Health economic evaluations frequently include projections for lifetime costs and health effects using modeling frameworks such as Markov modeling or discrete event simulation (DES). Markov models typically cannot represent events whose risk is determined by the length of time spent in state (sojourn time) without the use of tunnel states. DES is very flexible but introduces Monte Carlo variation, which can significantly limit the complexity of model analyses. Methods. We present a new methodological framework for health economic modeling that is based on, and extends, the concept of moment-generating functions (MGFs) for time-to-event random variables. When future costs and health effects are discounted, MGFs can be used to very efficiently calculate the total discounted life-years spent in a series of health states. Competing risks are incorporated into the method. This method can also be used to calculate discounted costs and health effects when these payoffs are constant per unit time, one-off, or exponential with regard to time. MGFs are extended to additionally support costs and health effects which are polynomial with regard to time (as in a commonly used model of population norms for EQ-5D utility). Worked Example. A worked example is used to demonstrate the application of the new method in practice and to compare it with Markov modeling and DES. Results are compared in terms of convergence and accuracy, and computation times are compared. R code and an Excel workbook are provided. Conclusions. The MGF method can be applied to health economic evaluations in the place of Markov modeling or DES and has certain advantages over both.