02-09-2014_16-40-43 / 2013 Пакеты прикладных программ
.pdf
|
0KOH'lQHUe ma611. 12.2 |
ApryMeHT |
OrmcaHHe apryMema |
nepHO.D: |
IlepHO.D:, .D:.illl KOTOporo 'lpe6yeTCHHaHTH BbHUiazy |
|
no rrpou;eHTilM (,n:oJDKeH 6b!Tb B HHrepaa.rre OT I .n:o |
|
apryMeHTil) |
Haq_rrepHO.D: |
HoMep rrepooro rrepHo,n:a IUiarexeii:, yqaCTByiomero |
|
B Bhl'IHCJieHHHX |
KOH_rrepHO.D: |
HoMep rrocJie,n:Hero nepHo,n:a IUiarexeii:, yqacmyio- |
|
mero a Bhl'IHCJieHHHx |
HOMHHaJihHaH_CTaBKa |
HoMHHaJihHaH ro.n:oaaH rrpou;eHTHaH craBKa |
peHHBeCT_HOpMa |
HopMa rrpH6hUIH, rronyqaeMoii: 3a ,n:eHhm, Haxo.D:H- |
|
ru;HeCH B HaJiffqHOM o6opore rrpH peHHBeCTHpOBaHHH |
<l>HHaHCOBaH_HOpMa |
HopMa rrpH6hUIH, BhIIUiaqHaaeMoii: 3a ,n:eHhm, Ha- |
|
XO.D:HIUHeCH B o6opore |
3<l><t>eKT_CTaBKa |
3<l><t>eKTHBHaH ro,n:oBaH rrpou;eHTHaH craBKa |
MHorHe qnrnaHCOBbie <l>YHKUHH HMeIOT O.UHHaKOBbie apryMeHTbI (Ta6JI. 12.2).
~ Excel ,ll,Jill pac'leTaonepanaii no K.pe,zurraM a laiiMaM
B cHcTeMe Excel cy:rn;ecTByeT rpynrra <l>YHKUHH, rrpe.n:tta:maqeHHbIX ,UJUI pacqeTa <l>HHaHCOBbIX orrepau;HH: ITO Kpe,UHTaM, ccy.uaM H Jai1MaM. 3TH pacqeTbl OCHOBaHbl Ha KOHu;erru;HH BpeMeHHOH CTOHMOCTH .ueHer, T. e. OHH rrpe.urronaraIOT HepaBHOI..J;eHHOCTb .ueHer, OTHOCHiu;HXCH K pa3HbIM MOMeHTaM BpeMeHH. 3Ta rpynrra <l>YHKUHH rrpe,n:HaJHaqeHa ,UJUI cne.uyIOrn;HX pacqeToB:
•orrpe.ueJieHIDI 6y.uy:rn;ei1 CTOHMOCTH (HapameHHOH CYMMbI);
•orrpe.ueneHIDI TeKYiu;eH CTOHMOCTH (HaqaJibHOro JHaqeHIDI);
•orrpe.ueneHIDI cpoKa IIJiaTe)K.a H rrpou;eHmoH: cTaBKH;
•pacqeTa rrep110.u~ecKHX IIJiaTexeH:, CBHJaHHbIX c rrorarneHHeM
JaHMOB.
06maH <l>OPMYJia pacqeTa, KOTOpaH B Excel HCIIOJibJyeTCH rrpH
BblqHCJieHHH <l>HHaHCOBbIX apryMeHTOB, CBHJaHHbIX c .ueHeXHbIMH
IIOTOKaMH, HMeeT BH,U
pmt (1 + rf -1 (1 + r · type)+ pv (1 + r)n +fa =0, (12.43) r
r.ue pmt - <l>HKCHpoBaHHaH (HeHJMeHHaH) rrep110,n:11qecKaH CYMMa IIJiaTe)K_a; n - o6mee qncno rrep110.uoB BhlIIJiaT; r - rrpou;eHTHaH cTaBKa
Ja O.UHH rrep110.u; type - |
qlfcJio 0 HJIH 1, 060JHaqa10mee rrep110.u rrpo- |
HJBO.UCTBa BbIIIJiaTbl (1 |
- B Haqane rrep110.ua IIJiaTexeH:, 0 - B KOH- |
u;e); pv - TeKYiu;aH CTOHMOCTb BKJia,Ua (3ai1Ma), no KOTOPOMY HaqHC-
160
JHIIOTCH npoueHTbl no CTaBKe r% HJIH TeKYIUaH CTOHMOCTh cepHH qmKCHpOBaHHbIX nepHO)l,JiqeCKHX IIJiaTexe:H; fv - 6yJzyI.UaH CTOHMOCTb BKJia.n;a (3aii:Ma) HJIH 6yJzyI.UaH CTOHMOCTb cepHH <l>HKCHpOBaHHbIX nePHO)l,JiqeCKHX IIJiaTexe:H.
Ec11H npoueHTHaH cTaBKa 3a nepHo.n: HaqHcJieHHH .n;JIH BhI- '-1.HcJieHHHHCnOJib3yIOT CJie,ll,yIOIUyIO <t>opMyny:
pmt· n + pv+fv =0. |
(12.44) |
<l>OPMYJihl (12.43) H (12.44) HCnOJib3yIOTCH B <i>YHKUHHX .63, KilEP, HOPMA, II3, IIIIJIAT.
Onpe)J,eJieHHe 6y)J.ylll.eii CTOHMOCTH
IlOHHTHe 6y.n:YIUei1 CTOHMOCTH OCHOBaHO Ha npHHUHne HepaBHOueHHOCTH .n:eHer B pa3Hbie MOMeHTbl BpeMeHH, TaK KaK BJIOXeHHH, C,ll,eJiaHHbie cero.n:HH, B 6yJzyI.UeM, KaK npaBHJIO, COCTaBHT 60JibIIIyIO
BeJIJiqlfHY.
