Thm nh d n u t Bi c1 Bquanhngkhinimhnlmvnhngnhnghachangbitbaongnthoam,gy tranh ci v tn km nhiu giy mc, bn cht ch thc ca d n u t suy cho cng ch n gin l vic b ra nhng ng tin ngy hm nay k vng s thu c chng v trong tng lai. Dng tin chi ra hm nay lthc nhng dng tin s thu v trong tng lai mi ch ld on,hycnlnhngconsvhn,ikhicgtgiartp,nmynlnhtrnnhng trang giy trng m thi. Chnh v ci ngy mai cha bit y m ai cng t ra c l khi ngh v d n. Nhngtintctnhthigian.Ti,bn,ccnhtbnvcBNgoichnquna,ai cng mun nhn c ng tin chc chn ngy hm nay (ng tin an ton) hn l nhng ng tin khng chc chn (ng tin ri ro) vo nm sau. Mt khc, cc ngun lc lun hn hp ch khng phi l v tn. Thm nh, la chn v quyt nh u t vo mt d n cng c ngha l chp nhn b quac hi u t vo mt d n khc 2.C nh vy, d n khng c g l gh gm c m tri li, n cha ng nhng iu rt gn givisuynghtnhincattcmingi.Nhngcuhithtnginvbnhthngnh vy s tr thnh ch dn dt cho cc tho lun ca chng ny. Do phm vi ca ch quyn sch, mt s ni dung su hn v thm nh d n s khng c dp cp n 3. Chng ny ch nhm tp trung tho lun nhng vn k thut: tnh thi gian ca tin t; k thut chit khu dng tin; h thng cc ch tiu nh gi d n, x l lm pht, k thut phn tch ri ro ca d n.I.V sao tin t c tnh thi gian Mt ng tin c gi tr khc nhau vo hai thi im khc nhau. Khong cch thi gian cng di v c hi sinh li cng cao th s khc bit trong gi tr gia hai thi im ca n cng ln. Quvy,nubnchobnthncamnhmnstin50ngnngvobuisng,n bui tra th nhn li 4. Lc y, 50 ngn l nh nhau, hay ni cch khc, bn khng thy c s khc bit no v gi tr thi gian ca tin t. Nhng nu bn mua c phiu ca Cng ty VaBiCo cch y hai nm vi gi 40 ngn ng mt c phiu, tt nhin mc ch mua (u t) l kim li, th li l cu chuyn khc. Sau khi mua, gi c phiu c lc tng cao hn 40 ngn, bn bo hy ch ln na kim li nhiu hn; c lc gi rtxungthphn40ngn,bnhyvngnslntrli.Hmnaytrnthtrngging40 ngn, v cn tin nn bn mang i bn. Bn tng b ra 40 ngn ng cch y hai nm, by gi

1 Trch chng 12, sch: K ton qun tr (2003), NXB i hc Quc gia Tp. HCM, NXB Thng k ti bn ln th hai, cng tc gi. 2 Khoa hc kinh t suy n cng l khoa hc v s khan him cc ngun lc. Qu vy, nu ngun lc l v tn th s khng cn kinh t hc v tt nhin khng cn phi thm nh d n v c mn hc k ton qun tr ny, cng khng cn na. 3 C th tham kho cc sch (cng tc gi): Phn tch hot ng doanh nghip (2000)-NXB HQG, NXB Thng k ti bn ln th su; Phn tch qun tr ti chnh (2002)-NXB HQG, NXB Thng k ti bn ln th ba. 4 gi l bn thn m, ai n ly li. Thm nh d n u t Prepared by NGUYEN TAN BINH23/9/2012 thu li cng ng 40 ngn ng. Lc ny, bn c ni l hu vn? Cu tr li chn hn l khng. V nh vy, bn tha nhn rng cng s tin 40 ngn ng, gi tr ca chng s khc nhau vo hai thi im khc nhau.C t nht l ba l do sau y c th dng gii thch v tnh thi gian ca tin t 5. 1.1Chi ph c hi ca tin ng tin lun c c hi sinh li, n c th dng u t v c li ngay lp tc. Ni theo cch hn lm l lun c chi ph c hi cho vic s dng tin 6. Khi bn u t vo c phiu cng c ngha l chp nhn b qua c hi sinh li t vic u t mua t 7. Nu li sut tin gi ngn hng l 10% nm, vic u t c phiu VaBiCo trn y ti thiu cng lm bn mt i c hi kim c s tin li l 8 ngn (= 40 ngn 20%) nu bn khim tn, hoc c th ni l nht gan, chp nhn hng mt li sut thp nht bng cch gi tit kim ngn hng (cha tnh n li kp 8). Dng tin u t vo d n l vic hy sinh li ch ngy hm nay k vng vo nhng li ch ln hn ngy mai.Ngay c khi bn s dng tin cho tiu dng cng vy. Mt s tiu dng hin ti s em li chobnthadngsmhnvcaohnlschidnhntnglai!Vnubnchu nhnthmchicxeSpacyhmnayutkimliv3nmsauchnglnocngchl chicSpacy! 9Bnphicthngvstrhontiudngny,phnthngllisut (hoc sut chit khu). S nghin cu phn k thut chit khu dng tin. 1.2Tnh lm pht T ngy c in ko v nng thn, Ngoi mun mua mt my bm nc ti vn rau ca Ngoi. Vn rau tng mt thi nui con by gi nui chu ang hc i hc nm th ba ngnh ktonmttrngihcdanhgiSiGn.Ngoic4triu,gimybm4,4triunn Ngoi khng tin. a chu cng "hin k" gi ngn hng mt nm sau tin mua my (li sut 10% nm). Khi Ngoi cm c 4,4 triu trong tay th gi my bm, c ngun gc nhp ngoi by gi tng hn 5 triu. Mt ln na Ngoi li khng tin.Ngoi li tip tc on lng ti tnggnh nc nh Ngoi tng quen chu ng sut mt i c cc, nhc nhn 10. ani,achu"trthc"nirngdsaoNgoicnglic0,4triu(?).Khng. Ngoi mt do phi ng mt th thu lm pht 11 m Ngoi no c bit bao gi.

5 Time value of money 6 Chi ph c hi (opportunity cost) c dp cp Chng 2 Phn loi chi ph. 7 Xt bn cht kinh t, kinh doanh t ai v mua bn chng khon l hon ton ging nhau. Nhng ngi trung gian hnghuhng n thun trn th trng chngkhon cgi bng ci tn rtp l"ccnhmigii chng khon" (brokers), va trung gian va tham gia mua bn c gi l "cc nh u t chng khon" (dealers), nhng sao nhng vai tr nh vy trong lnh vc a c th gi l "c" v "k u c"? 8 Ni theo ngn ng bnh dn l: "li m li con". 9 Ni theo cch bnh dn l: sng trc kh sau hoc l kh trc sng sau. trn i, khng c g l sng trc ri sng sau c ! 10 Ngoi khng c dp nng cao "nng sut lao ng nng nghip", nn kinh t b qua c hi "kch cu" v gp phn "chuyn i c cu kinh t". D tnh nu c my bm, Ngoi s trng thm mt "cao" (n v o ca mt lung t khong 400 m2 ngoi thnh pha Ty TP. HCM) rau na v s mua mt tivi mu 14 inch xem ci lng, nhng c m bnh d khng thnh.Thm nh d n u t Prepared by NGUYEN TAN BINH33/9/2012 1.3Tnh ri ro Ai m bit c ngy sau ri s ra sao? 12 Mt ng tin s nhn c trong tng lai chc chn l khng c g chc chn c. Nhng ri ro ca thin tai hay chin tranh, s thay i th ch chnh sch hay nhng th lc d dica th trngcnh tranh, trng thi nn kinh t tng trng hay suy thoi, ch trng chnh ph tip tc bo h hay m ra hi nhp, bnh yn hay khng hong vvvnnhngthrtkhnhlngkhc,lunrnhrp.Brangvntronghoncnh, ngi ta cn c mt phn thng b p 13. Vn khng phi l s ri ro, s th khng lm, m l chp nhn v nh i ri ro nh th no. Ri ro cng cao th phn thng i hi phi cng ln. Ngc li cng hon ton ng nh vy, li nhun cng nhiu th ri ro cng lm (high return, high risk) tr thnh bi hc s ng u tin cho mi kha hc v qun tr kinh doanh. C ngi mua bt ng sn vi hy vng t li sut 30% nm, trong khi c ngi chp nhngitit kim ngn hng hng li sut 6% nm. Cngiutchngkhoncngtylisut20%nmthcngcngichnmuatriphiu chnh ph li sut 7% nm. Khng c g l c. l s sng phng ca th trng. C hi l nh nhau i vi tt c mi ngi 14. II.K thut chit khu dng tin C th ni rng chit khu dng tin l ci trcca nn ti chnh hin i. N tr thnh mt kin thc cn bn khng ch dnh ring cho cc nh qun tr ti chnh m cn l ca bt k ai, bt k lnh vc hot ng no. Mt ch bn hng ch Bnh Ty cng tha bitrng cho vay tin vi mt li sut rt thp khi ch t bt k hp ng vi mt cng ty bo him nhn th.Trong mc ny, chng ta s nghin cu cc phng php chit khu dng tin cng nhng ng dng rt i thc ca chng. 2.1Gi tr tng lai ca mt ng Nu bn gi ngn hng 100 (n v tin), li sut 10% nm, mt nm sau bn s c: 110 = 100 + 100 10%= 100 (1 + 10%) Bn tip tc gi s tin 110 ngn hng, mt nm sau na bn s nhn c: 121= 110 + 110 10% = 110 (1 + 10%)Thay 110 = 100 (1 + 10%), ta c th vit: 121= 100 (1 + 10%) (1 + 10%)

11 Inflation tax. Mt nh lnh o phng Ty no tng ni rng, thu lm pht l mt loi thu tn bo nht trong lch s nhn loi. Khi bn cm trong tay 1 triu ng m gi tr ca n nh 0,5 triu th bn "ng" thu lm pht htmt nari.chng li s lm pht, ngitakhngct tin "digi"hay treo trn "ngn da" mphi a vo u t bng cch mua tri phiu, c phiu, ti thiu l gi tit kim. Theo cch , nn kinh t s c vn hot ng. Mt khi khng c g mua, ngi ta mua t th cng khng c g l c. 12 Que sera sera 13 Risk premium: ph thng ri ro. 14Tr nhng k c c thng tin ni b. T nh cc v lnh o ca mt s tp on va ph sn trong thi gian gn y (M) hoc nhiu quan chc ngnh a chnh v qui hoch "chm im" tuyt i chnh xc trn tm bn s c cng khai vo tun ti (!). Thm nh d n u t Prepared by NGUYEN TAN BINH43/9/2012 = 100 (1 + 10%)2 khi qut, t: PV = 100FV2= 121 r = 10% n = 2 Ta c: FV2 = PV (1 + r)2 Tng t cho FV3, FV4, FV5,,v: FVn = P (1 + r)n cng thc (1) Trong , PV :gi tr s tin hin ti (present value) r :li sut (rate) n :s nm 15 (number) FVn :gi tr tng lai (future value) ca s tin PV sau n nm, vi li sut l r, k ghp li (vo vn)lnm.Vcbit,Hs(1+r)n,nhntlmchogitrtPVbinthnhFVn chnh l gi tr tng lai ca 1 ng ng vi li sut l r, thi gian l n. (1+r)ncn cgi lh s tch ly hayh s li kp 16. V h s tch ly lun ln hn hoc bng 1 (> 1). Gi tr tng lai lun ln hn (hoc bng) vi gi tr hin ti. (Xem ph lc cc bng h s tch ly cui sch) Trong cng thc (1) v c cc cng thc tip theo ta thy c cc yu t: FV, PV, n, r. V d gi l "ton ti chnh", "chit khu dng tin" hay l g gh gm i na th vn l vic i tm gi tr cc yu t trn bng cc bi ton nhn chia, quy tc tam sut v cng n gin. Mt ln na, vn khng phi l tnh ton m l s vn dng chng nh th no trong i thc.Mt khc, tt c nhng g thuc v tnh ton c my tnh lm (to do), b no nh b ca con ngi ch dnh ngh (to think) m thi.

