Yuriy V. Trifonov, Doctor of Economics Professor, Dean of Economic Faculty Nizhniy Novgorod State University n.a. N.I. Lobachevsky, Russia

Transcription

1 Iraioal Joural of Bui a Social Scic Vol 2 No 21 [Scial Iu Novmbr 2011] PLANNING AN INVESTMENT PROGRAM OF A OMPANY IN VIEW OF REINVESTMENT OPPORTUNITIES Yuriy V Trifoov, ocor of Ecoomic Profor, a of Ecoomic Faculy Nizhiy Novgoro Sa Uivriy a NI Lobachvy, Ruia Srgy N Yahi, ocor of Ecoomic Profor, Ha of h Iovaio Maagm arm, Nizhiy Novgoro Sa Tchical Uivriy a RE Alyv, Ruia Egor V Kohlv, Ph i Ecoomic Aocia Profor, Sa a Muicial Maagm arm, Nizhiy Novgoro Sa Uivriy a NI Lobachvy, Ruia Srgy A Maarov Sior Tachr, Mahmaic a Sym Aalyi arm Volga-Vyaa Acamy of Public Amiiraio, Ruia A comay ivm rogram i raw u wih cific rfrc, uig a joi aalyi of margial co of caial (M) a ivm ooruiy chul (IOS) curv I i ugg o aly h moifi iral ra of rur (MIRR) iicaor ia of h iral ra of rur (IRR) iicaor for loig h IOS curv Th MIRR quaio ha b imrov o al wih h roblm of h circlig i rmiig h icou ra a calculaig h oimal ivm bug I h cox of a coiuouly chagig coomic virom, bui a riva ivor hav o ma fairly comlica fiacial ciio ha houl allow for may facor affcig h arg rofi margi Such facor iclu xral coomic coiio, uch a chag i h lgal virom of coomic acivii i h coury, ifluc of h coomic virom of forig courari a global cri a wll a iral coomic coiio, uch a h amou of ow fiacial ourc, icluig rofi a ha, a cri caabilii of bui a riva ivor Th abov coiio coml ivor o la hir ivm ooruii i orr o ovrcom crii iuaio a xa bui Th laig roc ivolv boh aalyzig iiviual ivm rojc a vlom of major ivm rogram icororaig a crai umbr of rojc Thi abl comai o coma variou mar gm Furhrmor, h abov rogram cao b imlm ul a comay ha quiy fu a cri caabilii uffici o fiac a fw rojc a a im I hi ca h ivor ha o choo h mo oimal rojc acag o miimiz xiur a icra h comay rofi From hr o w will u h rm maximum rmiibl amou of ivm o ma h oimal ivm bug Wh calculaig h oimal ivm bug, comai will ormally coruc margial co of caial (M) a ivm ooruiy chul (IOS) curv Th oimal ivm bug i whr h wo curv irc Th M curv i coruc ba o h wigh avrag co of caial (WA), uig h followig formula [1]: WA w ( 1T) w w, (1) whr w, w a w - cific wigh of liabilii, rfrr a oriary har, rcivly, i h oal caial valu; ( 1 T),, - como valu of liabilii, rfrr a oriary har, rcivly; - ir ra o liabilii; T rofi ax ra 307

