Exercise
A 1000-par value 30-year bond has an annual coupon rate of 7% paid semiannually. After an initial 10-year period of call protection, the bond is callable immediately following the payment of any of the 20th through the 59th coupons.
- If the bond is called before payment of the 40th coupon, the redemption value is 1250.
- If the bond is called immediately after the payment of any of the 40th through the 59th coupons, the redemption value is 1125.
- If the bond is not called, it will be redeemed at par.
To ensure that the bond will provide at least an annual nominal yield rate of 5% convertible semiannually, it must be assumed that the bond will be called or redeemed immediately after the payment of the nth coupon.
Calculate n.
- 20
- 39
- 40
- 59
- 60
Solution: C
During the first redemption period the modified coupon rate is 1000(0.035)/1250 = 2.80% which is larger than the desired yield rate. If redeemed during this period, bond sells at a premium and so the worst case for the buyer is the earliest redemption. The price if called at that time is
During the second redemption period the modified coupon rate is 1000(0.035)/1125 = 3.11% which is also larger than the desired yield rate and the worst case for the buyer is again the earliest redemption. The price if called at that time is
Finally, if the bond is not called, its value is
The appropriate price is the lowest of these three, which relates to the bond being called after the 40th coupon is paid.