ng lo lng cc cng thc! Tt c cc tnh ton trong chng ny (v c quyn sch) u c hng dn Excel.-V d 12.1:Tnh gi tr tng lai FVn Bn s c bao nhiu tin khi tt nghip i hc (4 nm) nu by gi (u nm th nht) bn mang 2 triu gi vo ngn hng, vi li sut c nh 10% nm. S tin 2 triu vi li sut 10% nm, sau thi gian 4 nm s tr thnh: FV = PV (1+r)n

15 C th ng dng vik on l tun, thng, qu, 6 thng. Trong d n thng l nm. Mt lu khc l, n lk on, l khong cch thi gian ch khng phi l k hiu nm lch. 16 Compounding factor Thm nh d n u t Prepared by NGUYEN TAN BINH53/9/2012 FV = 2(1+10%)4 = 2 1,46 = 2,92 triu ng (h s tch ly 1,46 c c ct 10% v hng 4 trong bng gi tr tng lai ca mt ng, phn ph lc cui sch)-V d 12.2:Tnh li sut r Li sut no lm cho s tin 2 triu tr thnh 2,92 triu sau 4 nm? 2,92=2(1+r)4 Vit cch khc: (1+r)= 41,46 =1,461/4=1,1 Vy, r = 0,1 hay 10% -V d 12.3:Tnh thi gian n Phi mt bao nhiu nm, tng sn phm qucni (GDP) bnh qun u ngica Vit Nam tng gp 2 ln so vi hin nay, nu nn kinh t chng ta phn u gi c tc tng trng u hng nm l 7,2%? 17 p dng cng thc (1) 2=(1+7,2%)n =(1,072)n Ly logarit 18 hai v Ln 2 = n Ln 1,072 Suy ra Kt qu: phi mt n 10 nm. -V d 12.4Tnh thi gian n (tip theo) Phi mt bao nhiu nm, tng sn phm qucni (GDP) bnh qun u ngica Vit Nam bng vi mc nm 1995 ca mt s quc gia? V d: GDP bnh qun u ngi ca Vit Nam hin nay l 450 la, v phn u t tc tng trng hng nm l 7,5% th cn lu lm. Bn s nh Excel tnh nhanh chng cho bn kt qu bun sau y 19.

17 Cha tnh n tc tng dn s. 18 Lgarit t nhin (Natural logarithm), cn gi l Logarit c se (e = 2, 7183) 19 Cltrongccschgiokhoacpmt,mngitaangcit,phidychotremsthtrngnctart ngho v hun c ni lo v iu . Thm nh d n u t Prepared by NGUYEN TAN BINH63/9/2012 GDP u ngi ca Vit Nam 450 Tc tng trng 7,5% H s tch ly 1 nm (=1+0,075)1,075 Ln 1,0750,07232Quc gia GDP ungi 1995 (USD) So viVit Nam (ln) Lni S nmcn thit (nm) Nht Bn9.640 884,4862 Hoa K 26.980 604,0957 Singapore 26.730 594,0856 Thailand 2.740 61,8125 HNG DN EXCEL (cc tnh ton trong nhng v d trn) (1)Bnh phng, cn s Bn c th s dng phm nng tnh nhanh cc php tnh ly tha, cn s nh sau: Ly tha: Shift v du ^. V d bn mun tnh 23, bn ch cn nh: =2^3 v OK, Excel s cho bn kt qu l 8. Cn s: Shift v du ^, m ngoc n, nh phn s vi t s l 1 v mu s l bc ca cn, ng ngoc n v OK.V d bn mun tnh 38bn s nh nh sau:= 8^(1/3), kt qu s l 2.(2)Hm Ln Tng t, dng phm nng tnh nhanh gi tr logarit. V d bn mun tnh Ln 88, bn s nh: =Ln(88), Excel s cho bn kt qu l 4,48.Nhng nu bn mun i thm cc hm Excel lm quen, ri thn vyu, th tng t cc hm thng k (Statistical) c hng dn cc chng trc, nhng by gi l hm ton v lng gic (Math&Trig). utinbnbmntfx,chnloihmMath&Trig,tnhmlLnchnghn,nhdi y: Thm nh d n u t Prepared by NGUYEN TAN BINH73/9/2012 Nh l ch cn tnh mt s thi, sau dng lnh copy b ph thy Excel tnh cc s cn li.(3)Hm FV Cng trong fx, bn chn hm ti chnh (financial) v bn s c rt nhiu th, trong c hm FV. Lu :Thm nh d n u t Prepared by NGUYEN TAN BINH83/9/2012 -Bn s b qua Pmt, n mc gi tr tng lai ca dng tin u, ta s tr li hm ny. Khisdngphmnngbnsbquabngcchbm2lnduphy,dungncchcckhai bo tng ng trong bng tnh trn y. =- FV(C1,C2,,C3) - c ch type dng khai bo thi im thanh ton, nu u k th khai 1, nu trng th Excel mc nh l 0, tc cui k 20. (4)Hm Goal seek Sau khi bn tnh FV ca 100 ng sau 3 nmvi li sut 10% l 133,1 ng, bygi bn munbitlisut12%thslbaonhiu,bnachutvo10%sathnh12%riOK(tc Enter)bnscngayktqumi.Tngt,bnsisnmLmciunyvbn lin kt cng thc trc . Nhng nu bn mun bit gi tr tng lai s l 172 ng th li sut phi l bao nhiu, th sao? Tt nhin bn s m mm, tc ln lt cho thay i li sut, mi ln mt t cho n khi no FV bng ng 172 mi thi!Nhng trong trng hp ny, c hm Goalseek (tm kim kt qu) gip bn 21. Excel: Tools/Goalseek Bnch cn bmOK th cha 10%(B1) s tr thnh 19,8% v chagi tr 133,1 ( B5) s tr thnh 172 lp tc.

20 Excelrtchuo,nhngiubnhthng,phbinvhplucnmcnhsn.ChnghnhmFV c mc nh l m v Excel hiu l tr nn bn li phi thm du tr vo pha trc thnh dng nh trn! Nhng chu o qu mc c khi cng c khi lm ta bc mnh. 21 Nhng hy nh, nhiu hm trn Excel khng phi ch dnh cho mt nhu cu duy nht. T tng , bn c th p dng tnh cho nhiu bi ton khc. Ngay c cng thcFV cng vy, bn thy rng n khng ch dnh ring cho vic tnh gi tr thi gian ca tin t. Thm nh d n u t Prepared by NGUYEN TAN BINH93/9/2012 Nu mun gi kt qu mi, bm OK; nu mun tr tr v gi tr c, bm Cancel. n nay th bn thy rng, vic tnh FV, PV, r, n l chuyn d nh mc tin trong ti. (5)Bng h s tin t Tc cc bng tnh gi tr tng lai (h s tch ly) v gi tr hin ti (h s chit khu) ca tin t (ph lc cui sch). Bn hy m Excel ra, np cc gi tr li sut nh mun nh sau: y chng qua cng vic lin kt cng thc, mt bi tp s ng u tin khi bt u lm quen vi bng tnh Excel.Thm nh d n u t Prepared by NGUYEN TAN BINH103/9/2012 Nhng phng h c bn cha bit nn ti hng dn c th mt cht 22. V ch mt ln ny thi, ln sau s vn tt hn. Bc 1: nh my cc li sut m bn thng dng v bao nhiu ty thch, theo hng (thm ch theo ct cng c); nh my s nm 1, 2, 3, 4 theo ct, nh l ch cn nh 1, 2 thi. V n s l mt dy s u, bn nh du khi (tc bi en) hai 1 v 2 ri copy xung n khi no mi tay th thi. Excel thng minh lun chu o v thu hiu bn. Bc2:tchuttiB2,gdubng(=),mngocn,nhs1,gducng(+), nhp chut vo B1 ch li sut, ng ngoc n, g du nn (^), nhp chut vo A2 ch s nm, Enter. B2 s hin ra h s 1.05. y l gi tr tng lai ca mt ng vi thi gian 1 nm v li sut 5%. Bc 3: Tri (c nh) A2 (bng cch t con tr vo ch A2 trn thanh cng thc ri bm mt ln F4, khi a ch b tri s xut hin du $ hai bn), bm Enter hoc nhp chut vo du "tick" (nm bn tri du "="), tr li. chut vo B2 v copy theo hng, ta s c hng h s trn. Bc 4: a chut tr li B2. Tri B1 (bng cch t con tr vo ch B1 trn thanh cng thc ri bm mt ln F4), m tri A2 (bng cch t con tr vo ch A2 trn thanh cng thc ri bm ba ln F4 23), bm Enter hoc nhp chut vo du "tick" , tr li. chut vo v tr B2 v copy theo ct, ta s c ct h s trn. C th bn tip tc cho ht bng. Lc ny, mt ngn (no ) ca tay tri h trn nt F4 chtri(bmmtlnF4)vmtri(bmbalnF4);tayphirchutncccnthit "tick" OK v copy. V c th, bn cng lm cho cc bng h s cn li nh trong phn ph lc. Khithchinxong,bnnhtrangtrchop(format)vlugili(ttnhin).Khicn thay i mt li sut no bn ch vic a chut ln cha cc li sut, nh my li sut mong mun bn s c cc h s thay i tng ng.

22Ch biv ti lhavibn rng:"Excel dlm, ai d chabit "chut" ui dihayngn u c thlm c". V nh rng: "Yan can cook th cc bn cng c th nu c".23 Nh l tri th bm mt ln, m tri th bm ba ln nt F4. Vy l m th kh hn? Thm nh d n u t Prepared by NGUYEN TAN BINH113/9/2012 2.2Gi tr hin ti ca mt ng T cng thc (1) ta suy ra: PV = ( )nFV1 r + cng thc (2) Trong , r: sut chit khu 24 Hoc c th vit cch khc: PV = ( )n1FV1 r+ d dng thy c trong , n1(1+r)gilhschitkhu 25.Vngclivihstchly,hschitkhulun nh hn hoc bng 1 (s 1). Gi tr hin ti lun nh hn (hoc bng) vi gi tr tng lai. (Xem ph lc 2-1 Cc bng tnh gi tr thi gian ca tin t cui sch).

24 Thng thng, trong khi tnh gi tr hin ti ngi ta gi r l "sut chit khu" vkhi tnh gi tr tng lai th gi l "li sut". Tuy nhin, khng c g quan trng trong cch gi ny. Nu mun, bn c th gi c hai cng l li sut hoc cng l sut chit khu cng khng sao. Trong phn nh gi d n sau ny, bn cn s thy sut chit khu chnh l "sut sinh li ca vn ch s hu" (return on equity) hay l "chi ph s dng vn" (cost of capital). Hoc, bn tng nghe: dng li sut th trng chit khu dng tin hay chit khu thng phiu, v.v 25Discounting factor Thm nh d n u t Prepared by NGUYEN TAN BINH123/9/2012 Lurngtrongcngthc(2),sutchitkhurvthigiannunmdimus. Ring n gin v mt s hc cng thy rng, thi gian cng di v sut chit khu cng cao th gi tr hin ti (PV) cng thp. Ngc li vi cng thc (1) tnh gi tr tng lai, thi gian n cng di li v li sut r cng cao th gi tr tng lai cng ln. -V d 12.5:Tnh gi tr hin ti PV Tng lai 5 nm sau, bn s nhn c s tin l 1610 (n v tin) th by gi gi tr ca n l bao nhiu, vi c hi sinh li ca vn l 10% nm? Gi tr hin ti ca s tin 1610 s nhn trong tng lai sau 5 nm, vi sut chit khu 10% s l: PV= ( )5116101 10%+ = 116101,610= 1610 0,261 = 1000 Trong,0,621lhschitkhu.Xemphlc,bnggitrhinticamtng,ct 10% v hng 5. Nu ai ha cho bn s tin l 1 ng sau 5 nm, vi li sut ngn hng gi nh l 10% nm, bn s ni rng: "hy a cho ti 0,621 ng by gi, cng c". Nu bn nhn 0,621 ng v mang gi n vo ngn hng th bn cng s c 1 ng sau 5 nm. Nicchkhc,0,621ngngyhmnay(hinti)stngng1ngsau5nm (tng lai), vi sut chit khu 10% nm. T y, ngi ta cn c mt khi nim gi l "dng tin tng ng" 26.-V d 12.6:Tnh sut chit khu r Ly v d 12.5, bn s hi rng vi sut chit khu no m ngi ta cho rng gi tr hin ti ca s tin 1610 s nhn c sau 5 nm ch l 1000. Bn s lm bi ton ly tha, cn s ging nh tnh li sut mc 1.1. Mt khc, by gi bn c cc cng c c lc trn Excel. Excel: Hm PV thc hin tng t nh FV hng dn trn y.= -PV(sut chit khu, thi gian, ,gi tr tng lai)/OK. (nh cch 2 du phy sau khai bo thi gian) 2.3Gi tr tng lai ca mt ng u nhau Cng thc 27:

