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Конспект лекций по курсу Менеджмент инвестиций

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Если инвестиции реально увеличивают балансы фирмы, то в целом все это
приведит к снижению ценности, т.к. оценка капитала падает за снижением
стоимости капитала, поэтому любые инвестиции, в т.ч. инвестиции в
реальные активы. В первую очередь необходимо рассматривать, как они
влияют на ценность фирм.

N oi/ee c?aiey yeiiiie/aneie oai?ee, oeaiiinoue oe?iu ?aaia noieiiioe
anao aa aoaeoueo iinooieaiee, iiyoiio oieueei oiaaea, eiaaea ana
?ann/aou i i?eaieeiinoe eiaanoeoeee i?iaiaeyony ia iiiaa eioi?iaoeee i
aeaiaaeiuo iinooieaiee, oi eiaanoi?u e aeaaeaeueoeu iieo/atho
i?aaenoaaeaiea i oii i?eaaaeao ee ?aaeecaoeey eiie?aoiiai i?iaeoa e
oaaee/aieth oeaiiinoe oe?iu. Oaeei ia?acii aeaiaaeiua iinooieaiey –
iniiaiiieiaathuea i?e anao ?ann/aoao i?eaieeiinoe eiaanoeoeee. Anee
aiai?eoue i iieacaoaea aeaiaaeiuo iinooieaiee, oi iie ?aaiu au?o/ea io
?aaeecaoeee – (niaieoiiua cao?aou+aii?oecaoeey)-auieaou i?ioeaioa –
oiea/aiiua iaeiae. A iieacaoaea aeaiaaeiua iinooieaiey naycaiu
eaoaai?ee: aeaiaaeiua i?eoiee (naycaiu n i?iaeaaeae oiaa?ia oe?iie,
iieo/aieai ieaoaaeae, iieo/aiea aeioiaea io eiaanoe?iaiiey) e aeaiaaeiua
iooiee (oe?ia i?eia?aoaao nu?uea e iaoa?eaeu, ?aaioieeai auiea/eaaaony
ca?. ieaoa, iiaeaea?aeeaaaony eaieoae a ?aai/ai ninoiyiee e o.ae.). A
iauaeou i?aaei?eieiaoaeueneie aeayoaeueiinoe eiaanoe?iaaiea i?ioiaeeo a
?aciuo oi?iao. Eeanneoeeaoeey eiaanoeoeee:

· io iauaeoa aeiaeaiee:

?aaeueiua e oeiainiaua

· ii oa?aeoa?o o/anoey:

i?yiua (eiaanoi? iaiin?aaenoaaiii o/anoaoao a auai?a iauaeoa
eiaanoe?iaaiey) e ia i?yiua (eiaanoeoeee /a?ac iin?aaeieea – oeaiiua
aoiaae e o.ae.)

· ii ia?eiaeo eiaanoe?iaaiey:

e?aoein?i/iua (neiaeaiea eaieoaea iaiaa aiaea – aeaiiceoiua aeeaaeu,
iieoiea na?oeoeeaoia e o.ae.) e aeieain?i/iua (aieaa aiaea)

· ii oi?iai nianoaaiiinoe:

/anoiua (aeiaeaiea n?aaenoa a?aaeaeaiaie e th?. eeoeaie ia
ainoaea?noaaiiie oi?iu nianoaaiiinoe), ainoaea?noaaiiua (ca n/ao
athaeaeaoa e aiaathaeaeaoiuo oiiaeia, ain. i?aaei?eyoeyie ca n/ao
nianoaaiiuo n?aaenoa), eiino?aiiua e niaianoiua (eiino?aiiua oe?iu e
i?aaei?eyoey aeaiiie no?aiu aianoa)

· ii ?aaeiiaeueiiio i?eciaeo:

aioo?e no?aiu e ca ?oaaaeii

oi?aaeaiea eiaanoeoeeiiiie aeayoaeueiinoueth ia iae?io?iaia naycaii
ia?ac?uaii n ioeaieie ninoiyiey e i?iaiice?iaaiey ?acaeoey
eiaanoeoeeiiiiai ?uiea, iiae eioi?ui iiieiaaony niaieoiiinoue
ioaeaeueiuo ?uieia: ?uiie i?yiuo eiaanoeoeee (i?ienoiaeeo iniiaiia
eiaanoe?iaaiea),

?uiie i?eaaoece?iaaiiuo iauaeoia (iauaeou – i?aaei?eyoey, i?iaeathueany
oeaeeeii), iaaeaeaeeiinoe (iaeaieueoea oaiiu ?acaeoey e iaeaieueoea
ia?niaeoeau), i?i/eo iauaeoia (niaieoiiue ?uiie aeey eiaanoe?iaaiey a
i?aaeiaou aioeeaa?eaoa, ae?aa. iaoaeeu e ae?oaea oeaiiinoe), oiiaeiaue
?uiie, aeaiaaeiue (naycai n iauaeoaie eae aeaiiceoiua aeeaaeu). Oaeay
eeanneoeeaoeey eiaanoeoeeiiiiai ?uiea iicaieyao iaeaieaa aeoaiei
i?iaiaeeoue aiaeec ?uiea, i?iaiice?iaaiea, ii?aaeaeyoue i?ei?eoaou
eiaanoe?iaaiey ia ii?aaeaeaiiii yoaia yeiiiie/aneiai ?acaeoey no?aiu.
?acaeoea ?uiea caaeneo io eaoaai?ee ni?in, i?aaeeiaeaiea, oeaia e
eiieo?aioeey. Aeoeaiinoue ?uiea ii?aaeaeyaony iooai eco/aiey ?uii/iie
eiiuthieoo?u. Aeey eiiuthieoo?u ?uiea a oeaeii e ioaeaeueiuo aai
neaiaioia oa?aeoa?iu neaaeothuea noaaeee:

· iiaeuai eiiuthieoo?u. naycai n iaeeaeaieai yeiiiieee a oeaeii, /oi
i?iyaeyaony a oaaee/aiee ni?ina ia iauaeou eiaanoe?iaaiey, ?anooo oeaiu
e eiieo?aioeey.

· eiiuthieoo?iue aoi. oa?aeoa?ecoaony ?aceei ?inoii ni?ina ia ana
eiaanoeoeeiiiua oiaa?u, eioi?ua ianiio?y ia ?ino i?aaeeiaeaiee
iieiinoueth oaeiaeaoai?eoue iaeuecy, o.a. ?anooo oeaiu ia ana iauaeou e
?anooo aeioiaeu.

· ineaaeaiea eiiuthieoo?u. naycaii ni nieaeaieai eiaanoeoeeiiiie
aeoeaiinoe ec-ca niaaea yeiiiieee aoeaeii, ioiineoaeueii iieiui
ianuuaieai ni?ina ia iauaeou eiaanoe?iaaiey e ecauoeii aai i?aaeeiaeaiey

· eiiuthieoo?iue niaae. iaeaieaa iaaeaaii?eyoiue ia?eiae n iiceoeee
aeoeaiinoe. naiue ieceee ni?in ia iauaeou eiaanoe?iaaiey e
aeayoaeuiinoue noaiiaeony oauoi/iie.

?acaeoea eaeao ii oeeeeo e ?uiie iinoiyiii iaiyaony, iiyoiio iaiaoiaeeii
eco/aoue eiiuthieoo?o, /oiau oi?ie?iaaoue ia i?aaei?eyoee yooaeoeaioth
eiaanoeoeeiiioth no?aoaaeth e i?eieiaoue iainiiaaiiua ?aoaiey. Eco/aiea
eiiuthieoo?u ioaaouaaao 3 yoaia:

· oaeouaa iaaethaeaiea ca eiaanoeoeeiiiie aeayoaeueiinoueth. oi?ie?oaony
nenoaia iieacaoaeae – ni?in, i?aaeeiaeaiea, oeaia e eiieo?aioeey,
i?aaiecoaony eo iiieoi?eia.

· aiaeec oaeouae eiiuthieoo?u ia eiaanoeoeeiiiii ?uiea e auyaeaiea
nia?aiaiiuo oaiaeaioeee aai ?acaeoey. auyaeaiea eciaiaiee a ia?eiae
iaaethaeaiey e n?aaiaiea n i?aaeuaeouei

· i?iaiice?iaaiea eiiuthieoo?u aeey auai?a iniiaiuo iai?aaeaiee
eiaanoeoeeiiiie no?aoaaee. iniiaiay caaea/a – i?iaiice?iaaiea oaeoi?ia,
oi?ie?othueo eeeia. I?ioeann i?iaiice?iaaiey iiaeii i?aaenoaaeoue a
aeaea 4 iineaaeiaaoaeueiuo noaaeee:

1. ioeaiea iae?iyeiiiie/aneeo iieacaoaeae. ii?aaeaeyaony
iae?iyeiiiie/aneee eeeiao a no?aia

2.ioeaieaaaony i?eaeaeaoaeueiinoue io?aneae yeiiiieee. iaiaoiaeeii aeey
?nouanoaeaiey io?aneaaoth aeeaa?neoeeaoeeth eiaanoeoeeiiiie
aeayoaeueiinoe

3. ioeaieaaaony e i?iaiice?oaony eiaanoeoeeiiiay i?eaeaeaoaeueiinoue
?aaeiia. iaiaoiaeeii aeey ?aaeiiaeueiie aeeaa?neoeeaoeee eiaanoeoeeiiiie
aeayoaeueiinoe, iniaaiii a noa?a ?aaeueiiai eiaanoe?iaaiey

4. ioeaiea eiaanoeoeeiiiie i?eaeaeaoaeueiinoe ioaeaeueiie eiiiaiee. aeey
i?eiyoey oaeoe/aneeo eiaanoeoeeiiiuo ?aoaiee.

oaeay iineaaeiaaoaeueiinoue i?iaiice?iaaiey iicaieyao iieo/eo
iaaeaaeioth eioi?iaoeeth aeey iac?aaieee no?aoaaee. iaeaieaa neiaeiue –
1 yoai. o?aaoao i?eaea/aiey iaoe?iie eioi?iaoeee. iaiaoiaeeii
inouanoaeyoue iiieoi?eia, ioaaouaathuee iniiaiua iieacaoaee e iieacaoaee
neaiaioia.

2 yoai enneaaeoaony aeeiaieea eiiuthieoo?u e ?anniao?eaaaony naycue yoie
aeeiaieee n oacaie yeiiiie/aneiai ?acaeoey no?aiu aoeaeii, o.e. iniiaiua
eciaiaiey i?ienoiaeyo i?e niaia oac aeaeiaie aeoeaiinoe.

3 yoai – i?iaiic ?acaeoey ?uiea ia aaca oaeoi?ia, aeeythueo aa aai
?acaeoea. aaca – ainoaea?noaaiiay yeiiiie/aneay iieeoeea a ?ac?aca
niaa?oainoaiaaiey a iaeanoe iaeiaia, e?aaeeoa e o.ae.

i?e auyaeaiee io?aneae, aucuaathuea iaeaieueoee eiaanoeoeeiiiue eioa?an,
oi oaeia i?iaiice?iaaiea inouanoaeyaony ia aaca ?aeoeiaa io?aneae.
i?eaeaeaoaeoiinoue ?aaeiiia ii?aaeaeyaony aiaeiae/ii io?aneyi, ii
iieacaoaee ioeaiee e oaeoi?u, aeeythuea ia i?iaiic – ae?oaea.

4 yoai – i?aaeiieaaaao auyaeaiea aeeciaiiai oeeeea eiiiaiee,
?anniao?eaaaiue eae niaia noaaeee: ?ino, ia noaaeeueiinoue, auaeeaaiea,
inouanoaeyaony iooai i?eiaiaiey aeeiaie/aneiai aiaeeca. ioeaiea
i?eaeaeaoaeueiinoe i?aaeiieaaaao i?iaaaeaiea iaoe?iiai oeiainiaiai
aiaeeca aeayoaeueiinoe. oaeie aiaeec, aeiiieiaiiue i?iaiicii, iicaieyao
ioeaieoue aeioiaeiinoue, n?iee aica?aoa eiaanoeoeee, aua?aoue iaeaieaa
cia/eiua ?enee. a i?ioeanna aiaeeca ?anniao?eaathony ?acee/iua aniaeou
aeayoaeueiinoe, ii n oi/ee c?aiey iauaeoa eiaanoe?iaaiey yae/aony aiaeec
eeeaeaeiinoe, oeiainiaie onoie/eainoe, i?eaueueiiioe eaieoaea.

————-

oi?aaeaiea eiaanoeoeeiiiie aeayoaeueiinoueth ia iee?io?iaia.

iniiaiie oeaeueth yaeyaony ?i?aaeaeaiea iaeaieaa yooaeoeaiuo iooae
?aaeecaoeee eiaanoeoeeiiauc no?aoaaee oe?iu ia ioaeaeueiuo yoaiao aa
?acaeoey. i?ioeann ?aaeecaoeee yoie oaee iai?aaeai ia ?aoaiea
niaaeothueo ciaea/:

· iaania/aiea aun?eeo oaiiia ?acaeoey oe?iu ca n/ao youaeoeaiie
eiaanoeoeeiiiie aeayoaeueiinoe

· iaania/aiea iaeneiecaoeee aeioiaeia io eiaanoeoeeiiiie aeayoaeueiinoe.
i?eaueue – iniiaiie iieacaoaeue. aeey ioeaiee iaiaoiaeeia /enoay
i?eaueue, iiyoiio iaiaoiaeeii auae?aoue iai?aaeaiey, eiathuea
iaeneiaeueioth noiio nenoie i?eauee

· iaania/aiea iaeneiecaoeee eiaanoeoeeiiiuo ?eneii. i?e i?eyee ?aoaiey,
naycaiiiai n ?eneii,neaaeoao ?enee oiaiueoaoue

· iaania/aiea oeiainiaie onoie/eainoe e ieaoaaeaniiniaiinoe a i?ioeanna
eiaanoeoeeiiiie aeayoaeueiinoe, o.e. eiaanoeoeee naycaiu n aieueoei
ioaee/aieai n?aaenoa. yoi iiaeao i?eaanoe e nieaeaieth
ieaoaaeaniiniaiinoe ?i ieaoaaeiui iayuaoaeonoaai. oi?ie?oy enoi/ieee
eiaanoeoee?iiuc ?ano?nia iaaei ca?aiaa i?iaiice?iaaoue eae auai? ieaaeao
aeeyiea ia oaeouoth ieaoaaeaniiniaiinoue oe?iu.

