Value of Reverse Factoring in Multi-stage Supply Chains

Transcription

1 Value o Revere Fatoring in Multi-tage Supply Chain Abtrat: We preent a mathematial model or integration, analyi, and optimization o operational and inanial proee within a upply hain. Speiially, we onider ommerial tranation o a large orporate utomer with a mall- or medium-ized upplier. We how how appliation o ere atoring inluene the operational and inanial deiion o thee irm. While ome empirial work on ere atoring exit within reearh literature, our model ontitute the irt analyti treatment o the problem, uing the value ramework o inanial theory. We how how the value o ere atoring reult rom, and i onditioned by (1 the pread in ernal inaning ot, (2 the operating harateriti o the upplier, inluding the implied working apital poliy, and (3 the rik-ree interet rate. Thu, in addition to providing managerial inight that integrate operational and inanial perpetive, our inding diloe an important relation o thee element to the broader maro-eonomi ont. Keyword: Supply Chain Finane; Revere Fatoring; Joint Prodution and Finanial Deiion; Capital Market Frition. 1. Introdution Sine the eminal paper o Modigliani and Miller (1958, it i well known that inanial and operational deiion are eparable when apital market are peret and there are no rition, e.g., taxe, tranation and inanial ditre ot, or inormation aymmetrie. In thi ideal ae, the oure o inaning neither aet operating plan nor reate additional value. Capital market in reality are not peret, however, and irm ae inanial ontraint and barrier when raiing ernal und. In partiular, apital market rition may reate a igniiant wedge between the ot o internal and ernal und or mall- and medium-ized enterprie (SME. A the wedge get larger, SME pay a greater ernal inaning premium and are alo more likely to under-invet and orgo poitive net preent value buine opportunitie (Hubbard, 1998; Carpenter and Peteren, Thi underinvetment an have negative reperuion urther along a upply hain, ine an SME may be a key upplier to a large orporation. We examine here a reent development that promie to addre uh problem: o-alled ere atoring arrangement, whih ailitate inormation elation and thu trigger aordable inaning within a upply hain. In a ere atoring arrangement, a orporation (whih we will requently alo denote by the term OEM and it upplier ( SME work together with a bank, in order to optimize the inanial low reulting rom trade. Thi optimization i poible when the orporation enjoy a lower hort-term borrowing ot than it upplier, a at that would typially be manieted by a relatively higher redit rating. Intead o ommuniating only with the upplier, the orporation regiter approval o the latter 1 Eletroni opy available at:

2 invoie on an inormation ytem that i aeible to all three partie. The term o the ere atoring ontrat entail that, by regitering approval on the ytem, the orporation guarantee that it will remit the orreponding amount to the bank, ater any agreed redit delay, or appliation to the upplier aount. I the upplier wihe to ae thee reeivable earlier than the agreed delay, the bank will advane payment with a diount that i baed on the orporation' borrowing rate, rather than the upplier. Thi more avorable rate i poible beaue the tranation i ully and tranparently ollateralized by the payment guarantee o the orporation, i.e., the orporation pay the bank at the end o the trade redit period, irrepetive o the inanial ondition o the upplier. Hene, ere atoring erve a a mehanim mitigating the inormational aymmetrie regarding the upplier aet and thereby enable heaper inaning. Figure 1. Revere Fatoring Mehanim Figure 1 depit the ere atoring mehanim. It highlight liquidity improvement and/or lower hort-term inaning ot or the upplier, but urther onideration how that imilar advantage or the orporation hould be poible. Prior to uing ere atoring, the upplier hort-term inaning expene are a untion o it own ot o ernal und and the time that it reeivable remain outtanding. I the redution in the ot o ernal und on tranation with the orporation i uiiently large, the latter may end the nominal trade redit period, while till leaving ome net beneit or the upplier. A longer trade redit period entail that the orporation will alo realize a redution in hort-term inaning need. The impat o aving rom ere atoring may be proound. Rajan and Zingale (1998 note that aount reeivable and aount payable repreent, repetively and on average, 17.8% and 15% o irm value in the United State. Internationally, thee igure range between 11.5% (average aount payable in Germany and 29.0% (average aount reeivable in Italy. Seiert and Seiert (2009 ind that ere atoring enable the orporation they tudy to realize average annual aving o $16 million on working apital inaning. The aggregate aving or SME may be even greater, ine the latter generally rely more heavily on hort-term debt inaning (Berger and Udell, Thi reliane an aue eriou 2 Eletroni opy available at:

3 problem epeially when redit i retrited. Shortage o working apital an lead to prodution delay, uboptimal toking level, higher prie, and even ae o inanial ditre among irm that are in priniple eonomially ound. Small wonder that ere atoring arrangement are een by many upply hain expert and manager a the great hope or eaing problem with upplier (Milne Nonethele, in an unertain buine environment with operational deiion making, it i not lear how ere atoring reate value and how the term o a ered atoring arrangement hould be peiied, in order to guarantee that the orporation and bank may realize ome beneit, without leaving nothing to the upplier. We provide a mathematial model or analyzing the operational and inanial beneit o ered atoring in a upply hain. To our knowledge, our work i the irt to provide a rigorou analyi o thi problem. We onider two enario or tohati demand. Firt, a ingle period make-to-order (MTO model, where the raw material purhae o the upplier an be delayed until the requirement o the orporation are ealed. Seondly, a make-to-tok model (MTS, where the upplier mut make a toking deiion prior to the realization o demand. In both ae, the term o any ere atoring arrangement mut be agreed at the outet. We aume that the upplier alternatively ha ae to onventional hort-term inaning, albeit at a le avorable rate. Our objetive i thu to determine the ondition under whih the ere atoring ontrat will be eonomially viable and reate value or eah party. Our work ontribute to the operation management literature rom three important angle. Firt, our model are at in the value ramework o inane: we diount or the rikine o loan and exlude redit arbitrage. Here it beome lear that the value o ere atoring i determined by the dierene in deadweight ernal inaning ot aed by the orporation and upplier, not the nominal redit pread. Conequently, alulation baed on nominal redit (whih i ommon in pratie may igniiantly ditort the magnitude o value alulation in ere atoring ontrat, generally to the diadvantage o the higher-rik upplier. Seond, we quantiy the value o ere atoring ontrat to the upply hain partiipant. We eal the linkage between (1 the pread o deadweight ernal inaning ot, (2 the operational harateriti o the upply hain (in partiular, demand volatility and the implied working apital poliy o the upplier and (3 the rik-ree interet rate. The interrelation o thee ator oer a key inight to manager who are going to negotiate the term o a ere atoring ontrat. Not only a greater pread o deadweight ernal inaning ot, but alo a greater volatility in demand allow the orporation to inreae it nominal payment period while retaining the partiipation o the upplier. We how, however, that the upplier beneit are highly enitive to thi payment period enion: a mall inreae in payment delay may entail a relatively large 3

