Before David John Clements was dropped off at the family home, he told the cabbie: "I've got to use an axe today".
Later that morning, his mother found the bloodied body of her 89-year-old husband next to an axe at the back of their home at Springvale, in Wagga Wagga in the NSW Riverina.
On Monday, 50-year-old Clements - who was diagnosed with a form of schizophrenia in 1992 - was found not guilty of murdering his father, Roger Clements, by reason of mental illness.
Acting Justice Jane Mathews explained her verdict to family members in the NSW Supreme Court in Sydney, saying it was clear Clements had killed his father on May 26, 2015.
"But what is also clear, from the psychiatric evidence, is that at the time he was mentally ill within the definition we have in law," she said.
According to the agreed facts, Clements spoke to his mother on the phone on the evening before the killing saying: "Tell dad to get out of my head".
He arrived at the family home on the morning of May 26, making the axe comment to the taxi driver, as well as asking about the times of Sydney trains.
Clements accompanied his father to a medical appointment, before the pair returned home and went out the back to cut wood.
About 45 minutes later, June Clements went out to see if either of them wanted lunch.
"She went to a wood pile and saw the deceased laying on the ground with a large amount of blood to the back of his head and a pool of blood on the ground," the facts said.
Hours later, police boarded a Sydney-bound train and found Clements in a carriage drinking a can of beer.
A pathologist found a cluster of blunt force injuries on the back of his father's head, noting there were no "defence type" injuries to indicate that he had seen the blows coming.
Justice Mathews ordered Clements to be detained in an appropriate facility until, or if, he is deemed by mental health experts to no longer pose a threat to the community or himself.