The credit analysis of transportation capacity supply chain finance based on core enterprise credit radiation

Abstract

This study examines the application of the business model of supply chain finance depending on the core enterprise, to the credit financing of transportation capacity enterprises. It studies the credit transmission characteristics regarding core enterprise credit radiation, presents the core enterprise credit segmentation and credit pricing, and transforms them into the calculation of credit guarantee and the default probability of core enterprises. Credit guarantee is regarded as a constraint of financial institutions’ credit decisions. Using probability density and logistic tools, we construct a profit maximization model for financial institutions and solve their optimal credit decision for a specific interest rate. Through numerical experiments, we verify the validity of the model and conclude that increasing the business volume between financing enterprises and core enterprises or reducing the probability of default can effectively improve financial institutions’ credit line.

Keywords

Credit segmentation credit pricing default probability transportation capacity financing credit decision

1 Introduction

Supply chain finance (SCF), an effective tool to solve the financing difficulties of small and medium-sized enterprises (SMEs), has entered a stage of rapid development. SCF has already been promoted by national policies and measures such as “Guiding Opinions on Actively Promoting Innovation and Application of Supply Chain,” “Public Notice on Evaluation Results of Pilot Cities and Enterprises in National Supply Chain Innovation and Application,” and “Guiding Opinions on Promoting the Healthy Development of SMEs.” However, it has also been driven by strong demand for financing by SMEs. Version 1.0 of SCF includes static activities, such as the factoring business based on receivables, the pledging business based on inventory, and the confirmation business based on prepayment. Version 2.0 includes dynamic activities, where logistics is driven by business flow, capital flow is driven by logistics, and capital flow promotes both logistics and business flow. Version 3.0 includes ecological activities, relying on information and big data as the core. Accordingly, the core of SCF credit has changed from pledging to credit financing. Although credit financing can restore the authenticity of business operations by relying on data such as from third-party, platform transactions, and trajectory data, and can accurately depict business scenarios, it is not widely used in market practice. In the existing credit financing market, credit is provided by non-bank financial institutions at a high cost. However, banks’ credit methods are mostly based on core enterprises and extend to the upstream and downstream enterprises of the supply chain to prevent and control the risks brought about by information asymmetry. The definition of SCF issued by the China Banking and Insurance Regulatory Commission (2019), it is clearly stated that “ ... relying on the core enterprises of the supply chain, based on the real transactions between the core enterprises and the upstream and downstream chain enterprises, integrating various information such as logistics, information flow and capital flow, to provide a package of comprehensive financial services such as financing, settlement and cash management for the upstream and downstream chain enterprises of the supply chain.” The reliance on core enterprises to implement SCF business has been widely accepted and promoted.

Transportation capacity SCF focuses on logistics enterprise financing, including freight receivable financing, freight payable financing, oil fee financing, road, bridge fee financing, and transport capacity credit financing. Compared to commodity SCF, there is insufficient financial data on transportation capacity financing enterprises. Additionally, several vehicles affiliate to operate, leading to fewer available mortgage assets. It is, therefore, difficult to meet the traditional credit index and credit evaluation requirements. However, transportation capacity enterprises often have large capital demand. Statistics from the China Federation of Logistics and Purchasing indicate the total cost of social logistics in 2019 at 14.6 trillion yuan, representing 14.7% of GDP. Thus, it is estimated that the transportation cost of highway logistics is about 7.7 trillion yuan, and the logistics company’s freight receivable account period is between 3 and 6 months, creating great pressure for cash advance payments.

Several questions arise: How can the generally accepted core enterprise model of SCF be applied to the credit financing of transportation capacity enterprises? Based on various information resulting from the real exchange between the core enterprise and the upstream and downstream supply chain enterprises, how to radiate credit to the transportation capacity financing enterprises? How do banks make credit lines and interest rate decisions for the core enterprise credit extension obtained by the financing enterprise?

Considering these challenges, we begin with the two aspects of credit segmentation and credit pricing, analyzing the default probability of transportation capacity financing enterprises, constructing a profit maximization model for financial institutions, and providing an analysis method for the credit line and interest rate decisions for transportation capacity SCF based on core enterprise credit radiation.

2 Literature review

The literature review is divided into three parts, considering the challenges mentioned in the introduction, such as applying SCF in transportation capacity enterprises, the radiation of core enterprise credit in the supply chain and the credit decision-making: (1) supply chain network and SCF (2) credit financing and (3) credit analysis.

2.1 Supply chain network and SCF

The earliest integration of logistics and finance can be traced back to the “grain warehouse” in Mesopotamia in 2400 BC and the “silver mine warehouse receipt” in Britain. Luo Qi and Zhu Daoli [1] first presented the concept of a financing warehouse. Accordingly, Zou Xiaopeng and Tang Yuanqi [2] presented the concept of logistics finance, and Berger et al. [3] further derived and presented the concept of SCF. Philipp Wetzel and Erik Hofmann [4] explored the superiority of SCF-oriented working capital management approaches from the perspective of supply chain network. Their findings fundamentally contradict the traditional school of thought. They proposed that SCF instruments such as reverse factoring can improve corporate performance under financial constraints and highlight the necessity of large-scale empirical SCF research.

However, the current research on SCF is on “warehouse” finance, such as inventory and order, and focuses on the SCF model, risk management, participant relationship analysis, and technical support. Few studies focus on “transportation” finance, such as three-party logistics (3PL) and small and micro transportation capacity enterprises.

The SCF model. Yu daiqin [5] and Qin Sijia [6] studied the financing mode solution of the transportation capacity supply chain. Wang Lan and Wang Kai [7] summarized the basic SCF model, and proposed that it included factoring and anti-factoring, dynamic discounting, in-transit supply chain financing, and purchase order financing. Song Hua [8] studied four SCF modes enabled by digital platforms, including traditional online SCF, circulating digital SCF, fusion digital SCF, and integrated digital SCF modes.

SCF risk management. Dai Xinqi [9], Zhang Wenjuan, and Lu Changli [10], and Zhang Jiantong et al. [11] studied the “eight major risks” of SCF, namely credit risk, operational risk, transaction risk, technical risk, supply chain risk, environmental risk, human risk and article risk.

