Studying abroad through my private university?

I currently attend a private university right now. I want to study abroad in the fall of 2017. My university offers exchange programs through ISEP and there are schools I am interested in. I have really gotten into the financial part!

With the exchange program I will continue to pay the same amount of tuition and room & board while I go to another school (hopefully in Australia by the way). Everything added up, I pay $45,500 each year. I was awarded $25,000 in scholarships and my financial aid will also help cover the costs of course. Breaking everything down I will still have around $10,000 left to pay out of pocket. I am only going for one semester so I just split that in half. Then I have to factor in the cost of my plane tickets, application fees, and regular living essentials while I am over there. I have not taken out any loans because my parents have paid of the remaining costs at the university I attend now… So if I study abroad I may have to take out a loan for a few thousand, which I’m not too worried about.

I may transfer after this year to a state/public school which is in my home state as well. I like the school I am at now, but I am missing out on a lot I feel like because, of the higher costs for one, since that limits some of the things I can do like studying abroad for example. But the state school has a wider range of academics and clubs/organizations. Would it be logical to transfer to that state school, who also offers the same exchange program? The state school is much cheaper and I will be paying less for the trip to the SAME school in Australia. I personally disagree with the fact that at my private university I am paying almost 3x more to study abroad when I could go an hour from home and everything be much cheaper… That’s just a con that comes with private schools! My last and final question is, I want to go on the trip in the fall of 2017. If I transfer to the state university after this spring, would I be able to do that? I feel like I would be able to but at the same time I wouldn’t be able to. I would be enrolling to go on this study abroad trip my first semester there and when I would come back I would definitely finish out my degree there without a doubt. Has anyone else ran into these issues?

Fwiw, I studied at a German Uni for a year and paid no tuition. My credits were transferable. I organized it myself, on site, after spending the summer at a Goethe Institute. While there, I met American students who paid full tuition at their unis, and all they got was minimal administrative support - literally about a single afternoon of work for visas, etc. - and an office to hang out in.