2 Th Scial Iu o omorary Rarch i Ar a Social Scic r for Promoig Ia, USA Each xhauio of o of caial como giv ri o a icoiuiy oi icoiuiy oi () o h M curv ar fou wih h followig formula [1]:, (2) 308 w whr amou of caial of a giv y a a lowr co, а w - har of caial of a giv y i h oal caial amou omo caial valu i h irval bw icoiuiy oi ar fi wih h followig formula [1] Noiribu rofi valu (%): 1 0 (1 g) g g, (3) P0 P0 whr 0 a 1 iz of a ivi r commo har i h curr a followig yar, rcivly (i moy ui), P 0 curr mar ric r commo har (i mu), g ra of icrm of yil a ivi o oriary har (%) Wh oiribu rofi i xhau, a comay may icra i quiy caial by iuig w oriary har I hi ca i h WA formula will b ubiu wih (valu of wly iu oriary har) ha i fi a follow: 1 g, (4) P0 (1 F ) whr F co of floaio of w oriary har o h mar (i mu) Prfrr har valu (%):, (5) P (1 F ) 0 whr iz of a aual ivi r rfrr har (i mu), F - co of floaio of w rfrr har o h mar (i mu) o of liabilii (в %): ( 1 T) (6) Th IOS i coruc uig IRR valu a h followig formula [1]: IF OF 0, (7) 0 (1 IRR) whr IF a IF - cah iflow a ouflow i yar, a rojc rio (yar) Wh cah rci from all h ivm rojc ur rviw rr aual auii, hr i a air way o fi IRR by uig h r aual auiy valu [2, 3]: PV R a ; IRR, (8) whr R aual aym amou a a ;IRR icou mulilir for aual auiy, which i fi a follow: 1 1 (1 IRR) a; IRR (9) (1 IRR) IRR 1 Kowig h imlmaio rio of ach rojc i yar a h icou mulilir valu, IRR for ach rojc may b fou uig h fiacial ablm a IOS curv ar h coruc a how i Fig 1 Th oimal ivm bug valu corro o h croig oi of h curv Such i h claical viwoi o calculaio of a comay oimal ivm bug, i rawbac big ha i irgar ay oibl rivm of rci from h curr rojc i ohr rojc or, a a miimum, i h ogoig bui W hrfor ugg a w aroach ha allow for uch oibilii

3 Iraioal Joural of Bui a Social Scic Vol 2 No 21 [Scial Iu Novmbr 2011] A will b how furhr, h ugg mho will hl la a bug for grar ivm If rivm oibilii ar a io accou, MIRR houl b fi ia of ach rojc IRR, uig h followig formula [1]: 0 OF (1 ) 0 IF (1 ) (1 MIRR), (10) whr ric of caial a which fu ar riv i h co mmbr of h quaio, i or If cah roc from ach ivm rojc ar auii, hr i a air way o fi MIRR wih h followig formula: R ; PV, (11) (1 MIRR) whr ; - aual auiy mulilir [2, 3] fi a follow: (1 ) 1 ; 1 Th MIRR will b qual o: R ; MIRR 1 (13) PV ( 1 ) (12) M a IOS curv coruc by MIRR ar ic i Fig 2 Show i h am figur i o li i h rviou IOS curv coruc by IRR L u ow coir h followig aar iuaio a a xaml of calculaig h comay oimal ivm bug uig h mho crib abov [1, 5] Aum ha a comay ha h caial rucur i bliv i oimal: 1 Oriary har (OS): 60% 2 Prfrr har (PS): 15% 3 Liabilii: 25% I h curr yar h comay xc o riv icom (NI) of 34,28572 mu; h ablih iz of ivi i 30%; rofi ax ra T 40% ; forca ra of icrm of yil a ivi g 9% r yar Whil i h rviou yar h comay ai h ivi mu r commo har, ow h har ll a h ric P 60 mu r har 0 Th comay may obai w caial a follow: 1 Iu of oriary har Th co of hir floaio o h mar (F ) will b 10% of h mar ric if h amou of iu har i u o 12,000 mu a 20% if h amou xc12,000 mu 2 Iu of w rfrr har Nw rfrr har wih aual ivi 11 mu r har may ll a h ric P mu r har Th co of hir floaio (F ), howvr, will b 5% if h amou of iu har i u o 7,500 mu a 10% if h amou xc 7,500 mu 3 Iu of w liabilii (bo) Liabilii of u o 5,000 mu may ll a a aual ra of 12%, ho from 5,001 mu o mu a a ra of 14% a ho i xc of mu a a ra of 16% 309

