Independent solution

How to solve this Bond Valuation question

Setup

Setup

First recover the purchase price from the anticipated call outcome using the semiannual rate equivalent to 10%.

j=(1.10)1/2−1=0.048809j=(1.10)^{1/2}-1=0.048809

Model

Model

The actual call occurs after one coupon, so the realized half-year return equates purchase price to that coupon plus call payment.

P=150a8‾∣ j+2900v8=2955.08P=150a_{\overline8|\,j}+2900v^8=2955.08

Compute

Compute

The realized half-year rate is 5.242%; compounding it twice gives 10.759% annually.

2955.08(1+k)=150+2960⟹k=0.052422955.08(1+k)=150+2960\Longrightarrow k=0.05242

Answer

Answer

Rounded to the choices, the realized annual yield is 10.8%, choice C.

i=(1+k)2−1=10.76%≈10.8%(C)\boxed{i=(1+k)^2-1=10.76\%\approx10.8\%\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 8 N; 4.88 I/Y; 150 PMT; 2900 FV; CPT PVPV = -2955.07END mode; I/Y is the official solution's rounded half-year rate.
  2. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 1 N; 2955.08 +/- PV; 0 PMT; 3110 FV; CPT I/YI/Y = 5.2426 per half-year; annual effective = 10.7598%END mode; purchase price is negative and the actual coupon-plus-call receipt is positive.