Independent solution

How to solve this Bond Valuation question

Setup

Setup

There are twelve quarterly coupon dates over three years, and the quarterly yield is 2%.

P=Xa12‾∣ 0.02+1000v12P=Xa_{\overline{12}|\,0.02}+1000v^{12}

Model

Model

Write prices before and after doubling the coupon while keeping redemption unchanged.

P+500=2Xa12‾∣ 0.02+1000v12P+500=2Xa_{\overline{12}|\,0.02}+1000v^{12}

Compute

Compute

Subtracting cancels redemption and the original coupon stream, leaving one annuity of X worth 500.

500=Xa12‾∣ 0.02⟹X=47.28500=Xa_{\overline{12}|\,0.02}\Longrightarrow X=47.28

Answer

Answer

Each original quarterly coupon is 47.28, nearest choice E.

X≈47(E)\boxed{X\approx47\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 12 N; 2 I/Y; 500 PV; 0 FV; CPT PMTPMT = -47.28This values only the incremental coupon annuity created by doubling coupons.