The quantity where bulk cost (including amortized membership) equals retail cost. Formula: (membership_fee / trips_per_month + bulk_price) / (retail_unit_price - bulk_unit_price) / (1 - spoilage_rate). Your monthly usage must exceed this to save money.
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How the Math Works
Spoilage reduces usable quantity. We multiply effective quantity by (1 - spoilage_rate). A 10% spoilage rate means only 90% of what you buy is actually used. This raises the break-even quantity and lowers projected savings.
The annual fee is split across your trips: membership_fee / trips_per_month / 12 = fee per trip. This per-trip cost is added to the bulk price in the break-even formula. More trips = lower fee per trip = easier to break even.