The preference for immediate negative events contradicts the minimizing loss principle given that the value of a delayed negative event is discounted by the amount of time it is delayed. However, this preference is understandable if we assume that the value of a future outcome is not restricted to the discounted utility of the outcome per se but is complemented by an anticipated negative utility assigned to an unoffered dimension, which we termed the "outgrowth." We conducted three studies to establish the existence of the outgrowth and empirically investigated the mechanism underlying the preference for immediate negative outcomes. Study 1 used a content analysis method to examine whether the outgrowth was generated in accompaniment with the delayed negative events. The results revealed that the investigated outgrowth was composed of two elements. The first component is the anticipated negative emotions elicited by the delayed negative event, and the other is the anticipated rumination during the waiting process, in which one cannot stop thinking about the negative event. Study 2 used a follow-up investigation to examine whether people actually experienced the negative emotions they anticipated in a real situation of waiting for a delayed negative event. The results showed that the participants actually experienced a number of negative emotions when waiting for a negative event. Study 3 examined whether the existence of the outgrowth could make the minimizing loss principle work. The results showed that the difference in pain anticipation between the immediate event and the delayed event could significantly predict the timing preference of the negative event. Our findings suggest that people's preference for experiencing negative events sooner serves to minimize the overall negative utility, which is divided into two parts: the discounted utility of the outcome itself and an anticipated negative utility assigned to the outgrowth.