Feral cats are some of the most destructive invasive predators worldwide, particularly in insular environments; hence, density-reduction campaigns are often applied to alleviate the predation mortality they add to native fauna.Density-reduction and eradication efforts are costly procedures with important outcomes for native fauna recovery, so they require adequate planning to be successful. These plans should include empirical density-reduction models that can guide yearly culling quotas, and resource roll-out for the duration of the culling period. This ensures densities are reduced over the long term and that resources are not wasted. We constructed a stochastic population model with cost estimates to test the relative effectiveness and cost-efficiency of two main culling scenarios for a 10-year eradication campaign of cats on Kangaroo Island, Australia: (a) constant proportional annual cull (one-phase), and (b) high initial culling followed by a constant proportional maintenance cull (two-phase). A one-phase cull of at least 0.35 of the annual population size would reduce the final population to 0.1 of its original size, while a two-phase cull with an initial cull of minimum 0.6 and minimum 0.5 maintenance cull would reduce the final population to 0.01 of its initial size within the 10-year time frame. Cost estimates varied widely depending on the methods applied (shooting, trapping, aerial poison baits, Felixer™ poison-delivery system), but using baiting, trapping and Felixers with additional shooting to meet culling quotas was the most cost-effective combination (minimum cost: AU$19.56 million; range: AU$16.87 million-AU$20.69 million). Our model provides an adaptable and general assessment tool for cat reductions in Australia and potentially elsewhere, and provides relative culling costs for the Kangaroo Island campaign specifically.