考慮應(yīng)收賬款質(zhì)量的供應(yīng)鏈無(wú)追索權(quán)保理融資模型

陳東彥，田春英，陳兆波

考慮應(yīng)收賬款質(zhì)量的供應(yīng)鏈無(wú)追索權(quán)保理融資模型

陳東彥1，田春英2，陳兆波3

（1.哈爾濱理工大學(xué) 理學(xué)院，黑龍江 哈爾濱 150080；2.哈爾濱理工大學(xué) 管理學(xué)院，黑龍江 哈爾濱 150080；3.太原科技大學(xué) 經(jīng)濟(jì)與管理學(xué)院，山西 太原 030024）

保理商通過(guò)買(mǎi)入應(yīng)收賬款為企業(yè)融通資金，并在授信額度內(nèi)提供買(mǎi)方信用擔(dān)保，從而影響供應(yīng)鏈的運(yùn)營(yíng)與融資決策?？紤]應(yīng)收賬款質(zhì)量對(duì)回款產(chǎn)生影響的情況，研究了無(wú)追索權(quán)保理合同下，面對(duì)保理商不同授信額度時(shí)，具有資金約束的供應(yīng)商如何確定最優(yōu)賒銷(xiāo)數(shù)量以及保理商如何選擇最優(yōu)的授信額度等問(wèn)題。研究表明，當(dāng)應(yīng)收賬款質(zhì)量高于一定的臨界水平時(shí)，保理商將通過(guò)較高的授信額度促使供應(yīng)商采取穩(wěn)健的賒銷(xiāo)策略，供應(yīng)鏈的總產(chǎn)量高于無(wú)資金約束時(shí)的水平；當(dāng)應(yīng)收賬款質(zhì)量低于臨界水平時(shí)，保理商將會(huì)降低授信額度，并導(dǎo)致供應(yīng)商采取冒險(xiǎn)的賒銷(xiāo)策略，供應(yīng)鏈的總產(chǎn)量能否達(dá)到無(wú)資金約束時(shí)的水平由應(yīng)收賬款質(zhì)量與供應(yīng)商投入全部資金時(shí)承擔(dān)的市場(chǎng)風(fēng)險(xiǎn)共同決定。通過(guò)數(shù)值分析，研究了不同保理費(fèi)率及應(yīng)收賬款質(zhì)量下無(wú)追索權(quán)保理融資對(duì)供應(yīng)鏈績(jī)效的影響，進(jìn)而得出了供應(yīng)商選擇融資與運(yùn)營(yíng)策略的條件。

供應(yīng)鏈；保理融資；應(yīng)收賬款質(zhì)量；無(wú)追索權(quán)

0 引言

在企業(yè)的財(cái)務(wù)報(bào)表中，因賒銷(xiāo)產(chǎn)生的應(yīng)收賬款通常占據(jù)總資產(chǎn)的一定比例。近年來(lái)，理論界對(duì)應(yīng)收賬款存在的原因、合理額度及其對(duì)供應(yīng)鏈績(jī)效的影響進(jìn)行了深入的研究，從不同的視角解釋了應(yīng)收賬款存在的合理性和必要性[1]。事實(shí)上，應(yīng)收賬款的提供方通常面臨以下兩個(gè)難題：一是當(dāng)自身的流動(dòng)資金緊張時(shí)，如何利用賒銷(xiāo)實(shí)現(xiàn)收益增長(zhǎng)；二是如何規(guī)避應(yīng)收賬款的持有風(fēng)險(xiǎn)。2008年金融危機(jī)之后，這兩個(gè)難題變得更加突出。一方面，銀行出于安全性的考慮不斷收縮銀根、提高貸款門(mén)檻，大量企業(yè)資金周轉(zhuǎn)困難；另一方面，因某個(gè)節(jié)點(diǎn)企業(yè)倒閉引致整條供應(yīng)鏈資金斷裂的現(xiàn)象時(shí)有發(fā)生，信用風(fēng)險(xiǎn)的傳遞性和破壞性對(duì)企業(yè)的潛在威脅比以往更加嚴(yán)重。

