This paper presents two sets of conditions under which a sole owner of a renewable resource stock who maximize s a nonlinear benefit function would find it more profitable to harvest the stock to extinction than follow a continuous harvesting strategy. When the minimum viable resource stock is positive, extinction is optimal as long as the initial resource stock is sufficiently small, regardless of the discount rate. When the minimum viable resource stock is zero and the discount rate exceeds the growth potential of the species extinction is optimal for sufficiently small initial stocks.