American Journal of Business Education September 2009 Volume 2, Number 6

Transcription

1 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 Tme Value Of Moe Ad I Applcao I Corporae Face: A Techcal oe O L Relaohp Bewee Formula Je-Ho Che, Alba Sae Uver, USA ABSTRACT Tme Value of Moe (TVM he mo mpora chaper he bac corporae face coure. I mperave o uderad TVM formula becaue he mpl mpora TVM cocep. Sude who reall uderad TVM cocep ad formula ca lear beer chaper of TVM applcao. Th echcal oe ed o pree more complee TVM formula ad l her relaohp from he row au perpecve o a rucor each ad ude lear. Alhouh TVM formula are alread avalable he exboo, h echcal oe provde aoher perpecve of pree ad ummarz TVM formula. The mplfcao or exeo of he row au formula o reach oher TVM formula dcued h oe. Keword: Tme Value of Moe Formula, The Grow Au. ITROUCTIO T me Value of Moe (TVM he mo mpora chaper he bac corporae face coure bue educao. Sude who reall uderad TVM cocep ad formula ca lear beer TVM applcao, uch a bod valuao, oc valuao, co of capal, ad capal bude. ue o he echolocal advaceme, TVM formula are bul he facal calculaor ad ude ca ulze fuco e o wor TVM calculao effcel. Alhouh facal calculaor help ude compue awer faer, uderad TVM formula ll mperave becaue hee formula mpl mpora TVM cocep. Wh old uderad of TVM formula, ude are able o def wha he queo a ad compue he correc awer b u eher formula or fuco e. Whe lear TVM, ude ma ee ma formula led he exboo. Some ude ma h hee formula are dffcul o uderad becaue he are cofued wh hee formula. I fac, mo of TVM formula are cloel relaed. Whe roduc TVM formula, he rucor ca claf hem uder dffere codo ad l her relaohp o oraze hem. Th wa eaer for ude o beer uderad hee formula ad he eece of TVM. Moreover, ude ca lear beer TVM applcao, auh laer chaper. TVM formula are avalable he exboo. Some exboo ol l frequel ued formula whle oher clude more formula. I addo, dffere exboo pree ad oraze TVM formula dffere wa. Th echcal oe ed o pree more complee TVM formula ad l her relaohp from he row au perpecve o a rucor each ad ude lear. Alhouh ma TVM formula led h echcal oe ca be foud he exboo, provde aoher perpecve of pree ad ummarz TVM formula. The mplfcao or exeo of he row au formula o reach oher TVM formula dcued h oe. The remader of h echcal oe orazed a follow. Seco decrbe he row au. Seco mplfe or exed he row au formula o reach oher TVM formula ad l her relaohp. Seco 4 coclude h oe wh able ummarz TVM formula dcued eco. 77

2 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6. THE GROWIG AUITY For he row au, he pame expeced o row a a coa rae for a fe umber of perod. The formula for he pree value ( of row au ad he fuure value ( of row au are how a follow ad derved Appedx A. Where row au row au (( ( ( ( : Pame a ed of he fr perod (Pame oe perod from oda : he pame rowh rae per perod : he ere rae per perod : umber of perod. OTHER TVM FORMULAS Oher TVM formula ca be acheved b mplf or exed equao ( or (, he formula for he or of row au... Pree Value Iere Facor Au (IFA, Pree value ere facor au (IFA, repree he of $ pame ( = $ occurred a ed of each perod for a fe umber of perod. IFA,, whch requre = $ ad = (zero rowh rae becaue of he ame amou of each perod, a pecal cae of of row au. Whe = $ ad =, equao ( wll be mplfed o he follow equao (. IFA (, ( Ma face ad accou exboo pu IFA, able he appedx. The umber able are made baed o equao (.... Pree Value ( of Ordar Au of ordar au mea he of ame ( > $ occurred a ed of each perod for a fe umber of perod. of ordar au, whch requre = (zero rowh rae becaue of he ame amou of each perod, a pecal cae of of row au. To e of ordar au, we ca eher mplf equao ( b aum = or ue o mulpl b equao (. So, le = equao ( or ue o mulpl b equao (. of ordar au ca be reached a follow. 78

