Independent solution

How to solve this Bond Valuation question

Setup

Setup

Express both bonds on the second bond's quarterly time scale.

3000=5000(1+j)−40⟹j=0.01285253000=5000(1+j)^{-40}\Longrightarrow j=0.0128525

Model

Model

Use the ten-year zero to infer the shared yield per quarter over forty quarters.

1000=950rqa60‾∣ j+950(1+j)−601000=950r_q a_{\overline{60}|\,j}+950(1+j)^{-60}

Compute

Compute

Then solve the fifteen-year bond price for its quarterly coupon rate and multiply by four.

rq=0.0141164,rannual=4rq=0.056465r_q=0.0141164,\qquad r_{\mathrm{annual}}=4r_q=0.056465

Answer

Answer

The annual coupon rate is approximately 5.65%, corresponding to choice D.

rannual≈5.65%(D)\boxed{r_{\mathrm{annual}}\approx5.65\%\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 40 N; 3000 +/- PV; 0 PMT; 5000 FV; CPT I/YI/Y = 1.28525
  2. 60 N; 1.28525 I/Y; 1000 +/- PV; 950 FV; CPT PMTPMT ≈ 13.41Annual coupon rate equals four times PMT divided by 950.