SCF participant relationship analysis. He Jing et al. [12] discussed the single-stage game and multi-stage game between new agricultural operators and banks. Ji Chunyang and Feng Bao [13] used an evolutionary game method to study the process between the platforms and regulatory agencies.

SCF technical support: Huwei Liu et al. [14] built a tobacco SCF service platform based on blockchain technology. Jian LI et al. [15] used a blockchain to generate intelligent contracts and improved the operation process of three SCF models: advance payment financing, accounts receivable financing, and inventory pledge financing.

2.2 Credit financing

Regarding credit financing, the research mainly focuses on three aspects:

Trade credit: Petersen and Rajan [16] emphasized that American companies, especially SMEs, were heavily dependent on trade credit when they could not obtain formal debt financing. Issakson [17] posited that trade credit gradually became an important short-term financing method. Abad and Jaggi [18] developed a supplier–retailer comprehensive inventory model in which suppliers provide trade credit to retailers. Stokes [19] indicated that trade credit was one of the most flexible short-term financing sources for most enterprises. Fabbri and Klapper [20] found that suppliers facing fierce competition were inclined to provide trade credit. Yang and Birge [21] indicated that trade credit as a risk-sharing mechanism could improve the efficiency of the supply chain system under uncertain market demand. Kouveils and Zhao [22] found that if a supplier provided an optimal trade credit contract to a retailer, the profits of the supplier, the retailer, and the supply chain would be optimal.

Credit guarantees: Green [23] demonstrated that a credit guarantee scheme effectively solved the high risks and loan mortgage shortages. Bass et al. [24] indicated that a credit guarantee could effectively improve the financing availability rate for SMEs and alleviate their financing pressure. Boschi et al. [25] and Cowan et al. [26], through empirical studies, verified that a credit guarantee could increase the availability of enterprise loans.

Credit risk: Credit risk includes an evaluation index, an index evaluation model, and risk prediction. (1) Regarding evaluation indicators for credit risk, Calabrese and Osmetti [27] believed that the credit risk of SMEs was affected by factors such as solvency, return on equity, per capita turnover, per capita value add, cash flow, bank loans exceeding turnover, the total cost of employees, and increased cost. Kang Cuiyu [28] constructed an index system for credit risk assessment of online SCF on three aspects: subject risk index, debt risk index, and risk index of supply chain relationship. (2) Regarding the risk index evaluation model, Liu and Cui [29] evaluated credit risk using structural equation modeling (SEM) and Grey relational analysis. Changfei [30] conducted empirical research on the SCF credit risk of listed companies using a logistic regression model. (3) Regarding risk prediction, Wang and MA [31] combined boosting with random subspace (RS) to predict the credit risk of enterprises. Zhu et al. [32, 33] integrated random subspace with RS-RAB to predict the credit risk of SMEs in SCF.

2.3 Credit analysis

The credit line and credit model have always been the focus of research. Agarwal [34] studied the demand for enterprise credit lines and factors affecting the credit line. Hau [35] studied the pricing of credit lines. Zhang Rui and Ye Hui [36] studied the overall credit of banks based on the credit evaluation of core enterprises, and determined the quota allocated to a single upstream and downstream according to the planning and allocation of working capital to debt repayment guarantee ability and credit quota. Chen and Zhou [37], under the framework of a structured model based on the influence of subsidiaries on the parent company’s default risk and the multi-objective decision of loan income management, constructed an optimal allocation model for the credit line of enterprise group members. He Jie [38] designed a general index system for dealer credit evaluation and determined the credit line according to different credit rankings. Wu Hongliang [39] built a public chain financial platform for commercial banks’ SCF credit mode with blockchain technology, shared SCF account books with the whole network, and issued credit token lines to core enterprises; the credit token lines can be recharged, split, used to change payment days, transferred, and get cash.

Based on the literature review, it can be seen that the application of credit characteristics to credit financing is a challenge worth discussing but rarely mentioned. In the existing credit financing of SCF, the subject of the rights and obligations concerning financial institutions remains with the core enterprise. It is an important but rarely studied topic to take financing demand enterprises as the subject of rights and obligations to make accurate credit decisions and analysis. Unlike prior literature, this paper considers the credit radiation characteristics of core enterprises in the supply chain, presents their credit segmentation and credit pricing derives the credit guarantee as an influencing factor of the credit decision of financial institutions, and constructs the model to form the optimal scheme. The innovations of this study can be summarized as follows: First, here the application of SCF from the perspective of “transportation” finance is studied; the characteristics of financing needs of transportation capacity enterprises are analyzed, and the credit granting mode of financial institutions relying on core enterprises under “transportation” finance is clarified. Second, in contrast to the traditional research of credit financing, this study examines the credit transmission characteristics from the perspective of core enterprise credit radiation, namely credit segmentation and credit pricing, and converts this characteristic into the problem of quantifiable credit guarantee and default probability. Third, it constructs the credit model of financial institutions under the constraint of core enterprise credit guarantee and default probability, and verifies the validity of the model through numerical experiments, making a methodological contribution to the growing body of SCF research.

3 Core enterprise credit radiation

In this paper, the core enterprises mentioned are those with the arrange, control, and coordination functions of capital and other resources in the transportation capacity supply chain. They have relatively perfect financial data capacity, including third-party logistics enterprises, plat-form logistics enterprises, front-end shippers, and end-user enterprises.

Radiation refers to the process in which energy emitted by a field source diffuses and transmits energy in all directions in the form of electromagnetic waves or particles. The core enterprise credit radiation refers to the process of diffusing, transferring, and splitting credit along the upstream and downstream of the supply chain in the form of credit segmentation and credit pricing with the core enterprise as the field source. The following section is a detailed explanation of the forms of credit segmentation and credit pricing.

3.1 Credit segmentation

In this paper, credit segmentation is defined as the process by which the core enterprise’s credit is spread and transmitted along the supply chain to the upstream and downstream cooperative node enterprises. The node enterprise accumulates credit by relying on the business relationship with the core enterprise, and according to the volume of business, obtains a credit guarantee from the core enterprise.