具有資金約束的供應(yīng)商在為下游企業(yè)提供延期付款時(shí)可以敘作保理業(yè)務(wù)，即以一定的對(duì)價(jià)將應(yīng)收賬款的所有權(quán)轉(zhuǎn)讓給專(zhuān)業(yè)的保理商，由保理商進(jìn)行應(yīng)收賬款的管理與催收直至到期收回現(xiàn)金。例如，沃爾瑪要求供應(yīng)商向其提供60天的延期支付，致使許多中小型供應(yīng)商通過(guò)將應(yīng)收賬款賣(mài)給銀行等專(zhuān)業(yè)保理機(jī)構(gòu)解決資金周轉(zhuǎn)問(wèn)題。保理按照應(yīng)收賬款轉(zhuǎn)讓后，保理商在未來(lái)無(wú)法收回賬面金額時(shí)能否向原持有人追索分為有追索權(quán)保理和無(wú)追索權(quán)保理兩大類(lèi)。雖然目前國(guó)內(nèi)保理業(yè)務(wù)以前者為主，但國(guó)際主流的形式和未來(lái)的發(fā)展方向均為無(wú)追索權(quán)保理，因?yàn)樗荏w現(xiàn)保理行為的法律屬性。在無(wú)追索權(quán)保理業(yè)務(wù)中，保理商因?yàn)槌袚?dān)了較大的風(fēng)險(xiǎn)，通常預(yù)先核定一個(gè)授信額度作為向供應(yīng)商提供融資的上限，并在該額度內(nèi)提供買(mǎi)方信用擔(dān)保，供應(yīng)商繼而依據(jù)授信額度決定賒銷(xiāo)規(guī)模。本文在應(yīng)收賬款質(zhì)量對(duì)回款產(chǎn)生影響的前提下，研究保理商如何決定授信額度、供應(yīng)商在給定授信額度下如何進(jìn)行賒銷(xiāo)決策。

本文的研究?jī)?nèi)容屬于供應(yīng)鏈融資領(lǐng)域，旨在解決供應(yīng)鏈運(yùn)營(yíng)與融資決策的交叉問(wèn)題。Buzacott 和 Zhang在需求不確定和市場(chǎng)不完全假設(shè)下驗(yàn)證了融資與運(yùn)營(yíng)聯(lián)合決策的必要性[2]，很多學(xué)者針對(duì)特定的融資模式、結(jié)合具體的實(shí)踐背景對(duì)這一問(wèn)題進(jìn)行了深入的探討。Kouvelis 和 Zhao在銀行外部融資框架下研究了存在破產(chǎn)成本時(shí)零售商的幾種不同訂貨策略，以及供應(yīng)商的最佳批發(fā)價(jià)格決策[3]。Yang 和Birge以同時(shí)存在多個(gè)信用提供方為背景，研究了兩種受償優(yōu)先權(quán)規(guī)則下供應(yīng)鏈的運(yùn)營(yíng)決策及績(jī)效水平[4]。王文利等研究了銀行通過(guò)設(shè)置融資上限控制風(fēng)險(xiǎn)時(shí)，供應(yīng)鏈訂單融資模式下的企業(yè)最優(yōu)運(yùn)營(yíng)策略[5]。Chen對(duì)比了應(yīng)收賬款融資與銀行直接融資對(duì)供應(yīng)鏈績(jī)效的影響[6]。Yan等應(yīng)用雙層Stackelberg博弈模型，研究了上游供應(yīng)商為零售商提供信用擔(dān)保從銀行獲得融資時(shí)交易各方的均衡策略[7]。Zhang等研究了下游零售商提前付款模式下的兩階段訂貨決策問(wèn)題，以及供應(yīng)商的定價(jià)策略[8]。占濟(jì)舟等建立了當(dāng)零售商受采購(gòu)資金約束時(shí),供應(yīng)鏈采取商業(yè)信用和存貨質(zhì)押兩種融資方式的決策模型,給出了這兩種融資方式的選擇策略[9]。Yang 等在古諾競(jìng)爭(zhēng)的框架下，研究了外部融資對(duì)供應(yīng)商及兩個(gè)相互競(jìng)爭(zhēng)的零售商均衡運(yùn)營(yíng)策略的影響[10]。以上文獻(xiàn)本質(zhì)上都是研究如何通過(guò)一定的決策機(jī)制實(shí)現(xiàn)供應(yīng)鏈風(fēng)險(xiǎn)的分擔(dān)與收益的共享，從而為供應(yīng)鏈融資問(wèn)題提供了一套科學(xué)的分析方法。