<l>YHKUHH .63 n03BOJIHeT paccqHTaTb 6y.n:YIUYlO HJIH HapaIUeHHyIO CTOHMOCTb cepHH <l>HKCHpOBaHHbIX rrepHO)l,JiqeCKHX IIJiaTexe:H, a TaK- )Ke 6y.n:YIUYlO CTOHMOCTb TeKYIUero 3HaqeHHH BKJia.n;a HJIH 3aii:Ma npH
IIOCTOHHHOH rrpoueHTHOH CTaBKe.
<l>YHKUHH B3PACIIl1C no3BOJIHeT paccqHTaTh 6yJzyI.Uee 3HaqeHHe HHBeCTHUHH IIOCJie HaqHcJieHHH CJIO)l(HblX npoueHTOB rrpH rrepeMeH-
HOH npoueHTHo:H crnaKe.
~ 63. PacqeT c noMOIUbIO <l>YHKUHH .63 6yJzyI.Ue:H CTOHMOCTH rrepHO,ll,JiqeCKHX IIOCTOHHHbIX IIJiaTexe:H H 6yJzyI.Uero 3HaqeHHH e.n:H- HOH CYMMbl BKJia.n;a HJIH 3ai1Ma OCHOBaH Ha noCTOHHCTBe rrpoueHTHOH
CTaBKH.
CHHTaKcHc B3(HopMa;qHc110_ nepHo.n:oa;BhIIIJiaTa;HJ;THrr). 3HaqeHHe, KOTOpoe B03BpaIUaeT <l>YHKUHH .63, - 3TO apryMeHT fv
H3 <i>OPMYJibl (12.43).
PaccMOTpHM paJJIJiqHbie aapHaHTbI HCIIOJib30BaHHH 3TOH <l>YHKUHH
rrpH perneHHH KOHKpeTHbIX 3a.n;aq.
1. JJ:orrycTHM, Heo6XO,ll,HMO paccqHTaTb 6y.n:YIUYlO CTOHMOCTb e.n:H- HOH CYMMbI BKJia.n;a HJIH 3aii:Ma, no KOTopo:H HaqHcJIHIOTCH CJIO)l(Hhie
rrpoueHThI onpe.n:e11eHHoe qHc110 rrepHo.n:oa:
|
(12.45) |
r.n:e pv - TeKYIUaH CTOHMOCTb BKJia.n;a |
(3aii:Ma); n - 06IUee qlfCJIO |
rrepHO,ll,OB HaqHcJieHHH npoueHTOB; r - |
rrpoueHTHaH CTaBKa no BKJia- |
;:i:y ( 3aii:MY).
3rn <l>OPMYJia COOTBeTCTByeT KJiaCCJiqeCKOH <l>OPMYJie pac'-leTaHa- paIUeHHOH CYMMbl BKJia.n;a no MeTO,ll,y CJIO)l(HblX rrpoueHTOB.
,n:.mi BbNHCJieHHH 6y.n:YIUero 3HaqeHHH e,ll,HHOH CYMMbl c noMOIUbIO <t>YHKUHH .63 HCnOJib3yIOTCH apryMeHTbI: H3, HOpMa, '-1.HCJIO_nepHO-
161
)];OB. IlpM 3TOM q>OpMYJia 6y)];eT MMeTb BM =B3(HOpMa;qMcJio_rrepMO- )];OB;H3).
IlpM perneHMM KOHKpeTHOH 3a,z:i;aqM BMeCTO Ha3BaHMH apryMeHTOB YKa3bIBaIOT cooTBeTCTByro11me qMcna.
2. PaccMOTpMM CMTYaII:MM, KOrJ:J:a IIJiaTe:xrn: rrpoM3BOMTCH cMcTeMaTMqecKM, a He O)];MH pa3, KaK B rrpe)];bUJ.YmeM IIPMMepe. 3TM IIJiaTe:xrn: MOryT ocyrnecTBJIHThCH B Haqane K<OK,ll;oro pacqeTHoro rrepMOJ:J:a (rrpettyMepaHJ:J:O) MJIM B KOHII;e (IIOCTttyMepaH)];O) B TeqeHMe n rrepMOJ];OB •
.[(orryCTMM, qTo B K<OK,ll;OM rrepMO)];e BHOCMTCH OJ];MHaKOBaH CYMMa. Tpe6yeTCH HaHTM COBOKYIIHyIO BeJittqMtty TaKMX BJIO)l(eHMH (MX 6yJ1:YIIIyIO CTOMMOCTb) B KOHII;e n-ro rrepMOJ];a J1:JIH o6oMX cnyqaeB. 0TJittqMe B pacqeTe rrpM 3TOM 3aKJIIOqaeTCH B TOM, qTo BO BTOpOM cnyqae He rrpOMCXOJ];MT HaqMcJieHMH rrpoII;eHTOB Ha IIOCJieJ];HMH BKJla,z:J;, T. e. Bee BKJla,rl;bl rrpettyMepaHJ:J:o YBeJittqMBaIOTCH Ha CJIO)l(Hhie rrpoII;eHThI Ha OJ:J:MH pacqeTHhIH rrepMOJ:J: 60JibIIIe, qeM BKJla,rl;bl IIOCTttyMepaH)];O.
