Independent solution

How to solve this Bond Valuation question

Setup

Setup

The two bonds share the same coupon stream and yield; only face and redemption differ.

2695.39=200a15‾∣+Fv152695.39=200a_{\overline{15}|}+Fv^{15}

Model

Model

Subtracting prices removes the coupon annuity and isolates the discounted face amount of Bond X.

3490.78=200a15‾∣+2Fv153490.78=200a_{\overline{15}|}+2Fv^{15}

Compute

Compute

Back-substitution determines the annuity factor, yield, and face amount 2,000.

Fv15=795.39,a15‾∣=9.5,F=2000Fv^{15}=795.39,\quad a_{\overline{15}|}=9.5,\quad F=2000

Answer

Answer

Its annual coupon 200 is 10% of face, so choice D is correct.

200/F=10.0%(D)\boxed{200/F=10.0\%\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; 15 N; 9.5 +/- PV; 1 PMT; 0 FV; CPT I/YI/Y = 6.3401END mode; the unit coupon annuity has price 9.5, so PV and PMT have opposite signs.
  2. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 15 N; 6.3401 I/Y; 795.39 +/- PV; 0 PMT; CPT FVFV = 2000.04END mode; I/Y is annual. The small excess over 2,000 is from displayed-input rounding.