As a node of the supply chain, whether the financing enterprise can gather the amount of credit is based on if the financing enterprises can achieve the credit financing threshold of financial institutions. The amount of aggregate credit can be determined as the guarantee or loss cover that the core enterprise can provide to the financing enterprise through credit financing, influencing the financing enterprise’s access to credit financing from the financial institution. As the core enterprise is the field source, the credit quantity it recognizes or is willing to spread and transmit to the node enterprise must be proportional to the node enterprise resources. In the supply chain, there is often a certain business relationship between core and node enterprises. In the transportation capacity supply chain, the relationship between the core and the upstream enterprises is freight collection and between the core and the downstream enterprises is freight payment. The financing guarantee for upstream enterprises can be transferred by realizing transportation commodities or pledging of accounts receivable, often covering the guarantee. For downstream enterprises, risk management is carried out through transportation expenses control. It is generally known that supply chain cooperative enterprises are those that cooperate to form long-term strategic partnerships. Furthermore, the supply chain itself has certain coordination and control. The freight payment in the transportation capacity supply chain has a certain accounting period. The freight amount of the node enterprise controlled by the core enterprise can cover the commodity value of a business to some extent. Therefore, it is only necessary to determine the business volume of cooperation between the financing enterprise and the core enterprise in the credit period, and the amount of guarantee or loss cover that the core enterprise is willing to provide to the financing enterprise. We determine the credit volume that the core enterprise recognizes, diffused to the financing enterprise. Given the unit freight rate in an accounting period, the total business amount, that is, the guarantee or loss cover amount can be calculated.

3.2 Credit pricing

Credit pricing here is defined as the influence value of the credit line given by financial institutions based on the degree of core enterprise credit guarantee obtained by node enterprises in the supply chain.

In credit financing, credit pricing is manifested by credit taken as a parameter or transforming it into the control constraint of financing decisions through a credit rating evaluation. For example, if the credit rating is A, the financing line can reach 90%, and if the credit rating is B, the financing line can reach 80%. Alternatively, the probability of default to determine the pricing can be used. The probability of default represents loss and risk. When the probability of default is low, the credit is represented as well, small risk, low loss, and high credit pricing. When the probability of default is high, the credit is represented as poor, high risk, high loss, and low credit pricing. The former method determines credit pricing in a hierarchical manner, which is one-sided and subjective. According to their risk tolerance level, financial institutions often have differences in the classification of the same enterprise’s credit rating. The latter, in the form of default probability, is related to the magnitude of the risk and the amount of loss. As a parameter index of credit financing decision-making, it is comprehensive and objective through quantitative methods such as mathematically optimal solutions, effectively reflecting credit pricing. Therefore, this study transforms the credit pricing problem into a measurement of the default probability of the core enterprise, and determines the issue of credit decision-making based on the credit value of the core enterprise’s credit radiation.

Cao Yong et al. [40] analyzed the applicability of four representative corporate default probability calculation models. Therefore, considering the model’s applicability and the ease of obtaining the financial indicators of core enterprises in the transportation capacity supply chain than those of SMEs in transportation financing, this study adopts the logistic regression model to calculate the default probability.

(1) Logistic Regression Model.

Let p_i be the default probability of the i-th transportation capacity core enterprise, x_ij is the value of the j-th financial indicator of the i-th transportation capacity core enterprise, $y_{i} = ln (\frac{p_{i}}{1 - p_{i}})$ is the i-th quantile of the default probability of the transportation capacity core enterprise, that is, as the explained variable of the linear regression part in the logistic model, the relationship between y_i and financial indicator x_ij is: $y_{i} = a + \sum_{j = 1}^{m} b_{j} x_{ij} + ɛ_{i}$ (1) i = 1, 2, 3 ... n, is the number of sample transportation capacity core enterprise, m is the number of financial indicators, a and b_j are model parameters, ɛ_i is the random error term, and ɛ_i ∼ N (0σ²).

The $\tilde{y_{i}}$ sample value can be obtained through the $\tilde{p_{i}}$ sample default probability: $\tilde{p_{i}} = \frac{r_{bi -} r_{f}}{r_{bi} + S} = \frac{r_{ni} \times (1 - r_{t}) - r_{f}}{r_{ni} \times (1 - r_{t}) + S}$ (2)

r_bi is the actual interest rate of the i-th sample transportation capacity core enterprise bonds, r_f is the interest rate of treasury bonds of the corresponding period, namely the risk-free interest rate, r_ni is the nominal interest rate of the sample enterprise bonds, r_t is the interest tax rate of the i-th sample enterprise bonds, and S is the default loss rate of the i-th sample enterprise bonds.

The sample value $\tilde{x_{ij}}$ can be obtained from the key financial indicators of the sample transportation capacity core enterprise.

Through the sample value $\tilde{y_{i}}$ , $\tilde{x_{ij}}$ , using SPSS multiple linear regression analysis to estimate the parameters a, b_j in formula (1), the financial indicator value is substituted into the calculated default probability quantile, and the logistic inverse transformation is performed to calculate the default probability of the i-th transportation capacity core enterprise as follows: $p_{i} = \frac{e^{y_{i}}}{1 + e^{y_{i}}}$ (3)

(2) Selection of key financial indicators.

As for the selection of financial indicators, according to the empirical research of Cao Yong et al. [40] on the selection of key financial indicators by logistic default probability models of different industries, the key financial indicators for the transportation warehousing industry include as Table 1.

Table 1

The key financial indicators for the logistic regression model

No.	Indicators category	Indicators name	Calculation formula
1	Profitability	Return on total assets x_i1	(Total profit + interest expense)/average total assets
2		Net profit rate x_i2	Net profit/Prime operating revenue
3		Interest cover multiple x_i3	EBIT/interest expense
4	Liquidity	Current ratio x_i4	Current assets/current liabilities
5		Long-term liabilities/shareholders’ equity x_i5	Same as indicator name
6		Asset liability ratio x_i6	Total assets/total liabilities
7		Net cash flow/current liabilities x_i7	Same as indicator name
8		Net cash flow/total liabilities x_i8	Same as indicator name
9	Capital structure	Working capital/total assets x_i9	Same as indicator name
10		Retained earnings/total assets x_i10	Same as indicator name
11	Operational capability
		Receivable turnover x_i11	Sales revenue/accounts receivable
12		Inventory turnover x_i12	Cost of sales/average inventory
13		Assets turnover x_i13	Total turnover/total asset value
14	Growth	Operating income growth rate x_i14	(Main business income of the current period - Main business income of the previous period)/Main business income of the current period
15		Total assets growth rate x_i15	Total assets growth in the current year/total assets at the beginning of the year
16		Growth rate of shareholders’ equity x_i16	Growth of shareholders’ equity in the current year /total amount at the beginning of the year
17	Scale	Total assets x_i17	Total assets

4 Model construction

4.1 Hypotheses and parameter setting

(1) Hypotheses.