2.1 . .[(JIH pacqern 6yJ:J:YIIIeH CTOMMOCTM cepMM <l>MKCMpOBaHHhIX rrepMO)];ttqeCKMX IIJiaTexeU:, ecJIM OHM BHOCHTCH B Haqane K<OK,ll;Oro rrepMOJ];a (TaK Ha3bIBaeMbIX o6H3aTeJibHhIX IIJiaTexeU: M rrpettyMepaHJ:J:O), MCIIOJlh3yeTCH qJOPMYJia
fv = pmt(l + r)+ pmt (1 + r)2 + ... + pmt(l + rr =
= pmt (1 + rr -1 (1 + r). |
(12.46) |
r |
|
3Ta <l>OPMYJia COOTBeTCTByeT <l>OPMYJie pacqern HapameHHOH CYMMbl IIOCTOHHHOH peHTbl rrpettyMepaH)];O (12.41).
IlpM pacqeTe c IIOMOIII;bIO <l>YHKII:MM B3 MCIIOJib3yIOTCH apryMeHTbI: HOpMa, qMcno_rrepMOJ:J:OB, BhIIIJiaTa, TMII = 1. Ha pa6oqeM JIMCTe Excel <l>OPMYJia (12.46) 6y)];eT MMeTb BM =B3(HOpMa;qMCJIO_rrepMO)];OB;BhIII-
JiaTa;l).
Pe3yJihTaT pacqern c rroMOIII;hIO <l>YHKII:MM B3 J:J:OJl)l(eH coBrra,ri;aTh
c pe3yJihTaTOM, rronyqeHHhIM no <l>OPMYJie
2.2. .[(JIH pacqern 6yJ:J:YIIIeH CTOMMOCTM cepMM <l>MKCMpOBaHHhIX rrePMOJ];ttqeCKMX IIJiaTexeU:, eCJIM BhIIIJiaThl IIPOMCXOMT B KOHII;e rrepMO- )];a (TaK Ha3bIBaeMbIX o6bJqHbIX IIJiaTexeU: MJIM IIOCTttyMepaHJ:J:O), <l>opMYJIY (12.45) CJie)];yeT MOJ:J:M$MII;MpOBaTh:
fv = pmt+ pmt(l+r)+ pmt(l+r)2 + ... + pmt(l+rr-1 =
= pmt (l + rr - 1 . |
(12.47) |
r |
|
<l>OPMYJia (12.47) COOTBeTCTByeT <l>OPMYJie (12.39) KJiaCCttqeCKOH MOJ];eJIM.
3arrMCh Ha pa6oqeM JIMCTe Excel, coorneTCTByromaH <PopMyne
(12.47), 6y)];eT MMeTb BM =B3(HopMa;qMcJio_rrepMOJ];OB;BhIIIJiaTa;0).
162
|
|
Ta61rnua 12.3 |
|
|
MeTO~ ea11aCJieeHJ1 nponeHToe e ro.zzy |
||
Mero.u |
06mee qf!CJIO rrepHO.UOB BhIIIJiaT |
IIpo11eHTIIasi CTaBKll Ja rrepHO.U |
|
ttaqHcJiemrn, % |
|||
|
|
||
E)((ero,1J;mm |
n |
k |
|
noJiyr0,1J;OBOH |
2n |
k/2 |
|
KsapTIUI1>m1H: |
4n |
k/4 |
|
Mecwrmm |
12n |
k/12 |
|
E)((e)J;Heam.m |
365n |
k/365 |
|
Onycnrn apryMeHT nm= 0, MO)l(HO 3TY 3anwc1> rrpe,1l;CTaBMTb B BM,D;e:
=o3(HOpMa;qwcno_rrepMO,ll;OB;BblnJiaTa) M IIO,ll;CTaBMTb BMeCTO apry-
MeHTOB COOTBeTCTBYJOIIJ;Me qwcna.
3aiJa1ta. Paccqi.naTh, KaKrui: C)'MMaOKaJKeTCSI Ha cqeTe, ecmr 27 ThIC. p. noJimKeHbI Ha 33 ro)J;a IIOLI 13,5 % ro)J;OBhIX. IIpoueHTbI HaqHcJISIIOTCSI KaJK)l;hie IIOJirO)J;a.
p e III e H He. ,LVuI pacqeTa HCIIOJib3yeM <l>OPMYJIY (12.45), TaK KaK Tpe6yeTC51 HaifTH 6y.ll:YIIlee 3Haqemi:e e)J;HHOH C)'MMhIBKJia)l;a. YqTeM, qTo a ycnoBHH Ja)J;aqH 3MaH1>1 ro)J;oaoH: rrpoueHT H qHcJio JieT BKJia)l;a. EcJIH rrpouem1>1 HaqHcJIS1IOTCS1 HeCKOJibKO pa3 B ro)J;, Heo6X0,1J;HMO paccqHTaTb 06111ee qffCJIO rrepHO)J;OB HaqHcJieHHSI rrpoueHTOB H CTaBKY rrpoueHTa 3a rrepHO)J; HaqHCJieHHSI. HaH6onee pacrrpocTpaHeHHhie MeTOLlhI HaqHcJieHHSI rrpoueHTOB a ro)J;y rrpHae)J;eHhI a Ta6n. 12.3.
IlpH IIOJiyro)J;OBOM yqeTe rrpoueHTa 06111ee qHCJIO rrepHO)J;OB HaqHCJieHHSI 6y)J;eT paBHO 33. 2 (apr)'MeHTqffcJio_rrepHO)J;OB), a CTaBKa 3a rrepHO)J; HaqucJieHHSI 13,5 %/2 (apr)'MeHTHOpMa). Ilo yCJIOBHIO 3a)l;aqu apr)'MeHT
3To 0Tpm1aTeJI1>Hoe qucno, 03Haqa10111ee BJIO:lKeHHe )J;eHer. l1crron1>- 3YS1 <l>YHKUHIO E3, JaIIHIIIeM:
E3(13,5%/2;33 *2;-27) = 2012,07 Thie. p.
