Busted Convertible Security
  
Sounds like a lesser-known, depressing Beach Boys song. All about how you were going to the beach and your car broke down..."Now, you're waiting for Triple A-A-A-A-AAAAAA."
In financial terms, the convertible here isn't a roofless car. It's a type of security. Specifically, it's a bond that can get turned into stock under certain conditions.
Usually, the owner of the bond has the option to turn the bond into a certain number of shares at a certain price. That price is known as the "conversion price." If the market value of the company's stock is well below the conversion price...that's a busted convertible.
So Beach Drive Inc. offers a convertible bond with the option to turn into stock at $25 per share. Right now, Beach Drive is trading at $5 per share. No one is going to do any converting for the foreseeable future. Busted convertible. "Now, you're waiting for Triple A-A-A-A-AAAAAA."
Thing is, a convertible bond should trade at a premium over normal debt for that company (assuming similar maturity and interest rates). After all, you have the same payout as the regular bond, but you also have the added option to take advantage of a high stock price, if the shares rise above the conversion price.
But in a busted convertible, that potential benefit is so far over the horizon that it doesn't impact the price. The convertible bond trades at the same price (or essentially the same price) as normal, run-of-the-mill bonds.