Abstract # Working Capital Exposure: A Methodology to Control Economic Performance in Production Environment Projects

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1 Abstract # Workng Captal Exposure: A Methodology to Control Economc Performance n Producton Envronment Projects Dego F. Manotas. School of Industral Engneerng and Statstcs, Unversdad del Valle. Cal, Colomba. Calle 13 No Tel Leonardo Rvera, Department of Industral Engneerng, Unversdad Ices. Cal, Colomba. Calle 18 No Tel POMS 21st Annual Conference Vancouver, Canada May 7 to May 10, 2010 Abstract The Cost-Tme Profle (CTP) s a tool that presents graphcally the accumulaton of drect costs on a product as t moves through the manufacturng process. CTP ncorporates the tme dmenson to the cost accumulaton, and the area under the CTP curve s the Cost-Tme Investment (CTI). In ths paper we propose a new measure, derved from the CTP: The Workng Captal Exposure. It wll be calculated valung the tmes and money amounts n whch the company worked wth ther own money at a certan rate, and the areas of the graph n whch the company worked wth the clent s money at a dfferent rate. It wll show for how long and for how much was the company exposed when workng n a project wth ther own money nstead of the customer s money. The assocated rsks wll be dscussed and further possbltes for probablstc research wll be presented. Keywords: Cost-Tme Profle, Workng Captal Exposure, Project Management, Cost, Investment.

2 1. Introducton Operatng managers have usually vewed nvestment as a statc number, $20 mllon, $200 mllon, and so on. As a statc entty, nvestment s dffcult to manage. One good example s nventores, whch requre extraordnary efforts to obtan reductons of even a few percentage ponts. Speakng dynamcally, nvestment s the flow of cash over the cycle tme of the busness process. It can be measured as cost per unt of tme over tme. In ths paper, we revst the Cost-Tme Profle (CTP) (Fooks, 1993), a graphcal representaton of how much money s spent on the manufacture of a product and for how much tme t remans nvested before beng recovered va sales. The CTP presents cost and tme data, nstead of operatng procedures or systems, therefore makng t an nterestng complement to Value Stream Mappng (Rother and Shook, 1998; Barker, 1994) for the complete representaton and montorng of a manufacturng system. Also, the area under the curve n the CTP represents the Cost-Tme Investment, whch has many smlartes to any regular nvestment. The Cost-Tme Investment mpacts the bottom lne by revealng hdden workng captal requrements. Ths fact makes the Cost-Tme Investment an mportant ndcator of the use of resources n the manufacturng of a product. The uses and applcatons of both the Cost-Tme Profle (CTP) and the Cost-Tme Investment (CTI) are all related to the smultaneous vsualzaton of the Cost and Tme dmensons and ther nteractons. There wll be a dscusson of these applcatons n subsequent sectons

3 However, when sellng dscrete products the costs domnate all the manufacturng and logstcs processes, and the company perceves revenues only at the very end of the cycle, when payment from customers s receved. In project management we have a dfferent stuaton, snce t s possble to receve cash advances even before ncurrng n any cost and n ntermedate ponts durng the lfe of the project, so t s necessary to assess the economc status of the project at any moment of ts duraton. For ths purpose we develop the Workng Captal Exposure (WCE), whch presents the economc poston of the project at any dscrete pont n tme and s able to represent cash advances at any moment and follow ther mpact on the management of the project. In ths paper the concepts and constructon of the Workng Captal Exposure (WCE) are presented through the use of a numercal example. Potental applcatons and transfer to other areas of Industral Engneerng and Manufacturng are dscussed, and questons to stmulate future research drectons are formulated. 2. The Problem Tradtonal product costng captures the product-related expendtures n a smple addtve manner. One of the bggest teachngs of the use of Value Stream Maps has been the dscovery that the tme t takes a product to flow through the process s usually much longer than t should. Ths dscovery hghlghts the mportance of consderng the tme dmenson and the tme-value of money on the costng of a product.