4 Th Scial Iu o omorary Rarch i Ar a Social Scic r for Promoig Ia, USA Th comay ivm caabilii ar how i Tabl 1 Tabl 1 omay Ivm aabilii Projc o a 0 (PV) (mu) Aual N ah Rci (R) (mu) A B E 20,000 20,000 2,1912 3, , , ,42784 L u fi icoiuiy oi o h margial co of caial (M) curv Projc Prio () (yar) icoiuiy oi ar rmi a follow W fir o ha h comay ha oiribu rofi (NP) i h followig amou: NP NI( 1 w ) 34,28572(1 03) 24,000 (mu), whr w aym of ivi i rcag o icom NI Tabl 2 alculaio of icoiuiy Poi l aial alculaio of icoiuiy Poi Orr Noiribu rofi 24, ,000 (mu) 06 OS allowig for F 10% 24,000 12,000 4 ( 10%) 60,000 (mu) 06 PS allowig for F 5% 7,500 3 ( 5%) 50,000 (mu) % liabilii 5,000 1 ( 12%) 20,000 (mu) % liabilii 2 ( 14%) 40,000 (mu) 025 L u ow rmi caial como valu i h irval bw Noiribu rofi (xhau i h irval from 0 o 40,000 mu): % 9% 1554% 60 Oriary har wih F 10% (40,001 o 60,000 mu): % 9% 1627% Oriary har wih F 20% (ovr 60,000 mu): 1718% Prfrr har wih F 5% (0 o 50,000 mu): % 1158% Prfrr har wih F 10% (ovr 50,000 mu): 1222% Liabilii a 12% (0 o 20,000 mu): ( 1T) 12% 06 72%

5 Iraioal Joural of Bui a Social Scic Vol 2 No 21 [Scial Iu Novmbr 2011] Liabilii a 14% (20,001 o 40,000 mu): ( 1T) 84% Liabilii a 16% (ovr 40,000 mu): ( 1T) 96% L u fi WA i h irval bw ach icoiuiy i h M curv I h irval from 0 o 20,000 mu, whr ( 1T) 72%, 1158%, 1554% : WA % % 0,6 1554% 1286% WA valu for h ohr irval of Tabl 2 ar fi i a imilar way: WA %, WA %, WA 14% 4, WA % M a IOS curv ar how i Fig 1 By ubracig h M curv from h IOS curv, w obai a ara corroig o h comay icom valu Th rojc IRR valu ar lai off o h IOS curv i craig orr o maximiz h ara, i i racic rojc houl b imlm i h orr B, E, c Fig 1 alculaio of h Oimal Ivm Bug Allowig for Rivm Nw caial (hou mu) Th comay houl acc h rojc B, E a a icar h rojc a A, ic hir IRR o o xc h margial valu of fu rquir o fiac ho rojc Th ivm bug oal 40,000 mu Furhrmor, h followig coiraio rgarig ivm ri houl b a io accou: 1 If h comay ri fir o imlm h rojc a h h ohr, i will riv icom from all h rojc, xc for h rojc A I hi ca, howvr, h ara obai by ubracig h M curv from h IOS curv will b l ha ha how i Fig 1, i h omay icom will b ifrior o h maximum oibl 2 If, for xaml, h rojc E a h h rojc B ar imlm h abov ara will ill b maximal Bu hi icra h ri, a whil h comay i imlmig h l rofiabl rojc E, a chag i law may occur, for xaml, ha will rv h mor rofiabl rojc B from big ubquly imlm Aohr xaml: aum ha h rojc B i o b carri ou joily wih aohr comay a by h im our comay coml h rojc E ha ohr comay may b facig riou fiacial harhi maig i imoibl o imlm h rojc B or, for xaml, may hav go bu I hi ca, agai, h b ivm ooruiy will b lo for u 311