Hypothesis 1: According to Zhang Dezhi et al. [41], and Li Weijian [42], customers’ demand for products is subject to a normal distribution. Transportation as a service link of products also follows a normal distribution. Therefore, this study assumes that the logistics volume between upstream and downstream enterprises and core enterprises also follows a normal distribution during the credit granting period.

Hypothesis 2: Zhang Yuhui [43] indicates that under risk neutrality, the decision-making subject aims to maximize returns and the model is based on the return function. Under risk avoidance, the decision-making subject’s goal is loss avoidance, and the model is based on the loss avoidance utility function. In this study, the model is constructed based on the maximization of returns and under the assumption that both financial institutions and financing enterprises are risk-neutral.

Hypothesis 3: The actual repayment amount of the financing enterprise is equally likely to exist everywhere within the interval between zero and the total repayment amount, and is subject to a uniform distribution.

(2) Parameter setting.

4.2 Guarantee amount

Further to the discussion on credit segmentation, the guarantee amount is the business value G between the financing enterprise and the core enterprise within the credit period, determined by the business volume Q, unit freight price P, and distance D. $G = QPD$ (4)

As a random variable, business volume Q obeys normal random distribution. The minimum business volume Q^* within the credit period determines the minimum guarantee amount. Q^* Is represented by the business volume when the credit period is 1.

Given a confidence level α, when the credit period is 1, the minimum business volume is Q^*, by the definition of α $α = \int_{- \infty}^{Q^{*}} f (Q) dQ$ according to R ∼ N (μ, σ²), So, $Z = \frac{R - μ}{σ} \sim N (0, 1)$ $α = \int_{- \infty}^{Q^{*}} f (Q) dQ = \int_{- \infty}^{- Z_{α}} φ (Z) dZ$ (5)

Where Z_α is the quantile of a standard normal distribution for a given confidence level α, and φ (Z) is the density function of a standard normal distribution. Because, $α = \int_{- \infty}^{Q^{*}} f (Q) dQ = \int_{- \infty}^{\frac{Q^{*} - μ}{σ}} φ (Z) dZ$ (6)

Combining (5) and (6) can get $\int_{- \infty}^{- Z_{α}} φ (Z) dZ = \int_{- \infty}^{\frac{Q^{*} - μ}{σ}} φ (Z) dZ$ , therefore, $- Z_{α} = \frac{Q^{*} - μ}{σ}$ after simplifying, it can get: $Q^{*} = - Z_{α} σ + μ$ (7)

By substituting Equation (7) into Equation (4), we can get: $G = QPD = Q * TPD = (- Z_{α} σ + μ) TPD$ (8)Z_α Is the quantile of a standard normal distribution for a given confidence level α, which can be obtained directly by looking up the table. σ Is the standard deviation of business volume when the credit period is 1, and μ is the expectation of the business volume when the credit period is 1, which can be determined by maximum likelihood estimation.

From Mathematical Statistics, if the population X ∼ N (μ, σ²) and X₁X₂ … X_n is a sample from population X, then the maximum likelihood estimators of μ and σ² are, respectively, $\bar{μ} = \bar{X} = \frac{1}{n} (X_{1} + X_{2} + \dots + X_{n})$ And $σ = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}}$ .

The transportation distance D is obtained according to the relevant requirements of the actual business volume order; the unit freight price P can be obtained according to the “China Highway Logistics Freight Weekly Index Report” issued by China Federation of Logistics & Purchasing, and the relevant data within one year before the start of credit period T. This study selects 35 groups of 105 highway transportation data from January 7, 2019 to December 20, 2019, and conducts a statistical analysis as follows:

Substituting P = 0.29 into (8), it can get: $G = (- Z_{α} σ + μ) TPD = 0.29 (- Z_{α} σ + μ) TD$ (9)

4.3 Default probability

According to the above calculation of default probability, parameters such as a, b_i and ɛ_i in Equation (1) require samples of transportation capacity core enterprises for calculation. Based on the characteristics of the highway transportation industry and the 17 key financial indicators of the logistic regression model described in Table 1, this study selects 20 samples of transportation capacity core enterprises, they are Deppon Express, SF Express, Changjiu Logistics, YTO Express, XMXYG Corporation, Sinotrans Limited, Milkway Chemical Supplychain Service Co., Ltd, Transfar, CMST Development Co., Ltd., C&D Inc., WZ Group, Bright Real Estate Group Co., Ltd, Eternal Asia, Xinning Logistics, Huapengfei Co., Ltd, Shanghai Shine-link International Logistics Co., Ltd., Yunda Express, STO Express, Ancksun, Xinjiang Tianshun Supply Chain Co., Ltd.

(1) The quantile of the default probability of sample $\tilde{y_{i}}$ and the sample default probability $\tilde{p_{i}}$ .

Through cninf (http://www.cninfo.com.cn/new/index) and the NATIONAL INTERBANK FUNDING CENTER (http://www.chinamoney.com.cn/chinese/) query, the above 20 enterprises’ company-related data were collected. r_t is the interest tax rate of the sample enterprise bonds usually taken as 20%, and S is the default loss rate of the sample enterprise bonds usually taken as 0.6264 (Cao Yong et al. [40]). The risk-free interest rate is calculated according to the coupon rate of the treasury bonds in adjacent periods (if the distance between the two periods is the same, the mean value is taken).

Among the 20 sample highway transportation enterprises selected in 2019, only ten had bond issuance data. These were industry leaders or enterprises that were previously state-owned, as shown in Table 4. Given the integrity of the data, this study considers ten enterprises as numerical samples to determine the quantile of default probability for the sample $\tilde{y_{i}}$ and the sample default probability $\tilde{p_{i}}$ .