4 dereae in upplier beneit. Payment period enion thu ultimately prove to be an ineiient trategy rom a upply hain perpetive, ine it interat with the operation o the upplier and redue the total available beneit. We ind that upplier with aggreive working apital polie will be more enouraged to ue ere atoring, and the total beneit or the upply hain are alo larger in thi ae. The rikree rate o interet doe not inluene the total beneit to the upply hain, but a lower rik-ree rate give the orporation le inentive to oer ere atoring to the upplier. Thi latter inding yield intereting maroeonomi poliy impliation: in a redit queeze (like the reent redit rii o 2008, the pread in ernal inaning ot between orporation and SME will tend to widen, augmenting the potential value o ere atoring; yet lowering rik-ree rate (a ommon monetary poliy may diourage the reation o upply hain inane olution, urther limiting maller irm ae to apital. Third, in the MTS etting, we how that the ere atoring may promote a igniiant inreae in upplier toking level. Thi entail urther value reation within the upply hain, in addition to any diret beneit that ollow rom redution in ernal inaning ot. Sine the orporation hare in thee operational beneit (by enjoying inreaed ervie level, it i le inlined in thi ae to end the nominal payment period ompared to the MTO etting. We urther oberve that the orporation beneit due to operational enhanement (operational beneit may greatly exeed the diret inanial beneit due to redued ernal inaning ot. For the upplier, under uual eonomi ondition, diret inanial beneit dominate the operational beneit. We alo how that operational enhanement and value reation doe not neearily imply eah other when the rik ree rate i poitive. Through a et o numerial analye, we oberve that ere atoring, when implemented optimally and under reaonable eonomi ondition, may yield a upply hain value inreae o 2 10%, due to enhaned operating and inaning ondition. 2. Literature Review The interae o operation and inanial management i a burgeoning new area o reearh (Birge et al., 2007, and our work it naturally with thi literature. It i alo loely related, however, to reearh tream that traditionally addre the element o our problem, uh a mall buine inane and trade redit. Moreover, although we laim to provide the irt analyti tudy o the ere atoring mehanim, we note that other author have preented important oneptual and empirial work on upply hain inane. 4

5 A mentioned in our introdution, the poibility that ere atoring may oer ome advantage to irm reult rom the ailure o market or at leat, the market or hort-term ommerial inane to atiy the requirement o the amou Modigliani-Miller theorem (Modigliani and Miller, Where apital market are imperet, the oure o inaning may impat other management deiion within the irm, and ultimately alo the ability o irm to reate value (Mayer and Smith, 1982; Smith and Stulz, 1985; Froot et al., 1993; Stulz, Irrepetive o the aue, reearh on mall buine inane onirm that the inaning ot aed by large orporation are igniiantly lower than what their SME upplier an realize. For intane, Henney and Whited (2007 etimate that marginal equity lotation ot or large irm tart at 5.0%, while the orreponding igure or mall irm i 10.7%; bankrupty ot amount repetively to 8.4% or 15.1% o apital. Gome et al. (2003, in a general equilibrium aet priing model, argue that bankrupty ot o 5% an add 1.2% to the equity premium. A the bankrupty ot (relative to the irm value and other apital market rition uh a inormation aymmetrie and tranation ot are uually more evere or SME (Cornell and Shapiro, 1988; Shane, 2003, thee irm pay a larger deadweight ernal inaning ot ompared to their larger ounterpart. A thee rition get more evere, ae to apital by thee mall irm an be totally ut. The exitene o uh dierene i alo a key motivation or irm ue o trade redit. Shwartz (1974 provide an early ormalization o the inaning advantage it provide. When eller have better ae to apital market than their utomer, trade redit allow them to oer better ondition than the utomer ould obtain through onventional inaning. From a dierent angle, Smith (1987 ugget trade redit a a reening mehanim or upplier to evaluate their utomer deault rik. Many other inane and eonomi theorit have tudied trade redit. See Peteren and Rajan (1997 or a detailed iew. More reently, trade redit ha been reeiving attention rom reearher working at the operation-inane interae. Gupta and Wang (2009 onider the impat o trade redit on upply hain ontrating and inventory management and how that a bae tok poliy i till optimal under trade redit, provided the poliy itel i adjuted to math the redit term oered by the upplier. Lee and Rhee (2011 and Yang and Birge (2011 invetigate trade redit a a tool or upply hain oordination and ind that it erve a a rik haring mehanim. While ome onnetion to trade redit i lear, the ere atoring mehanim i dierent in everal way, a our analyi will how. A major ontrat i evident in the orientation o the partie onerned: the redit provider in ere atoring i ituated downtream in the upply hain, while a typial trade redit arrangement involve a inanially ontrained mall retailer that reeive inaning rom a large upplier. More importantly, a ere atoring tranation bring no additional rik or the orporation, ine it i already obligated to pay the aount reeivable held by the upplier. In addition, when oupled with an enion o the payment period, ere atoring entail that the orporation 5

