Oura and some of its shareholders plan to offer 50 million common shares at an estimated price of $40 to $44 per share in an initial public offering, the smart ring maker said Monday in a Form S-1 filing.

Oura is offering 13.5 million shares, while selling shareholders are offering 36.5 million shares. The underwriters have an option to purchase up to an additional 7.5 million shares from the selling shareholders.

The company expects to have 320.9 million shares outstanding immediately after the offering, it said. Oura has applied to list on the Nasdaq Global Select Market under the ticker "OURA."

Oura estimates net proceeds of approximately $532.6 million, based on an assumed IPO price of $42 per share.

The company plans to use around $526.4 million of the proceeds to cover expected tax withholding and remittance obligations associated with the net settlement of restricted stock units.

The remainder will fund general corporate purposes, including technology development, working capital, operating expenses and capital expenditures.

The company said Eli Lilly (LLY) has indicated an interest in buying up to $100 million of shares, and funds affiliated with Dragoneer Investment Group have indicated an interest in buying up to $300 million of shares, at the IPO price.