Table 2
Parameter setting table

Parameter category Parameter symbol Parameter definition

Guarantee amount G Business value, reflecting the amount of guarantee

T Credit cycle

P Unit freight price (yuan/ton/km)

Q Business volume during the credit period (ton)

D Distance (km)

Q ^* When the credit period is 1, the minimum business volume between the financing enterprise and the core enterprise

R The random variable, indicating the business volume between the financing enterprise and the core enterprise when the credit period is 1

Z The parameter of the standard normal distribution

Z _α The quantile of a standard normal distribution for a given confidence level α

α Given confidence level

μ The expectation of the business volume when the credit period is 1,

σ The standard deviation of business volume when the credit period is 1

X₁X₂ … X_n The sample value of a group of business volume when the credit period is 1 is usually composed of the previous data of the enterprise

Default probability p _i The default probability of the i-th transportation core enterprise

x _ij The value of the j-th financial indicator of the i-th transportation core enterprise

y _i The i-th quantile of default probability of transportation core enterprise

i = 1, 2, 3 … n The number of sample transportation core enterprise

m The number of financial indicators

$\tilde{p_{i}}$ The sample default probability of the i-th transportation core enterprise

$\tilde{x_{ij}}$ The sample value of the j-th financial indicator of the i-th transportation core enterprise

$\tilde{y_{i}}$ Sample value of the i-th quantile of default probability of transportation core enterprise

a Logistic model parameters

b _j Logistic model parameters

ɛ _i Logistic model random error term

σ ² The variance of the random error term

r_bi The actual interest rate of the i-th sample enterprise bonds

r_f The interest rate of treasury bonds of the corresponding period

r _ni The nominal interest rate of the sample enterprise bonds

r _t The interest tax rate of the sample enterprise bonds

S The default loss rate of the sample enterprise bonds.

x _i1 Return on total assets

x _i2 Net profit rate

x _i3 Net profit rate

x _i4 Current ratio

x _i5 Long-term liabilities/shareholders’ equity

x _i6 Asset liability ratio

x _i7 Net cash flow/current liabilities

x _i8 Net cash flow/total liabilities

x _i9 Working capital/total assets

x _i10 Retained earnings/total assets

x _i11 Receivable turnover

x _i12 Inventory turnover

x _i13 Assets turnover

x _i14 Operating income growth rate

x _i15 Total assets growth rate

x _i16 Growth rate of shareholders’ equity

x _i17 Total assets

Credit model L Credit line

r Credit rate of financial institutions

c _t The transaction cost rate of credit granting

c _g Credit supervision cost rate

c _s The financing cost rate of credit funds

x The actual repayment amount of the financing enterprise

Parameter category	Parameter symbol	Parameter definition
Guarantee amount	G	Business value, reflecting the amount of guarantee
	T	Credit cycle
	P	Unit freight price (yuan/ton/km)
	Q	Business volume during the credit period (ton)
	D	Distance (km)
	Q ^*	When the credit period is 1, the minimum business volume between the financing enterprise and the core enterprise
	R	The random variable, indicating the business volume between the financing enterprise and the core enterprise when the credit period is 1
	Z	The parameter of the standard normal distribution
	Z _α	The quantile of a standard normal distribution for a given confidence level α
	α	Given confidence level
	μ	The expectation of the business volume when the credit period is 1,
	σ	The standard deviation of business volume when the credit period is 1
	X₁X₂ … X_n	The sample value of a group of business volume when the credit period is 1 is usually composed of the previous data of the enterprise
Default probability	p _i	The default probability of the i-th transportation core enterprise
	x _ij	The value of the j-th financial indicator of the i-th transportation core enterprise
	y _i	The i-th quantile of default probability of transportation core enterprise
	i = 1, 2, 3 … n	The number of sample transportation core enterprise
	m	The number of financial indicators
	$\tilde{p_{i}}$	The sample default probability of the i-th transportation core enterprise
	$\tilde{x_{ij}}$	The sample value of the j-th financial indicator of the i-th transportation core enterprise
	$\tilde{y_{i}}$	Sample value of the i-th quantile of default probability of transportation core enterprise
	a	Logistic model parameters
	b _j	Logistic model parameters
	ɛ _i	Logistic model random error term
	σ ²	The variance of the random error term
	r_bi	The actual interest rate of the i-th sample enterprise bonds
	r_f	The interest rate of treasury bonds of the corresponding period
	r _ni	The nominal interest rate of the sample enterprise bonds
	r _t	The interest tax rate of the sample enterprise bonds
	S	The default loss rate of the sample enterprise bonds.
	x _i1	Return on total assets
	x _i2	Net profit rate
	x _i3	Net profit rate
	x _i4	Current ratio
	x _i5	Long-term liabilities/shareholders’ equity
	x _i6	Asset liability ratio
	x _i7	Net cash flow/current liabilities
	x _i8	Net cash flow/total liabilities
	x _i9	Working capital/total assets
	x _i10	Retained earnings/total assets
	x _i11	Receivable turnover
	x _i12	Inventory turnover
	x _i13	Assets turnover
	x _i14	Operating income growth rate
	x _i15	Total assets growth rate
	x _i16	Growth rate of shareholders’ equity
	x _i17	Total assets
Credit model	L	Credit line
	r	Credit rate of financial institutions
	c _t	The transaction cost rate of credit granting
	c _g	Credit supervision cost rate
	c _s	The financing cost rate of credit funds
	x	The actual repayment amount of the financing enterprise

Table 3

Unit freight price analysis

Model/Load	9.6 m/18 ton	13.5 m/25 ton	17.5 m/27 ton
Unit freight price (yuan/ton/km)	0.28	0.28	0.31
Average freight price (yuan/ton/km)	0.29

