Hi:
I'm wondering why you aren't starting a business to produce this app yourself?
Develop a prototype, show it to likely users, take their feedback to refine the product, build a marketing plan, launch the product and generate sales. Once you've proven that it sells and customers value it, this company could look at the decision to acquire it as a no-brainer.
Also, in terms of what to expect, this company you have your eye on would likely be looking to pay the fair value of your company, which probably has no correlation to their market value.
If you wish to discuss, send me a PM through Clarity for 15 free minutes.
Cheers,
Kerby

Ideas have little value. Technology, traction, and team have value. Look at many of the high-value applications (Instagram, WhatsApp, etc.) and see exactly how far they had to get prior to being interesting to Facebook. Making an assumption you know what the execution plan for an $11 B company may be is a fast way to being ignored. Design the system, file for patents (but do not be delusional about the time, cost, and actual grant - these are years in process and cost hundreds of thousands in many cases - and often get gutted or rejected). Even then, 5% (or even 1%) of a company that has revenues of $11 B is simply a non starter. Patents will not protect you - there are many ways around that, particularly with that kind of capital.

Your ask of between 1% and 5% of an 11b company comes out to between 100m and 550m for an idea. Without knowing your idea but with no patent, no track record of revenue or proof of concept, it's a steep ask.

At the very least, you need to make sure to have it patented before bringing it to the company, because it would be very easy to build the app at a much lower cost than your ask.