6 reeive additional redit rom it upplier, whih to ome degree will oet the beneit that the latter may realize through a heaper borrowing rate. Depite it apparent potential, the mehanim o ere atoring ha reeived relatively little attention within the reearh ommunity. Studie that look peiially at ere atoring retrit themelve to onveying high-level managerial aement (e.g., Seiert and Seiert, 2009 or ue inanial ratio to alulate the beneit that hould reult or partiipant (e.g., Randall and Farri, We aim here to develop a rigorou ramework by integrating inanial and operational deiion making to eal the value reation mehanim o ere atoring and undertand how key market ator ondition thi value reation mehanim and ditribution. Turning inally to other reent reearh at the interae o operation and inane, we note requent imilaritie with our onern, even though no other work peiially addree the ere atoring problem. Babih and Sobel (2004 tudy the oordination o operational and inanial deiion, in order to maximize the expeted diounted proeed rom an initial publi oering. Buzaott and Zhang (2004 link the inanial apaity and operating deiion o a retailer by inorporating an aetbaed ontraint on the total amount o borrowing. In a newvendor etting, they how that a lender hould preer to limit the ize o a loan to the retailer, intead o harging a higher borrowing rate. Dada and Hu (2008 preent a imilar analyi, whih ormalize the problem a a Stakelberg game and prove the uniquene o the equilibrium. Protopappa-Sieke and Seiert (2010 onider the determination o optimal order quantity when a irm i ubjet to working apital retrition. Our work i alo related to Xu and Birge (2006, Hu et al. (2010 and Kouveli and Zhao ( The Bae-Cae Model: Make-to-Order with Determiniti Demand Size In our bae-ae model o ere atoring, we onider an SME that ae tohati demand arrival rom a orporate buyer. The demand ize i determiniti, and the SME operate in a make-to-order ahion. The SME i apital-ontrained and may need to borrow in order to inane operation and meet urrent liabilitie. At t = 0 the SME ha ah reerve o magnitude y. Pre-exiting urrent liabilitie, uh a rent and rate, are due at end o the period, t = τ. During the period, the irm may generate ah low rom operation, but the timing o ah reeipt depend on the timing o demand rom the OEM. For eae o expoition we aume that demand i realized at a ingle time-point and prodution i intantaneou. We denote the arrival time o demand by a random variable that ha probability denity untion (. and upport [0,]. Demand ize i ontant and equal to in thi bae ae (in ubequent etion, demand ize will alo be tohati with expetation. Upon arrival o the demand, the SME purhae the required raw material or ah, reate the inal produt, and ell it to the OEM on redit. Eah unit o the inal produt i old or prie p and inur a raw material ot. The demand arrival thu 6

7 intantaneouly redue the ah reerve o the SME by and reate an aount reeivable (AR o ize p. The nominal payment delay rom the OEM to the SME i l time unit, o the AR would normally be reeived ater thi delay. To avoid trivial ae, we aume that it i eonomial to ue ernal und to meet the demand. Our model alo eaily end to the ae where the SME i allowed a payment delay when purhaing raw material. The SME ue it ah reerve and ah generated rom operation to meet the urrent liabilitie a they ome due. I thi internal ah i not uiient, ernal und are reeived. In addition to any rik premium, the ernal inane provider harge deadweight ot to the SME, whih we denote by β. That i, under the rik-neutral meaure, ernal und to the SME ot β per dollar above the rik-ree rate, r. Thee deadweight ot may arie rom the diret and indiret ot o bankrupty and inanial ditre, a well a rom inormational aymmetrie between manager and outide invetor and tranation ot (Froot et al., Thu we denote the total ernal inaning ot paid by the SME a r = (r +β. By the ame argument, ernal und are available to the OEM at the ot r o = (r +β. (Note that thee are not the nominal interet rate the partie ae. Sine etablihed orporation are, in general, le expoed to apital market rition, the deadweight ot or the OEM would be maller than or the SME, i.e., we take r > r o > r. We aume that the SME ixed aet are inaned by a enior long-term debt that i due to be repaid at the end o the period. Thi enior debt inlude ovenant whih may delay or otherwie retrit the repayment o any junior debt that ome due beore the end o the period. In partiular, thee retrition ould be impoed by the enior debtholder i the market value o the ixed aet ell below a peiied threhold (. Leland While we do not expliitly model the value proe or the SME ixed aet, thi underlying aumption drive the redit (deault rik o the bank loan and the allied rik premium that the SME mut pay to obtain a junior loan. Hene, the redit rik o the SME i olely determined by the ixed aet and not inluened by the urrent buine tranation with the orporate buyer (. Froot et al., Relaxing thi aumption would only reult in marginal inight while igniiantly limiting analytial tratability. For impliity, we aume that OEM i an etablihed orporation with negligible deault rik. So, the deadweight ot o ernal und or the OEM, β, i olely driven by tranation ot. We aume that (1 the SME i eonomially viable and (2 only need to borrow i the AR i not reeived beore the ixed ot are due (thi latter aumption will be relaxed when we diu the tohati demand ize in Setion 4. The OEM ha uiient internal inaning and doe not need ernal und. The ree ah reerve o both the SME and the OEM earn the rik-ree rate. During the period, ah inlow and outlow to the SME take plae in the ollowing order. 7

8 1 At t = 0. SME tart operation with y amount o initial ah reerve (liquid aet. 2 At t =. SME reeive the order rom the OEM and imultaneouly plae an order with it downtream upplier or the prourement o raw material. Raw material are purhaed or ah and are reeived intantaneouly. Thi redue the SME ah reerve to r ye. For eae o expoition, we aume the SME tart operation with uiient ah to make the raw material purhae. All other expene aoiated with the order are due at the end o the period. The OEM intantaneouly reeive the inal good rom the SME and ell them to the inal utomer( or w per unit. 3 At t =. Short-term liabilitie o the SME ome due. Thi event entail two poible ae I l then the AR i reeived no later than the moment when the hort-term liabilitie are due, ah reerve at the end o period are and inaning i not needed. r r ( r ( l y ye e pe, I l > then the AR are reeived ater the hort-term liabilitie are due, the ah reerve at the end o period are r r (, y ye e and thi i inuiient to pay External und in the amount o r ( r Le ye 0 are reeived at a ot o r. Thee ernal und are repaid at time l, i.e., when the SME reeive the AR. Due to the redit rik involved in the debt, the unertain loan repayment i denoted by D. 4 At t ˆ. The SME loe it aount and i liquidated. The bae-ae model deription and notation are ummarized in Figure 2 below. Figure 2. The MTO Model Deription with Conventional External Finaning Order arrival o ize ξ Δt = l Duration o inaning [ ] l Firm i liquidated t = 0 t = l l t = t = t= Timeline +y Initial ah reerve Material purhae Short-term liabilitie L Loan reeipt D Loan repayment p Reeived payment Cah low A ere atoring arrangement entail three dierene to the hema o ah low preented in Figure 2. Firt, the SME may ell it approved invoie (aount reeivable to the bank and reeive a loan maturing at the nominal payment time o the OEM, whih rom the bank perpetive i aured by the reditworthine o the OEM. Seond, the OEM may end the nominal payment period, and third, 8