3 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 ( ordar au IFA, (4... Pree Value ( of Au ue Compar au due wh ordar au, we ca fd he follow relaohp. au due ( (5 ordar au The dealed proof of equao (5 how Appedx B. Ue equao ( o mulpl b (+. We e IFA, ( ( ( ( ( ( IFA, (6 Combe equao (4, (5, ad (6. of au due ca be wre a follow. IFA ( IFA (7 au due, (,.. Fuure Value Iere Facor Au (IFA, Fuure value ere facor au (IFA, repree he fuure value ( of $ pame ( = $ occurred a ed of each perod for a fe umber of perod. IFA,, whch requre = $ ad = (zero rowh rae becaue of he ame amou of each perod, a pecal cae of of row au. Whe = $ ad =, equao ( wll be mplfed o he follow equao (8. IFA, (( (8 Ma face ad accou exboo alo pu IFA, able he appedx. The umber able are made baed o equao (8.... Fuure Value ( of Ordar Au of ordar au mea he of ame ( > $ occurred a ed of each perod for a fe umber of perod. of ordar au, whch requre = (zero rowh rae becaue of he ame amou of each perod, a pecal cae of of row au. To e of ordar au, we ca eher mplf equao ( b aum = or ue o mulpl b equao (8. So, le = equao ( or ue o mulpl b equao (8. of ordar au ca be reached a follow. 79

4 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 (( ordar au IFA, (9... Fuure Value ( of Au ue Compar au due wh ordar au, we ca fd he follow relaohp. au due ( ( ordar au The dealed proof of equao ( alo how Appedx B. Ue equao (8 o mulpl b (+. We e IFA, (( ( (( ( ( (( IFA, ( Combe equao (9, (, ad (. of au due ca be wre a follow. IFA ( IFA ( au due, (,.. Perpeu ad Soc Valuao (Zero Growh Commo Soc ad Preferred Soc... Perpeu Perpeu defe ha he ame amou of per perod occur forever. Therefore, he ame for each perod ( =, zero rowh rae ad he umber of perod fe (. Aa, baed o equao (, whe = ad,. 4 So, he pree value of perpeu wll become perpeu (... Soc Valuao: Commo Soc (Zero Growh Model Zero rowh commo oc aume ha he expeced fuure dvded per perod wll be he ame ad wll la forever. Acuall, h he ame uao a wha we dcued for perpeu. The formula o calculae he value of oc oda (P hould be he ame a equao ( excep u dffere oao. P (4 I equao (4,, he expeced fuure dvded per hare per perod, le equao ( ad, he requred rae of reur o commo oc per perod, le equao (. 8

5 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6... Soc Valuao: Preferred Soc Preferred oc ha he ame uao a perpeu ad zero rowh commo oc. The fxed amou of dvded expeced o la forever. Aa, he formula o calculae he value of preferred oc oda (V p hould be he ame a equao ( ad (4 excep u dffere oao. p V p (5 p I equao (5, p, he fxed amou of preferred oc dvded per hare per perod, le equao ( ad equao (4. p, he requred rae of reur o preferred oc per perod, le equao ( ad equao ( Soc Valuao: Commo Soc (Coa Growh Model The coa rowh model aume ha he oc dvded per perod expeced o row a he coa rae ( forever ( ad he requred rae of reur hould be reaer ha he dvded rowh rae ( >. The coa rowh model le he row perpeu. Aa, baed o equao ( ad ue (= (+ ad o ubue for ad, repecvel. Whe > ad, P (. The value of oc oda (P wll be a follow. (6 Where : Toda (ju pad dvded : vded a he ed of perod (vded oe perod from oda 6 Equao (6 ca be exeded o he follow equao (7 o calculae he value of oc perod from oda, P. ( ( P ( P ( (7.5. Two-Sae Growh Soc Valuao Some frm have uperormal rowh rae for he fr few ear due o rapd expao ad laer o bac o he ormal rowh rae, whch coue forever. Th he cae of wo-ae rowh oc. For wo-ae rowh oc, he dvded rowh rae for he fr ae (fe umber of perod. The dvded rowh rae for he ecod ae coa a from perod + ul f. The uao he fr ae le he row au o equao ( ca be ued he fr ae o compue he. The coa rowh model ca be appled o he ecod ae. P, he value of oc perod from oda, + /( baed o equao (7. +, he dvded per hare a perod +, hould be (+ (+ h wo-ae rowh cae. To fd he of P, we eed o dcou P bac perod. The formula for he value of wo-ae rowh oc oda (P ca be wre a follow. 8

