Present and Future Value Formulae for Uneven Cash Flows Based on Performance of a Business

Transcription

1 Itertol Jourl of Bkg d Fce Volue 8 Issue Artcle 0--0 reset d Future Vlue Forule for Ueve Csh Flows Bsed o erforce of Busess Aeh Tefer Tesse Costructo d Busess Bk, Etho, [email protected] Follow ths d ddtol works t: htt://eublctos.bod.edu.u/jbf Recoeded Ctto Tesse, Aeh Tefer 0 "reset d Future Vlue Forule for Ueve Csh Flows Bsed o erforce of Busess," Itertol Jourl of Bkg d Fce: Vol. 8: Iss., Artcle. Avlble t: htt://eublctos.bod.edu.u/jbf/vol8/ss/ Ths Jourl Artcle s brought to you by the Fculty of Busess t eublctos@bod. It hs bee cceted for cluso Itertol Jourl of Bkg d Fce by uthorzed dstrtor of eublctos@bod. For ore forto, lese cotct Bod Uversty's Reostory Coordtor.

2 Tesse: Ueve Csh Flows The Itertol Jourl of Bkg d Fce, Volue 8 Nuber, 0: ges 8-7 RESENT AND FUTURE VALUE FORMULAE FOR UNEVEN CASH FLOW BASED ON ERFORMANCE OF A BUSINESS Aeh Tefer Tesse Costructo d Busess Bk, Etho Abstrct Couttol ethods for reset d future vlue clcultos re dffcult whe the fr's csh flow coe s ueve. The fr s decso to vest or borrow bsed o ueve csh flows eeds sle ethod to rrve t the reset vlue of ueve csh flows. Ths er s ttet to slfy the curret tedous clcultos. A ethodology to quckly estte the reset/future vlue of ueve csh flows s vluble to rcttoers the bkg d fcl dustres. Keywords: Ueve csh flow, reset vlue forul, Future vlue forul, erforce rte, Rte of growth, Ueve csh flow coe, Ecooc vlue dded JEL Clssfcto: C0. Itroducto Moey hs dfferet vlues t dfferet te erods, whch s the foudto of te vlue of oey clcultos. The lterture o ths toc s by ow hstorc. Aog the resos ofte cted re: te referece, flto reu, rsk reu, d roductvty. Cooudg d dscoutg techques re cooly eloyed to clculte the te vlue of oey. The reset d future uty foruls develoed through such techque re, by defto, for equl out of erodc csh flows. They hve the followg shortcogs, rtculrly lght of bkg sttuto: They do ot esly llow for the clculto of csh flows tht grow ccordg to the roject s erforce, rtculrly whe such erforce s vrble. 7 ublshed by eublctos@bod, 0

3 Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. They ssue costt csh flows throughout the roject s lfe, whch s urelstc. A roject whose erforce does ot chge ccordg to the rket stutos throughout the roject lfe y be out of tue wth the rket. They do ot cosder future flto rtes, whch could lso be vrble. Iflto s ssued to occur t costt rte. Sce flto reduces the urchsg ower of oey, cosderg the future flto effect o roject csh flows wll reduce the fr s ueected loss. They do ot cosder fleblty of deosts bks or fleblty of yets by credtors to the bks. Ag, the hgh ossblty of ueve csh flows. Ths er ttets to resolve the bove robles through offerg sler ethod to coute ueve csh flows.. Busess Asects of Ueve Csh Flows We lk the su of the ueve csh flows, ether for vestet or for reyets of borrowed los, to the erforce of the fr. A ew busess hs sll out of csh t tl stge. Evetully, fter coverg the estblshet cost, the lqudty out o hd grows ccordgly. The growth of the fr s csh flow wll the deed o ts erforce. Whe erforce roves, ts rofts d csh flows crese. As result, the deostor c deost the ecess out bove hs/her busess cosuto. Ths ecess y crese fro erod to erod ccordg to the busess erforce t lter stge of roftblty. Trdtol fce esures of fr s erforce re rofts, ergs er shre ES, retur o vestet ROI, free csh flows FCF, ctl roductvty K, lbor roductvty L, d retur o ctl eloyed ROCE. Ech gores csh d cost of ctl so s to geerte the trget roft Breley d Myers, 00:. A ore colete esure of erforce of busess fr s ecooc vlue dded EVA whch rovdes the oey vlue creted for vestor gve erod of te by weghtg the roft geerted gst the cost of ctl eloyed Frer, Ross, Westerfeld d Jord, htt://eublctos.bod.edu.u/jbf/vol8/ss/

