The usual approach is a total divided by a recipient count. It produces a number that is simultaneously too much for most of the list and not enough for the people the program exists for.
Tier before you total
Decide the tiers first: a modest gift for the broad list, something considered for active relationships, and something genuinely good for the accounts that matter. Then count how many fall into each. The total falls out of that, and it is defensible in a way an average is not.
Budget the packaging as a line
For gifting specifically, presentation is not a finishing touch — it is most of how the gift reads. A good product in a poor box reads as cheaper than a modest product presented well. Give it its own line so it is not the thing that gets cut in the last round.
Personalization costs less than people expect
A recipient's name on an item or a written card is a small cost against the total and is disproportionately what gets remembered. It is usually the highest-return line in the budget.
Include fulfillment
Gifts go to individuals, which means individual shipments, address handling and a small percentage of returns and reships. If the list is international, add duties and documentation. This is the line that surprises people at approval.
Decide the timing
A single December send competes with everybody else's December send. Spreading gifting across the relationship — a welcome, a milestone, a thank-you after a difficult project — usually costs the same and lands better, but it needs held stock rather than one seasonal order.
Leave a contingency
Lists grow after the order is placed. Every gifting program has late additions, and having spare finished gifts is far cheaper than a second short run.
Corporate gifting covers running this as a program, and warehousing covers holding stock across the year.