6 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 8 P P ( ( ( ( ( ( (8 I equao (8, ca be reaer ha bu mu be le ha. Th mea he uperormal rowh rae of he fr ae ca be reaer ha he requred rae of reur bu he ormal rowh rae of he ecod ae mu be le ha he requred rae of reur..6. Bod Valuao The value of bod he um of pree value of fuure coupo pame a ed of each perod ad he pree value of face value (par value a maur. The eld (eld o maur repree he aual rae of reur a veor ca ear f he or he hold he bod ul maur. The aual coupo bod mae he coupo pame a ed of each ear ad he face value (par value pame a maur. The value of aual coupo bod (V B calculaed a follow. 7 B F F IFA F V ( ( ( ( ( (, (9 Where = umber of ear = Aual coupo pame (= aual coupo rae face value = Bod eld (or called eld o maur F = Bod face value (par value, whch eerall aumed $, The pree value of fuure coupo pame a ed of each ear le he pree value of ordar au o equao (4 ca be ued h par. The pree value of face value (par value a maur le he pree value of a lump um, whch rearraed from equao (C..6.. Ieral Rae of Reur (IRR Aa, bod valuao formula ca be wre a follow.

7 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 V B ( ( F ( (... ( ( F ( ( Rearrae equao ( b mov V B o he rh of = o e ( ( ( V B... ( F ( ( The eral rae of reur (IRR mehod, ofe ued he capal bude, defe ha IRR he dcou rae, whch mae he e pree value ( equal o zero. Baed o defo, IRR ca be expreed a follow. CF IRR CF CF CF CF... ( IRR ( IRR ( IRR CF ( IRR ( Compar equao ( ad (, we ee ha he al veme (CF, eave (cah ouflow le he value of bod ha veor pa for oda ( V B ad IRR le he eld ( bod valuao. I edou ad me coum o fd mauall ce we eed o ue ral ad error mehod. We uuall ue he facal calculaor fuco e o fd. I addo o u I/Y e o fd, we ca ue IRR e o fd becaue he eld le he eral rae of reur. 4. COCLUSIO From he dcuo he prevou eco, we ca ow ha TVM formula are cloel relaed. Baed o dffere codo, we ca mplf or exed he formula of row au o reach oher formula. The follow able ummarze TVM formula ad l her relaohp dcued he prevou eco. Table : Summar of Formula Uder he Codo of of Grow Au [eq (] become Exeo = $, =, ad fe IFA, [eq (] IFA, (+ = IFA,- + [eq (6] > $ ( $, =, ad fe of Ordar Au [eq (4] of Ordar Au (+ = of Au ue [eq (5] of Au ue = IFA, (+ = > $, =, ad fe ( (IFA,- + [eq (7] of Perpeu [eq (] Zero Growh Model [eq (4] Value of Preferred Soc [eq (5] Coa Growh Model [eq (6] P = + /( = P (+ [eq (7] > $, ad fe ( The equao umber for each formula, eq (#, how he brace [ ]. 8

8 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 Table : Summar of Formula Uder he Codo of of Grow Au [eq (] become Exeo = $, =, ad fe IFA, [eq (8] IFA, (+ = IFA,+ [eq (] > $ ( $, =, ad fe of Ordar Au [eq (9] of Ordar Au (+ = of Au ue [eq (] of Au ue = IFA, (+ = (IFA,+ [eq (] The equao umber for each formula, eq (#, how he brace [ ]. Table : Two-Sae Growh Soc Valuao ad Bod Valuao Combao Valuao Sae: of Grow Au Two-Sae Growh Soc Valuao [eq (8] d Sae: Coa Growh Model (Exeo Par: of Ordar Au Bod Valuao [eq (9] d Par: of a Lump Sum (Implcao: Yeld he IRR. [eq (, (, (] The equao umber for each formula, eq (#, how he brace [ ]. AUTHOR IFORMATIO Je-Ho Che a facul member a Collee of Bue, Alba Sae Uver. He ha experece of each corporae face, bue ac, ad prcple of mcroecoomc. H rece reearch ere clude fxed come ecure ad eraoal face. REFERECES. Brham, Euee F. ad Joel F. Houo, Fudameal of Facal Maaeme, Coce 5 h Edo, Thomo Souh-Weer, Mao, Oho, 6.. Ro, Sephe A., Radolph W. Weerfeld, ad Bradford. Jorda, Fudameal of Corporae Face, 8 h, McGraw-Hll/Irw, ew Yor, ew Yor, 8. Appedx A: ervao of he Pree Value ( of Grow Au ad he Fuure Value ( of Grow Au A mple wa leared hh chool mahemac o derve a eomerc ere ca be a follow. Suppoe a eomerc equece a, ar, ar, ar,..., ar ( erm ad r a commo rao. Le S be a eomerc ere, whch he um of erm of a eomerc equece. S a ar ar ar... ar (A rs ar ar ar... ar ar (A (A (A [Subrac equao (A from equao (A], he ve ( r S a( r Therefore, a( r S r (A 84

