Final answer:
Option D. Physical observation of a client's inventory count primarily satisfies the audit assertion of existence, confirming the actual presence of inventory items reported on the balance sheet.
Step-by-step explanation:
The primary assertion satisfied by physically observing the client's count of inventory is existence. When an auditor observes a company's inventory count, they are confirming that the inventory listed on the balance sheet physically exists. This procedure is directly tied to the existence objective of audit assertions, which concerns whether assets or liabilities of the entity are genuine and actually exist at a given date. Existence relates to whether the inventory items actually exist physically. By physically observing the client's count of inventory, you are verifying that the items are present and exist in reality.
Other assertions like rights and obligations (rights) address whether the entity has legal claim to the inventory, valuation is about whether the inventory is recorded at correct amounts according to GAAP, and completeness ensures that all inventory that should be recorded is indeed recorded. However, physically counting the inventory primarily serves to confirm its existence.