26 Equivalence.Thm nh d n u t Prepared by NGUYEN TAN BINH133/9/2012 FVA = ( )n1 r 1A r (+ ( ( cng thc (3) Trong , A l s tin u (Annuity) -V d 12.7:Tnh FVA Mi u nm, bn mang 100 (n v tin) u nhau gi vo ngn hng, vi li sut l 10%. Sau 5 nm bn s c s tin l bao nhiu? FVA = ( )51 10% 1100 10% (+ ( ( FVA =| | 1006,105610,5 =Trong , 6,105 l gi tr tng lai ca 1 ng u nhau (xem ph lc v cc bng tnh gi tr tin t)6,105 chng qua l tngcng ccgi tr tng lai ca 1 ng vi li sut 10% v (khong cch) thi gian ln lt l 0, 1, 2, 3, 4. S dng cng thc (1), bn tnh gi tr tng lai ca tng 1 ng v cng li nh sau: 1: Gi tr tng lai ca 1 ng vi r = 10% sau 0 nm.1,1: Gi tr tng lai ca 1 ng vi r = 10% sau 1 nm.1,21: Gi tr tng lai ca 1 ng vi r = 10% sau 2 nm. 1,331: Gi tr tng lai ca 1 ng vi r = 10% sau 3 nm. 1,464: Gi tr tng lai ca 1 ng vi r = 10% sau 4 nm. Cng:6,105: Gi tr tng lai ca 1 ng u nhau sau 5 nm vi li sut r = 10%.Chng ta s lu n s 0 (m ti c tnh in m): -Ly tha trong cc cng thc l ch khong cch thi gian ch khng phi nm lch. -Thi im chi 1 ng ln cui cng cng chnh l thi im tnh FV nn khong cch thi gian l 0. [=(1+10%)0=1] -V d 12.8:Tnh A Mt cng ty mun c s tin 610,5 triu u t my mc thit b vo 5 nm ti th hng nm phi dnh s tin u nhau l bao nhiu, bit li sut nm l 10%. T cng thc (3), ta suy ra: A = FVA ( )n1 r 1 r (+ ( (

27 Nu thch, bn c th t chng minh cng thc ny bng cch tnh gi tr tng lai ca tng mn tin ca tng nm ri tng hp li, hoc c th xem chng 7, sch Phn tch hot ng doanh nghip hoc chng 7, sch Phn tch qun tr ti chnh, cng mt tc gi v nh xut bn.Thm nh d n u t Prepared by NGUYEN TAN BINH143/9/2012 = 610,5 ( )51 10% 1 10% (+ ( ( = 610,5 6,105 = 100 -V d 12.9:Tnh n Bnvngiyucabnumiratrng,tchcphngthngc2triungv manggi vo ngn hng, vi li sut 1% thng. Bit baogi i uyn ng mi c s tin 38 triu lm l hp hn? Hy bm ly cng thc gc: FVA = ( )n1 1% 12 1% (+ ( ( = 38 (triu ng) C t nht l ba cch bn i tm n (s thng). (i)Bn c nhn ln chia xung, chuyn v qua li, khi thun li th ly Ln hai v tnh n. (ii)Bn hy tnh h s trong ngoc, trng hp ny thy r h s bng 19 (= 38 2), tra bng gi tr tng lai mt ng u nhau ti ct r=1% v xem ng vi hng n bng bao nhiu, chnh l s cn tm. (iii)BndnghmNpertrnExcel.Ttnhintikhuynbnchncchthbavkhngqun hng dn di cui mc ny. Hai bn cng tnh thy khng cn bao lu na, ch c 17,5 thng na thi (n=17,5). -V d 12.10:Tnh r C2cngtybohimnhnth:AvBpdngphngthcbnbohim(tclvay tin ca khch hng y) nh sau: Athuucabnhngqul1,5triung,nusau5nmmkhngcgxyra,tc chng c tai nn g c th cng ty s tr li cho bn s tin l: 31,17 triu ng. Bthuucabnhngqul1,4triung,nusau6nmttcvnbnhyn,tcnh tri bn chng h hn g m cng ty vn cha ph sn 28, th h s tr li cho bn s tin l: 35,11 triu ng. Bn chn mua bo him (tc cho vay) cng ty no ng v phng din li sut? gii bi ton ny (cng gip cho cc i l thnh thong vn gi in cho bn y), bn c cng thc, mm mui v sn sng ch bin. FVA chnh l s tin bn s nhn khi kt thc hp ng, A l s tin bn phi tr u hng qu,

28 Nu h mang tin ca bn i mua c phiu ca Enron hay WorldCom hay cho mt cng ty no vay ging nh Nc hoa Thanh Hng trc y, l kt y !Thm nh d n u t Prepared by NGUYEN TAN BINH153/9/2012 n l s k (s qu), v d nu 5 nm l 20 qu.(1) Vi cng ty A Ta vit li cng thc (3) d theo di FVA = ( )n1 r 1A r (+ ( ( 31,17=( )201 r 11,5 r (+ ( ( H s trong ngoc, tc gi tr tng lai ca 1 ng bng nhau vi thi gian l 20 k v li sut l r, s bng: ( )201 r 1 r (+ ( ( = 20,78 r = 0,4% (li sut qu, tc 1,6% nm 29) V nguyn tc, bn s tra bng gi tr tng lai ca 1 ng bng nhau hng 20 tm thy h s 20,78, ri nhn ngc ln xem ng vi ct r l bao nhiu.n y, bn s bo rng khng c s no ging nh vy trong bng c,ch c gngn thi. L ra ti phi tho lun vi bn phng php ni suy (m vn phi dng n bng h s) tnh r trong trng hp ny nhng tm thi ti li mun chn cch khc.Th nht, bng h s l do bn t lp ( hng dn trn) mun li sut no m chng c; th hai, bn cng bit s dng hm ly tha, cn s, c bit l Goalseek. V th ba, n s c hng dn tnh trn Excel cui mc ny.(2) Vi cng ty B Cch tnh tng t, r = 0,38% (li sut qu, tc 1,5% nm) 2.4Gi tr hin ti ca mt ng u nhau Lmtcngthccrtnhiupdngtrongthct,nhtlcclnhvcuttrnth trng ti chnh - tin t. Cng thc, suy ra t (1) v (3): PVA = ( )nn1 r 1A r(1 r) (+ (+ ( cng thc (4)

29 Tm thi b qua li sut thc v li sut danh ngha cho rc ri. S gp li mc lm pht, trong chng ny. Thm nh d n u t Prepared by NGUYEN TAN BINH163/9/2012 -V d 12.11:Tnh PVA Bn bit gi thu nh (tr hng nm, vo cui nm) l 500 (n v tin). Nhng nu ngi cho thu i ly trc mt ln cho 5 nm th bn nn thng lng vi h gi bao nhiu? Nu li sut bnh qun th trng l 10%. PVA = ( )551 10% 1500 10%(1 10%) (+ (+ ( = 500 [3,791] = 1895 (n v tin) 30 Hschitkhu3,791chnhlgitrhinticamtngbngnhauvithigianl5 nm v sut chit khu l 10%. (Xem ph lc h s chit khu cui sch). 3,791chngqualtngcngccgitrhintica1ngvisutchitkhu10%v (khong cch) thi gian ln lt l 1, 2, 3, 4, 5. S dng cng thc (2), bn tnh gi tr hin ti ca tng 1 ng (ph lc h s chit khu cui sch) v cng li nh sau: 0,909: Gi tr hin ti ca 1 ng vi r = 10% sau 1 nm.0,826: Gi tr hin ti ca 1 ng vi r = 10% sau 2 nm.0,751: Gi tr hin ti ca 1 ng vi r = 10% sau 3 nm. 0,683: Gi tr hin ti ca 1 ng vi r = 10% sau 4 nm. 0,621: Gi tr hin ti ca 1 ng vi r = 10% sau 5 nm. Cng:3,791: Gi tr hin ti ca 1 ng u nhau sau 5 nm visut chit khu r = 10%.(Lu rng, thi gian cng di gi tr hin ti cng nh) -V d 12.12:Tnh r BndtnhmuamtchicxegnmyhiuBadDreamIIIgihintitrnthtrngl 2000 USD, khng tin nn bn phi mua tr gp. Chaicahngbnxembnschn:CahngGiaLongvcahngHngVng. Phng thc thanh ton ca hai ca hng c cho trong bng di y. Bn s chn mua ti ca hng no, ng v phng din li sut? Gi xe hin ti2000 CH Gia LongCH Hng Vngn v Tr ngay400500USD Tr chm16001500USD Mi ln tr300225USD S ln tr68ln Thi gian tr1216thng Li sut (2 thng)3,48%4,24%Li sut (1 thng)1,74%2,12%

30 Ch khng phi l: 500 5 = 2500! Thm nh d n u t Prepared by NGUYEN TAN BINH173/9/2012 -V d 12.13:Tnh A GimuatrngaycachiclaptophiuGreenField(vitnhxchtay-notebook)l1000 USD, nu mua (bn) tr gp vi li sut bnh qun th trng l 10% nm, tr u trong 3 nm th mi ln tr s l bao nhiu?T cng thc (4), ta suy ra: A = PVA ( )nn1 r 1 r(1 r) (+ (+ (

= 1000 ( )331 10% 1 10%(1 10%) (+ (+ ( = 1000 2,487 = 402 USD Trong , h s chit khu 2,487 l gi tr hin ti ca 1 ng u nhau vi sut chit khu 10% v thi gian l 3 nm (xem ph lc cui sch). Ta c th ng dng lp mt lch tr n nh sau: Li sut nm10% Vay n (u nm 1)1,000Nm0123 N u k1,000 698 366Li pht sinh100 70 37Tr u, trong :402 402 402- N gc302 332 366- Li vay100 70 37N cui k1,000 698 366 0Lu : Cc tnh ton c lm trn s ( bt ri mt!) v, du chm (.) hay phy (,) trn Excel c biu hin kiu ting Anh ( tp nhn cho quen!). Khi bn tp trung cao vo nhng iu ct li hay tng ca vn , bn s bit b qun nhng iu vn vt (!) 31. -V d 12.14:Tnh n Nhmgi chn nhn vin gii, cng ty quyt nh mi nhn vin cng lm ch cng ty bng cch bn mt l c phiu tr gi 20 triu cho anh (hay c) ta, tr vo lng mi thng 0,5 triu. Lisutbnhqunthtrnghinti6%nm(theocchnginl0,5%thng),phitrbao nhiu thng lng mi xong? Tng t v d 2.3.3 ca i uyn ng trn y, nhng bn s tnh n trong cng thc (4), gi tr hin ti ca dng tin u.

