BT 6 c tr c tc 800 cho mt CP.

Li gii

Po = 42,8 ng

P1 = 55 ng

DIV = 800

Quyn mua c phiu = 45 - 33,6 ng = 11,4 ng

T sut sinh li = (Div + (P1 - Po) + quyn mua CP)/Po = 2.4400/45.800 = 57%

Cu 11: Gi s NH ca bn c VTC l 500 t v vn vay l 190, vn vay c thi gian o hn bnh qun l 6 thng. Gi s G NH ny kinh doanh mo him v dng tt c vn trn cho vay u t cc danh mc u t di hn c thi gian o hn bnh qun D = 15 nm. Li sut hin ti l 8%. Hy xc nh im v ca ngn hng ny.

Cu12: Khi no trang Web http:www.investinginbonds.com/calcs/tipscalulator v thay cc thng s ca TP quc t do VN va pht hnh, th nhn c cc thng tin sau: (Gi TP ny l 98,228$).

- YTM: 7,13 (li sut o hn bnh qun)

- Duration: 7,525 (thi gian o hn bnh qun)

- Convexity: 64,953 ( li)


2. Nu li sut thng tng 1% th gi TP gim bao nhiu $?

Li gii:

P = 98,228

dy = 1%

YTM = 7,13%

MD = 7,525

li = 64,953

1. MoD = MD/(1+YTM)

2. % thay i gi = -MoD ( dy + 1/2 li ( (dy)2

Hoc D = MoD * gi (PO) = X

Nu li sut th trng tng 1% th gi TP gim X

Cu 13: Ngn hng d kin cng b li sut gi tit kim tr sau l 11% nm. Nu p dng hnh thc tr li trc th 11% trn tng ng vi mc li sut tr trc l:

Li sut tr trc bao gi cng nh hn li sut tr sau:

Li sut tr trc = li sut tr sau / 1 + li sut tr sau = 11/1/11 = 9.9

Cu 14: Ngn hng cng b li sut gi tit kim 1 nm l 8,4% li sut ny tng ng vi li sut kp 3 nm l:

CT li gp = (1 + r)n - 1 = (1 + 0.084)3 - 1 = 27.4%

Cu 15: Ngn hng cng b li sut gi tit kim thng l 1%, li sut ny tng ng vi li sut kp nm l:

a. (1 + r)n*12 - 1 = (1 + 0.01)12 - 1 = 12,68%.

Cu 16: Gi tit kim 8000$ trong 15 nm, li sut 15% sau ta c:

FVn = FV (1 + r)n = 8000 (1 + 0.15)15 = 65096Cu 17: Sau 25 nm na bn v hu, ngoi tin lng, bn mun c thm mi nm 120tr ng t tin gi tit kim tiu xi v i du lch nm chu. Hin bn cha c ng no d tr. Trong 25 nm ti nn kinh t thi k pht trin nhanh nn li sut tin gi t mc 10% nm v k t khi bn v hu li sut tin gi ny ch t 8% nm. Nu bn mun t mc tiu trn th t nay hng nm bn phi b mt khon tit kim bao nhiu.

Li gii FVA (n, r) = C(1 + r)n - 1/r

120 tr/10% = C[1 + 8%)25 - 1] / 8% ( C = 16.414.535 ng.

c c khon tin trn th mi nm phi gi NH l 16.414.535

Cu 18: Ngn hng bn ang xem xt u t vo 1CP X, li sut mong i l 11%, li sut tn phiu kho bc 8%, li sut u t bnh qun ca th trng c phiu l 12%, CP ang xem xt c h s ri ro ( = 1/2 ca bnh qun th trng, bn khuyn lnh o nn u t v:

E(R) = Rf + ( (Rm - Rf) = 0.08 + 0.5(0.12 - 0.08) = 10%.

Cu 19: u t 1 c phiu c li sut mong i = 16%, li sut tri phiu kho bc l 7%, h s ri ro (() = 2, mc b ri ro c phiu l 4%. Bn c th u t vo c phiu ny v:

Mc b ri ro: E (Rp) = Rm ( Fr

E(ri) = Rf ( ( (Rm - Rf) = 0.07 - 2 (0.04) = 15% < 16%.

C th u t vo c phiu ny.

Cu 20: Gi c phiu hin ti l 37.000, d on gi c phiu trong 1 nm na, bng iu tra ta c cc s liu sau:

GiS ngi d onPi (xc sut)Pi Ri

50300,30,3 ((50 - 37)/37)

40300,3

30200,2

32200,2

- Mc sinh li k vng

E(R) = Pi Ri = 0,3 (50 - 37/37) + 0,3 ((40-37/37))

+ 0,2((30-37/37)(32-37/37) = 6,49%

Mc ri ro u t (phng sai)

= Pi(Ri ( Er)2 = 0,3 ((50 - 37/37) - 6,49%)2 = 0,3 ((50 - 37/37)

- 6,49%)2 + 0,2 ((50 - 37/37) - 6,49%)2 + 0,2((50 - 37/37) - 6,49%)2

So snh t s phng ai trn E(R) - nu > 1 l mc ri ro cao.

Cu 21: Trn th trng c 2 loi chng khon vi thng s nh sau:

Xc xut60%40%

Li sut CK A20%4%

Li sut CK B2%24%

Bn hy xc nh li sut k vng v ri ro u t vo 2 CK trn theo cc phng n u t nh sau:

a. 100% vo CK A

b. 100% vo CK B

c. 50% vo A v 50% vo B

Bn c nhn xt g khng v kt qu tnh c?

Li gii

a:EA = (KA ( P = 13.6%

b:EB = (RB ( P = 10.6%

c:EAB = EA WA + EB WB = 0,122 = 12,2%

Cu 22: Cng ty A, B c xc sut mc sinh li cc nm ti nh sau:

Tnh trng kinh t Xc xut WiKh nng sinh li ca A % EAKh nng sinh li ca B % EB

Tng trng mc 10.2-128



a) Mc sinh li mong i ca A v B.

E(Ra) = Pi Ri = 0,2 (-12) + 0,4(18) + 0,4 (24) = 144

E(RB) = Pi Ri = 0,2 (8) + (0,4) (-2) + 0,4 (-10) = -3,2

b) nh gi ri ro u t cho mi CP

= Pi (Ria ( E (Ra))2 = 0,2 (-12 - 14,4)2 + 0,4(18 - 14,4)2

+ 0,4(24 - 14,4)2 = 181,44 = 13%.

= Pi (Rib ( E (Rb))2 = 0,2 (8 - (-3,2))2 + 0,4(-2 - (-3,2)2

+ 0,4 (-10 - (3,2))2 = 44,15 = 6,64%

c) Covar a, b = Pio ((Ria ( E (rb) (Rib ( E (rb)) = 0,2 (-12 - 14,4) (8 + 3,2) + 0,4 (18 - 14,4) (-2 ( (-3,2) + 0,4 (24 ( 14,4) (-10 - (-3,2) = -83,52

Nu Covar (A, B) < 0 li sut A, B ngc chiu ( kt hp nhau.

Cu 23: Bn ang s hu danh mc u t gm 4 c phiu v T s

Loi c phiuGi th trng ()PiMc sinh li

A10.000.0000,110%

B20.000.0000,214%

C30.000.0000,316%

D40.000.0000,415%

A. Mc sinh li tng th ca bn

E(r) = Pi Ri = 0,1 ( 10 + 0,2 ( 14 + 0,3 ( 16 + 0,4 ( 15 + 14,6%

Cu 24: Cng ty ca bn ang xem xt u t vo mt loi c phiu c li sut mong i l 25%. Li sut ca tn phiu kho bc l 8%, mc b ri ro khi u t vo th trng c phiu l 9%, c phiu ang xem xt c h s ri ri ( = 2. Bn khuyn lnh o nu:

a. u t

b. Khng u t

E(R) = FR + ( (Rm - Rf) = 0.08 + 0.15 (0.12 - 0.08) = 10%

Cu 25: Mt danh mc c li sut c tnh l 20%, lch chun 20%. Tn phiu kho bc li sut l 7%. Nh u t c h s ngi ri ro A = 6

E = 20%, ( = 20%, Rf = 7%, A = 6

p dng CT tnh mc chp nhn phng n u t

U = E(p) ( 0.5 * A * (2 = 8% > Rf = 7% ( chp nhn u t.

Cu 26: Gi s ch s VN-Index hin ti l 540 im, d on c ch s ny vo cui nm nay, bng phng php iu tra mt s chuyn gia phn tch chng khon, chng ta c t liu nh sau:

VN-Index sau 1 nm S ngi d on

50020

55020

60030

65020

70010

a. Hy d bo mc sinh li k vng khi u t vo VN-Index

b. Hy d bo mc ri ro khi u t vo VN-Index

Li gii: Pi = S ngi trn TS ngi = 20 trn 100% = 0,2

% tng gim VN-IndexT trng (Pi)

-0.0740.2

0.02850.2

0.11110.3

0.20370.2

0.29630.1

E(R) = (R ( P = 0.0926 = 9.26%

( =

Cu 27: Tri phiu chnh ph pht hnh ngy 15/7/2002, ang bn vo ngy 22/11/2004, F = 100.000, C = 9%, Mc = 5 nm, li sut di hn chit khu l 8%. Vit cng thc nh gi tri phiu.

15/7/2002 15/7/2003 15/7/2004 15/7/2005 15/7/2006 15/7/2007

22/11/2004+ S ngy cn li ca TP m = (30-22+1) + (4th ( 30 ng + 1) = 130 ngy

+ S ln tr li cn li = 2007 - 2005 + 1 = 3

+ p dng cng thc tnh li sut theo ngy (t 22/11/2004 ( 15/7/2005)

(1 + r)Mc/365 = a.

PV1 = C/(1 + R)1 + C(1 + R)2 + C/(1 + R)3 + F//(1 + R)3 == Po = P1/(1 + r)a

Cu 28: Cng tri gio dc c mnh gi l 500.000, thi gian o hn 5 nm, li sut gp = 40%/nm, cn 2 nm o hn ang bn gi 600.000 , li sut tit kim di hn 2 nm ang l 8%, trn quan im gi tr tri phiu v gi tit kim nh nhau, c mua c tri phiu trn khng? v sao?

Po = 500.000, n = 5 nm, r = 40% / 5 nm, li sut bnh qun 1 nm

+ 0,4 ( 1 = 7% = C

P = C / (1 + r) + C / (1 + r)2 + F / (1 + r)2 = (500.000 ( 7%) / (1 + 0,08)

+ (500.000 ( 7%) / (1 + 0,08)2 + (500.000) / (1 + 0,08)2 = 491.083

Khng nn u t v 491.083 < 600.000

Cu 29: Khch hng mun u t tri phiu A

- Thi gian o hn 4 nm, F = 100 ngn

- Tri phiu Zero coupon

- Li sut yu cu ca khch hng 9%

a) Gi tri phiu Zero coupon

PV = F / (1 + r)n = 100/1.094 = 70,84

b)Thi gian o hn bnh qun D = 4 (v y l TP khng li nh k th D chnh bng thi gian o hn.

c) Thi gian o hn bnh qun iu chnh MD

MD = -D/1 + y = -4/1.09 = -3,87

d) li (C)

kinh doanh = n(n + 1) / (1 + y)2 = 4 * 5/1.042 = 16.83

e)Gi tri phiu thay i ? % theo D, C, nu li sut yu cu ca khch hng tng 1% dP / P = MD dy + 1/2 K dy2 = -3,57*0.01 + 1/2 * 16,83*0.01 = 0,03.

Nu li sut tng 1% th gi TP thay i 3,59% theo C v MD.

Cu 30: Gi s n v bn ang s hu 1 lng tri phiu, k hiu CP4AS40 pht hnh ngy 18/01/2002, do cn vn G ca bn ang c nh bn chng vo ngy bn ang lm kim tra (30/5/2007). Bit rng F = 100 ngn ng, C = 7,4%; M = 10 nm; Li sut yu cu m gim c t ra l 8,4% (li sut di hn chit khu). Bn hy vit 3 cng thc nh gi TP trn.

