Mary purchased a 10-year par value bond with an annual nominal coupon rate of 4% payable semiannually at a price of 1021.50. The bond can be called at 100 over the par value of 1100 on any coupon date starting at the end of year 5 and ending six months prior to maturity.

Calculate the minimum yield that Mary could receive, expressed as an annual nominal rate of interest convertible semiannually.

• 4.7%
• 4.9%
• 5.1%
• 5.3%
• 5.5%

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

Solution: B

Given the price is less than the amount paid for an early call, the minimum yield rate for this callable bond is calculated based on a call at the latest possible date. Thus, for an early call, the effective yield rate per coupon period, j, must satisfy

[[math]] \mathrm{Price} = 1021.50=22a_{\overline{19}| j}+1200 v_{j}^{19}. [[/math]]

Using the calculator, j = 2.86%. We also must check the yield if the bond is redeemed at maturity. The equation is

[[math]]1021.50=22a_{\overline{20}| j}+1100 v_{j}^{20}[[/math]]

. The solution is j = 2.46% Thus, the yield, expressed as a nominal annual rate of interest convertible semiannually, is twice the smaller of the two values, or 4.92%

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