Independent solution

How to solve this Bond Valuation question

Setup

Setup

Both bonds have the same price but different yields, so first determine that price from Bond A's known cash flows.

X=40a10‾∣ 0.03+1000(1.03)−10=1085.30X=40a_{\overline{10}|\,0.03}+1000(1.03)^{-10}=1085.30

Model

Model

Use Bond B's 3.5% half-year yield to isolate its unknown semiannual coupon in a second price equation.

1085.30=Ca10‾∣ 0.035+1000(1.035)−101085.30=Ca_{\overline{10}|\,0.035}+1000(1.035)^{-10}

Compute

Compute

The coupon is 45.2566 per half-year; doubling and dividing by face converts it to the nominal annual coupon rate.

C=45.2566C=45.2566

Answer

Answer

The result is 9.05%, which is choice D.

y=2C/1000=9.05%(D)\boxed{y=2C/1000=9.05\%\quad\text{(D)}}

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; 10 N; 3 I/Y; 40 PMT; 1000 FV; CPT PVPV = -1085.30END mode; I/Y is the half-year yield for Bond A.
  2. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 10 N; 3.5 I/Y; 1085.30 +/- PV; 1000 FV; CPT PMTPMT = 45.2566END mode; I/Y is Bond B's half-year yield. Twice the coupon divided by face gives the annual coupon rate.