6 Th Scial Iu o omorary Rarch i Ar a Social Scic r for Promoig Ia, USA 3 I Fig 1 h croig oi of M a IOS curv i aily obai L u aum aohr iuaio wh IRR 1396% If h rojc may b acc arially h roblm i co wih If, howvr, i may oly b acc i whol w o calcula h wigh avrag valu of fu ba o WA 3 a WA 4 a comar i wih IRR 4 Wha will ha if w a io accou h rojc ri? Th h caial valu u o a mor riy rojc houl b aju uwar, whra i houl b lowr for rojc wih lowr ha mium ri I hi ca h ircio of h w M curv wih IOS curv i u o fi h icom valu of w rojc ha ar almo a riy a h comay xiig a Moifyig h claical aroach o calculaio of h oimal ivm bug, w will calcula MIRR for ach rojc i h irval bw h icoiuii i h IOS curv, arragig h rojc i h orr a how i Fig 1 or i a a a rivm ra for calculaio, ig o whhr or o a comay ha xhau i oiribu rofi Projc B (0 o mu): 5 ( ) 1 5;15,54% , MIRR 5 B (1654%) MIRR valu i h ohr irval bw icoiuii ar obai i a imilar way: Projc E ( o 30,000 mu): MIRR E 1578% Projc (30,000 o 40,000 mu): MIRR 149% Projc (40,000 o 60,000 mu): MIRR 1514% Projc A (ovr 70,000): MIRR 1459% A M a IOS curv coruc by MIRR ar ic i Fig 2 Show i h am figur i o li i h rviou IOS curv coruc by IRR Fig 2 alculaio of h Oimal Ivm Bug Allowig/No Allowig for Rivm 312 Nw caial (hou mu)

7 Iraioal Joural of Bui a Social Scic Vol 2 No 21 [Scial Iu Novmbr 2011] A vi from Fig 2, MIRR MIRR Hc, i woul m mor logical a fir igh o lay off fir MIRR a h MIRR i IOS curv I hi ca, boh moifi iral ra of rur hav o b rcalcula ic i h irval from 30,000 o 60,000 mu rivm i ma a iffr ra I houl b o ha h rivm ra 15905% for h rojc i h avrag of wo valu, i i h irval from 30,000 o 40,000 mu 1554% a a ha from 40,000 o 50,000 mu 1627% Projc (30,000 o 50,000 mu): MIRR 1493% Projc (50,000 o 60,000 mu): MIRR 1529% Th if w irchag w MIRR a MIRR valu w will obai h w IOS curv how i Fig 3 I ma h rojc houl b imlm bfor h rojc Nw caial (hou mu) Fig 3 alculaio of h Oimal Ivm Bug wih Rivm Ta io Accou a Projc Imlm i h Nw Orr I hi ca, h ara bw M a IOS curv i h irval from 30,000 o 60,000 mu will b 0409 i fracio, whra wih h rviou rojc imlmaio orr i wa 0412 i h am irval I ma ha havig h rojc imlm i h rviou orr, i a how i Fig 2, i mor avaagou o h ivor A alo from Fig 2, if calculaio a accou of rivm ooruii, i MIRR calculaio, all h fiv ivm rojc ar rofiabl ic hir MIRR i mor ha WA for h rojc o b carri ou If rivm i o a io accou, i IRR calculaio, oly h rojc B, E a houl b imlm bcau hir IRR i mor ha WA If calcula by MIRR, h oimal ivm bug will b 70,000 mu I i much mor ha 40,000 mu i ca of IRR calculaio Th ara bw IRR a WA curv, whr IRR WA, i 1156 i fracio a ha bw MIRR a WA, whr MIRR WA i 1339, which ugg ha allowac for rivm i mor coomically bficial I h abov xaml h a of calculaig h oimal ivm bug ha b olv aily ough bcau w i o hav o icou cah ouflow OF i h lf i of h MIRR quaio I gral, h followig quaio houl b u for MIRR ia of h rviou o (10): 313

