An investor purchases a 10-year callable bond with face amount of 1000 for price P. The bond has an annual nominal coupon rate of 10% paid semi-annually. The bond may be called at par by the issuer on every other coupon payment date, beginning with the second coupon payment date. The investor earns at least an annual nominal yield of 12% compounded semi-annually regardless of when the bond is redeemed.

Calculate the largest possible value of P.

• 885
• 892
• 926
• 965
• 982

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

For a bond bought at discount, the minimum price will occur at the latest possible redemption date.

[[math]] P=50a_{\overline{20}|0.06}+1000(1.06)^{-20}=885.30. [[/math]]

(When working with callable bonds, the maximum a buyer will pay is the smallest price over the various call dates. Paying more may not earn the desired yield.)

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.