Ask HN: Buying a business to use as an ad vehicle

Situation:

Let's say you’re a startup that is ready to publicly launch a new web service. You could spend $633k in advertising (print, online banners, search engine placement, etc.) or you could buy a business with a product already inside your target customers.

Example Business background:

The pre-existing business mentioned above is a decade old with customers like Airbus, John Deere, etc., government agencies, universities, small law offices, small businesses, and soccer moms. Customers spend anywhere from $20 to $20k. One product in particular could be made free and millions of downloads a year would be the end result. This "free" product could be a message proxy for your new web service.

Question:

What is good way to calculate that buying the above business to use its products, website, and SEO as an ad or awareness engine is better for your brand and message? How would you go about proving that this path (mathematically) is more sound than traditional means?