To solve the problem of setting threshold default risk criterion to select retailer eligible for trade credit granting, a novel method of solving simultaneous equations is proposed. This method is based on the bilevel programming modeling of trade credit decisions as an interaction between supplier and retailer. First, the bilevel programming is set up where the supplier decides on credit terms at the top level considering a retailer’s default risk, and the retailer determines the order quantity at the lower level in response to the credit terms offered. By solving this bilevel programming, the relationship between the optimal terms and the corresponding default risk can be derived. Second, set the extreme scenario where the threshold default risk is approached as the point causing a zero marginal profit to the supplier. Another equation describing this particular scenario can also be derived. Thus, a system of two equations with two unknown variables can be obtained where the exact threshold default risk criterion can be found by solving them. A numerical example is presented as an illustration of the method proposed. It shows that the threshold criterion can be uniquely determined when the financial costs, inventory costs, and the marketing parameters of supplier and buyer are specified. To solve the problem of setting threshold default risk criterion to select retailer eligible for trade credit granting, a novel method of solving simultaneous equations is proposed. This method is based on the bilevel programming modeling trade trade decisions as an interaction between supplier and retailer. First, the bilevel programming is set up where the supplier decides on credit terms at the top level considering a retailer’s default risk, and the retailer determines the order quantity at the lower level in response to the credit terms offered. By solving this bilevel programming, the relationship between the optimal terms and the corresponding default risk can be derived. Second equation set the extreme scenario where the threshold default risk is approached as the point causing a zero marginal profit to the supplier. Another Equation describing this particular scenario can also be derived Thus, a system of two equations with two unknown variables can be obtained where the exact th reshold default risk criterion can be found by solving them. A numerical example is presented as an illustration of the method proposed. It shows that the threshold criterion can be uniquely determined when the financial costs, inventory costs, and the marketing parameters of supplier and buyer are specified.