Accounts receivable LTV ratio optimization based on supply chain credit

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1 32 6 Vol 32 No JOURNAL OF SHENZHEN UNIVERSITY SCIENCE AND ENGINEERING Nov 2015 / Transportation Logistics F A doi /SP J Accounts receivable LTV ratio optimization based on supply chain credit Sun Ximei 1 Yu Bo 2 and Han Biao 1 1 College of Economics Shenzhen University Shenzhen P R China 2 School of Economics Xiamen University Xiamen Fujian Province P R China Abstract Assuming that the supplier and the core enterprise's default rate is exogenous we define supply chain credit on the basis of the framework of supply chain comprised of the supplier the core enterprise and the bank The decision model on bank loan to value LTV ratio is developed and analyzed It is shown that the optimal LTV ratio exists and the optimal LTV ratio based on the supply chain is higher than that for the supplier financing alone At certain conditions the bank's optimal LTV is positively correlated to supply chain credit the effect of the core enterprise and the product sale price while it is negatively correlated to accounts receivable amount product wholesale price and the degree of risk aversion of the bank The numerical simulation results will be helpful for banks to choose financing direction and account receivable optimal LTV ratio Key words supply chain finance supply chain accounts receivable financing credit level supply chain credit loan to value ratio Received Accepted Foundation National Natural Science Foundation of China 10YJC Science and Technology Research Project of Road Transportation Management Bureau of Guangdong Province Corresponding author Associate professor Sun Ximei szusxm@163com Citation Sun Ximei Yu Bo Han Biao Accounts receivable LTV ratio optimization based on supply chain credit J Journal of Shenzhen University Science and Engineering in Chinese http / /journalszueducn

2 % 1 80% 30% 12% 50% ~ 60% % 2 Hofmann 3 1 Demica 4 43% % Stackelberg Xu 14 http / /journalszueducn

3 η 0 η 1 F x = 0 s 0 < s ω R r 0 r < R 1 - η 1 λ 2 λ 1 / 1 + R = λ 0 λ 0 λ λ B ρ η M m Π B x U δ R E U δ 1 ρ η M m / M = η ρ η M m / m = 1 - η 2 ρ η M m / η > 0 3 ρ 1 M m = M ρ 0 M m = m m M 0 < m < M < B 1 1 η η 1 - η λb 3 3 η = η = ρ η M m 1 2 ω c p p ω c x 1 Fig 1 f x F x u σ x 0 f x = 0 http / /journalszueducn A A The flow chart of supply chain accounts receivable financing 20

4 ω 2 4 s f x 3 p 4 1 x 0 x ρ η h H 5 λb R B λ 1 / 1 + R = λ 0 λ 0 Π 1 B x = p - s x + Bs /ω - λb 1 + r 2 2 ρ η h H 6 U δ R = Π B Π B 0 Π { 2 B x = λb R - r 3 δπ B Π B < 0 2 x x 0 x 1 2 Π B δ 3 δ 3 x x δ p 3 > λω 1 + r δπ 1 B x x < x 0 A Π 1 U δ R = B x x 0 x < x 1 A Π 2 B x x < x 1 A Π 2 B x x x 1 p s 4 x 0δΠ 1 E U δ R = 1 - ρ η M m B x f x dx + Π B x = pmin B ω x + smax B ω - x 0 λb 1 + r Π B x = 0 1 x 0 = λ 1 + r - s /ω B x < x p - s 0 5 x > x 0 0 E U δ R = λb R - r ρ η M m 2 3 Π B x = λb R - r x 1 1 x 1 = x 0 < x 1 λ 1 + R - s /ω B r < R p - s ρ η M m B x f x dx + x0 x 1Π 1 x 1Π 2 ρ η M m 0 B x f x dx + x1 + Π 2 B x f x dx p - s 0 x 1F x dx + δ x 0F x dx 5 6 http / /journalszueducn 6

5 λ E U δ R = 0 λ 1 + R F x 1 + δ r F x 0 = R - r / 1 - ρ η M m 9 λ λ 0 λ B = min λ 0 λ * R - r ρ η M m 1 + R + δ λ B 9 λ B = r < R - r ρ η M m 1 + R F x 1 λ + δ r F x 0 λ < min λ 0 λ * ρ η M m > R - r r + δ r 1 + R + δ r R - r ρ η M m > R + δ r λ 0 E U δ R > 0 6 λ 0 λ 1 λ = 1 λ E U δ R B = min λ 0 1 = λ 0 = B R - r ρ η M m λ 1 + R F x 1 λ + δ r F x 0 λ E U δ R B 2 = - λ 2 p - s 1 - ρ η M m 1 + R 2 f x 1 λ + δ r 2 f x 0 λ E U δ R < 0 E U δ R λ B η > 0 > λ B η = 0 λ 2 9 η η = p - s R - r ρ 2 η M m 1 + R 2 f x 1 + δ r 2 f x 0 ρ η M m η 11 2 ρ η M m η > 0 λ* η > 0 η 0 η 1 λ B η > 0 > 2 λ B =min λ 0 λ B η 0 λ B η = 1 ψ 1 h H = h λ B η = 0 η = 0 η > 0 http / /journalszueducn

