Refer to the attachment for a perfectly competitive firm
This firm should shutdown at any price below:
In the short-run the firm managers must simply try "to cover variable costs", In the short-run they must pay the fixed costs whether they operate or not.
Fixed costs are irrelevant (in the short-run) when the firm decides whether to shut down or operate.
In the short run a firm knows it must pay these fixed costs regardless of whether or not it produces. The firm only considers the costs it can save ...
This explains the computation of shut down point