Li gii:

18/1/2002 18/1/2006 18/1/2007 18/7/2008 18/172009 18/7/2010

30/5/2007

T1 = 12ng; T2 = 28ng; T3 = 30ng; T4 = 31ng; T5 = 30ng ( TS = 131 ngy

S ngy t 30/5 n 18/1 cn 365 ( 131 = 234 ngy, t 234/365 l (C1/ Po = 7,4/(1 + 0.084)( + 7,4/(1 + 0.084)(+1 + 7,4/(1 + 0.084)(+2

+ 7,4/(1 + 0.084)(+3 + (7,4 + 100)/(1 + 0.084)(+4

C2/ P(-1) = 7,4/(1 + 0.084)1 + 7,4/(1 + 0.084)2+ 7,4/(1 + 0.084)3

+ 7,4/(1 + 0.084)4 + (7,4 + 100)/(1 + 0.084)5

Po = P(-1) ( (1 + 8,4)1 - (

C3/ P(1) = 7,4 + 7,4/(1 + 0.084)1 + 7,4/(1 + 0.084)2 + 7,4/(1 + 0.084)3

+ (7,4 + 100)/(1 + 0.084)4

P(1) = 8,4 + 7,4PVA1 (4, 8,4%) + 100PV (4, 8,4%)

Po = P(1) / (1 + 8,4)(

Cu 31: (p dng m hnh godan)

Mt cng ty X c ROE = 12,5% (thu nhp trn vn ch s hu ROE). Cty chia c tc hng nm 40% (D/E = 40%). Bit rng cng ty c tnh thu nhp ca 1 CP nm ti = 3$ (EPS = 3$), li sut chit khu theo yu cu ca th trng vi cng ty l 10% (r = 10%).

Tnh gi c phiu ca Cng ty ny?

ROE = 12.5%D/E = 40%

EPS = 3$

r = 10%

P0 = ?

P0 = DIV1/(r-g) m b = 1 - DIV/EPS

g = ROE*b = 12.5*(1-40%) = 7,5%

DIV1 = P1 * 40% = 3$*40% = 1,2$

(( P0 = DIV1/(r-g)/(10% - 7,5%) = 1.2/2.5% = 48$.Cu 32: p dng m hnh chit khu 2 giai on

Mt cng ty Y d on chia c tc 2$ cho mt c phn mi nm trong vng 3 nm ti v sau tc tng trng c tc l 6% mi nm. Gi s ls chit khu 10%.

Tnh gi c phiu?

DIV = 2$ trong 3 nm

G4 = 6%

r = 10%

P0 = ?

P0 = PV(D3) + PV (P3)

PV(D3) = 2/(1+0.1) + 2/(1.1)2 +2/(1.1)3 = 4.97

P3 = D4/(r-g) = D3*(1 + g4)/(r-g4) (1+r)3 = 2(1+0.06)/(0.1-0.06)*(1.1)3

= 39.82

P0 = 4.97 + 39.82 = 44.79

Cu 33:

Nu bn mua 1 CP vi gi 40$, hin nay d tnh CP c hng c tc 2$ vo cui nm T1 v c tc c d on s tng u 7% hng nm. Hy tnh t sut li nhun mong i trn c phiu

P0 = 40$

DIV1 = 2$

g = 7% r = ?

P0 = DIV1/(r-g) ( r = DIV1/P0 + g = 2/40 + 7% = 5% + 7% = 12%

Cu 34:

Mt cng ty ABC d on chia c tc 3$/1CP trong vng 4 nm ti sau tc tng trng c tc l 7.5% hng nm. Gi s li sut chit khu 12%. Tnh gi c phiu.G5 = 7.5%

r = 12%

P0 = ?P0 = PV(D4) + PV(P4)

PV(D4) = DIV1/(1+r) + DIV2/(1+r)2 + DIV3/(1+r)3 + DIV4/(1+r)4 (a)P4 = DIV5/(r-g) = DIV4*(1+g5)/(r-g)

(b)

3/1.12 + 3/1.122 + 3/1.123 + 3/1.124 3*1.075/(0.12-0.075)*1.124 = 54.66$Cu 35:

Cng ty CP XYZ c mc tng trng c tc trong 3 nm u l 25%, nhng nm tip theo tc tng trng n nh mc 7%. C tc trong ln tr gi gn nht l 1.2$, li sut theo yu cu 12.4%. Hy xc nh gi CP ngy hm nay?

g = 25%DIV0 = 1.2$ g4 = 7%r = 12.4%

P0 = ?P0 = PV(D3) + PV(P3)

= DIV1/ (1+r) + DIV2/(1+r)2 + DIV3/(1+r)3 + P3/(1+r)3

= DIV0 (1+g)/(1+r) + DIV0 (1+g)2/(1+r)2 + DIV0 (1+g)3.(1+g4)/(1+r)3.(1-g4)

= 37.17

Cu 36: Gi s VCB sau khi CPH vo u nm 2007 v tr c tc trong 3000/c phiu cui nm nay v c mc tng trng c tc trong ba nm tip theo l 50%/nm, nhng nm sau tc tng trng c tc mc 10%. LS yu cu ca bn i vi CP ny l 20%. Hy nh gi CP VCB vo u nm ti vi cc thng tin d bo trn.

Li gii:D0 = 2000

g1 = 50%

n1 = 3 nm

g = 10%; r = 20%

D1 = D0 (1 + g1) = 4500

D2 = D0 (1 + g1)2 = 6750

D3 = D0 (1 + g1)3 = 10125

D4 = D0 (1 + g1)4 (1 + g2) = D3 (1 + g2) = 11.137,5

P3 = D4/(r + g2) = 111.375

P0 = D1/(1 + r) + D1/(1 + r)2 + P3/(1 + r)3 = 78.750

Cu 37: Cng ty XYZ c mc tng trng c tc trong 3 nm u l 25%, nhng nm tip c tc tng trng c c tc n nh l 7%. C tc trong ln tr gn nht l 1.2$. Li sut yu cu ca nh u t vi c phiu ny l 12.4%. Xc nh c phiu m nh u t chp nhn mua.

G(1(3) = 25%, r = 12,4%, g(4) = 7%, Do = 1,2$

C tc c chia trong 4 nm ln lt tng nm nh sau:

D1 = Do (1 + G) = 1,2 (1 + 0,25) = 1,5

D2 = D1 (1 + G) = 1,5 (1 + 0,25) = 1,875

D3 = D2 (1 + G) = 1,875 (1 + 0,25) = 2,3437

D4 = D3 (1 + G) = 2,3437 (1 + 0,07) = 2,5078

Gi CP m nh u t chp nhn mua

P4 = D4 / (r-g4) = 2,5078 / 0,124 ( 0,07 = 46,441

Cu 38: Nm ngoi Cng ty A tr c tc 6000 /CP, c tc ny tng u 5% trong nhng nm qua v c kh nng tng nh vy trong tng lai. Nu li nhun yu cu ca bn vi c phiu l 13%, CP ang c bn vi gi 72.000. Trn quan im gi tr bn c nn mua CP ny khng?

Ta c D1 = D0 (1 + g)1 = 6000 (1 + 0,05)1 = 6300

Po = D1 / (r-g) = 6300 / (0,13-0,05) = 78.750

Nh u t nn mua v 78750 > 72000

Cu 39; T l tng trng c tc ca 1 Cng ty 10% v c th duy tr nh vy trong tng lai: t l chit khu dng thu nhp l 15%. P/E ca Cng ty l 5.5. Ta c th d bo kh nng tr c tc ca cng ty t cc thng tin l:

(1-b) = DIV/EPS = kh nng tr c tc

g = 10%, P/E = 5.5, r = 15%

P/E = (1-b) (1+g) / (r-g) === (1-b) = 25%.

Cu 40: Mt cng ty c t l n / Tng TS = 0.4, tng n = 200 tr trn li rng sau thu l 30 tr, ROE = ?

ROE = Tn rng / Vn CSH = 30 / 300 = 10%

Tng n / Tng ti sn = 0.4, Vn CSH = Tng TS - Tng n = 300

Cu 41: T l tng trng c tc ca Cng ty = 11.25%, h s hon vn CSH l 15%, kh nng tr c tc l:

g = 11.25%, ROE = 15%

g = ROE*b--b = g/ROE = 0.75 --- (1-b) = 25%

Cu 42: T l chia c tc ca 1 cng ty l 2.5%, h s hon vn ch s hu l 15%. D bo kh nng tng trng ca cng ty l:

G = ROE ( b = 25% (1 - 15%) = 21,25%

Trong ROE: kh nng sinh li ca vn

Cu 43: Cng ty A c li sut yu cu 16% c c tc hin ti l 3000, nu gi hin ti ca c phiu ny l 55000, gi s t l tng trng c tc u th tng trng c tc l bao nhiu?

Po = Do (1 + g) / r - g ( g = Po (r - g) / Do - 1

Cu 44: 1 ngn hng c tng ti sn l 200 t, trong vn vay l 150 t, li thun ca ngn hng nm nay c th l 15 t, t l c tc d kin ch l 3 t. Bn d bo mc tng trng ca c tc trong tng lai

g = ROE ( b = (TN rong/VCSH) (1 - DPS/P)

= (15/(200-150))*(1-3/15) = 0.24 = 24%.

Cu 45: Ngn hng bn c tng ti sn l 1900 t ng, trong vn vay l 900 t ng, li thun ca ngn hng nm nay c th l 420 t d, c tc d kin chi l 190 t ng, bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin trn.

Li gii(TS = 1900 t

( N = 900 t

( Vn CSH = 1900 - 900 = 1000

ROE = 420/1000 = 0,42

Li nhun thun = 420 t

C tc chi = 190 t

g = ROE ( t l gi li

= 0,42 ( (1 - 190/420) = 0,23 = 23%

Cu 46: 20 nm na v hu. D nh tch gp tin gi tit kim hng li c thm mi thng 2 triu (hin cha c ng no). Trong 20 nm ti li sut 9%/nm. Sau LS 0,5%/thng. Hi bn phi gi bao nhiu tin mi nm?

sau 20 nm na nhn 2tr/thng t tin gi tit kim th s tin cn gi vo l: PV = FV/r = 2/0,005 = 400tr.

Gi s tin hng nm phi gi vo TK l X sau 20 nm na ta thu c s tin 400tr l:

400tr = X.FVA(20,9) ( X = 400/FVA (20,9) = 400/51,160 = 7,92.

Cu 47: NH c tng TS l 200, trong vn vay l 170. Li thun ca NH nm nay l 15, c tc d kin l 3. Hy d bo mc tng trng c tc trong tng lai.

VA = 200VL = 170D = 3

g = ROE . b

ROE = thu nhp rng / vn c ng = 15/30 = 0,5

b = 1 - D/E = 1 - 3/15 = 0,8

g = 0,5 . 0,8 = 0,4 = 40%.

Cu 48: Gi s NH ang s hu mt lng tri phiu CP, k hiu CP4A3403 pht hnh ngy 24/9/2003. Do cn vn, G NH nh bn chng vo ngy 7/6/2006. Bit rng F = 100 ngn, C = 9,7%; Mc = 15 nm; li sut di hn chit khu l 10%. Hy vit 3 cng thc nh gi TP trn.

T 7/6/06 n 24/9/06 c:8/6 n 30/6:23 ngy (30-8+1)

1/7 n 31/7:31 ngy

1/8 n 31/8:31 ngy

1/9 n 24/9:24 ngy (24 + 1 - 1)

Tng:

109 ngy

t 109/365 = (

Cch 1 (tnh t ngy o hn v thi im bn):

Po = (C*PVA(n,r) + Mc*PV(n,r)

= 9,7/(1,1() + 9,7/(1,1(+1) + ... + 9,7/(1,1(+12) + 100/(1,1()

Cch 2: Tnh v P-1: Po = P-1 * 1,1 (1-()

P-1 = 9,7/1.1 + 9,7/1,12 + ... + 9,7/1,113 + 100/1,113

= 9,7 + PVA ((, 10%)

Cch 3: Tnh v P+1: Po = P+1trn(1,1a)

P1 = 9,7/1,1 + 9,7/(1,12) + ... + 9,7/(1,112) + 1000/(1,113)

Cu 49: Ch s Vnindex hin l 540 im, d on tr gi ca ch s ny vo cui nm bng phng php iu tra, mt s chuyn gia c t liu sau:

Vnindex 1 nm sauS ngi d onMc chnh lchPiRia- D bo mc sinh li k vng khi u t vo VNindex

b- D bo mc ri ro khi u t vo Vnindex.

