A significant reduction in energy use in the building stock is a major challenge for the future, and doing this in a cost-effective manner is important. This study uses an optimization approach to identify life cycle cost (LCC) optimal energy efficiency measures (EEMs) to implement as part of a renovation of a multifamily building in Sweden. The studied building is a multifamily building with a lightweight concrete construction and an exhaust air ventilation system, built in 1961. The optimization tool OPERA-MILP is used. The energy renovation approaches are compared to both the performed energy renovation of the building and a validated dynamic energy simulation model in IDA ICE 4.8. The results show that under the given framework conditions and assumptions it is not cost-optimal to improve the thermal performance of the building envelope or to implement heat recovery ventilation measures to reduce the space heating demand in the building when considering a life cycle of 40 years. Balanced mechanical ventilation system with heat recovery is cost-effective when an energy saving target of 40% is introduced. The energy renovation of the building has a slightly higher LCC than the cost-optimal level, and it would have been more cost-effective to add more insulation to the façade instead of the attic to achieve the same level of energy saving. A sensitivity analysis has been performed to reveal the effect of the discount rate, energy price, cost of EEMs, thermal properties of the building envelope and windows’ solar heat gain factors on the LCC.