9 the bank may harge an additional premium or providing ere atoring ervie, i.e., a tranation ot. Thu we haraterize a ere atoring ontrat by a vetor o three parameter: (1 r, the ere atoring inaning ot or the SME, (2 l, the ere atoring payment period o the OEM, and (3 b, the inanier ee. The inanier ee harged or the ervie i an additional deadweight ot or inaning, i.e., r r b ro b. The SME deide whether to aept the ontrat v ( r, l, b. Revere atoring an generate value by reduing the deadweight inaning ot o the SME. The aving are then hared between the SME and the OEM baed on the ontrating term. All partiipant are aumed to maximize irm value. Furthermore, we aume that demand rik i diveriiable while the redit rik o the SME i driven by the hange in the value o the ixed aet whih i orrelated with the market and annot be ully diveriied. Hene, there exit a rik premium or loan iued to the SME. Under the rik-neutral meaure, the value o the loan iued to the SME i E L Q ( D, (1 r l e where l = ( give the duration o the loan, and E Q denote expetation with repet to the rik l neutral deault probabilitie o the SME. Note that r doe not inlude the rik premium. The ame et o aumption alo applie to the OEM and we take the deadweight ot o inaning, i.e., the market rition, to be ontant over time. In what ollow, we ue a irt-order Taylor erie approximation when diounting ah low and ue thee value or the analytial model. Exat reult only lightly dier due to the ompounding o interet rate. The ollowing propoition deribe the beneit and the partiipation ontraint o eah party or a given ere atoring ontrat. All proo are inluded in the appendix. PROPOSITION 1. In an MTO buine environment, the ere atoring ontrat v ( r, l, b generate the ollowing beneit or eah party. me (i For the SME, A( l L( ( b A( l L( pr ( l l, oem (ii or the OEM, r p( l l, total (iii or the entire upply hain, A( l L( ( b A( l L(, Where L( y and A( l denote the lo untion, i.e., E[ l ] orl l, l. In Propoition 1, untion L(. and A (. denote repetively the SME borrowing amount and the expeted duration o borrowing. The SME beneit are deribed by three term: (1 A( l L(, the expeted ernal inaning ot o the SME without ere atoring; (2 9

10 ( ba ( l L(, the expeted ernal inaning ot with ere atoring; and (3 p r ( l l, the opportunity ot o ere atoring, reulting rom any payment period enion l l impoed by the OEM. The SME an only beneit rom the ere atoring ontrat i the net expeted ot o inaning dereae under ere atoring. The OEM ollet additional rik-ree earning on the amount o AR or the duration o the payment period enion. (Reall that the OEM i aumed to have uiient internal und and doe not need ernal inaning. Nonethele, total beneit are independent o the rik-ree rate and determined by the pread o ernal inaning ot between the OEM and SME. In partiular, when there are no market rition, ere atoring reate no value or the upply hain, whih i in line with tandard inanial theory. We alo note, however, that alulation baed on the nominal pread in inaning rate, whih inlude a rik premium, an ditort thee reult, generally to the diadvantage o the more riky upplier. The value o ere atoring to the upply hain member depend on three key market ator: (1 the pread o deadweight ot o apital between the SME and the OEM; (2 the working apital poliy and operational harateriti o the SME; and (3 the rik-ree rate. A the redit pread between the partie widen, the SME experiene a larger dereae in it deadweight ot o inaning and beneit more rom ere atoring. The working apital poliy determine how oten and how muh ernal unding i needed by the SME. It i determined by the initial ah reerve, hort-term liabilitie and the operational harateriti uh a the relative ize and the volatility o SME buine. In partiular, an aggreive working apital poliy (i.e., lower ah reerve, more volatile buine, higher hort-term liabilitie, et. implie more need or hort-term inaning and hene more beneit or the SME through ere atoring, and vie vera. Finally, we ee that opportunity ot to the SME i inreaing (and beneit thu dereaing with the rik-ree rate, and thi value i tranerred diretly to the OEM. The OEM beneit rom ere atoring i driven by the expeted buine volume with the SME, the rikree interet rate, and the payment period enion. The OEM working apital aving are inveted in hort-term liquid aet and earn an additional rik-ree interet rate or the duration o payment period enion. Table 1 below how the enitivity o the beneit deribed in Propoition 1 to key parameter. l l r Aggreivene o WCP Supplier Inreae Dereae Inreae Dereae Dereae Inreae OEM Dereae Inreae Contant Contant Inreae Contant Total Inreae Dereae Inreae Dereae Contant Inreae Table 1. Senitivity o Revere Fatoring Beneit 10

