By Stephen Nellis and Liana B. Baker SAN FRANCISCO (Reuters) - Snap Inc’s initial public offering filing seemed to show a company with a basic math problem: the company's cost of revenue for 2016 - the amount it had to spend just to keep the messaging service running - was $47 million higher than its $405 million in sales. The high cost of revenue, which in Snap's case consists mainly of payments to Alphabet Inc's Google for hosting the service, means that, on an annual basis, Snap lost money on every one of its 158 million users in 2016, even before accounting for salaries, office rents or anything else. Snap revealed in its IPO prospectus, filed with securities regulators on Thursday, that it will pay Google at least $2 billion over the next five years.