Final answer:
The statement is true; in a perpetual inventory system, the purchaser records the same journal entry for both a purchase return and a purchase allowance, involving a debit to Accounts Payable and a credit to Inventory.
Step-by-step explanation:
True, under the perpetual inventory system, the journal entry for a purchase allowance is indeed the same as that for a purchase return. When a purchaser agrees to a purchase allowance, it means they have kept the goods but at a reduced price, due to some issue like defects or a discrepancy in the order.
The journal entry in both cases, purchase return and purchase allowance, would involve debiting Accounts Payable (reducing the liability owed to the supplier) and crediting Inventory (reducing the asset value to reflect the return or lesser value of the goods as a result of the allowance).