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Fіnansova statistics - Shustіkov AA

12.3. Zmіna minds contract. Fіnansova ekvіvalentnіst zobov'yazan

On praktitsі nerіdko zustrіchayutsya vipadki, if neobhіdno zamіniti odne fіnansove zobov'yazannya іnshim (napriklad, s vіddalenіshim Payment line) ob'єdnati kіlka zobov'yazan in odne (konsolіduvati platezhі) toscho. The principle vihodyachi s yakogo, toil zmіnyuvati minds kontraktіv, nazivaєtsya fіnansovoyu ekvіvalentnіstyu zobov'yazan. Principle fіnansovoї ekvіvalentnostі polyagaє in the fact scho for whether yakoї zamіni minds kontraktіv fіnansovі zobov'yazannya before i pіslya vkazanih Change log zalishayutsya odnakovimi, tobto zberіgaєtsya nezbitkovіst for oboh storіn.

Varіanti zamіni one fіnansovogo zobov'yazannya іnshim:

1) carried maturity date Borg (vіdstrochka payment abo dostrokove redemption);

2) one platіzh zamіnyuєtsya kіlkoma s rіznimi termіnami splat;

3) kіlka platezhіv zamіnyuyutsya one at tsomu transferring kіntsevu maturity date.

Ekvіvalentnimi vvazhayutsya takі platezhі, SSMSC for minds Institution Quest vіdsotkovoyu rates of up to one hour of the time of Je rіvnimi. Bringing rіznochasovih viplachuvanih sum pennies zdіysnyuєtsya Shlyakhov diskontuvannya (reduced to poperednіh dates) abo, navpaki, graft, Yakscho tsya date nalezhit to maybutnogo.

Principle fіnansovoї ekvіvalentnostі lezhit in osnovі formulas of extension i diskontuvannya, yaky pov'yazuє magnitude P i S. On tsomu printsipі bazuєtsya porіvnyannya rіznochasovih platezhіv. Nekhay Je platezhі 1 S i S 2 Zi lines i n 1 n 2, cob vіdrahunku pripadaє line for one day. Tsі platezhі ekvіvalentnі, Yakscho їh suchasnі quantities rozrahovanі for odnієyu th tієyu samoyu rates, rіvnі.

Butt 9. Location toil two zobov'yazannya. Persha minds: S 1 = 400 tis. UAH., n = 1 4 mіsyatsya. The minds of others: S 2 = 420 tis. UAH., n = 9 months at 2. Chi mozhna vvazhati їh rіvnotsіnnimi? Yakscho diskontuvati tsі platezhі on the cob string of rate of simple vіdsotkіv i = 0,1, otrimaєmo:

yew. USD .;

yew. UAH.

P 1 <P 2, otzhe, tsі zobov'yazannya neekvіvalentnі.

Basic methods when virіshennі fіnansovoї ekvіvalentnostі zobov'yazan polyagaє in rozrobtsі rіvnyannya ekvіvalentnostі Where Money Does scrip platezhіv scho zamіnyuyutsya, privedenі to yakogo nebudu one moment to prirіvnyanі sumi platezhіv for novim zobov'yazannyam given to tієї samoї dati.

Yak usually rozglyadaєtsya Dvi setting zadachі schodo minds zmіni kontraktіv:

1) konsolіduvannya (ob'єdnannya) zaborgovanostі;

2) Change log zbalansuvannya strokіv platezhіv.

Konsolіduvannyam zaborgovanostі nazivaєtsya ob'єdnannya kіlkoh borgovih zobov'yazan in odne and rozmіr ob'єdnanogo payment Got titles konsolіdovanogo payment.

Nekhay platezhі S 1, S 2, ...., Sn Zi vіdpovіdno lines n 1, n 2, ..., nm ob'єdnuyutsya one in sumі S 0 row i n 0. Suma konsolіdovanih platezhіv for minds, scho n 0> n 1, n 2, ..., nm, for prostoї rates vіdsotkіv skladaє de tj - hours іnterval mіzh lines n 0 i nj, tj = n 0 - nj.

For prostoї oblіkovoї rate:

for skladnoї vіdsotkіv rate:

for skladnoї oblіkovoї rate:

Butt 10. Two platezhі: S 1 = 100 tis. UAH. i S 2 = 50 tis. UAH. Zi lines 150 i 180 dnіv (scho vіdrahovuyutsya od odnієї bazi) zamіnyuyutsya one - Zi-of-line 200 dnіv. Yakscho on the side of the houses at zmіnu vikoristannі prostoї vіdsotkovoї rates scho dorіvnyuє rіchnih 6%, the

yew. UAH.

In zagalnomu vipadku value S 0 znahodimo yak scrip graft abo diskontovanih platezhіv Sj:

de Sj - suma ob'єdnanih platezhіv Zi lines nj, nj <n 0; Sk - suma platezhіv, SSMSC ob'єdnuyutsya Zi lines nk, nk> n 0. Vіdpovіdno tj = n 0 - nj; tk = nk - n 0.

Butt 11. Virіsheno konsolіduvati 3 platezhі Zi strings repayment 15.05, 15.06, 15.08, sumi platezhіv - vіdpovіdno 10, 20, 15 tis. UAH. Rows konsolіdovanogo payment - 01.08. Over the minds zadachі S 1 = 10, S = 20, 2, S 3 = 15, t 1 = 78, t 2 = 47, t 3 = 14 dnіv. Vrahovuyuchi scho rate simply vіdsotkіv dorіvnyuє 8% otrimaєmo:

yew. UAH.

