This paper starts from the observation that the primary surplus of the government must be financed out of a country's GDP. Assuming that the interest rate on public debt exceeds the growth rate of GDP, it is demonstrated that a sustainable debt policy is not compatible with a rising public debt to GDP ratio in the long-run. Further, if the primary surplus does not positively react to a rising debt to GDP ratio, a sustainable debt policy is excluded if the initial debt ratio exceeds a certain threshold. This holds independent of whether primary surpluses are set at their maximum values.