A past cost is a cost that has already been incurred and cannot be changed by any future decision, which makes it the same thing as a sunk cost. Older accounting dictionaries use the two terms interchangeably, and most modern texts prefer sunk cost.
Why past costs are ignored in decisions
When managers choose between alternatives, only costs that differ between the options matter. These are relevant costs, and a past cost can never be one because it is the same whichever option is chosen. Suppose a company paid $40,000 for a machine three years ago and is deciding whether to replace it with a faster model. The $40,000 is gone either way. The decision should compare only the future costs and benefits: the price of the new machine, any amount received for the old one, and the difference in operating costs and output. What the company gives up by keeping the old machine is an opportunity cost, which does count.
Paying too much attention to past costs is a well-known bias, sometimes called the sunk cost fallacy, which leads people to continue failing projects because of how much they have already spent. Past costs still matter elsewhere, however. Financial statements record most assets at historical cost, and that past cost sets the depreciation charge and the tax basis used to work out a gain or loss when the asset is sold. They are irrelevant only to the choice about what to do next.