31 Trong khi ging bi, ti rt thch cu hi ca sinh vin i loi nh: " tng (hay trit l) ca vn ny l g?", v hon ton khng thch nhng cu hi nh: "s ny u ra?", "lm sao m tnh c?". Thm nh d n u t Prepared by NGUYEN TAN BINH183/9/2012 PVA = 20 = 0,5 ( )nn1 0,5% 1 0,5%(1 0,5%) (+ (+ ( Bn s bin i, ly Ln v tnh n nh trn y. Tuy nhin hy xem hng dn trn Excel cui mc ny. thy n = 45 thngTisaokhngphil40thng(=200,5)?nginlgingnhcngtychonhn vin ny vay (vi li sut 6% nm) ch khng phi cho mn khng. V vy c cu hi vui. Sau khi cng khai cch tnh trn, nhn vin than phin rng, li sut th trng hin nay l 12% nm sao cng ty tnh vi ti ch 6% nm? Bn s tr li ra sao v s bo li cho nhn vin thi gian tr lng l bao nhiu thng? TrnbngtnhExcelbndi,bnchcnthayi6%trthnh12%thyrng,thi gian tr lng s ko di ti 51 thng! Nh rng, trong cng thc PV ni chung, r nm di mu s, r cng ln th PV cng nh. Nm na l, thu 20 triu, thi gian phi di hn. 2.5Quan h gia gi tr hin ti v gi tr tng lai ca cc dng ngn lu Khi nu cng thc (4) gi tr hin ti ca dng tin u nhau, ta thy rng n c suy ra t cng thc (3) gi tr tng lai ca dng tin u nhau. Trong khi , gi tr hin ti ca dng tin u nhau l tng cng gi tr hin ti ca tng dng ngn lu n (cng thc 2), v gi tr tng lai ca dng tin u nhau l tng cng gi tr tng lai ca tng dng ngn lu n (cng thc 1). Bn thy y! Bn v anh hng Lng Sn Bc tp trung c ri y. Mt tnh ton trong bng sau y gip bn t tm tt tng v cc mi quan h gia cc dng tin. Li sut10% Thi gian (nm)5 012345Cng Ngn lu hin ti10001000100010001000-- H s tch ly1,1,11,211,3311,464-6,105 Gi tr tng lai 10001100121013311464-6105 Sut chit khu10% Thi gian (nm)5 012345Cng Ngn lu tng lai-10001000100010001000- H s chit khu -0,9090,8260,7510,6830,6213,791 Gi tr hin ti -9098267516836213791 Ta c: 6105 l gi tr tng lai ca dng tin u nhau l 1000 vi r=10%, thi gian n=5 Thm nh d n u t Prepared by NGUYEN TAN BINH193/9/2012 3791 l gi tr hin ti ca dng tin u nhau l 1000 vi r=10%, thi gian n=5 Gia chng c th c mi lin h no khng? Nuxem6105lmtdngngnlunsnhntrongtnglaisau5nm,visut chit khu 10%, gi tr hin ti s l: S dng cng thc (2): PV = ( )5161051 10%+ = 161051,610= 6105 0,621 = 3791(Trong , 0,621 lgi tr hin ti ca 1 ng vi thi gian l 5 nm v sut chit khu l 10%.) Nu xem 3791 l mt dng ngn lu n hin ti, gi tr tng lai sau 5 nm, vi li sut 10%, s l: S dng cng thc (1): FV = 3791 (1+10%)5 = 3791 1,610 = 6105 (Trong , 1,610 l gi tr tng lai ca 1 ng vi thi gian l 5 nm v li sut l 10%.) Hoc nhn cch khc, = 3791 0,621 = 6105 nyclbnnhunnhuynnhvkthutchitkhudngtinvbnhon ton c th t tin vo nhng ngy i thi v ng dng chng vo cc bi ton trong i thc. 2.6Gi tr hin ti ca dng tin u v tn T cng thc (4) PVA = ( )nn1 r 1A r(1 r) (+ (+ ( Ta c th vit li PVA = ( )nA 11 -r1 r ( (+ ( Khi n ln ( ), thn1(1 r) + 0Thm nh d n u t Prepared by NGUYEN TAN BINH203/9/2012 V PVA s c vit n gin nh sau PVA = Ar;hoc r = AAPV;hoc A = PVA r -V d 12.15:Tnh PVA Chnh ph c ch trng giao khon, bn, cho thu doanh nghip nh nc. V nh l bn doanh nghip ang hot ng ch khng phi bn thanh l ti sn gii th doanh nghip, hai vic ny rt khc nhau.D kin dng thu nhp hng nm tng i n nh ca cng ty thuc tnh B l 20 triu, bn s mua doanh nghip ny vi gi no nu sut sinh li mong mun ca bn l 10% nm. Doanh nghip lun c gi nh l hot ng lin tc, khng thi hn 32, v vy gi tr ca n c th l: PVA = Ar=2010%= 200 triu -V d 12.16:Tnh r Nhngtichtrgi 33cngtykhong100triuthi.Vnginlchisinhlicho ng tin ca ti l: r = AAPV= 20 20%100 =-V d 12.17:Tnh A Ngi bn ti, lm n kh khn doc ch chnh sch nng n tnh T quyt nhchuyn vn v tnh B tr gi cng ty 300 triu, trong khi sut sinh li i hi ca anh ta cng ch l 10%. Anh ta tnh ton v k vng thu nhp hng nm ca cng ty l bao nhiu? A = PVA r = 300 10% = 30 triu. -V d 12.18:Tnh A (tip theo) Cng ty kinh doanh v pht trin nh Qun Bnh Thnh c chnh sch bn nh tr gp cho ngi ngho, dnh u tin cho nhng c dn thnh ph th thit, c h khu t nm 1975 n nay cha c nh . Gi hin ti ca cn h l 100 triu, tr mi nm 2 ln trong vng 50 nm. Cng ty c Thnh ph cho vay v bo m c nh li vay l 8% nm (4% cho 6 thng). Theo bn, mi ln tr nn bao nhiu? Bn c th xem 50 nm (100 ln tr) l v tn, v bn c th ngh mi ln tr l: A = PVA r = 100 triu 4% = 4 triu

32 Xem ph lc Cc nguyn tc k ton cn bn cui sch. 33 K c mua ca nh nc cng phi xem hng v tr gi. l th trng m, thun mua va bn. Nu nh nc ch rao bn nhng sn phm ti, c th l cc doanh nghip quc doanh o ut chun b em chn, th mi mi khng bn c ci no c. Cc cng ty cn tm tm th nh nc mun bn cng khng c v cc gim c c th gi qu. C phn ha m cn phi do cch chc, hung h g bn. Thm nh d n u t Prepared by NGUYEN TAN BINH213/9/2012 Bn c th s dng cng thc (4), vi cc thnh phn:P = 100 triu ;n = 100 ln ;r= 4% Ta cng c: A = 4 triu. HNG DN TRN EXCEL (i)Gi tr tng lai ca dng tin u (FVA) Vn trong fx/ financial/ FV nh hng dn trn y, dng s liu v d 12.7, tnh FVA nh sau S dng hm FV ca dng tin u cng ging nh FV ca mt s tin n trn y, thm ch cn d hn. Thc ra hm FV sanh ra phc v cho vic ny, tc tnh gi tr tng lai ca dng tin u. (Trn kia, ta mn tnh s tin n). Trong bng c 3 gi tr cn khai bo ln lt: Rate: li sut (hay sut chit khu) Nper: S k on (thi gian) Pmt: S tin (tr) u Nh vy, nu s dng phm nng, bn ch cn nh: = FV(li sut, thi gian, s tin u)/OK.(ii)Gi tr hin ti ca dng tin u (PVA) Vn trong fx/ financial/ PV nh hng dn, dng s liu v d 12.11, tnh PVA nh sau Thm nh d n u t Prepared by NGUYEN TAN BINH223/9/2012 Vn l hm PV s dng tnh s tin n, nhng by gi n gin hn = PV(sut chit khu, thi gian, s tin u)/OK. (iii)Tnh s tin u (A) trong cng thc FVA Hm PMT (payment) trong fx/ financial. S dng s liu trong v d 12.8 trn y, ta tnh s tin u A nh sau: Thm nh d n u t Prepared by NGUYEN TAN BINH233/9/2012 Nu s dng phm nng, bn s nh (g):=PMT(li sut, s nm, ,gi tr tng lai)/OK. (lu 2 du phy sau s nm, tng ng vi bng tnh trn) (iv)Tnh s tin u (A) trong cng thc PVA Vn l hm PMT trn y nhng thao tc cn n gin hn nhiu. n gin l bi v hm PMT ra i dng cho mc ch ny, tc tnh A trong cng thc PVA. S dng v d 12.13 v mua tr gp, ta tnh trn Excel nh sau: Thm nh d n u t Prepared by NGUYEN TAN BINH243/9/2012

Nu s dng phm nng, bn s nh:=PMT(sut chit khu, s nm, gi tr hin ti)/OK. (khng cn 2 du phy nh trong cng thc FVA) (v)Tnh r trong cng thc FVA Hm RATE (li sut) trong loi hm financial (ti chnh), trong fx.S dng v d 12.10, tnh li sut cng ty A.Thm nh d n u t Prepared by NGUYEN TAN BINH253/9/2012 Lu : VihmFVphighim,tcphinhthmdutr-khikhaibo,vExcelhiul tr. Nu s dng phm nng (phm tt), ta nh: =Rate (S k, S tin u, ,Gi tr tng lai) (nh cch 2 du phy , sau S tin u. (vi)Tnh r trong cng thc PVA Dngsliutrongvd12.12,muaxeBadDreamIIItrgptasdnghmRatetrong Excel nh sau: Thm nh d n u t Prepared by NGUYEN TAN BINH263/9/2012 Hm Rate trong gi tr hin ti n gin hn trong gi tr tng lai, ch cn khai bo lin tc (khng cch hai du phy). = Rate (S k tr, -S tin tr u, Gi tr hin ti)/OK. (Nh nh du tr - trc Pmt, v Excel hiu l tr.) Ch cn tnh cho ca hng Gia Long, copy sang cho ca hng Hng Vng. (vii)Tnh n trong cng thc FVA S dng hm Nper trn Excel: Thm nh d n u t Prepared by NGUYEN TAN BINH273/9/2012 Excel/ fx/ financial/ Nper34 =Nper(li sut,s tin u, ,gi tr tng lai)Lu: cch 2 du phy sau s tin u; s tin u Excel hiu l tr 35, nn phi c ghi m (0 c ngha l dng tin thu vo ln hn dng tin chi ra; v ngc li, NPV0 l s giu c hn ln, ti sn ca nh u t s n ln hn sau khi thc hin d n.C th nhng ch tiu khc (sau y) cng l nhng thc ogi tr dn, ng di cc gc nhn khc nhau. Tuy nhin, khng mt nh u t no, k c cc d n ca chnh ph 38, m li khng quan tm n s giu c hn ln ny. Chnh v l do , ch tiu NPV c xem l ch tiu mnh nht dng nh gi cc d n u t.

37 Nghin cu chng 14. 38 C quan nim cho rng, nhng d n phc v nhim v chnh tr, x hi, tc d n cng (public project) th khng cn thm nh hiu qu kinh t. l mt tng sai lm, duy ch. K c cc d n thuc nhng lnh vc nhy cm nht, mc d kh khn nhng hon ton c th lng ha c cc dng thu, chi v do , vn c th s dng ch tiu giu c hn ln ny. (Tc gi hy vng rng quyn Thit lp v thm nh d n u t, d nh xut bn trong tng lai gn, s cp k lng v gi ti chnh v gi kinh t cng cc phn tch x hi ca mt d n u t) Thm nh d n u t Prepared by NGUYEN TAN BINH303/9/2012 Nu bn thch th hin tr tu hn, tc ngi c phi nhc c u, thm ch kh hiu, khi ngh ti NPV th bn vit nh sau 39: NPV = ( )( )ni iii 0B C1 r=+ Hoc c th vit cho gn hn: NPV =( )ni ii 0PVB C= Trong ,i : k hiu cc nm ca d n (lu : cui nm 0 bng u nm 1) r : sut chit khu n :s nm (hay s k) ca d n PV :gi tr hin ti (thi im nm 0) Bi: dng thu (ngn lu vo) ca nm th iCi: dng chi (ngn lu ra) ca nm th i (Bi Ci) :dng rng (ngn lu rng40) ca nm th i PV (Bi Ci) :gi tr hin ti rng ca nm th i ni 0 =:tng cng cc gi tr hin ti (t 0 n n) Din ngha cng thc ny ra ting B Ngoi th vn l: hiu s gia gi tr hin ti ca cc dng thu v gi tr hin ti ca cc dng chi d kin ca mt d n u t. Mt ln na, cng thc ch l hnh thc tm tt cc tng, mt khi bn nm k phn hn bn c th d dng t vit ra cc cng thc theo bt c hnh thc no, vi nhng k hiu no, m bn thch.-V d 12.19: Tnh NPV ca d n Bn mun u t mt ca hng photocopy trc cng trng i hc ca bn v t tn n liSinhVin.Dkindnschodngngnlurng(NCF:netcashflows)vocuicc nm nh bng sau (n v tin). Trong , NCF l hiu s ca dng thu v dng chi. Ti mt nm no , NCF0 c ngha l dng thu ln hn dng chi 41. Gi nh rng, my mc thit b sau 5 nm khng cn gi tr tn dng (nu d kin c gi tr tn dng th n s tr thnh mt dng thu t vic thanh l ti sn vo nm cui d n, tc nm th 5); v sut sinh li i hi cho ng vn hin ti ca bn l 20% nm (nh hn bn khng lm, v bn cn c c hi u t khc cng ha hn sinh li 20%).ng lo lng cc tnh ton m trc ht hy xc nh cc tng chnh cho bi ton ny.

