DE SOTO, Mo. — A Missouri woman sent a goodbye e-mail to her former boyfriend, then apparently shot and killed her three daughters before turning the gun on herself, authorities said Thursday.

The bodies of 22-month-old Faith Ehlen, Autumn Cochran, 10, and Alyssa Cochran, 11, were found in a vehicle parked outside the home of the former boyfriend, about 45 miles south of St. Louis.

Their mother, 32-year-old Lisa Cochran, was found dead on the front porch steps.

Jefferson County Sheriff Glenn Boyer said a shotgun purchased by Cochran at a Walmart was found beside her. “The purchase of the shotgun, and compiling everything we have so far, leads us to believe we’re dealing with a murder-suicide and not a homicide,’’ he said.