Improvements in fuel efficiency and economy are significantly important both for today's nuclear power reactors and for new, advanced nuclear reactor designs. Burnable absorbers (BA), which are a key component in fuel efficiency and economy, are being developed to improve fuel cycle flexibility and to reduce some of the performance drawbacks associated with their use. In this study, a novel concept is studied: Discrete Burnable Absorber Pins (DBAP) containing ZrB2 and UB2 which have immense potential for fuel efficiency and fuel cycle economy, analysed by Monte Carlo particle transport methods. It has been shown that the use of each type of discrete burnable absorber pin provides an increase in reactivity at the end of fuel life compared to the situation without a BA. This is attributed to the change in 239Pu breeding in the region adjacent to the BA.