Independent solution

How to solve this Bond Pricing and Yields question

Setup

Setup

Recover the original semiannual coupon from the 40-period purchase equation.

900=Ca40‾∣0.05+900(1.05)−40900=Ca_{\overline{40}|0.05}+900(1.05)^{-40}

Model

Model

At year 10, price the 20 remaining old-bond periods at the buyer's 4% half-year yield.

P10=Ca20‾∣0.04+900(1.04)−20P_{10}=Ca_{\overline{20}|0.04}+900(1.04)^{-20}

Compute

Compute

The coupon is 45.00 and sale price is 1022.31. Setting that price equal to the new bond gives coupon 38.2836.

P10=CNa20‾∣0.04+1100(1.04)−20P_{10}=C_Na_{\overline{20}|0.04}+1100(1.04)^{-20}
CN=38.28364993C_N=38.28364993

Answer

Answer

The new semiannual coupon is approximately 38, selecting choice B.

CN≈38(B)\boxed{C_N\approx38\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVM · 40 · N · 5 · I/Y · 900 · +/- · PV · 900 · FV · CPT · PMTPMT = 45.00
  2. 20 · N · 4 · I/Y · 45.00 · PMT · 900 · FV · CPT · PVPV = -1022.31
  3. 1100 · FV · 1022.31 · +/- · PV · CPT · PMTPMT = 38.28