Direct air capture, the removal of carbon dioxide from air, requires special sorbents, with high capture capacity, fast kinetics and long lifetime. Beyond that they also need to be affordable. However, since air capture is still in an early development stage, costs are still uncertain. We present a techno-economic model to value a sorbent based on the CO2 market price and the most important sorbent characteristics: cycle time, loading capacity, and rate of degradation. The model gives a net present value equation for any air capture sorbent, whether it uses a moisture swing, pressure swing or thermal swing for regeneration and makes it possible to estimate the maximum allowable budget for any air capture sorbent, i.e., the sorbent value. The analysis aims to focus the rapidly growing field of air capture sorbent development onto the most important parameters. The value of a sorbent is dramatically affected by its longevity. To be economically viable, the typical sorbent must survive tens if not hundreds of thousands of loading and unloading cycles. The model can also be used to investigate the interactions between different sorbent parameters. For example, the correlation between loading capacity and cycle time makes it possible to determine the cycle time that optimizes the economics of an air capture device. Our analysis highlights the significance of some neglected parameters in air capture cost analysis such as cycle duration and stability of the sorbent. Finally, the analysis can also be adapted to post-combustion flue gas sorbents.