What type of shares may private companies have?

Private companies can issue both unlimited and limited shares, making this answer the correct choice.

Limited shares are typically the most common type for private companies, as they limit the shareholders' liability to the amount unpaid on their shares. This provides a layer of protection for personal assets, encouraging investment while mitigating risk for the owners.

Unlimited shares, on the other hand, do not have such restrictions on liability. Shareholders are responsible for the company’s debts without any limit, which can potentially expose their personal assets. However, private companies may still choose to issue unlimited shares depending on their specific financial structure and strategic considerations.

A company by guarantee, while not a share structure primarily, represents a different mechanism for liability where members guarantee a certain amount towards the company’s debts, but this does not conflict with the concept of shares—it simply presents an alternative form of capital structure. Therefore, private companies retain the flexibility to opt for either type of share issue which is why both unlimited and limited shares coexist in the framework of private companies.