· ecuneaiea iooae onei?aiey ?aaeecaoeee eiaanoeoeeiiiuo i?ia?aii.
iaiaoiaeeii iaeaieaa auno?i i?iaiaeeoue, o.e. yoi iiinianoaoaue
yeiiiie/aneiio ?acaeoeth, o.e. iiyaeyaony aeiiieieoaeueiue iioie a aoaea
i?eauee io eiaanoeoeee, nie?auathony n?iee e?aaeeoiuo ?ano?nia, auno?ay
?aaeecaoeey i?ia?aii niinianoaoao nieaeaieth ?ene?a, naycaiiuo n
iaaeaaii?eyoiie eiiuthieoo?u.

ana caaea/e oanii acaeiinaycaiu. iaania/aiea aunieeo oaiiia ?acaeoey
iiaeao aaoue aeinoeaiooi ua n/ao iiaeai?a yoaaeoeaiuo i?iaeoia e ca n/ao
onei?aiey ?aaeecaoeee eiaanoeoeeiiiuo i?ia?aii. n o/aoii anao caaea/
eiaanoeoeeiiiiai iaiaaeaeiaioa, ii?aaeaeythony ooieoeee eiaanoeoeeiiiiai
iaiaaeaeiaioa:

· enneaaeiaaiea aiaoiae eiaanoeoeeiiiie n?aaeu e i?iaiice?iaaiea
eiiuthieoo?u – enneaaeothony i?aaiaua oneiaey e aiaeece?oaony oaeouay
eiiuthieoo?a ?aiea. nineaaeyaony i?iaiic ?uiea a ?ac?aca ioaeaeueiuo
neaiaioia.

· ?ac?aaioea no?aoaae/aneec iai?aaeaiee eiaanoeoeeiiiie aeayoaeue.
ii?aaeaeythony oaee e caaea/e

· ?ac?aaioea no?aoaaee oi?ie?iaaiey ?ano?nia ue?iuth iauay iio?aaiinoue
a ?ano?nao, ii?aaeaeyaony iio?aaiinoue a ?ano?nac, aiciiaeiinoue
eniieueciaaiey caaiiuo n?aaenoa, niioiioaiea eniieueciaaiey nianoaaiiuo
e caaiiuo n?aaenoa, i?aaeioa?auaiea nieaeaiey ieaoaaeaniiniaiinoe e
oeiainiaie onoie/eainoe a aoaeouai ia?eiaea.

· iiene e ioeaiea i?eaeaeaoaeueiinoe ioaeaeueiuo i?iaeoia e ioai?
iaeaieaa yooaeoeaiuo ec ieo. eco/aaony iieiaeaiea ia eiaanoeoeeiiiii
?uiea, ioae?athony i?iaeou, niioaaonoaothuea no?aoaaee, i?iaieeony
aeenia?oecaei?iaeoia, ?ann/eouaaaony o?iaaiue aeioiaeiinoey e ae?eaea
iieacaoaee yeiiiie/aneie youaeoeaiinoe. ii yoe iiieacaoaeyi i?iaiaeyo
?aiaee?iaaiea i?iaeoia

· ioeaiea eiaanoeoeeiiiuo ea/anoa ioaeaeueiuo ueiainiauo eino?oiaioia e
auai? iieaieaa youaeoeaiao. ?anniao?eaathony i?aaeeiaeaiea eino?eiaioia.
iniiaa eino?oiaioia – aeoeee

· oi?ie?iaaiea oiiaeiaiai ii?ouaey e ioeaiea ii e?eoi?eyi aeioiaeiinoe
?enea e eeeaeaeiinoe. i?e ?aaeecaoeee yoie\ooieoeee n o/aoii aiciiaeiiai
e i?eaea/aieth iauaia eiaanoeoeeiiiuo ?ano?nia ii eaaeaeiio i?iaeoo
i?iecaiaeeony eo ioai? aeey iaiin?aaenoaaiiie ?aaeecaoeee. i?e
oi?ie?iaaiee ii?ooaey iioeiece?othon/ i?iii?oeee iaaeaeo ?aaeueiuie e
ueiainiauie eiaanoeoeeyie aoeaeii. ia aoi?ii yoaia a ?ac?aca eaaeaeie ec
ui?i ii niioiioaieth aeioiaeiinoe e ?enea iiaeae?athony iaeaieaa
aeooaeoeaiua i?iaeou. ia 3 yoaia ii?aaeaeyaony eeeaeaeiinoue ii?ooaey.
yoio ii?ooaeue aioia e ?aaeecaoeee.

· oaeouaa ieaie?iaaiea e iia?aoeaiia oi?aaeaiea ioaeaeueiuo i?ia?aii e
i?iaeoia. aeey iaania/aiea oi?aaeaiey ?ac?aaaouaathony oaeouea ieaiu.
aaaeioth ?ieue ea?atho eaeaiaea?iua ieaiu ?aaeecaoeeioeaeueiuo i?iaeoia
e athaeaeaou yoeo i?iaeoia

· ?aaeecaoeey iiieoi?eiaa. ii?aaeaeyaony nenoaia
iieacaoaeae,ia?eiaee/iiioue nai?a, i?e/eiu ioeeiiaiey iieacaoaeae e
o.ae.

· iiaeaioiaea ?aoaiee i naiaa?aiaiiii auoiaea ec iayooaeoeaiuo
eiaanoeoeeiiiuo i?iaeoia e ?aeiaanoe?iaaiea eaieoaea. yooaeoeaiinoue
iiaeao auoue ieceie e neaaeoao auoiaeeoue ec i?iaeoa. oi?iu auoiaea:
?aaeecaoeey, neeyiea,aeoeeiie?iaaiea e o.ae. i?iaiaeeony ei??aeoe?iaea
ii?ooaey iooai iiaeai?a ae?eaeo i?iaeoia, eoaea ?aeiaanoe?oaony
inaiaiaeaeaaiue eaieoae

· ?ac?aaioea eiaanoeoeeiiiie no?aoaaee. oi?ie?iaaiea oeaeae e auai?
yooaeoeaiuo iooae aeinoeaeaiey

————

oi?ie?iaaiea eiaanoeoeeiiiie no?aoaaee

neiaeiue oai?/aneee i?ioeann, iniiaaiiue ia i?iaiice?iaaiee eiiuthieoo?u
?aiea. i?e oi?ie?iaaiee no?aoaaee eaeao iiene e ioeaiea aeueoa?iaoeaiuo
aa?eaioia eiaanoeoeeiiiuo ?aoaiee. neiaeiinoue ui?ie?iaaiey
eiaanoeoeeiiiuo noiaoaaee a oii, /oi iia iinoiyiii ei??aeoe?oaony n
o/aoii iaiythueony oneiaee. i?aaeiinueeie yaeyaony aaciaay no?aoaaey
yeiiiie/aneiai ?acaeoey. no?aoaaey iiae/eiaia no?aoaaee e aeieaeia n iae
niaeaniauaaoueny ii oaee e ii ?acaeoeth. no?aoaaey – aeaaiue oaeoi?
?acaeoey eiiiaiee a niioaaoneaee n eca?aiiie oe?iie aaciaie noiaoaaee.
i?ioann oi?ie?iaaiey no?aoaaee ninoieo ec yoaiia:

1. ii?aaeaeaiea ia?eiaea oi?ie?iaaiey no?aoaaee (caaeneo io
i?aaeneacoaiinoe ?acaeoey yeiiiieee aoeaeii, iaiaoiaeeii o/eouaaoue
i?iaeieaeeoaeueiinoue ia?eiaea aaciaie no?aoaaee, io?aneaaoth
i?eiaaeeaaeiinoue e ?acia? oe?iu)- 2. oi?ie?iaaiea no?aoaae/aneeo oeaeae
eiaanoeoeeiiiie aeayoaeueiinoe (enoiaeeo ec oeaeae aaciaie no?aoaaee.
iiaoo auoue noi?ie?iaaiu a aeaea iaania/aiey i?e?inoa eaieoaea, a aeaea
?inoa i?eaueueiinoe eiaanoeoeee,a aeaea eciaiaiey i?iii?oeee a oi?iao
?aaeueiiai e oeiainiauo eiaanoeoeee e o.ae.) – 3. ?ac?aaioea iaeaieaa
yooaeoeaiuo iooae

?aaeecaoeee no?aoaae/aneeo oeaeae eiaanoeoeeiiiie aeayoaiueiinoe – 3.1
?ac?aaioea no?aoaae/a?eeo iai?aaeaiee eiaanoeoeeiiiie aeayoaeueiinoe
(aace?oaony ia nenoaia oeaeae yoie aeayoaeueiinoe. ?aoathony caaea/e:
ii?aaeaeyaony niioiioaiea ?aceeniuo oi?i eiaanoe?iaaiey ia ioaeaeueiuo
yoaiao eiaanoe?iaaiey, ii?aaeaeyaony io?aneaaay e ?aaeiiaeueiay
iai?aaeaiiinoue eiaanoeoeiiiie aeayoaeueiinoe. yoi aaaeiue yeaiaio
oeiainiaie no?aoaaee. iaania/eaaao aania?aaieioth aeayoaeueiinoue,
youaeoeaiia eniieueciaaiea nianoaaiiuo n?aaenoa e oaaee/aiea oeiainiaie
onoie/eainoe ue?iu a aeieain?i/iii ia?eiaea) – 3.2 ?ac?aaioea no?aoaaee
7777777777 (inouanoae/aony ii yoaiai: i?iaiice?iaiiea iio?aaiinoe a
iauaia ?ano?nia, eco/aiea aiciiaeiinoe oi?ie?iaaiey enoinieee ec ?aciuo
?ano?nia, ii?aaeaeyaony iaoiaeu oeiaine?iaaiey ioaeaeueiuc i?a?aii e
i?iaeoia, iioeiecaoeey no?oeoo?u enoi/ieea ui?ie?iaaiey ?ano?nia) – 4.
eiie?aoecaoeey eiaanoeoeeiiiie no?aoaaee ii ia?eiaeai aa ?aaeecaoeee
(ii?aaeaeyao iiieaaeiaaoaeueiiioue e n?iee aeinoeaeaiey ioaeaeueiuo
oeaeae, e iaaiia/eaaaony aiaoiyy e aioo?aiiyy neio?iiecaoeey
eiaanoeoeiiiie no?aoaaee n aaciaie no?aoaaeae oe?iu. aioo?aiiyy
caeeth/aaony n neio?iiecaoeeae ioaeaeueiuo iai?aaeaiee eiaanoeoeee
iaaeaeo niaie)- 5. ioeaiea ?ac?aaioaiiie eiaanoeoeeiiiie no?aoaaee
(ii?aaeaeyaony ia aaca neaaeethueo e?eoa?eaa: niaeaniaaiiinoue no?aoaaee
eiaanoe?iaaiey n aaciaie, aioo?aiiyy naaeaine?iaaiiiioue oeaeae e
iai?aaeaiee eayoaeueiinoe, niaeaniaaiiinoue no?aoaaee n aiaoiae n?aaeie,
?aaeecoaiinoue no?aoaaee n o/aoii eiathuaainy iioaioeeaea oe?iu,
i?eaieeiinoue o?iaiy ?enea e ?acoeueoaoeaiinoue eiaanoeoeiiiie
no?aoaaee).

——-

?ac?aaioea aa?eaioia eiaanoeoeiiiuo i?iaeoia.

iaeaieaa aaaeiue aii?in – ?acia? eiaanoeoeee, oae eae anoaao aii?in ia
o?iaia ioaaonoaaiiinoe, naycaiiue n i?eiyoeai ?aoaiey. iiaeoiio ?acee/ia
aeoaeia, a caaeneiinoe io ?acia?a. iiyoiio e?iia aeeooa?aioeeaoeee i?aaa
i?e i?eiyoee ?aoaiey, iiaeao auoue iinoaaeai aii?in n ia?aie/aieai
iaeneiaeueiie aaee/eiu eiaanoeoeee. yoi iiaeii i?iienaoue a onoaaiuo
aeieoiaioao oe?iu. iiyoiio iaiaoiaeeii onoaiaaeeaaoueea?a?oeth
e?eoa?eaa. n iiceoee oi?aaeai/aneiaioia?niiaea oe?iu i?iaeou
eeanieoeoee?othony:

i?eciaee:

· aaee/eia o?aaoaiuo eiaanoeoeee: e?oiiua, o?aaeeoeeiiiua e iaeeea

· oei i?aaeiieaaaaiuo aeioiaeia: nie?auaiea cao?ao, aeioiae io
?anoe?aiey, auoiae ia iiaua ?aiee naaoa, yeniainey a iiaua nua?u
aeuiana, nieaeaiea ?enea i?iecaiaenoaa e nauoa, nioeeaeueiue youaeo

· oei ioiioaiee: iacaaeneiinoue, aeueoa?iaeeaiinoue, eiiieaiaioa?iinoue,
caiauaiea

· oei aeaiaaeiiai iioiea: i?aeeia?iue, ia i?aeeia?iue

· ioiioaiea e ?eneo: ?eneiaua, aac?eneiaua

aeinoaoi/ii oneiaiia aeaeaiea. iai?eia?, ioeaiea ?acia?a i?iaeoa caaeneo
io ?acia?a oe?iu. oeaee ioeaiee iiaoo auoue ?aciuie, a ?acoeueoaou ia
anaaaea iinyo oa?aeoa? i?eauee. iiaoo auoue yeiiiie/anee oueuoi/iua
i?iaeou, ii iinyo einaaiiue aeioiae. iaiaoiaeeii auaeaeyoue
acaeiicaaeneiinoue. eiiieaiaioa?iua i?iaeou, anee i?eiyoea iaeiiai
niinianoaoao ?inoo aeioiaeia ii ae?oaiio(ei), iiyoiio auyaeaiea
eiiieaiaioa?iinoe iiae?acoiaaaao ?anniio?aiea i?iaeoia a eiiieaena. yoi
aaaeii i?e i?eiyoee i?iaeoa anie auai? ii iiiiaiiio e?eoa?eth i/aaeaeiui
ia yaeyaony. aeaa i?iaeoa yaeythony caiauaaiuie, anee i?eiyoea iaeiiai
i?eaieeo e nieaeaieth aeioiaeiinoe ii ae?oaiio(ei).

iioie i?aeeia?iue, anee ninoieo ec enoiaeiie aaeeiia?aiaiiie eiaanoeoeee
eee a oa/aiee ianeieueeeo iineaaeiaaoaeueiuo aaciauo ia?eiaeao e
iineaaeothueo i?eoieao aeaiaaeiuo n?aaenoa. anee /a?aaeothony i?eoiee e
iooiee, oi i?iaeo ia i?aeeia?iue. i?iaeou ?acee/athony ii ioaiaie ?enea.
iaiaa ?eneiaaiiua – ain. caeac n nicaeaieia i?iecaiaenoa e oaoiieiaee

———

iiiyoea e aeai?eoiu eniieuecoaiua aeey ?ac?aaioee

ethaie eiaanoeoeeiiiue i?iaeo iiaeii ioa?aeoa?eciaaoue n ?aciuo noi?ii.
eaaeaeay noi?iia aaaeia ii-naiaio, ii oeiainiaue aniaeo ea?aao
iaeneiaeueioth ?ieue.

eaoaai?ee, eiathuea iaeneiaeueiia cia/aiea aeey ioeaiee ueiainiaie
noi?iiu:

a. eaeie iaiaoiaeei iauai ?ano?nia?

a. aaea iaeoe enoi/ieee a o?aaoaiue iauai e eaeiaa eo oeaia?

a. ieoiyony ee iaeaeaiiua aeiaeaiey, o.a. aeinoaoi/ai ee iauai
iinooieaiee a n?aaiaiee n iauaiii eiaanoeoeee?

oeiainiaua neoaeau aeieaeiu o/anoaiaaoue a ioaaoa ia 1-ue aii?in, ii ia
ii?aaeaeytho ia 100%. ioaaou ia 2 e 3 aii?in ioaa/atho ia 100%
oeiainiaua neoaeau.

