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This paper firstly presents a brief review of the FND (fictitious nodal demand)-based iterative DCOPF algorithm to calculate locational marginal price (LMP), which is proposed in a previous work. The FND-based DCOPF algorithm is particularly suitable for simulation and planning purposes. Then, this paper employs the FND algorithm to analyze the sensitivity of LMP with respect to loads. Tests are performed on the PJM 5-bus system and the IEEE 30-bus test system. A simple, explicit equation of LMP sensitivity is presented and validated. Also, a special case of infinite sensitivity under the step change of LMP is discussed. It is shown that if the operating point is close to the critical load level of LMP step change, the sensitivity is less reliable and may not be applied to a large variation of load. Finally, future works and concluding remarks are presented.