目前，專(zhuān)門(mén)針對(duì)于保理融資的研究相對(duì)較少。在定性研究方面，Smith 和Schnucker、 Summers 和 Wilson從應(yīng)收賬款管理方式選擇的視角對(duì)企業(yè)的保理決策依據(jù)進(jìn)行了系統(tǒng)性的實(shí)證研究，證實(shí)了彌補(bǔ)流動(dòng)資金的不足是企業(yè)選擇保理的原因之一[11]、[12]。Klapper以墨西哥Nafin銀行系統(tǒng)面向中小企業(yè)開(kāi)展的反向保理實(shí)踐為例，研究了保理對(duì)緩解中小企業(yè)資金壓力的作用[13]。在定量研究方面，Sopranzetti構(gòu)建了應(yīng)收賬款保理的經(jīng)濟(jì)模型，通過(guò)對(duì)經(jīng)濟(jì)金融領(lǐng)域中的“銀行貸款出售行為”模型進(jìn)行拓展，得到了賣(mài)方將應(yīng)收賬款出售給保理商的動(dòng)因和條件[14]。Tanrisever等構(gòu)建了“按訂單生產(chǎn)”和“按庫(kù)存生產(chǎn)”兩種生產(chǎn)類(lèi)型下的單周期反向保理定量模型，研究了保理的費(fèi)率、利率及延期付款期限的確定方法[15]。林強(qiáng)等構(gòu)建了信息不對(duì)稱(chēng)下的供應(yīng)商與零售商的委托代理模型，并用數(shù)值算例驗(yàn)證了保理融資相對(duì)于普通貸款的優(yōu)勢(shì)[16]。于輝等在批發(fā)價(jià)格契約模型的基礎(chǔ)上，研究了不同的保理?xiàng)l件對(duì)供應(yīng)鏈決策的影響，認(rèn)為保理合同使得零售商能夠從供應(yīng)商處獲得擔(dān)保收益，從而改變了雙方的目標(biāo)函數(shù)并影響了整個(gè)供應(yīng)鏈的績(jī)效[17]。Vliet等從應(yīng)收賬款的持有成本出發(fā)，構(gòu)建了賒銷(xiāo)企業(yè)的多階段庫(kù)存模型，研究了供應(yīng)商向下游客戶(hù)提供延期付款同時(shí)敘作保理的動(dòng)機(jī)和條件[18]。Lekkakos等應(yīng)用動(dòng)態(tài)規(guī)劃方法，得出了供應(yīng)商無(wú)外部融資以及通過(guò)反向保理融資兩種情況下的最優(yōu)庫(kù)存策略，證明保理增加了供應(yīng)商的流動(dòng)資金、提高了其運(yùn)營(yíng)效率[19]。Huang等研究了同時(shí)面對(duì)匯率風(fēng)險(xiǎn)及國(guó)外買(mǎi)家的信用風(fēng)險(xiǎn)時(shí)，國(guó)內(nèi)供應(yīng)商如何通過(guò)保理提高期望收益，以及金融機(jī)構(gòu)最優(yōu)保理融資率的確定方法[20]。Grüter 等基于金融理論及隨機(jī)流動(dòng)性需求模型，研究了反向保理對(duì)企業(yè)的價(jià)值，指出反向保理對(duì)供應(yīng)鏈的貢獻(xiàn)除了利率的降低還體現(xiàn)在為鏈上企業(yè)提供了潛在生產(chǎn)機(jī)會(huì)[21]。

