Startups are famous for setting big, hairy goals. Carmine “Tom” Biscardi wants to catch Sasquatch—and is planning an initial public offering to fund the hunt.

Mr. Biscardi and his partners hope to raise as much as $3 million by selling stock in Bigfoot Project Investments. They plan to spend the money making movies and selling DVDs, but are also budgeting $113,805 a year for expeditions to find the beast. Among the company’s goals, according to its filings with the Securities and...