Gii:

a- = (Ri.Pi = 0,2*(-7,4) + 0,2*1,8 + 0,3*9,2 + 0,2*20,3 + 0,1*29,6 =

b-(2 = (Pi.(R-i) =

( =

50020-400,2-7,4

55020100,21,8

60030500,39,2

650201100,220,3

700101600,129,6

Cu 50: Cng tri gio dc c mnh gi 100.000, thi gian o hn l 5 nm, c li sut gp 40%/5 nm, cn 3 nm na o hn ang bn gi 110.000, li sut tit kim di hn 3 nm ang l 8%/nm. Trn quan im li sut u t TP v gi tit kim nh nhau; c mua c TP trn khng, v sao?

P = (F+C)/(1+r)3 = (100.000 + 100.000*0,4)/(1,083) = 140.000/1,2597

P = 111.136 > 110.000 ( Nn mua tri phiu ny v gi bn thp hn gi tr

Cu 51: Cng ty c mc tng trng c tc trong 3 nm u l 25%, nhng nm tip theo c tc tng trng c tc n nh mc 7%. C tc trong ln tr gn nht l 1,2$. Li sut yu cu ca nh u t i vi CP ny l 12,4%. Xc nh gi CP m nh u t chp nhn mua vo u nm th 3.

DIVn = DIV0*(1+g)n

DIV1 = 1,2 * 1,25 = 1,5 DIV2 = ... = 1,875 DIV3 = ... = 2,3437

DIV4 = DIV3 * (1+g4) = 2,34*1,07 = 2,5078

P3 = DIV4/(r - g4) = 2,5078/(0,124 - 0,07) = 46,4407

P0 = PV(D3) + PV(P3)

= DIV0(1-g)/(1+r) + DIV0*(1+g)2/(1+r)2 + DIV0*(1+g)3/(1+r)3

+ DIV3*(1+g4)/)(r-g4)(1+r)3 = 37,1744

Cu 52: Vo trang web... v thay cc thng s ca TP quc t do VN va pht hnh, ta nhn c cc thng tin sau (gi TP l 98,228$): YTM : 7,13 (LS o hn bnh qun; Duration : 7,525 (thi gian o hn bnh qun); Convexti: 64,953 ( li). Hy tnh thi gian o hn bnh qun iu chnh ca TP ny. Nu LS th trng tng 1% th gi TP gim bao nhiu $.

a. Modified duration MD = D/(1+r) = 7,525/(1+0,0713) = 7,024

Vy thi gian o hn bnh qun iu chnh l 7,024 nm.

b. $D = MD ( gi = 7,024 ( 98,228 = 689,8995$

Vy nu li sut th trng tng 1% th gi TP gim 6,8995$.

Cu 53: NH c ngha v tr n theo thi hn v gi tr theo bng sau:

SauLng tin cn tr n tn dng ngun vn, NH nh dng chin lc T vo DMTP vi cc loi TP hin c nh sau:

- TP coupon 1 nm C = 9%, F = 100000

- TP chit khu 2 nm C = 0, F = 100000

- TP coupon 3 nm C = 8%, F = 100000

- TP zero coupon 4 nm, F = 100000

Y = 7%

Hy xc nh mt DM T sao cho tng s tin chi ra cho DM ny l b nht (ch cn lp bi ton)

1 nm 20.000.000

2 nm 40.000.000

3 nm 38.000.000

4 nm 60.000.000

Gii:Dng tin:

Dng tin nm 1:109x1 + 8x3

= 20.000.000

2:

100x2 +8x3 =40.000.000

3:

108x3 =38.000.000

4:

100x4 =60.000.000

Gi cc loi tri phiu:

P1 = 109/1,07 = 101,87

P3 = 8/1,07 + 8/1,072 + 108/1,073 = 102,62

P2 = 100/1,072 = 87,34

P4 = 100/1,074 = 76,29

iu kin:V = min

V = 101,87x1 + 87,34x2 + 102,62x3 + 76,29x4 = min

Cu 54: C hai loi CK vi thng s sau:

Xc xut 60%40%Hy xc nh LS k vng v ri ro u t vo 2 CK trn theo cc phng n u t nh sau:

a) 100% CK A b) 100% vo CK B c) 50% vo A v 50% vo B C nhn xt g v kt qu

Li sut CK A20%4%

Li sut CK B2%24%

Er(AB)11%14%

Phng n 1: 100% APhng n 2: 100% B

ErA = 0,6 * 20 + 0,4 * 4 = 13,6%ErB = 0,6 * 2 + 0,4 * 24 = 10,8%

(A2 = 0,6(20-13,6)2 + 0,4(4-13,6)2 (B2 = 0,6(2-10,8)2 + 0,4(24-10,8)2

(A =(B =

Phng n 3:

Er(AB) = 0,6 * 11 + 0,4 * 14 = 12,2

(AB2 = 0,6(11-12,2)2 + 0,4*(14-12,2)2

(AB =

Cu 55: Mt NH c 30 t vn t c, vn vay l 150 t. Vn vay c thi gian o hn bnh qun l 6 thng. G kinh doanh mo hiu v dng tt c vn cho vay u t vo cc DM T di hn c thi gian o hn bnh qun D = 15 nm. Li sut chit khu hin ti l 8%. Hy xc nh im v ca ngn hng ny.

DA = 200 t

PA = 15 nm r = 8%

DL = 150 t

PL = 6 thng = 6/12 = 0,5

Ta c $DL = DL.PL = 1*0,5*150/1,08 = 64,44 t

$DA = DA.PA = 1*15*200/1,08 = 2777,78 t

1. Li sut tng 1% TS n gim 69,44

2. Li sut tng 1% th TS c gim 2.777,78

Khi li sut tng (r ( TS n gim 69,44; gi tr ti sn n = 150 - 69,44(rKhi li sut tng (r ( TS n gim 2777,78; gi tr ti sn c = 200-2777,78(r

NH v khi ti sn t c = 0 ( 150 - 69,44(r = 200 - 2777,78(r

( (r = 1,85

Vy khi LS t 8 + 1,85 = 9,85 th NH mt kh nng thanh ton. im v ca ngn hng l 9,85%.

Cu 56: Gi s Vietcombank sau khi c phn ho (u 2006) v tr c tc cui nm ny v c mc tng trng c tc trong 4 nm tip theo l 20%/nm, nhng nm sau c tc tng trng c tc n nh mc 8%. LS yu cu ca bn i vi CP ny l 15%. Tnh gi CP Vietcombank vo lc CPH u nm ti vi cc thng tin trn.

Po = (DIVttrn(1+r)t + M/(1+r)t

= {10*0,2/1,15 + 10*0,2*(1+0,2)/1,152 + 10*0,2*(1,22)/(1,153) + 10*0,2*(1,23)/(1,154) + 10*0,2*(1,24)/(1,155) + 10*0,2*(1+0,08) + ... + 10*0,2*1,24*(1,08n)/(1,15(n+5)

= 7,42% + (1/(1,154))*(4,187/(15%-8%)) = 41.290

Cu 57: CP A v B c xc sut mc sinh li nh sau cho cc nm ti:

Tnh trng KTXc xut Kh nng sinh li AKh nng sinh li Ba) Tnh mc SL mong i ca A v

b) nh gi ri ro u t vo mi CP

c) Tnh tch sai mong i ca LN A&B

d) Tnh h s tng quan ca LN A&B.

A&B c th kt hp tr kh ri ro trong DM T hay khng? V sao?

Tng trng mc 10,2-128



a)ERA = (Wi.RiA = 0,2*(-12) + 0,4*18 + 0,4*24 = 14,4

ERB = (Wi.RiB = 0,2*8 + 0,4*(-2) + 0,4*(-10) = -3,2

b) (A2 = (Wi*(RiA - ERA)2

= 0,2*(-12-14,4)2 + 0,4*(18-14,4)2 + 0,4*(24-14,4)2

= 181,44 ( (A = 13,47

(B2 = (Wi*(RiB - ERB)2

= 0,2*(8+3,2)2 + 0,4*(2+3,2)2 + 0,4*(-10+3,2)2

= 44,16 ( (B = 6,64

c)CovAB = (Wi*(RiA - ERA) * (RiB - ERB)

= 0,2*(-12-14,4)*(8+3,2) + 0,4*(18-14,4)*(2+3,2)

+ 0,4*(24-14,4) *(-10+3,2) = -83,52

d) pAB = covAB/dA.dB = -83,52/(13,47*6,64) = 0,962

( c th kt hp A, B trong mt danh mc

Do pAB gn -1 ( quan h A, B cht ch.

Cu 58: Mt nh T c 10.000.000 d nh u t trong thi hn 2,5 nm vo danh mc cc tri phiu nh sau:

- TP A, tri phiu chit khu, thi gian o hn 3 nm, F = 100.000

- TP B, tri phiu coupon 6%, thi gian o hn 2 nm, F = 100.000

Li th trng hin l 10%. Hy xc nh sao cho DM trn t mc tiu ra v phng trnh c ri ro theo phng php trung ho ri ro li sut.

WA : t l u t vo TP A

WB : t l u t vo TP B

R = 10%

WA + WB = 1

WADA + WBDB = 2,5

D = {)1*C/(1+r) + 2*C/(1+r)2 + ... + n*C/(1+r)n}/P

PA = F/(1+r)3 = 100000/1,1=3 = 75,131

PA = C1/(1+r) + (C2+F)/(1+r)2 = 6000/(1,1) + 6000+100000)/(1,12)

= 93,058

DA = {3*10000/(1+0,1)3}/75131 = 3

(DA = {M*F/(1+r)n}/PA)

DB = 1*{6000/(1+0,1)} + 2*{6000+100000)/(1+0,1)2} = 1,94

Ta c WA + WB = 1 v WADA + WBDB = 2,5

( WA = 0,53 WB = 0,47

Vy s tin u t vo TP A l 1.000.000 * 0,53 = 530.000

s tin u t vo TB B l 1.000.000 * 0,47 = 470.000

s TP A cn mua l:530.000/75,131 = 70,54 tri phiu

s TP B cn mua l:470/000/93,058 = 56,50 tri phiu.

Cu 59: Gi CP Cng ty A c h s ( = 3. LS tn phiu kho bc l 7%, mc b ri ro th trng CK hin ti l 8% (rm - rf = 8%). Li sut u t CP Cng ty ny gn y l 30%. Dng cng thc m hnh nh gi TS vn (CAPM) xem xt th trng c nh gi CP ny cao hn gi tr hay khng. Gii thch.

M hnh CAPM: R = Rf + ((Rm - Rf=) = 7 + 3*8 = 31% > 30%.

( Gi CP ny c nh gi thp hn gi tr.

Cu 60: Qu VF1 c k hoch u t vo danh mc vi c cu nh sau:

a- Chng khon nim yt 20%

b- Chng khon cha nim yt 30%

c- Tri phiu chnh ph 10%

d- u t khc 10% (bt ng sn)

Gi s ta c thng tin v ri ro nh sau: ri ro ca CK cha nim yt (a) l 8%; ca b l 12%, d l 15%. TP Chnh ph c coi l phi ri ro v cc thng s v tch sai nh sau:

cov(a,b) = 96

cov(a,d) = -110

cov(b,d) = -140

cov(a,c) = 0

cov(c,b) = 0

cov(c,d) = 0

Hy d bo ri ro ca VF1 theo danh mc u t v thng s cho.

(P2 = (Wi.(i2 + (Wi.Wf * cov(ri,rf)

0,2.(12 = 0,2 * 0,082Cu 61: Nm ngoi Cng ty A tr c tc 6000/c phiu. C tc ny tng u khong 5%/nm trong nhng nm qua v c kh nng tng nh vy trong tng lai. Nu li nhun yu cu ca bn i vi CP ny l 13%, CP ny ang c bn gi 72.000. Trn quan im gi tr bn c nn mua CP ny khng, v sao?