6 λ* > 0 λ 2 B = min λ 0 λ * ρ λ B ρ 0 λ B ρ 9 ρ ρ = R 2 f x 1 + δ r 2 f x 0 R - r p - s 1 - ρ λ B B 9 B B = - p - s B [ λ 1 + R - s ] ω 1 + R f x 1 + [ λ 1 + R - s ] ω δ r f x 0 [ λ 1 + R - s ] [ λ 1 + R - s ] ω 1 + R 2 f x 1 + < 0 ω δ r 2 f x 0 λ B B p p = 1 + R [ λb 1 + R - Bs ] ω f x 1 + δ r [ λb 1 + r - Bs ] ω 1 + R p - s f x 1 + δ r p - s f x 0 f x λ* p > 0 λ B 0 p 9 δ 5 p - s 1 + r F x R 2 F x 1 + δ r 2 F x 0 < 0 λ B δ δ = http / /journalszueducn

7 δ = ρ η M m = ηm η m f x 1 = 100 槡 2π e - x B = ω = 2 6 s = 1 8 p = 3 M = m = 0 94 η = 0 5 R = r = δ = 1 2 Matlab A 3 Fig 3 The relationship of banks' optimal LTV and supply chain credit level Fig 2 The relationship of banks' expected utility and loan to value LTV η Fig 4 The relationship of banks' optimal LTV and product sales price http / /journalszueducn

8 M Li Shaowen Factoring industry for blowout N International Commercial Daily in Chinese N Hofmann E Supply chain finance-some conceptual insights J /OL Logistik Management Innovative Logistikkonzepte https / /www alexandria unisg ch /export /DL /29025 pdf DOI / Demica Supply chain finance a third report from demica EB /OL http / /www demica com / images / PDFs / supply_chain_finance_strengthening pdf 5 Chen Xiangfeng Zhu Daoli The supply chain logistics provider's system value study under capital constraint J Journal of Systems Engineering in Chinese J Chen Xiangfeng Zhu Daoli Ying Wenjun Financial and operation decisions in budget-constrained supply chain 2 J Journal of Management Sciences in Chinese 3 J Li Yixue Wang Shouyang Feng Gengzhong Decision of 5 loan-to-value ratios of seasonal inventory / pledge financing based on logistics finance J Journal of Management 6 Sciences in Chinese J YJC Li Yixue Feng Gengzhong Xu Yu Research on Loanto-value ratio of inventory financing under randomly-fluctu- szusxm@163com J 2015 ant price J Systems Engineering-Theory and Practice in Chinese / References 1 The development of Chinese small and medium-sized enterprises yearbook newsroom China's small and medium-sized enterprise yearbook 2013 M Beijng Enterprise Management Press 2013 in Chinese J Li Yixue Wang Shouyang Feng Gengzhong Practical development and theoretic review of logistics finance-a new discipline direction J Systems Engineering-Theory and Practice in Chinese http / /journalszueducn

9 J Cao Wenbin Ma Cuixiang The analysis of accounts 10 Sun Ximei Zhao Guokun Wang Ying Effect analysis receivable financing game based on supply chain finance on supply chain performance based on inventory pledging financing J Journal of Shenzhen University Science and Engineering in Chinese J Journal of Business Research in Chinese J J Yi Xuehui Zhou Zongfang Study on loan-to-value ratios Sun Ximei Yu Bo Han Biao Accounts receivable financing decision optimization based on Stackelberg model of bank in the supply chain finance J Chinese Journal of Management Science in Chinese J Journal of Shenzhen University Science and Engineering in Chinese Stackelberg 18 Han Dongping Guo Meijia Deng Xiuli The empirical research on the relationship between social capital and the J level of credit of small and medium-sized enterprise J 12 Zhang Qinhong Zhao Quanwu Research on loan-to-value ratios of standard inventory financing when demand is stochastic J Chinese Journal of Management Science in Chinese 101 J Yu Hui Zhen Xueping Loan-to-value ratios model of pledge by warehouse receipts for small and medium enterprises J Chinese Journal of Management Science in Chinese J J Xu Lihe Wang Shouguo The analysis of the supply chain financing model based on the accounts receivable C / / International Conference on Management Science and Engineering Mosco IEEE Lu Qihui Zeng Lifei Zhou Weihua The decision analysis and the value research of supply chain accounts receivable financing J Journal of Management Science in Chinese J Accounting Communication in Chinese J Sun Ximei Zhao Guokun Study on loan-to-value ratios of inventory pledging based on supply chain credit level J Chinese Journal of Management Science in Chinese 20 Project team of supply chain finance of Shenzhen Development Bank and China Europe International Business School Supply chain finance new finance in new economy M Shanghai Shanghai Yuandong Press in Chinese M J http / /journalszueducn

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