Example: Yield-to-call and yield-to-worst

Consider a 10-year, semiannual-pay 6% bond trading at 102 on January 1, 2014. The bond is callable according to the following schedule:

Callable at 102 on or after January 1, 2019.

Callable at 100 on or after January 1, 2022.

Calculate the bond’s YTM, yield-to-first call, yield-to-first par call, and yield-to-worst.

Answer:

The yield-to-maturity on the bond is calculated as:

N = 20; PMT = 30; FV = 1,000; PV = –1,020; CPT → I/Y = 2.867%

2 × 2.867 = 5.734% = YTM

To calculate the yield-to-first call, we calculate the yield-to-maturity using the number of semiannual periods until the first call date (10) for N and the call price (1,020) for FV:

N = 10; PMT = 30; FV = 1,020; PV = –1,020; CPT → I/Y = 2.941%

2 × 2.941 = 5.882% = yield-to-first call

To calculate the yield-to-first par call (second call date), we calculate the yield-to-maturity using the number of semiannual periods until the first par call date (16) for N and the call price (1,000) for FV:

N = 16; PMT = 30; FV = 1,000; PV = –1,020; CPT → I/Y = 2.843%

2 × 2.843 = 5.686% = yield-to-first par call

The lowest yield, 5.686%, is realized if the bond is called at par on January 1, 2022, so the yield-to-worst is 5.686%.