考虑应收账款质量的供应链无追索权保理融资模型

陈东彦，田春英，陈兆波

考虑应收账款质量的供应链无追索权保理融资模型

陈东彦1，田春英2，陈兆波3

（1.哈尔滨理工大学 理学院，黑龙江 哈尔滨 150080；2.哈尔滨理工大学 管理学院，黑龙江 哈尔滨 150080；3.太原科技大学 经济与管理学院，山西 太原 030024）

保理商通过买入应收账款为企业融通资金，并在授信额度内提供买方信用担保，从而影响供应链的运营与融资决策。考虑应收账款质量对回款产生影响的情况，研究了无追索权保理合同下，面对保理商不同授信额度时，具有资金约束的供应商如何确定最优赊销数量以及保理商如何选择最优的授信额度等问题。研究表明，当应收账款质量高于一定的临界水平时，保理商将通过较高的授信额度促使供应商采取稳健的赊销策略，供应链的总产量高于无资金约束时的水平；当应收账款质量低于临界水平时，保理商将会降低授信额度，并导致供应商采取冒险的赊销策略，供应链的总产量能否达到无资金约束时的水平由应收账款质量与供应商投入全部资金时承担的市场风险共同决定。通过数值分析，研究了不同保理费率及应收账款质量下无追索权保理融资对供应链绩效的影响，进而得出了供应商选择融资与运营策略的条件。

供应链；保理融资；应收账款质量；无追索权

0 引言

在企业的财务报表中，因赊销产生的应收账款通常占据总资产的一定比例。近年来，理论界对应收账款存在的原因、合理额度及其对供应链绩效的影响进行了深入的研究，从不同的视角解释了应收账款存在的合理性和必要性[1]。事实上，应收账款的提供方通常面临以下两个难题：一是当自身的流动资金紧张时，如何利用赊销实现收益增长；二是如何规避应收账款的持有风险。2008年金融危机之后，这两个难题变得更加突出。一方面，银行出于安全性的考虑不断收缩银根、提高贷款门槛，大量企业资金周转困难；另一方面，因某个节点企业倒闭引致整条供应链资金断裂的现象时有发生，信用风险的传递性和破坏性对企业的潜在威胁比以往更加严重。

具有资金约束的供应商在为下游企业提供延期付款时可以叙作保理业务，即以一定的对价将应收账款的所有权转让给专业的保理商，由保理商进行应收账款的管理与催收直至到期收回现金。例如，沃尔玛要求供应商向其提供60天的延期支付，致使许多中小型供应商通过将应收账款卖给银行等专业保理机构解决资金周转问题。保理按照应收账款转让后，保理商在未来无法收回账面金额时能否向原持有人追索分为有追索权保理和无追索权保理两大类。虽然目前国内保理业务以前者为主，但国际主流的形式和未来的发展方向均为无追索权保理，因为它更能体现保理行为的法律属性。在无追索权保理业务中，保理商因为承担了较大的风险，通常预先核定一个授信额度作为向供应商提供融资的上限，并在该额度内提供买方信用担保，供应商继而依据授信额度决定赊销规模。本文在应收账款质量对回款产生影响的前提下，研究保理商如何决定授信额度、供应商在给定授信额度下如何进行赊销决策。

本文的研究内容属于供应链融资领域，旨在解决供应链运营与融资决策的交叉问题。Buzacott 和 Zhang在需求不确定和市场不完全假设下验证了融资与运营联合决策的必要性[2]，很多学者针对特定的融资模式、结合具体的实践背景对这一问题进行了深入的探讨。Kouvelis 和 Zhao在银行外部融资框架下研究了存在破产成本时零售商的几种不同订货策略，以及供应商的最佳批发价格决策[3]。Yang 和Birge以同时存在多个信用提供方为背景，研究了两种受偿优先权规则下供应链的运营决策及绩效水平[4]。王文利等研究了银行通过设置融资上限控制风险时，供应链订单融资模式下的企业最优运营策略[5]。Chen对比了应收账款融资与银行直接融资对供应链绩效的影响[6]。Yan等应用双层Stackelberg博弈模型，研究了上游供应商为零售商提供信用担保从银行获得融资时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两阶段订货决策问题，以及供应商的定价策略[8]。占济舟等建立了当零售商受采购资金约束时,供应链采取商业信用和存货质押两种融资方式的决策模型,给出了这两种融资方式的选择策略[9]。Yang 等在古诺竞争的框架下，研究了外部融资对供应商及两个相互竞争的零售商均衡运营策略的影响[10]。以上文献本质上都是研究如何通过一定的决策机制实现供应链风险的分担与收益的共享，从而为供应链融资问题提供了一套科学的分析方法。

