1. Under U.S. tax law, an S corporation cannot be owned by a C corporation -- so this isn't an option.
2. An LLC is a pass-thru entity. If a C corporation owns a share of the LLC, and the LLC is sold, then the owners of the LLC would share directly in the profits, which would be passed-through to the C corporation. The gain on sale of the LLC would be taxable to the C corporation, and it would be up to the C Corporation directors to determine whether or not to pay out some of those gains as dividends.
3. The means by which to avoid the double tax on sale would be to operate the new product under a division of the existing C corporation, and then "spin-off" that division as an asset of the C corporation. If there is a concern about limiting liability by having a separate business entity, then the option is to suffer the additional gain on sale, or purchase liability insurance to cover the potential liability cost (which would probably be less than the tax liability -- but, that's a question to determine with your insurance agent and tax professional [CPA, tax attorney, etc.]).
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