Sony Corp. said Monday it would write down nearly $1 billion on its film and TV studio after a dismal year at the box office that included such disappointments as the reboot of “Ghostbusters,” the Ang Lee drama “Billy Lynn’s Long Halftime Walk” and “Da Vinci Code” sequel “Inferno.”

The company attributed the write-down primarily to the decline in home-entertainment spending, which fell 7% in the U.S. last year as DVD sales continued to plummet and growth in digital sales slowed. Consumers favored subscription streaming services...