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With the advent of AI technologies, humans and robots are increasingly teaming up to perform collaborative tasks. To enable smooth and effective collaboration, the topic of value alignment (operationalized herein as the degree of dynamic goal alignment within a task) between the robot and the human is gaining increasing research attention. Prior literature on value alignment makes an inherent assumption that aligning the values of the robot with that of the human benefits the team. This assumption, however, has not been empirically verified. Moreover, prior literature does not account for human's trust in the robot when analyzing human-robot value alignment. Thus, a research gap needs to be bridged by answering two questions: How does alignment of values affect trust? Is it always beneficial to align the robot's values with that of the human? We present a simulation study and a human-subject study to answer these questions. Results from the simulation study show that alignment of values is important for trust when the overall risk level of the task is high. We also present an adaptive strategy for the robot that uses Inverse Reinforcement Learning (IRL) to match the values of the robot with those of the human during interaction. Our simulations suggest that such an adaptive strategy is able to maintain trust across the full spectrum of human values. We also present results from an empirical study that validate these findings from simulation. Results indicate that real-time personalized value alignment is beneficial to trust and perceived performance by the human when the robot does not have a good prior on the human's values.