32 6 Vol 32 No 6 2015 11 JOURNAL OF SHENZHEN UNIVERSITY SCIENCE AND ENGINEERING Nov 2015 / Transportation Logistics 1 2 1 1 518060 2 361005 F 830 56 A doi 10 3724 /SP J 1249 2015 06652 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 518060 P R China 2 School of Economics Xiamen University Xiamen 361005 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 2015-04-23 Accepted 2015-10-14 Foundation National Natural Science Foundation of China 10YJC630320 Science and Technology Research Project of Road Transportation Management Bureau of Guangdong Province Corresponding author Associate professor Sun Ximei E-mail 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 2015 32 6 652-660 in Chinese http / /journalszueducn
6 653 15 16 17 18 2012 33 4 19 54 5 58 6% 1 80% 30% 12% 50% ~ 60% 2013 95 693 4 16 43% 2 Hofmann 3 1 Demica 4 43% 1 1 61% 5 6 7 8-9 10 Stackelberg 11 12 13 1 Xu 14 http / /journalszueducn
654 32 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 < 1 1 3 1 3 1 2 2 B 1 1 η η 1 - η 1 2 2 λb 3 3 η = 1 4 5 η = 0 3 1 - 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 - 1 3 1 2 2 1 20 The flow chart of supply chain accounts receivable financing 20
6 655 3 ω 2 4 s f x 3 p 4 1 x 0 x 0 1 1 - ρ η h H 5 λb 1 1 7 + 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 1 1 + 7 p 3 > λω 1 + r 3 2 3 6 2 δπ 1 B x x < x 0 A - 2 1 Π 1 U δ R = B x x 0 x < x 1 A - 2 4 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 2 2 1 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 - 1 - 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 0 1 - 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 - 1 0 x 0F x dx 5 6 http / /journalszueducn 6
656 32 3 λ E U δ R = 0 λ 1 + R F x 1 + δ - 1 1 + r F x 0 = R - r / 1 - ρ η M m 9 λ λ 0 λ B = min λ 0 λ * 7 1 2 R - r - 1 - ρ η M m 1 + R + δ - 1 1 + λ B 9 λ B = r < R - r - 1 - ρ η M m 1 + R F x 1 λ + δ - 1 1 + r F x 0 λ < min λ 0 λ * ρ η M m > R - r 10 1 + r + δ - 1 1 + r 1 + R + δ - 1 1 + r R - r ρ η M m > 1-1 + R + δ - 1 1 + 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 - 1 - ρ η M m λ 1 + R F x 1 λ + δ - 1 1 + r F x 0 λ 7 2 2 2 E U δ R B 2 = - λ 2 p - s 1 - ρ η M m 1 + R 2 f x 1 λ + δ - 1 1 + r 2 f x 0 λ 8 8 2 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 - 1 1 + 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
6 657 3 12 λ* > 0 λ 2 B = min λ 0 λ * ρ λ B ρ 0 λ B ρ 9 ρ ρ = 1 1 + R 2 f x 1 + δ - 1 1 + r 2 f x 0 R - r p - s 1 - ρ 2 12 4 2 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 - 1 1 + r f x 0 [ λ 1 + R - s ] [ λ 1 + R - s ] ω 1 + R 2 f x 1 + < 0 ω δ - 1 1 + r 2 f x 0 λ B B 0 5 4 9 p p = 1 + R [ λb 1 + R - Bs ] ω f x 1 + δ - 1 1 + r [ λb 1 + r - Bs ] ω 1 + R p - s f x 1 + δ - 1 1 + r p - s f x 0 f x 0 13 13 λ* p > 0 λ B 0 p 9 δ 5 p - s 1 + r F x 0-1 + R 2 F x 1 + δ - 1 1 + r 2 F x 0 < 0 λ B δ 0 6 6 δ = http / /journalszueducn
658 32 0 994 9 3 δ = 0 985 1 4 2 1 3 ρ η M m = ηm + 1 - η m 500 100 f x 1 = 100 槡 2π e - x-500 2 2 100 2 B = 100 00 ω = 2 6 s = 1 8 p = 3 M = 0 994 m = 0 94 η = 0 5 R = 0 058 6 r = 0 038 6 δ = 1 2 Matlab 4 1 6 2 A 3 Fig 3 The relationship of banks' optimal LTV and supply chain credit level 4 3 9 4 2 Fig 2 The relationship of banks' expected utility and loan to value LTV 4 2 4 η Fig 4 The relationship of banks' optimal LTV and product sales price 0 940 http / /journalszueducn
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