DIV1 = DIV-1(1-g)2 = 6000 ( (1+005)2 = 6.615

Po = DIV1/(r-g) = 6615/(0,13-0,05) = 82.687 > 72000 ( mua c.

Cu 62: Cng ty A c LS yu cu l 16% v c tc hin ti l 3000. Nu gi hin ti ca c phiu ny l 55000. Gi s t l tng trng c tc u th tng trng c tc l bao nhiu"

P0 = DIV1/(r-g) = DIV0.(1+g)/(r-g)

55000 = {3000*(1+g)/(0,6-g)} ( g = 20,34%

Cu 63: Mt khch hng ang mun u t vo TP A c cc thng s:

- Thi gian o hn 4 nm, F = 100000

- Tri phiu zero cupn

- Li x' yu cu ca khch hng l 9%

Hy gip khch hng xc nh:

- Gi TP m ngi u t chp nhn mua

- Thi gian o hn bnh qun (D)

- Thi gian o hn bnh qun iu chnh (MD)

- li (C)

- Gia TP bin i bao nhiu % theo D v C nu li sut yu cu ca khch hng tng 1%. Gii thch kt qu cho khch hng.

a) P0 = 100/1,09 = 70,84

b) D = 4 v l tri phiu chit khu

c) MD = (-1/(1+y))*D = (-1/1,09)*4 = -4/1,-9 = -3.67

d) k = -n(n+1)/(1=y)2 = 4*5/(1,092) = 16,83

Dp/p = MD.dy + (k.dy2) = -3,67*0,01 + (16,83*0,012) = 4,645$

Tc l nu li sut thay i tng 1% th gi TP thay i 4,645% theo c li v MD.

( - Tri phiu ng gi 70.840

- Thi gian thu hi vn l 4 nm.

- 1% thay i li sut th 4,645% thay i v gi theo c C v MD

Cu 64; C s liu 2 CO nh sau:

NmLi sut u t CP ALi sut u t CP Ba- Xc nh thu nhp k vng u t vo A v B

b- Ri ro u t vo A v B

c- Tch sai ca A&B

d- H s tng quan gia A&B

Gii thch cc kt qu tnh c

2002-5%4%

200310%-2%

2004-4%8%

20057%-9%

a-

b-

c-

d- p(A,B) = {cov(A,B)}/((A.(B) = -45,67/(7,4*8,25) = -0,748

Cu 65: Tri phiu chit khu, F = 1000000. Thi gian o hn M = 10 nm. Li sut chit khu l 9,5%

a. Hy nh gi TP ny.

b. Nu bn mua c tri phiu trn gi 350.000 th bn c li sut u t bnh qun l ?

( (g = ROE.b)

Cu 64: Mt ngn hng c phn c tng ti sn l 200 t ng, trong vn vay l 150 t ng. Li thun ca ngn hng nm nay c th l 15 t ng. T l c tc d kin ch l 3 t ng. Bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin .

Cu 66: Gi s Ngn hng bn ang s hu mt lng tri phiu chnh ph, k hiu CP4 0502 pht hnh ngy 08/08/02, Gim c ca bn ang c bn chng vo ngy hm nay (9/05/05) (nm nay khng phi l nm nhun). Bit rng F = 100 ngn ; C = 8,1%; M = 5 nm; li sut di hn chit khu l 8%.

Bn hy gip Gim c ca mnh nh gi TP trn (ch cn vit mt cng thc nh gi)

Cu 67: Cng tri gio dc c mnh gi l 200 000 ng, thi gian o hn l 5 nm, c li sut gp 40%/5 nm, cn 3 nm na o hn, ang bn gi 220.000 . Li sut tit kim di hn ba nm ang l 8%/nm. Trn quan im li sut u t tri phiu v gi tit kim nh nhau, c mua c tri phiu trn khng? V sao?

Cu 68: Gi s ch s VN Index hin l 230 im, d on tr gi ca ch s ny mt nm sau, bng phng php iu tra mt s chuyn gia phn tch chng khon, ngi ta c t liu nh sau:

Vn Index sau 1 nm S ngi d on

20010

25030

28030

32020

a) Hy d bo mc sinh li k vng khi u t vo Vn-Index

b) Hy d bo mc ri ro u t vo Vn-Index.

Cu 69 Cng ty c phn XYZ c mc tng trng c tc trong 3 nm u l 25%, nhng nm tip theo c tc tng trng c tc n nh mcs 7%. C tc trong ln tr gn nht l 1,2$. Li sut yu cu ca nh u t i vi c phiu ny l 12,4%. Hy xc nh gi CP m nh u t chp nhn mua vo u nm th 3.

Cu 70: Cng ty A c li sut yu cu l 16% v c c tc hin ti l 3.000. Nu gi hin ti ca c phiu ny l 55.000. T l tng trng c tc l bao nhiu?

Cu 71: Mt ngn hng c vn t c l 20 t v vn vay l 180 t. Gi s NH ny kinh doanh mo him v dng vn vay ngn hn 6 thng u t vo danh mc tri phiu di hn c D = 10 nm. Li sut chit khu hin ti l 7%. Hy xc nh im v ca Ngn hng ny (mc li sut tng ln cn thit ti sn t c ca Ngn hng = 0).

Cu 72: Bn ang s hu danh mc u t gm 4 c phiu v thng s ca chng nh sau:

Loi c phiuGi tr th trng ()Mc sinh li (%)

A150 000 0008

B20 000 00014

C30 000 00016

D10 000 00015

Hy xc nh mc sinh li v k vng tng th ca bn.

Cu 73: Ngn hng ca bn c ngha v tr n theo thi hn v gi tr theo bng sau:

SauLng tin cn tr n

1 nm 20 000 000

2 nm 40 000 000

3 nm 38 000 000

4 nm 60 000 000

tn dng ngun vn, Ngn hng nh dng chin lc u t vo danh mc tri phiu vi cc loi tri phiu hin c nh sau:

- Tri phiu coupon 1 nm c C = 9%, F = 100 000

- Tri phiu chit khu 2 nm, C = 0; F = 100 000

- Tri phiu coupon 3 nm, C = 8%; F = 100 000

- Tri phiu zero coupon 4 nm; F = 100 000

Bn hy gip lnh o xc nh mt danh mc u t sao cho tng s tin chi ra cho danh mc ny l b nht (ch yu cu lp lun bi ton).

Cu 74: Ta c s liu v 2 c phiu theo bng sau:

Tnh trng KTXc xut Li sut u t

vo CP ALi sut u t

vo CP B

Suy thoi20%-5%6%

Bnh thng 40,%10%-2%

Kh 30%-45%8

Hng thnh10%7%9%

Bn hy:

a) Xc nh thu nhp k vng u t vo A v B

b) Ri ro u t vo A v B

c) Tch sai ca A v B

d) H s tng quan gia A v B

Hai c phiu ny c th kt hp vi nhau trong danh mc u t tr kh ri ro khng? V sao?

Cu 75: Cng tri gio dc c mnh gi l 200.000 ng, thi gian o hn l 4 nm, c li sut gp 40%/4 nm cn 3 nm na o hn, ang bn gi 220.000, li sut tit kim di hn hai nm l 8%/nm, trn quan im gi tr tri phiu, c mua c tri phiu trn khng? V sao?

Cu 76: Bn mun n khi v hu (15 nm na) ngoi tin lng hu bnh qun mi thng bn c thm 1 triu ng tiu xi, t nay n lc v hu mi nm bn phi gi vo tit kim bao nhiu lc v hu khon tin dnh dm ca bn c mc sinh li tho mn mun ca bn, gi s trong 15 nm ti t nc trong giai on pht trin nn li sut bnh qun mc cao l 9% nm, cn t khi bn v hu kinh t pht trin n nh nn li sut ch mc 0,5% thng.

Cu 77: Tri phiu chnh ph pht hnh ngy 15/7/2002, ang bn vo ngy 22/11/2004, F = 100.000, C = 9%, M = 5 nm, li sut di hn chit khu l 8%. Vit mt cng thc nh gi tri phiu trn.

Cu 78: Gi mt c p hiu Hapohaco hin ti l 37.000 , d on gi c phiu ny trong 1 nm sau, bng phng php iu tra mt s chuyn gia phn tch chng khon, ngi ta c t liu sau:

Gi $S ngi d on

5030

4030

3020

3220

Hy d bo mc ri ro u t vo Haphaco vi t liu.

Cu 79: Cng tri gio dc c mnh gi l 500.000 , thi gian o hn l 5 nm, c li sut gp 40%/nm, cn 2 nm na o hn, ang bn gi 600.000 , li sut tit kim di hn 2 nm ang l 8%/nm, trn quan im gi tr tri phiu c mua c tri phiu trn khng? V sao?

Cu 80: Cng ty XYZ c mc tng trng c tc trong 3 nm u l 25%, nhng nm tip theo c tc tng trng c c tc n nh mc 7%. C tc trong ln tr gn nht l 1.2$. Li sut yu cu ca nh u t i vi c phiu ny l 12.4%. Hy xc nh gi CP m nh u t chp nhn mua.

Cu 81: Nm ngoi cng ty A tr c tc 6000 /1 c phiu, c tc ny tng u khong 5% nm trong nhng nm qua v c kh nng tng nh vy trong tng lai. Nu li nhun yu cu ca bn i vi c phiu ny l 13%, c phiu ang c bn gi 72.000 . Trn quan im gi tr bn c nn mua c phiu ny khng? V sao?

Cu 82: C phiu Cng ty A v B c xc sut mc sinh li nh sau cho cc nm ti:

Tnh trng kinh t Xc sut Kh nng sinh li ca AKh nng sinh li ca B




a. Tnh mc sinh li mong i ca A v B

b. nh gi ri ro u t vo mi c phiu

c. Tnh tch sai mong i ca li nhun A v B

d. Tnh h s tng quan ca li nhun A v B

A v B c th kt hp tr kh ri ro trong danh mc u t hay khng?


Loi c phiu Gi tr th trng Mc sinh li (%)

A10.000.00010

B20.000.00014

C30.000.00016

D40.000.00015

Hy xc nh mc sinh li tng th ca bn.

Cu 84: Mt khch hng ang mun u t vo tri phiu A c cc thng s sau:

- Thi gian o hn 4 nm; F = 100 ngn

- Tri phiu Zero cupn

- Li sut yu cu ca khch hng l 9%


a. Gi tri phiu m ngi u t chp nhn mua

b. Thi gian o hn bnh qun (D)

c. Thi gian o hn bnh qun iu chnh (MD)

d. li (C)

e. Gi TP bin i bao nhiu % theo D v C nu li sut yu cu ca khch hng tng 1%

f. Gii thch kt qu cho khch hng.

Cu 85; Gi mt c phiu REE hin ti l 28$, d on gi c phiu ny trong 1 nm sau, bng phng php iu tra mt s chuyn gia phn tch chng khon ngi ta c t liu nh sau:

Gi $S ngi d on

215

2810

3020

3210

365

Hy d bo mc ri ro u t vo REE vi t liu trn. Gii thch kt qu.

Cu 85: Cng tri gio dc c mnh gi l 200.000 , thi gian o hn l 4 nm, c li sut gp 40%/nm, cn 3 nm na o hn, ang bn gi 220.000 , li sut tit kim di hn 2 nm ang l 8%/nm, trn quan im gi tr tri phiu c mua c tri phiu trn khng? V sao?

Cu 86: Bn mun v hu (15 nm na) ngoi tin lng hu bnh qun mi thng bn c thm 5 triu ng tiu xi, t nay n lc v hu mi nm bn phi gi vo tit kim bao nhiu lc v hu khon tin dnh dm ca bn c mc sinh li tho mn mun ca bn, gi s trong 15 nm ti t nc trong giai on pht trin nn li sut bnh qun mc cao l 9% nm, cn t khi bn v hu kinh t pht trin n nh nn li sut ch mc 0,5% thng.

Cu 87: Cng ty ABC d on chia c tc 3 USD/1CP trong vng 4 nm ti v sau tc tng trng c tc l 7.5% hng nm. Gi s li sut chit khu l 12%. nh gi c phiu ny.

