Is it permissible to exchange currency outside the bank for the purpose of profit when purchasing goods for a customer?

The agent is not allowed to take the profit for himself; rather, it belongs to his principal, unless the principal voluntarily relinquishes it to him. This is because any increase gained by the agent reverts to his principal, just as any loss would fall upon him. This is based on the Hadith (definition) of Urwah al-Bariqi: The Prophet, peace and blessings be upon him, gave him a dinar to buy a sheep for him. So he bought two sheep, sold one of them for a dinar, and came to the Prophet with a dinar and a sheep. The Prophet then prayed for blessings upon him.