3aiJa1ta. IIpe,1l;rrono:lKHM, ecTb )J;Ba aapuaHTa HHBeCTHpoaaHHSI cpe,1l;CTB
B TeqeHHe qeTbipex JieT: B Haqane KaJK)l;Oro ro)J;a IIO)J; 26 % ro)J;OBhIX MJIH B KOHUe KaJK)l;Oro ro)J;a IIO)J; 38 % ffi)J;OBbIX. IIycTh exero)J;HO BHOCHTCSI 300 ThIC. p. Orrpe,1l;eJIHTb, CKOJibKO )J;etter OKaJKeTCSI Ha cqeTe B KOHUe qeTBepToro ro)J;a rrpH KaJK)l;OM aapHaHTe HHBeCTHpOBaHHSI.
Pe III e H He. TaK KaK B ,1J;aHHOM cnyqae rrpoH3BOLISITCSI rrepHOLIH'leCKHe IIJiaTeXH )J;JISI pacqeTa HCIIOJib3yeM <l>OPMYJibl (12.46) - rrepBbIH aapttaHT (06S13aTeJibHbie IIJiaTeXH) H (12.47) - BTOpoH: aapMaHT (061>1qH1>Ie IIJiaTeXH).
B rrepBOM aapHaHTe Hapa111eHHIDI CTOHMOCTb rrepaoro BKJia)l;a pa3MepoM
300 ThIC. p. K KOHuY qeTBepToro ro)J;a c yqeTOM Ha'IHCJieHHSICJIOXHbIX rrpoueHTOB COCTaBHT:
300(1 +0,26)4 =756,14 TblC. p.
DY.ll:YIIIIDI CTOHMOCTb K KOHuY qeTBePTQro ro,1J;a COCTaBHT:
163
BTOporo BKm1,n;a 300 (1 +0,26)3 =600,11 TbIC. p.; TPCTbero BKJia,D;a - 300 (1+0,26)2 = 476,28 TbIC. p.; UOCJie,!Ulero BKJia,n;a 300 ( 1 + 0,26) = 378 TbIC. p.
COBOKYJIH<UI CTOHMOCTb BJIOXCHHH K KOHI.Jy 'ICTBCPTOroro,n;a ,ll;OCTHrHeT: 756,14+ 600,11+476,28+378= 2210,53 TblC. p.
Bo BTOpOM BapHaHTe upo:u;eHTbl Ha UOCJIC,ll;HHH BKJia,n;, c,n;eJiaHHbIH B KOH- :u;e 'ICTBepTorouepHo,n;a, He Ha'IHCIDIIOTCH.
Haparn;eHH<UI CTOHMOCTb COCTaBHT: TPCThero BKJia,D;a 300 (1+0,38) = 414 TbIC. p.;
BTOporo BKJia,D;a 300 (1+0,38)2 = 571,32 TbIC. p.; uepBoro BKJia,n;a 300 (1+0,38)3 = 788,42 TbIC. p.
COBOKYJIH<UI CTOHMOCTb BJIO)KCHHH K KOHI.Jy 'ICTBepTororo,n;a COCTaBHT: 788,42 + 571,32 + 414 + 300 = 2073,74 TbIC. p.
IlpH HCUOJib30BaHHH <l>YHKUHH .63 yKa.JbIBaIOT apryMeHTbl ,ll;IDI uepBoro BapHaHTa:
HOpMa = 26 %, 'IHCJIO_uepHO,ll;OB= 4, BbIUJiaTa =-300, THU= 1;
,n;IDI BI'OporoBapmurra HOpMa = 38 %, 'IHCJio_uepHo,n;oB= 4, BbIUJlaTa = -300. ApryMeHT THU = 0 MO)KHO onycTHTb.
CoOTBeTCTBCHHO COBOKYJIH<UI CTOHMOCTb BJIO)KCHHH COCTaBHT:
.63(26%;4;-300;1) = 2210,53 TbIC. p.
.63(38%;4;-300) = 2073,74 TbIC. p.
Pac'IeTblUOKa.JaJIH, 'ITOupe,n;UO'ITHTCJlbHeeuepBbIH BapHaHT HHBCCTHpoBaHHH.
~ 63PACilHC. Ec;rn rrpo:u;eHTHaH CTaBKa MeHHeTCH c TeqeHHeM BpeMeHH, TO AJlll pacqeTa 6y;zymero 3HaqeHHH HHBeCTHI.J;HH (e.n;HHOH CYMMhl) IIOCJie HaqHcJieHHH CJIO)l(}fblX rrpo:u;eHTOB MO)l(HO HCIIOJib30BaTh <l>ymanno B3PACIIMC.
CHHTaKcHc B3PACIIMC(HHBeCTHI.J;HH, {CTaBKal ;cTaBKa2; ...;cTaBKaN}).
IlpH HCIIOJib30BaHHH MaCCHBa rrpo:u;eHTHbIX CTaBOK {CTaBKal;cTaBKa2; ... ;cTaBKaN} CTaBKH Heo6xo.n;HMO BBO;:J;HTb He B BH.n;e rrpo:u;eHTOB, a KaK qffcJia, HarrpHMep {O, 1;O,15;0,05}. 0.n;HaKO rrpoII.J;e 3aIIHCaTh BMeCTO MaCCHBa CTaBOK COOTBeTCTB}'IOII.J;HHHHTepBaJI gqeeK, co.n;epxaII.J;HX 3HaqeHHH rrepeMeHHbIX rrpo:u;eHTHbIX CTaBOK.