A?AIAIIAss NOIEIINOUe AeAIAA

a?aiaiiay noieiinoue aeaiaa – aaaeiue aniaeo i?e ioeaiea. i?e/eiu yoiai:
eioeyoeey, ?anoe?eaoeany aiciiaeiinoe i?eaea/aiey a?aiaiii naiaiaeiuo
n?aaenoa, niyoea ia?aie/aiee oi?ie?iaaiey ?ano?nia i?aaei?eyoee e ae?.
iiyaeaoayny naiaiaea a iaieioee?iaiiee aeaiueaaie i?eaaea e iniciaieth
uaeoa, ioi eaiueae eiatho aua iaeio ca?aeoa?enoeeo – a?aiaiioth
oeaiiinoue. 2 aniaeoa: 1 – iaanoeaiaiea iaee/iinoe ai a?aiaie, o. e.
eiaaony eioeyoeey e 2 – ia?auaiea eaieoaea e aeaiaaeiuo n?aaenoa, o.e.
ethaay eiiiaiey aeieaeia eiaoue iaeioi?ua naiaiaeiua n?aaenoaa.
cia/eiinoue yoiai iauaeoa iauyniyaony: ?ooeiiinoueth,
i?aaeinoa?iaeaiiinoueth e niaeoeyoeaiinoueth. a iauai aeaea, a?aiaiiay
noieiinoue au?aaeaia o?acie: “?oaeue naaiaeiy e ?oaeue iaeeaeaaiue e
iieo/aieth a aoaeouai ia ?aaiu”. i?inoaeoei aeaeii oeiainiaie naeaeee
yaeyaony i?aaeinoaaeaiea noiiu pv i?e oneiaee /oi /a?ac a?aiy t aoaeao
aica?auaia noiia fv. oeaeueth iaeaeaeeaaiey yaeyaony iieo/aiea i?eauee.
?acoeueoaoeaiinoue iiaeao auoue ioeaiaia eae ?aciinoue pv-fv eee
ia?an/eouaaaony ioiineoaeueiue iieacaoaeue, ii iie ia iiaeoiaeyo oaea
eae ia niiinoaaeiu a i?ino?ainoaa, iiyoiio iieuecothony noaaeaie. e
iieacaoaeue ii?aaeaeyaony iooai ioiioaiey i?e?iuaiey enoiaeiie noiiu e
aaciaie aaee/eia, a ea/anoaa enoiaeiie iiaeii a?aoue fv eee pv. oaeei
ia?acii noaaea ?ann/eouaaaony 2 niiniaaie. 1-ue i?eacaoaeue – i?ioeaio,
?ino, ii?ia aeioiaea e o.ae. 2-ie – o/aoiay noaaea eee aeeneiio.

Nenoaia ?anoiaeeiinoe o yoeo iieacaoaeae?aceenia. Eiaaea eiaai aeaei n
i?iaiicaie e ?an/aoaie i?e ioeaiea eiaanoeoeeiiiuo i?iaeoia, eiatho
aeaei n i?ioeaioiie noaaeie, iioyoi ia iaiaa?eaaaony. Aiaeec i?iaeoia,
iniiaaiiue ia oi?iaeeciaaiiuo aeai?eoiao iiaeao auiieiyoueny a
ioiineoaeueii noaaeeueiie yeiiiie/aneie ianoaiiaea. I?e ianoaaeeueiinoe
i?ioaioiay noaaea oi?ie?oaony ia aaca o/aoiie noaaea OeA e iia
aeinoaoi/ii aaeeea. I?iaiiciua ?an/aou ia o?aaotho eaeie-eeai oi/iinoe,
o.e. ?acoeueoaou oaeeo ?an/aoia – eiaeeeaoi?u e i?eaioe?u, a ia oi/iua
ioeaiee. Iiyoiio iiiaiaa?eaioiua ?an/aou e eniieueciaaiea aa?iyoiinoiuo
ioeaiie e ?acee/iuo eieoaoeeiiiuo iiaeaeae ia o?aaoao aunieie oi/iinoe.
O?e aaee/eiu, i?enoonoaothuea a ethaie oeiainiaie naeaeea: aeaa caaeaiu,
a o?aouey iaecaanoia. I?ioeann, a eioi?ii caaeaia i?ioeaioiay noaaea e
ia/aeueiay noiia – ia?auaiea, a eiaaea ecaanoiu aeeneiio e iaeeaeaaiay e
iieo/aieth noiia – aeeneiioe?iaaiea. A ea/anoaa eiyooeoeeaioa
aeeneiioe?iaaiey iiaeao auoue eniieueciaaia i?ioeaioiay noaaea –
iaoaiaoe/aneia aeeneiioe?iaaiea eee o/aoiay noaaea – aaieianeia
aeeneiioe?iaaiea. Yeiiiie/aneee niune ueiainiaie iia?aoeee caeeth/aaony
a ii?aaeaeaiee aaee/eiu oie noiiu, eioi?ie aeaeaao ?aniieiaaoue eiaanoi?
ii ieii/aiee oeiainiaie iia?aoeee. I?e?iuaiiay noiia caaeneo io noaiaie
?enea, caaenyuee io aeaea aeciana, a eioi?ue i?ienoiaeeo eiaanoe?iaaiea.
Yeiiiie/aneee niune aeeneiioe?iaaiey caeeth/aaony ai a?aiaiiii
oii?yaei/eaaiee aeaiaaeiuo iioieia ?acee/iuo a?aiaiiuo ia?eiaeia.
Eiyyoeoeaio aeeneiioe?iaaiey iieacuaaao, eaeie aaeaaiaeiue i?ioeaio
aica?aoa iiaeao iieo/eoue eiaanoi? ia eiaanoe?oaiue ei eaieoae. I?e yoii
eneiiay aaee/eia PV iieacuaaao eae au oaeouoth (naaiaeiyoithth
noieiinoue) aoaeouea iaeeaeaaiua e iieo/aieth noiiu. I?e ia/eneaiee noii
aaeaaiaeii, ?a/ue eaeao i aeene?aoiii ia/eneaiee. 2 iaoiaea aeene?aoiiai
au/eneaiey – i?inouo (Rn=P*(1+r*n), o.a. iaeciaiiay aaca) e neiaeiuo
i?ioeaioia (ia/eneaiea i?ienoiaeeo n iauae noiiu, aeeth/athuae
ia/eneaiiua e iaaino?aaiaaiiua i?ioeaiou, o.a aaca ?anoao Fn=P*(1+r)^n).
Eniieueciaaiea neiaeiiai i?ioeaioa a neo/aa iiiaie?aoiiai aai ia/eneaiey
aieaa eiae/ii. Anee ia/eneaiea i?ienoiaeeo ii i?inoiio i?ioeaioo, oi
aeioiaeu iaiaoiaeeii eniieueciaaoue. Fn=P*(1+r)^n) – aaciaay oi?ioea,
iiyoiio aeey oaeianoaa eniieuecotho iaicia/aiea – FM1(r;n),
iaania/eaathuee ia?auaiea noieiinoe, iiyoiio iiaeii i?aia?aciaaoue:
Fn=P*FM1(r;n). Cia/aiey r e n – oaaoee?iaaiu. Ioeaieaay
oeaeaniia?aciinoue aeiaeaiee, enoiaeyo ec oiai, aoaeoo ee yoe aeiaeaiey
i?eaueueiu i?e aeiionoeiii o?iaia ?enea, /ai aeueoa?iaoeaiua aeiaeaiey.
Iinueee eiaanoi?a i?e auai?a iauaeoa eiaanoe?iaaiey: eioeyoeey anoue
anaaaea, oaiiu eciaiaiey oeai ia oiaa?u iiaoo ioee/aoueny io oaiiia
eioeyoeee, aeaeaoaeueii ia?eiaee/aneia ia/eneaiea eee iinooieaiea
aeioiaea ia eiaanoe?oaiue eaieoae ia ieaea ii?aaeaeaiiiai o?iaiy.
Aaee/eia P=Fn*FM2(r;n) eee = Fn / (1+r)^n. Yeiiiie/aneee niune oaeiai
i?aaenoaaeaiey a oii, /oi i?iaiice?oaiay aaee/eia aeaiaaeiuo iinooieaiee
/a?ac n eao n iiceoeee oaeouaai aeiy aoaeao iaiueoa eee ?aaia cia/aieth
P, o.e. (1+r)^n aieueoa 1. Aeey eiaanoi?a Fn /a?ac n eao e 77777
iaeeiaeiau ii naiae oeaiiinoe. Eniieuecoy P=Fn*FM2(r;n) iiaeii
i?eaiaeeoue aeioiaeu iaeeaeaaiua e iieo/aieth a oa/aiea ?yaea eao. A
yoii neo/aa eiyyoeoeaio aeeneiioe?iaaiey /eneaii ?aaai noaaea,
onoaiaaeeaaaiie eiaanoi?ii, o.a. aeioiaeo, eioi?ue eiaanoi? oi/ao
iieo/eoue ia eiaanoe?oaiue ei eaieoae. Ii?aaeaeyy eiyyoeoeaio
aeeneiioe?iaaiey iau/ii enoiaeyo ec aaciianiiai eee aa?aioe?iaaiiiai
o?iaiy aeioiaeiinoe oeiainiauo eiaanoeoeee, eioi?ue iaania/eaaaony OeA
ii aeeaaeai eee i?e iia?aoeeyo n oeaiiuie aoiaaaie. I?e yoii iiaeao
aeaaaoueny iaaeaaaea ca ?ene e /ai ?eneiaaiiaa i?iaeo eee oeiainiaue
eiio?aeo, oai aieueoa ?acia? i?aiee ca ?ene. A yo?i neo/aa eiyooeoeeaio
aeeneiioe?iaaiey ?aaai RF (noaaea ?aoeiaine?iaaiey) + RR (i?aiey ca
?ene). Ioeaiea ?enea iiaeao i?iecaiaeeony n iiceoeee aoaeouaai: iniiaaii
ia n?aaiaiee 2-oo noii: 1-ay noiia aa?aioe?iaaia, a aoi?ay noiia
?ann/eouaaaony ?i oi?ioea Fn=P*(1+r)^n.). I?e o/aoa ?enea iaiaoiaeeii
?ann/eouaaoue aeeneiioe?iaaiiua ioeaiee. FM2(r;n) – aeeneiioe?othuee
iiiaeeoaeue. Yeiiiie/aneee niune: iieacuaaao naaiaeiyoithth oeaio iaeiie
aeaiaaeiie aaeeieoeu aoaeouaai i?e caaeaiiii o?iaia aeioiaeiinoe R e
/anoioa ia/eneaiey i?ioeaioia N.

—————-

Ioeaiea aeaiaaeiiai iioiea.

—————-

Iaeei ec iniiaiuo yeaiaioia oeiainiaiai aiaeeca e eiaanoeoeeiiiiai
aiaeeca. Aeaiaaeiue iioie – c1, c2, … cn. Aaia?e?oaony a oa/aiea
iiiaeo eao a ?acoeueoaoa ooieoeeiie?iaaiey eaeiai-eeai oeiainiaiai
aeoeaa. Yeaiaiou iioiea iiaoo auoue iacaaeneiuie eee naycaiiuie iaaeaeo
niaie eaeei-oi ii?aaeaeaiiui aeai?eoiii. I?aaeiieiaeei, /oi iioiee
iaeiiiai?aaeaiiua. N/eoaaony, /oi aaia?e?oaiua aeioiaeu a oa/aiea
ii?aaeaeaiiiai eee eiie?aoiiai ia?eiaea a?aiaie eiatho ianoi a ia/aea
ia?eiaea eee a eiioea ia?eiaea. Yoe iioiee neiioeaio?e?iaaiu ia iaeio ec
a?aieoe iioiea. Anee iioiee a ia/aea, oi iioie – i?aioia?aiaei, a anee a
eiioea ia?eiaea – iinoioia?aiaei. Ia i?aeoeea iinooieaiea ?ani?aaeaeaii
a ia?eiaea ia ?aaiiia?ii, iiyoiio oaeiaiae ana iinoo?eaiey ioiineoue a
eiiaoe ia?eiaea. Iiyoiio oi?ie?othony ?aaiua a?aiaiiua ia?eiaeu, /oi
iicaieyao i?iaiaeeoue ioeaiee. I?aioia?aiaei oa?aeoa?ai aeey iaeiieaiey
aeaiaaeiuo n?aaenoa aeey aeaeueiaeoaai eiaanoe?iaaiey.