Cu 88: C phiu cng ty A v B c xc sut mc sinh li nh sau cho cc nm ti:

Tnh trng kinh t Xc sut Kh nng sinh li ca AKh nng sinh li ca B

Tng trng mc 10.21420

Tng trng mc 20.4-5-2

Tng trng mc 30.4109



c. Tnh tch sai mong i ca li nhun A v B

d. Gii thch kt qu tnh c phn B

e. A v B c th kt hp gim thiu ri ro trong danh mc u t khng? V sao?

Cu 89: C mc sinh li ca CK A = 25%, h s ( = 2, RF = 8,4%, Rm = 16% c nn u t khng?

a. u t

b. Khng u t

So snh mc sinh li ca CK A v mc sinh li ti thiu phi c trn th trng. p dng cng thc:

E(Ri) = Rf + ( [E(Rm) - Rf] = 8.4 + 2 (16 - 8.4) = 23.6%

Do RA = 25% > 23.6% ( u t.

Cu 90: Mt danh mc c li sut c tnh l 20%, lch chuyn l 20%. Tn phiu kho bc li sut l 7%. Nh u t c h s ngi ri ro A = 6.

a. Du t

b. Khng u t

So snh mc sinh li ca tn phiu kho bc vi mc sinh li iu chnh ( tnh n h s ngi ri ro) ca nh u t:

Tm tt:

E (porotio) = 20%; ( = 20%; Rf = 7%; A = 6

p dng cng thc tnh mc chp nhn phng n u t (qun l danh mc)

U = E(p) - 0.5 ( A ( (2 = 20 - 0.05 ( 6 ( 202 = 8%

Do U = 8% > Rf = 7% ( Chp nhn u t

Chn phng n a.

(H s trong cng thc l 0.5 c chuyn i thnh 0.005 quy i n v ca ( t (%)2 thnh %.

Cu 91: Mt ngi sp v hu hy vng mi nm s c mt khon tin 48 triu, vy by gi mi nm anh ta phi gi vo ngn hng mt khon tin l bao nhiu, bit 8 nm na anh ta mi ngh hu. Trong 8 nm ti li sut lun mc 9%/nm. Sau 8 nm li sut ch cn mc 6%/nm.

Tm tt:

FV = 48 triu, r = 9%, n = 8, C = ?

Mt dng tin u vi li sut khng i (9%) trong 8 nm s tr thnh mt chui nin kim c nh. Gi nh tin c gi vo cui mi nm. p dng cng thc tnh gi tr tng lai ca mt dng tin ta c:

Kt lun: Vy, c c 48 triu sau 8 nm na th vo cui nm ngi phi gi ngn hng mt khon tin c nh l 4.35 triu

Cu 92: Gi s ngn hng bn ang s hu mt lng tri phiu chnh ph, k hiu CP$0502 pht hnh ngy 08/08/2002, Gim c ca bn c bn chng vo ngy hm nay 13/05/2005 (nm nay khng phi nm nhun). Bit rng F = 100.000, M = 5 nm (C = 8,1%) li sut di hn chit khu l 8%.

Bn hy gip gim c ca mnh nh gi tri phiu trn (ch cn vit 1 cng thc nh gi).

Cu 93: Cng tri gio dc c mnh gi l 200.000 , thi gian o hn l 5 nm, c li sut gp 40%/nm, cn 3 nm na o hn, ang bn gi 220.000 , li sut tit kim di hn 3 nm ang l 3%/nm, trn quan im li sut u t tri phiu v gi tit kim nh nhau, c mua c tri phiu trn khng? V sao?

Cu 94: Gi s ch s Vn-Index hin l 230 im, d on tr gi ca ch s ny mt nm sau, bng phng php iu tra mt s chuyn gia phn tch chng khon ngi ta c t liu nh sau:

Vn-Index sau 1 nm S ngi d on% tng gim VN-IndexT trong (Pi)

20020-13,0420% (0.2)

2503008,7030% (0.3)

2803021,4030% (0.3)

3202039,1320% (0.2)

a) Hy d bo mc sinh li k vng khi u t vo Vn-Index?

b) Hy d bo mc ri ro u t vo Vn-Index?

Cu 95: Gi s Cng ty c phn XYZ c mc tng trng c tc trong 3 nm u l 2.5%/nm, nhng nm tip theo c mc tng trng c tc n nh mc 7%/nm. C tc trong ln tr gn nht l 12.000. Li sut yu cu ca nh u t i vi c phiu ny l 12.4%. Hy xc nh gi c phiu m nh u t chp nhn mua vo u nm th 3?

Cu 96: Cng ty A c li sut yu cu l 16% v c c tc hin ti l 3.000. Nu gi hin ti ca c phiu ny l 55.000. Gi s t l tng trng c tc u th tng trng c tc l bao nhiu?


Vn-Index sau 1 nm S ngi d onMc sinh li (%)T trong (Pi)

A150.000.000 (0.75)80.75

B20.000.000 (0.10)140,10

C20.000.000 (0.10)160,10

D10.000.000 (0.05)150,05

200.000.000

Hy xc nh mc sinh li k vng tng th ca bn.

Cu 98: Ngn hng ca bn c ngha v tr n theo thi gian v gi tr theo bng sau:

Sau Lng tin cn tr n ()

1 nm 20.000.000

2 nm 40.000.000

3 nm 38.000.000

4 nm 60.000.000

tn dng ngun vn, ngn hng nh dng chin lc u t vo danh mc tri phiu vi cc loi tri phiu hin c nh sau:

- Tri phiu coupon 1 nm c C = 9%, F = 100.000

- Tri phiu chit khu 2 nm; F = 100.000

- Tri phiu coupon 3 nm c C =8 % ; F = 100.000

- Tri phiu zero coupon 4 nm ; F = 100.000

Bn hy gip lnh o xc nh mt danh mc u t sao cho tng s tin chi ra cho danh mc ny b nht (ch yu cu lp bi ton)

Cu 99: Mt nh u t c khon tin 10 triu v d nh u t trong thi hn 2.5 nm vo danh mc u t c cc tri phiu nh sau:

Tri phiu A: TP chit khu, thi gian o hn 3 nm, f = 100 ngn ng

Tri phiu B: TP c coupon 6%, thi gian o hn 2 nm, F = 100 ngn ng

Li sut th trng hin ang l 10%. Bn hy xc nh gip nh u t mt danh mc 2 tri phiu nu trn sao t mc tiu ra v phng trnh ri ro.

Cu 100: S liu v hai c phiu theo bng sau:

Tnh trng kinh t Xc sut Li sut u t vo c phiu ALi sut u t vo c phiu A

Suy thoi20%-5%6%

Bnh thng 40%10%-2%

Kh30%-4%8%

Hng thnh10%7%-9%

Bn hy:

a. Xc nh thu nhp k vng u t vo A v B

b. Ri ro u t vo A v B

c. Tch sai ca A v B

d. H s tng quan gia A v B

Hai c phiu ny c th kt hp vi nhau trong danh mc u t tr kh ri ro khng? V sao?

Cu 101: Tri phiu chit khu, F = 1.000.000 . Thi gian o hn M = 10 nm.

a. Hy xc nh gi tri phiu ny, nu li sut yu cu ca bn l 9,5%

b. Nu bn mua c tri phiu trn gi 350.000 th bn c li sut u t bnh qun l bao nhiu?

Cu 102: Gi s cu trc li sut nm ngang vi mc li sut 12%/nm. Bn mun thit k mt danh mc u t vo k u t 30 thng gm 2 loi tri phiu sau:

- Tri phiu A: Li sut coupon 8%/nm (tr li theo nm), thi gian o hn 2 nm.

- Tri phiu B: Li sut coupon 10%/nm (tr li theo nm), thi gian o hn 3 nm.

- C hai loi tri phiu trn u c mnh gi 1.000.000 .

Cu 103: Cn 20 nm na bn s v hu. Bn d nh tch gp mt s tin gi tit kim hng li vo lc ngh hu vi mc tiu l c thm mi thng 1 triu ng ngoi lng hu. By gi cho n lc bn v hu l thi k pht trin bn lu.

Sut bnh qun ca th trng l 9% nm. Lc bn v hu (20 nm sau) kinh t n nh nn li sut ch c 0,5%/thng. Nu nm no bn cng b mt mn tin vo tit kim nh nhau, th mi nm bn ch b bao nhiu thc hin c mc tiu ca mnh.

Cu 104: Mt ngn hng c phn c tng ti sn l 400 t ng, trong ti sn c c t vn vay l mt na. Lia thun ca ngn hng nm nay c th l 30 t ng. T l c tc d kin chi l 10 t ng. Gi s doanh nghip tng trng u trong tng lai. Bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin .

Cu 105: Gi s Ngn hng bn ang s dng mt lng tri phiu chnh ph, k hiu CP + A0304 pht hnh ngy 03/03/2002, Gim c ca bn ang c bn chng vo ngy hm nay (ngy thc hin kim tra). Bit rng F = 100 ngn ng C = 9,4% tr sau, mi ln; M = 15 nm; li sut yu cu l 10%.

Bn hy gip Gim c ca mnh nh gi TP trn (ch cn vit 3 cng thc nh gi)

Cu 106: Cng tri gio dc c mnh gi l 100.000 ng, thi gian o hn l 5 nm, c li sut gp 40%/5 nm gm 3 nm na o hn ang bn gi 110.0o00 ng li sut tit kim di hn ba nm ang l 8% nm. Trn quan im li sut u t tri phiu v gi tit kim nh nhau, c mua c tri phiu trn khng, v sao?

Cu 107: Gi s ch s Dow Lone cng nghip hin l 10400 im, d on tr gi ca ch s ny mt nm sau, bng phng php iu tra mt s chuyn gia phn tch nhng chng khon ngi ta c liu nh sau:

DJCN

sau 2 nm S ngi

d on

1020025

1040025

1080025

1120025

a) Hy d bo mc sinh li k vng khi u t vo DJCN

b) Hy d bo mc ri ro u t vo DJCN.

Cu 108: Gi s Vietcombank s c phn ho xong v u nm sau (2007), c tc d kin tr vo cui nm 2007 l 20% v trong 3 nm tip theo c tc tng trng 10% nm, nhng nm tip theo c tc tng trng c tc n nh mc 7%. Li sut yu cu ca bn vi c phiu ny l 12%. Bn hy nh gi c phiu ny vo lc pht hnh u nm ti.

Cu 109: Cng ty A c li sut yu cu l 16% v c c tc hin ti l 3000. Nu gi hin ti ca c phiu ny l 55.000. Gi s t l tng trng c tc u th tng trng c tc l bao nhiu?


Tnh trng kinh tXc sutKh nng sinh li ca A, (%)Kh nng sinh li B (%)




a) Tnh mc sinh li mong i ca A v B

b) nh gi ri ro u t vo mi c phiu

c) Tnh tch sai mong i (expected convariance) ca li nhun A&B

A v B c th kt hp tr kh ri ro trong danh mc u t hay khng? V sao?

Cu 111: Mt ngn hng c tng vn l 200 t ng, trong c 30 t ng vn t c. Vn i vay c thi gian o hn bnh qun l 6 thng. Gim c Ngn hng l ngi kinh doanh mo him nn ly ton b vn vay mua t hp tri phiu c thi gian o hn bnh qun l 15 nm. Li sut chit khu ca th trng l 7%. Hy xc nh im v ca Ngn hng ny.

Cu 112: Mt nh u t c khon tin 10 000 000 v d nh u t trong thi hn 2,5 nm vo danh mc u t c cc tri phiu nh sau:

- Tri phiu A: TP chit khu, thi gian o hn 3 nm, F = 100 000

- Tri phiu B: TP coupon 6%, thi gian o hn 2 nm, F = 100 000

Li sut th trng hin ang l 10%. Bn hy xc nh gip nh u t mt danh mc 2 tri phiu nn trn t mc tiu ra v phng trnh c ri ro theo phng php trung ho ri ro li sut.

Cu 113: Cng tri gio dc c mnh gi l 200.000 ng, thi gian di hn hng nm, c li sut gp 40%/nm, cn 3 nm na o hn ang bn gi 2200 li sut tit kim di hn ba nm ang l 8%/nm. Trn quan im li sut u tri phiu v gi tit kim nh nhau, c mua c tri phiu trn khng? V sao?

