The Time Value of Money in Financial Management

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Clifford Rich
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1 The Time Value of Moey i Fiacial Maagemet Muteau Irea Ovidius Uiversity of Costata irea.muteau@yahoo.com Bacula Mariaa Traia Theoretical High School, Costata baculamariaa@yahoo.com Abstract The Time Value of Moey is a importat cocept i fiacial maagemet. The Time Value of Moey (TVM) icludes the cocepts of future value ad discouted value. It is madatory for a fiacial professioal to kow ad operate the specific techiques of TVM. Withi the preset article we preset the basic otios ad illustrate their applicatio i the field of ivestmet projects. The case studies preseted are valuable for a efficiet fiacial maagemet. Key words: time value of moey, preset value, future value J.E.L. classificatio: G2; G32; M2. Itroductio The cocept of Time Value of Moey (TVM) has a large applicability i the fiacial maagemet of compaies, i bakig, o the capital market ad i day to day life. Damodara sed:,,there are three reasos why a dollar tomorrow is worth less tha a dollar today: Idividuals prefer preset cosumptio to future cosumptio. To iduce people to give up preset cosumptio you have to offer them more i the future. Whe there is moetary iflatio, the value of currecy decreases over time. The greater the iflatio, the greater the differece i value betwee a dollar today ad a dollar tomorrow. If there is ay ucertaity (risk) associated with the cash flow i the future, the less that cash flow will be valued. (Damodara, 200) But why is TVM cocept ecessary i bakig? People with spare fuds ad the desire to ivest them could decide to directly led them to borrowers i exchage for periodic repaymets of the pricipal ad iterests. However, this would ivolve resources ad costs for both the leder ad the borrower: () O the oe had, it is extremely difficult for the leder to have a accurate picturs of the borrower s situatio i terms of guaratee, so leder would have to moitor the borrower so as to assess the security of the ivestmet; (2) O the other had, the borrower might wat a larger loa tha the leder is able to provide or perhaps eeds the moey for a loger period of time tha the leder ca afford. (Paiego, Muñoz MLM, 205 p 4) The cocept of TVM is used i fiacial maagemet ad withi the selectios methods of ivestmet projects. 2. The cocept of Time Value of Moey The TVM is the cocept accordig to which a sum of moey owed i the preset has a greater value tha the value of the same sum received at a momet i the future. Thus, it is take ito accout the opportuity of the oe presetly owig the sum of moey to ivest it ad to obtai future gais such as iterest or profit. The techiques used i order to make possible comparig ad 593

2 calculatig the time value of moey iclude: Compoudig, Discoutig, Capitalizatio, Idexig. Withi the preset paper we shall focus o the first two techiques.,,i fact, most of Time Value of Moey formulas are closely related. Whe itroducig TVM formulas, the author ca classify them uder differet coditios ad lik their relatioships to orgaize them. (Che J. K, 2009, p 77) Compoudig represets the coversio of a curret (today) amout of moey ito a future (a future year) amout of moey, through the compoudig factor or the compouded iterest factor. The formula is: V V o ( + k), where: V o the iitial ivested capital (the preset day sum of moey); k the profitability rate requested / expected by the ivestor; the time iterval existig betwee the preset momet ad the future momet for which the future value of the capital is estimated V the value of the capital estimated for a certai future momet; (+k) represets the compoudig factor.,,future Value is the value at some future time of a preset amout of moey, or a series of paymets, evaluated at a give iterest rate. (Kuhlemeyer, 2008),,Discoutig is the techique that calculates the preset value of a future sum of moey (that ca be received or paid). Discoutig requires computig the discouted (preset) value of the amout of moey (cash flows) that are goig to be received at future momets i time. V 0 V ( + k ) Preset Value is the curret value of a future amout of moey, or a series of paymets, evaluated at a give iterest rate. (Kuhlemeyer, 2008) 3. Applyig discoutig i the selectio methods of ivestmet projects The evaluatio of ivestmet projects of compaies is a importat part of the efficiet fiacial maagemet ad presumes takig the followig madatory steps:. Quatifyig the costs of the ivestmet project is the iitial decidig step, with importat effects over the ext steps ad over the fial selectio decisio. 2. Estimatig the cash flows (CF) that will result followig the implemetatio of the ivestmet project. 3. Determiig the cost of capital or the discout rate 4. Discoutig the cash flow geerated by the exploitatio of the ivestmet. 5. Comparig the preset value of the estimated cash flows with the prior computed costs of the project. If the preset discouted value of cash flows of the respective project is larger tha the implemetatio costs, the the project may be accepted as beig profitable. Otherwise, the project is ot to be implemeted. I order to select the profitable ivestmet projects we ca use the payback period (PP) method or the NPV (et preset value) method. Case study. A model of determiig the discouted payback period I a compay it is sought to icrease productivity by acquirig a ew techological lie. There are two optios to make this ivestmet ad the icomig ad outgoig flows are sythesized i 594

