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The introduction of hippos into the wild in Colombia has been marked by their rapid population growth and widespread dispersal on the landscape, high financial costs of management, and conflicting social perspectives on their management and fate. Here we use population projection models to investigate the effectiveness and cost of management options under consideration for controlling introduced hippos. We estimate there are 91 hippos in the middle Magdalena River basin, Colombia, and the hippo population is growing at an estimated rate of 9.6% per year. At this rate, there will be 230 hippos by 2032 and over 1,000 by 2050. Applying the population control methods currently under consideration will cost at least 1–2 million USD to sufficiently decrease hippo population growth to achieve long-term removal, and depending on the management strategy selected, there may still be hippos on the landscape for 50–100 years. Delaying management actions for a single decade will increase minimum costs by a factor of 2.5, and some methods may become infeasible. Our approach illustrates the trade-offs inherent between cost and effort in managing introduced species, as well as the importance of acting quickly, especially when dealing with species with rapid population growth rates and potential for significant ecological and social impacts.