Value-based decision-making provides a theoretical framework to investigate apathy and impulsivity-two notable disturbances in Huntington's disease (HD). Whilst existing work has examined decisions requiring comparison between two options, many everyday choices involve a different class of decision: whether to continue to pursue a current course of action or switch to an alternative. We investigated whether reward and cost sensitivity in a 'stay or leave' foraging task would be associated with HD apathy and/or impulsivity. People with HD (n = 37) and controls (n = 40) performed a foraging task where the costs of leaving were effort (low and high) and time (short and long). Apathy and impulsivity were measured using questionnaires, and their associations with patch-leaving times were examined using linear mixed models. People with HD and controls stayed longer as costs to leave increased, in line with theoretical predictions. There was also a significant positive association between individual sensitivity to effort and delay costs. Apathy in HD was not associated with altered effort or delay cost sensitivity. Impulsivity in HD was associated with increased sensitivity to delay-but not effort-costs. Sensitivity to changing effort and time costs in a foraging context differs as a function of apathy and impulsivity in HD. The effects of these costs on foraging decisions also differ from previous work assessing cost sensitivity in HD using binary choice tasks, underlying the importance of decision context in interpreting associations with clinical syndromes in a value-based decision-making framework.