4 To address these two problems, the Cost-Tme Profle (CTP) was developed (Fooks, 1993). However, CTP handles easly the addton of costs wthout the alternaton of revenues or advances, therefore makng t nconvenent to handle projects. It also does not consder overhead, whch can be an mportant part of project expendtures. The problem then becomes to develop a tool to report the economc status of the project n real tme to nclude the occurrence of cash advances and the consderaton of overhead. Ths tool, called Workng Captal Poston (WCE), s derved from CTP. CTP wll be presented n the next secton and from there the development of WCE wll be presented. 3. Defnton of Cost-Tme Profle A Cost-Tme Profle s a chart that presents the Accumulated Cost at any moment n the manufacturng of a product. Fgure 1 shows an example of a Cost-Tme Profle. Accumulated Cost wat actvty Total Cost materals Cost-Tme Investment Tme Fgure 1: Example of a Cost-Tme Profle The CTP curve has dfferent types of elements (Rvera and Chen, ): - Actvtes: The Actvtes are represented as ascendng lnes (postve slope), snce at each unt of tme the total accumulated cost ncreases. (Assumpton: Actvty Costs are unformly dstrbuted over the duraton of the actvty, unless they can be further dssected n the tme dmenson). For Project Management there wll be a cost

5 component (overhead) that occurs every tme unt even f no drect actvty n the project s happenng, - Materals: The addton of Materals to the process s presented as a vertcal lne, assumng that materals are receved nstantaneously. Ths cost of materals wll contnue un-recovered untl the end of the process. - Wats: At certan moments n the process, no actvty s beng performed. Therefore, there s no actve addton of cost to the Total Accumulated Cost and for ths reason Wats are represented as horzontal lnes (or zero slope lnes). Wats are not very relevant for Project Management, because every day that passes generates costs due to payroll and overhead. - Total Cost: Ths s the heght of the graph at ts endng. It represents the dollar amount that has been spent as cost n the manufacture of the product. - Cost-Tme Investment: The area under the CTP curve represents how much and for how long costs have been accumulated durng the manufacturng process. It s the composton of the cost and tme dmensons (Rvera and Chen, ). 4. Constructon of the Cost-Tme Profle To properly buld a Cost-Tme Profle, several ntermedate steps need to be accomplshed. We need to know when the dfferent components of the CTP happen. We also need to know how much does each of the component cost. Combnng the knowledge of the prevous two ponts we fgure out how much does every tme unt of the manufacturng process cost. Fnally, wth the nformaton from the prevous fndngs, we calculate the Accumulated Cost

6 at every tme unt, and chart t to obtan the Cost-Tme Profle and calculate the Cost-Tme Investment. For ths case, we wll follow an example wth a smple project network wth seven actvtes. The necessary nformaton s presented n Table 1 and Fgure 2. Actvty Id Tme (months) Cost Rate ($/month) Materals ($) A 5 1,000 7,600 B 7 4,700 C 6 1,800 D 3 3,200 E 4 2,500 8,900 F 12 3,900 9,400 G 6 1,100 Table 1: Project network nformaton A 1 Begn B 2 C 3 F D End 4 G E Fgure 2: Smple Project Network 4.1. When do the components of the CTP happen? Buld the Process Map: The frst thng to do s to descrbe the project, ncludng the relevant actvtes, materal releases and wats. Ths can be accomplshed usng a Network Graph such as those employed n Project Management representatons (Hller and Lebermann, 1995). Fgure 2 presents an example of such a graph. Buld the schedule of actvtes: The schedule of actvtes should present when each component of the Cost-Tme Profle starts and fnshes. In ths case, ths s a depcton of the current state of the process; therefore a smple Gantt chart can be used. Fgure 3 presents the Gantt chart for the example that s beng presented here.

7 Id A B C D E F G Materals A 76 E 89 F 94 Overhead Monthly Cost Rate (00) Fgure 3: Gantt Chart for the example project How much cost happens at each tme unt? Fgure 3 presents the Gantt chart for the project, and also the cost rates for each component of the project. The frst secton presents the monthly cost rates for actvtes, then the cost of materals s presented at those moments where t happens, and fnally the overhead rate s added. The last lne (Monthly cost rate) presents the resultng cost to apply for each tme unt (month) 4.2. How much Accumulated Cost do we have at each moment? Buldng on the nformaton from the prevous ponts, t would be analogous to buld a second array of the same dmenson. In each poston of the array, we would have the Accumulated Cost, bascally the value of the prevous poston plus the cost ncrement n the correspondng tme unt. Fgure 4 presents such an array. Month Accumulated Cost (00) Fgure 4: Accumulated cost at each tme unt