11 The n propoition ormalize the partiipation ontraint o eah party and the value reation ondition or the entire upply hain. PROPOSITION 2. In an MTO buine environment, the ollowing partiipation ontraint apply to the ere atoring ontrat v ( r, l, b : (i or the SME, A( l L( ( b A( l L( pr ( l l, (ii or the OEM l l, (iii or the entire upply hain A( l ( b A( l. The OEM require a non-negative payment period enion while the SME partiipation ontraint i non-trivial, due to the interation o payment period and inaning ot with the operating harateriti and working apital poliy. While the bank ee, b, linearly traner wealth rom the SME to the bank, the payment period enion ha a more omplex eet on the beneit o the SME. The total eet o the payment period enion i a ompound o two ditint ub-eet. Firt, a the payment period inreae, the SME bear the ra ot o inaning over a longer time period. Seond, with longer payment period, it i more likely that the SME will deplete it internal ah and need ernal und. Together, thee ub-eet entail that the peii partiipation ontraint o the SME, when viewed a the maximum inaning rate allowable in the ered atoring ontrat v ( r, l, b not only a dereaing untion o l, the payment period under ere atoring, but alo typially tritly onvex. Thi relationhip between l and β i urther moderated by the magnitude o the rik-ree rate: a r inreae, the partiipation ontraint beome more limiting and the SME demand a larger redution in it ot o ernal und. Likewie, the partiipation ontraint i more retritive when the SME ollow a onervative working apital poliy, ine in thi enario it ue ernal und le oten, while paying the ame opportunity ot or ere atoring. Finally, it i important to note that when the rik-ree rate i poitive, the partiipation ontraint o the upply hain and the SME diverge. In partiular, a ere atoring ontrat whih generate value or the upply hain may be rejeted by the SME i the opportunity ot o payment period enion i uiiently large. Figure 3 below illutrate the preeding diuion o the partiipation ontraint o the SME. For the numerial analye we onider a bae ae with the ollowing parameter: w = 15, p = 12, = 10, r = 0.02, β = 0.12, b = 0.01, β = 0.01, µ = 100, l = 0.3, l = l +0.1, = 1000, and y =1000. Thee parameter are ued througout the remainder o the paper, unle otherwie mentioned. We aume that the demand arrival time i uniormly ditributed over a period o one year, i.e., = 1. The reult or other plauible demand arrival ditribution, uh a trunated normal, are qualitatively the ame., i 11

12 Figure 3. SME Partiipation Contraint a a Funtion o r, l and r (a Under Aggreive WCP (y=1000 (b Under Conervative WCP (y=1250 N, we deribe the optimal ere atoring ontrat or eah party and or the entire upply hain. PROPOSITION 3. In an MTO buine environment, the ere atoring ontrat v( r, l, b maximize (i the SME expeted beneit when ( r r b, l l, b 0. The maximum beneit or the SME me i ( A( l L(. (ii The OEM expeted beneit when ( r r b, l l, b 0. The maximum beneit or the OEM, oem pr l ( l, where l i the payment period that make the SME partiipation ontraint tight, i.e., A( l L( A( l L( pr ( l l. (iiithe total upply hain beneit when ( r r b, l l, b 0. The maximum upply hain total beneit i ( A( l L(. A ere atoring ontrat maximize the SME beneit when the payment period remain the ame and the loan i iued at the borrowing rate o the OEM (i.e., when there are no bank ee or ere atoring. The OEM break even under thi ontrat and the SME reeive all beneit that reult rom mitigating apital market rition. Thi olution alo maximize the total upply hain beneit, whih in thi ae are equal to the total expeted aving in deadweight ot o inaning. Sine the OEM only beneit rom an inreae in the payment period, the OEM maximum beneit our when the bank ee equal zero and the payment period i inreaed to the point where the SME break even. Nonethele, Corollary 1 below how that the OEM an at bet rat only a ration o the total upply hain beneit. 12

13 COROLLARY 1. In an MTO buine environment, inreaing the payment period allow the OEM to rat at mot only a ration o the total upply hain beneit, i.e., oem pr ( l l 1, total L( ( A( l (2 where i dereaing in and, inreaing in, r and y. The OEM i unable to realize a maximum beneit equal to the maximum total upply hain beneit beaue o operational interation that reult when the payment period i ended. A diued above, inreaing the payment period not only impoe a larger inaning period but alo inreae the hane that the SME will run hort o ah due to the arrival o buine opportunitie during the period. Thi operational impat entail a non-linear redution in the SME beneit, limiting the poibilitie or payment period enion. Contrat that do inlude an enion are thu ineiient, wating ome potential beneit o ere atoring. The ollowing igure how the OEM maximum ration ratio,, a a untion o the rik-ree rate, the SME original deadweight ot o inaning, and the working apital poliy o the SME. Figure 4. OEM Maximum Extration Ratio and Abolute Value Generation (a Impat o r and β on (b Impat o r and WCP on Propoition 1 and Corollary 1 how that the maximum beneit ration that the OEM an individually apture rom the ere atoring ontrat inreae with the rik-ree rate. A the redit pread inreae, however, (note that i ixed the maximum beneit o the OEM grow at a lower rate than the total beneit. The OEM annot eiiently rat thee additional beneit by inreaing the payment period due to the non-linear partiipation ontraint o the SME. Hene dereae (Figure 4(a. The ame reaoning explain the analogou eet o an aggreive working apital poliy (Figure 4(b. 13

14 4. Make-to-order with Stohati Demand Size and Timing In thi etion, we end our bae-ae analyi by allowing demand ize a well a demand arrival time to be tohati. For the analytial derivation, we aume a general ditribution or the demand ize,, with a probability denity untion (., umulative denity untion, F (., mean, and tandard deviation. For the numerial reult we adopt a normal ditribution. For notational bity, we ue the variable deined in the piou etion to denote their analog here. The buine model i till make-to-order, but the SME may now alo need to eek inaning upon demand realization, i internal ah i too little to proure all raw material needed to meet the OEM order. Further borrowing may alo be needed at the end o the period, in order to make repayment o hort-term liabilitie. Nonethele, we maintain the aumption that the diounted value o the SME aount reeivable i alway greater than any ah hortage that the SME experiene at the end o the period. Thi allow u to diretly ompare the ere atoring and ernal inaning option. (Allowing the irm to ue ernal inaning to over the hortage in exe o the AR i poible but doe not generate additional inight. We ind that the main reult rom the preeding analyi apply to the preent ae. The ollowing propoition deribe the beneit to eah party. PROPOSITION 4. In an MTO buine environment with tohati demand ize and timing, the ere atoring ontrat v ( r, l, b generate the ollowing beneit or eah party: me (i For the SME, L( l ( b L( l pr ( l l, oem (ii or the OEM, pr ( l l, total (iii or the entire upply hain, Ll ( ( bll (, where, l 1 l 2 3 Ll ( E [( y li li ( yli ], l l,, l l {, : y(1 r /, ( y(1 r /( (1 r (, l}, {, : y(1 r /, l}, {, : y(1 r / }, or l l and l. Propoition 4 i analogou to Propoition 2, but the expeted inaning requirement ha a dierent orm, given by L(.. In partiular, with tohati demand ize, there are three poible ae where inaning our. I (, then ah reerve are inuiient to proure all needed raw 3 material and the SME borrow to loe the hortage when demand arrive. Note that ine the prodution and ale are intantaneou, the reulting aount reeivable an be ued to inane the purhae o raw material (in pratie thi an be aomplihed through a bridge loan whih i repaid one the AR i 14

