A business case for an intranet is like the business case for a bathroom; you can live without them (and use others), but you’re a fool if you do.
Social media has morphed to the intranet, and the intranet is becoming increasingly social. However, like the Internet, email, telephone, and other business transforming technology, the need for a social intranet is more implicit, rather than explicit. We all need email, don’t we? But did you need a business case to get your corporate email account?