Shares of streaming-music-service operator Pandora Media (P) have gained 81% so far in 2018.

The big jump is no surprise, since satellite radio veteran Sirius XM Holdings (SIRI 0.96%) is buying the company in a $3.5 billion deal. But that was the proposed buyout price at the announcement in late September -- Pandora is actually worth just $2.8 billion today.

There are actually good reasons for all of that. Let me walk you through why Sirius is buying Pandora in the first place, and then we'll get around to why the deal's value has fallen 21%  in less than two months.

Two rows of chess pawns, each guarding its side of the board. In the center stands a single king that is half white, half black.

Sirius and Pandora -- two longtime rivals -- are joining forces. Image source: Getty Images.

What Sirius XM sees in Pandora

The two companies have been rivals for many years. Fellow Motley Fool contributor Rick Munarriz first called Pandora a possible buyout target for Sirius way back in 2007. The idea of combining the leading satellite-based music service with this household name in streaming over the internet is not new at all.

In more concrete terms, Sirius XM wants to cross-promote satellite services in North America to Pandora's 70 million active users while also pushing online radio plans to its own user base of 36 million subscribers and 23 million trial-plan listeners.

Sharing content between the two platforms could also make sense, giving Sirius XM's portfolio of premium programming a wider audience. At the same time, Pandora's technology know-how should help the company improve its satellite offerings in new ways. Putting Pandora's radio service within easy reach for Sirius' industrywide collection of in-car entertainment clients could add significant value to the merger target over time.

And of course, doubling up this way should make artists and talk-radio hosts more likely to strike a deal with this singular entertainment giant.

In broad strokes, that's why a business combination makes sense. Why now? Well, Pandora has been kind of rudderless since founder and CEO Tim Westergren was pushed out in the summer of 2017, and the company always seems to be fighting for its life against legal and regulatory threats. Share prices peaked in early 2014 and have plunged 75% since then, making it a more affordable buyout target.

And Sirius shares have doubled in value over the same period of nearly five years. The stock's rising price and generous valuation ratios give the company a powerful dealmaking tool.

Stock-based deal pricing

And that's exactly what Sirius used. The Pandora buyout is structured as a stock-swap deal that will let shareholders exchange each Pandora stub for 1.44 freshly printed shares of Sirius. The company is not adding any actual cash to the transaction.

That's why Pandora's market value has been changing even though it has a firm buyout offer on the table. When Sirius XM's share price moves, so does Pandora's. Since Sept. 24, the difference between the two stock returns stands at roughly 1%. Pandora's shares are also trading less than 2% below that magic ratio of 1.44 times Sirius XM's market price. That's basically a rounding error, leaving very little room for arbitrage investors to make money here. As far as the market is concerned, this is a done deal.

Ironically, part of the reason behind Sirius XM's falling share prices is that investors have to account for the planned printing of 388 million new shares. Beyond that, the stock is trading at generous valuation ratios such as 26 times earnings and 20 times free cash flows, exposing investors in Sirius and Pandora to volatility. These stocks are priced for perfection; anything less than that can hurt both of their stock prices in a hurry (and in unison).