SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW.

SUPPLIER FINANCING AND STOCK MANAGEMENT. A JOINT VIEW. Lucía Isabel García Cebrán Departamento de Economía y Dreccón de Empresas Unversdad de Zaragoza Gran Vía, 2 50.005 Zaragoza (Span) Phone: 976-76-10-00 ext.4667 e-mal: lgarca@posta.unzar.es Rodolfo Salnas Zárate Departamento de Economía y Empresa Unversdad de La Roja Edfco untlano La Cgüeña, 60 26.004 Logroño (Span) Phone: 941-29-93-79 e-mal: rodolfo.salnas@dee.unroja.es ABSTRACT Tradtonally, nventory models have served to make decsons pertanng to the external purchase of raw materals or components. Nevertheless, these models do not consder the relatonshp exstng between purchasng and fnancng polces. A decson process s proposed n ths report, the objectve of whch s to mnmse a cost functon based on the usual one used for nventores, but that brngs together all of the effects that purchasng can have n a busness. Key words: supplers, fnancng, nventores. 1.- INTRODUCTION All busnesses, to a greater or lesser degree, need to resort to the exteror n order to supply themselves wth the raw materals and components necessary for carryng out ther producton process and, n ths way, obtan the product that they offer to the market. In spte of the mportance that external supples have n the producton actvty, Operatonal Management manuals do not tend to have a secton dedcated exclusvely to them and the repercussons that they can have; rather, there are only references about the role or characterstcs of supplers when other subjects are presented. Thus, for example, from a descrptve pont of vew when talkng about Just-n-Tme, t s recommended that a busness have a co-operatonal type of relatonshp wth ts supplers. Also, when dealng wth the sze of the busness, subcontractng or supply resources comng form other 1

busnesses are proposed as alternatves to vertcal ntegraton. But also n subjects that are treated from a more analytcal pont of vew, reference s made to purchasng by the busness, such as the case wth nventory models. When selectng a suppler, the techncal and economc-fnancal characterstcs of the product that s offered should be the prmary concern. Leavng asde the possblty for negotaton and co-operaton wth supplers, busnesses should pay attenton to the techncal characterstcs of the components that they are gong to acqure, choosng that suppler whose product adapts best to the partculars of ther producton process or to the propertes of the good that they make. The economc-fnancal characterstcs of the acqured raw materal refer prmarly to ts purchase prce and payment condtons. Ther consderaton when makng decsons referrng to supplers serves ether to choose the one that offers the best economc condtons, wth other aspects beng equal, or to select the one that provdes the better relatonshp between the techncal propertes and the prce. In ths report, an analytcal approach s gong to be adopted that leads to the best purchasng polcy, whch s specfed by the selecton of the suppler who wll supply the product acqured from the exteror and by the calculaton of the purchase lot value. In the proposed model, only the economc condtons offered by the alternatve supplers are gong to be consdered, assumng that the remanng condtons are smlar for all of them. The models proposed for nventory management provde a sutable startng pont for the proposed objectve. Bascally, they set up a soluton based on the purchase lot value, usng as the objectve the mnmsaton of costs generated by the actual product acquston and by ts warehouse management (order ssung and mantenance)¹. Usually, for determnng the optmum purchase lot, nventory management models are proposed for a sngle suppler, wth no reference appearng to the suppler selecton process. But, although t s not very frequent to see ths process used when selectng alternatve supplers, ths use could be arrved at naturally and logcally. It becomes obvous that the dfferent purchase prces proposed by the alternatve supplers are not only gong to mean dfferent acquston costs, but they are also gong to cause dfferent costs for stock management. Thus, mantenance costs tend to be dvded nto warehousng costs and fnancng costs, both beng able to be expressed as a percentage over the monetary value of the average nventory, whch s calculated startng wth the purchase prce. Also, the ssung costs that are carred by recevng an order can be dfferent accordng to who s the suppler. In summary, t deals wth choosng that suppler whose economc condtons lead to the optmum purchasng polcy wth the least cost. Wth respect to the fnancng costs ncluded n the mantenance costs, Operatonal Management manuals pose dfferent stuatons that can be grouped together n the followng way: 2

