value of bond's call option at different yields

why is the value of a bond’s call option greater at lower yields?

C’mon - think about it - what is the call option for and when might it be used? If a company issues callable notes at 7% and interest rates go to 20% what good is that call option?

Because at lower yields, the issuers tend to call the bonds and reissue at lower rate. There is a risk associated with this tendency and the issuers have to pay the callable bond holders a certain amount for accepting this risk. That’s why the value is higher.

yes - got it - thanks to you both. not sure why i didn’t see this before - certainly seems obvious in retrospect.