9 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 For he row au, he pame (, occurred a he ed of each perod, expeced o row a he coa rae ( for a fe umber of perod ( fe. he ere rae per perod. Therefore, he of row au calculaed a follow. row au ( ( ( ( (... ( Sce row au a eomerc ere, we ca appl o equao (A. Subue follow. S row au, a, ad r equao (A. The, equao ( derved a row au The of row au calculaed a follow. row au ( ( ( ( (... ( Sce row au a eomerc ere a well, we ca appl o equao (A. Subue derved a follow. S row au, a (, ad r equao (A. The, equao ( ( ( row au ( (( ( Appedx B: Relaohp bewee Ordar Au ad Au ue Ordar au repree he ame amou of pame ( a ed of each perod for a fe umber of perod (. The me le of ordar au a follow. 85

10 Amerca Joural of Bue Educao Sepember 9 Volume, umber Baed o he above me le, of ordar au ad of ordar au ca be expreed a follow. ordar au ( (... ( ( (B ordar au ( ( (... ( (B Au due repree he ame amou of pame ( a be of each perod for a fe umber of perod (. The me le of au due a follow Baed o he above me le, of au due ad of au due ca be expreed a follow. au due... (B ( ( ( au due ( ( ( (... ( (B4 Compar equao (B wh (B, we ca fd ha f (B (+, wll be (B. au due au due ( Thu, equao (5 proved. ordar au Compar equao (B wh (B4, we ca fd ha f (B (+, wll be (B4. ( Thu, equao ( proved. ordar au Appedx C: Fd IFA, b Compoud IFA, for Perod The mo bac TVM formula ( (C 8 To fd IFA,, we ca ulze equao (C o compoud IFA, for perod. Subue IFA, (equao ( for ad plu equao (C. Therefore, 86

11 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 IFA, ( ( ( ( ( (( EOTES To emphaze he mporace of TVM, Brham ad Houo (6 move TVM from Chaper 6 o Chaper o allow ude loer me o de TVM maeral before lear TVM applcao chaper ad add more eco he coe of TVM chaper o help ude beer uderad TVM. Ro e al. (8 ue wo chaper o roduce TVM ad add real world example ad ed-of-chaper mcae o ehace TVM coe. Whe ( of row au calculaed, he dcou (compoud rae. Aoher wa o fd IFA, o compoud IFA, for perod. See he deal Appedx C. 4 Smlarl, equao ( ca be acheved baed o equao (4. Whe, become equao (.. The, equao (4 wll 5 p Equao (5 ca be rearraed a p. p he requred rae of reur o preferred oc from he veor V p perpecve ad he co of preferred oc from he frm perpecve. Th formula ca be ued a a compoe for calcula he frm wehed averae co of capal f he frm ue he preferred oc. 6 Equao (6 ca be rearraed a., whch co of he dvded eld ( /P ad he capal a eld P (, he requred rae of reur o commo equ from he veor perpecve. he co of commo equ from he frm perpecve. Th formula ca be ued a a compoe for calcula he frm wehed averae co of capal. 7 Alhouh mo bod are emaual coupo bod, for mplc he aual coupo bod ued for demorao. We ca modf equao (9 b replac wh, replac wh /, ad replac wh / o fd he value of emaual coupo bod. 8 We ca rearrae equao (C o e l,, or. ( l( 87

12 Amerca Joural of Bue Educao Sepember 9 Volume, umber 6 OTES 88