15 l reated. I (, then, in addition to inaning the purhae o raw material, the SME need to 2 l borrow to inane the payment o the hort-term liabilitie at the end o the period. I (, then 1 the SME doe not need to borrow to inane the purhae o raw material, but need to borrow to inane the payment o hort-term liabilitie. The ret o the reult rom Setion 3 hold here with light modiiation, but analytial tratability i limited. Propoition 3 and Corollary 1 till hold with inaning need L(. deined a in Propoition 4, and l i the poitive value whih make the SME partiipation ontraint tight, i.e., N we provide a et o numerial analyi to illutrate the L( l ( b L( l r p ( l l. impat o demand ize volatility on the reult. For the numerial analyi, we ue the ame et o parameter value a in Setion 3. Figure 5. Eet o Demand Volatility (a on the SME Partiipation Contraint (b on ( on the Generated Value o the SME π me Variability in demand ize inreae the need or ernal und, o the beneit o ere atoring or the SME inreae with the variane o demand ize (Figure 5(. Thi lead to an expanion o the SME partiipation region, a hown by Figure 5(a. Higher demand variane alo inreae the OEM maximum beneit, ine the payment period an be ended urther while retaining the SME partiipation. Nonethele, thi exaerbate the ineiienie reulting rom payment period enion. The OEM maximum beneit inreae with variane, but the maximum ration ratio o the OEM dereae a depited in Figure 5(b, ine the total beneit inreae ater. 5. Make-to-Stok (MTS Model We now reat our model in a make-to-tok (MTS etting, where the SME need to produe and tok inventory prior to reeiving demand rom the OEM. We retrit the inaning poibility to only the end o the period, i.e., inaning will only be needed or the hort-term liabilitie aordingly, we impoe 15

16 upper and lower limit on the demand ize. The problem ould o oure be ended to allow or other poible inaning need, a in the model o Setion 4. A noted in that ae, however, the additional inight generated are marginal, while analytial tratability i greatly urtailed. The timeline o event and other aumption or the MTS problem are a ollow. 1 At t = 0. SME deide how muh to produe and tok, Q, in order to meet the OEM orthoming demand. The SME purhae raw material or ah. A in the MTO ae, we aume that delivery and prodution lead time are zero. Aordingly, ah reerve immediately dereae to y Q. We aume the SME ha uiient ah to make the raw material purhae. Other hort-term liabilitie, are due at the end o the period. 2 At t =. OEM oberve demand and plae an order o ame ize with the SME. The SME immediately deliver the maximum quantity it inventory allow to meet the order, i.e., the SME ell min(, Q. We aume that exe inventorie have zero alvage value and exe demand i lot. 3 At t =. Short-term liabilitie are due. Thi event entail two poible ae I l the AR i reeived no later than the moment when hort-term liabilitie are r r ( due, ah reerve at the end o the period are y ( yq e pmin(, Q e, and thi i uiient to pay under the optimal poliy and the wort-ae demand enario I l >, the AR i not reeived beore hort-term liabilitie are due. Cah reerve at r the end o period are only y ( y Q e and inuiient to pay under the optimal poliy r Hene the SME inane the hortage amount ( y Q e at the ot r. The inaned und are repaid upon maturity o the AR. 4 At t ˆ. The SME loe it aount and i liquidated. The MTS model deription with onventional ernal inaning i depited in Figure 6 below. Figure 6. MTS Model Deription with Conventional External Finaning Order arrival o ize ξ Δt = l Duration o inaning [ ] l Firm i liquidated t = 0 t = l l t = t = t= Timeline +y Q Initial ah reerve Material purhae Short-term liabilitie L Loan reeipt D Loan repayment pmin(, Q Reeived payment Cah low 16

17 The ere atoring arrangement hange the term o inaning in the ame way it doe in the MTO ae. The inaning ot beome r intead o r, and the OEM end the nominal payment period rom l to l. Here the outtanding AR i pe min(, Q, and thu depend on the prodution quantity a well a the realization o demand. We irt haraterize the optimal quantity or the SME. Thi orm the bai or urther analyi o value reation in thi etion. PROPOSITION 5. In an MTS buine environment, the optimal prodution quantitie o the SME, or the repetive ae o onventional ernal inaning and ere atoring, are given by The orreponding optimal value or the SME are p p Q F (, Q F (. 1 1 p p V Q pe Q r l Q L Q A l me ( min(, (1 ( ( ( -, V Q pe Q r l Q b L Q A l me ( min(, (1 ( ( ( ( -, where LQ ( Qy0, orq Q, Q and (1 A( - l, (1 ( b A( - l, p p(1 r ( l, p p(1 r ( l and E[ ]. Propoition 5 how that the optimal prodution level o the SME i haraterized by a newvendor-type olution, modiied by the deadweight ernal inaning ot, payment period, and the rik-ree rate. In partiular, under otly ernal inaning, the nominal purhaing ot o the SME inreae by the expeted ernal inaning ot, (1 A( - l, and the ale prie redue by the expeted value lot due to delay in the olletion o enue, p p(1 r ( l. With ere atoring, the lower deadweight inaning premium ( b redue the eetive unit ot, while the payment period enion ( l l non-linearly inreae the inaning need and the unit ot, a well a linearly reduing the eetive ale prie in proportion to the rik-ree rate. Aordingly, the operational enhanement due to ere atoring depend on the net eet o thee ator on the inaning ot o the SME. Rearranging the ritial ratio in Propoition 5, we oberve that the SME produe more with ere atoring i A( - l (1 r ( l ( b A( - l (1 r ( l r ( l l (3 We reer to thi ontraint a the operational enhanement ontraint (OEC. We n deribe the beneit and the partiipation ontraint (PC o eah party in the upply hain. PROPOSITION 6. In an MTS buine environment, the ere atoring ontrat v ( r, l, b generate the ollowing beneit or eah party. 17