39 Ti th vn c lo lng rng, cng thc rc ri lm cho ngi ta s vkhng mun nghin cu tip tc, b l c hi nhn ra rng ni dung ca vn tht v cng n gin, thit thc v hu ch.40 Xem thm chng 13 Bo co ngn lu 41 Xem bo co ngn lu ca d n chng 13 Bo co ngn lu. Thm nh d n u t Prepared by NGUYEN TAN BINH313/9/2012 -Th nht, chi ph c hi s dng vn ca bn l 20% s chnh l sut chit khu (r = 20%) ca d n. -Stinrng(hiuscadngthuvdngchi)ghitrongccnm1,2,,cnghaltrong tng lai 1, 2, nm na, bn mi thu c. Trong khi , dng tin rng 10.000 th phi chi ra by gi (cui nm 0 hay u nm 1) -Bn s a cc dng tin rng d kin thu c trong tng lai v gi tr hin ti (cng vi thi im dng chi, tc nm 0) thng qua sut chit khu r=20%. -Cui cng, hiu s gia chng, tc NPV s tr li cho bn cu hi v hiu qu d n. Kt qu: NPV = 684>0 Sut chit khu20% Nm012345 NCF(10,000) 5,0004,5003,5002,0001,000NPV 684 C t nht l hai cch 42 bn tnh c NPV = 684. Cch 1: Tnh gi tr hin ti tng dng tin (theo cng thc 1) ri cng li, nh sau: Gi tr hin ti cc dng thu: S dng cng thc (1) vi r = 20%, n ln lt l 1, 2, 3, 4, 5, ta tnh c cc gi tr hin ti ca cc dng thu nh sau. PV1 =5000 11(1 20%) += 5000 0,833 = 4.166 Trong,0,833lgitrhinticamtngvithigianl1nmvr=20%.(Xem ph lc v bng h s tin t cui sch) Tng t, PV2 =4500 21(1 20%) += 4500 0,694 = 3.124 V tip tc, PV3 = 3500 0,579 = 2.027 PV4 = 2000 0,482 = 964 PV5 = 1000 0,402 = 402 Cng PV1 n PV5 = 10.684 (lm trn s): tng gi tr hin ti cc dng thu. Gi tr hin ti cc dng chi:

42 Ti trnh by hai cch ch nhm gip bn c d hiu. Cn nu l sinh vin th bn c th phn loi hai cch nhng theo mc ch khc: cch dng i thi ht mn trn lp (c v khng cho mang bng tnh), cch dng thi trn my tnh (v cng l cch tnh trong i tht sau ny). Thm nh d n u t Prepared by NGUYEN TAN BINH323/9/2012 PV0 = 10.000 01(1 20%) += 10.000 1 = 10.000 (Stin10.000chivothiimtnhgitrhinti,khngckhongcchthigian,n=0.V (1+20%)0 = 1) Gi tr hin ti rng (NPV): NPV = 10.684 10.000 = 684 (n v tin) Cch 2: S dng hm NPV trn Excel (hng dn cui mc ny). 3.1.2Nhng sai lm thng gp khi s dng NPV (i)Dng ngn lu v li nhun Tachcthngngnmnirng,NPVlgitrhinticaccdngtinchkhng phillinhun.Vlinhunkhngphildngtin(ngnlu).Rngclinhngkhngc tin tip tc hot ng v vn phi ph sn C l tt nht l bn nn dnh cht thi gian qu bu ca bn xem nhng vn nh vy Chng 13 Bo co ngn lu. (ii)Gi tr hin ti ca dng chi v tng vn u t Nu ta vit: NPN = PV (dng thu) - Tng vn u t, l hon ton khng chnh xc, thm ch l sai v nguyn l 43. V sao?Gi nh d n ca hng photocopy i Sinh Vin trong v d 12.19 trn y c chia lm 2 ln u t: cui nm 0 (u nm 1) u t 7000; v cui nm 1 (u nm 2) u t 3000 th kt qu nh gi d n cho bi ch tiu NPV s hon ton khc. C hai cch bn ngh (v tnh) v kt qu mi ny. Th nht, mt cch ngn gn, s tin 3000 n mt nm sau mi chi, gi tr hin ti ca n ch l:PV1 = 3000 11(1 20%) += 3000 0,833 = 2499 C th ni cch khc, hin ti ch cn chi ra 2499 gi vo ngn hng (gi nh cng li sut 20% nm) th mt nm sau, tc n lc cn chi u t cng s nhn c 3000.Nh vy, gi tr hin ti ca dng chi ch l: 7000 + 2499 = 9499 S tin u t s tit kim c 501 (= 10000 - 9499).

43 Nu bn ngh nh th chng t bn hy cn nh hng bi cn bnh c, bnh bao cp. C ngh rng thm nh d n l lm sao cho d n trn tra, va lngai nhm xin c giy php v nhn c vn! Cn bnh i km l bnh hnh thc, bnh khnh thnh, cho mng u t mt ln, trong qu trnh u t ch c dng chi ra m thi. Trong khi , khng ai cm d n khch sn 12 tng, ang xy tng 5 th t tng trt n tng 3 c th bt u khai thc. Thm nh d n u t Prepared by NGUYEN TAN BINH333/9/2012 NPV gi y s l: 10684 - 9499 = 1185NPV tng ln mt gi tr bng vi s tit kim c, tc 501 (=1185 - 684) Th hai, mt cch chuyn nghip hn, ta lp li bo co ngn lu ca d n v tnh NPV cho dng ngn lu rng (NCF) mi nh sau: Sut chit khu20% Nm012345 NCF(7,000) 2,0004,5003,5002,0001,000NPV1185 Nhn xt: -Ngn lu rng cui nm 0 (u nm 1) ch l: - 7000 -Ngn lu rng cui nm 1 (u nm 2) ch l: 2000 (=5000 - 3000)(iii)Sut chit khu - mt vn nan gii Ginhdngngnlucxcnh 44,mtsthayitrongsutchitkhuslm thay i NPV. Tr li v d 12.19 ca d n ca hng photocopy i Sinh Vin trn y, gi nh mt nh utkhcchorngchiphchisdngvncaanh(hayc)tal30%.Vidngngnlu rng gi nh ging ht nhau, kt lun v hiu qu d n s ra sao? NPV= -92820%) chng hn, th bn tha mn v c th quyt nh u t. Theo nh ngha trn y, IRR l mt sut chit khu m ti NPV=0, nh vy nu ta chn sutchitkhur=20%slmchoNPV>0(vr0thIRR>r. Nh vy, hai iu kin ny cng c tha. By gi, gi nh mong mun sut sinh li t d n l r = 30%, trong khi IRR vn l 24% ( 0 th IRR > r Tng t, bt c im no bn chn trn ng NPV phn bn di trc honh, tc phn NPVIRR. Hoc c th pht biu cho thun cu: Khi NPV< 0 th IRR< r Tnh:-Gii phng trnh ng thng dng y=a+bx=0 tm IRR. Nu bn chn mt r no , chng hn r=20%, tng ng vi NPV=684; V bn chn mt r khc, chng hn r=30%, tng ng vi NPV=-928. Nh vy, bn c hai to ca hai im. Qua bn c th vit phng trnh ng thng theo cng thc: 1 12 1 2 1y y x xy y x x = Thay cc gi tr x1, x2, y1, y2 vo v a v dng phng trnh y=a+bx, cho bng 0 tm x, tc IRR.Nu qun, bn c th xem li chng 3 Cc phng php k thut s dng trong phn tch. -p dng ng thc tam gic ng dng tnh IRR. T cc im chn trn y, bn s lp c ng thc tam gic ng dng v tm c IRR. Cng c th gi l phng php ni suy, theo cng thc sau: IRR = r1 + (r2 - r2) 11 2NPVNPV NPV+ Trong , (r2 r1)>0 r2 > r1 Dng v d d n Ca hng photocopy i Sinh Vin tnh IRR trn y ta kim nghim li cng thc: r1 = 20% NPV1 = 684 r2 = 30% NPV2 = -928 Theo cng thc ta c: IRR = 20% + (30% - 20%) 684 24%684 928 =+ Thm nh d n u t Prepared by NGUYEN TAN BINH393/9/2012 3.2.3ng dng IRR trong u thu tri phiu Bn c bo thy cuc u thu tri phiu chnh ph tht bi, tc ngi mua hay ngi cho vay (l cc ngn hng u t) v ngi bn hay ngi i vay (i din l B Ti chnh) khng gp nhau. B Ti chnh i gi 92000 ng, cc ngn hng tr gi (cao nht) ch l 85000 ng. Bit rng tri phiu c mnh gi 100.000 (ng), li sut tri phiu c nh 8% nm (c tc trcnhminm:8000ng,nmcuicngtrlivvngc:108.000ng),thigiano hn 5 nm. Tt nhin B Ti chnh l ngi i vay nn mun li sut thp v cc ngn hng, l ngi cho vay nn mun li sut cao. Nhng cc li sut l bao nhiu? B Ti chnh mun li sut l 10% nn gi gi 92000 ng. Nm012345 NCF(92,000)8,0008,0008,0008,000108,000 IRR10% Cc ngn hng mun li sut l 12% nn tr gi 85000 ng. Nm012345 NCF(85,000)8,0008,0008,0008,000108,000 IRR12% Tng t nh vy, nu bn l i din ca ngn hng NCB i u thu. Ra i xp c dn rng: c th xung ti 11,5% th rng, thp hn th v, bn s tr gi cao nht cho l tri phiu l bao nhiu? 52 Nm012345 NCF(87,202)8,0008,0008,0008,000108,000 IRR11,5% Chc hn l bn cn nh hm i tm kt qu Goal Seek nghin cu t u hm. Xem li cht nh!

52 Nh gi sn cng thc trn Laptop, ch khng phi ngi m ni suy! Thm nh d n u t Prepared by NGUYEN TAN BINH403/9/2012 Ch cn vic bm nt OK, mt ci nt d nht, to nht 53, cha 12% s thnh 11.5%, cn cha gi tr (85,000) s tr thnh gi tr m bn ch i: (87,202).3.2.4Nhng nhc im ca IRR Trong mt s trng hp d n c nhng dng ngn lu bt ng, IRR khng th tnh c. V d: C mt d n khai thc m, u nm 1 (cui nm 0) chi ra 1200, cui nm 1 thu v 5000. Nm 2 v nm 3 sau phi chi tin san lp, tr li mt bng c cho nh nc. Bo co ngn lu ca d n, c th nh sau: Visutchitkhu10%,yldnrtchiuqu(NPV=1437),tuynhinIRRlbao nhiu?Haynicchkhc,visutchitkhunoslmchoNPV=0?Ttnhinkhngthtnh c. Nhcimkhc,trongtrnghpsosnhlachndnctnhloitrnhau,ktqu IRR thng khng th dn n kt lun hoc c kt lun sai lch. V d:C dng ngn lu ca 2 d n A v B nh sau: Nm01 D n A (1,000)1,400 IRRA =40% D n B(10,000) 14,000 IRRB =40% Gi nh ngun lc khng hn ch, nu ch dng ch tiu n c IRR nh gi, ta thy c hai d n u nh nhau, u c IRR l 40%. V bn khng th kt lun d n no tt hn. (Nu bn ni d n B c v li nhiu hn, tc l bn s dng mt ch tiu khc ri!) By gi ta thay i mt cht trong dng ngn lu ca d n B v cho sut chit khu l 10% (tt nhin cho c 2 d n). Tnh NPV?