<l>YHKI.J;HH B3PACITMC (attrJIHHCKHH BapHaHT FvSchedule) HMeeT BH.n;
FvSchedule = HHBeCTHI.J;HH. (1 + CTaBKal). (1 + CTaBKa2) .... x
X (1 + CTaBKaN). |
(12.48) |
<l>OPMYJia (12.48) COOTBeTCTByeT KJiaCCffqeCKOH <l>OPMYJie ( 12.19) AJlll pacqern HapaI:u;eHHOH CYMMbl BKJia.n;a no MeTO;:J;y CJIO)l(}fbIX rrpo- :u;eHTOB rrpH HCIIOJib30BaHHH rrepeMeHHbIX CTaBOK.
3aiJa11a. Ilo 06JIHra:QHH HOMHHaJIOM 100 TbIC. p., BblnymCHHOil: Ha IIICCTb JICT, upe,n;yCMOTPCH CJIC,n;yIOID;HH uopH,n;OK Ha'IHCJICHHHnpo:u;eHTOB: uepBblH ro,n; 10 %, ,n;Ba uocne,n;y10rn;HX ro,n;a 20 %, ocTaBIIIHecH TPH ro,n;a 25 %. Pacc'IH-
164
3aMernM, 'ITOpac'leTbIc 11c11011b3oeamt:eM <l>YHKUHH HI13 H II3 HBJUIIOTCH 'laCTHbIMHCJIY'laHMHllPH Bbl'IHCJieHHHTeicyll.{eH CTOHMOCTH O)l(H,IJ,aeMbIX llOXOllOB H pacXOllOB, KOTOpbie B o6rn;eM CJIY'lae MOryT
6h1Th 11epeMeHHhIMH H rrpoHCXO)l;HTb e pa3Hb1e 11epHO)l;bI epeMeHH. Pac'leT c llOMOill;bIO <l>YHKUHH II3 llpHMeHHIOT llPH )l;eHe)J(J{bIX llOTOKax paBHOH eeJIH'IHHbIH paBHhIX HHTepea11ax Me)l{)ly 011epau;HHMH. <l>YHKUHH HII3 MOXeT HCllOJib30BaTbCH llPH pac'leTe)l;eHe)J(J{blX llOTOKOB 11epeMeHHOH BeJIH'IHHbl,llPOHCXO)l;Hill;HX qepe3paBHbie11p0Mexyn<H epeMeHH. <l>YHKUHH q11cTH3 1103BOJIHeT Bbl'IHCJIHTb'IHC'I)'IOTeKyllzyJO CTOHMOCTb 11epeMeHHbIX )l;eHe)J(J{bIX llOTOKOB, HBJUllOill;HXCH HeperyJIHpHbIMH.
<l>ymmHB 03. 3Ta <l>YHKUHH 11pe)l;HaJHa'leHallJIH pac'leTaTeicyll.{eH CTOHMOCTH e)l;HHOH C)'MMblBKJia)l;a (3aHMa) H 6y.z:cyIUHX <l>HKCHpoeaHHbIX IIJiaTexeH. 3TOT pac'leTHBJUleTCH o6paTHbIM pacqeTY 6y.z:cyIUeH
CTOHMOCTH llpH OOMOill;H <l>YHKUHH o3.
CHHTaKcHc II3(ttopMa;KIIep;eh1IIJiarn;6c;TH11).
3tta'lettHe,Kornpoe B03BpamaeT <l>YHKUHH II3, - 3TO apryMeHT pv HJ <t>opMyJihI (12.43).
PaccMOTpHM HcnoJib3oerume 3TOH <l>YHKUHH B KOHKpeTHbIX pacqerax.
1. ,[(011ycTHM H3BeCTHO 6y)l;ymee (Haparn;eHHOe) 3Ha'leHHeBKJia)l;a
(3aHMa). Tpe6yeTCH 011pe)l;eJIHTb Teicyll.{ee JHa'leHHe3Toro BKJIMa, T. e. C)'MMY,KOTOPYJO HeOOXOllHMO llOJIO)l(HTb Ha C'leTcero)l;HH, 'IT06blB KOHUe 11epHO)l;a OHa)l;OCTHrna 3a)l;aHHOfO 3Ha'leHHH.3To 3Ha'leHHeMO)l(-
HO 110.JIY'IHTbH3 <l>OPMYJibl (12.45): |
|
pv = fv |
(12.49) |
(1+ rf |
|
<l>opMyJia (12.49) COOTBeTCTByeT <t>opMyJie (12.23) KJiaCCH'leCKOH
MO)l;eJIH.
IlpH HCllOJibJoeattuu <l>YHKUHH TI3 ll1IH pac'leTae o6rn;eM BHlle Te-
Icyll.{ero JHa'leHHHBKJIMa MO)J(J{O 3a11ucaTh: =Il3(ttopMa;KIIep;;6c).
2. IlpellIIOJIO)l(HM Te11epb, 'ITOTpe6yeTCH HaHTH TeKyIIzyJO CTOHMOCTb 6y.z:cyIUHX 11epHO)l;H'leCKHXllOCTOHHHbIX IIJiarexeH, KOTOpbie llpOH380MTCH B tta'laJieHJIH Kottu;e Ka)l(lloro pac'leTHoro11epHo)l;a. Cornactto KOHI..J;ellUHH epeMeHHOH CTOHMOCTH, 'leMllaJibIIIe OTCTOHT OT HaCTOHmero MOMeHTa llOCTYIIJieHHe HJIH paCXOllOBaHHe cpe)l;CTB, TeM MeHh-
IIIYIO TeKymYJO uettHOCTb otto 11pe.D:CTaBJU1eT. TaKHM o6pa3oM, 11pH
llpO'IHXpaBHbIX YCJIOBHHX TeKymaH CTOHMOCTb BKJIMOB 11peH)'MepaHllO 60JibIIIe, 'leMTeicyll.{aH CTOHMOCTb BKJia)l;OB llOCTH)'MepaH)l;O.