- If the funds that fnance the nventores are external, then the fnancng costs correspond to the nterest to be pad; ths recommendaton s found, for example, n Fernández Sánchez and Vázquez Ordás (1994), Parra Guerrero (1196) and Slack et al (1998); - If own funds are used to fnance nventores, the opportunty cost of the commtted funds s taken as an assocated cost; n addton to the three works mentoned n the prevous case, reference s also made to ths possblty n Tersne (1988), Wnston and Albrght (1997) and Spper and Bulfn Jr. (1998). Another queston ncluded n the economc condtons that a suppler offers are the payment condtons. In the case where there s the possblty for a prompt payment dscount on the purchase prce, the provder, n addton to the product tself, s provdng fnancng to the busness. Ths fnancng has an mplct cost that depends on the offered dscount and payment term. Addtonally, funds obtaned through supplers can be desgnated for fnancng assets other than nventory. Fnally, nventory fnancng through supplers only consttutes one of the alternatves for obtanng funds, whch wll be used by busnesses f ts cost s less than the rest. Therefore, one could conclude that fnancng and purchasng polces n a busness are ntmately related through the selecton of the supplers and the decson about whether to make use or not of the fnancng funds that they provde. Nevertheless, the purchasng polcy obtaned startng wth nventory management models does not explctly consder ths relatonshp, rather, at most, the recommendatons n ths regard are lmted to proposng the suppler's cost of fnancng f what he supples s used. The model proposed n ths paper, nevertheless, s gong to allow jontly consderng decsons on the purchasng polcy (whch suppler s chosen and the sze of the purchase lot) and on the fnancng source for those purchases², for whch all repercussons have to be taken nto account that the acquston of products n the exteror have for the busness. In ths proposal, t s gong to be consdered that the objectve of the busness s to mnmse a cost functon that ncludes, n addton to the costs for acquston, order ssung, and storage, the costs for fnancng the nventory (whch, along wth the three prevous tems, would lead us to the usual functon n stock management) and remanng assets. Along wth optmsng that functon, the proposed model s completed by a decson procedure n stages, after whch the soluton s reached that ndcates what the purchasng and fnancng polcy for the busness must be. Obtanng ths soluton s not just gong to serve to make recommendatons pertanng to busnesses, but t wll also enable the analyss of repercussons that are consdered jontly n all of ther effects n the purchasng polcy, for whch a comparson wll be made between the results obtaned n the usual nventory models and those n ths report. The report structure s the followng: n the second secton, the model s presented that s proposed n order to obtan the optmum purchasng polcy whle jontly consderng all of the effects that t has on the busness; n that secton, the ntal assumptons of the model, the decson process that should be followed, and the cost functon equatons accordng to dfferent cases that could arse are developed separately; the last secton s dedcated to the conclusons, and an apprasal s made of the results obtaned n comparson wth tradtonal nventory models. 3

2.- PROPOSED MODEL The selecton of a suppler for a certan raw materal or component s gong to follow a seres of crtera: economc-fnancal condtons, techncal characterstcs of the product, and the exchange characterstcs (tme and frequency of delvery, uncertanty, guarantees ). The model proposed n ths report analyses the selecton between supplers of perfectly alke goods, assumng complance by the supplers wth some mnmum techncal requrements. Pror selecton based on techncal characterstcs and other possble requrements s taken as a fact, whch enables attenton to be centred on the economcfnancal condtons (prce and payment condtons) offered by the possble supplers and on ther relatonshp wth some of the exchange condtons, such as delvery tme and the sze of the order lot. The characterstcs of the offer made by each suppler are gong to have an mpact on costs, whch we can break down n the followng way: - Acquston costs: they are the actual purchase costs plus the accompanyng servce costs. Included among the latter s a fnancal servce cost derved from deferred payment when t supposes gvng up a dscount for prompt payment or a surcharge s establshed on the deferred quanttes. - Inventory management costs: they are made up of the orgnatng costs, breakage costs, and mantenance costs. The latter, n addton to the costs for warehousng and for rsk carred by nventores, ncludes a fnancng cost for the nventores, whch s where the attenton of the model presented n ths report s centred, and t s gong to consst prmarly n a proposal for modfyng the Wlson formula. Dealng wth ths cost dffers when fnancng comes from fnancal nsttutons or from own resources, the case n whch fnancng s the frut of the payment condtons provded by supplers. In the frst case, the fnancng cost can be handled lke one more mantenance cost, dependng on the sze of the order lot; nevertheless, n the second case, ths cost s gong to be ncluded n the costs for the fnancal servce provded by the suppler, and t s gong to be handled lke one more acquston cost, snce t s ndependent of the nventory management polcy. - Savngs n fnancng costs: they wll occur when the suppler fnancng costs are less than the costs from sources of alternatve fnancng. Not only wll t affect fnancng for the product nventory n queston, but t wll also generate a fnancng surplus as nventory s consumed, whch wll be recovered n current tems that n any other way would have to be fnanced at a greater cost. The model that s posed presents a cost functon that attempts to gather together all of these effects caused by the purchase of stock. In ths way, we can purchase from among alternatve supplers, keepng n mnd the cost mpact of the two prevous decsons: what the sze of the order s gong to be and what the source of fnancng s n each case. 2.1.- Intal assumptons The followng hypotheses are assumed n ths model: 1. There are two alternatve supplers who offer an dentcal product under the followng condtons: ' - Cp s the unt purchase prce of the product f the prompt payment dscount s not used. - dto s the dscount for prompt payment that the suppler offers. - td s the perod durng whch, f payment occurs, the offered dscount s appled. - tp s the maxmum deferred payment perod that the suppler allows. 4