Ioeaiea aeaiaaeiiai iioiea auiieiyaony a ?aieao ?aoaiey 2-oo caaea/:

· i?yiay: n iiceoeee aoaeouaai. i?aaeiieaaaao noiia?ioth ioeaieo
ia?auaiiiai aeaiaaeiiai iioiea, o.a. a iniiaa ioeaiee eaaeeo aoaeouay
noieiiioue, o.a. aeaiaaeiue iioie – ?aaoey?iia ia/eneaiea ia eaieoae, oi
ii noaia neiaeiac i?ioeaioia a iniiaa eaaeeo ?an/ao ii oi?ioea 4

· ia?aoiay: n iiceoeee ianoiyuaai. ioaeaeueiua yeaiaiou aeaiaaeiiai
iioiea aaia?e?othony a ?acee/iaa a?aiaiiua eioa?aaeu, a aeaiueae eiatho
a?aiaiioth oeaiiinoue e i?yii noiie?iaaoue iaaiciiaeii, iiyoiio
iaiaoiaeeii i?eaiaeeoue iioie e iaeiiio iiiaioo a?aiaie, /oi
i?iecaiaeeony ii oi?ioea 6. Yoe oi?ioeu caaenyo io aeaea iioiea

Eiaiii ia?aoiay caaea/a yaeyaony iiiiaiie caaea/ae i?e ioeaiea
eiaanoeoeeiiiuo i?iaeoia. Eeth/eaui iiiaioii a ?anniao?eaaaiuo noaiao
yae/aony iie/aeeaia oneiaea i oii, /oi ioeaiea aaaeaony ?acoiiui
eiaanoi?ii e aeaiueae iaiaaeeaiii eiaanoe?othony. I?e ioeaiea iioiea,
o.a. e i?e ia?auaiee e i?e aeeneiioe?iaaiee i?aaeiieaaaaony noaia
neiaeiuo i?ioeaioia. Aiioeoao – /anoiue neo/ae aeaiaaeiiai iioiea, i?e
eioi?ii aeaiaaeiia iinooieaiea a eaaeaeue ia?eiae a?aiaie iaeeiaeiau.
Oe?iei eniieuecotho i?e ioeaiea aeieaiauo e aeieaauo oeaiiuo aoiaa.
Oe?iei eniieuecoaony a aiaeeca i?iaeoia e i?e aiaeeca a?aiaeu e
a?aiaeiuo ieaoaaeae. Aeey ioeaiea noieiinoe aiioeoaoia iiaeii
iieueciaaoueny ui?ioeaie 4 e 6. Aeaaiaea?y niaoeeoeee aiioeoaoa, yoe
ui?ioeu aeaeieciaiythony: aeey ioeaiee iinoioia?aiaei i?e a-iinoiyiiua
iinooieaiey e r-noaaea i?ioeaioa, FV=A*FM3(r;n), a aeey i?aioia?aiaei –
FV=A*FM3(r;n)*(1+n), aaea FM3(r;n)=((1+r)^n/

Yeiiiie/aneee niune FM3 caeeth/aaony a neaaeothuai: iieacuaaao /aio
aoaeao ?aaia noiia?iay aaee/eia n?i/iiai aiioeoaoa a iaeio aeaiaaeioth
aaeeieoeo e eiioeo n?iea aai aeaenoaey. Aeaiiue iiiaeeoaeue /anoi
eniieuecoaony e cia/aiea caaeneo io n e r.

PV=A*FM4(r;n)

PV=A*FM4(r;n)*(1+n)

FM3(r;n)=((1+r)^n/

77777

Yeiiiie/aneee niune FM4: iieacuaaao, /aio ?aaia n iiceoeee oaeouaai
iiiaioa aaee/eia aiioeoaoa n ?aaoey?iuie aeaiaaeiuie iinooieaieyie a
?acia?a iaeiie aeaiaaeiie aaeeieoeu, i?iaeieaeathueany n ?aaiuo
ia?eiaeia n caaeaiiie i?ioeaioiie noaaeie r.

A caiaaeiie i?aeoeea e aann?i/iui aiioeoaoai ioiinyo aiioeoaou ia 50 e
aieaa eao. I?e yoii ecaanoai ?acia?eaiaeiauo iinooieaiee, a a ea/anoaa
r-i?ioeaio OeA.

——————

iaaei aeiienaoue

——————

Oeaia eaieoaea e aa ?ieue a ioeaiea eiaanoeoeeiiiuo i?iaeoia

Ethaay eiiiaiey ioaeaeaaony a enoi/ieeao n?aaenoa aeey oeiaine?iaaiey
naiae aeayoaeueiinoe. A caaeneiinoe io aeeeoaeueiinoe nouanoaiaaiey,
enoi/ieee n?aaenoa iiaeiioaeaeeoue ia e?aoein?i/iua e aeieain?i/iua.
I?eaea/aiea eiie?aoiiai enoi/ieea oeiaine?iaaiey naycaii n cao?aoaie.
Anee iu i?eaeaeaai eaieae a aoaea aeioiaea io i?iaeaaee aeoeee, oi iauay
noiia n?aaeno, eioi?oth iaaei caieaoeoue, au?aaeaiiay a i?ioeaioao e
iauaio – NN (oeaia eaieoaea). N?aaenoaa aeeeoaeueiiai iieueciaaiey
oeiaine?othony ca n/ao aeieain?i/iuo enoi/ieeia n?aaenoa.

—-

o?iaaiue ?aioaaaeueiinoe iniiaiiai eaieoaea, eioi?ue aeieaeia
iaania/eoue oe?ia, /oi au ia aeiionoeoue oiaiueoaiey noieiinoe oe?iu.
Iiyoiio ?acee/atho:

· oeaia eaieoaea – eiee/anoaaiii au?aaeaaony a aiaeiaii ianeoaeeaaiee
nianoaaiieeia e eiaanoi?ia

· ioeaiea eaieoaea – au?aaeaaony /a?ac aaee/eio nianoaaiiiai eaieoaea,
noieiinoue oe?iu e o.ae.

Nouanoaoao eiee/anoaaiiay acaeiinaycue yoeo iieacaoaeae. Iai?eia?, anee
a eiaanoeoeeiiiii i?iaeoa aeioiaeiinoue iaiueoa oeaiu eaieoaea, oi
eaieoaeece?iaaiiay noiei?noue oe?iu ii caaa?oaiee i?iaeoa oiaiueoeony,
iiaeoiio oeaia eaieoaea – eeth/aaie yeaiaio, naycaiiue n i?eiyoeai
?aoaiey eiaanoeoeeiiiiai oa?aeoa?a. Aiaeec no?oeoo?u ianneaa aaeaina,
oa?aeoaoecothuee enoi/ieee n?aaenoaiieacuaaao, /oi iniiaiuie aeaeaie
yae/thony aioo?aiiea enoi/ieee: onoaaiue eaieoae, ia?ani?aaeaeaiiay
i?eaueue e oiiaeu nianoaaiiuo n?aaenoa. I?e/eiu ia?aciaaiey, aeiey e eo
aaee/eia a aaethoa aaeaina iiaeao auoue ?acee/ia. Enoiaey ec nianoaaiiuo
aiciiaeiinoae, aeaaeaeueoeu e o/anoieee oi?ie?otho yoio eaieoae eae
aeinoaoi/iue aeey oie aeayoaeueiinoeTH ?aaee eioi?ie oe?ia e nicaeaaony.
Oiiaeu nianoaaiiuo n?aaenoa – ioeiaeaiiay e ?ani?aaeaeaieth i?eaueue e
oaeea oiiaeu oi?ie?othony auioaeaeaiii a aeaea ?aca?aiiai eaieoaea eee
iniciaii, eiaaea iaiaaeaea? i?aaeiieaaaao, /oi aeinoeaaaiia oaeei
ia?acii ?anoe?aiea aeayoaeueiinoe i?aaenoaaeyao niaie aieaa auaiaeiia
?aciauaiea eaieoaea, /ai ecuiaiea i?eauee e iai?aaeaiea aa eethi ia
iio?aaeaiea, eeai a ae?oaea noa?u aeciana. A?aiaiii i?eaea/aiiua
n?aaenoaa ia?acothony ia i?aaei?eyoee a ?acoeueoaoa a?aiaiiiai eaaa
iaaeaeo iieo/aieai oiaa?ii-iaoa?eaeueiuo oeaiiinoae e eo iieaou.
Ii?aaeaeaiea oeaiu – ia oeaeue. Aeaiiue iieacaoaeue ioeaieaaao
aeayoaeueiinoue oe?iu a aeieain?i/iie ia?niaeoeaa. Oeaia eaieoaea
iieacuaaao i?eaeaeoaeueiiioue oe?iu aeey eiaanoi?ia, eioi?ua iiaoo
noaoue niaeaaeaeueoeaie oe?iu. Oeaia iaeioi?uo caaiiuo enoi/ieeia
oa?aeoa?ecoao eiiiaieth ii i?eaea/aieth enoi/ieeia. N?aaeiaacaaoaiiay
oaia eaieoaea oe?iu – iniiaiie iieacaeaeue i?e ninoaaeaiee athaeaeaoa
eaieoaeueiuo aeiaeaiee. Oeaia eaaeaeiai ec i?eaaaeaiiuo enoi/ieeia
?acee/ia, iiyoiio oeaio eaieoaea eiiia?/aneie eiiiaiee iaoiaeyo ii
oi?ioea n?aeiae a?eoiaoe/aneioe acaaoaiiie. Aeaiiue iieacaoaiue
?ann/eouaaaony ii aiaeiaie eioi?iaoeee e iniiaiay neiaeiinoue aicieeaao
i?e ii?aaeaiaiee oeaiu eaieoaea, iieo/aiiiai ec eiie?aoiiai enoi/ieea
n?aaenoa. Yeiiiie/aneay eioa?i?aoaoeey oeaiu eaieoaea oa?aeoa?ecoao,
eaeoth noiio neaaeoao caieaoeoue ca i?eaea/aiiea aaeeieoeu eaieoaea ec
eiie?aoiiai enoi/ieea. Anee a ioiioaiee iau/ii oiaa?a oeaia –
aaniethoiay ioeaiea, oi a ioiioaiee enoi/ieeia n?aaenoa i?aaeei
?aaainoaa oeaiu n iiceoeee iieoiaoaey e i?iaeaaoea ia?ooaaony. Oaeea
?acee/ey aicieeatho ec-ca iaeiaiiaeiaeaiey i?eauee: noaaea
?aoeiaine?iaaiey OeA + 3% i?e auieaoa i?ioeaioia ii e?aaeeoo ioiineony
ia naaanoieiinoue i?iaeoeoeee, a inoaeueiia ca n/ao i?eauee. Oeaio
eiiiaiee iaiaoiaeeii ciaoue, oaea eae oeaia eaieoaea – yoi ioaea/a ia
aeiaeaiiua eiaanoi?aie ?ano?nu e oeaia eniieuecoaony aeey ii?aaeaeaiey
?uii/iie ioeaiea eaieoaea. Oaeaea iiaeii i?iaiice?iaaoue eciaiaiea oeai
ia aeoeee naiae oe?iu a caaeneiinoe io iaeeaeaaiuo aeeaeaeaiaeia. Oeaia
caaiiuo n?aaenoa annioeee?oaony n i?ioeaioii. Iaeeiecaoeey ?uii/iie
noieiinoe – aeaaiay caaea/a iaiaaeaeiaioa oe?iu, /oi aeinoeaaaony ca
n/ao ieieiecaoeee oeaiu i?eaeaeaaiiai eaieoaea. Oeaia eaieoaea –
eeth/aaie oaeoi? i?e aiaeeca eiaanoeoeeiiiuo i?iaeoia.

————–

No?oeoo?a enoi/ieeia n?aaenoa eiiiaiee.

Iiaeii auaeaeeoue 5 enoi/ieeia eaieoaea, oaioeioi?uo iaiaoiaeeii ciaoue
aeey ?ann/aoa n?aaeiaacaaoaiiie oeaiu:

· aaieianeea nnoaeu e caeiu

· iaeeaaoeeiiiua caeiu

· i?eaeeeae?iaaiiua aeoeee e iaueiiaaiiua aeoeee

· ia?ani?aaeaeaiiay i?eaueue

—– NOAIA —–

A iauai aeaea oeaia iiaeao i?aaenoaaeaii iaooeiie oeaiu eaieoaea:

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931300F3931300F3930F00F3930E00F3930C00F3930C00F3930C00F3930C00F3930C00F3
930C00F3930C00F3930C00F3930B00F3930B00F3930B00F3930B00F3930B00F3930B00F3
930B00F3930B00F3930B00F3930B00F3930B00F3930B00F3930B00F3930E00F3930F00F3
931000F3931600F3931900F3930A000000250303001300F3931300F3931A00F3930A0000
00250303003000F3932C00F3933E00F3930E000000250305005C00F3935800F3936C00F3
937F00F3939000F3930E00000025030500AB00F393A700F393BC00F393CF00F393DF00F3
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00A701F393A501F393B501F393C901F393DB01F3930E00000025030500FC01F393F501F3
930802F3931C02F3932B02F3930E000000250305004B02F3934702F3935A02F3936F02F3
932B02F3930E000000250305008802F3938402F3939602F393A602F393B402F3930E0000
0025030500D202F393CC02F393DE02F393F002F393FF02F3930E000000250305001903F3
931203F3932703F3933A03F393FF02F3930E000000250305005603F3935003F3936103F3
937303F393FF02F3930E000000250305008D03F3938B03F3939F03F393B103F393FF02F3
930A00000025030300CA03F393C803F393D803F3930A00000025030300F503F393F103F3
930204F3930E000000250305001D04F3931904F3932804F3933904F393FF02F393080000
00250302004F04F3934B04F39306000000250301005A04F393B6000000250359001B00F3
931B00F3931B00F3931B00F3931600F3931A00F3932200F3933000F3933E00F3934C00F3
935B00F3936A00F3937700F3938500F3939200F393A000F393AD00F393BB00F393C800F3
93D600F393E300F393EF00F393FD00F3930A01F3931501F3932101F3932C01F3933901F3
934601F3935401F3936101F3936D01F3937801F3938501F3939101F3939C01F393A901F3
93B501F393C201F393D001F393DD01F393EA01F393F801F3930402F3931102F3931E02F3
932C02F3933A02F3934802F3935402F3936202F3937002F3937E02F3938C02F3939802F3
93A602F393B502F393C302F393D202F393DF02F393EB02F393F802F3930603F3931403F3
932103F3932F03F3933D03F3934A03F3935603F3936403F3937303F3938103F3939203F3
939F03F393AD03F393BA03F393C603F393D403F393E003F393EC03F393F903F3930604F3
931104F3931F04F3932B04F3933804F3934604F3935304F3935904F3931C00000025030C
004404F3934404F3933D04F3934604F3934E04F3935D04F3935D04F3935804F3934804F3
933804F3932704F3931F04F39308000000250302000400F3930B00F39316000000250309
003200F3933200F3933200F3932B00F3932400F3931900F3931000F3930800F3930500F3
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938E00F3939C00F393AA00F393B800F393CA00F393DA00F393EB00F393F900F3930701F3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93C202F393C002F393BF02F393BC02F393BB02F393BC02F393BE02F393BF02F393BF02F3
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933502F3934202F3935002F3936202F3937402F3938602F3939802F393A802F393B702F3
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937B01F3938C01F3939B01F393AA01F393B901F393C901F393D901F393E801F393F901F3
930802F3931802F3932802F3933902F3934902F3935902F3936802F3937402F3938402F3
939602F393AC02F393BC02F393CC02F393D702F393E602F393F602F3930603F3931403F3
932103F3932803F3932A000000250313003203F3933203F3932C03F3932A03F3932803F3
932803F3932603F3932403F3931F03F3931C03F3931A03F3931A03F3931A03F3931A03F3
931903F3931903F3931903F3932003F3932303F39336000000250319000701F3930701F3
930001F393FC00F393F600F393F100F393EE00F393EC00F393EC00F393EC00F393EC00F3
93EC00F393EC00F393EC00F393EC00F393EC00F393E800F393E700F393E600F393E800F3
93EA00F393EE00F393F200F393FA00F3930001F3931800000025030A009D03F3939D03F3
939A03F3939803F3939703F3939703F3939A03F3939B03F3939D03F3939D03F3932C0000
00250314008903F3938903F3938903F3939303F3939E03F393AF03F393C103F393D103F3
93E003F393E703F393EA03F393EA03F393E303F393DA03F393CA03F393BE03F393AF03F3
939D03F3939B03F3939803F3933800000025031A00F900F393F900F393F900F393F900F3
93F600F393F100F393EC00F393E800F393E300F393E000F393DC00F393DA00F393DD00F3
93E300F393EA00F393EC00F393F600F3930001F3930E01F3931501F3931901F3931901F3
931701F3931701F3931701F3931701F3931400000025030800D500F393D500F393DD00F3
93EB00F393FE00F3931001F3932001F3932701F39314000000250308000704F3930704F3
930A04F3930E04F3931104F3931504F3931604F3931804F39330000000250316000704F3
930704F3930204F3930004F3930704F3931404F3932204F3932B04F3932D04F3932204F3
932304F3932804F3933804F3934404F3934C04F3934A04F3934004F3933104F3932204F3
931104F3931004F3930D04F39328000000250312005C00F3935C00F3935C00F3936300F3
936900F3936800F3935E00F3934F00F3934200F3933B00F3933700F3933E00F3934A00F3
935A00F3936800F3937800F3938700F3939100F39308000000FA02000000000000000000
00040000002D01010004000000F0010000030000000000*ai aieueoa i?aaeeiaeaiea,
oai iaiueoa oeaia. Ni?in i?yiii?ioeaiiieiaeai i?aaeeiaeaieth. O?iaaiue
oaiu eaieoaia oa?aeoa?ecoao oaeouaa iioeiaeueiia iieiaeaiea oeaiu
enoinieea n iiceoeee ?uiea. Iniiaiua yeaiaiou:6 nnoaeu aaiea e
auiouaiiua i?aaei?eyoeai iaeeaaoeee. Nnoaea aaiea aeieaeia
?anniao?eaaoueny n o/aoii iaeiaa ia i?eaueue, a i?ioeaiou io e?aaeeoa
aeeth/athony a naaanoieiinoue. Iiyoiio oeaia aaeaieoeu oaeiai enoi/ieea
aeaeao iaiueoa, /ai oiea/eaaaiue aaieo i?ioeaio. Caeiu, iieo/aiiua
i?aaei?eyoeai io oicyenoaothueo noauaeoia ioee/athony io aaieianeeo,
o.e. i?ioeaiou ca iieueciaaiea oaeeie caeiaie ia ioiinyony ia
naaanoieiinoue i?iaeoeoeee. Aiaeiae/ii e n iaeeaaoeeiiiuie caeiaie.
Oeaia iaeeaaoeeiiiiai caeia aieaa neaoinoe/ia ii n?aaiaieth n oeaiie
aaieianeiai e?aaeeoa. Iaeeaeaaiay e oaeoe/aneay oeaia iaeeaaoeeiiiiai
caeia iiaeao auoue ia i?aaeneacoaiay. O.e. ?aciauaea iaeeaaoeee
i?ienoiaeeo /a?ac aeeeea?ia, oi oeaia aeaiiiai enoi/ieea caaeneo io
aeiiieieoaeueiiai ia?aiao?a (cao?aou ia ?aciauaiea oeaiiuo aeiaa).
Niaeanii ii?iaoeaiui aeieoiiaioai, noiiu e oieaoa i?ioeaioia ii
iaeeaaoeeyi io?aaeathony ii n/. 80 eee n/ 89, ii aac oiaiueoaiey
iaeiaiiaeaaaaiie i?eauee, o.a. yoe noiiu ?ann/eoaiu ia iineaiaeiaiaie
aaca.

