Blue Waves Pty Ltd (Blue Waves) operates three surfing stores in Queensland. On 8 June 2019, Allan was appointed to the position of Managing Director of Blue Waves for a period of two years. A return was lodged with ASIC indicating his appointment as a managing director on that date. Allan was not formally reappointed after 8 June 2021, but he has continued to act as a managing director. The terms of Allan's appointment, which were set out in a contract between him and Blue Waves and were also in Blue Waves' constitution, included a restriction to the effect that he was not to commit the company to borrowing transactions in excess of 50,000. Any such transaction was to remain subject to the approval of the board of directors. On 15 July 2022, Allan, purportedly acting on behalf of Blue Waves, signed a loan contract with Bank of Sydney, pursuant to which the bank agreed to lend the company $100,000 in order to refurbish the company's office. The transaction was not referred to the board. The bank was not aware of either the contents of Allan's contract, or the company's constitution. The board has since discovered the loan contract and stopped all repayments on the loan. Bank of Sydney has called in the loan and is suing Blue Waves for the principal amount, together with all outstanding interest. Is Blue Waves legally bound by the loan contract signed by Allan? Give reasons and cite full authority for your answer.