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I understand that when interest rate falls, the bondholder may be forced to return the bond and reinvest at a lower rate.

Can someone answer why the issuer would do so; what advantage does he or she have by calling it back?

They get to issue new debt at the lower rate.

Think about having a mortgage on a house and rates drop. You re-fi and get a new mortgage, it's the exact same thing. The company and issue new debt and reduce their future interest expense, just like a homeowner can re-fi and reduce future interest expense.

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