Tim Cook, CEO of Apple, smiles during a demonstration of the newly released Apple products following the launch event at the Steve Jobs Theater in Cupertino, California, September 12, 2018.

Jefferies initiated coverage of Apple's stock with a buy rating on Monday, estimating the tech giant can build "a massive" services business on its core iPhone business.

"We believe AAPL's stable iPhone business will serve as the foundation upon which it can build a massive, recurring and high margin Services business," Jefferies analyst Timothy O'Shea said in a note.

O'Shea said the firm believes the services business could make up 25 percent of Apple's revenue by fiscal year 2020, as well as 40 percent of the company's gross profit.

"Applying a higher multiple compared to the lower margin hardware business, we see a significant opportunity for investors as Services alone could be worth $111 to $177 per share by that time," O'Shea said.

"Services growth will be led by App Store and Apple Music, and we see an opportunity to introduce new services over time," O'Shea added.

Apple shares rose 1.2 percent in early trading before turning around and selling off to close down 1.9 percent. Jefferies has a $265 a share 12-month price target on Apple, which represents a 22 percent premium on the stock from Friday's close of $216.30 a share.

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