18 (i For the SME, me pemin( Q, pemin( Q, ( Q Q L( Q A( - l ( b L( Q A( - l, oem (ii or the OEM, E Q w p E Q w p (iii or the upply hain, min(, min(,, total we ( min( Q, Emin( Q, Q ( Q LQ ( A( - l ( blq ( A( - l, where w w(1 r, L( Q Q- y or Q, Q and the orreponding partiipation ontraint require that the expeted beneit are non-negative. A in the MTO ae, the payment period enion ha a non-linear eet on the partiipation ontraint o the SME. However, the eet i now more omplex, due to it interation with the prodution deiion. The OEM partiipation ontraint alo trade o inanial and operational beneit a the payment period varie. Note that the partiipation ontraint o the SME doe not neearily oinide with the quantity enhanement ondition deribed above, unle the rik-ree rate i zero. In the ollowing we deribe the relationhip between the partiipation and quantity enhanement ontraint o the SME. COROLLARY 3. In an MTS buine environment, (i when r =0, the SME partiipation and operation enhanement ontraint are idential and given by A( l ( b A( l, (ii when r >0, there exit a threhold ŷ uh that i y( yˆ then the SME partiipation ontraint i tighter (looer than the operational enhanement ontraint. When the rik-ree rate i zero, there i no opportunity ot or ere atoring, and hene p = p = p. In thi ae, a quantity enhanement implie a redution in the net unit ot, i.e., <, and hene alo implie value reation. When the rik-ree rate i poitive, however, ere atoring involve an opportunity ot depending on the rik-ree rate and the payment period enion. In partiular, thi eet tranlate into a redution in the eetive ale prie p <p. So, in thi ae, a quantity enhanement doe not neearily improve the value, ine the redution in the ale prie may dominate beneit ariing rom the redution in the unit ot (even when the ritial ratio inreae. Figure 7(a provide a numerial illutration o thi phenomenon. For the numerial analyi, we ue the ame bae ae a in Setion 3 together with σ = 20. A the SME working apital poliy beome more onervative (i.e., y inreae, the divergene o partiipation and operational enhanement ontraint beome more emphaized (Figure 7(b. I the SME ha a very onervative working poliy (or example, when the initial ah reerve are well above the ixed payment, then very little inaning i needed but a relatively large opportunity ot i inurred. In thee ae, thi opportunity ot i more likely to dominate the beneit o operational 18

19 enhanement. Indeed, Figure 7(b how that when y yˆ, a the working apital poliy o the SME beome more onervative (i.e., a y inreae, the wedge between OEC and PC widen. In thi ae, even i operation are enhaned, the SME would rather rejet a ere atoring ontrat. Figure 7. Comparion o Partiipation (PC and Operation Enhanement (OEC Contraint (a Eet o r (b Eet o y ( Eet o y On the other hand, Corollary 3 alo how that a the SME need greater inaning (i.e., when yˆ the partiipation ontraint beome tighter than the operational enhanement ontraint. That i, the SME hooe to partiipate, even i prodution quantity dereae due to ere atoring. In thee ae, SME opportunity ot or ere atoring i relatively low ine in expetation he borrow a larger amount. So, inanial aving may dominate a poible redution in value due to redued operating level. In Figure 7(, we illutrate eet o proit margin (or equivalently the eet o a hange in the unit ot,. Inreaing the proit margin (lowering provide the irm with more internal ah low to meet the ah outlow, and hene reult in a imilar eet to inreaing initial ah reerve y. In what ollow, we numerially explore the value generated by ere atoring or the SME and OEM a deribed in Propoition 6 above. We deine the perentage value generation or the SME a 100[ V me ( me ( ]/ me Q V Q V ( Q. Thi i analogouly deined or the OEM. Figure 8(a-( below how that ere atoring may lead to igniiant value reation or the SME. In partiular, ere atoring oer more value generation or low proit margin SME (high with aggreive working apital polie (low y that operate in buine environment with long initial payment period (high l and pay a high ot or ernal und (high β. In uh ae, the SME on average need to borrow a larger um o money or a longer period o time and pay a higher ot or thee und. In Northern European ountrie, payment period are typially le than 90 day, o value generation rom ere atoring will be lower. In China and Southern European ountrie uh a Spain and Italy, payment period approah (and even exeed ix month (Euler Herme, 2012, o value generation will be muh greater there, provided ontrat are implemented properly. Thu it i no urprie that Santander Group, a 19

20 Spanih bank, i a leading provider o ere atoring ervie. Nonethele, it i alo important to note that the ended payment period l quikly redue the total value generation, a we aw in the MTO ae. Inight on value generation or the OEM (Figure 8(d-8( are imilar. Under the MTS model, in addition to the ended payment period, l, the OEM may alo igniiantly beneit rom quantity enhanement at the SME. In partiular, a β,, and l go up, the OEM hare a igniiant portion o the quantity enhanement beneit due to ere atoring and hene the OEM beneit quikly go up. A expeted thi eet i more emphaized when the OEM margin i low (i.e., w i low. Figure 8. Perentage Value Generation or the SME and the OEM (a Impat o β, and l on the SME (b Impat o l and on the SME ( Impat o l and y on the SME (d Impat o β, and l on the OEM (e Impat o l and on the OEM ( Impat o l and w on the OEM We now explore the identiied beneit in greater detail. Under the MTS operating model, value o ere atoring tem both rom redued ernal inaning ot a well a enhaned operating level at the SME. Firt, uppoe the SME doe not hange it operating plan under the ere atoring heme and produe the amount Q. The entire beneit o the SME are then due to the redution in ernal inaning ot. We deine the quantity SME: F V Q V Q to be the inanial beneit o the me me me ( ( me F r p( l l Emin( Q, L( Q A( - l ( b A( - l. (4 20