I?e ?ann/aoaeoaiu iaiaoieeii o/eouaaoue ?acieoeo iaaeaeo oeaiie
iaeeaaoeeae e aa ia?eoeaoaeueiie noieiinoueth. Noieiinoue iiaeao auoue
auoa ca n/ao ?anoiaeea ii yiennee e i?iaeaaeae ia oneiaeyo aeeneiioa. N
iiceoeee ?ann/aoa oeaiu eaieoaea iaiaoiaeeii auaeaeeoue:

i?eaeeeae?iaaiiua aeoeee

iaueiiaaiiua aeoeee

ia?ani?aaeaeaiiay i?eaueue (ana enoi/ieee, e?iia onoaaiiai eaieoaea).
Aeiey enoi/ieea i/aiue iaea. I?e/eia ?acaeaeaiey onoaaiiai eaieoaea ia 2
yeaiaioa: ia iaueiiaaiiua e i?eaeeeae?iaaiiua a oii, /oi
i?eaeeeae?iaaiiua aeoeee – aea?eae, ni/aoathuee naienoaa iaueiiaaiiuo
aeoeee e caaiiiai eaieoaea, ii i?eioeeieaeueiuo ?acee/ee a ioeaiea oeaiu
eaieoaea ia iaaethaeaaony. Aeoeeiia?u a iaiai ia nianoaaiiua n?aenoaa
?ann/eouaatho ia aeeaeaeaiaeu. N iiceoeee eiiia?/aneioe i?aaiecaoeee,
oeaia oaeiai eno?/ieea ?aaia o?iaith aeeaeaeaiaeia, oiea/eaaaiuo
aeoeeiia?ai, o.e. ii i?inoui aeoeeyi aeeaeaeaiae ecaanoai, oi oeaia
enoi/ieea ec i?eaeeeae?iaaiiuo aeoeee ?ann/eouaaaony . I?ioeaio ii
i?eaeeeaa?iaaiiua aeoeeyi caaeneo io yooaeoeaiie ?aaiou eiiia?/aneie
i?aaiecaoeee, iiyoiio oaia enoi/ieea iaueiiaaiiuo aeoeee iiaeii
?ann/eoaoue n iaiueoae oi/iinoueth. Iaeaieueoaa ?ani?ino?aiaiea iieo/eea
iiaeaeue Ai?aeiia e iiaeaeue NAPM (iiaeaeue ioeaiee noieiinoe
oeiainiaiai aeoeaa). Iiaeaeue Ai?aeiia: Kt=Kd+Kc. I?e/eiu:

· aeaiiua n?aaenoaa iiaeeecothony auno?i e ia o?aaotho niaoeeaeueiiai
iacaiecia eae a neo/aa yiennee aeoeee (iaeeaaoeee)

· yoio enoi/iee iaoiaeeony aeaaaaea ae?oaec, aaeaeo oiai, /o ia
aiuieeiao aeienneiiiuo ?anoiaeia

· ii aaciianai, o.a. caueuai io iaaaoeaiie eioi?iaoeee i iiaie yiennee

Aaee/eia eio?ai?aoe?oaony. Iieo/aiiay oe?iie i?eaueue iinea iaiaoiaeeiuo
io/eneaiee iiaeeaaeeo ?ani?aaeaeaieth n?aaee aeaaeaeueoeaa iaueiiaaiiuo
aeoeee e iaeeaeaaiay ioaea/a io oaeiai ?aeiaanoe?iaaiey aeieaeia auoue
ia iaiueoa /aii io aeueoa?iaoeaiuo eiaanoeoeee oie aea noaiaie ?enea,
eia/a aeaaeaeueoeu iaueiiaaiiuo aeoeee i?aaeii/ooo iieo/aoue
aeeaeaeaiaeu, a ia niaeanyony ?aeiaanoe?iaaoue aeeaeaeaiaeu, aeaoeoo
eneaoue aieaa yooaeoeaiua niiniau aeiaeaiey. ?aeiaanoe?iaaiea i?eaaee
?aaiineeueii i?eia?aoaieth aeoeeiia?aie iiauo aeoeee naiae oe?iu, o.i.
oeaia enoi/ieeia n?aaenoa ia?ani?aaeaeaiiay i?eaueue ?aaia oeaia
enoi/ieea iaueiiaaiiay aeoeey. Ia i?aeoeea ethaay i?aaiecaoeey
oeiaine?oao naith aeayoaeueiinoue ec ?acee/iuo enoi/iee?a e a ea/anoaa
ieaou ca eniieueciaaiiua a aaine?iaaiiua ?ano?nu oe?ia auiea/eaaao
aiciaa?aaeaeaiea. Oeaia enoi/ieea = noiia ?anoiaeia ii iaania/aieth
aeaiiiai enoi/ieea.

———————————-

E?eoa?ee ioeaiee eiaanoeoeeiiiuo i?iaeoia

———————————-

Iaoiae ii?aaeaeaiey n?iea ieoiaaiinoe eiaaanoeoeee.

Oe?iei ?ani?ino?aiai a ie?a e ia i?aaeiieaaaao a?aiaiiie
oii?yaei/aiiinoe aeaiaaeiuo iinooieaiee. Caaeneo io ?aaiiia?iinoe
iinooieaiey ae?oiaeiinoe io eiaanoeoeee. Anee aeioiae ?aaiiia?ai, oi
?ann/eouaaaony aeaeaieai cao?ao ia aaea/eio aiaeiaiai aeioiaea,
iaoneiaeaiiiai yoeie cao?aoaie. Aneei?eaueue ?ani?aaeaeaia ia
?aaiiia?ii, oi ?ann/eouaaaony i?yiui iiaen/aoii eao, a oa/aiee eioi?uo
eiaanoeoeey aoaeao iiaaoaia. I?e ?anniio?aiee ae?iaiie /anoe n?iea,
iaiaa?eaaaony, /oi aeioiae ?ani?aaeaeai ?aaiaia?ii a oa/aiee anaai
n?iea. I?e o/aoa a?aiaiiiai oaeoi?a iioiee ai??aeoe?othony n o/aoii
n?aaeiaacaaoaiiie noieiinoe eaieoaea. Oaeaea iieuecothony iiiaeeoaeae
FM2. I?iaeo, i?eiyoue ii PP iiaeao auoue ia i?eiyo iinea ei??aeoe?iaee.
I?iaeo i?eieiaaony, anee n?ie ieoiaaiinoe ia i?aauoaao iaeioi?iai
eeieoa. Iaaeinoaoee iieacaoaey: ia o/eouaaao aeeyiea aeioiaeia
iineaaeieo ia?eiaeia; ia aeaeaao ?acee/ey iaaeaeo i?iaeoaie n
iaeeiaeiaie noiiie eiiioeyoeaiuo aeioiaeia, ii ?acee/iui ?ani?aaeaeaieai
aa ii aiaeai; ia iaeaaeaao naienoaii aaeaeeoeaiinoe. I?e neooaoeee,
eiaaea iaiaaeaeiaio oe?iu icaai/ai aieueoa eeeaeaeiinoueth, a ia
i?eaueueiinoueth. Aeaiiue iaoiae oi?io a neooaoeee, eiaaea eiaanoeoeee
nii?yaeaiu n aunieie noaiaiueth ?enea. *ai ei?i/a n?ie ieoiaaiinoe, oai
iaiaa ?eneiaaiue i?iaeo. A ioee/ea io ae?oaeo ioaiie, PP iicaieyao
iieo/eoue ioeaiee i eeeaeaeiinoe e ?eneiaaiiinoe i?iaeoa.

——————-

Iaoiae ?an/aoa eiyooeoeeaioa yooaeoeaiinoe eiaanoeoeee.

Ii ia i?aaeiieaaaao aeeneiioe?iaaiea iieacaoaeae aeioiaea e aeioiae
oa?aeoa?ecoaony iieacaoaeai /enoie i?eauee: PN=i?eaueue-iaeiae. Eiyoo.
yooaeoeaiinoe ARR ?ann/eouaaony aeaeaieai n?aaeiaaiaeiaie ii?iu i?eauee
ia n?aaeithth aaee/eio eiaanoeoeee. Aiciiaeii onoaiiaeaiea ii?iaiaiai
cia/aiey, n eioi?ui aoaeao n?aaieaaoueny ARR. Eiaao iaaeinoaoee,
iaoneiaeaiiua ia o/oaieai a?aiaiiie noieiinoe aeaiaaeiiai iioiea e ia
aeaeaao ?aceenee iaaeaeo i?iaeoaie n iaeeiaeiaie noiiie n?aaeiaaiaeiaie
i?eauee, ii aa?uee?iaaiiie ii aiaeai, a oaeaea ia aeaeaao ?acee/ee.

————————–

I?ioeai?a/eainoue e?eoa?eaa ioeaiee.

?aoaiea i i?eiyoee ?aoaiey ia anaaaea i/aaeaeii, oae eae auai? ioaeiiai
e?eoa?ey iiaeao “iiii/ue” i?e auai?a i?iaeoa. Ineiaeiyaony neoaoeey
eiaaea auai? noieo ia?aae auai?ii ii ianeieueeei e?eoa?eyi.

Ec anao e?eoa?eaa, ?aaeueiuie e?eoa?eyie yaeythony NPV, PI e ARR. Ii
i?iaeaia auai?a e?eoa?ey inoaaony.

I EE AAe NPV IRR PI

A -700 250 43618 16 1,06

B -100 40 18979 21,9 1,19

A-B 600 210 24639 15 1,05

Anee i?iaeou aeueoa?iaoeaiua, oi auai? ia i/aaeaeai, o.e. o A aieueoa
NPV, a o B – aieueoa PI. ?aeiiaiaeoaony auae?aoue i?iaeo n aieueoei NPV,
o.e. ia?aueaaiea yeiiiie/aneie iiue – aeaaiay oeaeaaay onoaiiaea. Iiaeii
naeaeaoue ?an/ao eiyooeoeeaioa IRR aeey i?e?inoiuo iieacaoaeae aeioiaea,
e anee IRR aieueoa oi oeaeaniia?acii i?eieiaoue i?iaeo n aieueoeie
eaieoaeueiuie aeiaeaieyie. A neo/aa i?ioeai?a/ee aieaa i?aaeii/oeoaeai
NPVTH o.e. aeaao aa?iyeiinoioth ioeaieo i?e?inoa noieiinoe eiiia?/aneie
i?aaiecaoeee a neo/aa i?eiyoey i?iaeoa e e?eoa?ee iieiinoueth ioaa/aao
iniiaiie oeaee iaiaaeaeiaioa.

—————————————————-

N?aaieoaeueiay oa?aeoa?enoeea NPV e IRR.

Iie iiaoo i?ioeai?a/eoue ae?oa ae?oao. IRR eiaao ?yae iniaaiiinoae,
i?e/ai iaeioi?ua ec ieo ineiaeiytho auai?. Anee aeiiouaia ioeaea a
auai?a eiyooeoeeaioa,oi ianeieueei aniea aa?iyoiinoue oauoi/iinoe ia
i?aeoeea, ianiio?y ia i?eaueueiinoue i?e ?an/aoao. *ai aieueoa IRR ii
n?aaiaieth n oeaiie eaieoaea, oai aieueoa ?aca?a aaciianiinoe. *ai
aieueoa PI i?aauoaao 1, oai aieueoa ?aca?a aaciianiinoe. Ii ii NPV
iaeuecy auynieoue ?ene.