- Sub-ndex ndcates the suppler that s beng referenced ( = 1, 2). 2. Purchase fnancng can be obtaned through two alternatve routes: through the suppler who supples the product or through an alternatve source at an annual cost r. Ths fnancng source can be what s offered by banks, fnancng through the busness' own resources, an average of both can also be consdered as an alternatve source, etc. 3. The product nventory acqured from the suppler s managed accordng to the Instantaneous Supply model wthout Breakage. Decsons are made, as a result, under condtons of certanty. It s a good dea to make a seres of comments about the mplcatons that varables used n the model have. Frst of all, the fnancng cost obtaned through the suppler s an mplct cost that arses from the exstence of the dscount for prompt payment, so that f ths dscount s not ' taken advantage of, the unt prce Cp reflects what s pad for the physcal product and for obtanng fnancng. For ths reason, we are gong to consder the unt prce mnus the dscount as the prce that the suppler covers for all of the features and characterstcs of the product, except for the fnancal ones. We wll denote ths net prce as Cp, and t s calculated as: ' Cp = Cp * (1- dto ) or, equvalently, ' Cp Cp = (1- dto ) In ths way, we can break down the acquston cost Cp ' *, beng the total number of unts acqured per year, nto the two prevously ndcated components: purchase cost, whch ncludes the cost of the product tself and the accompanyng non-fnancal servces, and the cost of the fnancal servces: ' dto Cp * = Cp * + * Cp * (1- dto ) Secondly, fnancng obtaned through supplers serves to fnance nventory tems of the acqured product, but t leaves a surplus that s gong to be able to be dedcated to fnancng other assets. Fnally, the cost of fnancng from supplers (Cfp) s calculated accordng to the formula that appears n Bachller, Lafuente, and Salas (1982), assumng a smple captalsaton: dto Cfp = * 1 dto tp - td Whch leaves our acquston costs as: ' (tp - td ) Cp * = Cp * Cfp * * Cp * + In ths formula, t s taken nto account that durng the perod n whch the dscount for prompt payment s vald, free fnancng s obtaned. 2.2.- Decson process The model for choosng the optmum purchasng polcy that s proposed n ths report ncorporates a decson process that ndcates the steps to follow by busnesses n those cases where they have varous alternatve supplers from whch to choose, exclusvely consderng the economc-fnancal condtons that they provde. These steps are those detaled below: 5