現(xiàn)有研究涉及了保理的合同參數(shù)確定、保理業(yè)務(wù)績(jī)效分析乃至保理融資下供應(yīng)鏈節(jié)點(diǎn)企業(yè)的運(yùn)營(yíng)策略等方面，但均未對(duì)保理商授信額度的確定方法進(jìn)行深入探討。根據(jù)國(guó)內(nèi)外金融機(jī)構(gòu)網(wǎng)站上對(duì)保理相關(guān)產(chǎn)品及其業(yè)務(wù)流程的介紹，保理商在核定授信額度時(shí)，遵循的通常是金融機(jī)構(gòu)綜合授信的一般思路，即通過(guò)信用評(píng)級(jí)指標(biāo)對(duì)債務(wù)人的資信水平、債務(wù)違約風(fēng)險(xiǎn)進(jìn)行總體評(píng)價(jià)，將評(píng)價(jià)結(jié)果作為授信的主要依據(jù)。這種操作方法沒(méi)有體現(xiàn)保理授信以應(yīng)收賬款為基礎(chǔ)的本質(zhì)，無(wú)法建立授信業(yè)務(wù)未來(lái)收益與應(yīng)收賬款回款的直接關(guān)系，故不利于保理商在控制風(fēng)險(xiǎn)的同時(shí)實(shí)現(xiàn)收益最大化，本文的研究目的之一正是探究這一問(wèn)題。另外，針對(duì)應(yīng)收賬款的研究通常沒(méi)有考慮其質(zhì)量高低的問(wèn)題，而實(shí)踐中金融機(jī)構(gòu)依據(jù)應(yīng)收賬款提供融資時(shí)無(wú)疑要將這一指標(biāo)作為重點(diǎn)考察的對(duì)象，尤其是保理商十分重視的“授信前調(diào)查”本質(zhì)上也是對(duì)應(yīng)收賬款質(zhì)量的全面評(píng)估。本文從融資功能和擔(dān)保功能入手，應(yīng)用單周期報(bào)童模型，研究無(wú)追索權(quán)條件下供應(yīng)鏈保理融資的授信額度以及企業(yè)的運(yùn)營(yíng)決策問(wèn)題，分析應(yīng)收賬款質(zhì)量、保理費(fèi)率對(duì)雙方?jīng)Q策及保理合同效果的影響。本文從理論上豐富了供應(yīng)鏈融資的研究?jī)?nèi)容，為資金約束企業(yè)利用保理緩解資金壓力、改善經(jīng)營(yíng)績(jī)效給出了決策參考，同時(shí)為金融機(jī)構(gòu)合理制定授信政策提供了一定的理論依據(jù)。

1 問(wèn)題描述與假設(shè)

1.1 問(wèn)題描述

無(wú)追索權(quán)保理融資下當(dāng)事人的決策過(guò)程及銷(xiāo)售期末的收益分配情況可通過(guò)圖1描述。

圖1 無(wú)追索權(quán)保理融資決策過(guò)程

Figure 1 The sequence of events in non-recourse factoring

1.2 模型假設(shè)

2 無(wú)資金約束時(shí)供應(yīng)商的賒銷(xiāo)策略

本文證明略。

3 有資金約束時(shí)供應(yīng)商的賒銷(xiāo)策略

3.1 供應(yīng)商的可選策略

3.2 授信額度與供應(yīng)商的策略選擇

4 保理商的授信額度決策

由引理1可以得到兩個(gè)結(jié)論，一方面，保理商知道過(guò)低的授信額度將導(dǎo)致供應(yīng)商的冒險(xiǎn)行為，因此會(huì)在采取低授信的同時(shí)實(shí)行上限控制，保理商的這種“自我保護(hù)”機(jī)制雖然抑制了供應(yīng)鏈總產(chǎn)量的提升，但能有效避免信用風(fēng)險(xiǎn)過(guò)高對(duì)各方的潛在威脅。另一方面，保理商如果決定采取高授信策略，就會(huì)根據(jù)提高授信后供應(yīng)商的應(yīng)對(duì)策略及其對(duì)自身收益和風(fēng)險(xiǎn)的影響選擇唯一的最優(yōu)授信額度。

