The Torah (Vayikra 21:8) writes regarding a Kohen, "Ve'kidashto" ("You shall sanctify him"), which establishes an obligation to grant a Kohen certain privileges. This obligation applies even nowadays, when there is no Beit Ha'mikdash. Therefore, if, for example, a group of people line up for Netilat Yadayim (hand washing) or to board a bus, there is, according to many authorities, including Rabbi Yosef Shalom Elyashiv (contemporary Rabbi in Israel), a Torah obligation to allow the Kohen to proceed to the front of the line.
However, this obligation does not apply in situations where inviting a Kohen to the front of the line would cost a person money. Thus, for example, if there is a line at the bank, and by allowing a Kohen to go first one will lose time from his workday, thereby causing him financial loss ("time is money"), he is not required to invite the Kohen to the front of the line.
