The two most traditional and conventional transportation modes, private vehicles, and public transit, may be disrupted due to the advent of shared autonomous vehicles (SAVs), which can offer affordable on-demand mobility solutions leading to a transformed transportation system. However, little is known about the attributes affecting mode choice decisions and the impacts of the emergence of SAVs on travel behavior. A stated preference survey consisting of choice experiments, distributed online in October and November 2017 to residents of the Chicago-Naperville-Elgin, IL-IN-WI metropolitan statistical area, is used to determine the perceived impacts that SAVs may have on mode choice decisions and the corresponding value of travel time savings. Based on a representative sample (in terms of age and gender) of 400 responses, random parameter (mixed) logit models are developed to investigate the factors that affect mode choice decisions in short- and long-term scenarios. Value of travel time savings (VTTS) is calculated using the marginal rate of substitution derived from the mixed logit models. The results indicate that the option of sharing the AV ride is not as preferable as single occupant AVs across all market segments, which may challenge the benefits that this emerging technology can bring to shared transportation modes. Further, it was found that VTTS is lower for SAVs compared to single occupancy AVs regardless of the time horizon.