目前，专门针对于保理融资的研究相对较少。在定性研究方面，Smith 和Schnucker、 Summers 和 Wilson从应收账款管理方式选择的视角对企业的保理决策依据进行了系统性的实证研究，证实了弥补流动资金的不足是企业选择保理的原因之一[11]、[12]。Klapper以墨西哥Nafin银行系统面向中小企业开展的反向保理实践为例，研究了保理对缓解中小企业资金压力的作用[13]。在定量研究方面，Sopranzetti构建了应收账款保理的经济模型，通过对经济金融领域中的“银行贷款出售行为”模型进行拓展，得到了卖方将应收账款出售给保理商的动因和条件[14]。Tanrisever等构建了“按订单生产”和“按库存生产”两种生产类型下的单周期反向保理定量模型，研究了保理的费率、利率及延期付款期限的确定方法[15]。林强等构建了信息不对称下的供应商与零售商的委托代理模型，并用数值算例验证了保理融资相对于普通贷款的优势[16]。于辉等在批发价格契约模型的基础上，研究了不同的保理条件对供应链决策的影响，认为保理合同使得零售商能够从供应商处获得担保收益，从而改变了双方的目标函数并影响了整个供应链的绩效[17]。Vliet等从应收账款的持有成本出发，构建了赊销企业的多阶段库存模型，研究了供应商向下游客户提供延期付款同时叙作保理的动机和条件[18]。Lekkakos等应用动态规划方法，得出了供应商无外部融资以及通过反向保理融资两种情况下的最优库存策略，证明保理增加了供应商的流动资金、提高了其运营效率[19]。Huang等研究了同时面对汇率风险及国外买家的信用风险时，国内供应商如何通过保理提高期望收益，以及金融机构最优保理融资率的确定方法[20]。Grüter 等基于金融理论及随机流动性需求模型，研究了反向保理对企业的价值，指出反向保理对供应链的贡献除了利率的降低还体现在为链上企业提供了潜在生产机会[21]。

现有研究涉及了保理的合同参数确定、保理业务绩效分析乃至保理融资下供应链节点企业的运营策略等方面，但均未对保理商授信额度的确定方法进行深入探讨。根据国内外金融机构网站上对保理相关产品及其业务流程的介绍，保理商在核定授信额度时，遵循的通常是金融机构综合授信的一般思路，即通过信用评级指标对债务人的资信水平、债务违约风险进行总体评价，将评价结果作为授信的主要依据。这种操作方法没有体现保理授信以应收账款为基础的本质，无法建立授信业务未来收益与应收账款回款的直接关系，故不利于保理商在控制风险的同时实现收益最大化，本文的研究目的之一正是探究这一问题。另外，针对应收账款的研究通常没有考虑其质量高低的问题，而实践中金融机构依据应收账款提供融资时无疑要将这一指标作为重点考察的对象，尤其是保理商十分重视的“授信前调查”本质上也是对应收账款质量的全面评估。本文从融资功能和担保功能入手，应用单周期报童模型，研究无追索权条件下供应链保理融资的授信额度以及企业的运营决策问题，分析应收账款质量、保理费率对双方决策及保理合同效果的影响。本文从理论上丰富了供应链融资的研究内容，为资金约束企业利用保理缓解资金压力、改善经营绩效给出了决策参考，同时为金融机构合理制定授信政策提供了一定的理论依据。

1 问题描述与假设

1.1 问题描述

无追索权保理融资下当事人的决策过程及销售期末的收益分配情况可通过图1描述。

图1 无追索权保理融资决策过程

Figure 1 The sequence of events in non-recourse factoring

1.2 模型假设

2 无资金约束时供应商的赊销策略

本文证明略。

3 有资金约束时供应商的赊销策略

3.1 供应商的可选策略

3.2 授信额度与供应商的策略选择

4 保理商的授信额度决策

由引理1可以得到两个结论，一方面，保理商知道过低的授信额度将导致供应商的冒险行为，因此会在采取低授信的同时实行上限控制，保理商的这种“自我保护”机制虽然抑制了供应链总产量的提升，但能有效避免信用风险过高对各方的潜在威胁。另一方面，保理商如果决定采取高授信策略，就会根据提高授信后供应商的应对策略及其对自身收益和风险的影响选择唯一的最优授信额度。

综上，保理商实施授信时以应收账款质量为主要依据，资质较好的零售商可以使供应商获得更多保理授信，从而有机会实现更高的收益。实践中，企业进行赊销交易时可以通过一定的价格折扣、延长付款期等方式来争取优质客户。然而，对于保理商而言，则要警惕供应商为了骗取高额授信，同零售商进行勾结，利用虚假交易等手段对其财务报表进行粉饰，因此，保理商在授信中务必加强对零售商的审查与监督，确保应收账款质量评估结果的准确性和可靠性。

5 数值分析

图2 保理融资下供应商的期望收益曲线

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

注：虚线代表供应商采取冒险型策略、实线代表供应商采取稳健型策略

图3 供应商融资策略选择

Figure 3 The supplier’s financing strategies

6 结束语

本文研究了一个自有资金缺乏的供应商，在向供应链下游企业提供交易信用的情况下，从保理商处获得无追索融资的额度问题。首先，分析了无追索权保理融资模式下当事人的博弈过程。其次，给出了供应商可能采取的策略以及保理商如何针对供应商的可能策略确定最优的授信额度。最后，通过数值分析研究了保理费用、应收账款质量对供应商收益的影响。在赊销贸易背景下，如果零售商承担有限责任，则供应商实际上承担了较大的信用风险，保理合同本质上是针对该信用风险提供了一种风险分担机制。本文证明了保理商最优授信额度的存在性并明确了供应商的策略选择方法。由于模型较复杂，供应商接受合同的条件只能通过数值算例进行分析，而没能给出解析形式。另外，本文将商品的残值设为0，而实践中保理商通常会将未售出商品作为第二道权益保障，未售出商品变现的难易程度将会对现有结论产生较大的影响。这些问题将在后续的研究中继续深入。

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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

国家自然科学基金资助项目（71171069）

陈东彦（1964—），女，江西赣州人；哈尔滨理工大学理学院教授，博士生导师；研究方向：系统优化、供应链管理。

中文编辑：杜 健；英文编辑：Boping Yan