The right way to do this is setup a landing page with clear value proposition and ask for free/paid email signups. Then spend some $ on google adwords and facebook ads to get some traffic.
You can get the estimate for getting users to the top of the funnel this way. Then you can use standard heuristics like "2% conversion rate" .
I have seen CPA to be as high as $200 in the beginning.
Also remember that virality might be your enemy. If single user utility is not as strong as the network utility.