Considering Spotify's last financing round I believe in November gave the company a $4 billion pre-money valuation and recent IPO discussions are in the $6 to $8 bin range, $3.2 billion doesn't seem that ridonkulous.
What is says to me is that a) Apple knows that streaming is the future and that the current iTunes purchase model is dated b) that Apple is having a hard time quickly/efficiently getting a solid streaming service to market, and c) the executive team believes the Beats Audio streaming service is the quickest, most cost-efficient way to enter this market. Internal financial analysis probably takes into account the advantages a combination with Apple would bring, such as the hundreds of millions of captive iTunes accounts--mgmt probably has models showing they're getting a bargain long-term assuming they can leverage the iTunes customer base and Apple's other global advantages.
Couldn't have said it better myself - why are the majority of people on here so concerned about the gaudy headphones? Seems pretty straightforward to me - and I like it.