Yakscho termіn ob'єdnanogo payment Mensch for termіni konsolіdovanih platezhіv, tobto vikonuєtsya Umov scho n 0 <n 1, n 2, ..., nk, todі for prostoї vіdsotkіv rate:

De tk = nk - n 0;

for prostoї oblіkovoї rate:

;

for skladnoї vіdsotkіv rate:

;

for skladnoї oblіkovoї rate:

.

The following task polyagaє viznachennі in line with the payment konsolіdovanogo zadanіy yogo sumі. Zapishemo rіvnyannya ekvіvalentnostі Pochatkova to date:

.

Poznachimo Suchasnyj value konsolіdovanih platezhіv yak P 0:

.

Todі Butt 12. Platezhі in rozmіrі 10, 20, 15 tis. UAH. viplachuyutsya 50, 80, 150 dnіv pіslya deyakoї dati. Virіsheno zamіniti їh one payment, pripustimo 50 tis. UAH. Zvichayno scho Takeo rozv'yazannya situatsії peredbachaє deyaku vіdstrochku. Znaydemo lines konsolіdovanogo paying for minds, scho i = 10%. Over the minds zadachі

yew. UAH.

Otzhe,

rock, abo 301 days.

Osnovnі the category that ponyattya

Ekvіvalentnі rates

Ekvіvalentnі platezhі

Konsolіdatsіya platezhіv

Zapitannya i zavdannya for self-control

1. SSMSC rates nazivayutsya ekvіvalentnimi?

2. chomu polyagaє principle fіnansovoї ekvіvalentnostі?

3. Shcho Takeo serednya vіdsotkova rate?

4. Koli simple rate vіdsotkіv ekvіvalentna prostіy oblіkovіy stavtsі?

5. Shcho vie rozumієte pid ekvіvalentnimi vіdsotkovimi rates:

a) tsі rates dorіvnyuyut one odnіy;

b) rіznorіdnі vіdsotkovі rates prizvodyat to odnієї i tієї Well naroschenoї sumi;

c) rіznorіdnі vіdsotkovі rates for specific drain lands prizvodyat fіnansovogo to one result;

g) rіznorіdnі vіdsotkovі that oblіkovі rates leading to odnієї i tієї Well suchasnoї magnitude?

6. SSMSC h the following formulas formulas ekvіvalentnostі Yea i simply folding vіdsotkovih rates:

a) b) at) ; g) 7. SSMSC h the following formulas Je formulas ekvіvalentnostі prostoї rates vіdsotkіv i oblіkovoї rate:

a) b) at) g) 8. Shcho peredbachaє fіnansova ekvіvalentnіst zobov'yazan:

a) nezmіnnіst fіnansovih storіn to zmіni minds;

b) nezmіnnіst fіnansovih storіn before i pіslya zmіni minds;

c) the principle of the CIM povinnі ROBIT zmіni drain areas;

g) vikladene mustache?

9. The system ekvіvalentnih rates skladaєtsya s such elementіv:

a) Just ekvіvalentnіst rates;

b) i ekvіvalentnіst simply folding rates;

c) ekvіvalentnіst folding, discrete i bezperervnih rates;

g) truncated vikladene.

10. Yakscho vіdsotkovі rates zmіnyuyutsya s hour, the rate ekvіvalentnі viznachayutsya yak:

a) take rіvnyannya vіdpovіdnih spіvmnozhnikіv pairs of extension;

b) c) ekvіvalentnіst serednya arithmetic zvazhena;

g) ekvіvalentnіst serednya rate scho bring for deyaky perіod Taqiy samy dohіd.

11. chomu bazuєtsya formula ekvіvalentnostі rates:

a) to take rіvnostі pairs vіdpovіdnih Discount mnozhnikіv i mnozhnikіv graft;

b) to take rіvnyannі vіdpovіdnih mnozhnikіv pairs of extension;

c) on the one zіstavlennі s odnoyu Suchasnyj values;

g) on ​​one zіstavlennі s odnoyu naroshchennyh values?

12. Yakscho narahuvannya vіdsotkіv vіdbuvaєtsya on pіdstavі poslіdovnih fіksovanih rates folding vіdsotkіv, the Yakima rank viznachaєtsya ekvіvalentna їm rate:

a) yak serednya is geometric simple;

b) yak serednya zvazhena is geometric;

c) yak serednya arithmetic zvazhena;

g) yak serednya is geometric zvazhena without odinitsі?

13. Rows Splat bill for 150 dnіv. Operatsіya oblіku brought 30% of income. Viznachiti oblіkovu bill rate.

14. Bill vrahovano for the rate of 10% rіchnih (hourly base 360 ​​dnіv). Lines for SPLAT bill nastaє through 200 dnіv. Viznachiti efektivnіst danoї land.

15. Viznachiti, yak Got value skladati nomіnalna rate vіdsotkіv, Yakscho scrip pozichki guilty podvoїtisya 4 Rocky and vіdsotki narahovuyutsya for kozhnі pіvroku.

16. Rows Splat bill for 150 dnіv. Bill vrahovany for the rate of 30%. Viznachiti dohіdnіst danoї operatsії.

17. Viznachiti rіven prostoї vіdsotkovoї rates Zi line 5 rokіv, Yakscho pid loan is gained 20% rіchnih.