With the growing pressure to reduce the environmental footprint of aviation, new and efficient propulsion systems must be investigated. The current research looks at the operating characteristics of a turbofan engine in a parallel hybrid-electric propulsion system. Electric motors are used to supply power in the most demanding take-off and climb phases to achieve the required thrust, which allows the turbofan to be redesigned to maximize the cruise performance (to some extent). It was found that the turbofan's cruise efficiency can be improved by 1.0% by relaxing the constraints of take-off and climb. It was found that the surge margins of compressors limit the amount of power that could be electrically supplied. On a short-range mission, the hybrid-electric propulsion system showed a potential to reduce around 7% of fuel burn on an A320 class aircraft. Most of these savings are however achieved due to fully electric taxiing. The weight of the electrical propulsion system largely offsets the efficiency improvements of the gas turbine during cruise flight. A system dedicated for fully electric taxiing system could provide similar savings, at less effort and costs. Given the optimistic technology levels used in the current analysis, parallel hybrid-electric propulsion is not likely to be used in the next-generation short to medium range aircraft.