Personally, I don't think this is a very good idea, for a number of reasons.
First, a company has invested time and money into their website, perhaps quite a lot of either or both. Most won't appreciate somebody essentially telling them that their design is "wrong," which is what you would be implying.
Next, by including it in your portfolio, you are automatically implying that you created or worked on the website, even if you give credit otherwise. At best, this may be considered bad taste; at worst, you could be infringing on copyright laws. Think about it this way - when you do become a successful web designer, do you want somebody taking a website you've spent many hours and creative energy on, and claiming it as his/her own?
There is really nothing wrong with using a company's website for inspiration, although you may want to use a number of websites for that. You can see what kinds of things (products and/or services) are found on that kind of website.
What you will want to do is to make something more generic for a portfolio, until you get actual clients that you have designed yourself. Come up with a company name and create a logo, etc.
There are plenty of ideas out there, and room for innovation, that you don't have to steal another site. Creativity is a hallmark of web design.