NEW YORK—A lot has changed in the year and a half since radio industry leader Clear Channel Communications Inc. struck a deal to go private. Credit markets seized up, radio advertising continued to falter and another radio buyout deal failed.

All that helps explain why Clear Channel didn’t mind taking a lower price and slightly higher lending rates to settle a dispute with its lenders late Tuesday, clearing the way for the long-delayed buyout deal to proceed.

The final $36 per-share price was 8 percent below the latest offer of $39.20, and even below the original price ...