- Frst of all, t has to be decded for each one of the alternatve supplers n case they are chosen, f fnancng would be obtaned through that suppler or through the alternatve fnancng source avalable to the busness. The alternatve chosen wll be the one that provdes fnancng at a lesser cost, so t s therefore necessary to compare value r wth the correspondng Cfp. - Next, t wll be necessary to wrte down the cost functon that generates the product purchase, takng nto account the fnancng source already chosen n the prevous phase. The selecton of one or another fnancng source s not reflected n a mere change n the value of ths specfc cost, but rather t modfes the functonal form to adopt. The ndependent varable n ths cost functon wll be the suppler purchase lot. - What the optmum purchase lot would be for each one of the supplers s calculated, the result obtaned s carred over to the correspondng cost functon, and fnally the suppler s chosen who generates lower costs for the busness. The fnal soluton to the posed problem s the purchase lot to acqure from the selected suppler usng the fnancng source selected n the frst stage. 2.3.- Costs and sze of the order when r < Cfp In ths case, the selected fnancng source has to be the alternatve to the one gven by the suppler, so that the cost functon resultng from the product purchase s the followng: CT = Cp * + Ce q q q + Ca *Cp * + r *Cp * r *Cp * td * 2 2 where: q : the order lot from suppler. Ce : ssung costs for an order from suppler ; t s consdered that ths cost can vary among supplers. Ca: warehousng costs, gven n percentages over the purchase prce; t s assumed that they are ndependent from the selected suppler. The frst four terms of ths cost functon are the typcal ones from nventory models, and they nclude the total costs of acquston and order shppng, n addton to some mantenance costs that nclude those for warehousng and fnancng. The last term ncludes the possblty for takng advantage of zero cost fnancng that the suppler offers over td. Ths possblty represents a cost savngs, and t s the only modfcaton that s made regardng the typcal cost functon from the nstantaneous supply model. It s necessary to ntroduce ths last term so that the cost functons of the two stuatons regardng the fnancng costs consdered n ths report nclude all of the purchasng effects and, therefore, are comparable. At the tme that the nventored merchandse s apprased, the cost that exclusvely groups together product servces, other than the fnancal ones, has been consdered as the purchase cost, nstead of the one that s expressed by the varables gven n percentages (warehousng cost and fnancng cost). The value of the optmum purchase lot that mnmses the prevous cost functon s the one obtaned usng the Wlson formula: q = 2 * Ce (Ca + r) * Cp * 6

2.4.- Costs and sze of the order when r > Cfp If the fnancng provded by the suppler s the cheapest alternatve and, as a result, t s used, the cost functon wll have to nclude the purchase, ssung, and storage costs, and t wll have to consder that, n addton to nventory fnancng, the funds provded by the suppler can also be fnancng other assets. In order to wrte the cost functon equaton n ths case, two dfferent stuatons are gong to be consdered: a) The payment perod s less than the tme for one cycle, calculated q as t = *. In ths case, untl the dscount tme s fulflled, free fnancng s obtaned for the value of Cp * q durng td. From ths moment untl suppler s pad for the product, Cp * q fnancng s beng obtaned durng (tp - td ) at cost Cfp. Both types of fnancng are appled to the product nventory as well as to other assets. Once deferment perod tp has fnalsed, the nventory must be fnanced usng the alternatve source, whose cost s r, untl the next product entry nto the warehouse occurs, and a new cycle s started. The stuaton n ths case would be the one represented n fgure 1. Cp q Fgure 1 Cp q(td) Cp q(tp) td tp Inventory fnancng at zero cost Inventory fnancng at cost Cfp Inventory fnancng at cost r t Tme Fnancng other current tems at zero cost Fnancng other current tems at cost Cfp b) The payment perod exceeds the tme for one cycle t. The nventores, n ths case, are permanently fnanced by the suppler, and wth respect to the rest of the assets, each purchase serves to fnance durng the cycle the excess funds from the nventores, and once the cycle has transpred, all of the fnancng obtaned serves to fnance assets other than nventores. The stuaton would be what s reflected n fgure 2. 7

Cp q Fgure 2 Cp q(td) td t tp Tme Inventory fnancng at zero cost Inventory fnancng at Cfp cost Fnancng other current tems at zero cost Fnancng other current tems at Cfp cost In the frst case cted, the cost functon should group together the followng components: CT = Acquston cost + Launchng cost + Warehousng cost + Fnancng cost for Inventores and other Assets at Cfp + Inventory Fnancng Cost at r Fnancng Cost Savngs from other Assets. If we develop each one those tems, and we smplfy the resultng equaton, the resultng cost functon s: CT = Cp * + Ce q + Ca *Cp q * + Cfp 2 tp * - td *Cp * + r *Cp q * tp 2 * where the fnal fgure s the smplfed expresson of the terms that nclude the dfference between the nventory fnancng costs durng the perod n whch fnancng from supplers s not avalable and the cost savngs n fnancng from other assets. Ths term can have postve as well as negatve values, dependng on whch component has greater weght. Gven that the fnancng costs from supplers are ndependent of the selected lot sze, we can re-ntroduce the cost of these fnancal servces nto the acquston cost, leavng the equaton for total costs as follows: q q CT = Cp' * + Ce + Ca *Cp * + r *Cp * tp * q 2 2 The optmum order lot that mnmses ths functon s: 2*Ce * q = (Ca + r)*cp Ths lot s apparently the same as what we obtaned n the case where r < Cfp. Even stll, the nterpretaton of the effect of fnancal cost r on ths decson s not the same. In ths case, r groups together not the cost for mantanng nventores (hgher as the average nventores are greater), but rather the opportunty cost that s meant by havng to resort to a more expensve fnancng source: the fnancng amount from supplers s ndependent of the sze of the orders, whle the need for nventory fnancng ncreases wth t; as a result, the relevant cost s r, whch means the opportunty cost that the busness supports whle mantanng a stock level greater than what the suppler fnances. 8