Cu 114: Gi s ch s Vn - Index hin l 230 im, d on tr gi ca ch s ny mt nm sau, bng phng php iu tra mt s chuyn gia phn tch chng khon ngi ta c t liu nh sau:VN-Index 1 nm sauS ngi d on

20010

25030

28030

32020


b. Hy d bo mc ri ro khi u t vo VN-Index.

Cu 115: Cng ty c phn XYZ c mc tng trng c tc trong 3 nm u l 25% nhng nm tip theo c tc tng trng c tc n nh mc 7%. C tc trong ln tr gn nht l 1,2$. Li sut yu cu ca nh u t i vi c phiu ny l 12,4%. Hy xc nh gi CP m nh u t chp nhn mua vo u nm th 3.

a)***********

b) Khng u t

c) Khng xc nh c v khng c li khuyn

Cu 116: Tri phiu chit khu F = 10.000. Thi gian o hn M = 10 nm.

a) Hy nh gi TP ny

b) Nu bn mua c tri phiu trn gi 350000 th bn c li sut u t bnh qun l:

Cu 117: Mt ngn hng c phn c tng ti sn l 200 t ng, trong vn vay l 150 t ng. Li thun ca ngn hng nm nay c th l 15 t ng. T l c tc trong tng lai bng cc thng tin .

Cu 118: Gi s Ngn hng bn ang s hu mt lng tri phiu Chnh ph, k hiu CP4-0502 pht hnh ngy 08/08/2002, Gim c ca bn ang c bn chng vo ngy hm nay (9/05/05) (nm nay khng phi l nm nhun). Bit rng F = 100 ngn ng: C = 8,1%; M = 5 nm; li sut di hn chit khu l 8%.

Bn hy gip G ca mnh nh gi TP trn (ch cn vit 1 cn thc nh gi)

Cu 119: Ngn hng ca bn c ngha v tr n theo thi hn v gi tr theo bng sau:SauLng tin cn tr n d

1 nm20 000 000

2 nm40 000 000

3 nm38 000 000

4 nm60 000 000

tn dng ngun vn, Ngn hng nh dng chin lc u t vo danh mc tri phiu vi cc loi tri phiu hin c nh sau:

- Tri phiu coupon 1 nm c C = 9%, F = 100 000

- Tri phiu chit khu 2 nm, C = 0; F = 100 000

- Tri phiu coupon 3 nm, c = 8%; F = 100 000

- Tri phiu zcro coupon 4 nm; F = 100 000

Bn hy gip lnh o xc nh mt danh mc u t sao cho tng s tin ch ra cho danh mc ny l b nht (ch yu cu lp bi ton).

Cu 120: Mt ngn hng c vn t c l 20 t v vn vay l 180 t. Gi s NG nay kinh doanh mo him v dng vn vay ngn hn 6 thng u t vo danh mc tri phiu di hn c D = 10 nm. Li sut chit khu hin ti l 7%. Hy xc nh im v ca Ngn hng ny. (mc li sut tng ln cn thit ti sn t c ca Ngn hng bng O).


Loi c phiuGi tr th trng ()Mc sinh li (%)

A150 000 0008

B20 000 00014

C30 000 00016

D10 000 00015

Hy xc nh mc sinh li k vng tng th ca bn

Cu 122: Cng ty ABC d on chia c tc 3 USD, trong vng 1 nm ti sau tc tng trng c tc l 7,5 hng nm. Gi c li sut chit khu l 12% . nh gi c phiu ny.

Cu 123: C phiu cng ty A v B c xc sut mc li nh sau cho cc nm ti:

Tnh trng kinh t Xc sutKh nng sinh li ca A (%)Kh nng sinh li ca B (%)






c. Tnh tch sai mong i (expected covariance) ca li nhun A &B

d. Tnh h s tng quan ca li nhun A&B


Cu 124: Tri phiu A c cc thng s sau:

- Thi gian o hn 4 nm

- Tri phiu Zcro copn

- Li sut th trng l 8%

- Mnh gi l 100 000


a) Gi tri phu



d) li (C)

Gii thch kt qu cho khch hng.

Cu 125: Mt nh u t c khon tin 10 trd v d nh u t trong thi hn 2,5 nm vo danh mc u t c cc tri phiu nh sau:

- Tri phiu A: TP chit khu, thi gian o hn 3 nm , F = 100 ngn ng

- Tri phiu B: TP c coupou 6% thi gian o hn 2 nm, kF = 100 ngn ng.

- Li sut th trng hin ang l 10%. Bn hy xc nh gip nh u t mt danh mc 2 tri phiu nn trn sao t mc tiu ra v phng trnh c ri ro.

Cu 126: Cng tri gio dc c mnh gi l 500 000 ng, thi gian o hn l 5 nm, c li sut gp 40%/5 nm cn 2 nm na o hn ang bn gi 600000, li sut tit kim di hnnm dng l 8%/nm. Trn quan im gi tr tri phiu, c mua c tri phiu trn khng? V sao?

Cu 127: Cng ty c phn XYZ c mc tng trng c tc trong 3 nm l 25% nhng nm tip theo c tc tng trng c tc n nh mc 7%. C tc trong ln tr gn nht l 1,2$. Li sut yu cu ca nh u t i vi c phiu ny l 12,4%. Hy xc nh CP m nh u t chp nhn mua.

Cu 128: Nm ngoi cng ty A tr c tc 6000/1 c phiu, c tc ny tng u khong 5% nm trong nhng nm qua v c kh nng tng nh vy trong tng lai. Nu li nhun yu cu ca bn i vi c phiu ny l 13%; c phiu ang c bn gi 72000. Trn quan im gi tr bn c nn ma c phiu ny khng? V sao?






Cu 130: Mt khch hng ang mun u t vo tri phiu A c cc thng s sau:

- Thi gian o hn 4 nm: F = 100 ngn

- Tri phiu Zcro coopon.

- Li sut yu cu ca khch hng l 9%.


a) Gi tri phiu m ngi u t chp nhn mua



d) li (C)

e) Gi TP bin i bao nhiu % theo D v C nu li sut yu cu ca khc hng tng 1%

Gii thch kt qu cho khch hng.

Cu 131: Mt nh u t c khon tin 10 tr v d nh u t trong thi hn 2,5 nm vo danh mc u t c cc tri phiu nh sau:

- Tri phiu A: TP chit khu, thi gian do hn 3 nm, F = 100 ngn

- Tri phiu B: TP c coupon 6%, thi gian o hn 2 nm, F = 100 ngn ng.

Li sut th trng hin ang l 10%. Bn hy xc nh gip nh u t mt danh mc 2 tri phiu nu trn sao t mc tiu ra v phng trnh c ri ro.

Cu 132: Sau 20 nm na bn v hu, ngoi tin lng hu bn mun c thm 1 thng 2.000.000 ng t tin gi tit kim tiu xi. Hin bn cha c ng no d tr. Trong 20 nm ti nn kinh t trong thi k pht trin nhanh nn li sut tin gi ch 0,5% thng. Nu bn mun t mc tiu trn th bn phi b mt khn tin tit kim bao nhiu hng nm?

sau 20 nm va nhn c 2 triu ng 1 thng t tin gi tit kim th sau 20 nm na s tin gi l:

PV = FVA (n ((, 0,005) =

Gi s gi s tin hng nm phi gi vo l C th ta c ch sau 20 nm ta li thu c s tin l 400tr th ta li c:

( (tr)

Cu 133: Ngn hng ca bn c tng ti sn l 200 t ng, trong ****** l 170 ty ng. Li thun ca ngn hng nm nay c th l 15t ng. T l c tc d kin ch l 3 t ng. Bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin trn:

VA = 200 t

VL = 170 t;

D = 3;

r = 15

g = REC x k

ROE = thu nhp rng/ vn c ng = 15 / (200 - 170) = 50% = 0,5

b = 1 - O/E = 1 - 3/15 = 0,8

( g = ROE x b = 0,5 x 0,8 = 0,4 ( 40%

Cu 134: Gi s n v bn ang s hu 1 lng tri phiu Chnh ph k hiu CP4A3403 pht hnh ngy 24/9/2003, do cn vn gim c ca bn ang c nh bn chng vi ngy bn lm bi kim tra bit rng:

F = 100 ngn ng

C = 9,7%

M = 15 nm, li sut yu cu m Gim c t ra l 40%. Bn hy vit 3 cng thc nh gi TP trn (******************)

T F/6/06 n 24/9/06 c: 8/6 - 30/6; 23 ngy (30-8+1= 23)

1/7 - 31/7: 31 ngy

1/8 - 31/8: 31 ngy

1/9 - 24/9: 24 ngy (24 - 1 + 1 = 24)

( = 109/365 ngy

C1:

C2: Tnh v: P - 1 = Po = P-1. 1,1

C3: Tnh v P+1 = Po =

Cu 135: Khi no trang Web http: www.investinginbonds.com/calcs/tipscalculator v thay cc thng ca TP quc t do VN va pht hnh, th nhn c cc thng tin sau: (Gi TP ny l 98,228$).




a). Hy tnh thi gian o hn bnh qun iu chnh ca TP ny

b) Nu Li sut thng tng 1% th gi TP gim bao nhiu

a) Modified Durution

f o hn binh qun iu chnh l: 7,024 nm

$ D = MD x gi = 7,024 x 98,228 = 689,95$

( Nu li sut th trng tng 1% th gi IP s gim 6,8995$

Cu 136: Gi s ch s Vn-index hin ti l 540 im, d on tr gi ch s ny vo cui nm nay bng phng php iu tra mt s chuyn gia phn tch chng khon chng ta c t liu nh sau:

Vn-index 1 nm sauS ngi d onP'tMc chnh lch Vn-index

50020 = 0,2%20%-40

55020 = 0,2%20%10

60030 = 0,3%30%60

65020 = 0,2%20%110

70010 = 0,1%10%160

a. Hy d bo mc sinh li k vng khi u t vo VN-nidex?

b. Hy d bo mc ri ro khi u t vo Vn-index?

a) Mc sinh li k vng khi u t vo Vn-Index l:

= 500 x 20% + 550 x 20% + 600 x 30% + 650 x 206 + 700 x 10% = 590

b) D bo mc ri ro khi u t vo VnIndex

(2 = (. Pi (R - )2=

= 62,45

Cu 137: Gi s Viet combank sau khi c phn ha vo u nm 2006 v tr c tc 20% cui nm ny v c mc tng trng c tc trong 4 nm tip theo l 20% nm, nhng nm sau c tc tng trng c tc n nh mc 8%. Li sut yu cu ca bn i vi c phiu ny l 15%. Hy tnh gi c phn Vietcmbank vo lc c phn ha u nm ti vi cc thng tin d bo trn.

- Gi s CP Vietcombank c xc nh

=

=

Cu 138: Gi CP 41.290 () cng ty A c h s ( = 3. Li sut tn phiu kho bc l 7% mc b ri ro th trng chng khon hin ti l 8%. Li sut u t P cng ty ny gn y l 30%. Dng cng thc m hnh nh gi ti n xem xt th trngc nh gi CP ny cao hn gi tr hay khng? gii thch?

M hnh: CAMP

R( = Rf + B (RM - Rf)

= 7% + 3 + 8% = 0,31 = 31% > 30%

Gi c phiu ny c nh gi thp hn gi tr ( Khng.


DA = 200 t (1900)

PA = 15 nm

r = 8%

DL = 150 t (950)

PL = 6 thng = 0,5

Ta c:

$ DL = t

dp = D/ (1+r) x ng x P ( vn vay

DA =

$ t

1. Li sut tng 1% ti sn n gim 69,44

2. Li sut tng 1% th TS c gim 2,777,78

Khi li sut tng (r ( TS n gim 69,44

Gi tr TS n = 150 - 69,44

Khi li sut tng (r ( TS c gim 2.777,7

Gi tr c = 200 - 2777,7 (r

- Khi TS c = 0 th:

150 - 69,44 (r = 200 - 2777,7 (r

2.708,34 (r = 50 ( (r = 1,85

- Khi li sut t 8 + 1,85 = 9,85% th ngn hng mt kh nng thanh ton.

im v n ca ngn hng l 9,85%.