2.1. Pac'leTTeKyrn;eH CTOHMOCTH cepHH 6y.z:cyIUHX llOCTOHHHbIX 11e-
pHO)l;H'leCKHX ( o6H3aTeJibHbIX) IIJiarexeH, llpOH3BOllHMbIX B Ha'laJie Ka)l(llOro 11epHO)l;a H llHCKOHTHPOBaHHbIX HOpMOH llOXO)l;a r, llpOH380llHTCH 110 <l>OPMYJie
1- 1
pv = pmt |
(l+rf (l+r). |
(12.50) |
r
166
<l>opM)'Jia(12.42), COOTBeTCTByIDW:ruI KJiaCCH11eCKOM MO,n;emi:, no3BOmleT paccq1uaTb COBpeMeHIIyID CTOHMOCTb IlOCTO.HHHOM peHTbl npeH)'MepaH,n;O.,nm. pacqern 3TOM BeJIHqHHbl npH IlOMOW:H <l>YHKIJ;HH n3 HCilOJib3yIDT apryMeHTbl: HOpMa, Knep, BblITJiaTa, a TaIOKe THil =1.
06:w;rur <t>opMyJia ,n;JI.H perneHH.H 3TOM Ja,n;aqH 6y.n;eT HMeTb BH.n; =03(HOpMa;KITep;BhIITJiaTa;;l).
2.2. ,nm. pacqern TeKYrn;e:H CTOHMOCTH IlOCTO.HHHbIX nepHO,ll;H11eCKHX nJiaTexe:H, npOH3BO,ll;HMblX B KOHIIe nepHo.n;a (o6bJqHbIX ITJiaTexe:H), cpopM)'JIY(12.50) CJie,n;yeT MO.llH<l>HIIHPOBaTh:
1- |
1 |
|
pv = pmt |
(1 + rr |
(12.51) |
|
r |
|
AHanorH11HruI <t>opM)'JiaKJiaccH11ecKo:H Mo,n;eJIH - |
(12.40). CoOT- |
|
BeTCTByrorn;rur .n;aHHOMY pacqeTY <t>opM)'JiaB Excel 6y.n;eT HMeTb BH.n;
=03 (HOpMa, Knep, BbIITJiaTa).
TaK KaK no YMOJil!aHHIO apl)'MeHTTHIT paBeH 0, em MO)l{HO He ~bmaTh.
3aiJa'la. <l>HpMe n01pe6yeTCR 5000 ThIC. p. qepe3 12 neT. Onpe,11;eJIHTh CYMMY e.llHHOro Te:icymero BKJia,na, KOTOPYJO He06XO.llHMO noJio:>KHTh Ha ,11;eno3HT, eCJIH npou:eHTHaR CTaBKa no HeMY COCTaBJlj{eT 12 % B ro,ll.
p e III e H He. ,LI.mi: pacqeTa HCnOJib3yeM <l>OPMYJIY ( 12.49) HJIH COOTBeTCTBYIOIIIYJO eii 3anHCb <l>YHKUHH Il3. TaK KaK HOpMa = 12 %, Knep = 12, 6c = 5000, 3anHIIIeM:
Il3( 12%;12;;5000) =-1283,38 TbIC. p.
Pe3yJibTaT pacqern nonyqHJicR OTpHU:aTeJibHblH, nocKOJibKY TIO CYMMa, KOTOPYJO Heo6XO,llHMO BJIO)!(HTb.
3aiJa'la. EcTb ,11;sa sapHaHTa nOKYUKH .llOMa: 3aDJiaTHTb cpa3y 99 000 TblC. p. HJIH B paccpoqKY - no 940 TbIC. p. e:lKeMecsi:qHo B TeqeHHe 15 neT. Onpe,n;e- JIHTb, KaKOH BapHaHT npe,n;noqTHTeJibHee, eCJIH npou:eHTHaR CTaBKa COCTaBJIReT 8 % ro,llOBbIX.
p e III e H H e. ,LI.mi: cpaBHeHHR npHBe,11;eM 3TH ,lleHe:lKHbie noTOKH K 0,llHOMY nepHO.llY BpeMeHH, T. e. paccqHTaeM TeKYIIIYJO CTOHMOCTb 6y.llYIUHX <l>HKCHpoBaHHblX nepHO.ll}fqeCKHX BblilJlaT. .[{onyCTHM, ~ BblilJlaTbl npoHCXO,llHT B KOHU:e KIDK.UOro pacqeTttoro nepHo,n;a. Ilo ycnoBHIO 3a,naqH nepHO.ll HaqHcneHHR npo- u:eHTOB paneH Mecsi:u:y. Ilo Ta6JI. 12.3 onpe,n;eJIHM o6mee q}ICJIO nepHO.llOB BblilJlaT Knep = 15 ·12 H npou:eHTH}'IOCTaBKY 3a nepHO,ll HaqHCJieHHR HOpMa= 8 %/12. PacqeT MO:lKHO BbIDOJIHHTb no <l>OPMYJie (12.51) HJIH c Hcnonb3oBaHHeM <l>YHKUHH Il3:
Il3(8%/12;15* 12;-940) = 98 362,16 TblC. p.
3anpaIIIHBaeMaR u:eHa (99 000 TblC. p.) 60JibIIIe paccqHTaHHOH Te:icymeH CTOHMOCTH nepH0,1J;ffqeCKHX BblDJiaT, CJie,llOBaTeJibHO, HeBbirO.llHO noKYUaTb ,llOM cpa3y, nyqIIIe paCTRffYTb DJiaTe)!(H Ha 15 JieT.
