A control apparatus is used with a vehicle including an engine, a storage battery, and an electrical load. The control apparatus works as an automatic engine stop and restart system and calculates a SOC lower limit that is a minimum value of state of charge (SOC) of the battery required to continue to stop the engine in an idle stop mode. The control apparatus also calculates an amount of electric power expected to be consumed by the electrical load during the idle stop mode and determines an idle stop enable SOC at which the idle stop mode is entered and which is selected to be the sum of the SOC lower limit and a SOC of the battery which at least compensates for the consumed amount of electric power. This ensures chances to stop the engine in the idle stop mode and improves fuel economy.