Independent solution

How to solve this Callable Bond Yield Protection question

Setup

Setup

A guaranteed yield must hold under every permitted redemption date. Use 2.5% per half-year and coupon 30.

j=0.05/2=0.025j=0.05/2=0.025
C=30C=30

Model

Model

Price the bond separately to each possible call or maturity date.

P10=30a20‾∣j+1,060v20P_{10}=30a_{\overline{20}|j}+1{,}060v^{20}
P15=30a30‾∣j+1,030v30P_{15}=30a_{\overline{30}|j}+1{,}030v^{30}
P20=30a40‾∣j+1,000v40P_{20}=30a_{\overline{40}|j}+1{,}000v^{40}

Compute

Compute

The three price limits are 1114.56, 1118.95, and 1125.51.

min⁡(P10,P15,P20)=1,114.562\min(P_{10},P_{15},P_{20})=1{,}114.562

Answer

Answer

The highest purchase price that preserves the target under every call is 1115, choice A.

Pmax⁡≈1,115(A)\boxed{P_{\max}\approx1{,}115\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 20 · N; 2.5 · I/Y; 30 · PMT; 1060 · FV; CPT · PV−1114.56Repeat for N = 30, FV = 1030 and N = 40, FV = 1000; select the smallest price magnitude.