Independent solution

How to solve this Bond Valuation question

Setup

Setup

Both bonds have the same face, term, and yield, so combine their redemption values and coupon rates.

1600=2(1000v20)+1000(2r+0.01)a20‾∣ 0.101600=2(1000v^{20})+1000(2r+0.01)a_{\overline{20}|\,0.10}

Model

Model

Bond B contributes one additional percentage point of coupon, making the combined coupon rate 2r plus 0.01.

1.6=0.29729+17.02713r+0.085141.6=0.29729+17.02713r+0.08514

Compute

Compute

Substituting the 20-year discount and annuity factors isolates r at 0.0715.

r=1.6−0.29729−0.0851417.02713=0.0715r=\frac{1.6-0.29729-0.08514}{17.02713}=0.0715

Answer

Answer

Bond A's annual coupon rate is 7.15%, which is choice B.

r=7.15%(B)\boxed{r=7.15\%\quad\text{(B)}}

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; 20 N; 10 I/Y; 1600 +/- PV; 2000 FV; CPT PMTPMT = 153.0162END mode; I/Y is annual. The combined purchase is negative and both bonds' combined receipts are positive.