綜上，保理商實(shí)施授信時(shí)以應(yīng)收賬款質(zhì)量為主要依據(jù)，資質(zhì)較好的零售商可以使供應(yīng)商獲得更多保理授信，從而有機(jī)會(huì)實(shí)現(xiàn)更高的收益。實(shí)踐中，企業(yè)進(jìn)行賒銷(xiāo)交易時(shí)可以通過(guò)一定的價(jià)格折扣、延長(zhǎng)付款期等方式來(lái)爭(zhēng)取優(yōu)質(zhì)客戶(hù)。然而，對(duì)于保理商而言，則要警惕供應(yīng)商為了騙取高額授信，同零售商進(jìn)行勾結(jié)，利用虛假交易等手段對(duì)其財(cái)務(wù)報(bào)表進(jìn)行粉飾，因此，保理商在授信中務(wù)必加強(qiáng)對(duì)零售商的審查與監(jiān)督，確保應(yīng)收賬款質(zhì)量評(píng)估結(jié)果的準(zhǔn)確性和可靠性。

5 數(shù)值分析

圖2 保理融資下供應(yīng)商的期望收益曲線

Figure 2 The supplier’s expected profit curves under factoring finance

注：虛線代表供應(yīng)商采取冒險(xiǎn)型策略、實(shí)線代表供應(yīng)商采取穩(wěn)健型策略

圖3 供應(yīng)商融資策略選擇

Figure 3 The supplier’s financing strategies

6 結(jié)束語(yǔ)

本文研究了一個(gè)自有資金缺乏的供應(yīng)商，在向供應(yīng)鏈下游企業(yè)提供交易信用的情況下，從保理商處獲得無(wú)追索融資的額度問(wèn)題。首先，分析了無(wú)追索權(quán)保理融資模式下當(dāng)事人的博弈過(guò)程。其次，給出了供應(yīng)商可能采取的策略以及保理商如何針對(duì)供應(yīng)商的可能策略確定最優(yōu)的授信額度。最后，通過(guò)數(shù)值分析研究了保理費(fèi)用、應(yīng)收賬款質(zhì)量對(duì)供應(yīng)商收益的影響。在賒銷(xiāo)貿(mào)易背景下，如果零售商承擔(dān)有限責(zé)任，則供應(yīng)商實(shí)際上承擔(dān)了較大的信用風(fēng)險(xiǎn)，保理合同本質(zhì)上是針對(duì)該信用風(fēng)險(xiǎn)提供了一種風(fēng)險(xiǎn)分擔(dān)機(jī)制。本文證明了保理商最優(yōu)授信額度的存在性并明確了供應(yīng)商的策略選擇方法。由于模型較復(fù)雜，供應(yīng)商接受合同的條件只能通過(guò)數(shù)值算例進(jìn)行分析，而沒(méi)能給出解析形式。另外，本文將商品的殘值設(shè)為0，而實(shí)踐中保理商通常會(huì)將未售出商品作為第二道權(quán)益保障，未售出商品變現(xiàn)的難易程度將會(huì)對(duì)現(xiàn)有結(jié)論產(chǎn)生較大的影響。這些問(wèn)題將在后續(xù)的研究中繼續(xù)深入。

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A supply chain non-recourse factoring finance model considering the quality of the accounts receivable