21 Any other beneit to the SME in exe o me me me me a O [ V ( Q V ( Q ] F me F ome rom enhanement in operation. We deine thee, where the term in braket i the total beneit rom Propoition 6(i. Thi lead to me O p Emin( Q, Emin( Q, ( Q Q. (5 The inanial beneit are very imilar to the beneit in the MTO ae, whih make intuitive ene. One the prodution level i ixed, the SME ave the expeted dierential in deadweight inaning ot, and pay the opportunity ot that reult rom any payment period enion by the OEM. Beneit or loe arued beyond thi amount are driven by the hange in the prodution level. We an alo ditinguih the inanial and operational beneit o ere atoring or the OEM: oem F r p( l l Emin( Q,, (6 oem O ( wp ( Emin( Q, Emin( Q,. (7 When the prodution level i ixed, the OEM earn the rik-ree rate on the expeted buine volume or the duration o payment enion. Remaining beneit to the OEM ollow rom quantity enhanement at the SME level, whih i deribed by OEM margin i large (i.e., ( w p ( Emin( Q, Emin( Q,. Intuitively, when the w p i high and the rik-ree rate i low, operational beneit in (7 are likely to dominate the inanial beneit in (6. The total beneit or the SME in Figure 8 are motly due to aving in ernal inaning ot. Figure 9 how the relative ontribution o operational beneit to the total value generation (i.e., 100 O me /( F me O me, whih i mall or our bae ae. Intuitively, i the SME net operating margin i low, then the ernal inaning ot have a igniiant eet on the prodution volume and ere atoring would entail a igniiant inreae in prodution amount. However, thi hange in the operating level would have a relatively mall eet on the net proit ine the operating margin i thin, and inanial aving due to redued ernal inaning ot would have a muh bigger eet. On the other hand, when the net operating margin o the SME i high it need le ernal inaning and the ot o ernal und ha a relatively mall eet on the quantity deiion. Indeed, rom Figure 9 we oberve that operational beneit are dominated by the inanial beneit or the SME. Although not preented in Figure 9, we have numerially oberved that the operational beneit may exeed 50% i the payment period i very high (l > 0.8 and the SME proitability i very low (>11. 21

22 Figure 9. The Relative Size o Operational Beneit Compared to the Total Beneit or the SME (a Impat o l (b Impat o ( Impat o l For the OEM, however, operational beneit may eaily dominate the inanial beneit. In partiular, quantity enhanement at the SME immediately tranlate into higher ervie level or the OEM, and when the OEM proit margin i large thi may reate beneit well in exe o the inanial beneit ariing rom ended payment period. Figure 10 how the parameter pae where the operational beneit due to quantity enhanement aount or more than 50% o total value generation or the OEM. We oberve that the operational beneit tend to dominate the inanial beneit with larger redit pread, longer nominal payment period, greater OEM proitability, maller SME proitability and horter payment period enion. In general, under thee ae, there will be a larger quantity enhanement at the SME. Figure 10. Condition under Whih the Operational Beneit Dominate the Finanial Beneit o the OEM (a Impat o l (b Impat o ( Impat o w The n propoition diue the individually optimal ere atoring ontrat or eah party. PROPOSITION 7. In an MTS buine environment, a ere atoring ontrat v ( r, l, b maximize (i the SME expeted beneit when ( r r, l l, b 0, (ii the OEM expeted beneit when ( r r, l l, b 0, where and l olve l arg max{ Emin( Q, w p Emin( Q, w p }, lll 22

23 p E Q p E Q Q Q L Q A l min(, min(, ( ( ( - ( b L( Q A( - l 0 (iii The total upply hain beneit when ( r r, l l, b 0. A in the MTO ae, the SME beneit and total upply hain beneit are maximized when the payment period i not ended and there i no tranation ot or ere atoring. However, or the OEM an interior olution an be optimal in the MTS ae. Due to the internalized operational beneit, the OEM may preer not to make the SME partiipation ontraint binding, but may rather ariie ome diret inanial beneit in return or higher toking level at the SME. Thi depend to a large ent on the proit margin o the OEM. I the OEM proit margin i relatively large, then the marginal value o inreaing the payment period i low and may even beome negative beore the SME partiipation beome tight. When the OEM proit margin i relatively low, it i more likely to ollet all the inanial beneit by making the SME partiipation tight. (In order to ou on the eet o ere atoring we exluded the poibility o reduing payment period below l, the original level. 6. Diuion Thi reearh eal the interation o operational and inanial deiion in a upply hain where inaning i ailitated by a ere atoring arrangement. We diloe the value reation mehanim o ere atoring and explain how thi value i onditioned by key market ator. We onider make-toorder and make-to-tok model and explore the impat o ere atoring on the operating deiion and the value impliation o the upply hain member. In Setion 6.1 below we diu the managerial impliation o our inding, then we oer onluion and aknowledge limitation in Setion Managerial Impliation Our analyi o ere atoring ontrat link their potential or value reation to (1 the pread o ernal inaning ot between the OEM and the SME, (2 the operational harateriti o the SME (in partiular, demand volatility and the implied working apital poliy and (3 the rik-ree interet rate. The interrelation o thee ator ontitute a key inight or manager who will negotiate the term o a ere atoring ontrat. In an MTO environment, manager hould ae their deadweight ernal inaning ot, working apital poliy and the rik-ree interet rate to value ere atoring agreement. Revere atoring i mot beneiial to the upply hain member when the pread in deadweight inaning ot i high, nominal payment period are long, the demand volatility i high, and the SME employ an aggreive working apital poliy. The rik-ree interet rate doe not impat the total value generation, but it igniiantly inluene the individual beneit o the OEM and SME. A low rik-ree interet rate 23