Time value of money Interest formulas Project evaluations Inflation and CPI Financial risk and financing

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1 2YHUYLHZ )LQDQLDO$QDO\VLV 3ULHU Hioshi Sakamoo Humphey Isiue of ublic Affais Uivesiy of Miesoa Time value of moey Iees fomulas ojec evaluaios Iflaio ad CI iacial isk ad fiacig A5721 Moey - 1 A5721 Moey - 2 /HQGHU0DNHVDQ,QYHVWHQW 7LH9DOXHRI0RQH\ ~ Today is woh moe ha omoow ~ Leig somebody use you moey a a give ime. Loses his/he puchase powe fo ha ime. Ges compesaed whe he moey is eued a a lae ime. A5721 Moey - 3 A5721 Moey - 4 %RUURZHU%RUURZV Ca cosume poduc/sevice usig somebody else s $. Gais his/he puchase powe fo ha ime. Needs o compesae he lede whe he moey is eued a a lae ime. 7LH9DOXHRI0RQH\ Compaiso: ives oday s $1 oday eceive omoow s $1 omoow You moey loses puchase powe ove ime due o iflaio. Today is woh moe ha fuue. Tomoow is available oly if oday is suvived. A5721 Moey - 5 A5721 Moey - 6 1

2 ,QWHUHVW5DWH,QWHUHVW)RUXODV ~ ese value of a pojec ~ A ae of chage of a $ value. Ohe aes: Discou ae Iflaio ae (Ieal) ae of eu A5721 Moey - 7 A5721 Moey - 8 3UHVHQW9DOXHµ Simple example: Wha is he pese value,, of ex yea s $11 (=), give =10%? $11 = = $10 ( ) 3UHVHQW9DOXHµLQJHQHUDO Wha is he pese value,, of $ i he fuue,, ha is peiods away, give? = ( ) A5721 Moey - 9 A5721 Moey - 10 &DVK)ORZ'LDJUD e.g. Maieace cos Capial ivesme Compoudig peiod (e.g. yea) Reveue Cos,QWHUHVW)RUXODV To calculae pese value Deped o ypes of: paymes»sigle, equal ad gadie iees compoudig»discee (ad coiuous) A5721 Moey - 11 A5721 Moey

3 6LQJOH3D\HQW (TXDO3D\HQWV = ( ) : iees ae Equivale of equal fuue paymes (1 + ) 1 = A (1 + ) A=A j : iees ae A5721 Moey - 13 A5721 Moey - 14 *UDGLHQW3D\HQWV Uifom gadie G (-1)G *UDGLHQW3D\HQWV Geomeic gadie 1 1 (g) -1 : iees ae g: ae of icease of fuue paymes 1 = G (1 + ) 1 : iees ae A5721 Moey - 15 ( g ) 1 1 = g g (1 + ) g whee g = 1 g A5721 Moey - 16 &RQWLQXRXV&RSRXQGLQJ Uifom gadie,q5hdolw\ Cash flow ae moe complicaed: = G e 1 e 1 : iees ae 1 = G (1 + ) 1 A5721 Moey A5721 Moey

4 +RZ'R<RX&RSDUH$OWHUQDWLYHV" Examples: 3URMHW(YDOXDWLRQV ojec A: ~ Compaig Aleaives ~ ojec B: A5721 Moey - 19 A5721 Moey RH7HKQLTXHV Ne ese Value (NV) Beefi-Cos aio Ieal Rae of Reu (IRR) ayback peiod Capialized equivale Capial ecovey wih eu ojec balace 1HW3UHVHQW9DOXH139 Sum of he pese value of e cash flow i each of he fuue peiods 0 Ne pese value Reveue, R Cos, C A5721 Moey - 21 A5721 Moey - 22 &DOXODWLQJ139 Equivale pese value of a pojec NV = R C = 0 (1 + )... Ohes: Aual equivale ad e fuue value 3 %HQHILW&RVW5DWLR%&5 Raio of pese-value beefi o pese-value cos 0 ese value of beefis, B ese value of coss, C Beefi Cos B C A5721 Moey - 23 A5721 Moey

5 ,QWHUQDO5DWHRI5HWXUQ,55 Iees ae ha makes NV zeo. Choose a pojec wih he lowes IRR. o a pojec ha equies advaced ivesme NV = 0 = = 0 (1 + R C i * ) whee i * is IRR A5721 Moey - 25,SOLDWLRQVWR3XEOL3URMHWV iacial aalysis becomes ecoomic aalysis. No-moeay beefis mus be icluded, as well as o-moeay coss. BCR aalysis becomes icky! Some coss may be cosideed egaive beefis, ad vice vesa. NV ad IRR mehods wok fie. A5721 Moey - 26,QIODWLRQDQG&3, &RQVXHU3ULH,QGH[&3, ice idex of eail goods/sevices fo a give yea. ice idex is a aio of a pice i a give yea o ha i he base yea ~ eal iees ae ~ Ref. US Bueau of Labo Saisics hp:// A5721 Moey - 27 A5721 Moey - 28,QIODWLRQ Rae of icease i CI ove he peiod of iees o yea, he iflaio ae, f, is calculaed by: CI CI 1 f = CI 1 whee CI is deemied a he ed of each yea. 5HDO,QWHUHVW5DWHU Also called: iflaio-fee iees ae cosa-dolla iees ae = 1 f The omial iees ae,, mus be geae ha iflaio ae, f, i ode fo a posiive eal iees ae. A5721 Moey - 29 A5721 Moey

6 )LQDQLDO5LVNV ~ Risk Maageme i ojec iacig ~ :KDWLVULVN" obabiliy of a advese effec = Magiude (oucome) x obabiliy = Hazad x Exposue (i public healh) Diffee A5721 Moey - 31 A5721 Moey QHUWDLQW\ Uceaiy abou fuue Rage of possible values e.g. Rage of possible cos fo yea Complicaes pojec evaluaios Sesiiviy aalysis may be used. ([SHWHGµ2XWRH Temiology fom saisics The mea of oucome Allows sepaaio of aleaive evaluaios ad isk compaisos Risk associaed wih uceaiy A5721 Moey - 33 A5721 Moey RID3URMHWZLWK5LVN A example: Oucome A B C obabiliy NV [$] -30,000 10, Mos likely oucome Risks associaed wih his pojec ([DSOHRQW G RQW G Oucome A B C obabiliy NV [$] -30,000 10, Expeced NV of he pojec, E: E( oucome) = 0.1NVA + 0.6NVB + 0.3NVC = 3, , = 3,030 A5721 Moey - 35 A5721 Moey

7 2WKHU7HKQLTXHV Sesiiviy aalysis Expeced vaiace Moe Calo aalysis Decisio Tees ayoff Maix Maximi/Maximax Maximax Rules Huwicz Rule Miimax Rege Rule (QGRI)LQDQLDO$QDO\VLV A5721 Moey - 37 A5721 Moey