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Callable Bond Question

I am a little confused with callable bond and simply just buying the bond back from a issuer's perspective.
First all callable bond would likely to be called when the interest rate fall. From my understanding that works the same thing as a call option where there would be a strike price and such so when a issuer call the bond back when at higher bond value they would profit from the difference.
Now couldn't the issuer simply just buy the bond back ? when interest increase, which means the bond value decrease, therefore the company now can play less to buy back their debt.

I don't see the difference of the two or when to use one or the other from an issuer's point of view. Can someone clarify this for me ?

As you rightly point out, issuers could benefit in either scenario.

when rates increase, the market price of debt falls (provided credit ratings and other risks are the same), the economic value of issuer's liability decreases and hence they can buy back their debt. however this decision would be based on factors such as availability of funds for debt repurchase and target capital structure. for example it might not always make sense to repurchase debt using equity funds when equity funding is more expensive. also, put options could provide downside protection to investors that limits the benefit to issuer.

when rates fall, it would make sense for issuers to utilize any call provisions. however this would differ from debt repurchase in that rather than retire the debt, it would make sense for the borrower to refinance at the lower rate.

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