Sorry, but extra charges are supposed to apply where a phone conversation is sought. Noting you are unwilling to pay for a phone conversation, I will attempt to address your answer as follows.
Your case against your employee will be clearest if you have a written contract that specifically restricts your employee from competing with, or to use your intellectual property for private purposes, but absent a clear contractual term to that effect, your ability to take action against your employee is problematic. This is one of the reasons it is important to have a written and well thought through employment contract for all staff.
Although it creates some uncertainty, without a suitable written contractual term, you may still be able to take legal action or disciplinary action if you can demonstrate your employee has misused something that is the property of you as the employer (whether physical, or intellectual property, or whether he has use his time working for you to run his own business) then it would appear he has breached his duties to you as his employer. Essentially he is breaching an implied term of his employment contract.
acted in a way which conflicts with his duties to you as an employer, but whether this is grounds for a law suit or for summary dismissal will depend on exactly how serious the misconduct is. Absent a clear contractual prohibition, a court or the Fair Work Commission will not find that an employee has done anything wrong just because he does some similar work outside of normal hours, but may take a far more serious view if your staff member has taken your companies customer list and is trying to convert your customers to his. The former is not a problem at all as far as the law is concerned, and the later would likely be grounds for both summary dismissal and a damages claim.
If you cannot identify anything that your staff member has actually taken from your company, or cannot prove he has been operating his competing business on your time, then your case against him may be problematic.
If you can prove he was working on your time, then he is clearly in the wrong, but if not, and you are only really able to establish that he is operating a business in competition with ou, then the following link may assist your understanding of what employees are allowed or not allowed to do even without a formal contract:
If you can show he is in the wrong, whether you can simply dismiss your employee will depend on how serious his misconduct was. One phone call on your time for his own purposes, is likely only cause for a warning, whereas spending hours running his own business when he should be running yours, would likely be accepted by the Fair Work Comission as grounds for summary dismissal.
If you have a follow up question I'd be happy to assist you further.
Otherwise, please rate my answer.