Animate letters of a logo to collapse into each other

If you have a copy of the logo in Illustrator, you can put each letter on a separate layer and animate the position, scale, and opacity of each letter. If you don't have the font, you will have to generate letters for A and S to spell Gold Coast. You'll repeat the process but reverse the animation for the second set of words.

If you have access to the font, you could use a Text animator and two or four copies of the words you want to end up with.

There is no real easy way to morph one letter into another, but you could try scaling or a distortion effect combined with blend modes to make the transition more interesting. Don't forget Motion Blur. 

One more suggestion: It takes about 2 seconds to read the words and recognize the difference between the two phrases, so it would probably be a good idea to start with a complete transition between words that does not take longer than about one and a half seconds. You'll just have to fiddle with things.

You may want to look at a few text transition tutorials using Text Animators. If you have an example of the look you want, post a link, and maybe we can give you more concrete suggestions.