———————————————–

Eiaeea i?eiaiaiey aace?oaony ia eaeayo oai?ee iieaciinoe. ?anniao?eaay
iiyeaiaioii aeaiaaeiue iioie ?eneiaiai iiiaeoa, eiaanoi? a ioiioaiee
yoiai iioiea iuoaaony ioeaieoue, eaeay aa?aioe?iaiiay, o.a. Aac?eneiaay
noiiaoaeaiaa aio iio?aaoaony, /oi au auoue eiaeaua?aioiui a auai?a
iaaeaeo yoie e iaeeaeaaiie noiiaie, o.a. ?eneiaie aaee/eiie E-iai
iioiea. A?aoe/anee ?ene au?aaeaaony ii e?eaui aac?acee/iinoe
(eiaeaoa?aioiinoe).

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iaoiaeeii n?aaieoue ?enee. E?eaay aac?acee/ey iieacuaaao, /oi aeey iaai
iaeeiaeiai i?eaieei ethaie ec aa?eaioia: iieo/aiea 10 iei. iaaa?iyea,
eee iieo/aiea 20 iei. n aa?iyoiinoueth 50%.

Oeiu e?eauo aac?acee/ey:

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4D0E04904D1504904D1404904D0C04904D0604904DFB03904DFF03904D0704904D190490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· AA – eiaanoi? aac?acee/ai e ?eneo

· AB – aic?anoaao iai?eyoea e ?eneo. Oaii i?e?inoa o?aaeaiiai aeiciaea
iia?aaeaao oaii i?e?inoa ?enea, o. a. iacia/eoaeueiia iiauoaiea ?enea
i?aaeiieaaaao nouanoaaiiia iiauoaiea aeioiaea.

· AC – oauathuaa iai?eyoea ?enea, o.a. i?eiaaeeaaeeo ?eneiaaiiiio
eiaanoi?o

· AD – iaeciaiiia iai?eyoea ?enea

Ia i?aeoeea ioiioaiea e ?eneo iienuaaaony e?eaie AA.

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6B6F2044726177696E672C4D3230302C5832362C592D38313134322C2C04000000030108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?
eiaao iioeeii n aeioiaeii 5.000 eee 7.000 ?oa. n aa?iyoiinoueth 0.5.
Oeaia eiio?aeoa 6.000. Aeaiiue eiio?aeo ?eneiaue. Ioiioaiea eiaanoi?a e
?eneo iienuaaaony e?eaie aac?acee/ey. Iaeeaeaaiay iieaciinoue
iaoiaeeony:

Ul=Ua*0,5+0,5*Ub. Anee eiaanoi? niaeaneony n iieoieie, oi iaeeaeaaiay
iieaciinoue Ul a ii?aaeaeaiiie noaiaie aeieaeia oa?aeoa?eciaaoueny
i?aeeiaoie oi/ee I, iaoiaeyuayny ia ia?ana/aiee. I?eia?aoaiea eiio?aeoa
ia i/aiue aaaiaeii, o.e. Um>Ul. Eiaanoeoeey aeieaeia auoue oaeiaie,
/oiau aa iieaciinoue niaiaaeaea n iieaciinoue aeioiaea. Aaee/eia
aac?eneiaiai yeaeaaeaioa caaeneo io aeaoo oaeoi?ia: noaiaie auioeeinoe
e?eaie e ?eneiaanoe iaeeaeaaiiai
aeioiaea.wmetafile80100090000035F000000020015000000000004000000030108000
50000000B0200000000050000000C0206000500070000001004010001000100010005000
00002010100000008000000FA0200000400000000000000040000002D010000080000002
5030200040002000500040008000000FA0200000000000000000000040000002D0101000
4000000F00100001500000026060F0020005461696B6F2054657874496E6B2C4D3230302
C5633372C50302C55302C54302C030000000000

I?aeou A e A eiatho iaeeiaeiao i?iaeieaeeoaeueiinoue ?aaeecioeee – 4
aiaea e eiatho iaeeiaeiaoth oeaio ?aaeecaoeee – 10%.

Eiaanoeoeee ii i?iaeoo A – 42 iei., a ii A – 35 iei.

Aiaeec i?iaeoia a oneiaeyo ?enea

Pk-aeaiaaeiue iioie

Ie-iiieaeathuee eiyooeoeeaio

OPk- ioei??aeoe?iaaiiue aeaiaaeiue iioie

AIAe A A

Pk Ie IPk Pk Ie OPk

1 20 0,9 18 15 0,9 13,5

2 20 0,9 18 20 0,75 15

3 15 0,8 12 20 0,75 15

4 15 0,75 10,5 10 0,6 6

IC -42 -42 -42 -35 -35 -35

NPV 20,5 10,5 22,9 9,4

N?aaiaiea iieacuaaao, /oi ii NPV A i?aaeii/oeoaeueiaa, /ai o A. Ii anee
o/anoue ?ene, annioeee?othueeny n eaaeaeui i?iaeoii, oi noaeaeaiea ?acei
eciaieoueny, e i?aaeii/oeoaeueiaa noaiao i?iaeo A.

———————–

Iii?aaea ia ?ene eiyooeoeeaioa aeeneiioe?iaaiey.

———————–

Aeaiiay iaoiaeeea ia i?aaeiieaaaao ei??aeoe?iaee yeaiaioa aeaiaaeiiai
iioiea. Caeanue aaiaeeony eeoue iii?aaea e eiyooeoeeaioo
aeeneiioe?iaaiey.

—–

I?iione – 1 eaeoeey

—–

Athaeaeao eaieoaeueiuo aeiaeaiee. Oi?ie?iaaiea athaeaeaoa.

——————————-

Aeaaiay caaea/a: ioai? e ?aaeecaoeey i?iaeoa inouanoaeyaony a ?aieao
athaeaeaoa. I?e ?ac?aaioea i?iaeoa iaiaoiaeeii o/eouaaoue ?/ae
eiie?aoiuo enoiaeiuo i?aaeiinueie:

· I?iaeou eiaeo auoue aeueoa?iaoeaiuie e iacaaeneiuie

· Aeeth/aiea i/a?aaeiiai i?iaeoa a athaeaeao i?aae?ieaaaao iaoiaeaeaiea
enoi/ieea aai oeiaine?iaaiey

· Oeaia eaieoaea, eniieuecoaiay aeey ioeaiee i?iaeoa ia i?aaeiao eo
aeeth/aiey a athaeaeao ia iaycaoaeueii aeieaeia auoue iaeeiaaiaie aeey
anao i?iaeoia ii?ooaey, o.a. iia iiaeao iaiyoueny, a caaeneiinoe io
noaiaie ?enea, aaia?e?oaiiai oai eee eiui i?iaeoii

· N ?inoii iauaia eaieoaeueiuo aeiaeaiee, oeaia eaieoaea oaaee/eaaaony e
iiyoiio /enei i?aeo?a, i?eieiaaiuo e oeiaine?iaaieth ia iiaeao auoue
aaneiia/ii aieueoei

· Nouanoaoao ?yae ia?aie/aiee ii ?ano?niui e a?aiaiiui ia?aiao?ai,
eioi?ua neaaeoao oneouaaoue i?e ?ac?aaioea i?iaeoa

Ia i?aeoeea eniieuecotho 2 iiaeoiaea e oi?ie?iaaieth athaeaeaoa:

· ia i?eiaiaiee e?eoa?ey IRR

Ana aeinooiiua i?iaeou oii?yaei/eaathony ii IRR, i?iaiaeeony eo
iineaaeiaaoaeueiue i?iniio?. I/a?aaeiie i?iaeo, IRR eioi?iai
i?aainoiaeeo oeaio eaieoaeaTH. Ioae?aaony aeey ?aaeecaoeee. Aeeth/aiea
i?iaeoa a ii?ooaeue o?aaoao i?eaea/aiey iiauo enoi/ieeia, a oae eae
aeciiaeiiioe oe?iu ii iiaeeecaoeee nianoaaiiuo n?aaenoa ia?aie/aiu,
ia?aueaaiea ii?ooaey i?eaiaeeo e oaaee/aieth noieiinoe eaieoaea
(aic?anoaao oeiainiaue ?ene). Caeanue iaeeoei i?eiaiaiea 2-oo
oaiaeaioeee: iiieii ?anoe?aiey ii?ooaey eiaanoeoeee, aioo?aiiyy ii?ia
iaaeaao, a oaia eaieoaeae?anoao. I/aaeaeii, /oi anee /enei i?iaeoia
eaiaeeaeaoa ia aeeth/aiea a ii?ouaeue aaeeei, oi ianooiaao iiiaio,
eiaaea aioo?aiiy/ ii?ia ?aioaaaeueiinoe aoaeao iaiueoa oeaiu eaieoaea e
aeeth/aiea neaaeothuaai i?iaeoa a ii?ooaeue ia oeaeaniia?acii. Oieueei
iinea eiiieaeoaoeee ii?ooaey ia iniiaa IRR n iaeiia?aiaiiuiien/eneaieai
i?aaeaeueiie oeaiu eaieoaea, noaiiaeony aiciiaeiui ?ann/eoaoue noiia?iue
NPV, aaia?e?oaiue aeaiiui ii?ooaeai.

·
wmetafile80100090000033200000000001300000000001300000026060f001b00546169
6b6f20496e6b53706163652c5330303130302c55302c5430000400000003010800050000
000b0200000000050000000c025d006f0005000000020101000000030000000000wmetaf
ile80100090000033200000000001300000000001300000026060f001b005461696b6f20
496e6b53706163652c5330303130302c55302c5430000400000003010800050000000b02
00000000050000000c025d006f0005000000020101000000030000000000ia
i?eiaiaiee e?eoa?ey NPV

Anee iao ia?aie/aiee, oi a iaeaieaa iauai aeaea iaoiaeeea
athaeaeaoe?iaaiey aeeth/aao i?ioeaaeo?u: onoaiaaeeaaaony cia/aiea
eiyooeoeeaioa aeeneiioe?iaaiey: eee iauaa cia/aiea aeey anao i?iaeoia
eee eiaeeaeaeoaeueiia ii anai i?iaeoai, a caaeneiinoe io enoinieea
oeiaine?iaaiey. Ec aeueoa?iaoeaiuo i?iaeoia auae?aaony i?iaeo n
iaeneiaeueiui NPV. I?e aaaaeaiee ia?aie/aiee ii oeaia eie n?ieai
iaoiaeeea oneiaeiyaony, oae eae aecieeaao iaiaoiaeeiiioue iioeiecaoeee
athaeaeaoa.

—————

Iioeiecaoeey athaeaeaoa eaieoaeueiuo aeiaeaiee.

—————

Anee nouanoaotho ia?aie/aiey ii oeiainiaui ?ano?nai, oi neaaeoao
ioia?aoue oaeea i?iaeou, /oi au iieo/eoue iaeaieueooth auaiaeo io
eiaanoe?iaaiey, a /anoiinoe /a?ac oi?ie?iaaiea oeaeaaie onoaiiaee ia
iaeneiecaoeeth noiia?iiai NPV. Oeiiaua neooaoeee, o?aaothuea
iioeiecaoeee eiaanoeoeee:

· I?ino?ainoaaiiay iioeiecaoeey. Iauay noiia oeiainiauo ?ano?nia ia aiae
ia?aie/aia naa?oo, eiaaony ianeieueei iacaaeneiuo i?iaeoia n noiia?iuie
eiaanoeoeeyie, i?aauoathuea eiathueany ?ano?nu; iaiaoiaeeii ninoaaeoue
ii?ooaeue, iioeiece?othuee noiia?iue aiciiaeiue i?e?ino eaieoaea. Anee
aa?eaioia iiiai, oi ia?aai? aa?eaioia ia i?aaeiao niioaaonoaey
ia?aie/aieyi – yoi i/aiue neiaeii. A caaeneiinoe io oiai, iiaeaeathony
ee ae?iaeaieth aa?eaiou eee iao, oi aiciiaeii ?aceiaeaiea caaea/:

?anniao?eaaaiua i?iaeou iiaeaeathony ae?iaeaieth:

Iiaeii ?aaeeciauaaoue /anoue i?iaeoia, i?e yoii e ?anniio?aieth aa?aony
niioaaonoaothuay aeiey eiaanoeoeee e aeaiaaeiuo iinooieaiee. A yoii
neo/aa iauai eiaanoeoeee a ioiioaiee aeaiiiai i?iaeoa iiaeao auoue
neieue oaiaeii iaeui. Iaeneiaeueiue noiia?iue yooaeo aeinoeaaaony i?e
iaeaieueoae yooaeoeaiinoe eniieueciaaiey aeiaeaiiuo n?aaenoa, o.a. ?a/ue
eaeao i iaeneiecaoeee ioaea/e ia aeiaeaiiue eaieoae.
Iineaaeiaaoaeueiinoue aeaenoaee:

1. ?ann/eouaaaony eiaeaen ?aioaaaeueiinoe = i?eaaaeaiiue aeaiaaeaue
iioie iinooieaiee / iooiea

2. I?iaeou oii?yaeu/eaathony ii oauaaieth eiaanoeoeee

3. A ii?ooaeue eiaanoeoeee aeeth/athony ia?aua E-i?iaeoia, eioi?ua a
noiia iiaoo auoue i?ioeiaine?iaiiu eiiia?/aneie i?aaiecaoeeae.
I/a?aaeiie i?iaeo aa?aony a aai /anoe, eioi?ay iiaeao auoue
i?ioeiaine?iaaia (inoaoi/iue i?eioeei).