4 Tesse: Ueve Csh Flows Sce EVA cosders the out of ctl vested, the retur ered o ctl d the cost of ctl WACC reflectg the rsk djusted requred rte of retur - t s thought to hve ll the chrcterstcs of colete esure though t s vld oly for short erod of te. Furtherore, sce EVA s esure of both erforce d vlue, t s ssued to be ethod to detere the vlue creted, bove the requred retur, for the shreholders. The fr cretes welth for the shreholders whe the reveue of the fr eceeds the cost of dog busess d the cost of ctl. A busess fr cretes vlue for ts shreholders o the bss of ostve EVA rther th sly kg ccoutg rofts. The ostve gtude of EVA dctes the busess fr s rovg ts et csh retur o vested ctl. The creetl EVA fro yer to yer wll result chge the rket vlue of the fr Dodr, 00. Accoutg forto bout the fr s erforce for sgle ccoutg erod s vluble. A ger wth good kowledge bout the fr s erforce y redct future erforce of the fr o the bss of the st fcl stteets wth soe degree of ccurcy. If records of st tred re vlble, erforce rtes c be detered to roject the csh flows of the fr vestet d of the fr bk lo reyets Aleder Hlto Isttute, 998: - d -. Sce the fr's erforce rte s ofte ssued to be rogressve, the csh flow of the fr c be ssued to grow fro erod to erod. erforce rte s ercetge by whch the curret erforce of fr ths cse, EVA grows fro the revous erod.. Methodology Assue busess fr decdes to borrow oey fro bk or credtor. Ths ofte volves recevg csh ow echge for rose to ke yets the future erods. The lo reyet outs usully re set to clude terest d orto of the rcl. Bsed o ths oto, ech of the et erod s reyet out s clculted by cosderg the recedg reyet, the roject erforce, d the terest rte. At tl reyet erod, the reyet out s ssued to be sll d fed wthout erforce cosderto. However, the secod erod reyet out grows 9 ublshed by eublctos@bod, 0

5 Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. ccordg to the busess erforce. A busess erforce esurg tool, EVA, c be clculted s follows: EVA= [djusted et oertg roft fter tes ANOAT] [ctl], or EVA = ROCE WACC K where, ROCE s retur o ctl eloyed, WACC s the weghted verge cost of ctl, d K s ctl eloyed. Fro the bove, busess fr c crese ts EVA by cresg the NOAT geerted by estg ctl, reducg the WACC, d vestg ew rojects where the retur o ctl eceeds the WACC. Assue tht the frst sll reyet out to be the followg reyets c be clculted s: Such tht Reyet erod Reyet Aout.... Where = lo erod, = erforce rte, y rbtrry fgure greter th zero, whch c be esured s the ercetge by whch the + th erod EVA grows fro the th erod EVA. Tht s: 70 htt://eublctos.bod.edu.u/jbf/vol8/ss/

6 Tesse: Ueve Csh Flows EVA EVA EVA The reso for the choce of the erforce rte s s eressed relto s to revet the csh flows fro eggerted chges. EVA s rojected et coe for the - erod lo; d s the bk terest rte whch s dded to the erforce rte sce the th erod reyet should cot orto of the rcl out d the terest out for the erod. It s ots,.e., betwee 0 d. s: The reset vlue of the future csh flows of the lo reyets c be eressed r r.... Aother sect of fr s decso to vest csh ow order to receve csh, goods or servces the future. Let the erodc csh vestet be s: erod Ivestg Csh W -T W -T W - - T - where W, T for betwee 0 d.e., 0< +<. T = s the fr erforce ecludg bk s deost terest. The deost terest rte 7 ublshed by eublctos@bod, 0