Table 4

The sample default probability and quantile of default probability

No.	Enterprise abbreviation	Bond name	Bond code	Issue date	Deadline	Nominal interest rate r_n (%)	Actual interest rate (%)	Risk-free rate r_f (%)	Default probability $\tilde{p_{i}}$	Quantile $\tilde{y_{i}}$
1	SF Express	19 SF TAISEN SCP003	011901913	2019.08.21	270D	3.3	2.64	2.46	0.0028	–5.8753
2	YTO Express	19 YTO JIAOLONG SCP001	011902051	2019.09.02	268D	3.95	3.16	2.46	0.0106	–4.5326
3	XMXYG	19XMXYG SCP003	011901891	2019.08.19	90D	3.1	2.48	2.46	0.0003	–8.0880
4	Sinotrans Limited	19SINOTRANS ABN001 PRIORITY	081900643	2019.12.23	189D	3.45	2.76	2.25	0.0078	–4.8460
5	Transfar	19 HUANCP001	041900115	2019.03.21	366D	6.3	5.04	2.48	0.0378	–3.2362
6	CMST Development	19 CMST DEVELOPMENT SCP001	011901768	2019.08.06	270D	3.59	2.872	2.46	0.0063	–5.0627
7	C&D Inc.	19 JIAN SCP002	011901404	2019.06.20	270D	3.1	2.48	2.46	0.0003	–8.0880
8	WZ Group	19 WZ GROUP SCP009	011903057	2019.01.21	270D	3.45	2.76	2.31	0.0069	–4.9721
9	Bright Real Estate	19 BRIGHT REAL ESTATE SCP002	011901929	2019.08.22	180D	3.87	3.096	2.46	0.0097	–4.6285
10	Eternal Asia	19 ETERNAL ASIA MTN002	101901103	2019.08.16	3Year	5.4	4.32	2.75	0.0234	–3.7293

(2) Sample value of the financial indicator $\tilde{x_{ij}}$ .

Based on the analysis, 17 key financial indicators were selected as the explanatory variables for the logistic model. The financial indicators for the ten sample transportation enterprises are shown in Table 5.

Table 5

Financial indicators of sample enterprises

j = 17\i = 10	SF Express	YTO Express	XMXYG	Sinotrans Limited	Transfar	CMST Development	C&D Inc.	WZ Group	Bright Real estate	Eternal Asia
x_i1%	9.80	15.33	5.70	7.53	6.27	4.16	6.32	6.61	4.59	4.07
x_i2%	4.91	7.03	0.65	4.14	4.44	1.20	2.72	1.14	6.69	0.23
x _i3	9.55	71.46	3.39	8.22	3.74	3.54	6.43	5.17	4.08	1.19
x _i4	0.40	1.83	1.34	1.55	1.15	1.37	1.75	1.12	1.84	1.07
x_i5%	22.57	28.49	32.77	48.27	35.33	19.69	96.04	27.95	166.05	31.06
x _i6	2.06	2.44	1.55	1.83	1.82	2.03	1.33	1.51	1.21	1.25
x _i7	0.58	0.84	0.22	0.76	0.38	0.54	0.17	0.21	0.24	0.06
x _i8	0.44	0.49	0.18	0.46	0.27	0.43	0.12	0.18	0.15	0.05
x _i9	–0.22	0.20	0.18	0.18	0.06	0.14	0.38	0.07	0.45	0.05
x_i10%	3.94	22.74	5.65	21.62	9.34	23.16	10.24	10.24	10.56	4.51
x _i11	12.33	19.65	47.95	7.42	12.28	28.53	41.67	50.76	9.55	5.44
x _i12	118.06	446.48	16.45	246.95	10.53	29.03	2.32	16.96	0.33	7.14
x _i13	1.27	1.38	4.27	1.26	0.68	1.69	1.29	3.49	0.28	1.61
x_i14%	27.60	37.45	15.11	5.68	5.10	15.13	28.26	8.65	–1.50	2.27
x_i15%	30.96	41.19	20.28	–1.33	24.30	16.74	23.95	0.12	37.43	–8.19
x_i16%	12.10	25.97	21.67	7.81	7.74	5.50	24.39	10.17	20.60	–0.20
x_i17100 million yuan	716.15	199.69	547.93	614.94	299.30	225.39	2174.54	860.53	744.26	433.92

(3) Parameter solution.

The $\tilde{y_{i}}$ , $\tilde{x_{ij}}$ Values import multivariate linear regression analysis using SPSS 25. Choosing the way of variable into the equation for the “input” result is shown in Table 6.

Table 6

Model overview of quantile of default probability

Model	R	R-Square	Adjusted R-Square	Errors in standard estimates	Change statistics
					R-Squared change	F charge	Freedom degree	Freedom degree	Significance charge
1	1.000^a	1.000	.	.	1.000	.	9	0	.

^aPredictive variable:(constant) x_i17, x_i15, x_i10, x_i13, x_i1, x_i4, x_i5, x_i7, x_i14.

^bDependent variable: y_i.

Table 6 shows that after excluding 8 explanatory variables x_i2, x_i3, x_i6, x_i8, x_i9, x_i11, x_i12 and x_i16, the square root R of the determined coefficient of the model is 1.000, and the determined coefficient R² is also 1.000. The ratio of common variables between the explanatory variable and the explained variable is high, and the fitting degree of the model and data is good.

In Table 7, the final model with the explained variable y_i after excluding some explanatory variables has a good fit. Therefore, impact statistics are not calculated for the t value of the significance test and the significance of the regression coefficient. Meanwhile, ANOVA results show that y_i has a significant linear relationship with x_i1, x_i4, x_i5, x_i7, x_i10, x_i13, x_i14, x_i15, and x_i17. The regression equation can be obtained as follows: $\begin{matrix} y_{i} = - 1.876 + 55.477 x_{i 1} - 2.061 x_{i 4} - \\ 1.032 x_{i 5} - 7.748 x_{i 7} + 21.846 x_{i 10} - 0.873 x_{i 13} - \\ 12.356 x_{i 14} + 1.047 x_{i 15} - 0.001 x_{i 17} \end{matrix}$ (10)

Table 7

Regression coefficients of the quantile model of default probability

Model		Non standardized coefficient		Standardized coefficient	t	Significance Beta	Collinearity statistics
		B	Standard error				Tolerance	VIF
1	(constant)	–1.876	0.000	.	.
	x _i1	55.477	0.000	1.148	.	.	.137	7.287
	x _i4	–2.061	0.000	–0.556	.	.	0.121	8.282
	x _i5	–.1.032	0.000	–.291	.	.	0.081	12.363
	x _i7	–7.748	0.000	–1.263	.	.	0.083	12.067
	x _i10	21.846	0.000	1.006	.	.	.079	12.661
	x _i13	–0.873	0.000	–.655	.	.	0.505	1.981
	x _i14	–12.356	0.000	–0.975	.	.	0.076	13.232
	x _i15	1.047	0.000	0.108	.	.	0.146	6.836
	x _i17	–0.001	0.000	–0.269	.	.	.163	6.150

^aDependent variable: y_i.