8 Th Scial Iu o omorary Rarch i Ar a Social Scic r for Promoig Ia, USA 0 OF (1 WA ) 0 IF (1 ) (1 MIRR) (14) Such moificaio of MIRR calculaio i xlai a follow Sic rivm i oly coomically ou if harholr (oriary harholr) obai h rur qual o ha hy ow hav o oriary har or highr rur, or houl b u i h quaio a a rivm ra (if h comay i currly iuig oriary har) I h lf i of h la quaio, h wigh avrag co of caial (WA) houl b a a a icou ra, bcau i racic, wh h oimal ivm bug i calcula, a acag of ivm rojc i coir, for ach of which i or i aum a a icou ra Y for comarabiliy of MIRR of iffr rojc icouig i rform a a igl ra Followig h raiio of h Amrica fiacial chool [1], h margial co of caial (M) valu may b a a uch a uivral ra, which o h joi curv of ivm ooruiy chul (IOS) a margial co of caial (M) i h wigh avrag co of caial (WA) a h croig oi of h abov curv If w follow h rcommaio [1] a ubiu h ra i h lf a righ i of h rviou MIRR quaio wih h ra WA commo for all h rojc a iu, i will giv ri o h circlig roblm crib by h auhor Thi roblm coi i a chag i h ivm ooruiy curv (i MIRR curv), rulig i a w croig oi of MIRR a WA curv, ha will corro o a w icou ra for all h rojc ur rviw Thu, by alyig h w moifi quaio ia of h rviou o o fi MIRR, w will rolv h abov circlig roblm ha la, amog ohr roblm, o ifii uaig of h oimal ivm bug Thi may riouly affc h corrc ciio maig a o h amou of moy a ivor houl alloca o imlm a ivm rojc acag If h MIRR ra i ali h ivm ri i a by h am four oiio rfrr o i h oimal ivm bug calculaio uig IRR Wha follow ar h baic cocluio w hav arriv a: 1) Wh calculaig h oimal ivm bug, allowac houl b ma for oial rivm of rci from h curr ivm rojc Thi roblm may b co wih if moifi iral ra of rur (MIRR) allowig for ivm ooruii ar lai off o h ivm ooruiy chul (IOS) curv ia of iral ra of rur (IRR) of h rojc Th a grar oimal ivm bug may b la 2) W ugg ha h MIRR fiig quaio offr i fiacial liraur b moifi a follow: cah ouflow by yar houl b icou a h wigh avrag co of caial (WA) ra rahr ha by h ric of caial (ra of rur o oriary har) Thi allow h cary fiacial calculaio o b o for h ir ivm rojc acag Th ric of caial (ra of rur o oriary har) houl b u a a rivm ra i h righ i of h MIRR quaio Thi hl al wih h roblm of circlig i uaig h oimal ivm bug/rogram calculaio Th obai rul may fi fairly wi u i variou iuri boh by comai a riva ivor Rfrc Brigham EF, Gai L Irmia Fiacial Maagm 4h Fory Worh; Philalhia; Sa igo; Nw Yor; Orlao; Aui; Sa Aoio; Toroo; Moral; Loo; Syy; Toyo: Th ry Pr, 1993, vol 1, , , hyri EM Fiacial mahmaic Mocow: lo, 2007, , 107 Kruchwiz L Iviiorchug ROlbourg; Vrlag; Much; Wi: Olbourg Wichafvrlag GmbH, 2000 S Yahi SN, Kohlv EV, Maarov SA Slcig A Iovaio Projc Ur icou Ra Ucraiy // Iraioal Joural of Bui a Social Scic r for Promoig Ia (PI), USA Vol 2 No 6; Aril 2011, Yahi SN, Yahia NI, Kohlv EV Iovaio a ivm comai fiacig Nizhiy Novgoro: VGIPU, 2010,