7 7 should ot be cluded to the roject erforce sce t s lwys less th the bk ledg terest rte. = bk terest rte whch s betwee 0 d. = vestg erod. T W A orto of erforce rte by whch the ecess bove cosuto wll be sved bk ccout. Therefore the future vlue of vestet csh flows s: r r T W T W T W where:,.,,,, such tht;...,,.,,, Let the th erod csh flow, erforce rte, d the dscout rte belog to the do of y ubers tht c thetclly be eressed s eleets of the rel ubers of set of R,.e.,.,, R eleets. stdsfor where The, the su of csh flow for erods c be eled s follow:.... Ths c be eressed s 0 for,.. Slttg the ters s: Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. htt://eublctos.bod.edu.u/jbf/vol8/ss/

8 7 Collectg the ters the brckets yelds: Multlyg both sdes by : gves, for,.... Sce the forul of geoetrc rogresso t rto = c be eressed s: Sobel d Lerer,99:-, t follows tht: Equvletly ths c be eressed s: Tesse: Ueve Csh Flows ublshed by eublctos@bod, 0

9 7 Let 0, the t follows tht: 9... z z Fro ths eresso let us ssue tht the csh flow of roject for ech erod c be defed s whch c be wrtte s,.,,,, Or:...,,.,,, such tht + or d 0 =. Substtutg ths, we hve: ultlyg both sdes of the equto by -, we obt: Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. htt://eublctos.bod.edu.u/jbf/vol8/ss/

10 If the bk terest rte s eressed s, by substtutg t relto d ultlyg both sdes of the equto by +, we hve the followg:.... Suose tht the bove equto, d ddg both sdes of the equto we obt the followg reset vlue forul: r r.... The tl csh flow the bove forul grows rogressvely fro oe erod to other by ultlyg rogressve erforce rtes of the erods. Ech of the erodc csh flows cots terest rte tht ebodes flto rte d rsk whch ght he the future. Furtherore ech of the erodc csh flow cots the erod erforce rte tht c ove log wth the stregth of the busess. 9 Tesse: Ueve Csh Flows ublshed by eublctos@bod, 0

11 Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. Now, let us cosder equto 0. Settg = +, deductg fro both sdes, d the ddg both sde of the equto, we hve the followg future vlue forul: t s correct W T W T Ths c be wrtte s:.... W T... r r W T W T W T... where W, T for betwee 0 d.e., 0< +< ; = erforce rte such tht or, d T = s the fr erforce ecludg the bk s deost terest. The rest of the ottos re s defed before see the seget bove relto. I su, we hve focused o how busess frs detere ther csh flow or outflow bsed o ther ecooc roft or ecooc vlue dded. As show by the forule bove, the frst yet, whch s ecess bove cosuto, for yet of debt or for svg to bk ccout s reltvely sll. The et fter the frst out rogresses or grows log wth the busess fr s erforce rte. Sce ths erforce rte shows the reltve level of growth of oe s fr, curret to lst ecooc roft, t ebrces ll ctvtes of the fr. As EVA fluctutes fro erod to erod, the et csh left to the fr lso fluctutes fro erod to erod. These fluctutos re reflected by the rte. 7 htt://eublctos.bod.edu.u/jbf/vol8/ss/ 0