Substituting (10) into (3), the default probability is obtained as follows: $p_{i} = \frac{e^{- 1.876 + 55.477 x_{i 1} - 2.061 x_{i 4} - 1.032 x_{i 5} - 7.748 x_{i 7} + 21.846 x_{i 10} - 0.873 x_{i 13} - 12.356 x_{i 14} + 1.047 x_{i 15} - 0.001 x_{i 17}}}{1 + e^{- 1.876 + 55.477 x_{i 1} - 2.061 x_{i 4} - 1.032 x_{i 5} - 7.748 x_{i 7} + 21.846 x_{i 10} - 0.873 x_{i 13} - 12.356 x_{i 14} + 1.047 x_{i 15} - 0.001 x_{i 17}}}$ (11)

4.4 Credit model

Based on the analysis, this study clarifies credit segmentation and credit pricing. Additionally, it determines the quantitative expression for the credit gathered by credit segmentation as guarantee quota, and the credit pricing expression represented by the default probability of core enterprises to build a profit maximization model for financial institutions.

The net income function Q of financial institutions may be expressed as follows: $QL = L (r - c_{t} - c_{g} - c_{s}) - {[L (1 + r) - x]}^{+}$ (12)

In the above formula (12), L is the credit line; r is the credit rate of financial institutions or the expected rate of return - generally, the higher the default probability, the greater the credit risk and the higher the interest rate; c_t is the transaction cost rate for granting credit; c_g is the credit supervision cost rate; c_s is the financing cost rate for credit funds; x is the actual repayment amount for the financing enterprise, which is a random variable in the interval of [0, L (1 + r)], whose probability density function is f (x), and whose distribution function F (x) is strictly monotonically increasing and differentiable; (x) ⁺ means max(x, 0), then [L (1 + r) - x] ⁺ represents the amount of outstanding funds by the financing enterprise at the end of the credit period.

Then, the expected profit is: $EQL = L (r - c_{t} - c_{g} - c_{s}) - \int_{0}^{L 1 + r} f (x) dx$ (13)

Among them, $\int_{0}^{L (1 + r)} [L (1 + r) - x] f (x) dx$ is the expectation of outstanding funds from the financing enterprise.

Through profit maximization analysis of the credit line and interest rate, the optimization problems faced can be expressed as $\begin{matrix} max_{L ⩾ 0} EQL = L (r - c_{t} - c_{g} - c_{s}) \\ - \int_{0}^{L 1 + r} [L (1 + r) - x] f (x) dx \\ subject to : L (r - c_{t} - c_{g} - c_{s}) - \\ \int_{0}^{L 1 + r} [L (1 + r) - x] f (x) dx ⩾ 0 \\ r ⩾ c_{t} + c_{g} + c_{s} \\ L ⩽ (1 - p_{i}) G \end{matrix}$ (14)

First, solve the constraint problem, L ⩽ p_iG which means that the value of x must be in the interval [0, (1 - p_i) G (1 + r)]. Because x obeys a uniform distribution, the density function is $f (x) = \frac{1}{(1 - p_{i}) G (1 + r)}$ , and the expected profit can be expressed as: $\begin{matrix} EQL = L (r - c_{t} - c_{g} - c_{s}) - \\ \int_{0}^{L 1 + r} \frac{[L (1 + r) - x]}{(1 - p_{i}) G (1 + r)} dx = L (r - c_{t} - c_{g} - c_{s}) - \\ \int_{0}^{L (1 + r)} \frac{L (1 + r) x - \frac{1}{2} x^{2}}{(1 - p_{i}) G (1 + r)} = L (r - c_{t} - c_{g} - c_{s}) - \\ \frac{L^{2} (1 + r)}{2 (1 - p_{i}) G} \end{matrix}$ (15)

Secondly, because $\frac{dEQ (L)}{dL} = r - c_{t} - c_{g} - - c_{s} - \frac{L (1 + r)}{(1 - p_{i}) G}$ , $\frac{d^{2} EQ (L)}{{dL}^{2}} = - \frac{(1 + r)}{(1 - p_{i}) G} < 0$ ,

The expected profit for a financial institution is a concave function of L, that is, the existence of the optimal credit line L. That is to say, if $\frac{dEQ (L)}{\partial L} = r - c_{t} - c_{g} - c_{s} - \frac{L (1 + r)}{(1 - p_{i}) G} = 0$ , the following can be obtained: $L^{*} = \frac{(1 - p_{i}) G (r - c_{t} - c_{g} - c_{s})}{1 + r}$ (16)

When $L^{*} = \frac{(1 - p_{i}) G (r - c_{t} - c_{g} - c_{s})}{1 + r}$ , there is an optimal credit line L^*, and for a given enterprise, different credit rates correspond to different optimal credit lines.

5 Numerical experiments and result analysis

In this section, a series of values, such as x_i1, x_i4, x_i5, c_t and c_g, are set to analyze the changes in the credit line, interest rate, and profit of financial institutions. In the entire numerical experiment, the parameters such as r₀, c_t, c_g, change in the effective range, and the basic parameter environment is set as follows: c_t = 0.5%, c_g = 1%, c_s = 5%, α = 95%, Z_α = 1.65, σ = 500, 518(tons), μ = 872, 456(tons) (These obtained according to annual reports of 2017 and 2018) of company code: 002800, T = 1, D = 1000(km).

According to the company’s (code: 002800) 2018 annual report, when x_i1 = 2.03%, x_i4 = 1.71, x_i5 = 15.09%, x_i7 = 0.11, x_i10 = 21.46%, x_i13 = 0.95, x_i14 = -6.74%, x_i15 = 27.87%, x_i17 = 10.01, it can be determined that p_i = 42.34%, G = 13, 514, 377 (yuan), (1 - p_i) G = 7, 792, 124 (yuan).

When r = 7%, xɛ [0, 8337572] L^* = 36, 412, EQ = 91; when r = 8%, xɛ [0, 8415494] L^* = 108, 224, EQ = 812, and so on.

(1) The influence of different interest rates on the credit line and profit

When other parameter values remain unchanged while r changes, the optimal credit line L and the corresponding expected profit EQ for financial institutions could be calculated according to Equations (13) and (15), namely (2) basic L and (3) basic EQ as shown in Table 8. When the business volume increases by 10%, the corresponding optimal credit line and expected profit, namely (4) business volume increases by 10% L and (5) business volume increases by 10% EQ as shown in Table 8. When the default probability decreases by 10%, the corresponding optimal credit line and expected profit, namely (6) the default probability decreases by 10% L and (7) the default probability decreases by 10% EQ as shown in Table 8.

