In terms of never having done it before, this is true of most software projects. If you're building the same house from the same plans then this is the same as say installing a Wordpress blog, easy to estimate. But if you were to ask how long it would take to build Wordpress from scratch, even having a Wordpress sample app, it would be very hard. Not only that but there are a lot of assumptions. Is it for a handful of visitors or are we talking a million visitor blog?
Ignoring that, let's go back to the pharma example. How long do you estimate developing a new drug will take? It's not the first drug your company has developed. Anything beyond a week is hard to estimate.
Back to your estimate of 25% within 4-8 weeks, this would never be accepted because it could mean anything.
The worse part, I an tell you right now, even if new functionality or changes are added, you will be elf to 4-8 weeks, the 25% will be ignored. And in most cases management will hold you to 4 weeks because this is what was sold to their bosses.