Looking at things from another angle, why do you feel the need to offer a client a free or reduced rate website at all?
Is it because you are not confident of your selling skills?
Think how much more money you would make if you worked to improve your sales and marketing skills, so that you can acquire new clients who will pay the full rate for the job.
Giving websites away is a desperate solution, and not really necessary. As others have commented, lack of a portfolio of 'genuine' clients is not actually a major obstacle to winning business. Web designer portfolios can put off as many potential clients as they attract, in many cases.
You won't get good referrals from your too-cheap websites, either. Let's say you do an 8 page website for a very cheap rate of $200. Months later your new client then refers his friend. His friend wants a 4 page website, and will expect to pay $100 for it, or maybe $80 because he's 'doing you a favour'. This is how 'cheap people' think and act in the real world.
By forgetting about the 'web design' for a bit, and first putting together an efficient sales and marketing process, you will avoid all this nonsense and make much more money.