53 Ti thy, sau khi khai bo (np s) xong, nhng ngi t tin thng ging mt ci tht mnh nt ny (OK hay Enter), hnh nh t thng! Thm nh d n u t Prepared by NGUYEN TAN BINH413/9/2012 Sut chit khu10% Nm01 D n A (1,000)1,400 IRRA =40%NPVA=273D n B(10,000) 13,000 IRRB =30%NPVB=1,818Chng l no bn li chn A do c IRR cao hn B (40%>30%), trong khi B lm cho bn giu c hn ln rt nhiu so vi A (1818>273)!Nhnutrny,haidncthiimbtukhcnhau,chtiuIRRkhngth phn bit c d n no hiu qu. V d: Xt IRR v NPV ca 2 d n di y. Sut chit khu20% Nm0123NPVIRR D n A(10,000)12,500 417 25% D n B--(10,000)12,500 289 25% Hai d n u c IRR=25%, trong khi NPVA>NPVB rt nhiu (417>289).Tngt,khngthsdngIRRsosnhhaidnccngthiimbtunhng vng i khc nhau.V d: Thm nh d n u t Prepared by NGUYEN TAN BINH423/9/2012 Sut chit khu20% Nm0123NPVIRR D n A(10,000) 12,500417 25% D n B(10,000) - 18,500706 23% IRRA>IRRB (25%>23%), tuy nhin NPVA 1; Ngc li NPV < 0 BCR < 1. Tuy nhin, khi so snh cc d n c tnh loi tr nhau, mt mnh ch tiu BCR i khi bp mo kt qu nh gi. V d: Sut chit khu20% Thm nh d n u t Prepared by NGUYEN TAN BINH433/9/2012 Nm01NPVBCR D n A(6,000)9,0001,5001.25 D n B(10,000)14,0001,6671.17 D n A c BCR ln hn (1.25>1.17), tuy nhin d n B li mang li ca ci rng ln hn (1667>1500).Mt nhc im khc na l, vic xc nh chi ph ca d n khng thng nht cng c th lm sai lch ch tiu ny. C quan im cho rng chi ph so snh trong cng thc ny ch nn tnh theo chi ph u t ban u (investment cost); trong khi , quan im khc th tnh trn ton b chi ph (total cost).3.4K hon vn tnh trn ngn lu HiutthutngPaybackPeriod(PP),lthigiancnthitthuhicvnut. Nhiudnkhanhimhoclthucvothigianhuyngvn,chtiunythngtrahu dng. n gin, nhn dng ngn lu rng (NCF: net cash flows) trn bo co ngn lu ca d n thy c nm hon vn. K hon vn cng c th tnh trn dng ngn lu chit khu (DCF: discounted cash flows), tc c tnh n gi tr thi gian ca tin t. Tuy nhin qua nhiu th nghim ta thy khng c chnh lnh nhiu so vi cch tnh ch da trn dng ngn lu 54. 3.5Sut sinh li k ton c dch t nhm tAccounting Rate of Return (ARR), l t lgia dng thu bnh qun hng nm so vi tng dng chi (hoc bnh qun). Cng thc: ARR =Ngan lu vao bnh quanTong ngan lu ra Theo v d d n Ca hng Photocopy i Sinh Vin, ARR l: ARR = (5000 4500 3500 2000 1000)/532%10000+ + + +=ChtiuARRcnggiptamtcchnhnvhiuqudn,tuynhinncngccc nhc im tng t: khng tnh thi gi tin t v khng quan tm quy m cng nh vng i ca d n. Ch tiu ARR i khi cng c tnh n gin bng cch da trn li nhun bnh qun nh ROI di y.

54 tng can l, tnhgi trhin ti dngngn lu ti thiim bt k. Ti nmno, gitrbng 0lnm hon vn. Thm nh d n u t Prepared by NGUYEN TAN BINH443/9/2012 3.6Sut sinh li ca vn u t c hiu t thut ng Return on Investment (ROI), l mt ch tiu n gin n v cng, ch tnh trn li nhun v khng da vo dng ngn lu v gi tr thi gian ca tin t. Cng thc:ROI = Li nhuan bnh quan hang namVon au t Ngoi nhc im phi tin t v phi thi gian nh nu trn, vn u t trong ch tiu ROI c tnh rt ty tin: c khi tnh trn tng vn u t, c khi tnh trn vn u t bnh qun (c tr khu hao vn qua tng nm).Lu rng, nu li nhun thng nht vi dng ngn lu, mc d him khi, th ROI s bng vi ARR trn y. V d: D n X c vn u t 100 triu, li nhun bnh qun hng nm l 20 triu th ROI s l: ROI =20 20%100 =3.7K hon vn tnh trn li nhun L mt cch nhn khc v ROI, c vit ngc li vi ROI nh sau: PPNI 55 = Von au tLi nhuan bnh quan hang nam Theo v d trn: PPNI = 100 5 (nam)20 =3.8Cch nhn khc v NPV v IRR Thcramcnynhmdingiithm,lmchochtiuvuaNPVdhiuhnmthi. Mc khc, trong s kt hp vi NPV cng lm r thm bn cht ca IRR.ChtiugitrhintirngNPVnhchngtanghincuvnhnthylmtch tiu mnh m, ng tin cy, gii thch s giu c hn ln cho ch u t sau khi thc hin mt d n kinh doanh. Nhng ch tiu ny, ngoi nhc im l vic xc nh sut chit khu ph hp, cn mt khuyt im hm oan na l: kh hiu. Sau y l mt ngh v cch tip cn vi ch tiu ny 56. V d: C dng ngn lu t mt d n nh sau Nm 0123

55 K hiu NI (Net Income: li rng) phn bit vi PP tnh trn dng ngn lu. 56 Ti vit thm mc ny, v ti tin rng nhn v tng lai thng lm cho ngi ta d hnh dung hn, n l kiu t duy thun chiu. Cng ging nh hc ton vy, hc ton cng trc ri mi ton tr, nhn ri mi chia, ly tha ri mi cn s, vi phn ri tch phn, gi tr tng lai c cp trc gi tr hin ti. Thm nh d n u t Prepared by NGUYEN TAN BINH453/9/2012 NCF-500300400200 Sut chit khu: 10% Bng kt qu thm nh: NPV = 254 IRR=39% -Vn 1: Gii thch ch tiu NPV v IRR bng hnh nh li sut. Gi P = 500 l vn u t Nu gi vo ngn hng gi nh vi li sut r = 39% nm, sau 3 nm ta c s tin: FC = 500 (1 + 39%)3 = 1330 Nu u t d n v to ra cc dng thu, gi tr ca dng thu ny sau 3 nm cng l: 1330 FB = 300 (1+39%)2 + 400 (1+39%)1 + 200 (1+39%)0 FB = 576 + 554 + 200FB = 1330 Nh vy, ta c th hiu IRR nh l mt sut sinh li ha vn, v u t cho d n hay gi ngn hng u nh nhau. Nhng lu rng sut sinh li 39% ch c thng qua u t, khng th c mt li sut tin gi cao nh vy c. -Vn 2: Gii thch ch tiu NPV v IRR bng hnh nh gi tr tng lai. By gi ta cng tnh F n nm th 3 tuy nhin ch vi li sut 10%, l sut sinh li mong mun. Ta c: FB = 300 (1+10%)2 + 400 (1+10%)1 + 200 (1+10%)0 = 363 + 440 + 200 = 1003 Gi tr tng lai n nm th 3 ca vn u t P= 500 (cng vi r=10%) l:FC = 500 (1+10%)3 = 665,5 Nutagichnhlchgitrtnglaicadngthu(FB)vgitrtnglaicadngchi (FC) bng mt tn gi l NFV (Net future value: gi tr tng lai rng), ta c: NFV = 1003 665,5 = 337, 5 T ta thy rng li ch trong tng lai s ln hn nu u t vo d n thay v gi ngn hng (hay dnh cho cc hot ng khc trong hin ti) vi li sut 10%. NuaNFV=337,5vgitrhintiNPV(r = 10%)tacngscNPV=254,thng nht vi gi tr NPV bng kt qu thm nh trn y. n 3NFV 337,5NPV= = =254(1+r) (1+10%) -Vn 3: Mt cch nhn khc v sut sinh li ni b IRR. Thm nh d n u t Prepared by NGUYEN TAN BINH463/9/2012 Trong khi tnh IRR, ta xem nh l mt sut sinh li ca cc dng u t v ti u t ca d n. Nhng li sut thc t s l g? Theo tnh ton trn, gi tr tng lai ca cc dng thu (r=10%) l: 1003. Bn hy t cu hi rng, gi tr vn u t P = 500 tr thnh F = 1003, li sut r cn c l bao nhiu? Ta c th vit: 500 (1+r)3 = 1003 (1+r)3 = 1003 500 = 2,006Suy ra: (1+r) = 32,006= 1,26 r = 0,26 hay 26% Ngi ta cn gi r = 26% l Sut sinh li ni b hiu chnh. 3.9Bng tm tt kt qu tnh ton ca cc ch tiu Kt qu cc ch tiu ca d n Ca hng Photocopy i Sinh Vin nh sau: Sut chit khu20% Nm012345 NCF(10,000) 5,0004,5003,5002,0001,000NPV684 (n v tin)IRR24% B/C1.07 (ln)PP2 (nm)ARR32%3.10Bng tm tt u khuyt im ca cc ch tiu Ch tiuu imKhuyt im NPV Gi trhin ti rng Tnh gi tr tin t theo thi gian, tnh n quy m d n, p ng yu cu giu c hn ln, ti a ha ngun ca ci. L ch tiu mnh m, thuyt phc. - Kh hiu - Kh tm sut chit khu, tc rt kh xc nh chi ph s dng vn. IRR Sut sinh lini b - C tnh trn dng ngn lu, tc thng tin ni b t d n. - D tnh, d hiu (th hin l phn trm) - C lc khng tnh c do dng ngn lu thay i bt thng - D dn n kt lun sai lm khi so snh cc d n c tnh loi tr nhau - Khng tnh n quy m, thi im d n - C tnh n gi tr tin t theo thi- C nhiu cch xc nh chi ph, Thm nh d n u t Prepared by NGUYEN TAN BINH473/9/2012 BCR (B/C) T s Li ch& Chi ph gian - H tr gii thch cho NPV - Thy c hiu qu ng vn dn n kt lun sai - Khng xt quy m v vng i d n PPCF K hon vn tnh trn dng ngn lu - c s dng nhiu do d hiu, d tnh ton -Huchviccdncriro cao - Khng quan tm n sut sinh li -CthmuthunviNPVkhiso snh d n loi tr nhau. Thm nh d n u t Prepared by NGUYEN TAN BINH483/9/2012 ARR Sut sinh lik ton - Tng i d hiu, d tnh ton - C da vo dng ngn lu v tnh trn ton b vng i d n - Khng quan tm n quy m, tui th d n - C nhiu cch hiu khc nhau ROI Sut sinh li ca vn u t - D hiu v da trn li nhun ch khng rc ri khi phi da trn dng ngn lu - D tnh ton v khng cn tnh gi tr tin t theo thi gian - Khng quan tm n quy m, tui th d n - Khng da vo dng ngn lu - D c nhng quan im khc nhau v xc nh vn u t -D c quan im khc nhau v xc nh li nhun (trc hay sau thu) PPNI K hon vn tnh trn li nhun - D hiu - D tnh ton - c s dng nhiu do chu nh hng ca nn kinh t k hoch. -Khngquantmnquym,tui th d n - Khng da vo dng ngn lu v chit khu - Khng quan tm n sut sinh li - D sai lm khi so snh la chn d n loi tr nhau HNG DN TRN EXCEL (cc hm NPV, IRR) (i)Hm NPV Bn vo: Excel>Fx>Financial>NPV Dng d liu ca d n Ca hng Photocopy i Sinh Vin tnh NPV nh sau: Thm nh d n u t Prepared by NGUYEN TAN BINH493/9/2012 So vi phin bn 98, Excel XP ny hi iu mt t. y bng Function chia trn v di, Windows 98 th chia hai bn: bn tri l loi hm (category), bn phi l tn hm (name). C l cng l cch m Microsoft lm mi sn phm 57.H no th cng bm OK c tip bng sau: Khaibothnht:Rate(sutchitkhu)bngcchnhpchutvosutchitkhu( C1). Khai bo th hai: nh du khi dng ngn lu t nm 1 n nm 5. Nguyn tc l, cha mt nm quay v. Tip theo, a chut ln thanh cng thc, bm du +, nhp chut vo cha dng ngn lu rng u tin (nm 0)/OK.