Table 8
The impact of interest rate, business volume and default probability on credit line and profit

(1) r (2) Basic L (3) Basic EQ (4) business volume increases by 10% L (5) business volume increases by 10% EQ (6) default probability reduces by 10% L (7) default probability reduces by 10% EQ

7% 36412 91 40053 100 39086 98

8% 108224 812 119046 893 116172 871

9% 178718 2234 196590 2457 191843 2398

10% 247931 4339 272724 4773 266138 4657

11% 315897 7108 347487 7818 339095 7630

12% 382649 10523 420914 11575 410749 11296

13% 448220 14567 493041 16024 481135 15637

14% 512640 19224 563904 21146 550286 20636

15% 575940 24477 633534 26925 618234 26275

16% 638148 30312 701963 33343 685011 32538

17% 699293 36713 769222 40384 750647 39409

18% 759402 43666 835342 48032 815170 46872

(1) r	(2) Basic L	(3) Basic EQ	(4) business volume increases by 10% L	(5) business volume increases by 10% EQ	(6) default probability reduces by 10% L	(7) default probability reduces by 10% EQ
7%	36412	91	40053	100	39086	98
8%	108224	812	119046	893	116172	871
9%	178718	2234	196590	2457	191843	2398
10%	247931	4339	272724	4773	266138	4657
11%	315897	7108	347487	7818	339095	7630
12%	382649	10523	420914	11575	410749	11296
13%	448220	14567	493041	16024	481135	15637
14%	512640	19224	563904	21146	550286	20636
15%	575940	24477	633534	26925	618234	26275
16%	638148	30312	701963	33343	685011	32538
17%	699293	36713	769222	40384	750647	39409
18%	759402	43666	835342	48032	815170	46872

As shown in Table 8, when the basic setting parameters remain unchanged, the credit line L and the expected profit EQ increase with an increase in the interest rate r. When the business volume increases by 10%, and other parameters remain unchanged, both the credit line and the expected profit show an increasing trend at the corresponding interest rate. When the default probability is reduced by 10% and other parameters remain unchanged, at the corresponding interest rate, the credit line and expected profit also show an increasing trend, and the incremental effect resulting from the increase in business volume is more pronounced.

(2) The influence of different credit lines on profits under the same interest rate.

When r = 10% and other parameters remain unchanged, the influence of different credit lines on expected profit is shown in Table 9 (the same table also shows the results for r = 12%).

Table 9

The influence of different credit lines on expected profits for r = 10% and r = 12%

	Credit line L	Expected profits EQ		Credit line L	Expected profits EQ
r = 10%	123996	3254	r = 12%	191325	7892
	148759	3645		229589	8839
	173552	3948		267854	9576
	198345	4165		306119	10102
	223138	4295		344384	10418
	247931	4339		382649	10523
	272724	4295		420914	10418
	297517	4165		459179	10102
	322310	3948		497444	9576
	347103	3645		535709	8839
	371897	3254		573974	7892

When r = 10% and other parameters remain unchanged, the credit line L = 247, 913, and the maximum expected profit for financial institutions is EQ = 4, 339; similarly, r = 12% yields a credit line L = 382, 649, and the maximum expected profit for financial institutions is EQ = 10, 523. The optimal credit line and expected profit are consistent with the corresponding interest rates as in Table 8, suggesting that the model is effective.

By setting the basic parameter environment, the optimal credit line of financial institutions can be effectively obtained using the credit model, and the model results obtained by changing different parameter conditions are also consistent with the actual operation. For example, an increase in business volume means that the closer the relationship between financing enterprises and core enterprises, the more credit radiation of the core enterprises are gathered in the credit segmentation; the guarantee amount provided by core enterprises will increase, the risk faced by financial institutions will decrease, and the credit line will increase correspondingly. The default probability decreases, meaning that the credit risk is smaller, credit value is higher, and the credit line of financial institutions also increases accordingly.

6 Conclusion and inspiration

This paper starts with applying the SCF mode based on core enterprises to the credit financing of transportation capacity enterprises. First, the literature research indicates that the current research on SCF is mainly around “warehouse” finance, and “transportation” finance is relatively rare. Moreover, the application description of supply chain finance relying on core enterprises is more, while research on credit mechanism of credit around core enterprises is scarce. Therefore, from the perspective of “transportation” finance, this paper first expounds on the credit radiation process of core enterprises, and defines credit segmentation and credit pricing. In other words, credit segmentation is reflected in the fact that the financing enterprise obtains a credit guarantee from the core enterprise according to its business volume with the core enterprise. Credit pricing is reflected in the influence value of the credit line given by the financial institution according to the recognition degree of the core enterprise credit guarantee obtained by the node enterprise of the supply chain. Using the business volume Q between financing enterprises and core enterprises, that obeys a normal distribution, the business value G is calculated, to determine core enterprises’ guarantee for financing enterprises. Based on the logistic regression model, 17 financial indicators of ten sample enterprises were selected for multiple linear regression analysis to obtain the default probability expression. By combining the credit guarantee and default probability, the profit model for financial institutions was constructed, and the optimal expression for the credit line was calculated through the uniform distribution of repayment line x. Finally, through numerical experiments, the optimal credit line and expected profit under different interest rates were analyzed, concluding that the credit line and profit increase when the business volume increases or the default probability decreases. The business volume has a significant effect on the increase in the credit line. Simultaneously, the influence of different credit lines on profits under the same interest rate is analyzed, and the optimal profit value of financial institutions is obtained, and the profit value is consistent. The constructed model is effective. It realizes the analysis of the credit radiation mechanism of core enterprises and the decision of the credit line of financial institutions, providing a theoretical basis for the promotion of SCF credit financing in transportation capacity enterprises relying on core enterprises.

Furthermore, this study does not demonstrate that the business volume of financing enterprises is normally distributed and that the repayment amount obeys a uniform distribution. Additionally, only a few factors that influence the credit line analysis were selected in the numerical experiment. Financial indicators, freight rates, distance, credit cycle, and other variables that influence the credit line and interest rate were not elaborated further. These will be the subject of further research in the follow-up articles.

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