CHEN Dongyan1, TIAN Chunying2, CHEN Zhaobo3

(1. School of Science, Harbin University of Science and Technology, Harbin 150080, China;2. School of Management, Harbin University of Science and Technology, Harbin 150080, China;3. School of Economics and Management, Taiyuan University of Science and Technology, Taiyuan 030024, China)

Deferred payment methods are common in the buyer's market, and it results in accounts receivable accounting for a significant proportion of the liquid assets of manufacturer production. Although the theory has proved that such transaction credit is an effective mechanism for improving supply chain performance, when it has liquidity restrictions and faces higher credit risk, suppliers often need to transfer accounts receivable to factor for cash in order to reduce the risk. In the case of non-recourse factoring financing, the Factoring Chamber approves a credit line for a specific retailer before the buyer and the seller sign the sales contract, and provides the supplier with financial support and buyer credit guarantee to the extent of the limit. In this way, on the one hand, the supplier obtains more production funds; on the other hand, the factor takes greater risks in the process of seeking profit maximization, which has two practical problems: a) How much credit should the factor provide to the supplier? b) How many products should the supplier produce after the factoring financing is obtained?

This paper studies the above problems by constructing the Stackelberg game model in the framework of the Newsboy model. This model is widely used in the field of supply chain finance to describe related problems with uncertain market demand. In practice, the factor needs to conduct a detailed review of the retailer's credit before credit is granted, and makes a decision based on the survey results. In this paper, the difference in quality of accounts receivable is specially considered in the modeling, and the quality of accounts receivable is studied to understand how it influences the factor’s optimal credit decision and the number of transaction credits sold by the supplier under a given amount. First, the optimal credit sales strategy for suppliers without financial constraints is given. Second, credit sales decisions of suppliers with financial constraints under a certain credit line are discussed. Third, how the factor can determine the credit line based on the quality of the accounts receivable, under the premise of predicting the possible countermeasures of the supplier, is studied. Further, numerical examples are used to study the impact of factoring financing on supply chain performance. The main conclusions of the study are as follows:

(1) When the quality of accounts receivable is above the critical level, the credit line of the factor is higher, the supplier can adopt a stable credit sales strategy, and the total output of the supply chain is higher than the production level without the capital constraint. The reason is that the factoring business shifts the market demand risk from the supplier to the lower margin cost factoring, which helps to reduce the double marginal effect of the supply chain. Suppliers increase the amount of credit sales when the factor provides more credit or the quality of the receivables increases.

(2) When the quality of accounts receivable is below the critical level, the factor will control the credit line and cause the supplier to adopt a risky credit strategy. At this time, only when the supplier's capital demand, determined by the combination of receivables quality and market risk, is less than the factoring credit limit, the supply chain can achieve the optimal output without the capital constraint. If the supplier's credit sales strategy is the same as when there is no capital constraint, whether the subsequent sales volume increases or decreases with the quality of the receivables depends on the current market risk under the given sales volume.

(3) Numerical examples show that the effect of factoring financing on supplier income depends on the factoring rate and the quality of accounts receivable: when a factoring rate is given, the supplier's expected return depends on the quality of the accounts receivable. When the quality of accounts receivable is given, except for some exceptional cases, the expected return of the supplier always decreases as the factoring rate increases. Further, the conditions for the supplier to select the financing and operating strategy are obtained when the factoring rate and the quality of the accounts receivable are variable.

Supply chain; Factoring financing; Quality of receivables; Non-recourse

2017-10-29

2018-08-23

Supported by the Natural Science Foundation of China (71171069)

F224，C931.1

A

1004-6062(2020)04-0101-008

10.13587/j.cnki.jieem.2020.04.011

2017-10-29

2018-08-23

國(guó)家自然科學(xué)基金資助項(xiàng)目（71171069）

陳東彥（1964—），女，江西贛州人；哈爾濱理工大學(xué)理學(xué)院教授，博士生導(dǎo)師；研究方向：系統(tǒng)優(yōu)化、供應(yīng)鏈管理。

中文編輯：杜 健；英文編輯：Boping Yan