Cng thc s dng vo bi tp trn:

Cu 140: Qu u t VFI c k hoch u t vo danh mc vi c cu nh sau

a. Chng khon nim yt 20%

b. Chng khon cha nim yt 30%

c. Tri phiu Chnh ph 40%

d. u t khc 10% (Bt ng sn,...)

Gi s ta c thng tin v ri ro nh sau: Ri ro ca chng khon nim yt (a l 8%), ri ro ca b l 12%, ri ro ca d l 15%, tri phiu Chnh ph coi l phi ri ro v cc thng s v tch sai nh sau:

Cov(a, b) = 96, Cov (a,c) = 0, Cov (a,d) = -110, Cov (c,b) = 0, Cov (b, d) = -140,

Cov (c,d)= 0

Hy d bo ri ro ca VF1 theo danh mc u t vi thng s cho trn y.

*******

0,2 (12 = (0,2)2 (8%)2 x Cov ((2)

0,3 (22 =(0,3)2 . (12)2 x Cov (ri, r3) = **********

0,4 (32 = (0,4)2 (15%)2 x Cov (r1, r4) = Cov (r4; r10 = -110

0,1 (42 = (0,1)2 (10%) x Cov (r2; r4) = Cov (r4; r20 = -140

= 13,77 + (-0,64) = 17,13

Op = = 4,14%

Cu 141: Ta c s liu v 2 c phiu theo bng sau:

NmLi sut u t vo CPALi sut u t vo CP B

2002-5%4%

200310%-2%

2004-4%8%

20057%-9%

Bn hy

a) Xc nh thu nhp k vng u t vo A & B

b) Ri ro u t vo A & B

c) Tch sai ca A & B

d) H s tng quang gia A & B

Gii thch cc kt qu tnh c

a)

b)

( 6A = 8,24

c)

=

Cu 142: Cn 20 nm na bn s v hu. Bn d nh tch cp mt s tin gi tit kim hng li vo lc ngh hu vi mc tiu l c thm mi thng mt triu ng ngoi lng hu. By gi cho n lc v hu l thi k pht trin nn li sut bnh qun ca th trng l 9% nm. Lc bn v hu (20 nm sau) kinh t n nh nn li sut ch c 0,5%/thng. Nu nm no bn cng b mt mn tin vo tit kim nh nhau, th mi nm bn phi b bao nhiu thc hin c mc tiu ca mnh.

Cu 143: Mt ngn hng c phn c tng ti sn l 400 t ng, trong ti sn c c t vn vay l mt na. Li thun ca ngn hng nm nay c th l 30 t ng. T l c tc d kin chi l 10 t ng. Gi s doanh nghip tng trng u trong tng lai. Bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin :

TL:

Vn ch s hu = 400 - 200 = 200 t ng

ROE = 30 t / 200 t = 15%; b = (30 - 10) / 30 = 66.67%

g = ROE.b = 15% x 66.67% = 10%.

Cu 144: Gi s ngn hng bn ang s hu mt lng tri phiu chnh ph, k hiu CP4A0304 pht hnh ngy 03/03/2002, Gim c ca bn ang c bn chng vo ngy hm nay (ngy thc hin kim tra). Bit rng F = 100 ngn ng; C = 9,4% tr sau, mt ln; M =15 nm; li sut yu cu l 10%. Bn hy gip gim c ca mnh nh gi TP trn (ch cn vit 3 cng thc nh gi).

Cu 14: Cng tri gio dc c mnh gi l 100.000 ng, thi gian o hn l 5 nm, c li sut gp 40%/5 nm cn 3 nm na do hn ang bn gi 110.000 ng, li sut tit kim di hn 3 nm ang l 8%/nm. Trn quan im li sut u t tri phiu v gi tit kin nh nhau, c mua c tri phiu trn khng? V sao?

P = (F ( C) / (1 ( r)3 = (100.000 ( 100.000 x 40%) / (1 ( 8%)3+ = 140.000/1,2597P = 111.136 > 110.000

( nn mua cng tri ny.

Cu 145: Gi s ch s Dow Jone cng nghip hin l 10400 im, d on tr gi ca ch s ny mt nm sau, bng phng php iu tra mt s chuyn gia phn tch chng khon ngi ta c t liu nh sau:

DJ CN sau 1 nm (Rj+S ngi d onPiRiPi

10200250,252550

10400250,252600

10800250,252700

11200250,252800

10.650

a. Hy d bo mc sinh li k vng khi u t vo DJCN

b. Hy d bo mc ri ro u t vo DJCN

TL:

a. ER = ( RiPi = 0,25 x 10200 + 0,25 x 10400 + 0,25 x 10800 + 0,25 x 11200

= 10650

b. (2 = (pi x (Ri - ER)2= 0,25 (10200 - 10650)2 + 0,25 (10400 - 10650)2

+ 0,25 (10800 - 10650)2 + 0,25 (11200 - 10650)2= 0,25 (122500 + 62500 + 22500 + 302500) = 127500

( = 357

Cu 146: Gi s Vietcombank s c phn ha xong vo u nm sau (2007), c tc d kin tr vo cui nm 2007 l 20% v trong 3 nm tip theo c tc tng trng 10% nm, nhng nm tip theo c tc tng trng c tc n nh mc 7%. Li sut yu cu c phiu ca bn vi c phiu ny l 12%. Bn hy nh gi c phiu ny vo lc pht hnh u nm ti.

Cu 147: Cng ty A c li sut yu cu l 16% v c tc hin ti l 3000 ng. Nu gi hin ti ca c phiu ny l 55.000. Gi s t l tng trng c tc u th tng trng c tc l bao nhiu?

P0 = (3000 x (1 + g)) / (1,6 - g) = 55000

( g = 10%








c. Tnh tch sai mong i (expected covariance) ca li nhun A &B

d. Tnh h s tng quan ca li nhun A&B


TL:

a. ER(A) = ( wiRiA = 0,2 x (-12) + 0.4 x 18 + 0,4 x 24 = 14.4

ER(B) = ( wiRiB = 0,2 x 8 + 0,4 x (-2) + 0,4 x (-10) = -3,2

b. (A2 = (wi x (RiA - ERA)2 = 0,2 x (-12) - 14.4)2 + 0,4 (18-14.4)2

+ 0,4 x (24-14,4)2 = 181.44

( (A = 13.47

(32 = (wi x (RiB - ERB)2 = 0,2 x (8 - (-3,2))2 + 0,4 (-2-(-3,2))2

+ 0,4 x (-10-(-3.2))2 = 44.16

( (B = 6.64

c. CovA3 = (R (R1A - ERA) (RiB - ERB) = -83.52

d. (A3 = covA3/(A(B = - 8352 / (13.47* 6.64) = -0,962

( C th kt hp A, B trong mt danh mc

Do (AB ***** - 1 ( A, B quan h cht ch

Cu 149: Mt ngn hng c tng s vn 200 t, trong 30 t vn t c. Vn vay c thi gian o hn bnh qun gn 6 thng. Gim c ngn hng l ngi kinh doanh mo him nn ly ton b vn vay mua t hp tri phiu c thi gian o hn bnh qun l 15 nm. Li sut chit khu ca tt l 7%. Xc nh im v ca ngn hng ny?

TL:

Vn i vay = 200 - 30 = 170 t ng

Thi gian o hn bnh qun l 6 thng ( DL = 6/12 = 0.5

SDL = 1/(1+y) x (DtPt) = 1/1,07 x (0.5 * 170) = 79.4

SDA = 1 / (1+y) x (DAPA) = 1/1,07 x (15*200) = 2803.7

( Gi tr ti sn c khi li sut tng (y l: 200 - 2803.7*(y

Gi tr ti sn n khi li sut tng (y l: 170 - 79,4 * (y

( (= 1,1%.

Vy khi li sut tng n mc 8,1% th ngn hng mt kh nng thanh ton.

Cu 150: Mt nh u t c khon tin 10.000.000 v d nh u t trong thi hn 2,5 nm vo danh mc cc tri phiu nh sau:

- TP A: tri phiu chit khu, thi gian o hn 3 nm, F = 100.000

- TPB: Tri phiu coupon 6%, thi gian o hn 2 nm, F = 100 hn **** x th trng hin ang l 10%. Bn hy xc nh gip nh u t danh mc 2 TP trn sao cho t danh mc tin ra v phng trnh c ri ro theo bin php trung hfa ri ro li sut.

TL:

w1 - t l u t vo TPA

w2 - t l u t vo TPB

( = 10%

w1 = w2 = 1

w1 DA + w2D2 = 25

= [(1 x C / (1+r) + 2x C/ (1+r)2 + D + nx (C/(1+r)0] / P

PA = F / (1 + r)3+ = 100000 / 1.13 = 75131

PB = C1 / (1 + r) + (C2 + F) / (1 + r)2 = 6000 / (1 + 10%) + (6000 + 100000) / (1 + 10%)2 = 930.58

DA = [3 x 100000 / (1 + 1,1)3] / 75131 = 3

DB = 1 x ([6000 / (1 + 10%)] + 2 x [(6000 + 100000) / (1 + 10%)2] = 1.94

C: w1 + w2 = 1

v w1. 3 + w2 . 1.94 = 2.5

( w1 = 0,53;w2 = 0.47

( S tin u t vo TP A l 10000000 x 0.53 = 5300000

S tin u t vo TP B l 10000000 x .47 = 4700000

STP A cn mua l: 5300000/75131 = 70.54 TP

S TP B cn mua l: 4700000 / 93058 = 56.50 TP

Cu 151: Sau 20 nm na bn v hu, ngoi tin lng hu bn mun c thm 1 thng 2.000.000 ng t tin gi tit kim tiu xi. Hin bn cha c ng no d tr. Trong 20 nm ti nn kinh t trong thi k pht trin nhanh nn li sut tin gi ch 0,5% thng. Nu bn mun t mc tiu trn th bn phi b mt khn tin tit kim bao nhiu hng nm?

Cu 152: Ngn hng ca bn c tng ti sn l 200 t ng, trong vn vay l 170 t ng. Li thun ca ngn hng nm l 15 t ng. T l c tc d kin ch l 3 t ng. Bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin trn.

Cu 153: Gi s n v bn ang s hu 1 lng tri phiu Chnh ph k hiu l PC4A34D3 pht hnh ngy 24/9/2003. Do cn vn, gim c ca bn ang c nh bn chng vo ngy bn lm bi kim tra.

Bit rng: F = 100.000 ng

C = 9.7%

M = 15 nm, li sut yu cu m gim c t ra l 10%

Bn hy vit 3 cng thc nh gi tri phiu trn.

Cu 154: Khi vo trang web http:// www.investinginbonds.com/cales v cho thy cc thng s ca Tri phiu quc t do Vit Nam va pht hnh, ta nhn c cc thng tin sau (gi tri phiu ny l 98,228$).

- YTM: 7,13 (Li sut o hn bnh qun)

- Duration: 7,525 (Thi gian o hn bnh qun)


a. Hy tnh thi gian o hn bnh qun iu chnh ca tri phiu ny?

b. Nu li sut th trng tng 1% th gi Tri phiu gim bao nhiu $?

Cu 155: Gi s ch s Vn-index hin ti l 540 im, d on tr gi ch s ny vo cui nm nay bng phng php iu tra mt s chuyn gia phn tch chng khon chng ta c t liu nh sau:

Vn-index 1 nm sauS ngi d onP'tMc chnh lch Vn-index

50020 = 0,2%20%-40

55020 = 0,2%20%10

60030 = 0,3%30%60

65020 = 0,2%20%110

70010 = 0,1%10%160

a. Hy d bo mc sinh li k vng khi u t vo VN-nidex?

b. Hy d bo mc ri ro khi u t vo Vn-index?

Cu 156: Gi s Ngn hng ca bn c vn t c l 50 t v vn vay l 150 t . Vn vay c thi gian o hn bnh qun l 6 thng. Gi s Gim c ngn hng ny kinh doanh mo him v dng tt c vn cho vay u t vo cc danh mc u t di hn c thi gian o hn bnh qun l D = 15 nm. Li sut chit khu hin ti l 8%. Hy xc nh im v ca Ngn hng ny.

