Based on a mathematical model, the efficiency of a boiler for different utilizations of the exhaust gas energy is systematically investigated. The analysis is carried out for a biomass boiler, which is a novel aspect of the study. It is shown that condensing conditions using a condensing boiler leads to higher efficiencies. Beyond this, it is additionally shown that further efficiency increases can be achieved by the incorporation of a so-called enthalpy wheel, which is a rotary heat and mass exchanging device, even without using the condensation energy. The enthalpy wheel can be operated as a regenerative heat exchanger to preheat the combustion air, which enhances the boiler efficiency. Further, it can additionally serve to moisture recovery, by transferring moisture from the exhaust gas into the combustion air, when its surfaces are covered by a desiccant material. It is shown that the highest efficiencies are obtained when an enthalpy wheel is operated for simultaneous heat and moisture recovery. It is also shown that the exit temperature of the condensing heat exchanger is an important parameter, not only for the case without an enthalpy wheel but also for the enthalpy wheel case, having a substantial influence on the boiler efficiency.