Independent solution

How to solve this Yield to Worst question

Setup

Setup

Compute the yield for every redemption outcome that the issuer may choose. Use 19 periods with redemption 1,200 and 20 periods with redemption 1,100.

1021.50=22a19‾∣ j+1200v19⟹2j=5.72%1021.50=22a_{\overline{19}|\,j}+1200v^{19}\Longrightarrow2j=5.72\%

Model

Model

Solving the two bond equations gives nominal annual yields convertible semiannually of 5.72% and 4.92%. A guaranteed return uses the lower of these scenario yields.

1021.50=22a20‾∣ j+1100v20⟹2j=4.92%1021.50=22a_{\overline{20}|\,j}+1100v^{20}\Longrightarrow2j=4.92\%

Compute

Compute

The yield to worst is therefore 4.92%, reported as 4.9%.

jmin⁡(2)=4.92%j^{(2)}_{\min}=4.92\%

Answer

Answer

The calculation gives 4.9% for yield to worst, matching published choice B.

j(2)=4.9%(B)\boxed{j^{(2)}=4.9\%\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 2nd CLR TVM; 19 N; 1021.50 +/- PV; 22 PMT; 1200 FV; CPT I/Y; × 2 =5.72Nominal annual yield for the call outcome.
  2. 2nd CLR TVM; 20 N; 1021.50 +/- PV; 22 PMT; 1100 FV; CPT I/Y; × 2 =4.92Nominal annual yield for maturity; this is the yield to worst.