~ Hil3. 3Ta <l>YHKIJ;H.H npe.n;HaJHaqeHa .llJl.H BbJqHCJieHH.H qffCTOM TeKYrn;e:H CTOHMOCTH (NPV) nepHO,ll;Jf'leCKHXITJiaTexe:H nepe-
MeHHOM BeJIH11HHbl KaK CYMMbl O)l{H,ll;aeMbIX ,n;oxo,n;oB H pacxo,n;oB:
167
NPV =f, value;;• |
(12.52) |
i=I (1 + r) |
|
r.ue r - HOpMa .UHCKOHTHpOBaHIDI (cpe,UIDUI ueHa KaIIHTaJia); n - q11c110 BblIIJiaT H IIOCTYIIJieHHH; value; - 3HaqeHIDI BbIIIJiaT H IlOC'fYIIJieHHH.
<l>opM}'Jia(12.52) COOTBeTCTByeT <t>opM}'Jie (12.38) KJiaCCJ.lqeCKOH MO,UeJIH.
MeTO.U onpe.ueJieHIDI qffCTOH TeKYUieH CTOHMOCTH qacTO rrpHMeIDIeTCH npH oueHKe 3<l><l>eKTHBHOCTH HHBeCTHUHH. OH noJBOJIHeT onpe-
.uenHTh HIDICHIOIO rpaHHuy npH6bIJibHOCTH H HCITOJib30BaTb ee B KaqeCTBe Kp:UTepIDI npH BbI6ope HaH60Jiee 3<l><l>eKTHBHOfO npoeKTa. ,llHCKOHTHpOBaHHe O)l(lf,UaeMhIX .UOXO.UOB H paCXO.UOB Il03BOJIHeT yqeCTb HJ,aep)IQ(lf npHBJieqeHIDI KaITHTa.n:a. I1011o:xrnreJihHOe JHaqeH:ue NPV
HBJIHeTCH IlOKaJareJieM roro, ~ npoeKT npHHOCHT qffCTYJO npH6bIJib CBOHM HHBecropaM IIOCJie IlOKpbITIDI Bcex CBHJaHHbIX c HHM paCXO.UOB.
CHHTaKCHC HI13(HopMa;cYMMal;cYMMa2; ... ;cYMMaN). CqHTaeTCH, qTo HHBeCTHUIDI, qffCTaH TeKYUiaH CTOHMOCTb KOTO-
poli BhNHCJIHeTcH c noMOIUhIO <l>YHKUHH HI13, Haq11HaeTcH Ja O.UHH rrep110.u .uo .uaTbI apfYMeHTa CYMMal H JaKaffqHBaeTCH c nocne.uHHM JHaqeHHeM B cnHcKe. Ecn:u nepBhIH .ueHe:>KHhIH BJHoc npHXO.UHTCH Ha Haqa.n:o nepBoro nep110.ua BhIIIJiaT, TO nepBoe JHaqeH:ue cne.uyeT .uo6aBHTh (HJIH BbNeCTb, eCJIH 3TO JaTpaTbl) K pe3yJihTaTY <l>YHKUHH HI13, HO He BKJIIOqaTb ero B CITHCOK apfYMeHTOB.
3aoa'la. Httaecnn.1.HH B npoeKT K KOHIJ.Y nepaoro ro.n.a ero peanHJaIJ.HH cocrnm1T 10 000 p. B nocne,1.1;y101I.1,He TpH ro.n.a m1rn.n.a10TcH ro.n.oable .n.oxo.n.b1 no npoeKTY 3000, 4200 H 6800 p. J13.n.ep:>KKH npHBJietieHHH KanHTana 10 %. Pac- C'IHTaTb'IHCTYIOTeKYllJ.YIO CTOHMOCTb npoeKTa.
p e ill e H He. TaK KaK HHBeCTHUHH 10 000 p. OTHOCHTCH He K Ha'laJibHOMY MOMeffTY, Ha KOTOpbIJ:\: npOH3BO,ll.HTCH pactieT, TO 3TO 3Ha'leHHeCJie.n.yeT BKJIIOqffTb B cnHCOK apryMeHTOB. IlOCKOJibKY 3TOT .n.ette:lKHbIH noTOK OTHOCHTCH
K JaTpaTilM, TO CYMMa 10 000 JanHCblBaeTCH co 3HaKoM MHffYC. OcTanbHble
.n.eHe:lKHble nOTOKH npe,ll.CTilBJIHIOT co6oH ,ll.OXO,ll.bl, n03TOMY OHH ~bmaIOTCH co 3HaKOM IIJIIOC. qHCTYIO TeKYllJ.YIO CTOHMOCTb npoeKTil MO:lKHO 3aIIHCaTb B CJie- ,l.l;ylOII.l,eM BH.D.e:
Hil3( 10%;- l 0 000;3000;4200;6800) =1188,44 p.
IlonyqeHttoe 3HatieHHe npe.n.cTaBJIHeT co6oH: a6coJIIOTffYIO npH6blJib OT BJIO:lKeHHH 10 000 p. qepe3 ro.n. c yqeTOM H3,ll.ep:iKeK npHBJie'leHHHKanHTana.
3aoa'la. 3aTpaTbI no npoeKry B HatianbHbIH MOMeHT ero peanH3aUHH coCTaBJIHIOT 37000 p., a O:lKH,ll.aeMble .IJ;OXO,ll.bl 3a nepBble nHTb JieT: 8000, 9200, 10 000, 13 900 H 14 500 p. Ha illeCTOH ro.n. O)l(H,ll.aeTCH y6blTOK B 5000 p. Qetta KanHTana 8 % ro,ll.OBbIX. PaCC'IHTilTb'IHCTYIOTeKYllJ.YIO CTOHMOCTb npoeKTa.
