Final answer:
Noah should recognize a total of $5,850,000 in revenue from gift cards in 2016, which includes $5,400,000 from redeemed gift cards and $450,000 from gift cards that are unlikely to be redeemed.
Step-by-step explanation:
The question relates to revenue recognition for gift cards in accounting, particularly when to recognize revenue associated with gift cards that are sold but not redeemed. According to revenue recognition principles, Noah should recognize revenue when it is earned and realizable. In 2016, Noah sold $6,000,000 in gift cards; out of this amount, $5,400,000 worth of gift cards were redeemed. The revenue associated with these redeemed gift cards should be recognized. Additionally, $450,000 of the remaining gift cards are considered unlikely to be redeemed because they have passed the expiration period determined by Noah. This amount can also be recognized as revenue because it has been concluded that these cards will never be used to make purchases. Therefore, the total gift card revenue Noah should recognize in 2016 is the sum of the redeemed gift cards and the expired gift cards, which equals $5,850,000 ($5,400,000 + $450,000).