Values have been proposed to be important predictors of emotions about products, which in turn have been proposed to be associated with acceptability of these products. While support for this theory has been found in the environmental domain, it has not been studied in other domains, such as the domain of digital risks. The main objective of this study was to examine if three values (hedonism, personal security, and privacy) are predictors of emotions about a smart home device (a smart speaker), and if, in turn, those emotions influence the acceptability of the device (operationalized as adoption attitude). Additional objectives were to test whether the relation between risk-related values and emotions strengthens when people receive a value-tailored warning, and whether privacy as a value is a valuable addition to the 19 value scale by Schwartz and colleagues. With a scenario study (N = 623), we found, first, that privacy as a value could indeed be distinguished from the other values. Second, the values hedonism and privacy, but not personal security, predicted either or both positive and negative emotions towards a smart device, and in turn the acceptability of the smart device. Third, the effects of the values privacy and personal security on emotions were not strengthened by a value-tailored warning. Fourth, two additional values were identified that also explained emotions and in turn acceptability of the smart device, being power-resources and tradition. Fifth, privacy was found to be a valuable addition to the 19 value measurement, which explained emotions over and above the other 19 values. The study thus shows that values are also important predictors of emotions and in turn acceptability in the context of digital risks, with privacy as an important newly developed value that contributes to a more in-depth understanding of consumer decision making in this context.