P e ill e H H e. B 3TOM cnyqae HeT tteo6xo.n.HMOCTH .D.HCKOHTHpoaaTb HatianbHble 3aTpaTbl no npoeKry, TaK KaK OHH OTHOCHTCH K HaCTOHII.l,eMY MOMeHTY H HX TeKYllJ.aH CTOHMOCTb paBHa 37 000 p . .llmI cpaBHeHHH 3aTpaT c 6y.n.ymHMH
168
JlOXO,llaMH H y6hITKaMH UOCJie,llHHe He06XO.llHMO npHBeCTH K HaCTmnueMY MOMeHry. IlycTb .llOXO.llhl BBe.lleHhl cooTBeTcTBeHHO B H'Ieil:KHBl: B5. Tor.Ila 'IHCTYJOTeKYIUYJO CTOHMOCTb npoeKTa MO:)f(HO 3aUHCaTb B CJie.llYIOIUeM BH,lle:
HII3(8 %;Bl:B5;-5000)-37 000 = 3167,77 p.
<l>ymauur 'IHCm3.3Ta cp)'HKIJ;IDIII03BOJUleT paccqu:TbIBaTb qu:c- T)'IOTeicyllzyIO CTOHMOCTb Heperym1pHbIX rrepeMeHHbIX BbIIUiaT H IIOC1)'1IJieHU:H:
XNPV = ~ |
value; |
(12.53) |
"'-' |
do-d· ' |
|
i=l (1 |
+ r) 365 I |
|
r.n;e r - rrpoueHTHasI CTaBKa (HOpMa .n;HCKOHTHpOBaHIDI); d; - |
.u;aTa i-H |
|
orrepauu:u:; do - .u;aTa ffYJieBoii orrepauu:u: (HaqaJibHasI .u;arn); |
value; - |
|
CYMMa i-H: orrepauu:u:.
Cu:maKcu:c 1fHCTH3(cTaBKa,{cYMMa0;cYMMal; ...;cYMMaN},{.u;arn0; JJ.arnl;... ;.u,arnN}).
LJ:aTbl orrepauu:H: )J,OJDKHbl COOTBeTCTBOBaTb C}'MMaMBbIIUiaT H IIOC1)'1IJieHHH.PacqeT rrpou:3BO.U.HTC.R Ha .u.aTY OCYIUeCTBJieHIDI rrepBoii orrepauu:u:, T. e. Ha TeKYmYJO .u;a'fY.TaKHM o6pa30M rrepBasI C}'MMa(CYMMaO) He .u,u:cKOHTu:pyeTCH. Ecnu: Tpe6yeTcH c.u,enaTh pacqeT Ha .u.aTY, rrpe.u,IIIecTByiomyio .u,aTe rrepBoil orrepauu:u:, cne.u,yeT 3a,u;aTh apryMeHT CYMMaO, paBHhlM ffYJIIO. Ecnu: rrpe.u;rronaraeTcH HeCKOJibKO orrepauu:it (mKH,LJ,aeMbIX IIOC1)'1IJieHHHH BbIIUiaT), MO)l{}{O YKa3aTb CCblJIKH Ha ,RqeHKH, co.u,epxamu:e .u,aTbl u: CYMMhl orrepauu:H: B o6~HOM cpopMaTe.
3ailarul. MHBeCTHUIDI pa3MepoM 10 MJIH p. OT 1HIOJUI1998 r., npHHeceT .llOXO-
.llhl: 2750 ThIC. p. 15 ceHn16pH 1998 r., 4250 TbIC. p. 1HOH6pH1998 r., 5250 ThIC. p. 1 HHBapH 1999 r. HopMa .llHCKOHTHpOBaHHH 9 %. Onpe.rr;eJIHTb 'IHCTYJOTeicy- lll)'IO CTOHMOCTb HHBeCTHUHH Ha 1 HIOJIH 1998 r. H Ha 1 HIOJIH 1999 r.
IloMeCTHM B H'Ieil:KHBl: El ,llaThl BhIUJiaT H nocryUJieHHif, a B H'Ieil:KH B2: E2 - CyMMhl onepauHil:. Ha'laJibHhlifUJiaTe)I{ .rr;oJl)l(eH 6h1Th BKJIIO'leHB 'IHCJIOapryMeHTOB co 3HaKOM MffHYC (H'Ieil:KaB2 = -10000). B H'Ieil:icyAl noMeCTHM .nary 1.07.1997, a B H'IeificyA2 - ttyJieaoe 3Ha'leHHe.qHCTYJO TeKYIUYJO CTOHMOCTb HHBeCTHUHH Ha 1 HIOJIH 1998 r. H Ha 1 HIOJIH 1999 r. 3aUHllleM B CJie.llYIOIUeM BH,lle:
qMCTH3(9%,B2: E2,Bl: El)= 1856,25 Thie. p.; qMCTH3(9 %,A2: E2,Al: El)= 1702,99 Thie. p.
IlpH ttyJieBhIX Ha'laJibHblX3aTPaTax (H'Ieil:KaB2 = 0) TeKYIUaH CTOHMOCTb 6y.llYIUHX.llOXO.llOB Ha 1.07.1998 r. COCTaBHT 11856,25 ThIC. p.
Onpe,zi;eneHHe cpou WiaTelKa a npoQeHTHoii CTa.BKH
<l>}'HKIJ;HH3TOH rpyrrrrhl II03BOJUllOT HaxO,!l;HTb BeJiu:qu:Hbl, pacqeT KOTOpbIX BeChMa 3aTpy.u,HeH, eCJIH BbIIIOJIHHeTCH BpyqHyio:
• o6mee qu:cJIO rrepU:O.U,OB IIOCTO.RHHbIX BblIUiaT, He06XO)J,HMbIX )J,JUI
.U,OCTHXeHIDI 3a,!l;aHHOrO 6yJJ.YIUero 3HaqeHIDI, H qu:cJIO rrepu:o.U,OB, qe-
169