57 Ging nh bia hay nc sui ng chai vy thi, nay c ln mai i c cao. Thi trang cng vy, c ht di ri n ngn. Thm nh d n u t Prepared by NGUYEN TAN BINH503/9/2012 Kt qu NPV = 684 xut hin, nt cm ln gi l nt OK. Bm vo vng kt qu ra chn trc , B4.Nhiu bn ch rng Excel d qu, ti sao khng khai bo mt ln cho ht dng tin m phi thm du cng + cho rc ri! Khng bit trong tng lai Microsoft c ci tin g khng nhng ti ngh rng khng th. Bi v nu qut ht c dng tin, th khng c ch quay v. Nu bn qut c dng tin t nm 0 th Excel cng tnh, nhng n s chit khu v nm -1 y! Cc lu khc: Khngphnbitdngngnlurngmhaydng,chginguyntcchalimt nm quay v. Gi nh dng ngn lu nm th 1:- 3000 th c ngha l, gi tr hin ti ca dng chi ch l: PV = -3000 11 -2500(1 20%) =+ C mt dng ngn lu ca mt nm no bng 0 th vn phi nh (g) vo s 0. V trng, Excel s cho rng dng ngn lu trc nm v sau nm cch nhau ch mt nm, t Excel s tnh sai. Nguyn tc ny cng p dng i vi hm IRR. (ii)Hm IRR Bn vo: Excel>Fx>Financial>IRR Vn dng d liu ca d n Ca hng Photocopy i Sinh Vin tnh IRR nh sau: Thm nh d n u t Prepared by NGUYEN TAN BINH513/9/2012 NgaycthaotctrnExcelcnggichotamtnghrngIRRrtdtnhton,chcn qut ht dng tin rng (NCF) c mt trong bo co ngn lu d n. l nhng thng tin c t d n, v ch cn da vo m khng cn thm bt c mt thng tin no khc t bn ngoi. Trong khi tnh NPV li phi cn n mt sut chit khu. IV.Lm pht v nh gi d n Lmphthiunginlsmtgicangtinhaylstnglntronggichnghalm gimscmuacangtin.Lmphtlhintngbnhthng,nthngtrctrongminn kinh t pht trin, tng trng. Ti sao cn thit phi tnh n vn lm pht trong cc d n u t? Mt d n thng ko di nhiu nm, d tnh lm pht cho dng ngn lu l s bo m cho hot ng bnh thng cadn.Gimtkilgamnguynliuuvo,chiphmtgilaongthiim5nmsau chc chn s khc nhiu so vi hin nay.4.1Ch s lm pht Ginhlmpht(haytclmpht)ckhiulgthchslmphthngnm c tnh nh sau: Ch s lm pht nm 1: = (1+g)0 (1+g) = (1+g)1 Ch s lm pht nm 2: = (1+g)1 (1+g) = (1+g)2 Ch s lm pht nm 3: = (1+g)2 (1+g) = (1+g)3 Ch s lm pht nm n: = (1+g)n-1 (1+g) = (1+g)n Thm nh d n u t Prepared by NGUYEN TAN BINH523/9/2012 V d: Bng 12-1: Ch s lm pht v t gi hi oiTc lm pht trong nc6% Tc lm pht nc ngoi4% T gi hi oi hin ti15,000Nm0123 Ch s lm pht trong nc1.001.061.121.19 Ch s lm pht nc ngoi1.001.041.081.12 Ch s lm pht tng i1.001.021.041.06 T gi hi oi k vng15,00015,28815,58215,882 Trong , ch s lm pht tng i l t lgia ch s lm pht trong nc v ch s lm pht nc ngoi. Ch s lm pht tng i = Chsolam phat trong ncChsolam phat nc ngoai Nu lm pht trong nc cao hn nc ngoi, ch s ny ln hn 1 (>1), t gi hi oi k vng trong tng lai s cao hn. Ngcli,nulmphttrongncthphnncngoi,chsnysnhhn1( 1: khi li sut th trng tng (gim) th sut sinh li vn ch s hu tng (gim) nhanh hn, b < 1: khi li sut th trng tng (gim) th sut sinh li vn ch s hu tng (gim) chm hn, b = 1: khi li sut th trng tng (gim) th sut sinh li vn ch s hu tng (gim) t l nh nhau, b < 0: khilisutthtrngtng(gim)thngcli,sutsinhlivnchshusgim (tng) 60.

59 C th hiu v tnh b nh l dc (slope) ca hai bin: rE v rM, nghin cu chng 3: Phng php k thut s dng trong phn tch. 60 V d sut sinh li ca c phiu cc cng ty sn xut v kh, phng tin chin tranh. Thm nh d n u t Prepared by NGUYEN TAN BINH583/9/2012 b = 0: li sut th trng khng nh hng g n sut sinh li vn ch s hu. Ni cch khc, rE bng ng vi li sut khng ri ro rF.Nhng vn ny chng ta s cn tip tc tho lun trong cc dp khc, nhng quyn sch chuyn bit khc. Tuy nhin, Vit Nam hin nay rt kh hoc khng th p dng m hnh CAPM ny, n gin v chng ta khng c d liu. Ni cch khc, chng ta vn cha c mt th trng ti chnh hot ng tri chy, cha ni n l hon ho. Xemphlccuichngvhsbtacamtsngnhnghvmtscngtyni ting ca M.V tit kim thi gian cng giy mc cha c ch cho vic thy bi xem voi, chng ta li phi quay v vi cu hi trc mt: lm sao xc nh c rE khi khng c gi th trng? Mt s tho lun v vn sut sinh li ca vn ch s hu c cp mc 3.1.2 trn y. VI.Cc quan im nh gi d n Trong phm vi ch quyn sch, cc quan im nn kinh t hay quan im chnh ph, quan im phc li x hi hay phn phi, khng c c hi cp. Mc ny ch tho lun vic nh gi d n trn quan im tichnh, tc quan imcacc nh u t, c thgm:ch u t v nh cho vay.6.1Quan im nh cho vayNh cho vay thm nh d n da trn dng ngn lu ca tng vn u t, tc xem xt ti tng dng ngn lu chi cho d n (k c phn ng thu) v tng dng ngn lu thu v (k c phn trcp,trgi).Quanimnhchovaycncgilquanimtngut.Theo,cc ngn hng cho vay s xc nh c tnh kh thi v mt ti chnh ca d n, nhu cu cn vay vn cng nh kh nng tr n gc v li vay ca d n. Mc ch xem xt d n l nhm nh gi s an ton ca s vn cho vay.Nhngtisaonhchovaylichcnquantmndngngnlucatngut?n gin v nh cho vay c u tin nhn trc dng thu ca d n m khng c ngha v phi chia s vi ch s hu.Ngay c khi d n gp ri ro th trng 61, tng dng thu ca d n ch va bng vi s tin cn tr (n gc v li vay), nh cho vay vn thu phn mnh, mi ri ro dn ht ln vai ch s hu. Sut chit khu s dng tnh NPV theo quan im nh cho vay l chi ph s dng vn bnh qun (WACC), v tng dng ngn lu bao gm hai ngun vn: n vay v vn ch s hu. 6.2Quan im ch u t Quan im ch u t, cn gi l quan im ch s hu hay quan im c ng, mc ch nhm xem xt gi tr thu nhp rng cn li ca d n so vi nhng g h c c trong trng hp khng thc hin d n. Khc vi quan im nh cho vay, ch s hu khi tnh ton dng ngn lu phicngvnvayngnhngvodngngnluvovtrkhontrlivayvngcdng ngn lu ra.

61 Business risk (market risk) Thm nh d n u t Prepared by NGUYEN TAN BINH593/9/2012 Ni cch khc, ch u t (ch s hu) quan tm n dng ngn lu rng cn li cho mnh, sau khi thanh ton n vay. SutchitkhusdngtnhNPVtheoquanimchshulchiphsdngvn (sut sinh li i hi) ca ch s hu, v ch tnh trn dng ngn lu ca ch s hu. Lu l, dng ngn lu ca ch s hu bng (=) dng ngn lu tng u t tr (-) dng ngn lu vay v tr n.V d 12.22: C s liu ca mt d n n gin nh sau: -Vng i d n: 2 nm -Tng vn u t (u nm 1, tc cui nm 0): 1000 (n v tin); trong , vn i vay: 400, li sut 8%, tr u (vn v li) trong 2 nm. -Tng dng ngn lu rng ca d n (cha tnh ngn lu vay v tr n): nm th 1: 800, nm th 2: 600 (n v tin).-Sut sinh li i hi ca vn ch s hu: 20%; thu sut bng khng. Hy thm nh d n theo hai quan im: nh cho vay v ch u t.Trc ht, ta tnh dng ngn lu tr n hng nm ( hng dn phn k thut chit khu dng tin trn y). Nm012 N u k400208 Li pht sinh3217 Tr n (u):224224 - N gc192208 - Li vay3217 N cui k4002080 WACC= 40% 8% + 60% 20% = 3,2% + 12% = 15,2%(i)Bo co ngn lu theo quan im tng u t (nh cho vay) Nm012 Tng ngn lu rng-1000800600 NPV vi WACC=15.2%147 IRR27% D n c tng dng chi u t nm 0 l: 1000, tng dng thu (rng) nm 1 l: 800 v nm 2 l: 600. l ngn lu ca tng u t, khng quan tm n c cu ngun vn. Thm nh d n u t Prepared by NGUYEN TAN BINH603/9/2012 (ii)Bo co ngn lu theo quan im ch u t (ch s hu) Nm012 Tng ngn lu rng-1000800600 Ngn lu vay v tr n400-224-224 Ngn lu ca ch s hu-600576376 NPV vi rE=20%141 IRR41% Vn ch s hu ch chi u t nm 0 l: 600, dng thu (rng) ca ch s hu trong nm 1 l: 576 v nm 2 l: 376. l ngn lu ca ch s hu, ch quan tm n dng ngn lu cn li cho mnh, sau khi tr (-) dng chi tr n. Mt lu c bit l, gi tr NPV chnh lch khng nhiugia hai quan im nhng i vi IRR th chnh lch kh ln (41%>>27%). Nu gi nh d n s dng 100% vn ch s hu m khng huy ng n vay, dng ngn lu ch s hu bng vi tng ngn lu rng th IRR theo quan im ch s hu cng bng viIRR theo quan im tng u t, tc ch bng 27%. Nh vy, tc ng by sut sinh li ca vn ch s hu li chnh l yu t n vay (!) Xem khi nim n by ti chnh chng 14.VII.Phn tch ri ro d nC th ni rng bt c d n no, khng t th nhiu cng u c ri ro. Cc nh u t lun hiu r v chp nhn iu ny. Tuy nhin h s quyt nh khng lm, khng phi v s, m cho n chng no h cha bit c kh nng ri ro l bao nhiu.Phntchrirolclngnchkhngphikhcphcn.Ngitanigim thiu ri ro ch khng ai ni phng trnh ri ro. Tuy nhin, chng ta khng bn v vn ny. V gim thiu hay phng trnh ri ro ng ngha vi lm nh hay khng lm 62.Phn tch ri ro y nhm tr li cu hi, liu vi mc ri ro nh vy, phn thng b pchonclthang?Mckhc,thicamingingtrcrirocngkhcnhau. Mt ng tng gim c doanh nghip nh nc 59 tui c vi cn bit th ni ngoi thnh, con ci hc nc ngoi, ti khon rng rnh nm by trm ngn -la s t chi mt d n c mc ri ro15%(ginhlnghacnhvy),vcthkhngcg,mtthmthtcng tch ly hng chc nm tri. Trong khi , mc ri ro ny l qu tuyt vi mt gim c tr, nhit tnh, n hc ng hong tui mi trn 29. Bn tip tc hnh dung thi ri ro tng t cng s khc nhau ty thuc vo gii tnh, tn gio, vng min, dn tc v nhng th rt kh nh lng khc na.C th phn bit thnh hai phng php phn tch ri ro: phn tch tt nh v phn tch bt nh.