3 Figure o.. Ivestmet optios \ - thousads of lei - Year Discouted cash-flow Optio A Optio B Iitial cost The egative value represets the costs of the iitial ivestmet ad the flows i year 4 are cumulated with the residual value of the compay at the time, thousads of lei. I the followig lies we shall aswer the questio: Which of the two projects should be chose usig the project selectio method PP? For the purpose of determiig the PP of the ivestmets there must be determied the cumulated discouted cash-flows for the two optios. (Figure 2) Figure o. 2. Cumulated discouted CF -thousads of lei- Cumulated cash-flow Year Opt. A Opt. B Iitial costs Substatiatig the decisio i fiacial maagemet is realized after computig the payback period for each project: Project A: The thousads of lei iitially ivested are paid back i two years plus a period of t days that we shall determie. I the third year we recuperate thousads of lei. We calculate the daily cash flow for year CF 3 / zi 5 479, 45 thousads of lei / day 365 The thousads of lei that remai at the ed of year 2, will be recuperated i: lei t 36,5 days 37 days 5479, 45 lei / day For project A it results a payback period of: PBP 2 years & 37 days. Project B: After 2 years, the iitial ivestmet is ot fully covered. Agai, we calculate the daily cash flow for year 3: CF 3 / zi 409, 58 thousads of lei / day 365 The thousads of lei that remai upaid at the ed of year

4 lei t 2 409,58 lei / zi PBP 2 years ad 84 days. 83,95 zile 84 zile We choise project A for implemetatio. Project A is the oe that proves agai as beig more effective for the compay. Case study 2. Model of determiig the NPV of the ivestmet The fiacial flows geerated by implemetig a ivestmet project are produced at differet momets i time. I order to determie the profitability of a ivestmet, we must compare the fiacial flows, at the same momet, a process realized takig ito accout the TVM. This may be accomplished through the discoutig procedure by which all the geerated flows of the ivestmet are mathematically traslated to the iitial momet of implemetatio of the project. The method used i selectig the profitable project is the Net Preset Value (NPV). If we have several projects that have positive NVP, we will implemet the oe with the greater et preset value. If the NVPs are close, we will choose the project requirig a smaller iitial ivestmet. For the calculatio of NVP we have the formula: NPV Net discouted cash flows - iitial ivestmet ad CFi CF CF2 CF Vetpreset i 2 ( + k) ( + k) ( + k) ( k) i + Thus, the NVP method does ot offer decisio makers ay certai iformatio regardig the order of acceptace for fiacig various aalyzed ivestmet projects, it oly aswers the questio: Are the projects acceptable?. We must decide, by usig the NPV method, if the followig project is profitable takig ito accout the data: Iitial ivestmet costs EUR; Cash flow i the ext 4 years: Year : EUR; Year 2: EUR; Year 3: EUR; Year 4: EUR. Discout rate: 2%. We discout the estimated cash flows ad we compare them with the prior computed costs of the ivestmet. (Fig 3) Figure o. 3. Net preset value -EUR- Year Cash flow Discouted rate Discouted (+k)i cash flow TOTAL: Iitial ivestmet: NPV EUR EUR EUR > 0, the project is profitable ad may be implemeted. 596

5 4. Coclusios TVM cocept stads at the basis of the profitability aalyses i fiacial maagemet. As the PP represets the period at the ed of which the iitial ivestmet equals that of the total cash flow geerated by the ivestmet project, we may say that this method is coected to the otio of ivestmet liquidity. The ivestmet liquidity is greater as the payback period is shorter. Discoutig, as a fiacial techique, allows the compariso of the reveue obtaied at differet momets i time with the iitial costs ecessary for the implemetatio of a ivestmet. This techique is useful i determiig the profitable projects, as it was preseted i the case study o 2. Damodara sed:,,preset value remais oe of the simplest ad most powerful techiques i fiace, providig a wide rage of applicatios i both persoal ad busiess decisios. Cash flow ca be moved back to preset value terms by discoutig ad moved forward by compoudig. The discout rate at which the discoutig ad compoudig are doe reflect three factors: () the preferece for curret cosumptio, (2) expected iflatio ad (3) the ucertaity associated with the cash flows beig discouted. (Damodara, 206). 5. Refereces Che J. K, Time Value Of Moey Ad Its Applicatios I Corporate Fiace: A Techical Note O Likig Relatioships Betwee Formulas, America Joural of Busiess Educatio September 2009, Volume 2, Number 6, p.77 Damodara, A., A Primer o the Time Value of Moey (accessed ) Kuhlemeyer G. A., Fudametals of Fiacial Maagemet, 2/e, Chapter 3, Time Value of Moey, Pearso Educatio Limited 2008, wps.pearsoed.co.uk/wps/media/objects/.../vw3e-03.pptx, (accessed ) Paiego MP, Muñoz MLM, Iteratioal Bakig Regulatio: the Basel Accords ad EU implemetatio of Basel III, 205, g. 4, eprits.ucm.es (accessed ) 597

CAPITAL PROJECT SCREENING AND SELECTION

CAPITAL PROJECT SCREENING AND SELECTION CAPITAL PROJECT SCREEIG AD SELECTIO Before studyig the three measures of ivestmet attractiveess, we will review a simple method that is commoly used to scree capital ivestmets. Oe of the primary cocers