8 4.3. Cost-Tme Profle The Cost-Tme Profle s the chart that presents the value of the Accumulated Cost at each tme unt. The Cost-Tme Investment s the summaton of all the postons n the array of Accumulated Cost. It s also the area under the CTP curve. The Total Cost s the heght of the Cost-Tme Profle at ts latest pont n tme. It s the Accumulated Cost at the last tme unt. It represents the addton of the costs ncurred durng the process wthout consderng the tme-value of money. Fgure 5 presents the Cost-Tme Profle for the example we have been followng Total Cost = $21,660 Accumulated Cost Month Cost-Tme Investment = 2,648,800 $-month Appled Interest Rate = 10% (annual) = % (monthly) Drect Cost = 21,660 + (2,648,800 * %) = $ 237, Drect Cost. Fgure 5: Cost-Tme Profle Chart and related calculatons for the Example case The Cost-Tme Investment represents a amount of money commtted n the product durng a certan perod of tme. Ths s analogous to securng a loan, where the user gets a sum and pays t back over tme. In ths analogy, the nterest payments are the cost of havng ths money for a certan tme; therefore we can use the same fgure and apply t to the Cost-Tme Investment. Because of ths, we argue that the Drect Cost of the product should be calculated as follows:

9 DrectCost = TotalCost + (Cost-Tme Investment * Appled Interest Rate) (Eq. 1) (Rvera, 2006). Appled Interest Rate represents whatever nterest rate the company deems approprate to apply n ths stuaton, be t the Internal Rate of Return, or the Cost of Captal, or a money market rate or any other the company chooses to use. Drect Cost captures the total dollar amount spent on the project, plus the tme value of money effect of the workng captal nvested n t. 5. Workng Captal Exposure 5.1. Constructon The Drect Cost, found through the constructon of the Cost-Tme Profle, s found under the assumpton that all costs and workng captal nvestments happen before any ncome s receved, as t s common for the manufacturng of tangble goods. Ths s not always the case for projects, n whch cash advances can be receved before the begnnng of the project and durng ts development. It s therefore necessary to further develop a tool that presents the status of the nvestment n workng captal at any moment durng the duraton of the project. Ths tool s what we call the Workng Captal Exposure (WCE). The WCE s analogous to fndng the Drect Cost at each tme unt. We wll now present some notaton and the constructon of the WCE. Notaton IR = Appled Interest Rate c = Cost that happens at tme unt AC = Accumulated Cost at tme unt ; AC = c k k = 0 (Eq. 2)

10 TC = Total Cost (at the end of the project); CTI = Cost-Tme Investment at tme unt ; CTI = AC k Drect Cost : TC = ACN (Eq. 3) k = 0 (Eq. 4) DC = TC + CTI * IR (Eq. 1) Drect Cost, as calculated above, s vald when calculated at the end of the project. However, f we want to fnd the Drect Cost at any moment durng the duraton of the project (WCE ) we need to replace TC and CTI for ther equvalent at a tme, so TC = AC and CTI = AC k k = 0. Replacng these n Equaton 1 we get WCE = Workng Captal Exposure at tme ; WCE = AC + IR * AC (Eq. 5) k= 0 k In Fgure 6 we present the chart and values for WCE for the example we are followng. Notce that WCE 22 = DC, whch s obvously expected. $ 250, , , ,000 50, Month Fgure 6: WPC for each tme unt Month WCP 1 20, , , , , , , , , , , , , , , , , , , , , , Impact of cash advances on the WCE The fgure for Workng Captal Exposure at the end of the example that we have followed so far s $217,301. However, ths fgure s obtaned consderng only costs (as t was explaned n CTP constructon). It s not uncommon that projects receve cash advances before begnnng

11 operatons, at ntermedate tmes durng executon and after fnshng operatons. In ths case, t s necessary to modfy the formula for the WCE (Equaton 5) to nclude the cash advances, consderng a 30% proft margn on the project and then dstrbutng the resultng prce ($310,431) n a $100,000 advance at tme 0, a $100,000 advance at month 11 and the remander of the money at the end of the project. How wll the WCE be affected by the presence of advances? We contend that the formula should be adjusted to consder the accumulated amount of money receved through advances. We shall call R (revenue) the advances receved at tme unt. Therefore, Equaton 5 should be adjusted as follows. WCE = AC k= 0 + IR * AC + R (Eq. 6) k k= 0 Usng ths new defnton, a comparatve profle s devsed (Fgure 7). The lne wth trangular markers presents the new poston (ncludng the consderaton of revenues) and the lne wth crcular markers presents the WCE wthout the consderaton of revenues. $ 250,000 $ 200,000 $ 150,000 $ 100,000 $ 50,000 $ $ 50,000 -$ 100,000 -$ 150,000 -$ 200,000 -$ 250,000 WCP (No Rev) WCP (+Rev) Fgure 7: Workng Captal Exposure (wth and wthout consderaton of Cash Advances)

