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I don't know of any such trade arrangement, of an old and broken radio for a new one. (HP, a company of high repute, does offer *some* cash-back on turning in old HP devices, sometimes a credit toward purchase of a new one, but that's a partial cash-back and a partial credit-toward-purchase.)
Would you like to know about the options for purchase of less-expensive Bose radio/CD-player devices?
Do you purchase from eBay, or your local craigslist.com, or would you consider doing so?
Let me know, so that I may advise you further, and give you the full information that would suit the need expressed in your question. Thanks.