12 Tesse: Ueve Csh Flows Fcg orgs, such s bks, use ordry uty forul to detere the lo ccty s well s the lo reyet of the borrower. The forul does ot cot y esure of the erforce of the borrower. Soe los becoe oerforg. To vod ths stuto, bks resort to ther ow rules d regultos to ze oerforg los. The reset vlue forul stted ths er clcultes the rojected fluctutg reyet outs log wth the erforce of the borrowg org bsed o the rel csh o hd, whch s the ecess bove the cosuto. The reset vlue forul eble the borrower, who hs o ecess csh o hd for vestet, to l to sve orto of coe ccordg to the ergs growth. Ths lso y rot ls for svg by those who hve low coe d those who re slred.. Alcto I Etho, ost busess uts use EVA s esure of both vlue d erforce. Notble eles re costructo frs d bks Col et l., 007. The followg lctos re bsed uo rel st dt of Etho bk for llustrto. Tble cots reset vlue d Tble d the rest future vlue clcultos. 77 ublshed by eublctos@bod, 0

13 Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. Tble : Coutto usg the forul develoed ths er, llos Yers Net oertg roft fter t Less: Cost of ctl Ecooc vlue dded erforce rte Bse Yer=0 00 yer= 00 yer= 00 yer= 00 yer= 007 yer= 008 yer= yer= V of EVA As we hve dscussed bove, erforce rte of ech yers s clculted o the bss of the followg forul: EVA EVA EVA Yeldg: Assue tht EVA0 s the bse yer ecooc vlue dded whch c be ssued s tl out. Iterest rte =0%. reset vlue of ech yer s EVA s clculted s: Frst yer V of EVA Secod yer V of EVA 7 htt://eublctos.bod.edu.u/jbf/vol8/ss/

14 Tesse: Ueve Csh Flows Thrd yer V of EVA Fourth yer V of EVA Ffth yer V of EVA Sth yer V of EVA Seveth yer V of EVA ublshed by eublctos@bod,. 0 7

15 Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. Eghth yer V of EVA Usg reset vlue forul for ueve csh flow, the reset vlue of ech erod s EVA s esly sued by the forul s follows: reset vlue of EVA = =.9 The ccurcy of ths result c be checked by the followg reset vlue forul r r =[ ][ ] =.9 whch s the surlus dollr out o roject. If the bk hd rojected csh flow or outflow stdg o bse yer, the vlue of those csh outs wth the gve lfe te would hve bee the bove clculted result. Ths hels the bk to decde, by corg wth the tl vestet, whether the vestet s fesble or ot. Ech of the bove clculted V of EVA s ostve ecet the lst ter for 009, whe the bk shows the lowest erforce. ostve EVA creses the vlue of the fr wheres egtve EVA reduces the vlue. As er ths er s recoedto, the bk 9 htt://eublctos.bod.edu.u/jbf/vol8/ss/

16 Tesse: Ueve Csh Flows should hve show rogressve erforces, otherwse the forule detect s the fr hs ot bee erfored well tht gve erod. It s very strog rt of the forule. Tke ow the cse of the bk deosts. The objectve of bk s ccetg deosts d ledg the to those wth lqudty shortge. Uder the uty foruls, the lo reyets dsregrd flto d rsk terest fluctutos. These y crete hrdshs for the borrowers, cludg defults. The future vlue forul of ths er hels the bk settg ts reserve requreets whle cosderg these fctors. Strtg wth the reltvely sll tl out tht wll rogress ccordg to the erforce of the bk, EVA s clculted. Usg g the bove dt d bsed o Tble bove, f the bk hd rojected ts csh reserve deosts by the ed of 009, t would hve hd the followg: Itl out EVA 0 = Deost terest rte =0% Tble : Couttol dt usg the forul develoed ths er, llos Yer Bse Yer=0 Yer= yer= yer= yer= Yer= Yer= Yer=7 erforce rte W T W T ublshed by eublctos@bod, 0

17 r r Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. Accordgly, the clculto of the curret csh flow to get the future vlue u to yer 008 s show below: Yer csh flow.0. 0 W T W T W T W T W W T 7 T Sug the csh vestet flows, we hve = = All the curret csh vestets of ech erod re ostve gtude ecet the lst yer. The egtve sg dctes tht the bk erforce ths erod s less th the ror yer. As c be see bove, the stes to rrve t the fl result s very tedous d te cosug. However, the future vlue forul of ths er clcultes the bove csh flow s esly s follow r r 7 =.0[ ] = htt://eublctos.bod.edu.u/jbf/vol8/ss/

