In a breed-and-burn (B&B) reactor, the reactor is first started with enriched uranium or other fissile material but thereafter can be refueled with natural or depleted uranium. B&B reactors have the potential to achieve >10% uranium utilization in a once-through fuel cycle versus <1% for light water reactors. A newly developed method for analyzing B&B reactors - the "neutron excess" concept - is used to determine the minimum amount of startup fuel needed to establish a desired equilibrium cycle in a minimum burnup B&B reactor. Here, a minimum burnup B&B reactor is defined as one in which neutron leakage is minimized and feed fuel can be discharged at uniform burnup. The neutron excess concept reformulates the k-effective of a system in terms of material depletion quantities: the total number of neutrons absorbed and produced by a given volume of fuel, which are termed "neutron excess quantities." This concept is useful because neutron excess quantities are straightforward to estimate using simple one-dimensional (1-D) and zero-dimensional (0-D) models. A set of equations is developed that allows the quantity of starter fuel needed to establish a given B&B equilibrium cycle to be expressed in terms of neutron excess quantities. A simple 1-D example of a sodium-cooled, metal fuel reactor with a startup enrichment of 15% is used to illustrate how the method is applied. An estimate for the required amount of starter fuel based on a 0-D depletion model is found to differ by only 3% from the actual amount computed using the 1-D example model.