A firm issues $500 million in twenty-year bonds with an annual coupon rate of 5%.The firm uses a sinking fund to repurchase 4% of the bond issue on each coupon payment date.What payment must they make on the twentieth and final coupon payment date?

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The bond issue is $500 million with an annual coupon rate of 5%, which means the annual coupon payment is $25 million ($500 million × 5%). The firm repurchases 4% of the bond issue on each coupon payment date, which is $20 million ($500 million × 4%). Therefore, the effective outstanding bond balance will decrease by $5 million ($25 million - $20 million) on each coupon payment date.

At the end of the 20th year, the outstanding bond balance will be $100 million ($500 million - 19 × $20 million). Therefore, the payment the firm must make on the twentieth and final coupon payment date will be the sum of the annual coupon payment ($25 million) and the outstanding bond balance ($100 million), which is $145 million (Choice C).

A Firm Issues $500 Million in Twenty-Year Bonds with an Annual