Module 1: Time Value of Money and Valuation of Cash Flows

Transcription

1 Moule : Te Value of Moey a Valuao of Cash Flows Ieres Moel Accuulae aou fuco A(): he accuulae aou a e fro a orgal prcpal, eoe as A(0) Accuulao fuco a(): he accuulae aou a e fro a orgal ese of $. Ths s a scale erso of A() wh a(0) =. The accuulao facor for a pero s ge by: A k a k A a A k A a k The effece eres I,k eare bewee a +k s he fferece accuulae aous: k, I A k A The effece rae of eres,k for he sae pero s ge by: k, A a Ak A ak a Whe he effece rae of eres s sae for all (copou eres), we hae: a k a k a a ak 0 ak Ak Aak k, Sple Ieres Copou Ieres Ieres s o eare o exsg Ieres s couously eare o Ieres Eare eres eres Use for Cash flows for less ha a year Cash flows for loger ha a year Accuulao Fucos Effece Ieres 0 a, A A Decreasg ak aak a 0 A A Cosa ak aak Effece Aual Rae of Dscou Ieres rae apples o he prcpal ow, for eres a he e of he pero Dscou rae apples o he prcpal a he e of he pero, for eres calculae ow k, k, A k A k, A k A k A A A A k A k Boh ehos are equale ways of scoug eres, so her accuulao fuco s equal: Sple Ieres Copou Ieres Accuulao Fuco a a

2 Ieres a Dscou Le be he scou facor: a The effece scou rae s esseally he PV of he effece eres eare: Noal Ieres Noal eres raes () are sll expresse as % p.a. bu payable hly,.e. hey hae seeral () copoug peros per year. The effece rae of eres correspog o () by: The accuulao for year s equal o he accuulao for / peros accuulae es: a a As log as s greaer ha, he he effece rae p.a. wll be GREATER ha he oal rae, sce ore copoug eas ore eres s eare o exsg eres: The oal scou rae s slar: for a a Force of Ieres The force of eres δ or ( ), a.k.a. he couously eres rae, s he eres rae whe eres s pa saaeously. The equale couous scou rae s ( ). e l l e l l Noe ha we hae: I geeral, whe coere o he equale effece eres: os aace sa os arrears

3 For hoogeeous eres, he effece eres rae ares wh e. Thus, he force of eres wll be a fuco of. Coser eres pa couously a a rae δ() oer a sall pero of e: A A A A A A A A A 0 A' A as 0 l l A To ge expresso for A(), we egrae boh ses fro 0 o : 0exp A A ss 0 The he accuulao fuco a he scou facor are he expoeal of he AREA uer he force of eres, whch s a fuco of : a exp ss exp ss 0 a 0 For exaple, sple eres s a ype of hoogeeous eres,.e. effece eres s ecreasg: Iflao Iflao s characerse by fallg alue of oey, whch leas o rsg prces. Iflao s easure by he CPI, represee by he prce ex fuco p() wh p(0)=. p The real eres rae p.a. r s he equal o he oey eres scoue by flao: r r Ths ONLY apples for effece raes: There are wo equale ehos of accoug for flao: Meho Meho Dscou oal alues wh oal eres Aap o real alue frs by scoug flao raes he use he ofe real eres rae A A A0 A0 r Easer f cash flows o o crease le wh flao Easer f cash flows crease le wh flao,.e. flao exe

4 Aues Auy s a srea of payes oer a specfe pero of e Ter Auy Auy-eae s pa arrears: a... s... a s s a Auy-ue are pa aace: a... s... a s s a Soe key ees are: a a a s s s a a s s a a s s a a s s k k k k a a a s s s Deferre Auy Deferre auy s a auy ha oly begs afer peros,.e. eferre for peros a a a a a a Perpeuy Perpeuy s a ype of auy ha coues efely: a... l a l a a a a... l a l A auy-eae s a perpeuy-eae less a perpeuy-eae elaye for years, as cacels ou all payes afer he h paye: a a a

5 Auy wh Mulple Payes per Year The prese alue of a auy-eae of payes per year of aou / per pero: a... a a j p s a s Where s he aual effece rae, j s he peroc effece rae correspog o he oal rae () wh copou peros, slarly: a a a s s Icreasg Auy For a auy creasg arhec progresso, we hae: Ia... a a a a a Ia Ia l a a l Is... Ia a a I a... a a a Ia Ia l Ia Is Is s s I geeral, f he al paye a e s P a he creases by Q per pero, we ca coser he cash flows ways: paye a P PQ Q paye a PQ PQ Q paye a P Q PQ Q Tha s, f creases sar afer year, he afer year woul hae crease - es PV Pa Q Ia P Q a Q Ia For a auy creasg geoerc progresso,.e. by +π per pero whe cash flows are exe o flao: 3 PV.... f f k f k AV PV