12 An mportant remark can be made from ths chart: In the case of WCP consderng the cash advances, the poston of the company s always negatve, whch means that throughout the duraton of the project the company always worked usng the captal of the clent entty. Ths s the deal scenaro for a project-orented company. 6. Conclusons and Future Research 6.1. The Workng Captal Poston at the end of the project s the proft obtaned In the example case, the fnal poston reflects the dfference between the total prce of the project and the WCE wthout consderng advances (Drect Cost n the CTP scheme). Ths was expected, and t s a useful tool to determne the proft obtaned n the project The WCE reflects the ownershp of the resources used A postve WCE means that the workng captal a company s usng s of ts ownershp. A negatve poston means that there are stll resources present from the cash advances and they have not been entrely consumed, therefore we are workng wth the clent s money, whch s the stuaton any company would lke to fnd tself n. Also, t opens the possblty for estmatng the effect of sellng unts at dfferent moments n tme, n the case of constructon project, for example Varable Interest Rates In hgh-nflaton economes (such as those n several Latn Amercan countres), t s common that the Central Bank ncreases nterest rates as a mechansm to control the demand of money

13 (to control nflaton). In long-term projects, the WCE would be affected as a result of the applcaton of ncreasng rates (as the terms lengthen, the rates ncrease) Cost of Captal Consderatons The use of a unque cost-of-captal rate for the project does not consder the varable nature of nterest rates facng the expectaton of proftablty that nvestors have for dfferent nvestment terms, that s, the term rate structure. Further research n ths area s needed to nvestgate the mpact of nvestor preferences and expectatons on the WCE for projects desgned for dfferent duratons (dependng on the complexty and captal requrements) The Treasury Effect When negatve postons (WCE < 0) happen, as a result of the cash advances receved, t could be argued that the treasurer could put the unassgned money to work n fnancal markets, generatng some fnancal ncome. Ths s called the Treasury Effect, and t would be hghly desrable for a project-orented company to generate the capablty of puttng the clent s money to work to generate some extra ncome for the project. Further research n ths area s advsed, as well n the estmaton of the dfferental between the cost-of-captal rate and the rate of return expected n fnancal markets The effect of tmng of the cash advances on the WCE When cash advances durng the executon of the project are consdered t s necessary to study the mpact of ther tmng on the WCE. Dependng on the amount and tme of recepton of

14 these advances, the Workng Captal Exposure on dfferent moments wll be affected and the exposton to use the company s resources or the clent s resources wll vary The mpact of uncertanty on the WCE Whereas productve envronments for projects n areas such as varablty present the executon tmes of actvtes, would be desrable to assess the possble behavor of the CTP and the WCE under condtons of rsk and uncertanty. Could be used such technques as Monte Carlo smulaton to estmate the WCE of the projects. References ROTHER, M., SHOOK, J. Learnng to See Value Stream Mappng to Add Value and Elmnate Muda. Brooklne, MA: The Lean Enterprse Insttute, FOOKS, J. H. Profles for performance: Total qualty methods for reducng cycle tme. Readng, MA: Addson-Wesley, 1993 HILLIER, F.S. LIEBERMANN, G.J. Introducton to Mathematcal Programmng. New York: McGraw-Hll, BARKER, R.C. The Desgn of Lean Manufacturng Systems Usng Tme based Analyss. Internatonal Journal of Operatons & Producton Management, 14 (11), 86-96, 1994 RIVERA, L. Inter-Enterprse Cost-Tme Proflng, Doctoral Dssertaton, Department of Industral and Systems Engneerng. Blacksburg, VA: Vrgna Tech, RIVERA, L. CHEN, F. Cost-Tme Proflng: Puttng monetary measures onto Value Stream Maps. Presented at IERC (Industral Engneerng Research Conference) Orlando, FL: Unted States, RIVERA, L. CHEN, F. Cost-Tme Proflng: Impact of Lean Tools on the Cost-Tme Investment of a Product. Presented at FAIM (Flexble Automaton and Intellgent Manufacturng Conference) Lmerck: Ireland, RIVERA, L. CHEN, F. Measurng the Impact of Lean Tools on the Cost-Tme Investment of a Product usng Cost-Tme Profles. Robotcs and Computer Integrated Manufacturng, paper accepted n 2006 for publcaton, awatng prntng,

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