Cu 157: Qu u t VF1 c k hoch u t vo danh mc vi c cu nh sau:a. Chng khon nim yt 20%

b. Chng khon cha nim yt 30%

c. Tri phiu Chnh ph 40%

d. u t khc 10% (Bt ng sn,...)

Gi s ta c thng tin v ri ro nh sau: Ri ro ca chng khon nim yt (a l 8%), ri ro ca b l 12%, ri ro ca d l 15%, tri phiu Chnh ph coi l phi ri ro v cc thng s v tch sai nh sau:

Cov(a, b) = 96, Cov (a,c) = 0, Cov (a,d) = -110, Cov (c,b) = 0, Cov (b, d) = -140,

Cov (c,d)= 0

Hy d bo ri ro ca VF1 theo danh mc u t vi thng s cho trn y.


VN-Index 1 nm sauS ngi d on

50020

55020

60030

65020

70010


b. Hy d bo mc ri ro khi u t vo VN-Index.

Li gii:

-0.0740.2

0.02850.2

0.11110.3

0.20370.2

0.29630.1

F(R) = (R x P = 0.0926 = 9.26%

( =

Cu 159: Gi s VCB sau khi CPH vo u nm 2007 v tr c tc trong 3000/c phiu cui nm nay v c mc tng trng c tc trong ba nm tip theo l 50%/nm, nhng nm sau tc tng trng c tc n nh mc 10%. LS yu cu ca bn /v CP ny l 20%. Hy nh gi CP VCB vo u nm ti vi cc thng tin d bo trn.

Li gii:

D0 = 2000

gt = 50%

n1 = 3 nm

g = 10%

r = 20%

D1 = D0 (1 + g1) = 4500

D2 = Do (1 + g1)2 = 6750

D3 = Do (1 + g1)3 = 10125

D4 = Do (1 + g1)4 (1 + g2) = D3 (1 + g2) = 11.137,5

P3 = D4/ (r + g2) = 111.375

P0 = D1 / (1 + r) + D2 / (1 + r)2 + P3 / (1 + r)3 = 78.750

Cu 160: Gi s bn mua c phiu BT6 vo ngy 26/7/2006 vi gi 42,8 ngn ng v sau n ngy 31/7 l ngy giao dch khng hng quyn mua trong t pht hnh mi vi t l 5: 1 (5 c phiu c mua 1 c phiu mi vi gi 33,6 ngn ng). Gi CP ngy vo phin trc 31/7 l 45 ngn ng. Gi CP ny vo ngy 4/10 l 55 ngn ng. Bn hy tnh t sut sinh li ca bn trong thi gian trn (26/7 ( 4/10) khi u t vo BT6. Bit rng s liu trn l s liu thc v trong thi gian BT 6 c tr c tc 800 cho mt cp.

Li gii

P0 = 42,8 ng

P1 = 55 ng

DIV = 800

Quyn mua c phiu = 45 - 33,6ng = 11,4 ng

T sut sinh li=(Div + (P1-P0) + quyn mua CP) / P0 = 2.4400/45.800 = 57%

Cu 161: Gi s NH ca bn c VTC l 500 t v vn vay l 190, vn vay thi gian o hn bnh qun l 6 thng. Gi s G NH ny kinh doanh mo him v dng tt c vn trn cho vay u t cc danh mc u t di hn c thi gian o hn bnh qun D = 15 nm. Li sut hin ti l 8%. Hy xc nh im v ca ngn hng ny.

Cu 162: Trn th trng c 2 loi chng khon vi thng s nh sau:

Xc sut60%40%

Li nhun CKA20%4%

Li nhun CKB20%24%

Bn hy xc nh li sut k vng v ri ro u t vo hai CK trn theo cc phng n u t nh sau:

a. 100% vo CKA

b. 100% vo CKB

c. 50% vo CKA v 50% vo CK B

Bn c nhn xt g khng v kt qu tnh c

Li gii:

a. E^ = (KA x P = 13,6^

(A = (((RB - EB)2 x P = 7,83%

b. EB = ( RB x P = 10,8%

(B = (((RB - EB)2 x P = 10,77%

c. EAB = EA x WA + EB x WB = 0,122 = 12,2%

(AB = (( (RA - EA) (RB - EB0 x P = - 0,8448

Cu 163: Sau 25 nm na bn v hu, ngoi tin lng, bn mun c thm mi nm 120 tr ng t tin gi tit kim tiu xi v i du lch nm chu. Hin bn cha c ng no d tr. Trong 25 nm ti nn kinh t thi k pht trin nhanh nn li sut tin gi t mc 10% v k t khi bn v hu li sut tin gi ny ch t 8% nm. Nu bn mun t mc tiu trn th t nay hng nm bn phi b mt khon tit kim bao nhiu.

Li gii:

120 tr/10% = C [(1 + 8%)25 - 1] / 8% ( C = 16.414.535 ng

Cu 164: Ngn hng bn c tng ti sn l 1900 t ng, trong vn vay l 900 t ng, li thun ca NH nm nay c th l 420 t ng, c tc d kin chi l 190 t ng, bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin trn.

Li gii:

( TS = 1900 t

( N = 900 t

( vn CSH = 1900 - 900 = 1000

ROE = 420/1000 - 0,42


C tc chi = 190 t

g = ROE x t l gi li

= 0,42 x (1 - 190/420) = 0,23 = 23%

Cu 165: Gi s n v bn ang s hu 1 lng tri phiu, k hiu CP4AS40 pht hnh ngy 16/6/2002, do cn vn G ca bn ang c nh bn chng vo ngy bn ang lm kim tra (23/4/2007, bit rng F = 100 ngn ng, C = 9,7%; M = 10 nm; Li sut yu cu m gim c t ra l 10%. Bn hy vit 3 cng thc nh gi TP trn.

Li gii:

TCS = 16/6/06 ( 23/04/07 = 311

t = 5 nm

P = (1 + r)tcs/D x [F x C%/r x [1 - 1/ (1+r)r ] + F / (1 + r)t]

Li l cho ti ngy thanh ton (Sch gio khoa trang 363)

Gi th trng = P - Li l






2. Nu Li sut thng tng 1% th gi TP gim bao nhiu $?

Li gii:

P = 98,228

dy = 1%

YTM = 7,13%

MD = 7,525

li = 64,953

1. MoD = MD/ (1 + YTM)

2. % thay i gi = - MoD x dy + 1/2 i li x (dy)2Cu 167: Tnh gi c phiu hin nay ca 1 cng ty bit cng ty c t l thu nhp trn vn s hu l 12,5%. Cng ty chia c tc hng nm l 40%. c tnh thu nhp ca 1 CP trong nm ti l 3$. Li sut chit khu theo yu cu l 10%.

ROE = 12,5%D = 40%

DIVo = 3$

r = 10%

p dng cng thc: Po = DIV1* (1 + g) / (r - g)

g = ROE * b = 12,5 * (1-0,4) = 7,5%

=> Po = 3 * (1+7,5)/ (0,1 - 0,075) = 64,5$


VN-Index 1 nm sauS ngi d on

50020

55020

60030

65020

70010


b.Hy d bo mc ri ro khi u t vo VN-Index.

Li gii:

-0.0740.2

0.02850.2

0.11110.3

0.20370.2

0.29630.1

F(R) = (R x P = 0.0926 = 9.26%

( = ((2 = (((R - Er)2 x P = 0.1156 = 11.56%

Cu 169: Gi s VCB sau khi CPH vo u nm 2007 v tr c tc trong 3000 /c phiu cui nm nay v c mc tng trng c tc trong ba nm tip theo l 50%/nm, nhng nm sau tc tng trng c tc n nh mc 10%. LS yu cu ca bn /v CP ny l 20%. Hy nh gi CP VCB vo u nm ti vi cc thng tin d bo trn.

Li gii:

D0 = 2000

g1 = 50%

n1 = 3 nm

g = 10%

r = 20%

D1 = D0 (1 + g1) = 4500

D2 = D0 (1 + g1)2 = 6750

D3 = D0 (1 + g1)3 = 10125

D4 = D0 (1 + g1)4 (1+g2) =D3 (1+g2) = 11.137,5

P3 = D4/ (r + g2) = 111.375

P0 = D1/(1+r) + D2/ (1 + r)2 + P3 / (1+ r)3 = 78.750

Cu 170: Ga s bn mua c phiu BT6 vo ngy 26/7/2006 vi gi 42,8 ngn ng v sau n ngy 31/7 l ngy giao dch khng hng quyn mua trong t pht hnh mi vi t l 5:1 (5 c phiu c mua 1 c phiu mi vi gi 33,6 ngn ng). Gi cp ngy vo phin trc 31/7 l 45 ngn ng. Gi cp ny vo ngy 4/10 l 55 ngn ng. Bn hy tnh t sut sinh i ca bn trong thi gian trn (26/7 ( 4/10) khi u t vo BT6. Bit rng s liu trn l s liu thc v trong thi gian BT6 c tr c tc 800 cho mt cp.

Li gii

Po = 42,8 ng

P1 = 55ng

DIV = 800

Quyn mua c phiu = 45 - 33,6 ng - 11,4 ng

T sut sinh li = (Div + (P1 - Po) + quyn mua CP)/ Po = 2.4400/45.800 = 57%


Cu 172: Trn th trng c hai loi chng khon vi thng s nh sau:

Xc sut60%40%

Li nhun CKA20%4%

Li nhun CKB20%24%

Bn hy xc nh li sut k vng v ri ro u t vo hai CK trn theo cc phng n u t nh sau:

a. 100% vo CKA

b. 100% vo CKB

c. 50% vo CKA v 50% vo CK B

Bn c nhn xt g khng v kt qu tnh c

Li gii:

a. E^ = (KA x P = 13,6^

(A = (((RB - EB)2 x P = 7,83%

b. EB = ( RB x P = 10,8%

(B = (((RB - EB)2 x P = 10,77%

c. EAB = EA x WA + EB x WB = 0,122 = 12,2%

(AB = (( (RA - EA) (RB - EB0 x P = - 0,8448

Cu 173: Sau 25 nm na bn v hu, ngoi tin lng, bn mun c thm mi nm 120 tr ng t tin gi tit kim tiu xi v i du lch nm chu. Hin bn cha c ng no d tr. Trong 25 nm ti nn kinh t thi k pht trin nhanh nn li sut tin gi t mc 10% v k t khi bn v hu li sut tin gi ny ch t 8% nm. Nu bn mun t mc tiu trn th t nay hng nm bn phi b mt khon tit kim bao nhiu.

Li gii:

120 tr/10% = C [(1 + 8%)25 - 1] / 8% ( C = 16.414.535 ng

Cu 174: Ngn hng bn c tng ti sn l 1900 t ng, trong vn vay l 900 t ng, li thun ca NH nm nay c th l 420 t ng, c tc d kin chi l 190 t ng, bn hy d bo mc tng trng ca c tc trong tng lai bng cc thng tin trn.

Li gii:

( TS = 1900 t

( N = 900 t

( vn CSH = 1900 - 900 = 1000

ROE = 420/1000 - 0,42


C tc chi = 190 t

g = ROE x t l gi li

= 0,42 x (1 - 190/420) = 0,23 = 23%

Cu 175: Gi s n v bn ang s hu 1 lng tri phiu, k hiu CP4AS40 pht hnh ngy 16/6/2002, do cn vn G ca bn ang c nh bn chng vo ngy bn ang lm kim tra (23/4/2007, bit rng F = 100 ngn ng, C = 9,7%; M = 10 nm; Li sut yu cu m gim c t ra l 10%. Bn hy vit 3 cng thc nh gi TP trn.

Li gii:

TCS = 16/6/06 ( 23/04/07 = 311

t = 5 nm

P = (1 + r)tcs/D x [F x C%/r x [1 - 1/ (1+r)r ] + F / (1 + r)t]

Li l cho ti ngy thanh ton (Sch gio khoa trang 363)

Gi th trng = P - Li l






2. Nu Li sut thng tng 1% th gi TP gim bao nhiu $?

Li gii:

P = 98,228

dy = 1%

YTM = 7,13%

MD = 7,525

li = 64,953

1. MoD = MD/ (1 + YTM)

2. % thay i gi = - MoD x dy + 1/2 i li x (dy)28/8/02

9/5/05

2tr

2tr

2tr

20 nm

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