OBJECTIVES: To develop an analytical method which quantifies the reasonable limits for any incremental cost-effectiveness ratio (ICER) defined by the slope of a line connecting two points on the cost-benefit plane. METHODS: Assume that the ICER of a target technology vs. its comparator is defined with two points at each of which a pair of cost and benefit is given on the C(cost)-E(benefit) plane. In order to find a cost-benefit function connecting the two points, an analytical method was developed by means of curve-fitting technique with exponential and quadratic modeling. The resultant cost-benefit function was further analytically expanded to the derivative, dC/dE, we call it "tangent limit". Example calculations of the tangent limits were conducted for each model. RESULTS: The analytical development resulted in the following equations of the cost-benefit function and the derivative for each modeling: C = Exp((E - p)/q) and dC/dE = (1/q) Exp((E - p)/q) for exponential model, whilst C = (1/q)E - p/q and dC/dE = 2E/q for quadratic model, where p and q are parameters determined by costs and benefits of the target technology and its comparator. Applying the equations for two hypothetical points, (7.6 QALY, US$100,000) and (8.6 QALY, US$150,000), we found that the ICER of 50 bounds with the lower and the upper limits, respectively, 40.6 and 60.8 US$(x1000)/QALY for exponential model, and as well, 46.9 and 53.1 for quadratic model. Those estimates were not so much different as the limits of 43.9 and 65.8 for the ICER of 54.1, obtained by the regression analysis presented in the ISPOR New Orleans 2013. CONCLUSIONS: Our approach can offer a simple and science-based method to estimate boundaries for any ICER. It would be useful for negotiations and decisions in value-based pricing in which a range of ICER must be considered beyond a single threshold ratio.