Audit firms look at what the Turnover of the company is and how many staff they employ. Then they think of the maximum they can charge (they will pitch the figure high - lets say £25,000). At that stage, the Managing Director of the company lies and tells the Audit Firm that he has had cheaper quotes and that he would only give them the audit if they charge no more than £15,000.
The partner of the audit firm will then put on a very disappointed look on his face and disappear into the night to "think about if such a low fee is at all possible".
Then surprise, surprise the next day he will come back to say YES, YES, YES he can do the audit for £15,000 after all and that he spent the whole night twisting the arms of the other partners in his firm to get them to agree this fee - but he can only offer that fee if the company will sign a contract appointing them as auditors TODAY. The reduced fee offer will only apply for today!
Then the MD of the company will put on a very disappointed look on his face and finally "agree" to sign the contract - unwillingly ofcourse.
The good news for the audit firm is that they would have done the audit for £10,000 anyways so they are happy, the MD of the company is happy because he has just "saved" himself a lot of money too.
Audit fees are just like any other market, the buyer and seller negotiate to find a figure that suits them both. There is no such thing as fees based on estimated time taken to do the audit. No modern company is so stupid as to sign a contract with an auditor based on a time taken basis as that will leave them open to extremely high and unlimited audit fees if their accounting systems turn out to be dodgy or bad.