62 iu ny cng ng trong ngha l ca cuc i: lm ln th khuyt im nhiu, ln thuyn th ln sng, vit nhiu th sai st nhiu. Tt nhin sai st th cn trnh nhng khng nhn ra mnh sai st th mi l iu khng khip. Thm nh d n u t Prepared by NGUYEN TAN BINH613/9/2012 -Phn tch tt nh (deterministic) l ch quan cho trc mt gi tr xc nh (v d mt gi bn c th), hi kt qu (v d NPV) s l bao nhiu. -Phntchbtnh,cngilphntchxcsut(probabilistic)haymphng (simulation),nhnggitrcanhntriroscxuthinmtcchbtnh,ngunhin khng nh trc. V tt nhin, kt qu cng l nhng gi tr mang tnh ngu nhin. Ging nh tr chiquaysccsngbcvy.PhngphpnyvthcnctngilmphngMonte-Carlo 63.Saunhiuln(trm,ngnln)th,ngitathycccquylut(phnphixcsut). Theo , c bao nhiu phn trm kt qu no ri vo khong no. T nh, xc sut NPV> chn Scenarios ta c bng sau: Bm nt Add (a vo) trn bng Scenario Manager (thit k kch bn) c bng Add Scenario (a kch bn vo) nh sau: Thm nh d n u t Prepared by NGUYEN TAN BINH643/9/2012 Thm nh d n u t Prepared by NGUYEN TAN BINH653/9/2012 ttnkchbn(tnhhung);giphmCtrlvnhpchut 64lnltvoccchnl cc bin c xem l ri ro, trong v d ny l cc bin: khi lng, gi bn n v, chi ph n v. Bm nt OK 65 c bng Scenario values (cc gi tr kch bn) nh sau: Sau khi nh my cc gi tr (ty bn nh ngha th no l tt, trong v d ny: khi lng: 1200, gi bn n v: 120 v chi ph n v: 60)vo bng, bm nt Add thit k kch bn tip theo,

64 Tt nhin ni chut trn nh vy th hiu l "chut tri".65 Ti thng a vi cc sinh vin rng, c thy nt no "cm" ln l bm ti, t s c. cnh tranh, cc cng ty phn mm lun ci tin cc sn phm ca mnh theo hng ngy cng tin li cho ngi s dng. Bit u mt ngy no Bill Gates li cho ra mt chng trnh Excel bng ting Vit (!). Lc y, bn s khng thy Tools m l Cc Cng C; khng phi lHelp m l Gip. Lc y l gip thc s, cn by gikhi bm nt Help bn thy cng rc ri hn l khi cha "gip" (!). Hy tin tng v hy bit ch i. Ch c iu trong lc ch i phi chu kh c bng ting Ty vy. Thm nh d n u t Prepared by NGUYEN TAN BINH663/9/2012 t tn kch bn mi (theo v d trn l kch bn trung bnh), bm nt OK ri a gi tr vo bng (ty bn nh ngha th no l trung bnh, trong v d ny: khi lng: 1000, gi bn n v: 100 v chi ph n v: 80), nh sau: Thm nh d n u t Prepared by NGUYEN TAN BINH673/9/2012 LitiptcbmntAddthitkkchbntiptheo,vcthlmti.Cuicng (khng mun thm kch bn na) th bm nt OK, ta s thy li bng u tin nhng gi y c cc tn ca cc kch bn c thit k nh sau: Bn c thy nt Show (ch ra) n "cm" ln khng? C a vt xanh (nhp chut) vo kch bn no bn mun ri bm nt Show, kt qu kch bn s hin ra. Trong bng trn y ang ch ra kch bn Tt, vi khi lng 1200, gi bn 120, chi ph n v 60 v li nhun 72,000. Thm nh d n u t Prepared by NGUYEN TAN BINH683/9/2012 By gi bn a vt xanh xung kch bn xu chng hn ri bm nt Show, kt qu s nh sau: Trong kch bn xu, trc ta nh ngha vi cc thng s: khi lng 800, gi bn 80, chi ph n v 110 v kt qu ch ra l 24,000. ChngtrnhScenariocngcungcpmtbngtmttcckchbn.cbngtmtt, dng lnh Summary \ chn Scenerio Summary c bng tm tt kt qu cc kch bn nh sau: Ghi ch (di bng): ct Gi tr hin hnh (gi tr gc) i din cho cc gi tr ca nhng thay i khi bo co tm tt kch bn c thitlp. Cc thay i ca mi kch bn c lm ni bt trong nn mu xm. Thm nh d n u t Prepared by NGUYEN TAN BINH693/9/2012 Bn thy c d dng khng? Chc may mn!7.2Phn tch bt nh Khc vi phn tch tt nh, nhng gi tr hay nhng tnh hung c xc nh trc tr licuhi"nu,th",trongphntchmphng,cngilphntchxcsut,michuyns hon ton l ngu nhin. Trongkhunkhquynschny,cckinthccnbnvthngktonkhngc cp,bnchvicxcnhvkhaiboccbinrirocadn(vd:gibn,khilng,lm pht) v cc bin kt qu (v d: NPV v IRR), chng trnh Crystalball s gip bn. y l mt phn mm c uy tn nht phn tch ri ro hin nay. Bn c th ln trang web theo a ch di y c phn mm ny. Thm ch khi bn ng k tr thnh thnh vin ca hi, hng thng hoc ngn hn bn s nhn c nhng thng tin, nhng cp nht, gii thiu sch mi xut bn hay c chia s kinh nghim g y v phn tch m phng. Cng c khi nhn thng bo mi tham d mt kha hun luyn ngn hn (2 ngy) v phn tch ri ro, vi hc ph gn c ngn bng Anh y (!) 66. From: "Decisioneering Newsletter" To: "Nguyen Tan Binh" Subject: Tomorrow's Forecast Newsletter - Issue #91 Date: Friday, September 20, 2002 12:57 PM www.crystalball.com To Nguyen Tan Binh: You are now receiving the HTML version of our newsletter. If you do not see the top banner or any images or large and colored fonts, then your e-mail program is not set to receive a full HTML newsletter. We are still publishing a plain text version, and if you would like to switch to that format, click on this link(http://www.crystalball.com/newsletter_list.html)You can also view this HTML newsletter online athttp://www.crystalball.com/newsletters/newsletter91.html SaukhigitCrystalballthnhcng,qucuphalxuthinthongquatrnmn hnhExcelvtrnthanhcngcxuthinthmCell, RunvCBTools(phinbnCrystalball97 khng c CBTools).

66 Cch khc, nu TP. HCM, bn c th n ng Tn Tht Tng v mang theo vi ngn ng (VND) ung c ph. Khng bit t bao gi, nhng ngi bn tr gii giang v tt bng li t tp v con ng c nhng hng me y th mng ny, h sn sng tip n nng hu v gip bn mt cch tn tnh. Bn ch cn h ng khu lnh: Crystal Ball. Chc bn toi nguyn.Thm nh d n u t Prepared by NGUYEN TAN BINH703/9/2012 V d: Phn tch m phng ri ro ca d n Ca hng photocopy i Sinh Vin, nh sau: Bin ri ro (d kin c nhiu bin ng trong thc t) c xc nh trong v d ny l: vn u t nm 0 v dng ngn lu rng nm 1. Bin kt qu (bin d bo) l NPV. -Bc1:Trctin,khaibobinriro(bingithit)bngcchtchutvo cha bin ri ro, theo v d l B3. Ln Cell >> chn Define Assumption (xc nh bin ri ro). Bm thanh Define Assumption, ta c bng sau: Thm nh d n u t Prepared by NGUYEN TAN BINH713/9/2012 Bngnycnhiuphnphixcsuttachn.Vdtachnphnphibnhthng (tc phn phi chun - normal distribution) >> OK, ta c bng tip theo: Bngnychotagitrtrungbnh(Mean)vmcnhlchchun(StdDev:Standard Deviation) l 10% so vi gi tr trung bnh. Tt nhin ta c th thay i theo mun. BmOKktthckhaibo.Tngt,tiptckhaibochoccbinrirotiptheo (nhiu bin cng c). Vi phin bn Crystalball 2000, sau khi khai bo, cha bin ri ro s t ng t nn mu xanh l cy. Thm nh d n u t Prepared by NGUYEN TAN BINH723/9/2012 -Bc2:Tiptheo,khaibobinktqu(bindbo)bngcchtchutvo cha bin d bo, theo v d l B4. Ln Cell >> chn Define Forecast (xc nh bin d bo), nh sau: Bm thanh Define Forecast, ta c bng sau: t tn bin, n v tnh (nu cn) >> bm OK hon tt khai bo. C th chn nhiu bin d bo, v d chn thm bin d bo l IRR chng hn.Vi phin bn Crystalball 2000, sau khi khai bo, cha bin d bo s t ng t nn mu xanh dng. -Bc3:LnRun>>chnRunPreferences,nhslnchymphng,vdnyl 1000 ln. tin cy mc nh l 95% (tt nhin bn c th chn mc tin cy khc: cao hoc thp hn). Thm nh d n u t Prepared by NGUYEN TAN BINH733/9/2012 BmOK.LnliRun>>bmRun.ChngtrnhCrystalballbtuchymphng. Mi ln m phng, mt gi tr ca bin ri ro s xut hin mt cch ngu nhin, v kt qu NPV s c tnh li v cho ra mt gi tr. Chng trnh thc hin 1000 ln nh vy (mt vi pht hoc lu hn ty vo tc my tnh ca bn v ty vo sc nng ca bi ton hay d n).Sau khi chy m phng xong, ta c bng sau: y l bng bo co u tin do chng trnh Crystalball cung cp sau khi thc hin 1000 ln m phng (1000 trials). Lm g vi bng ny y? Nt c hnh tam gicThm nh d n u t Prepared by NGUYEN TAN BINH743/9/2012 hng di cng bn s thy khong bin thin t tr v cc (-Infinity) n cng vcc (+Infinity), c th gi tr NPV thp nht l:- 2089 (n v tin) v cao nht l: 3383 (xem ch hai tam gic nh hai u trc honh). Tt nhin xc sut NPV ri vo khong ny chc chn phi l100%(xemCertainly=100%).Gingnhbnontuicbngimiquenvy.Nubn on khong t 15 n 51 th chc chn 100% s trng, nhng bn on khong 26, 27 g th xcsuttrngsthphn(nukhngcthngtinnothm!).Nhngkiuontuichctrng 100%, tc tin cy cao nh trn th chng cn ngha g na c, thm ch mt bn y! -Bc 4: Hi Crystalball tr li. V d hi: Xc sut d n c NPV 0 l bao nhiu? tr li, bn ch cn di chuyn tam gic bn tri v bn phi cho n khi cn tri bng 0. Bn s c thy xc sut ny l 74.58%, nh bng di y. Thm nh d n u t Prepared by NGUYEN TAN BINH753/9/2012 V d hi: Xc sut d n c NPV t gi tr trong khong t 505 n 2319 l bao nhiu? tr li, bn ch cn di chuyn tam gic bn tri v bn phi cho n khi cn tri bng 505; v di chuyn tam gic bn phi v bn tri cho n khi cn phi bng 2319. Bn s c thy xc sut ny l 50%, nh bng di y. Tng t, bn c tip tc hi v c di chuyn tam gic n ni cn thit. Thm nh d n u t Prepared by NGUYEN TAN BINH763/9/2012 Nhng khng phi ch c th, Crystalball cn cung cp cho bn nhng bo co, nhng tm tt cc thng s m t thng k, nhng th a dng theo mun. Bn hy c vo ca hng mc sc m chn. Hay mc tng quan (Correlation) gia cc bin ri ro i vi bin kt qu. PH LC: H S BETA (b) CA MT S CNG TY V NGNH KINH DOANH M Thm nh d n u t Prepared by NGUYEN TAN BINH773/9/2012 H S BETA (b) NGNHH S BETA (b) CNG TY NGNH *bCNG TYb Khch sn v dch v (9)1.55Cng ty my tnh Apple1.52 Hng khng (8)1.48Cng ty vin thng McCaw1.50 My tnh (10)1.48Hng khng Alaska1.44 Dch v tit kim, cho vay (13)1.45Hewlett Packard1.34 Dng c y t (53)1.42Timberland1.30 Thit b in (43)1.40Dch v y t Columbia-HCA1.28 May mc (25)1.37Microsoft1.24 Ca hng bn l (74)1.23Time Warner1.19 Thit b vin thng (17)1.27Ngn hng BankAmerica1.19 Ngn hng (99)1.12General Motor1.03 Chm sc sc khe - y t (64)1.02Boeing0.96 Thc phm (44)0.86AT & T 0.88 My nng c (4)0.83Cng ty in lc Duke0.44 Du kh, m phm (31)0.72Cng ty in lc Allegheny0.36 Vng bc qu (6)0.54Cng ty cng ch San Diego 0.32 (*) S trong ngoc l s lng cc cng ty trong ngnh. Ngun: Investment Data Book, thng 7/1994; Nh xut bn: Vestek Systems-San Francisco.