In the second case that we pose, when tp > t, the cost functon has the same shape, even though the nventory fnancng cost at r wll be zero and, therefore, the term q r * Cp * tp * 2 wll always take on negatve values. The optmum purchase lot that mnmses the costs wll adopt the same composton as n the prevous case, and consderatons about the meanng of r wll contnue to be vald n ths case. 3.- CONCLUSIONS It has been shown n ths report that when choosng a suppler, apprasng the offer n terms of prce and deferment condtons needs to jontly consder three factors: prce, deferment tme, and fnancng cost. These three factors consdered ndvdually can brng us to contradctory conclusons. Consderng the three jontly requres apprasng the product acquston costs as well as the costs derved from the nventory management polcy and the latter's mpact on the fnancng costs of other assets. The results obtaned, addtonally, present a case n whch, n spte of the fact that nventores are fnanced wth outsde funds (n ths case, those suppled by the suppler), the relevant fnancng cost - and whch has to be used when calculatng the optmum purchase lot - s the one from the alternatve sources, whch mples the use of an opportunty cost. On the one hand, ths starts to contradct the normally accepted proposal that the cost of fnancng nventores s the one from outsde sources f the funds used are of ths type, whch shows the need to use models lke the one n ths report that take nto account the repercussons that purchasng polcy has and that can be appled to each specfc stuaton wth the certanty that the result obtaned s the optmum one. On the other hand, the optmum purchase lot that s calculated through the Wlson formula, but usng alternatve sources for fnancng cost and not the suppler fnancng cost, leads to the recommendaton that consderng the fnancng cost n stock management as the opportunty cost s the only vald consderaton, and n ths report, addtonally, t has been pnponted: t must be the cost of sources of alternatve fnancng. Regardng selecton of the order sze, the decson about the lot s ndependent from the deferment condtons offered by the suppler once t s seen that the fnancal cost to be consdered s the one from the alternatve sources and not the one from the suppler. Now then, the apprasal of the effect of ths decson on costs does depend on sad condtons. Not consderng the deferment condtons wll not lead to an error n the decson on the quantty to acqure n each order, but t wll lead to an error n apprasng the costs that are generated. Fnally, n the case where suppler fnancng s used, f the purchase lot sze obtaned startng wth the recommendatons n ths report s compared wth that obtaned followng the more general proposals, whch conssts of ncludng the fnancng cost of the supplers n the mantenance cost, the frst s smaller. Wth ths, a reducton n the perod between two consecutve product orders s obtaned. In ths way, nventory fnancng needs are reduced, and gven that the funds suppled by the supplers are the same ndependent from the purchase lot sze, a greater fnancng volume s obtaned for other assets, whch results n a cost savngs, snce t means cheaper fnancng. 4.- BIBLIOGRAPHY BACHILLER, A., LAFUENTE, A. and SALAS, V. (1982): Gestón económco-fnancera del crculante. Edtoral Prámde. FERNANDEZ SANCHEZ, E. and VAZUEZ ORDAS, C.J. (1994): Dreccón de la Produccón II. Edtoral Cvtas. 9

PARRA GUERRERO, F. (1996): Gestón de Stocks. ESIC Edtoral. SIPPER, D. and BULFIN Jr, R.L. (1998): Planeacón y Control de la Produccón. McGraw Hll. SLACK, N., CHAMBERS, S., HARLAND, C., HARRISON, A. and JOHNSTON, R. (1998): Operatons Management. Ptman Publshng. TERSINE, R.J. (1988): Prncples of Inventory and materals management. North-Holland. WINSTON, W.L. and ALBRIGHT, S.C. (1997): Practcal Management Scence. Spreadsheet modelng and applcatons. Duxbery. 10