18 Tesse: Ueve Csh Flows. Cocluso The erforce of fr c be rojected fro ts coe stteet. However, order to roject fr et coe, there should be record of st tred regrdg the fr s erforce. Usg erodc ecooc roft wth ecooc vlue dded EVA roch, erforce rte of ech erod s esured s the rto of + th erod s rojected et EVA creet to the th erod s EVA. Ths wll result ueve csh flows. Further, t les tht ech rojected et ecooc roft d lo reyet occur the se drecto, whch tur les tht rojected et coe, lo reyet d rojected et csh flow wll hve the se drecto. As such, the borrower wll be eected ot to cur csh shortges sce et coe, lo reyet, d et csh flow re the se drecto. Thus, the borrower s guded to eet hs/her lo reyet oblgto roerly. I ost stces the fr s csh flows re ueve d s such oe cot roject the future csh recets or yets. A good eereced ger y forecst fleble csh flows bsed o the st dt such s coe stteet d blce sheet of the busess fr. As the erforce rte of the busess oves u or dow, the rojected csh flow oves the se drecto. I ths er, the erforce of busess fr s ssued to be rogressve,.e., ccelerted growth. The fr c cheve ts growth objectve ether by edg ts estg rket or eterg to ew rket. As the erforce rte oves fro oe erod to other, the lo reyets ove log wth the drecto of ths fluctuto. Hece, we hve ueve csh flows. We hve show how the reset d future vlues of such ueve csh flows y be clculted. The ethod tht we hve reseted y lso hel vestors rojectg ther csh flow or outflow ccordg to ther busess rogressve erforce rte. The foruls y lso fcltte the credtors or vestors decso kg rocess rrvg t relstc esures of fr s erforce. 7 ublshed by eublctos@bod, 0 7

19 Itertol Jourl of Bkg d Fce, Vol. 8, Iss. [0], Art. Author forto: Aeh Tefer Tesse s stff t the Costructo d Busess Bk s.c, Adds Abb, Etho. He y be reched v E-l [email protected] or Refereces Aleder Hlto Isttute, 998, Fcl Mgeet Hdbook, Globl Books d Subscrto Servces, New Delh, Chdr, rs,99. Fudetls of Fcl Mgeet, Thrd edto, Tt McGrw-Hll ublshg Coy Ltd, New Delh, Id. Dodr, Aswth, 00. Cororte Fce, Secod edto, Joh Wley & Sos, Ic., USA. Breley, R.A., d Myers, S.C., 00. rcles of Cororte Fce, McGrw-Hll Ic., New York, USA. Costructo d Busess Bk SC: Frer, Col, Stehe A. Ross, Rdolh W. Westerfeld d Brdford D.Jord, 007. Fudetls of Cororte Fce, Thrd edto, McGrw Hll Coes, Lodo, Uted Kgdo. dey, I M., 999. Fcl Mgeet, Eghth edto, Vks ublshg House Ltd, New Delh, Id. Mosch, A.N., 9. Iteredte Accoutg, Sth Edto, McGrw-Hll Ic., USA. Mddelto, D.R., 99. The Essece of Fcl Mgeet, retce Hll Itertol Ltd, Uted Kgdo. roctor, Ry, 00. Mgerl Accoutg For Busess Decsos, Secod edto, erso Educto Ltd, Egld. Relly, R.F., d Schwehs, R.., 000. Hdbook of Advced Busess Vluto, McGrw-Hll Coes, Ic., New York, USA.. Sobel, M.A., d Lerer, N., 99. College Algebr, Fourth edto, retce-hll, Ic., New Jersey, USA. 7 htt://eublctos.bod.edu.u/jbf/vol8/ss/ 8