I?eia?:

Aa?eaio A

eiaanoeoeee aei 55.000.000 (i?ieiaanoe?iaaii 30.000.000, aeioiaeu – 6 11
13 e 12 aaeaaiaeii)

NN – 10%

A – aei 90.000.000 (4 8 12 5) npv=2,68 pi= irr=15,6%

N – (12 15 15 15) npv=4,82 pi=1,121 irr=15,3%

D – (4 5 6 e 5) npv=1,37 pi=1,091 irr 13,9%

?ann/eoaoue NPV e IRR e eiaeaenu ?aioaaaeueiinoe eaaeaeiai i?iaeoa

Ii oauaaieth PI oii?yaei/eaathony:

Aa?eaio A

Eiaanoe?iaaiea aei 55.000.000

Aiciiaeiua ni/aoaiey:

A e A: 50.000.000, npv=5,19

A e D: 45.000.000, npv=3,88

B e D: 35.000.000, npv=4,38

C e D: 55.000.000, npv=6,19

· A?aiaiiay iioeiecaoeey

Iauay noiia ?aio?nia, aeinooiiay aeey oeiaine?iaaiey, ia?aie/aia naa?oo.
Eiathony ianeieueei aeinooiiuo iacaaeneiuo i?iaeoia, eioi?ua aaeaeo
ia?aie/aiiinoe ?ano?nia, iiaoo auoue ?aaeeciaaiu a ieaie?oaiii aiaeo
iaeiia?aiaiii, a aneaaeothuai aiaeo inoaaoeany i?iaeou eee eo /anoe
iiaoo auoue ?aaeeciaaiu. O?aaoaony iioeiaeueii ?ani?aaeaeeoue i?iaeou ii
aeaoi aiaeai. A iniiaa iaoiaeeee ninoaaeaiey iioeiaeueiiai ii?ooaey
caeeaaeuaaaony neaaeothuay eaeay: ii eaaeaeiio i?iaeoo ?ann/eouaaaony
niaoeeaeueiue eiaeaen, iieacuaathuee ioiineoaeueioth iioa?th NPV, anie
i?iaeo aoaeao ion?i/ai e eniieiaieth ia 1 aiae. I?iaeou n ieieiaeueiuie
cia/aieyie eiaeaena iiaoo auoue ioeiaeaiu ia neaaeothuee aiae.
Eeth/aaoth ?ieue ea?aao PI. A oneiaeyo i?aaeuaeouaai i?eia?a,
iaiaoiaeeii ninoaaeoue ii?ooaeue ia aeaa aiaea a oii neo/aa, anee iauai
eiaanoeoeee ia ieaie?oaiue aiae aoaeao ia?aie/ai 70.000.000. Iioa?e NPV
ninoaayo:

NPV1 – NPV a ia?aii aiaeo

DM – aeeneiioe?othuea iiiaeeoaeue

NPV0 – NPV a ioeaaii aiaeo

PNPV – iioa?e NPV

OI – aaee/eia ioeiaeaiiuo eiaanoeoeee

IP – eiaeaen aiciiaeiuo iioa?ue

I NPV1 DM NPV0 PNPV OI IP

A 2,61 0,9091 2,28 0,23 30 0,0077

B 2,58 0,9091 2,44 0,24 20 0,120

C 4,82 0,9091 4,38 0,44 40 0,011

D 1,37 0,9091 1,25 0,12 15 0,008

IP iieacuaaao /aio ?aaia aaee/eia ioiineoaeueiuo iioa?ue a neo/aa
ioeeaaeuaaiey i?iaeoa e eniieiaieth ia 1 aiae. Ec ?an/aoa aeaeii, /oi
iaeiaiueoea iioa?e aoaeoo i?e ioeiaeaiee i?iaeoa A, caoai D, C e A.

I E *E NPV

Eiaanoeoeee a 0 aiaeo:

B 20 100 2,68

C 40 100 4,82

D 10 67 0,92

Eoia: 70 8,42

Eiaanoeoeee a 1 aiaeo:

D 5 33 0,41

A 30 100 2,28

Eoia: 35 2,69

Eoiai: 11,11

Iauea iioa?e: 0,27 – min

———-

Iioeiecaoeey a oneiaeyo ?aeiaanoe?iaaiey aeioiaea.

———-

Ana aeioiaeu io aeiiieieoaeueiuo i?iaeoia iiaoo auoue eniieueciaaiu aeey
oeaeae eiaanoe?iaaiey. Ia iiiaio aiaeeca aeinooiiu neaaeothuea i?iaeou:

A -20 25 7

B -15 4 30

C -5 8 8

D — -45 69

CC – 12%

Ia?aae ninoaaeaieai ii?ooaey iaiaoiaeeii ?ann/eoaoue NPV e PI aeey
eaaeaeiai i?iaeoa i?e CC=12%

I NPV PI

A 7,9 1,4

B 12,5 1,83

C 8,5 2,7

D 15,6 1,37

PI ?ann/eouaaaony ia eiiaoe aiaea 0 n o/aoii iooieia e i?eoieia.

Iauai eaieoaeueiuo aeiaeai e ia?aie/ai a 0 aiaeo 20.000.000, oi anoaao
auai?: i?eiyoue i?iaeo A eee eiiaeiaoeeth B e C. N ioeaiee PI, oi B e C
aieaa auaiaeiu.

————-

Aa?iyoiinoiay iiaeaeue ?uiea

————-

Eiaanoi? ?aaeecoao ana aeoeau ii?ooaey (i?aa?auaao ii?ooaeue a
ia/aeueioth oi?io). ?aaeecaoeeiiiay noieiinoue ii?ooaey – W1. Iieoiea e
?aaeecaoeey inouanoaeythony ii ?uii/iui oeaiai. Eiaanoi? aeaeaao
iaeneiece?iaaoue eiia/ioth noieiinoue eiaanoe?iaaiiiai eaieoaea, noi
?aaiineeueii iaeneiecaoeee aeioiaeiinoe R x P. I?ioeann eiaanoe?iaaiey
noaeeeaaaony n o?oaeiinoyie aaeaeo iaii?aaeaeaiiinoe oeai e
?aaeeciaaiiuo aiciiaeiinoae. Naiia nouanoaaiiia, oi /oi ninoiyiea
ii?aaeaeyao oeaiu e aeioiaeiinoue aeoeaia ia aeaiiii ?uiea. Ninoiyiea
?uiea eciaiyaony ia ii?aaeaeaiiui ia?acii e eiaanoi? ia iiaeao oi/ii
i?aaenoaaeoue aoaeou a oeaiu e aeioiaeiinoe, oai ia iaiaa, ia iniiaa
?ao?iniaeoeaiie eioi?iaoeee, ii iia au caiaoeoue, /oi yoe eciaiaiey
iiaoi?ythony n ii?aaeaeaiiie /anoioie. Eiaanoi? caia/aao, oae eae
ninoiyiea iiaoi?yaony n ii?aaeaeiiiie /anoioie, iiaeii noi?ie?iaaoue
aa?iyoiinoioth iiaeaeue eiaanoeoeeiiiiai ?uiea. Aeaiioth iiaeaeue iiaeii
iienaoue neaaeothuei ia?acii: eiaaony iaeioi?ue ?uiie aeoeaia. Eeann
yoeo aeoeaia – A, ioaeaeueiue aeoea – a1, a2, a3, … an. Eeann
iaaiciiaeiuo ninoiyiee – S. Eaaeaeiio ninoiyieth i?eieoai ninoiyiea:
P(S)>0. Sum P(S)=1.

A iiaeaee Ia?eiaeoea yoi aeaeaaony neaaeothuei ia?acii:

Aeoeao A noaaeony a niioaaonoaea neo/aeiay aaeeneia R, eioi?ay
iieacuaaao aeioiaeiinoue A aeey aua?aiiiai eiaanoeoeeiiiiai ai?eciioa O.
Cia/aiea aeioiaeiinoe – r. Yoi cia/aiea eiaanoi? iiaeao au/enaeeoue ii
enoa/aiee eiaanoeoeeiiiiai ia?eiaea. Neo/aeiay aaee/eia – ooieoeey,
ii?aaeaeaiiay a i?ino?ainoaa. Nia?aiaiiia iaicia/aiea: Ra/S-R eee
ra=Ra(S). ?ani?aaeaeaiea aeey aeene?aoiie, o.a. i?eieiathuae eiie?aoiia
cia/aiea aeene?eoiie aaee/eiu, no?ieony neaaeothuei ia?acii:

· ia?a/eneaiea anao aiciiaeiuo cia/aiee

· Aeey eaaeaeiai rk i?e e=1…m ii?aaeaeytho aa?iyoiinoiia cia/aiea

?ani?aaeaeaiea aeene?aoiie neo/aeiie aaee/eiu iiaeii au?aceoue
oaaeeoeae.

—————-

!!! I?IIONE !!! (iaaeiaei ienaoue)

—————-

?ani?aaeaeaiea yaeyaony ooieoeeae. iuIaiin?aaenoaaiiia eniieueciaaiea
oaaeeoe i?e aieueoai eiee/anoaa aeoeaia cao?oaeieoaeueii. Ia i?aeoeea
aianoi ?ani?aaeaeaiee eniieuecothony ea/anoaaiiua oa?aeoa?enoeee
aaee/ei: aeenia?ney, noaiaea?oiia ioeeiiaiea e o.ae. R i?eieiaaony eae
neo/aeiay aaee/eia.

Eiaanoi?o aeinooiai ia aanue ?uiie, a aeinooiia oieueei aai /anoue,
aeeth/athuay aeoeau A2 e A3. Iiyoiio iaeuecy caauaaoue, /oi iu auae?aai
iaeeo/oee aeoea ii aeaoi e?eoa?eyi. A2 iaeaaeaao aieaa aunieie
aeioiaeiinoueth, ii e iaeaaeaao aieueoei ?eneii. I?aaeiieiaeei, /oi
eiaanoi?a oaeiaeaoai?yao aeioiaeiinoue io 2,5 aei 10%%. Ii ia ono?aeaaao
oaeie ?ene ii yoei aeoeaai. Eiaanoi? aianoi iaeiiai aeoeaa aoaeao
oi?ie?iaaoue ii?ooaeue. Yoa oa?aeoa?enoeea ii?aaeaeyaony neaaeothuei
ia?acii:

cov(R1,R2) =

= SUM(R1(S)-MR2) x (R2(S)-MR2) x P(S). Aeey auaeaeaiey ia?u nayce
iaaeaeo neo/aeiuie
aaee/eiaie,i?eaaaathoeii?ie?iaaietheiaa?eaoeee.Oaeayii?ie?iaaiiayaaee/ei
aiacuaaaony eiyooeoeeaioii ei??aeyoeee.

cor(R1,R2)=cov(R1,R2) / DR1,DR2

— I ? I I O N E E A E Oe E E —

Iaoiaeu ioeaiee iaaeaeaeeiinoe

1. Iaoiae eaieoaeecaoeee. Eniieuecoaony oieueei i?e aeioiaeiie
iaaeaeaeeiinoe. Aeioiaeu io aeaaeaiey iaaeaeaeeiinoueth iiaoo iinooiaoue
a aeaea oaeoueo e aoaeoueo aeaiaaeiuo iinooieaiee, ia?eiaee/aneeo
ieaoaaeae, oaeouae e aoaeouae yeiiiiee ia iaeiaao, i?e?anoa noieiinoe
iaaeaeaeeiinoe, iieo/aiiuo i?e aa i?iaeaaea a aoaeouai eee caeiaa iiae
eiioa/iue e?aaeeo, a aeaea iaeiaiauo naa?aaeaiee io i?iaeaaee, iaiaia
eee aea?aiey yoiai eiouanoaa a aoaeouai. Iaoiae iniiauaaaony ia o?ao
i?eioeeiao ioeaiee iaaeaeaeeiinoe:

· Iaeeaeaiey. Oa?aeoa?ecoao oi/eo c?aiey iieoiaoaey ia aoaeouaa e
ianoiyuoth noieiinoue. ?uii/iay noieiinoue- oaeouay noieiinoue aoaeoueo
auaiae, auoaeathueo ec i?aa aeaaeaiey eee ae?oaeo i?aa.

· Ni?ina e i?aaeeiaeaiey. oa?aeoa?ecoao oi/eo c?aiey ?uiea ia noieiinoue
iaiaia. Enoiaey ec yoiai, iiaeii ii?aaeaeeoue eae naie iioiee aeaiaaeiuo
n?aaenoa e ec ioiioaiea e noieiinoe oae e oaiaeaioeee eo eciaiaiey.

· Caiauaiey. Oa?aeoa?ecoao oi/eo c?aiey eioi?ie?iaaiiiai iieoiaoaey,
eioi?ue caieaoeo ca iauaeo noiio, aieueooth noieiinoe aiaeiae/iiai
iauaeoa iaeeiaeiaie iieaciinoe ia oii aea neaiaioa ?uiea e eioi?ua i?e
i?iaiica aoaeoueo aeioiaeia i?eaioe?oaony ia aeaiiua aiaeeca
niioaaonoaothueo iieoiaoaeae aiaeiae/iuo iauaeoia.

Enoiaey ec yoiai, ii?ia i?eauee, a?aiaeiay ieaoa e o.ae. ii?aaeaeythony
aiaeiae/iuie iieacaoaeyie ia ?uiea.

Iaoiaeu ia?aaiaea aeioiaea a noieiinoue:

· Iaoiae i?yiie eaieoaeecaoeee. Iniiaai ia eniieueciaaiee noaaee
eaieoaeecaoeee

Iniiaiua yoaiu:

1. Ioeaiea iioaioeeaeueiiai aaeiaiai aeioiaea

IAAe – aeioiae, eioi?ue iiaeii iieo/eoue io iaaeaeaeeiinoe i?e 100%
ooieoeeiie?iaaiee aac anao iioa?ue e ?anoiaeia. Caaeneo io ieiuaaee e
a?aiaeiie noaaee ca 1 i2 (eo i?iecaaaeaiea).

2. Ioeaiea iioa?ue io iaoieao e iaaeia?oaeaiiinoe iauaeoa.

I?iaiaeeony ia iniiaa aiaeeca ?uiea, oa?aeoa?a aai aeeiaieee,
i?eiaieoaeueii e iaaeaeaeeiinoe. III=IAAe-Neeaeee ia iaieaoaaee e
iaaeia?ocu.

3. ?an/ao ecaea?aeae ia yenieoaoaoeeth. I?e yoii en?ieuecoaony
?ao?iniaeoeaiue aiaeec e i?iaiiciue aeioiae. Eniieuecotho eioi?iaoeeth
aei e iinea iaeiaiiaeiaeaiey. Aaeeinoaaiiia oneiaea – iioieeeaeaiaaeiuo
n?aaenoa aeey ?acee/iuo iauaeoia iaiaoiaeeii ?ann/eouaaoue ia iaeiie
iniiaa, o.a. iaeuecy n?aaieaaoue aeioiaeu io ?ao?iniaeoeaiuo aeaiiuo n
i?iaiiciuie. Oaeaea iaaei n?aaieaaoue i?iaiicu ?anoiaeia. Ia?eiaee/aneea
?anoiaeu, iaania/eaathuea ii?iaeueioth ?aaioo iauaeoa – iia?aoeeiiiua
?anoiaeu (oneiaii iinoiyiiua, oneiaii ia?aiaiiua e ?anoiaeu ia caiauaiea
– eiatho ianoi 1 eee 2 ?aca ca ianeieueei eao e na?ueacii aa?uee?othony
ec aiaea a aiae. Iau/ii yoi ?anoiaeu ia ia?eiaee/aneoth caiaio auno?i
eciaoeaathueony eiiiaiaioia oeo/oaiey). Anee a ia?eiae n?iea aeaaeaiey
caiaia ia i?aaeoniao?eaaaony, oi ?anoiaeu ia o/eouaathony, ii
iaiaoiaeeii o/anoue eciin io ?aaa?nee (ia?ai?iaeaaee).

4. Ii?aaeaeaiea eoiaiaiai iieacaoaey aeioiaeia aeaiaaeiuo n?aaenoa
(/enoiai iia?aoeeiiiiai aeioiaea). Ia?an/eouaaaony aioaeouoth noieiinoue
iaoaeoa ianeieueeeie niiniaaie e auai? niiniaa caaeneo io
ea/anoaaieioi?iaoeee ia ?uiea. *IAe – aeaenoaeoaeueiue aaeiaie aeioiae
ca au/aoii anao ?anoiaeia, e?iia iaeiaia, aii?oecaoeee e aeieaia ii
e?aaeeoai.

5. Ii?aaeaeaiea eiyooeoeeaioa eaieoaeecaoeee R. Aeeth/aao aeioiae ia
eaieoae (eiiiainaoeey eiaanoi?o, eioi?ay aeieaeia auoue aio auiea/aia n
o/aoii oaeoi?a a?aiaie, ?enea e o.ae.) e aica?ao eaieoaea (iiaaoaiea
noiiu ia/aeueiiai aeiaeaiey). R o/eouaaao eiiiainaoeee ca aac?eneiaua
iaeeeaeaeiua eiaanoeoeee, ca ?ene, ca ieceoth eeeaeaeiinoue, ca
iaiaaeaeiaio e iii?aaeo ia ei??aeoe?iaeo noieiinoe iaaeaeaeeiinoe.
Niiniau ii?aaeaeaiey R:

· Iaoiae ?uii/iie auaeeiee. Iaeaieaa i?inoie, auno?ue e oi/iue aeey
iaaeaeaeeiinoe ii aeaiiui ia eiie?aoiii neaiaioa ii niiinoaaeiui
i?iaeaaeai, aiaeiae/iui ii naiei oa?aeoa?enoeeai e iieaciinoe iauaeoia
iaaeaeaeeiinoe. Oa?aeoa?enoeee: iioeaaoeey, ieaoaaeaniinieiinoue,
eiaanoeoeee e o.ae. Noieiinoue = *enoue iia?aoeeiiiue aeioiae /
Eiyooeoeeaio eaieoaeecaoeee. I?e i?aia?aciaaiee /enoiai iia?aoeeiiiiai
aeioiaea a noieiinoue, oi R = *IAe / Noieiinoue. Aeey aieaa oi/iiai
?an/aoa iaiaoiaeeii eniieueciaaoue aieueoa aeaiiuo. Noieiinoue = *AAe o
Ioeueoeieeeaoi?. Ioeueoeieeeaoi? = Oeaia i?iaeaae / *IAe

· Iaoiae eiiioeyoeaiiai iino?iaiey (noiie?iaaiey). Aeaeeo noaaeo ia
/anoe: i?iaeoiay noaaea (a %) e noaaea aica?aoa eaieoaea. I?iaeoiay
noaaea aeaeeony ia: aac?eneiaay, ia aeiiieieoaeueiue ?ene, eiiiainaoeey
ca ieceoth eeeaeaeiinoue, eiiiainaoeey ca iaiaaeaeiaio, iii?aaea ia
iiauoaiea (nieaeaiea) iaaeaeaeeiinoe. Aac?eneiaay noaaea – aaciaay, e
eioi?ie aeiaaaeythony inoaeueiua ninoaaeythuea. A neo/aa eniieueciaaiey
n?aaeiaaa?iiaeneeo iieacaoaeae, e aac?eneiaie noaaea i?eaaaeyaony i?aiey
ca ?ene eiaanoe?iaaiey (no?aiiaie ?ene). A ?O aa?oony ec noaaie ii
aeaiiceoai aunieiiaaeaaeiuo aaieia. Aac?eneiaay noaaea ii?aaeaeyao
ieieiaeueioth noaaeo ca eiaanoe?iaaiiue eaieoae n o/aoii oaeoi?a
a?aiaie. Iaaeaeaeeiinoue ieceieeeaeaeia e iii?aaea iaeiaeeeaeaeiinoue –
iii?aaea ia aeeeoaeueioth yenieoaoaoeeth i?e i?iaeaaea iauaeoa eee
iii?aaea ia a?aiy ii iieneo iiaiai a?aiaeaoi?a. Eiiiainaoeey ca
iaiaaeaeiaio – /ai ?eneiaaiiaa e neiaeiaa eiaanoeoeee oai aieaa
eiiiaoaioiiai o?iaiy oi?aaeaiey iie o?aaotho. Iaeuecy iooaoue n
oi?aaeaieai iaaeaeaeeiinoe. Noaaea aiciauaiey eaieoaea = 1 / *enei eao
aeey aica?aoa aeiaeaiiiai eaieoaea.

· Iaoiae naycaiiuo eiaanoeoeee

Aieueoeinoai iaaeaeaeeiinoe iieoiaaony n iiiiuueth caaiiiai eee
nianoaaiiiai eaieoaea. E?aaeeoi?u aeieaeiu i?aaeoniao?eaaoue iieo/aiea
eiieo?aioiie noaaee, niecia?eiie n i?aaeiieaaaaiui ?eneii eaieoaeueiuo
aeiaeaiee, eia/a e?aaeeoi? ia aeano aeaiaa. Eiaanoi?u nianoaaiiiai
eaieoaea aeieaeiu i?aaeiieaaaoue iieo/aiea eiieo?aioiuo aeioiaeia ia
aeiaeaiiua n?aaenoaa, niecia?eiua n iaeeaeaaiui ?eneii. Noaaea
eaieoaeecaoeee ia caaiiua n?aaenoaa iacuaaaony eiioa/iie iinoiyiiie =
Aaeaaiaeiua auieaou ia ianeoaeeaaiea aeieaa / Iniiaiay noiia eiioa/iie
nnoaeu. EI – ooieoeey i?ioeaioiie noaaee. Eiaaea oneiaey e?aaeeoa
ecaanoiu, oi EI ii?aaeaeytho ii oeiainiaui oaaeeoeai (EI=Noaaea
i?ioeaioa+Eiyooeoeeaio oiiaea iiaaoaiey). Noaaea, eniieuecoaiay aeey
eaieoaeecaoeee aeioiaea ii?aaeaeyaony: NE = Aeaiaaeiua iinooieaiey aei
au/aoa iaeiaa / Noiia aeiaeaiee nianoaaiiuo n?aaenoa. NE ni/aoaao a naaa
aica?ao aeiaeaiiiai eaieoaea. Iauay noaaea eaieoaeecaoeee aeieaeia
oaeiaeaoai?youe ii?aaeaeaiiiio o?iaith eiioa/iie iinoiyiiie aeey
e?aaeeoi?a e i?eoiea aeioiaea aeey eiaanoi?a nianoaaiiiai eaieoaea.
E?aaeeoiay eee aeieaiaay aeiey a noiia?iuo eiaanoeoeeyo a
iaaeaeaeeiinoue = Aaee/eia e?aaeeoa / Noieiinoue iaaeaeaeeiinoe. Aeiey
nianoaaiiiai eaieoaea = 1 – E?aaeeoiay aeiey eiaanoeoeee a
iaaeaeaeeiinoue. I?e ecaanoiie eiioa/iie iinoiyiiie (Ec) e noaaea
Eaieoaeecaoeee aeioiaea ia nianoaaiiue eaieoae (Rc), oi R=Ec o Ie? +
Rc(1-Ie?). Ie? iieo/atho ia iniiaa aeaiiuo ii niiinoaaeiui i?iaeaaeai e
?ann/eouaatho: Rc= Aeaiaaeiua iinooieaiey aei iaeiaiiaeiaeaiey /
Nianoaaiiue eaieoae. Acaaoaiiua noaaee iiaoo auoue ?ann/eoaiu i?e
oneiaee iieo/aiey oi/iuo noaaie aeey eaaeaeiai ec eiiiaiaioia e aeiee eo
aeeaaea. Oiaaea R=L x R1 + B x R2. Ia o/eouaaao nieaeaiea e iiauoaiea
noieiinoe eiouanoaa a oa/aiea ia?eiaea.

· Iaoiae eiaanoeoeeiiiie a?oiiu

·

· iaoiae Yeaoaea.

R = Rc x Mk? x C + Dep -app x SFF

C=Y+P x SFF – Ra

Rc – noaaea aeioiaea ia nianoaaiiue eaieoae

Ie? – ioiioaiea aaee/eiu eiioa/iiai e?aaeeoa e noieiinoe (eiioa/iay
aeiey a noiia?iii eaieoaea)

N – Eiioa/iue eiyooeoeeaio

Dep – Oiaiueoaiea noieiinoe eiouanoaa ca i?iaiice?oaiue ia?eiae

App – iiauoaiea noieiinoe eiouanoaa ca i?iaiice?oaiue ia?eiae

SFF – Eiyooeoeeaio oiiaea iiaaoaiey ii niioaaonoaothuae noaaea Y aeey
i?iaiice?oaiiai ia?eiaea

P – noaaea aeey ia?eiaea aeaaeaiey

SFF – *anoue eiioa/iiai e?aaeeoa, eioi?ay aoaeao iiaaoaia a
i?iaiice?oaiii ia?eiaea

Ra – Eiioa/iay iinoiyiiay

Iaoiae iiaeao auoue ?anniio?ai a aeaea aeai?eoia:

1. Niae?aaony eioi?iaoeey ia ioeaieaaaiii eiouanoaa. Ii?aaeaeyaony Rc=
?aaeueiue aeioiae ia eaieoaeueiua aeiaeaiey, eioi?ue eiaanoi? iaeeaeaao
iieo/eoue ca aanue ia?eiae aeaaeaiey eiouanoaii. Aeeth/aao i?eauee io
i?iaeaae e oauoee.

2. ?anniio?aiea Ie?. A Mkp ia ?anniao?eaathony eueaioiua oneiaey
e?aaeeoiaaiey.

3. Ii?aaeaeaiea oeie/iinoeeoneiaee e?aaeeoa e noaaee ii iaio. Ioiioaiea
eiaanoi?a e noaaea i?iaiice?oaii. Anee i?iaiic naeaeaoue iaeuecy, oi
iaeuecy i?eiaiyoue aeaiiue iaoiae.

4. Ai?eciio ?an/aoa. Neaaeoao ii?aaeaeeoue n?ie eniieueciaaiey
eiouanoaa. I?e ?ann/aoa N n iiiiuueth oaaeeoe Yeaoaea, a ea/anoaa
oeie/iiai ia?eiaea aeaaeaiey iaaeaeaeeiinoueth aiciiaeai auai?: 5, 10,
15 e 20 eao.

5. A??. Aieueooinoai eiaanoi?ia n/eoatho, /oi noieiinoue eiouanoaa
aoaeao ?anoe.

6. SFF. Ii?aaeaeyaony a oaaeeoeao Yeaoaea e oaeoe/anee ?anniao?eaaaony a
oaaeeoea “6 ooieoeeyo aeaiaa”.

O/ao aiciauaiey eaieoaeueiuc cao?ao a eiyooeoeeaioa eaieoaeecaoeee – R.

Iioiee aeioiaea ia eiaanoeoeee, iinooieaiey eioi?uo i?iaiice?othony
?aaiuie aeieyie a oa/aiee iaia?aie/aiiiai n?iea, a oaeaea anee ia
i?iaiice?oaony eciaiaiea noieiinoe ae?aeaiiiai eaieoaeaTH oi yoe iioiee
iiaoo auoue eaieoaeece?iaaiu ii noaaea aeeneiioa. A yoii neo/aa,
aiciauaiea eiaanoeoeeiiiuo cao?ao i?ienoiaeeo a iiiaio ?aaa?nee
(ia?ai?iaeaaee) e aanue iioie aeioiaeia yaeyaony aeioiaeii ia
eiaanoeoeee. Anee i?iaiice?oaony eciaiaiea noieiinoe aeoeaia, oi
aicieeaao iaiaoiaeeiinoue o/aoa aica?aoa eee aiuiauaiey eaieoaea a
eiyooeoeeaioa eaieoaeecaoeee.

Ii?yaeie ?an/aoa eiyooeoeeaioa eaieoaeecaoeee, anee:

1. Noieiinoue eaieoaea ia iaiyaony

Anee ?aaa?ney i?iecieaeao ii oeaia, ?aaiie ia?aiia/aeueiui eiaanoeoeeyi,
oi aeioiaeu i?iaiice?othony ii noieiinoe: I/R

2. Nieaeaaony noieiinoue eaieoaea

Noiia aiciauaiee aeieaeia auoue iieo/aia ec oaeouaai aeioiaea. R
aeieaeai aeeth/aoue aeioiae e aiciauaiea iaeeaeaaiie iioa?e. Niiniau
aiciauaiey:

· I?yiieeiaeiue aica?ao (iaoiae ?eiaa)

I?aaeiieaaaao, /oi aiciauaiea noiiu i?ienoiaeeo aaeaaiaeii ?aaiuie
/anoyie.

· Aica?ao eaieoaea ii oiiaeo aiciauaiey e noaaee aeioiaea ii
eiaanoeoeeyi (iaoiae Eiaoaea)

Ii?ia aica?aoa eiaanoeoeee eae ninoaaiay /anoue eiyooeoeeaioa
eaieoaeecaoeee ?aaia oaeoi?o oiiaea aiciauaiey i?e oie aea noaaea
i?ioeaioa, /oi e ii eiaanoeoeeyi. *anoue noiia?iiai iioiea aeioiaeia
iiaeao ninoaaeyoue ii?yaeea ni?iea, inoaoie iaania/eaaao aiciauaiea eee
aica?ao. Anee i?ienoiaeeo 100% iioa?y eaieoaea, oi /anoue aeioiaeia,
eaeouay ia aiciauaiea eaieoaea, ?aeiaanoe?iaaiiay ii i?ioeaioiie noaaea
au?anoaao ei ia?aiia/aeueiie iniiaiie noiia, o.a. i?ienoiaeeo iieiia
aiciauaiea eaieoaea.

· Aica?ao eaieoaea ii oiiaeo aiciauaiey e aac?eneiaie noaaee i?ioeaioa
(iaoiae Oineieueaea)

Eiiaaea eiaanoeoeee auaatho i/aiue i?eaueueiuie e aiciiaeiinoue
?aeiaanoe?iaaiey ii oie aea noaaea i?ioeaioa, /oi e o ia?aii?/aeueiiai
i?ioeaioa iaeiaa?iyoii. Aeey ?aeiaanoe?iaaiiuo n?aaenoa aiciiaeii
iieo/aiea aeioiaea ii aieaa ieceie aac?eneiaie noaaea i?ioeaioa. Iau/ii
i?e aeiaeaiee a iaaeaeaeeiinoue, oeie/iue eiaanoi? ?an/eouaaao ia ?ino
noieiinoe aeiaeaiiiai eaieoaea. Yoio ?an/ao no?ieony ia i?iaiica
iiauoaiey oeaiu caeaiee, caiee, ni?ina ia ii?aaeaeaiiua iauaeou
iaaeaeaeeiinoe. Iiyaeyaony iaiaoiaeeiinoue o/aoa i?e?inoa noieiinoe
eaieoaeueiuo aeiaeaiee.

3. Iiauoaaony noieiinoue eaieoaea

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